\n * @example\n * //animate example closed curve\n * var c1 = board.create('curve',[(u)=>4*Math.cos(u),(u)=>2*Math.sin(u)+2,0,2*Math.PI]);\n * var p2 = board.create('glider', [c1]);\n * var button1 = board.create('button', [1, 7, 'start animation',function(){p2.startAnimation(1,8)}]);\n * var button2 = board.create('button', [1, 5, 'stop animation',function(){p2.stopAnimation()}]);\n * \n * \n *\n * @example\n * // Divide the slider area into 20 steps and\n * // visit every step 30 msec. Stop after 2 rounds.\n * var n = board.create('slider',[[-2,4],[2,4],[1,5,100]],{name:'n'});\n * n.startAnimation(1, 20, 30, 2);\n *\n * \n * \n *\n */\n startAnimation: function (direction, stepCount, delay, maxRounds) {\n var dir = Type.evaluate(direction),\n sc = Type.evaluate(stepCount),\n that = this;\n\n delay = Type.evaluate(delay) || 250;\n maxRounds = Type.evaluate(maxRounds);\n maxRounds = (maxRounds !== 'undefined') ? maxRounds : -1;\n\n if (this.type === Const.OBJECT_TYPE_GLIDER && !Type.exists(this.intervalCode) && maxRounds !== 0) {\n this.roundsCount = 0;\n this.intervalCode = window.setInterval(function () {\n that._anim(dir, sc, maxRounds);\n }, delay);\n\n if (!Type.exists(this.intervalCount)) {\n this.intervalCount = 0;\n\n }\n }\n return this;\n },\n\n /**\n * Stop animation.\n * @name Glider#stopAnimation\n * @see Glider#startAnimation\n * @function\n * @returns {JXG.CoordsElement} Reference to itself.\n */\n stopAnimation: function () {\n if (Type.exists(this.intervalCode)) {\n window.clearInterval(this.intervalCode);\n delete this.intervalCode;\n }\n\n return this;\n },\n\n /**\n * Starts an animation which moves the point along a given path in given time.\n * @param {Array|function} path The path the point is moved on.\n * This can be either an array of arrays or containing x and y values of the points of\n * the path, or an array of points, or a function taking the amount of elapsed time since the animation\n * has started and returns an array containing a x and a y value or NaN.\n * In case of NaN the animation stops.\n * @param {Number} time The time in milliseconds in which to finish the animation\n * @param {Object} [options] Optional settings for the animation.\n * @param {function} [options.callback] A function that is called as soon as the animation is finished.\n * @param {Boolean} [options.interpolate=true] If path is an array moveAlong()\n * will interpolate the path\n * using {@link JXG.Math.Numerics.Neville}. Set this flag to false if you don't want to use interpolation.\n * @returns {JXG.CoordsElement} Reference to itself.\n * @see JXG.CoordsElement#moveTo\n * @see JXG.CoordsElement#visit\n * @see JXG.CoordsElement#moveAlongES6\n * @see JXG.GeometryElement#animate\n */\n moveAlong: function (path, time, options) {\n options = options || {};\n\n var i,\n neville,\n interpath = [],\n p = [],\n delay = this.board.attr.animationdelay,\n steps = time / delay,\n len,\n pos,\n part,\n makeFakeFunction = function (i, j) {\n return function () {\n return path[i][j];\n };\n };\n\n if (Type.isArray(path)) {\n len = path.length;\n for (i = 0; i < len; i++) {\n if (Type.isPoint(path[i])) {\n p[i] = path[i];\n } else {\n p[i] = {\n elementClass: Const.OBJECT_CLASS_POINT,\n X: makeFakeFunction(i, 0),\n Y: makeFakeFunction(i, 1)\n };\n }\n }\n\n time = time || 0;\n if (time === 0) {\n this.setPosition(Const.COORDS_BY_USER, [\n p[p.length - 1].X(),\n p[p.length - 1].Y()\n ]);\n return this.board.update(this);\n }\n\n if (!Type.exists(options.interpolate) || options.interpolate) {\n neville = Numerics.Neville(p);\n for (i = 0; i < steps; i++) {\n interpath[i] = [];\n interpath[i][0] = neville[0](((steps - i) / steps) * neville[3]());\n interpath[i][1] = neville[1](((steps - i) / steps) * neville[3]());\n }\n } else {\n len = path.length - 1;\n for (i = 0; i < steps; ++i) {\n pos = Math.floor((i / steps) * len);\n part = (i / steps) * len - pos;\n\n interpath[i] = [];\n interpath[i][0] = (1.0 - part) * p[pos].X() + part * p[pos + 1].X();\n interpath[i][1] = (1.0 - part) * p[pos].Y() + part * p[pos + 1].Y();\n }\n interpath.push([p[len].X(), p[len].Y()]);\n interpath.reverse();\n /*\n for (i = 0; i < steps; i++) {\n interpath[i] = [];\n interpath[i][0] = path[Math.floor((steps - i) / steps * (path.length - 1))][0];\n interpath[i][1] = path[Math.floor((steps - i) / steps * (path.length - 1))][1];\n }\n */\n }\n\n this.animationPath = interpath;\n } else if (Type.isFunction(path)) {\n this.animationPath = path;\n this.animationStart = new Date().getTime();\n }\n\n this.animationCallback = options.callback;\n this.board.addAnimation(this);\n\n return this;\n },\n\n /**\n * Starts an animated point movement towards the given coordinates where.\n * The animation is done after time milliseconds.\n * If the second parameter is not given or is equal to 0, setPosition() is called, see\n * {@link JXG.CoordsElement#setPosition},\n * i.e. the coordinates are changed without animation.\n * @param {Array} where Array containing the x and y coordinate of the target location.\n * @param {Number} [time] Number of milliseconds the animation should last.\n * @param {Object} [options] Optional settings for the animation\n * @param {function} [options.callback] A function that is called as soon as the animation is finished.\n * @param {String} [options.effect='<>'|'>'|'<'|'--'|'=='] animation effects like speed fade in and out. possible values are\n * '<>' for speed increase on start and slow down at the end (default), '<' for speed up, '>' for slow down, and '--' (or '==')\n * for constant speed during the whole animation.\n * @returns {JXG.CoordsElement} Reference to itself.\n * @see JXG.CoordsElement#setPosition\n * @see JXG.CoordsElement#moveAlong\n * @see JXG.CoordsElement#visit\n * @see JXG.CoordsElement#moveToES6\n * @see JXG.GeometryElement#animate\n * @example\n * // moveTo() with different easing options and callback options\n * let yInit = 3\n * let [A, B, C, D] = ['==', '<>', '<', '>'].map((s) => board.create('point', [4, yInit--], { name: s, label: { fontSize: 24 } }))\n * let seg = board.create('segment', [A, [() => A.X(), 0]]) // shows linear\n *\n * let isLeftRight = true;\n * let buttonMove = board.create('button', [-2, 4, 'left',\n * () => {\n * isLeftRight = !isLeftRight;\n * buttonMove.rendNodeButton.innerHTML = isLeftRight ? 'left' : 'right';\n * let x = isLeftRight ? 4 : -4;\n * let sym = isLeftRight ? 'triangleleft' : 'triangleright';\n *\n * A.moveTo([x, 3], 1000, { callback: () => A.setAttribute({ face: sym, size: 5 }) });\n * B.moveTo([x, 2], 1000, { callback: () => B.setAttribute({ face: sym, size: 5 }), effect: \"<>\" });\n * C.moveTo([x, 1], 1000, { callback: () => C.setAttribute({ face: sym, size: 5 }), effect: \"<\" });\n * D.moveTo([x, 0], 1000, { callback: () => D.setAttribute({ face: sym, size: 5 }), effect: \">\" });\n *\n * }]);\n *\n * \n * \n */\n moveTo: function (where, time, options) {\n options = options || {};\n where = new Coords(Const.COORDS_BY_USER, where, this.board);\n\n var i,\n delay = this.board.attr.animationdelay,\n steps = Math.ceil(time / delay),\n coords = [],\n X = this.coords.usrCoords[1],\n Y = this.coords.usrCoords[2],\n dX = where.usrCoords[1] - X,\n dY = where.usrCoords[2] - Y,\n /** @ignore */\n stepFun = function (i) {\n var x = i / steps; // absolute progress of the animatin\n\n if (options.effect) {\n if (options.effect === \"<>\") {\n return Math.pow(Math.sin((x * Math.PI) / 2), 2);\n }\n if (options.effect === \"<\") { // cubic ease in\n return x * x * x;\n }\n if (options.effect === \">\") { // cubic ease out\n return 1 - Math.pow(1 - x, 3);\n }\n if (options.effect === \"==\" || options.effect === \"--\") {\n return i / steps; // linear\n }\n // throw new Error(\"Callback moveTo(): valid effects are '==', '--', '<>', '>', and '<', given is '\" + options.effect + \"'.\");\n JXG.warn(\"Callback moveTo(): valid effects are '==', '--', '<>', '>', and '<', given is '\" + options.effect + \"'. Set it to '--'\");\n options.effect = '--';\n }\n return i / steps; // default\n };\n\n if (\n !Type.exists(time) ||\n time === 0 ||\n Math.abs(where.usrCoords[0] - this.coords.usrCoords[0]) > Mat.eps\n ) {\n this.setPosition(Const.COORDS_BY_USER, where.usrCoords);\n return this.board.update(this);\n }\n\n // In case there is no callback and we are already at the endpoint we can stop here\n if (\n !Type.exists(options.callback) &&\n Math.abs(dX) < Mat.eps &&\n Math.abs(dY) < Mat.eps\n ) {\n return this;\n }\n\n for (i = steps; i >= 0; i--) {\n coords[steps - i] = [\n where.usrCoords[0],\n X + dX * stepFun(i),\n Y + dY * stepFun(i)\n ];\n }\n\n this.animationPath = coords;\n this.animationCallback = options.callback;\n this.board.addAnimation(this);\n\n return this;\n },\n\n /**\n * Starts an animated point movement towards the given coordinates where. After arriving at\n * where the point moves back to where it started. The animation is done after time\n * milliseconds.\n * @param {Array} where Array containing the x and y coordinate of the target location.\n * @param {Number} time Number of milliseconds the animation should last.\n * @param {Object} [options] Optional settings for the animation\n * @param {function} [options.callback] A function that is called as soon as the animation is finished.\n * @param {String} [options.effect='<>'|'>'|'<'|'=='|'--'] animation effects like speed fade in and out. possible values are\n * '<>' for speed increase on start and slow down at the end (default), '<' for speed up, '>' for slow down, and '--' (or '==')\n * for constant speed during the whole animation.\n * @param {Number} [options.repeat=1] How often this animation should be repeated.\n * @returns {JXG.CoordsElement} Reference to itself.\n * @see JXG.CoordsElement#moveAlong\n * @see JXG.CoordsElement#moveTo\n * @see JXG.CoordsElement#visitES6\n * @see JXG.GeometryElement#animate\n * @example\n * // visit() with different easing options\n * let yInit = 3\n * let [A, B, C, D] = ['==', '<>', '<', '>'].map((s) => board.create('point', [4, yInit--], { name: s, label: { fontSize: 24 } }))\n * let seg = board.create('segment', [A, [() => A.X(), 0]]) // shows linear\n *\n *let isLeftRight = true;\n *let buttonVisit = board.create('button', [0, 4, 'visit',\n * () => {\n * let x = isLeftRight ? 4 : -4\n *\n * A.visit([-x, 3], 4000, { effect: \"==\", repeat: 2 }) // linear\n * B.visit([-x, 2], 4000, { effect: \"<>\", repeat: 2 })\n * C.visit([-x, 1], 4000, { effect: \"<\", repeat: 2 })\n * D.visit([-x, 0], 4000, { effect: \">\", repeat: 2 })\n * }])\n *\n * \n * \n *\n */\n visit: function (where, time, options) {\n where = new Coords(Const.COORDS_BY_USER, where, this.board);\n\n var i,\n j,\n steps,\n delay = this.board.attr.animationdelay,\n coords = [],\n X = this.coords.usrCoords[1],\n Y = this.coords.usrCoords[2],\n dX = where.usrCoords[1] - X,\n dY = where.usrCoords[2] - Y,\n /** @ignore */\n stepFun = function (i) {\n var x = i < steps / 2 ? (2 * i) / steps : (2 * (steps - i)) / steps;\n\n if (options.effect) {\n if (options.effect === \"<>\") { // slow at beginning and end\n return Math.pow(Math.sin((x * Math.PI) / 2), 2);\n }\n if (options.effect === \"<\") { // cubic ease in\n return x * x * x;\n }\n if (options.effect === \">\") { // cubic ease out\n return 1 - Math.pow(1 - x, 3);\n }\n if (options.effect === \"==\" || options.effect === \"--\") {\n return x; // linear\n }\n // throw new Error(\"Callback visit(): valid effects are '==', '--', '<>', '>', and '<', given is '\" + options.effect + \"'.\");\n JXG.warn(\"Callback visit(): valid effects are '==', '--', '<>', '>', and '<', given is '\" + options.effect + \"'. Set it to '--'\");\n options.effect = '--';\n }\n return x;\n };\n\n // support legacy interface where the third parameter was the number of repeats\n if (Type.isNumber(options)) {\n options = { repeat: options };\n } else {\n options = options || {};\n if (!Type.exists(options.repeat)) {\n options.repeat = 1;\n }\n }\n\n steps = Math.ceil(time / (delay * options.repeat));\n\n for (j = 0; j < options.repeat; j++) {\n for (i = steps; i >= 0; i--) {\n coords[j * (steps + 1) + steps - i] = [\n where.usrCoords[0],\n X + dX * stepFun(i),\n Y + dY * stepFun(i)\n ];\n }\n }\n this.animationPath = coords;\n this.animationCallback = options.callback;\n this.board.addAnimation(this);\n\n return this;\n },\n\n /**\n * ES6 version of {@link JXG.CoordsElement#moveAlong} using a promise.\n *\n * @param {Array} where Array containing the x and y coordinate of the target location.\n * @param {Number} [time] Number of milliseconds the animation should last.\n * @param {Object} [options] Optional settings for the animation\n * @returns Promise\n * @see JXG.CoordsElement#moveAlong\n * @example\n * var A = board.create('point', [4, 4]);\n * A.moveAlongES6([[3, -2], [4, 0], [3, 1], [4, 4]], 2000)\n * .then(() => A.moveToES6([-3, -3], 1000));\n *\n * \n * \n *\n */\n moveAlongES6: function (path, time, options) {\n return new Promise((resolve, reject) => {\n if (Type.exists(options) && Type.exists(options.callback)) {\n options.callback = resolve;\n } else {\n options = {\n callback: resolve\n };\n }\n this.moveAlong(path, time, options);\n });\n },\n\n /**\n * ES6 version of {@link JXG.CoordsElement#moveTo} using a promise.\n *\n * @param {Array} where Array containing the x and y coordinate of the target location.\n * @param {Number} [time] Number of milliseconds the animation should last.\n * @param {Object} [options] Optional settings for the animation\n * @returns Promise\n * @see JXG.CoordsElement#moveTo\n *\n * @example\n * var A = board.create('point', [4, 4]);\n * A.moveToES6([-3, 3], 1000)\n * .then(() => A.moveToES6([-3, -3], 1000))\n * .then(() => A.moveToES6([3, -3], 1000))\n * .then(() => A.moveToES6([3, -3], 1000));\n *\n * \n * \n *\n * @example\n * var A = board.create('point', [4, 4]);\n * A.moveToES6([-3, 3], 1000)\n * .then(function() {\n * return A.moveToES6([-3, -3], 1000);\n * }).then(function() {\n * return A.moveToES6([ 3, -3], 1000);\n * }).then(function() {\n * return A.moveToES6([ 3, -3], 1000);\n * }).then(function() {\n * return A.moveAlongES6([[3, -2], [4, 0], [3, 1], [4, 4]], 5000);\n * }).then(function() {\n * return A.visitES6([-4, -4], 3000);\n * });\n *\n * \n * \n *\n */\n moveToES6: function (where, time, options) {\n return new Promise((resolve, reject) => {\n if (Type.exists(options) && Type.exists(options.callback)) {\n options.callback = resolve;\n } else {\n options = {\n callback: resolve\n };\n }\n this.moveTo(where, time, options);\n });\n },\n\n /**\n * ES6 version of {@link JXG.CoordsElement#moveVisit} using a promise.\n *\n * @param {Array} where Array containing the x and y coordinate of the target location.\n * @param {Number} [time] Number of milliseconds the animation should last.\n * @param {Object} [options] Optional settings for the animation\n * @returns Promise\n * @see JXG.CoordsElement#visit\n * @example\n * var A = board.create('point', [4, 4]);\n * A.visitES6([-4, -4], 3000)\n * .then(() => A.moveToES6([-3, 3], 1000));\n *\n * \n * \n *\n */\n visitES6: function (where, time, options) {\n return new Promise((resolve, reject) => {\n if (Type.exists(options) && Type.exists(options.callback)) {\n options.callback = resolve;\n } else {\n options = {\n callback: resolve\n };\n }\n this.visit(where, time, options);\n });\n },\n\n /**\n * Animates a glider. Is called by the browser after startAnimation is called.\n * @param {Number} direction The direction the glider is animated.\n * @param {Number} stepCount The number of steps in which the parent element is divided.\n * Must be at least 1.\n * @param {Number} [maxRounds=-1] The number of rounds the glider will be animated. The glider will run infinitely if\n * maxRounds is negative or equal to Infinity.\n * @see JXG.CoordsElement#startAnimation\n * @see JXG.CoordsElement#stopAnimation\n * @private\n * @returns {JXG.CoordsElement} Reference to itself.\n */\n _anim: function (direction, stepCount, maxRounds) {\n var dX, dY, alpha, startPoint, newX, radius, sp1c, sp2c, res;\n\n this.intervalCount += 1;\n if (this.intervalCount > stepCount) {\n this.intervalCount = 0;\n\n this.roundsCount += 1;\n if (maxRounds > 0 && this.roundsCount >= maxRounds) {\n this.roundsCount = 0;\n return this.stopAnimation();\n }\n }\n\n if (this.slideObject.elementClass === Const.OBJECT_CLASS_LINE) {\n sp1c = this.slideObject.point1.coords.scrCoords;\n sp2c = this.slideObject.point2.coords.scrCoords;\n\n dX = Math.round(((sp2c[1] - sp1c[1]) * this.intervalCount) / stepCount);\n dY = Math.round(((sp2c[2] - sp1c[2]) * this.intervalCount) / stepCount);\n if (direction > 0) {\n startPoint = this.slideObject.point1;\n } else {\n startPoint = this.slideObject.point2;\n dX *= -1;\n dY *= -1;\n }\n\n this.coords.setCoordinates(Const.COORDS_BY_SCREEN, [\n startPoint.coords.scrCoords[1] + dX,\n startPoint.coords.scrCoords[2] + dY\n ]);\n } else if (this.slideObject.elementClass === Const.OBJECT_CLASS_CURVE) {\n if (direction > 0) {\n newX = (this.slideObject.maxX() - this.slideObject.minX()) * this.intervalCount / stepCount + this.slideObject.minX();\n } else {\n newX = -(this.slideObject.maxX() - this.slideObject.minX()) * this.intervalCount / stepCount + this.slideObject.maxX();\n }\n this.coords.setCoordinates(Const.COORDS_BY_USER, [this.slideObject.X(newX), this.slideObject.Y(newX)]);\n\n res = Geometry.projectPointToCurve(this, this.slideObject, this.board);\n this.coords = res[0];\n this.position = res[1];\n } else if (this.slideObject.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n alpha = 2 * Math.PI;\n if (direction < 0) {\n alpha *= this.intervalCount / stepCount;\n } else {\n alpha *= (stepCount - this.intervalCount) / stepCount;\n }\n radius = this.slideObject.Radius();\n\n this.coords.setCoordinates(Const.COORDS_BY_USER, [\n this.slideObject.center.coords.usrCoords[1] + radius * Math.cos(alpha),\n this.slideObject.center.coords.usrCoords[2] + radius * Math.sin(alpha)\n ]);\n }\n\n this.board.update(this);\n return this;\n },\n\n // documented in GeometryElement\n getTextAnchor: function () {\n return this.coords;\n },\n\n // documented in GeometryElement\n getLabelAnchor: function () {\n return this.coords;\n },\n\n // documented in element.js\n getParents: function () {\n var p = [this.Z(), this.X(), this.Y()];\n\n if (this.parents.length !== 0) {\n p = this.parents;\n }\n\n if (this.type === Const.OBJECT_TYPE_GLIDER) {\n p = [this.X(), this.Y(), this.slideObject.id];\n }\n\n return p;\n }\n }\n);\n\n/**\n * Generic method to create point, text or image.\n * Determines the type of the construction, i.e. free, or constrained by function,\n * transformation or of glider type.\n * @param{Object} Callback Object type, e.g. JXG.Point, JXG.Text or JXG.Image\n * @param{Object} board Link to the board object\n * @param{Array} coords Array with coordinates. This may be: array of numbers, function\n * returning an array of numbers, array of functions returning a number, object and transformation.\n * If the attribute \"slideObject\" exists, a glider element is constructed.\n * @param{Object} attr Attributes object\n * @param{Object} arg1 Optional argument 1: in case of text this is the text content,\n * in case of an image this is the url.\n * @param{Array} arg2 Optional argument 2: in case of image this is an array containing the size of\n * the image.\n * @returns{Object} returns the created object or false.\n */\nJXG.CoordsElement.create = function (Callback, board, coords, attr, arg1, arg2) {\n var el,\n isConstrained = false,\n i;\n\n for (i = 0; i < coords.length; i++) {\n if (Type.isFunction(coords[i]) || Type.isString(coords[i])) {\n isConstrained = true;\n }\n }\n\n if (!isConstrained) {\n if (Type.isNumber(coords[0]) && Type.isNumber(coords[1])) {\n el = new Callback(board, coords, attr, arg1, arg2);\n\n if (Type.exists(attr.slideobject)) {\n el.makeGlider(attr.slideobject);\n } else {\n // Free element\n el.baseElement = el;\n }\n el.isDraggable = true;\n } else if (Type.isObject(coords[0]) && Type.isTransformationOrArray(coords[1])) {\n // Transformation\n // TODO less general specification of isObject\n el = new Callback(board, [0, 0], attr, arg1, arg2);\n el.addTransform(coords[0], coords[1]);\n el.isDraggable = false;\n } else {\n return false;\n }\n } else {\n el = new Callback(board, [0, 0], attr, arg1, arg2);\n el.addConstraint(coords);\n }\n\n el.handleSnapToGrid();\n el.handleSnapToPoints();\n el.handleAttractors();\n\n el.addParents(coords);\n return el;\n};\n\nexport default JXG.CoordsElement;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *\n **/\n addParents: function (parents) {\n var i, len, par;\n\n if (Type.isArray(parents)) {\n par = parents;\n } else {\n par = arguments;\n }\n\n len = par.length;\n for (i = 0; i < len; ++i) {\n if (!Type.exists(par[i])) {\n continue;\n }\n if (Type.isId(this.board, par[i])) {\n this.parents.push(par[i]);\n } else if (Type.exists(par[i].id)) {\n this.parents.push(par[i].id);\n }\n }\n this.parents = Type.uniqueArray(this.parents);\n },\n\n /**\n * Sets ids of elements to the array this.parents.\n * First, this.parents is cleared. See {@link JXG.GeometryElement#addParents}.\n * @param {Array} parents Array of elements or ids of elements.\n * Alternatively, one can give a list of objects as parameters.\n * @returns {JXG.Object} reference to the object itself.\n **/\n setParents: function (parents) {\n this.parents = [];\n this.addParents(parents);\n },\n\n /**\n * Add dependence on elements in JessieCode functions.\n *\n * @param {Array} function_array Array of functions containing potential properties \"deps\" with\n * elements the function depends on.\n * @returns {JXG.Object} reference to the object itself\n * @private\n */\n addParentsFromJCFunctions: function (function_array) {\n var i, e, obj;\n for (i = 0; i < function_array.length; i++) {\n for (e in function_array[i].deps) {\n obj = function_array[i].deps[e];\n // 4.12.2025, 14.7.2026\n // addParents had to be removed since the type\n // of dependency is not clear.\n // Here, we have a functional dependency, not a geometric one.\n // addChild() adds the elements obj and this to both, decendants and ancestors.\n // It should not call addParents() because this would imply a geometric dependency.\n // this.addParents(obj);\n obj.addChild(this);\n }\n }\n return this;\n },\n\n /**\n * Remove an element as a child from the current element.\n * @param {JXG.GeometryElement} obj The dependent object.\n * @returns {JXG.Object} reference to the object itself\n */\n removeChild: function (obj) {\n //var el, el2;\n\n delete this.childElements[obj.id];\n this.removeDescendants(obj);\n delete obj.ancestors[this.id];\n\n /*\n // I do not know if these addDescendants stuff has to be adapted to removeChild. A.W.\n for (el in this.descendants) {\n if (this.descendants.hasOwnProperty(el)) {\n delete this.descendants[el].ancestors[this.id];\n\n for (el2 in this.ancestors) {\n if (this.ancestors.hasOwnProperty(el2)) {\n this.descendants[el].ancestors[this.ancestors[el2].id] = this.ancestors[el2];\n }\n }\n }\n }\n\n for (el in this.ancestors) {\n if (this.ancestors.hasOwnProperty(el)) {\n for (el2 in this.descendants) {\n if (this.descendants.hasOwnProperty(el2)) {\n this.ancestors[el].descendants[this.descendants[el2].id] = this.descendants[el2];\n }\n }\n }\n }\n */\n return this;\n },\n\n /**\n * Removes the given object from the descendants list of this object and all its child objects.\n * @param {JXG.GeometryElement} obj The element that is to be removed from the descendants list.\n * @private\n * @returns {JXG.Object} reference to the object itself\n */\n removeDescendants: function (obj) {\n var el;\n\n delete this.descendants[obj.id];\n for (el in obj.childElements) {\n if (obj.childElements.hasOwnProperty(el)) {\n this.removeDescendants(obj.childElements[el]);\n }\n }\n return this;\n },\n\n /**\n * Counts the direct children of an object without counting labels.\n * @private\n * @returns {number} Number of children\n */\n countChildren: function () {\n var prop,\n d,\n s = 0;\n\n d = this.childElements;\n for (prop in d) {\n if (d.hasOwnProperty(prop) && prop.indexOf('Label') < 0) {\n s++;\n }\n }\n return s;\n },\n\n /**\n * Returns the elements name. Used in JessieCode.\n * @returns {String}\n */\n getName: function () {\n return this.name;\n },\n\n /**\n * Add transformations to this element.\n * @param {JXG.Transformation|Array} transform Either one {@link JXG.Transformation}\n * or an array of {@link JXG.Transformation}s.\n * @returns {JXG.GeometryElement} Reference to the element.\n */\n addTransform: function (transform) {\n return this;\n },\n\n /**\n * Remove transformations of this element.\n * @param {JXG.Transformation|Array} transform Either one {@link JXG.Transformation}\n * or an array of {@link JXG.Transformation}s.\n * @returns {JXG.GeometryElement} Reference to the element.\n */\n removeTransform: function (transform) {\n return this;\n },\n\n /**\n * Remove all {@link JXG.Transformation}s of this element.\n * @returns {JXG.GeometryElement} Reference to the element.\n */\n clearTransforms: function () {\n return this;\n },\n\n /**\n * Decides whether an element can be dragged. This is used in\n * {@link JXG.GeometryElement#setPositionDirectly} methods\n * where all parent elements are checked if they may be dragged, too.\n * @private\n * @returns {boolean}\n */\n draggable: function () {\n return (\n this.isDraggable &&\n !this.evalVisProp('fixed') &&\n // !this.visProp.frozen &&\n this.type !== Const.OBJECT_TYPE_GLIDER\n );\n },\n\n /**\n * Translates the object by (x, y). In case the element is defined by points, the defining points are\n * translated, e.g. a circle constructed by a center point and a point on the circle line.\n * @param {Number} method The type of coordinates used here.\n * Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.\n * @param {Array} coords array of translation vector.\n * @returns {JXG.GeometryElement} Reference to the element object.\n *\n * @see JXG.GeometryElement3D#setPosition2D\n */\n setPosition: function (method, coords) {\n var parents = [],\n el,\n i, len, t;\n\n if (!Type.exists(this.parents)) {\n return this;\n }\n\n len = this.parents.length;\n for (i = 0; i < len; ++i) {\n el = this.board.select(this.parents[i]);\n if (Type.isPoint(el)) {\n if (!el.draggable()) {\n return this;\n }\n parents.push(el);\n }\n }\n\n if (coords.length === 3) {\n coords = coords.slice(1);\n }\n\n t = this.board.create(\"transform\", coords, { type: \"translate\" });\n\n // We distinguish two cases:\n // 1) elements which depend on free elements, i.e. arcs and sectors\n // 2) other elements\n //\n // In the first case we simply transform the parents elements\n // In the second case we add a transform to the element.\n //\n len = parents.length;\n if (len > 0) {\n t.applyOnce(parents);\n\n // Handle dragging of a 3D element\n if (Type.exists(this.view) && this.view.elType === 'view3d') {\n for (i = 0; i < this.parents.length; ++i) {\n // Search for the parent 3D element\n el = this.view.select(this.parents[i]);\n if (Type.exists(el.setPosition2D)) {\n el.setPosition2D(t);\n }\n }\n }\n\n } else {\n if (\n this.transformations.length > 0 &&\n this.transformations[this.transformations.length - 1].isNumericMatrix\n ) {\n this.transformations[this.transformations.length - 1].melt(t);\n } else {\n this.addTransform(t);\n }\n }\n\n /*\n * If - against the default configuration - defining gliders are marked as\n * draggable, then their position has to be updated now.\n */\n for (i = 0; i < len; ++i) {\n if (parents[i].type === Const.OBJECT_TYPE_GLIDER) {\n parents[i].updateGlider();\n }\n }\n\n return this;\n },\n\n /**\n * Moves an element by the difference of two coordinates.\n * @param {Number} method The type of coordinates used here.\n * Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.\n * @param {Array} coords coordinates in screen/user units\n * @param {Array} oldcoords previous coordinates in screen/user units\n * @returns {JXG.GeometryElement} {JXG.GeometryElement} A reference to the object\n */\n setPositionDirectly: function (method, coords, oldcoords) {\n var c = new Coords(method, coords, this.board, false),\n oldc = new Coords(method, oldcoords, this.board, false),\n dc = Statistics.subtract(c.usrCoords, oldc.usrCoords);\n\n this.setPosition(Const.COORDS_BY_USER, dc);\n\n return this;\n },\n\n /**\n * Moves the element to the top of its layer. Works only for SVG renderer and for simple elements\n * consisting of one SVG node.\n *\n * @returns {JXG.GeometryElement} {JXG.GeometryElement} A reference to the object\n * @example\n * // Move one of the points 'A' or ''B' to make\n * // their midpoint visible.\n * const point1 = board.create(\"point\", [-3, 1]);\n * const point2 = board.create(\"point\", [2, 1]);\n * var mid = board.create(\"midpoint\", [point1, point2]);\n * const point3 = board.create(\"point\", [-0.5, 1], {size: 10, color: 'blue'});\n *\n * mid.coords.on('update', function() {\n * mid.toTopOfLayer();\n * });\n * point3.coords.on('update', function() {\n * point3.toTopOfLayer();\n * });\n *\n * \n * \n *\n */\n toTopOfLayer: function() {\n if (this.board.renderer.type === 'svg' && Type.exists(this.rendNode)) {\n this.rendNode.parentNode.appendChild(this.rendNode);\n }\n\n return this;\n },\n\n /**\n * Array of strings containing the polynomials defining the element.\n * Used for determining geometric loci the groebner way.\n * @returns {Array} An array containing polynomials describing the locus of the current object.\n * @public\n */\n generatePolynomial: function () {\n return [];\n },\n\n /**\n * Animates properties for that object like stroke or fill color, opacity and maybe\n * even more later.\n * @param {Object} hash Object containing properties with target values for the animation.\n * @param {number} time Number of milliseconds to complete the animation.\n * @param {Object} [options] Optional settings for the animation:\n * Sets also the display of the inherits elements. These can be\n * JSXGraph elements or arrays of JSXGraph elements.\n * However, deeper nesting than this is not supported.\n *\n * @param {Boolean} val true: show the element, false: hide the element\n * @return {JXG.GeometryElement} Reference to the element\n * @private\n */\n setDisplayRendNode: function (val) {\n var i, len, s, len_s, obj;\n\n if (val === undefined) {\n val = this.visPropCalc.visible;\n }\n\n if (val === this.visPropOld.visible) {\n return this;\n }\n\n // Set display of the element itself\n this.board.renderer.display(this, val);\n\n // Set the visibility of elements which inherit the attribute 'visible'\n len = this.inherits.length;\n for (s = 0; s < len; s++) {\n obj = this.inherits[s];\n if (Type.isArray(obj)) {\n len_s = obj.length;\n for (i = 0; i < len_s; i++) {\n if (\n Type.exists(obj[i]) &&\n Type.exists(obj[i].rendNode) &&\n obj[i].evalVisProp('visible') === 'inherit'\n ) {\n obj[i].setDisplayRendNode(val);\n }\n }\n } else {\n if (\n Type.exists(obj) &&\n Type.exists(obj.rendNode) &&\n obj.evalVisProp('visible') === 'inherit'\n ) {\n obj.setDisplayRendNode(val);\n }\n }\n }\n\n // Set the visibility of the label if it inherits the attribute 'visible'\n if (this.hasLabel && Type.exists(this.label) && Type.exists(this.label.rendNode)) {\n if (this.label.evalVisProp('visible') === 'inherit') {\n this.label.setDisplayRendNode(val);\n }\n }\n\n return this;\n },\n\n /**\n * Hide the element. It will still exist but not be visible on the board.\n * Alias for \"element.setAttribute({visible: false});\"\n * @return {JXG.GeometryElement} Reference to the element\n */\n hide: function () {\n this.setAttribute({ visible: false });\n return this;\n },\n\n /**\n * Hide the element. It will still exist but not be visible on the board.\n * Alias for {@link JXG.GeometryElement#hide}\n * @returns {JXG.GeometryElement} Reference to the element\n */\n hideElement: function () {\n this.hide();\n return this;\n },\n\n /**\n * Make the element visible.\n * Alias for \"element.setAttribute({visible: true});\"\n * @return {JXG.GeometryElement} Reference to the element\n */\n show: function () {\n this.setAttribute({ visible: true });\n return this;\n },\n\n /**\n * Make the element visible.\n * Alias for {@link JXG.GeometryElement#show}\n * @returns {JXG.GeometryElement} Reference to the element\n */\n showElement: function () {\n this.show();\n return this;\n },\n\n /**\n * Set the visibility of an element. The visibility is influenced by\n * (listed in ascending priority):\n *
\n * This method is called three times for most elements:\n *
\n * <value> tags will not be evaluated if text is provided by a function\n *
\n * Sets the property plaintext of the text element.\n *\n * @private\n */\n this.updateText = function () {\n resolvedText = text().toString(); // Evaluate function\n if (ev_p && !ev_um && !ev_uk) {\n this.plaintext = this.replaceSub(\n this.replaceSup(\n this.convertGeonextAndSketchometry2CSS(resolvedText, false)\n )\n );\n } else {\n this.plaintext = resolvedText;\n }\n };\n } else {\n if (Type.isNumber(text) && this.evalVisProp('formatnumber')) {\n if (this.evalVisProp('tofraction')) {\n if (ev_um) {\n this.content = '\\\\(' + Type.toFraction(text, true) + '\\\\)';\n } else {\n this.content = Type.toFraction(text, ev_uk);\n }\n } else {\n digits = this.evalVisProp('digits');\n if (this.useLocale()) {\n this.content = this.formatNumberLocale(text, digits);\n } else {\n this.content = Type.toFixed(text, digits);\n }\n }\n } else if (Type.isString(text) && ev_p) {\n if (this.evalVisProp('useasciimathml')) {\n // ASCIIMathML\n // value-tags are not supported\n this.content = \"'`\" + text + \"`'\";\n } else if (ev_um || ev_uk) {\n // MathJax or KaTeX\n // Replace value-tags by functions\n // sketchoicon/sketchofont is ignored\n this.content = this.valueTagToJessieCode(text);\n if (!Type.isArray(this.content)) {\n // For some reason we don't have to mask backslashes in an array of strings\n // anymore.\n //\n // for (i = 0; i < this.content.length; i++) {\n // this.content[i] = this.content[i].replace(/\\\\/g, \"\\\\\\\\\"); // Replace single backslash by double\n // }\n // } else {\n this.content = this.content.replace(/\\\\/g, \"\\\\\\\\\"); // Replace single backslash by double\n }\n } else {\n // No TeX involved.\n // Converts GEONExT syntax into JavaScript string\n // Short math is allowed\n // Replace value-tags by functions\n // Avoid geonext2JS calls\n this.content = this.poorMansTeX(this.valueTagToJessieCode(text));\n }\n convertJessieCode = true;\n } else {\n this.content = text;\n }\n\n // Generate function which returns the text to be displayed\n if (convertJessieCode) {\n // Convert JessieCode to JS function\n if (Type.isArray(this.content)) {\n // This is the case if the text contained value-tags.\n // These value-tags consist of JessieCode snippets\n // which are now replaced by JavaScript functions\n that = this;\n for (i = 0; i < this.content.length; i++) {\n if (this.content[i][0] !== '\"') {\n this.content[i] = this.board.jc.snippet(this.content[i], true, \"\", false);\n for (e in this.content[i].deps) {\n this.addParents(this.content[i].deps[e]);\n this.content[i].deps[e].addChild(this);\n }\n }\n }\n\n updateText = function() {\n var i, t,\n digits = that.evalVisProp('digits'),\n txt = '';\n\n for (i = 0; i < that.content.length; i++) {\n if (Type.isFunction(that.content[i])) {\n t = that.content[i]();\n if (that.useLocale()) {\n t = that.formatNumberLocale(t, digits);\n } else {\n t = Type.toFixed(t, digits);\n }\n } else {\n t = that.content[i];\n // Instead of 't.at(t.length - 1)' also 't.(-1)' should work.\n // However in Moodle 4.2 't.(-1)' returns an empty string.\n // In plain HTML pages it works.\n if (t[0] === '\"' && t[t.length - 1] === '\"') {\n t = t.slice(1, -1);\n }\n }\n\n txt += t;\n }\n return txt;\n };\n } else {\n updateText = this.board.jc.snippet(this.content, true, \"\", false);\n for (e in updateText.deps) {\n this.addParents(updateText.deps[e]);\n updateText.deps[e].addChild(this);\n }\n }\n\n // Ticks have been escaped in valueTagToJessieCode\n this.updateText = function () {\n this.plaintext = this.unescapeTicks(updateText());\n };\n } else {\n this.updateText = function () {\n this.plaintext = this.content; // text;\n };\n }\n }\n },\n\n /**\n * Defines new content. This is used by {@link JXG.Text#setTextJessieCode} and {@link JXG.Text#setText}. This is required because\n * JessieCode needs to filter all Texts inserted into the DOM and thus has to replace setText by setTextJessieCode.\n * @param {String|Function|Number} text\n * @returns {JXG.Text}\n * @private\n */\n _setText: function (text) {\n this._createFctUpdateText(text);\n\n // First evaluation of the string.\n // We need this for display='internal' and Canvas\n this.updateText();\n this.fullUpdate();\n\n // We do not call updateSize for the infobox to speed up rendering\n if (!this.board.infobox || this.id !== this.board.infobox.id) {\n this.updateSize(); // updateSize() is called at least once.\n }\n\n // This may slow down canvas renderer\n // if (this.board.renderer.type === 'canvas') {\n // this.board.fullUpdate();\n // }\n\n return this;\n },\n\n /**\n * Defines new content but converts < and > to HTML entities before updating the DOM.\n * @param {String|function} text\n */\n setTextJessieCode: function (text) {\n var s;\n\n this.visProp.castext = text;\n if (Type.isFunction(text)) {\n s = function () {\n return Type.sanitizeHTML(text());\n };\n } else {\n if (Type.isNumber(text)) {\n s = text;\n } else {\n s = Type.sanitizeHTML(text);\n }\n }\n\n return this._setText(s);\n },\n\n /**\n * Defines new content.\n * @param {String|function} text\n * @returns {JXG.Text} Reference to the text object.\n */\n setText: function (text) {\n return this._setText(text);\n },\n\n /**\n * Recompute the width and the height of the text box.\n * Updates the array {@link JXG.Text#size} with pixel values.\n * The result may differ from browser to browser\n * by some pixels.\n * In canvas an old IEs we use a very crude estimation of the dimensions of\n * the textbox.\n * JSXGraph needs {@link JXG.Text#size} for applying rotations in IE and\n * for aligning text.\n *\n * @return {this} [description]\n */\n updateSize: function () {\n var tmp,\n that,\n node,\n ev_d = this.evalVisProp('display');\n\n if (!Env.isBrowser || this.board.renderer.type === 'no') {\n return this;\n }\n node = this.rendNode;\n\n\n /**\n * offsetWidth and offsetHeight seem to be supported for internal vml elements by IE10+ in IE8 mode.\n */\n if (ev_d === \"html\" || this.board.renderer.type === 'vml') {\n if (Type.exists(node.offsetWidth)) {\n that = this;\n window.setTimeout(function () {\n that.size = [node.offsetWidth, node.offsetHeight];\n\n // This would be the way to determine the height of a MathJax formula\n // rendered with SVG (i.e. using tex-svg-nofont).\n // This is needed if the text element's anchorY === 'middle'\n // and the text is included in a board.renderer.dumpToDataURI() call\n // with MathJax formulas.\n // if (Type.exists(node.firstChild) && node.firstChild.nodeName === 'MJX-CONTAINER' &&\n // Type.exists(node.firstChild.firstChild && node.firstChild.firstChild.nodeName === 'SVG')\n // ) {\n // // console.log(that.visProp.fontsize * 0.5)\n // // that.size[1] += 2 * that.visProp.fontsize;\n // that.size = [node.firstChild.firstChild.scrollWidth, node.firstChild.firstChild.scrollHeight];\n // }\n\n that.needsUpdate = true;\n that.updateRenderer();\n }, 0);\n // In case, there is non-zero padding or borders\n // the following approach does not longer work.\n // s = [node.offsetWidth, node.offsetHeight];\n // if (s[0] === 0 && s[1] === 0) { // Some browsers need some time to set offsetWidth and offsetHeight\n // that = this;\n // window.setTimeout(function () {\n // that.size = [node.offsetWidth, node.offsetHeight];\n // that.needsUpdate = true;\n // that.updateRenderer();\n // }, 0);\n // } else {\n // this.size = s;\n // }\n } else {\n this.size = this.crudeSizeEstimate();\n }\n } else if (ev_d === 'internal') {\n if (this.board.renderer.type === 'svg') {\n that = this;\n window.setTimeout(function () {\n try {\n tmp = node.getBBox();\n that.size = [tmp.width, tmp.height];\n that.needsUpdate = true;\n that.updateRenderer();\n } catch (e) {}\n }, 0);\n } else if (this.board.renderer.type === 'canvas') {\n this.size = this.crudeSizeEstimate();\n }\n }\n\n return this;\n },\n\n /**\n * A very crude estimation of the dimensions of the textbox in case nothing else is available.\n * @returns {Array}\n */\n crudeSizeEstimate: function () {\n var ev_fs = parseFloat(this.evalVisProp('fontsize'));\n return [ev_fs * this.plaintext.length * 0.45, ev_fs * 0.9];\n },\n\n /**\n * Decode unicode entities into characters.\n * @param {String} string\n * @returns {String}\n */\n utf8_decode: function (string) {\n return string.replace(/&#x(\\w+);/g, function (m, p1) {\n return String.fromCharCode(parseInt(p1, 16));\n });\n },\n\n /**\n * Replace _{} by <sub>\n * @param {String} te String containing _{}.\n * @returns {String} Given string with _{} replaced by <sub>.\n */\n replaceSub: function (te) {\n if (!te.indexOf) {\n return te;\n }\n\n var j,\n i = te.indexOf(\"_{\");\n\n // The regexp in here are not used for filtering but to provide some kind of sugar for label creation,\n // i.e. replacing _{...} with .... What is passed would get out anyway.\n /*jslint regexp: true*/\n while (i >= 0) {\n te = te.slice(0, i) + te.slice(i).replace(/_\\{/, \"\");\n j = te.indexOf(\"}\", i + 4);\n if (j >= 0) {\n te = te.slice(0, j) + te.slice(j).replace(/\\}/, \"\");\n }\n i = te.indexOf(\"_{\");\n }\n\n i = te.indexOf(\"_\");\n while (i >= 0) {\n te = te.slice(0, i) + te.slice(i).replace(/_(.?)/, \"$1\");\n i = te.indexOf(\"_\");\n }\n\n return te;\n },\n\n /**\n * Replace ^{} by <sup>\n * @param {String} te String containing ^{}.\n * @returns {String} Given string with ^{} replaced by <sup>.\n */\n replaceSup: function (te) {\n if (!te.indexOf) {\n return te;\n }\n\n var j,\n i = te.indexOf(\"^{\");\n\n // The regexp in here are not used for filtering but to provide some kind of sugar for label creation,\n // i.e. replacing ^{...} with .... What is passed would get out anyway.\n /*jslint regexp: true*/\n while (i >= 0) {\n te = te.slice(0, i) + te.slice(i).replace(/\\^\\{/, \"\");\n j = te.indexOf(\"}\", i + 4);\n if (j >= 0) {\n te = te.slice(0, j) + te.slice(j).replace(/\\}/, \"\");\n }\n i = te.indexOf(\"^{\");\n }\n\n i = te.indexOf(\"^\");\n while (i >= 0) {\n te = te.slice(0, i) + te.slice(i).replace(/\\^(.?)/, \"$1\");\n i = te.indexOf(\"^\");\n }\n\n return te;\n },\n\n /**\n * Return the width of the text element.\n * @returns {Array} [width, height] in pixel\n */\n getSize: function () {\n return this.size;\n },\n\n /**\n * Move the text to new coordinates.\n * @param {number} x\n * @param {number} y\n * @returns {object} reference to the text object.\n */\n setCoords: function (x, y) {\n var coordsAnchor, dx, dy;\n if (Type.isArray(x) && x.length > 1) {\n y = x[1];\n x = x[0];\n }\n\n if (this.evalVisProp('islabel') && Type.exists(this.element)) {\n coordsAnchor = this.element.getLabelAnchor();\n dx = (x - coordsAnchor.usrCoords[1]) * this.board.unitX;\n dy = -(y - coordsAnchor.usrCoords[2]) * this.board.unitY;\n\n this.relativeCoords.setCoordinates(Const.COORDS_BY_SCREEN, [dx, dy]);\n } else {\n this.coords.setCoordinates(Const.COORDS_BY_USER, [x, y]);\n }\n\n // this should be a local update, otherwise there might be problems\n // with the tick update routine resulting in orphaned tick labels\n this.fullUpdate();\n\n return this;\n },\n\n /**\n * Evaluates the text.\n * Then, the update function of the renderer\n * is called.\n */\n update: function (fromParent) {\n if (!this.needsUpdate) {\n return this;\n }\n\n this.updateCoords(fromParent);\n this.updateText();\n\n if (this.evalVisProp('display') === 'internal') {\n if (Type.isString(this.plaintext)) {\n this.plaintext = this.utf8_decode(this.plaintext);\n }\n }\n\n this.checkForSizeUpdate();\n if (this.needsSizeUpdate) {\n this.updateSize();\n }\n\n return this;\n },\n\n /**\n * Used to save updateSize() calls.\n * Called in JXG.Text.update\n * That means this.update() has been called.\n * More tests are in JXG.Renderer.updateTextStyle. The latter tests\n * are one update off. But this should pose not too many problems, since\n * it affects fontSize and cssClass changes.\n *\n * @private\n */\n checkForSizeUpdate: function () {\n if (this.board.infobox && this.id === this.board.infobox.id) {\n this.needsSizeUpdate = false;\n } else {\n // For some magic reason it is more efficient on the iPad to\n // call updateSize() for EVERY text element EVERY time.\n this.needsSizeUpdate = this.plaintextOld !== this.plaintext;\n\n if (this.needsSizeUpdate) {\n this.plaintextOld = this.plaintext;\n }\n }\n },\n\n /**\n * The update function of the renderer\n * is called.\n * @private\n */\n updateRenderer: function () {\n if (\n //this.board.updateQuality === this.board.BOARD_QUALITY_HIGH &&\n this.evalVisProp('autoposition')\n ) {\n this.setAutoPosition().updateConstraint();\n }\n return this.updateRendererGeneric('updateText');\n },\n\n /**\n * Converts shortened math syntax into correct syntax: 3x instead of 3*x or\n * (a+b)(3+1) instead of (a+b)*(3+1).\n *\n * @private\n * @param{String} expr Math term\n * @returns {string} expanded String\n */\n expandShortMath: function (expr) {\n var re = /([)0-9.])\\s*([(a-zA-Z_])/g;\n return expr.replace(re, \"$1*$2\");\n },\n\n /**\n * Converts the GEONExT syntax of the \n * Attention: for labels, [0, 0, 0, 0] is returned.\n *\n * @returns Array\n */\n bounds: function () {\n var c = this.coords.usrCoords;\n\n if (\n this.evalVisProp('islabel') ||\n this.board.unitY === 0 ||\n this.board.unitX === 0\n ) {\n return [0, 0, 0, 0];\n }\n return [\n c[1],\n c[2] + this.size[1] / this.board.unitY,\n c[1] + this.size[0] / this.board.unitX,\n c[2]\n ];\n },\n\n /**\n * Returns the value of the attribute \"anchorX\". If this equals \"auto\",\n * returns \"left\", \"middle\", or \"right\", depending on the\n * value of the attribute \"position\".\n * @returns String\n */\n getAnchorX: function () {\n var a = this.evalVisProp('anchorx');\n if (a === 'auto') {\n switch (this.visProp.position) {\n case \"top\":\n case \"bot\":\n return 'middle';\n case \"rt\":\n case \"lrt\":\n case \"urt\":\n return 'left';\n case \"lft\":\n case \"llft\":\n case \"ulft\":\n default:\n return 'right';\n }\n }\n return a;\n },\n\n /**\n * Returns the value of the attribute \"anchorY\". If this equals \"auto\",\n * returns \"bottom\", \"middle\", or \"top\", depending on the\n * value of the attribute \"position\".\n * @returns String\n */\n getAnchorY: function () {\n var a = this.evalVisProp('anchory');\n if (a === 'auto') {\n switch (this.visProp.position) {\n case \"top\":\n case \"ulft\":\n case \"urt\":\n return 'bottom';\n case \"bot\":\n case \"lrt\":\n case \"llft\":\n return 'top';\n case \"rt\":\n case \"lft\":\n default:\n return 'middle';\n }\n }\n return a;\n },\n\n /**\n * Computes the number of overlaps of a box of w pixels width, h pixels height\n * and center (x, y)\n *\n * An overlap occurs when either:\n * \n * The method tests 60 different angles (0 to 2π) at 3 different distances (radii).\n * It evaluates each position using calculateScore(radius, angle) and chooses the position with the highest score.\n * Then the label's anchor points and offset are adjusted accordingly.\n *\n * @returns {JXG.Text} Reference to the text object.\n */\n setAutoPosition: function() {\n var radius, angle, radiusStep,\n i,\n bestScore = -Infinity, bestRadius, bestAngle,\n minRadius = this.evalVisProp('autopositionmindistance'),\n maxRadius = this.evalVisProp('autopositionmaxdistance'),\n score,\n co, si,\n currentOffset = this.evalVisProp('offset'),\n currentRadius,\n currentAngle,\n numAngles = 60,\n numRadius = 4;\n\n if (\n this === this.board.infobox ||\n !this.element ||\n !this.visPropCalc.visible ||\n !this.evalVisProp('islabel')\n ) {\n return this;\n }\n\n // Calculate current position\n currentRadius = Math.sqrt(currentOffset[0] * currentOffset[0] + currentOffset[1] * currentOffset[1]);\n currentAngle = Math.atan2(currentOffset[1], currentOffset[0]);\n\n if (this.calculateScore(currentRadius, currentAngle) === 0) {\n return this;\n }\n\n // Initialize search at min radius\n radius = minRadius;\n // Calculate step size\n radiusStep = (maxRadius - minRadius) / (numRadius - 1);\n\n // Test the different radii\n while (maxRadius - radius > -0.01) {\n\n // Radius gets bigger so just check if its smaller than maxnumber of angles.\n for (i = 0; i < numAngles; i++) {\n\n // calculate angle\n angle = i / numAngles * 2 * Math.PI;\n\n // calculate score\n score = this.calculateScore(radius, angle);\n\n // if score is better than bestScore, set bestAngle, bestRadius and bestScore\n if (score > bestScore) {\n bestAngle = angle;\n bestRadius = radius;\n bestScore = score;\n }\n\n // if bestScore is 0, break, because it can't get better\n if (bestScore === 0) {\n radius = maxRadius;\n break;\n }\n }\n\n radius += radiusStep;\n }\n\n co = Math.cos(bestAngle);\n si = Math.sin(bestAngle);\n\n // If label is on the left side of the element, the anchorx is set to \"right\"\n if (co < 0) {\n this.visProp.anchorx = 'right';\n } else {\n this.visProp.anchorx = 'left';\n }\n\n // If label is on the bottom side of the element, so the anchory is set to \"top\"\n if (si < 0) {\n this.visProp.anchory = 'top';\n } else {\n this.visProp.anchory = 'bottom';\n }\n\n // Set offset\n this.visProp.offset = [bestRadius * co, bestRadius * si];\n\n return this;\n }\n\n // /**\n // * Computes the number of overlaps of a box of w pixels width, h pixels height\n // * and center (x, y)\n // *\n // * @private\n // * @param {Number} x x-coordinate of the center (screen coordinates)\n // * @param {Number} y y-coordinate of the center (screen coordinates)\n // * @param {Number} w width of the box in pixel\n // * @param {Number} h width of the box in pixel\n // * @param {Array} [whiteList] array of ids which should be ignored\n // * @return {Number} Number of overlapping elements\n // */\n // getNumberOfConflicts: function (x, y, w, h, whiteList) {\n // whiteList = whiteList || [];\n // var count = 0,\n // i, obj, le,\n // savePointPrecision,\n // saveHasInnerPoints;\n\n // // Set the precision of hasPoint to half the max if label isn't too long\n // savePointPrecision = this.board.options.precision.hasPoint;\n // // this.board.options.precision.hasPoint = Math.max(w, h) * 0.5;\n // this.board.options.precision.hasPoint = (w + h) * 0.25;\n // // TODO:\n // // Make it compatible with the objects' visProp.precision attribute\n // for (i = 0, le = this.board.objectsList.length; i < le; i++) {\n // obj = this.board.objectsList[i];\n // saveHasInnerPoints = obj.visProp.hasinnerpoints;\n // obj.visProp.hasinnerpoints = false;\n // if (\n // obj.visPropCalc.visible &&\n // obj.elType !== \"axis\" &&\n // obj.elType !== \"ticks\" &&\n // obj !== this.board.infobox &&\n // obj !== this &&\n // obj.hasPoint(x, y) &&\n // whiteList.indexOf(obj.id) === -1\n // ) {\n // count++;\n // }\n // obj.visProp.hasinnerpoints = saveHasInnerPoints;\n // }\n // this.board.options.precision.hasPoint = savePointPrecision;\n\n // return count;\n // },\n\n // /**\n // * Sets the offset of a label element to the position with the least number\n // * of overlaps with other elements, while retaining the distance to its\n // * anchor element. Twelve different angles are possible.\n // *\n // * @returns {JXG.Text} Reference to the text object.\n // */\n // setAutoPosition: function () {\n // var x, y, cx, cy,\n // anchorCoords,\n // // anchorX, anchorY,\n // w = this.size[0],\n // h = this.size[1],\n // start_angle, angle,\n // optimum = {\n // conflicts: Infinity,\n // angle: 0,\n // r: 0\n // },\n // max_r, delta_r,\n // conflicts, offset, r,\n // num_positions = 12,\n // step = (2 * Math.PI) / num_positions,\n // j, dx, dy, co, si;\n\n // if (\n // this === this.board.infobox ||\n // !this.visPropCalc.visible ||\n // !this.evalVisProp('islabel') ||\n // !this.element\n // ) {\n // return this;\n // }\n\n // // anchorX = this.evalVisProp('anchorx');\n // // anchorY = this.evalVisProp('anchory');\n // offset = this.evalVisProp('offset');\n // anchorCoords = this.element.getLabelAnchor();\n // cx = anchorCoords.scrCoords[1];\n // cy = anchorCoords.scrCoords[2];\n\n // // Set dx, dy as the relative position of the center of the label\n // // to its anchor element ignoring anchorx and anchory.\n // dx = offset[0];\n // dy = offset[1];\n\n // conflicts = this.getNumberOfConflicts(cx + dx, cy - dy, w, h, this.evalVisProp('autopositionwhitelist'));\n // if (conflicts === 0) {\n // return this;\n // }\n // // console.log(this.id, conflicts, w, h);\n // // r = Geometry.distance([0, 0], offset, 2);\n\n // r = this.evalVisProp('autopositionmindistance');\n // max_r = this.evalVisProp('autopositionmaxdistance');\n // delta_r = 0.2 * r;\n\n // start_angle = Math.atan2(dy, dx);\n\n // optimum.conflicts = conflicts;\n // optimum.angle = start_angle;\n // optimum.r = r;\n\n // while (optimum.conflicts > 0 && r <= max_r) {\n // for (\n // j = 1, angle = start_angle + step;\n // j < num_positions && optimum.conflicts > 0;\n // j++\n // ) {\n // co = Math.cos(angle);\n // si = Math.sin(angle);\n\n // x = cx + r * co;\n // y = cy - r * si;\n\n // conflicts = this.getNumberOfConflicts(x, y, w, h, this.evalVisProp('autopositionwhitelist'));\n // if (conflicts < optimum.conflicts) {\n // optimum.conflicts = conflicts;\n // optimum.angle = angle;\n // optimum.r = r;\n // }\n // if (optimum.conflicts === 0) {\n // break;\n // }\n // angle += step;\n // }\n // r += delta_r;\n // }\n // // console.log(this.id, \"after\", optimum)\n // r = optimum.r;\n // co = Math.cos(optimum.angle);\n // si = Math.sin(optimum.angle);\n // this.visProp.offset = [r * co, r * si];\n\n // if (co < -0.2) {\n // this.visProp.anchorx = 'right'\n // } else if (co > 0.2) {\n // this.visProp.anchorx = 'left'\n // } else {\n // this.visProp.anchorx = 'middle'\n // }\n\n // return this;\n // }\n }\n);\n\n/**\n * @class Constructs a text element.\n *\n *\n * The coordinates can either be absolute (i.e. respective to the coordinate system of the board) or be relative to the coordinates of an element\n * given in {@link Text#anchor}.\n * \n * HTML, MathJaX, KaTeX, ASCIIMathML, and GEONExT syntax can be handled.\n * \n * There are two ways to display texts:\n * \n * Parent elements can be two or three elements of type number, a string containing a GEONExT\n * constraint, or a function which takes no parameter and returns a number. Every parent element beside the last determines one coordinate.\n * If a coordinate is\n * given by a number, the number determines the initial position of a free text. If given by a string or a function that coordinate will be constrained\n * that means the user won't be able to change the texts's position directly by mouse because it will be calculated automatically depending on the string\n * or the function's return value. If two parent elements are given the coordinates will be interpreted as 2D affine Euclidean coordinates, if three such\n * parent elements are given they will be interpreted as homogeneous coordinates.\n * \n * The text to display may be given as string or as function returning a string.\n *\n * There is the attribute 'display' which takes the values 'html' or 'internal'. In case of 'html' an HTML division tag is created to display\n * the text. In this case it is also possible to use MathJax, KaTeX, or ASCIIMathML. If neither of these is used, basic Math rendering is\n * applied.\n * \n * In case of 'internal', an SVG text element is used to display the text.\n * @see JXG.Text\n * @example\n * // Create a fixed text at position [0,1].\n * var t1 = board.create('text',[0,1,\"Hello World\"]);\n * \n * Labels for lines, segments, curves and circles can be controlled additionally by the attributes {@link Label#position} and\n * {@link Label#distance}, i.e. for a segment [A, B] one could use the follwoing attributes:\n * \n * The styling of the supplied div is up to the user, see the style-tag in the example below for\n * one possibility. The CSS for the inner div, hosting the JSXGraph board, is supplied by the attributes\n * \n * By setting the attribute \"clip\" to false for selected\n * elements (like sliders and texts), these elements can be positioned outside of the JSXGraph board. For those elements,\n * the setting of the attributes \"frozen:true, fixed:true\" is recommended to make their position independent from zooming\n * or panning the board coordinates.\n * \n * However, not all elements will look good if displayed outside of the JSXGraph board - be careful.\n *\n * @param {String|Object} box id of or reference to the HTML element in which the board is painted into a sub-element of type div.\n * @param {Object} attributes An object that sets some of the board properties and properties of the sub-element containing the board.\n * See {@link JXG.Board} for a list of available attributes of the board.\n * Most of these attributes can also be set globally via {@link JXG.Options}.\n *\n * @returns {JXG.Board} Reference to the created board.\n *\n * @example\n *\n * // Styling of the outer div\n * <style>\n * .container {\n * display: flex;\n * align-items: center;\n * justify-content: center;\n * width: 800px;\n * height: 500px;\n * overflow: hidden;\n * border: 1px black solid;\n * border-radius: 10px;\n * background-color: #eee;\n * }\n * </style>\n * <div id=\"container\" class=\"container\"></div>\n * <script type=\"text/javascript\">\n * const board = JXG.appBox('container', {\n * jxgbox: {\n * // Styling of the inner div\n * cssStyle: 'width:640px; aspect-ratio:2/1; background-color: white',\n * cssClass: '',\n * id: 'jxgbox'\n * },\n * boundingbox: [-5, 5, 5, -5],\n * axis: true,\n * showFullScreen: true\n * });\n *\n * const point1 = board.create(\"point\", [4, 1], { name: 'A' });\n * const point2 = board.create(\"point\", [3, -1], {name: 'B'});\n * const point3 = board.create(\"point\", [6, -1], { clip: false });\n *\n * var sl = board.create('slider', [[-3, -6], [-1, -6], [-5, 1, 5]], {\n * clip: false,\n * frozen: true,\n * size: 16,\n * face: '[]',\n * name: 's'\n * });\n *\n * var graph = board.create(\"functiongraph\", ['s.Value() * x^3'], { clip: true });\n *\n * </script>\n * \n * A polygon is convex if for every pair of points, the line segment connecting them does not intersect\n * an edge of the polygon in one point.\n * A single line segment, a single point, or the empty set is considered as convex. A necessary condition for a polygon\n * to be convex that the angle sum of its interior angles equals ± 2 π.\n * \n * A path element might be specified as an array of coordinate arrays or {@link JXG.Coords}.\n * See the discussion at stackoverflow.\n *\n * @param {Array|Polygon|PolygonalChain} points Polygon or list of coordinates\n * @returns {Boolean} true if convex\n *\n * @example\n * var pol = board.create('polygon', [\n * [-1, -1],\n * [3, -1],\n * [4, 2],\n * [3, 3],\n * [0, 4],\n * [-3, 1]\n * ], {\n * vertices: {\n * color: 'blue',\n * snapToGrid: true\n * }\n * });\n *\n * console.log(\"JSXGraph example:\", JXG.Math.Geometry.isConvex(pol));\n * // > true\n *\n *\n *\n * \n * Non-homogeneous version.\n *\n * @param {Array|JXG.Point} p1 First point or its coordinates of the segment. Point object or array of length 3. First (homogeneous) coordinate is equal to 1.\n * @param {Array|JXG.Point} p2 Second point or its coordinates of the segment. Point object or array of length 3. First (homogeneous) coordinate is equal to 1.\n * @param {Array|JXG.Point} q Point or its coordinates. Point object or array of length 3. First (homogeneous) coordinate is equal to 1.\n * @return {Number} Signed area of the triangle formed by these three points.\n *\n * @see JXG.Math.Geometry.windingNumber\n */\n det3p: function (p1, p2, q) {\n var pp1, pp2, qq;\n\n if (Type.isPoint(p1)) {\n pp1 = p1.Coords(true);\n } else {\n pp1 = p1;\n }\n if (Type.isPoint(p2)) {\n pp2 = p2.Coords(true);\n } else {\n pp2 = p2;\n }\n if (Type.isPoint(q)) {\n qq = q.Coords(true);\n } else {\n qq = q;\n }\n\n return (pp1[1] - qq[1]) * (pp2[2] - qq[2]) - (pp2[1] - qq[1]) * (pp1[2] - qq[2]);\n },\n\n /**\n * Winding number of a point in respect to a polygon path.\n *\n * The point is regarded outside if the winding number is zero,\n * inside otherwise. The algorithm tries to find degenerate cases, i.e.\n * if the point is on the path. This is regarded as \"outside\".\n * If the point is a vertex of the path, it is regarded as \"inside\".\n *\n * Implementation of algorithm 7 from \"The point in polygon problem for\n * arbitrary polygons\" by Kai Hormann and Alexander Agathos, Computational Geometry,\n * Volume 20, Issue 3, November 2001, Pages 131-144.\n *\n * @param {Array} usrCoords Homogenous coordinates of the point\n * @param {Array} path Array of points / coords determining a path, i.e. the vertices of the polygon / path. The array elements\n * do not have to be full points, but have to have a subobject \"coords\" or should be of type JXG.Coords.\n * @param {Boolean} [doNotClosePath=false] If true the last point of the path is not connected to the first point.\n * This is necessary if the path consists of two or more closed subpaths, e.g. if the figure has a hole.\n *\n * @return {Number} Winding number of the point. The point is\n * regarded outside if the winding number is zero,\n * inside otherwise.\n */\n windingNumber: function (usrCoords, path, doNotClosePath) {\n var wn = 0,\n le = path.length,\n x = usrCoords[1],\n y = usrCoords[2],\n p0,\n p1,\n p2,\n d,\n sign,\n i,\n off = 0;\n\n if (le === 0) {\n return 0;\n }\n\n doNotClosePath = doNotClosePath || false;\n if (doNotClosePath) {\n off = 1;\n }\n\n // Infinite points are declared outside\n if (isNaN(x) || isNaN(y)) {\n return 1;\n }\n\n if (Type.exists(path[0].coords)) {\n p0 = path[0].coords;\n p1 = path[le - 1].coords;\n } else {\n p0 = path[0];\n p1 = path[le - 1];\n }\n // Handle the case if the point is the first vertex of the path, i.e. inside.\n if (p0.usrCoords[1] === x && p0.usrCoords[2] === y) {\n return 1;\n }\n\n for (i = 0; i < le - off; i++) {\n // Consider the edge from p1 = path[i] to p2 = path[i+1]isClosedPath\n if (Type.exists(path[i].coords)) {\n p1 = path[i].coords.usrCoords;\n p2 = path[(i + 1) % le].coords.usrCoords;\n } else {\n p1 = path[i].usrCoords;\n p2 = path[(i + 1) % le].usrCoords;\n }\n\n // If one of the two points p1, p2 is undefined or infinite,\n // move on.\n if (\n p1[0] === 0 ||\n p2[0] === 0 ||\n isNaN(p1[1]) ||\n isNaN(p2[1]) ||\n isNaN(p1[2]) ||\n isNaN(p2[2])\n ) {\n continue;\n }\n\n if (p2[2] === y) {\n if (p2[1] === x) {\n return 1;\n }\n if (p1[2] === y && p2[1] > x === p1[1] < x) {\n return 0;\n }\n }\n\n if (p1[2] < y !== p2[2] < y) {\n // Crossing\n sign = 2 * (p2[2] > p1[2] ? 1 : 0) - 1;\n if (p1[1] >= x) {\n if (p2[1] > x) {\n wn += sign;\n } else {\n d = this.det3p(p1, p2, usrCoords);\n if (d === 0) {\n // Point is on line, i.e. outside\n return 0;\n }\n if (d > 0 + Mat.eps === p2[2] > p1[2]) {\n // Right crossing\n wn += sign;\n }\n }\n } else {\n if (p2[1] > x) {\n d = this.det3p(p1, p2, usrCoords);\n if (d > 0 + Mat.eps === p2[2] > p1[2]) {\n // Right crossing\n wn += sign;\n }\n }\n }\n }\n }\n\n return wn;\n },\n\n /**\n * Decides if a point (x,y) is inside of a path / polygon.\n * Does not work correct if the path has hole. In this case, windingNumber is the preferred method.\n * Implements W. Randolf Franklin's pnpoly method.\n *\n * See https://wrf.ecse.rpi.edu/Research/Short_Notes/pnpoly.html.\n *\n * @param {Number} x_in x-coordinate (screen or user coordinates)\n * @param {Number} y_in y-coordinate (screen or user coordinates)\n * @param {Array} path Array of points / coords determining a path, i.e. the vertices of the polygon / path. The array elements\n * do not have to be full points, but have to have a subobject \"coords\" or should be of type JXG.Coords.\n * @param {Number} [coord_type=JXG.COORDS_BY_SCREEN] Type of coordinates used here.\n * Possible values are JXG.COORDS_BY_USER and JXG.COORDS_BY_SCREEN.\n * Default value is JXG.COORDS_BY_SCREEN.\n * @param {JXG.Board} board Board object\n *\n * @returns {Boolean} if (x_in, y_in) is inside of the polygon.\n * @see JXG.Polygon#hasPoint\n * @see JXG.Polygon#pnpoly\n * @see JXG.Math.Geometry.windingNumber\n *\n * @example\n * var pol = board.create('polygon', [[-1,2], [2,2], [-1,4]]);\n * var p = board.create('point', [4, 3]);\n * var txt = board.create('text', [-1, 0.5, function() {\n * return 'Point A is inside of the polygon = ' +\n * JXG.Math.Geometry.pnpoly(p.X(), p.Y(), pol.vertices, JXG.COORDS_BY_USER, board);\n * }]);\n *\n * \n * This method works also for transformed curves, since only the already\n * transformed points are used.\n *\n * @param {JXG.Curve} red\n * @param {JXG.Curve} blue\n * @param {Number|Function} nr\n */\n meetCurveRedBlueSegments: function (red, blue, nr) {\n var i,\n j,\n n = Type.evaluate(nr),\n red1,\n red2,\n blue1,\n blue2,\n m,\n minX,\n maxX,\n iFound = 0,\n lenBlue = blue.numberPoints,\n lenRed = red.numberPoints;\n\n if (lenBlue <= 1 || lenRed <= 1) {\n return [0, NaN, NaN];\n }\n\n for (i = 1; i < lenRed; i++) {\n red1 = red.points[i - 1].usrCoords;\n red2 = red.points[i].usrCoords;\n minX = Math.min(red1[1], red2[1]);\n maxX = Math.max(red1[1], red2[1]);\n\n blue2 = blue.points[0].usrCoords;\n for (j = 1; j < lenBlue; j++) {\n blue1 = blue2;\n blue2 = blue.points[j].usrCoords;\n if (\n Math.min(blue1[1], blue2[1]) < maxX &&\n Math.max(blue1[1], blue2[1]) > minX\n ) {\n m = this.meetSegmentSegment(red1, red2, blue1, blue2);\n if (\n m[1] >= 0.0 && m[2] >= 0.0 &&\n // The two segments meet in the interior or at the start points\n ((m[1] < 1.0 && m[2] < 1.0) ||\n // One of the curve is intersected in the very last point\n (i === lenRed - 1 && m[1] === 1.0) ||\n (j === lenBlue - 1 && m[2] === 1.0))\n ) {\n if (iFound === n) {\n return m[0];\n }\n\n iFound++;\n }\n }\n }\n }\n\n return [0, NaN, NaN];\n },\n\n /**\n * (Virtual) Intersection of two segments.\n * @param {Array} p1 First point of segment 1 using normalized homogeneous coordinates [1,x,y]\n * @param {Array} p2 Second point or direction of segment 1 using normalized homogeneous coordinates [1,x,y] or point at infinity [0,x,y], respectively\n * @param {Array} q1 First point of segment 2 using normalized homogeneous coordinates [1,x,y]\n * @param {Array} q2 Second point or direction of segment 2 using normalized homogeneous coordinates [1,x,y] or point at infinity [0,x,y], respectively\n * @returns {Array} [Intersection point, t, u] The first entry contains the homogeneous coordinates\n * of the intersection point. The second and third entry give the position of the intersection with respect\n * to the definiting parameters. For example, the second entry t is defined by: intersection point = p1 + t * deltaP, where\n * deltaP = (p2 - p1) when both parameters are coordinates, and deltaP = p2 if p2 is a point at infinity.\n * If the two segments are collinear, [[0,0,0], Infinity, Infinity] is returned.\n **/\n meetSegmentSegment: function (p1, p2, q1, q2) {\n var t,\n u,\n i,\n d,\n li1 = Mat.crossProduct(p1, p2),\n li2 = Mat.crossProduct(q1, q2),\n c = Mat.crossProduct(li1, li2);\n\n if (Math.abs(c[0]) < Mat.eps) {\n return [c, Infinity, Infinity];\n }\n\n // Normalize the intersection coordinates\n c[1] /= c[0];\n c[2] /= c[0];\n c[0] /= c[0];\n\n // Now compute in principle:\n // t = dist(c - p1) / dist(p2 - p1) and\n // u = dist(c - q1) / dist(q2 - q1)\n // However: the points q1, q2, p1, p2 might be ideal points - or in general - the\n // coordinates might be not normalized.\n // Note that the z-coordinates of p2 and q2 are used to determine whether it should be interpreted\n // as a segment coordinate or a direction.\n i = Math.abs(p2[1] - p2[0] * p1[1]) < Mat.eps ? 2 : 1;\n d = p1[i] / p1[0];\n t = (c[i] - d) / (p2[0] !== 0 ? p2[i] / p2[0] - d : p2[i]);\n\n i = Math.abs(q2[1] - q2[0] * q1[1]) < Mat.eps ? 2 : 1;\n d = q1[i] / q1[0];\n u = (c[i] - d) / (q2[0] !== 0 ? q2[i] / q2[0] - d : q2[i]);\n\n return [c, t, u];\n },\n\n /**\n * Find the n-th intersection point of two pathes, usually given by polygons. Uses parts of the\n * Greiner-Hormann algorithm in JXG.Math.Clip.\n *\n * @param {JXG.Circle|JXG.Curve|JXG.Polygon} path1\n * @param {JXG.Circle|JXG.Curve|JXG.Polygon} path2\n * @param {Number|Function} n\n * @param {JXG.Board} board\n *\n * @returns {JXG.Coords} Intersection point. In case no intersection point is detected,\n * the ideal point [0,0,0] is returned.\n *\n */\n meetPathPath: function (path1, path2, nr, board) {\n var S, C, len, intersections,\n n = Type.evaluate(nr);\n\n S = JXG.Math.Clip._getPath(path1, board);\n len = S.length;\n if (\n len > 0 &&\n this.distance(S[0].coords.usrCoords, S[len - 1].coords.usrCoords, 3) < Mat.eps\n ) {\n S.pop();\n }\n\n C = JXG.Math.Clip._getPath(path2, board);\n len = C.length;\n if (\n len > 0 &&\n this.distance(C[0].coords.usrCoords, C[len - 1].coords.usrCoords, 3) <\n Mat.eps * Mat.eps\n ) {\n C.pop();\n }\n\n // Handle cases where at least one of the paths is empty\n if (nr < 0 || JXG.Math.Clip.isEmptyCase(S, C, 'intersection')) {\n return new Coords(Const.COORDS_BY_USER, [0, 0, 0], board);\n }\n\n JXG.Math.Clip.makeDoublyLinkedList(S);\n JXG.Math.Clip.makeDoublyLinkedList(C);\n\n intersections = JXG.Math.Clip.findIntersections(S, C, board)[0];\n if (n < intersections.length) {\n return intersections[n].coords;\n }\n return new Coords(Const.COORDS_BY_USER, [0, 0, 0], board);\n },\n\n /**\n * Find the n-th intersection point between a polygon and a line.\n * @param {JXG.Polygon} path\n * @param {JXG.Line} line\n * @param {Number|Function} nr\n * @param {JXG.Board} board\n * @param {Boolean} alwaysIntersect If false just the segment between the two defining points of the line are tested for intersection.\n *\n * @returns {JXG.Coords} Intersection point. In case no intersection point is detected,\n * the ideal point [0,0,0] is returned.\n */\n meetPolygonLine: function (path, line, nr, board, alwaysIntersect) {\n var i,\n n = Type.evaluate(nr),\n res,\n border,\n crds = [0, 0, 0],\n len = path.borders.length,\n intersections = [];\n\n for (i = 0; i < len; i++) {\n border = path.borders[i];\n res = this.meetSegmentSegment(\n border.point1.coords.usrCoords,\n border.point2.coords.usrCoords,\n line.point1.coords.usrCoords,\n line.point2.coords.usrCoords\n );\n\n if (\n (!alwaysIntersect || (res[2] >= 0 && res[2] < 1)) &&\n res[1] >= 0 &&\n res[1] < 1\n ) {\n intersections.push(res[0]);\n }\n }\n\n if (n >= 0 && n < intersections.length) {\n crds = intersections[n];\n }\n return new Coords(Const.COORDS_BY_USER, crds, board);\n },\n\n /****************************************/\n /**** BEZIER CURVE ALGORITHMS ****/\n /****************************************/\n\n /**\n * Splits a Bezier curve segment defined by four points into\n * two Bezier curve segments. Dissection point is t=1/2.\n * @param {Array} curve Array of four coordinate arrays of length 2 defining a\n * Bezier curve segment, i.e. [[x0,y0], [x1,y1], [x2,y2], [x3,y3]].\n * @returns {Array} Array consisting of two coordinate arrays for Bezier curves.\n */\n _bezierSplit: function (curve) {\n var p0, p1, p2, p00, p22, p000;\n\n p0 = [(curve[0][0] + curve[1][0]) * 0.5, (curve[0][1] + curve[1][1]) * 0.5];\n p1 = [(curve[1][0] + curve[2][0]) * 0.5, (curve[1][1] + curve[2][1]) * 0.5];\n p2 = [(curve[2][0] + curve[3][0]) * 0.5, (curve[2][1] + curve[3][1]) * 0.5];\n\n p00 = [(p0[0] + p1[0]) * 0.5, (p0[1] + p1[1]) * 0.5];\n p22 = [(p1[0] + p2[0]) * 0.5, (p1[1] + p2[1]) * 0.5];\n\n p000 = [(p00[0] + p22[0]) * 0.5, (p00[1] + p22[1]) * 0.5];\n\n return [\n [curve[0], p0, p00, p000],\n [p000, p22, p2, curve[3]]\n ];\n },\n\n /**\n * Computes the bounding box [minX, maxY, maxX, minY] of a Bezier curve segment\n * from its control points.\n * @param {Array} curve Array of four coordinate arrays of length 2 defining a\n * Bezier curve segment, i.e. [[x0,y0], [x1,y1], [x2,y2], [x3,y3]].\n * @returns {Array} Bounding box [minX, maxY, maxX, minY]\n */\n _bezierBbox: function (curve) {\n var bb = [];\n\n if (curve.length === 4) {\n // bezierDegree == 3\n bb[0] = Math.min(curve[0][0], curve[1][0], curve[2][0], curve[3][0]); // minX\n bb[1] = Math.max(curve[0][1], curve[1][1], curve[2][1], curve[3][1]); // maxY\n bb[2] = Math.max(curve[0][0], curve[1][0], curve[2][0], curve[3][0]); // maxX\n bb[3] = Math.min(curve[0][1], curve[1][1], curve[2][1], curve[3][1]); // minY\n } else {\n // bezierDegree == 1\n bb[0] = Math.min(curve[0][0], curve[1][0]); // minX\n bb[1] = Math.max(curve[0][1], curve[1][1]); // maxY\n bb[2] = Math.max(curve[0][0], curve[1][0]); // maxX\n bb[3] = Math.min(curve[0][1], curve[1][1]); // minY\n }\n\n return bb;\n },\n\n /**\n * Decide if two Bezier curve segments overlap by comparing their bounding boxes.\n * @param {Array} bb1 Bounding box of the first Bezier curve segment\n * @param {Array} bb2 Bounding box of the second Bezier curve segment\n * @returns {Boolean} true if the bounding boxes overlap, false otherwise.\n */\n _bezierOverlap: function (bb1, bb2) {\n return bb1[2] >= bb2[0] && bb1[0] <= bb2[2] && bb1[1] >= bb2[3] && bb1[3] <= bb2[1];\n },\n\n /**\n * Append list of intersection points to a list.\n * @private\n */\n _bezierListConcat: function (L, Lnew, t1, t2) {\n var i,\n t2exists = Type.exists(t2),\n start = 0,\n len = Lnew.length,\n le = L.length;\n\n if (\n le > 0 &&\n len > 0 &&\n ((L[le - 1][1] === 1 && Lnew[0][1] === 0) ||\n (t2exists && L[le - 1][2] === 1 && Lnew[0][2] === 0))\n ) {\n start = 1;\n }\n\n for (i = start; i < len; i++) {\n if (t2exists) {\n Lnew[i][2] *= 0.5;\n Lnew[i][2] += t2;\n }\n\n Lnew[i][1] *= 0.5;\n Lnew[i][1] += t1;\n\n L.push(Lnew[i]);\n }\n },\n\n /**\n * Find intersections of two Bezier curve segments by recursive subdivision.\n * Below maxlevel determine intersections by intersection line segments.\n * @param {Array} red Array of four coordinate arrays of length 2 defining the first\n * Bezier curve segment, i.e. [[x0,y0], [x1,y1], [x2,y2], [x3,y3]].\n * @param {Array} blue Array of four coordinate arrays of length 2 defining the second\n * Bezier curve segment, i.e. [[x0,y0], [x1,y1], [x2,y2], [x3,y3]].\n * @param {Number} level Recursion level\n * @returns {Array} List of intersection points (up to nine). Each intersection point is an\n * array of length three (homogeneous coordinates) plus preimages.\n */\n _bezierMeetSubdivision: function (red, blue, level) {\n var bbb,\n bbr,\n ar,\n b0,\n b1,\n r0,\n r1,\n m,\n p0,\n p1,\n q0,\n q1,\n L = [],\n maxLev = 5; // Maximum recursion level\n\n bbr = this._bezierBbox(blue);\n bbb = this._bezierBbox(red);\n\n if (!this._bezierOverlap(bbr, bbb)) {\n return [];\n }\n\n if (level < maxLev) {\n ar = this._bezierSplit(red);\n r0 = ar[0];\n r1 = ar[1];\n\n ar = this._bezierSplit(blue);\n b0 = ar[0];\n b1 = ar[1];\n\n this._bezierListConcat(\n L,\n this._bezierMeetSubdivision(r0, b0, level + 1),\n 0.0,\n 0.0\n );\n this._bezierListConcat(\n L,\n this._bezierMeetSubdivision(r0, b1, level + 1),\n 0,\n 0.5\n );\n this._bezierListConcat(\n L,\n this._bezierMeetSubdivision(r1, b0, level + 1),\n 0.5,\n 0.0\n );\n this._bezierListConcat(\n L,\n this._bezierMeetSubdivision(r1, b1, level + 1),\n 0.5,\n 0.5\n );\n\n return L;\n }\n\n // Make homogeneous coordinates\n q0 = [1].concat(red[0]);\n q1 = [1].concat(red[3]);\n p0 = [1].concat(blue[0]);\n p1 = [1].concat(blue[3]);\n\n m = this.meetSegmentSegment(q0, q1, p0, p1);\n\n if (m[1] >= 0.0 && m[2] >= 0.0 && m[1] <= 1.0 && m[2] <= 1.0) {\n return [m];\n }\n\n return [];\n },\n\n /**\n * @param {Boolean} testSegment Test if intersection has to be inside of the segment or somewhere on the line defined by the segment\n */\n _bezierLineMeetSubdivision: function (red, blue, level, testSegment) {\n var bbb, bbr, ar,\n r0, r1,\n m,\n p0, p1, q0, q1,\n L = [],\n maxLev = 5; // Maximum recursion level\n\n bbb = this._bezierBbox(blue);\n bbr = this._bezierBbox(red);\n\n if (testSegment && !this._bezierOverlap(bbr, bbb)) {\n return [];\n }\n\n if (level < maxLev) {\n ar = this._bezierSplit(red);\n r0 = ar[0];\n r1 = ar[1];\n\n this._bezierListConcat(\n L,\n this._bezierLineMeetSubdivision(r0, blue, level + 1),\n 0.0\n );\n this._bezierListConcat(\n L,\n this._bezierLineMeetSubdivision(r1, blue, level + 1),\n 0.5\n );\n\n return L;\n }\n\n // Make homogeneous coordinates\n q0 = [1].concat(red[0]);\n q1 = [1].concat(red[3]);\n p0 = [1].concat(blue[0]);\n p1 = [1].concat(blue[1]);\n\n m = this.meetSegmentSegment(q0, q1, p0, p1);\n\n if (m[1] >= 0.0 && m[1] <= 1.0) {\n if (!testSegment || (m[2] >= 0.0 && m[2] <= 1.0)) {\n return [m];\n }\n }\n\n return [];\n },\n\n /**\n * Find the nr-th intersection point of two Bezier curve segments.\n * @param {Array} red Array of four coordinate arrays of length 2 defining the first\n * Bezier curve segment, i.e. [[x0,y0], [x1,y1], [x2,y2], [x3,y3]].\n * @param {Array} blue Array of four coordinate arrays of length 2 defining the second\n * Bezier curve segment, i.e. [[x0,y0], [x1,y1], [x2,y2], [x3,y3]].\n * @param {Boolean} testSegment Test if intersection has to be inside of the segment or somewhere on the line defined by the segment\n * @returns {Array} Array containing the list of all intersection points as homogeneous coordinate arrays plus\n * preimages [x,y], t_1, t_2] of the two Bezier curve segments.\n *\n */\n meetBeziersegmentBeziersegment: function (red, blue, testSegment) {\n var L, L2, i;\n\n if (red.length === 4 && blue.length === 4) {\n L = this._bezierMeetSubdivision(red, blue, 0);\n } else {\n L = this._bezierLineMeetSubdivision(red, blue, 0, testSegment);\n }\n\n L.sort(function (a, b) {\n return (a[1] - b[1]) * 10000000.0 + (a[2] - b[2]);\n });\n\n L2 = [];\n for (i = 0; i < L.length; i++) {\n // Only push entries different from their predecessor\n if (i === 0 || L[i][1] !== L[i - 1][1] || L[i][2] !== L[i - 1][2]) {\n L2.push(L[i]);\n }\n }\n return L2;\n },\n\n /**\n * Find the nr-th intersection point of two Bezier curves, i.e. curves with bezierDegree == 3.\n * @param {JXG.Curve} red Curve with bezierDegree == 3\n * @param {JXG.Curve} blue Curve with bezierDegree == 3\n * @param {Number|Function} nr The number of the intersection point which should be returned.\n * @returns {Array} The homogeneous coordinates of the nr-th intersection point.\n */\n meetBezierCurveRedBlueSegments: function (red, blue, nr) {\n var p, i, j, k,\n n = Type.evaluate(nr),\n po, tmp,\n redArr,\n blueArr,\n bbr,\n bbb,\n intersections,\n startRed = 0,\n startBlue = 0,\n lenBlue, lenRed,\n L = [];\n\n if (blue.numberPoints < blue.bezierDegree + 1 || red.numberPoints < red.bezierDegree + 1) {\n return [0, NaN, NaN];\n }\n if (red.bezierDegree === 1 && blue.bezierDegree === 3) {\n tmp = red;\n red = blue;\n blue = tmp;\n }\n\n lenBlue = blue.numberPoints - blue.bezierDegree;\n lenRed = red.numberPoints - red.bezierDegree;\n\n // For sectors, we ignore the \"legs\"\n if (red.type === Const.OBJECT_TYPE_SECTOR) {\n startRed = 3;\n lenRed -= 3;\n }\n if (blue.type === Const.OBJECT_TYPE_SECTOR) {\n startBlue = 3;\n lenBlue -= 3;\n }\n\n for (i = startRed; i < lenRed; i += red.bezierDegree) {\n p = red.points;\n redArr = [p[i].usrCoords.slice(1), p[i + 1].usrCoords.slice(1)];\n if (red.bezierDegree === 3) {\n redArr[2] = p[i + 2].usrCoords.slice(1);\n redArr[3] = p[i + 3].usrCoords.slice(1);\n }\n\n bbr = this._bezierBbox(redArr);\n\n for (j = startBlue; j < lenBlue; j += blue.bezierDegree) {\n p = blue.points;\n blueArr = [p[j].usrCoords.slice(1), p[j + 1].usrCoords.slice(1)];\n if (blue.bezierDegree === 3) {\n blueArr[2] = p[j + 2].usrCoords.slice(1);\n blueArr[3] = p[j + 3].usrCoords.slice(1);\n }\n\n bbb = this._bezierBbox(blueArr);\n if (this._bezierOverlap(bbr, bbb)) {\n intersections = this.meetBeziersegmentBeziersegment(redArr, blueArr);\n if (intersections.length === 0) {\n continue;\n }\n for (k = 0; k < intersections.length; k++) {\n po = intersections[k];\n if (\n po[1] < -Mat.eps ||\n po[1] > 1 + Mat.eps ||\n po[2] < -Mat.eps ||\n po[2] > 1 + Mat.eps\n ) {\n continue;\n }\n L.push(po);\n }\n if (L.length > n) {\n return L[n][0];\n }\n }\n }\n }\n if (L.length > n) {\n return L[n][0];\n }\n\n return [0, NaN, NaN];\n },\n\n bezierSegmentEval: function (t, curve) {\n var f,\n x,\n y,\n t1 = 1.0 - t;\n\n x = 0;\n y = 0;\n\n f = t1 * t1 * t1;\n x += f * curve[0][0];\n y += f * curve[0][1];\n\n f = 3.0 * t * t1 * t1;\n x += f * curve[1][0];\n y += f * curve[1][1];\n\n f = 3.0 * t * t * t1;\n x += f * curve[2][0];\n y += f * curve[2][1];\n\n f = t * t * t;\n x += f * curve[3][0];\n y += f * curve[3][1];\n\n return [1.0, x, y];\n },\n\n /**\n * Generate the defining points of a 3rd degree bezier curve that approximates\n * a circle sector defined by three coordinate points A, B, C, each defined by an array of length three.\n * The coordinate arrays are given in homogeneous coordinates.\n * @param {Array} A First point\n * @param {Array} B Second point (intersection point)\n * @param {Array} C Third point\n * @param {Boolean} withLegs Flag. If true the legs to the intersection point are part of the curve.\n * @param {Number} sgn Wither 1 or -1. Needed for minor and major arcs. In case of doubt, use 1.\n */\n bezierArc: function (A, B, C, withLegs, sgn) {\n var p1, p2, p3, p4,\n r,\n phi, beta, delta,\n // PI2 = Math.PI * 0.5,\n x = B[1],\n y = B[2],\n z = B[0],\n dataX = [],\n dataY = [],\n co, si,\n ax, ay,\n bx, by,\n k, v, d,\n matrix;\n\n r = this.distance(B, A);\n\n // x,y, z is intersection point. Normalize it.\n x /= z;\n y /= z;\n\n phi = this.rad(A.slice(1), B.slice(1), C.slice(1));\n if (sgn === -1) {\n phi = 2 * Math.PI - phi;\n }\n\n // Always divide the arc into four Bezier arcs.\n // Otherwise, the position of gliders on this arc\n // will be wrong.\n delta = phi / 4;\n\n\n p1 = A;\n p1[1] /= p1[0];\n p1[2] /= p1[0];\n p1[0] /= p1[0];\n\n p4 = p1.slice(0);\n\n if (withLegs) {\n dataX = [x, x + 0.333 * (p1[1] - x), x + 0.666 * (p1[1] - x), p1[1]];\n dataY = [y, y + 0.333 * (p1[2] - y), y + 0.666 * (p1[2] - y), p1[2]];\n } else {\n dataX = [p1[1]];\n dataY = [p1[2]];\n }\n\n while (phi > Mat.eps) {\n // if (phi > PI2) {\n // beta = PI2;\n // phi -= PI2;\n // } else {\n // beta = phi;\n // phi = 0;\n // }\n if (phi > delta) {\n beta = delta;\n phi -= delta;\n } else {\n beta = phi;\n phi = 0;\n }\n\n co = Math.cos(sgn * beta);\n si = Math.sin(sgn * beta);\n\n matrix = [\n [1, 0, 0],\n [x * (1 - co) + y * si, co, -si],\n [y * (1 - co) - x * si, si, co]\n ];\n v = Mat.matVecMult(matrix, p1);\n p4 = [v[0] / v[0], v[1] / v[0], v[2] / v[0]];\n\n ax = p1[1] - x;\n ay = p1[2] - y;\n bx = p4[1] - x;\n by = p4[2] - y;\n d = Mat.hypot(ax + bx, ay + by);\n\n if (Math.abs(by - ay) > Mat.eps) {\n k = ((((ax + bx) * (r / d - 0.5)) / (by - ay)) * 8) / 3;\n } else {\n k = ((((ay + by) * (r / d - 0.5)) / (ax - bx)) * 8) / 3;\n }\n\n p2 = [1, p1[1] - k * ay, p1[2] + k * ax];\n p3 = [1, p4[1] + k * by, p4[2] - k * bx];\n\n Type.concat(dataX, [p2[1], p3[1], p4[1]]);\n Type.concat(dataY, [p2[2], p3[2], p4[2]]);\n p1 = p4.slice(0);\n }\n\n if (withLegs) {\n Type.concat(dataX, [\n p4[1] + 0.333 * (x - p4[1]),\n p4[1] + 0.666 * (x - p4[1]),\n x\n ]);\n Type.concat(dataY, [\n p4[2] + 0.333 * (y - p4[2]),\n p4[2] + 0.666 * (y - p4[2]),\n y\n ]);\n }\n\n return [dataX, dataY];\n },\n\n /****************************************/\n /**** PROJECTIONS ****/\n /****************************************/\n\n /**\n * Calculates the coordinates of the projection of a given point on a given circle. I.o.w. the\n * nearest one of the two intersection points of the line through the given point and the circles\n * center.\n * @param {JXG.Point|JXG.Coords} point Point to project or coords object to project.\n * @param {JXG.Circle} circle Circle on that the point is projected.\n * @param {JXG.Board} [board=point.board] Reference to the board\n * @returns {JXG.Coords} The coordinates of the projection of the given point on the given circle.\n */\n projectPointToCircle: function (point, circle, board) {\n var dist,\n P,\n x,\n y,\n factor,\n M = circle.center.coords.usrCoords;\n\n if (!Type.exists(board)) {\n board = point.board;\n }\n\n // gave us a point\n if (Type.isPoint(point)) {\n dist = point.coords.distance(Const.COORDS_BY_USER, circle.center.coords);\n P = point.coords.usrCoords;\n // gave us coords\n } else {\n dist = point.distance(Const.COORDS_BY_USER, circle.center.coords);\n P = point.usrCoords;\n }\n\n if (Math.abs(dist) < Mat.eps) {\n dist = Mat.eps;\n }\n\n factor = circle.Radius() / dist;\n x = M[1] + factor * (P[1] - M[1]);\n y = M[2] + factor * (P[2] - M[2]);\n\n return new Coords(Const.COORDS_BY_USER, [x, y], board);\n },\n\n /**\n * Calculates the coordinates of the orthogonal projection of a given point on a given line. I.o.w. the\n * intersection point of the given line and its perpendicular through the given point.\n * @param {JXG.Point|JXG.Coords} point Point to project.\n * @param {JXG.Line} line Line on that the point is projected.\n * @param {JXG.Board} [board=point.board|board=line.board] Reference to a board.\n * @returns {JXG.Coords} The coordinates of the projection of the given point on the given line.\n */\n projectPointToLine: function (point, line, board) {\n var v = [0, line.stdform[1], line.stdform[2]],\n coords;\n\n if (!Type.exists(board)) {\n if (Type.exists(point.coords)) {\n board = point.board;\n } else {\n board = line.board;\n }\n }\n\n if (Type.exists(point.coords)) {\n coords = point.coords.usrCoords;\n } else {\n coords = point.usrCoords;\n }\n\n v = Mat.crossProduct(v, coords);\n return new Coords(Const.COORDS_BY_USER, Mat.crossProduct(v, line.stdform), board);\n },\n\n /**\n * Calculates the coordinates of the orthogonal projection of a given coordinate array on a given line\n * segment defined by two coordinate arrays.\n * @param {Array} p Point to project.\n * @param {Array} q1 Start point of the line segment on that the point is projected.\n * @param {Array} q2 End point of the line segment on that the point is projected.\n * @returns {Array} The coordinates of the projection of the given point on the given segment\n * and the factor that determines the projected point as a convex combination of the\n * two endpoints q1 and q2 of the segment.\n */\n projectCoordsToSegment: function (p, q1, q2) {\n var t,\n denom,\n s = [q2[1] - q1[1], q2[2] - q1[2]],\n v = [p[1] - q1[1], p[2] - q1[2]];\n\n /**\n * If the segment has length 0, i.e. is a point,\n * the projection is equal to that point.\n */\n if (Math.abs(s[0]) < Mat.eps && Math.abs(s[1]) < Mat.eps) {\n return [q1, 0];\n }\n\n t = Mat.innerProduct(v, s);\n denom = Mat.innerProduct(s, s);\n t /= denom;\n\n return [[1, t * s[0] + q1[1], t * s[1] + q1[2]], t];\n },\n\n /**\n * Finds the coordinates of the closest point on a Bezier segment of a\n * {@link JXG.Curve} to a given coordinate array.\n * @param {Array} pos Point to project in homogeneous coordinates.\n * @param {JXG.Curve} curve Curve of type \"plot\" having Bezier degree 3.\n * @param {Number} start Number of the Bezier segment of the curve.\n * @returns {Array} The coordinates of the projection of the given point\n * on the given Bezier segment and the preimage of the curve which\n * determines the closest point.\n */\n projectCoordsToBeziersegment: function (pos, curve, start) {\n var t0,\n /** @ignore */\n minfunc = function (t) {\n var z = [1, curve.X(start + t), curve.Y(start + t)];\n\n z[1] -= pos[1];\n z[2] -= pos[2];\n\n return z[1] * z[1] + z[2] * z[2];\n };\n\n t0 = JXG.Math.Numerics.fminbr(minfunc, [0.0, 1.0]);\n\n return [[1, curve.X(t0 + start), curve.Y(t0 + start)], t0];\n },\n\n /**\n * Calculates the coordinates of the projection of a given point on a given curve.\n * Uses {@link JXG.Math.Geometry.projectCoordsToCurve}.\n *\n * @param {JXG.Point} point Point to project.\n * @param {JXG.Curve} curve Curve on that the point is projected.\n * @param {JXG.Board} [board=point.board] Reference to a board.\n * @see JXG.Math.Geometry.projectCoordsToCurve\n * @returns {Array} [JXG.Coords, position] The coordinates of the projection of the given\n * point on the given graph and the relative position on the curve (real number).\n */\n projectPointToCurve: function (point, curve, board) {\n if (!Type.exists(board)) {\n board = point.board;\n }\n\n var x = point.X(),\n y = point.Y(),\n t = point.position,\n result;\n\n if (!Type.exists(t)) {\n t = curve.evalVisProp('curvetype') === 'functiongraph' ? x : 0.0;\n }\n result = this.projectCoordsToCurve(x, y, t, curve, board);\n // point.position = result[1];\n\n return result;\n },\n\n /**\n * Calculates the coordinates of the projection of a coordinates pair on a given curve. In case of\n * function graphs this is the\n * intersection point of the curve and the parallel to y-axis through the given point.\n * @param {Number} x coordinate to project.\n * @param {Number} y coordinate to project.\n * @param {Number} t start value for newtons method\n * @param {JXG.Curve} curve Curve on that the point is projected.\n * @param {JXG.Board} [board=curve.board] Reference to a board.\n * @see JXG.Math.Geometry.projectPointToCurve\n * @returns {JXG.Coords} Array containing the coordinates of the projection of the given point on the given curve and\n * the position on the curve.\n */\n projectCoordsToCurve: function (x, y, t, curve, board) {\n var newCoords, newCoordsObj,\n i, j, mindist, dist, lbda,\n v, coords, d, p1, p2, res, minfunc,\n t_new, f_new, f_old, dy,\n delta, delta1, delta2, steps,\n minX, maxX, minX_glob, maxX_glob,\n infty = Number.POSITIVE_INFINITY;\n\n if (!Type.exists(board)) {\n board = curve.board;\n }\n\n if (curve.evalVisProp('curvetype') === 'plot') {\n t = 0;\n mindist = infty;\n if (curve.numberPoints === 0) {\n newCoords = [0, 1, 1];\n } else {\n newCoords = [curve.Z(0), curve.X(0), curve.Y(0)];\n }\n\n if (curve.numberPoints > 1) {\n v = [1, x, y];\n if (curve.bezierDegree === 3) {\n j = 0;\n } else {\n p1 = [curve.Z(0), curve.X(0), curve.Y(0)];\n }\n for (i = 0; i < curve.numberPoints - 1; i++) {\n if (curve.bezierDegree === 3) {\n res = this.projectCoordsToBeziersegment(v, curve, j);\n } else {\n p2 = [curve.Z(i + 1), curve.X(i + 1), curve.Y(i + 1)];\n res = this.projectCoordsToSegment(v, p1, p2);\n }\n lbda = res[1];\n coords = res[0];\n\n if (0.0 <= lbda && lbda <= 1.0) {\n dist = this.distance(coords, v);\n d = i + lbda;\n } else if (lbda < 0.0) {\n coords = p1;\n dist = this.distance(p1, v);\n d = i;\n } else if (lbda > 1.0 && i === curve.numberPoints - 2) {\n coords = p2;\n dist = this.distance(coords, v);\n d = curve.numberPoints - 1;\n }\n\n if (dist < mindist) {\n mindist = dist;\n t = d;\n newCoords = coords;\n }\n\n if (curve.bezierDegree === 3) {\n j++;\n i += 2;\n } else {\n p1 = p2;\n }\n }\n }\n\n newCoordsObj = new Coords(Const.COORDS_BY_USER, newCoords, board);\n } else {\n // 'parameter', 'polar', 'functiongraph'\n\n minX_glob = curve.minX();\n maxX_glob = curve.maxX();\n minX = minX_glob;\n maxX = maxX_glob;\n\n if (curve.evalVisProp('curvetype') === 'functiongraph') {\n // Restrict the possible position of t\n // to the projection of a circle to the x-axis (= t-axis)\n dy = Math.abs(y - curve.Y(x));\n if (!isNaN(dy)) {\n minX = x - dy;\n maxX = x + dy;\n }\n }\n\n /**\n * @ignore\n * Find t such that the Euclidean distance between\n * [x, y] and [curve.X(t), curve.Y(t)]\n * is minimized.\n */\n minfunc = function (t) {\n var dx, dy;\n\n if (t < minX_glob || t > maxX_glob) {\n return Infinity;\n }\n dx = x - curve.X(t);\n dy = y - curve.Y(t);\n return dx * dx + dy * dy;\n };\n\n // Search t which minimizes minfunc(t)\n // in discrete steps\n f_old = minfunc(t);\n steps = 50;\n delta = (maxX - minX) / steps;\n t_new = minX;\n for (i = 0; i < steps; i++) {\n f_new = minfunc(t_new);\n\n if (f_new < f_old || f_old === Infinity || isNaN(f_old)) {\n t = t_new;\n f_old = f_new;\n }\n\n t_new += delta;\n }\n\n // t = Numerics.root(Numerics.D(minfunc), t);\n\n // Ensure that minfunc is defined on the\n // enclosing interval [t-delta1, t+delta2]\n delta1 = delta;\n for (i = 0; i < 20 && isNaN(minfunc(t - delta1)); i++, delta1 *= 0.5);\n if (isNaN(minfunc(t - delta1))) {\n delta1 = 0.0;\n }\n delta2 = delta;\n for (i = 0; i < 20 && isNaN(minfunc(t + delta2)); i++, delta2 *= 0.5);\n if (isNaN(minfunc(t + delta2))) {\n delta2 = 0.0;\n }\n\n // Finally, apply mathemetical optimization in the determined interval\n t = Numerics.fminbr(minfunc, [\n Math.max(t - delta1, minX),\n Math.min(t + delta2, maxX)\n ]);\n\n // Distinction between closed and open curves is not necessary.\n // If closed, the cyclic projection shift will work anyhow\n // if (Math.abs(curve.X(minX) - curve.X(maxX)) < Mat.eps &&\n // Math.abs(curve.Y(minX) - curve.Y(maxX)) < Mat.eps) {\n // // Cyclically\n // if (t < minX) {console.log(t)\n // t = maxX + t - minX;\n // }\n // if (t > maxX) {\n // t = minX + t - maxX;\n // }\n // } else {\n\n t = t < minX_glob ? minX_glob : t;\n t = t > maxX_glob ? maxX_glob : t;\n // }\n\n newCoordsObj = new Coords(\n Const.COORDS_BY_USER,\n [curve.X(t), curve.Y(t)],\n board\n );\n }\n\n return [curve.updateTransform(newCoordsObj), t];\n },\n\n /**\n * Calculates the coordinates of the closest orthogonal projection of a given coordinate array onto the\n * border of a polygon.\n * @param {Array} p Point to project.\n * @param {JXG.Polygon} pol Polygon element\n * @returns {Array} The coordinates of the closest projection of the given point to the border of the polygon.\n */\n projectCoordsToPolygon: function (p, pol) {\n var i,\n len = pol.vertices.length,\n d_best = Infinity,\n d,\n projection,\n proj,\n bestprojection;\n\n for (i = 0; i < len - 1; i++) {\n projection = JXG.Math.Geometry.projectCoordsToSegment(\n p,\n pol.vertices[i].coords.usrCoords,\n pol.vertices[i + 1].coords.usrCoords\n );\n\n if (0 <= projection[1] && projection[1] <= 1) {\n d = JXG.Math.Geometry.distance(projection[0], p, 3);\n proj = projection[0];\n } else if (projection[1] < 0) {\n d = JXG.Math.Geometry.distance(pol.vertices[i].coords.usrCoords, p, 3);\n proj = pol.vertices[i].coords.usrCoords;\n } else {\n d = JXG.Math.Geometry.distance(pol.vertices[i + 1].coords.usrCoords, p, 3);\n proj = pol.vertices[i + 1].coords.usrCoords;\n }\n if (d < d_best) {\n bestprojection = proj.slice(0);\n d_best = d;\n }\n }\n return bestprojection;\n },\n\n /**\n * Calculates the coordinates of the projection of a given point on a given turtle. A turtle consists of\n * one or more curves of curveType 'plot'. Uses {@link JXG.Math.Geometry.projectPointToCurve}.\n * @param {JXG.Point} point Point to project.\n * @param {JXG.Turtle} turtle on that the point is projected.\n * @param {JXG.Board} [board=point.board] Reference to a board.\n * @returns {Array} [JXG.Coords, position] Array containing the coordinates of the projection of the given point on the turtle and\n * the position on the turtle.\n */\n projectPointToTurtle: function (point, turtle, board) {\n var newCoords,\n t,\n x,\n y,\n i,\n dist,\n el,\n minEl,\n res,\n newPos,\n np = 0,\n npmin = 0,\n mindist = Number.POSITIVE_INFINITY,\n len = turtle.objects.length;\n\n if (!Type.exists(board)) {\n board = point.board;\n }\n\n // run through all curves of this turtle\n for (i = 0; i < len; i++) {\n el = turtle.objects[i];\n\n if (el.elementClass === Const.OBJECT_CLASS_CURVE) {\n res = this.projectPointToCurve(point, el);\n newCoords = res[0];\n newPos = res[1];\n dist = this.distance(newCoords.usrCoords, point.coords.usrCoords);\n\n if (dist < mindist) {\n x = newCoords.usrCoords[1];\n y = newCoords.usrCoords[2];\n t = newPos;\n mindist = dist;\n minEl = el;\n npmin = np;\n }\n np += el.numberPoints;\n }\n }\n\n newCoords = new Coords(Const.COORDS_BY_USER, [x, y], board);\n // point.position = t + npmin;\n // return minEl.updateTransform(newCoords);\n return [minEl.updateTransform(newCoords), t + npmin];\n },\n\n /**\n * Trivial projection of a point to another point.\n * @param {JXG.Point} point Point to project (not used).\n * @param {JXG.Point} dest Point on that the point is projected.\n * @returns {JXG.Coords} The coordinates of the projection of the given point on the given circle.\n */\n projectPointToPoint: function (point, dest) {\n return dest.coords;\n },\n\n /**\n *\n * @param {JXG.Point|JXG.Coords} point\n * @param {JXG.Board} [board]\n */\n projectPointToBoard: function (point, board) {\n var i,\n l,\n c,\n brd = board || point.board,\n // comparison factor, point coord idx, bbox idx, 1st bbox corner x & y idx, 2nd bbox corner x & y idx\n config = [\n // left\n [1, 1, 0, 0, 3, 0, 1],\n // top\n [-1, 2, 1, 0, 1, 2, 1],\n // right\n [-1, 1, 2, 2, 1, 2, 3],\n // bottom\n [1, 2, 3, 0, 3, 2, 3]\n ],\n coords = point.coords || point,\n bbox = brd.getBoundingBox();\n\n for (i = 0; i < 4; i++) {\n c = config[i];\n if (c[0] * coords.usrCoords[c[1]] < c[0] * bbox[c[2]]) {\n // define border\n l = Mat.crossProduct(\n [1, bbox[c[3]], bbox[c[4]]],\n [1, bbox[c[5]], bbox[c[6]]]\n );\n l[3] = 0;\n l = Mat.normalize(l);\n\n // project point\n coords = this.projectPointToLine({ coords: coords }, { stdform: l }, brd);\n }\n }\n\n return coords;\n },\n\n /**\n * Calculates the distance of a point to a line. The point and the line are given by homogeneous\n * coordinates. For lines this can be line.stdform.\n * @param {Array} point Homogeneous coordinates of a point.\n * @param {Array} line Homogeneous coordinates of a line ([C,A,B] where A*x+B*y+C*z=0).\n * @returns {Number} Distance of the point to the line.\n */\n distPointLine: function (point, line) {\n var a = line[1],\n b = line[2],\n c = line[0],\n nom;\n\n if (Math.abs(a) + Math.abs(b) < Mat.eps) {\n return Number.POSITIVE_INFINITY;\n }\n\n nom = a * point[1] + b * point[2] + c;\n a *= a;\n b *= b;\n\n return Math.abs(nom) / Math.sqrt(a + b);\n },\n\n /**\n * Determine the (Euclidean) distance between a point q and a line segment\n * defined by two points p1 and p2. In case p1 equals p2, the distance to this\n * point is returned.\n *\n * @param {Array} q Homogeneous coordinates of q\n * @param {Array} p1 Homogeneous coordinates of p1\n * @param {Array} p2 Homogeneous coordinates of p2\n * @returns {Number} Distance of q to line segment [p1, p2]\n */\n distPointSegment: function (q, p1, p2) {\n var x, y, dx, dy,\n den, lbda,\n eps = Mat.eps * Mat.eps,\n huge = 1000000;\n\n // Difference q - p1\n x = q[1] - p1[1];\n y = q[2] - p1[2];\n x = (x === Infinity) ? huge : (x === -Infinity) ? -huge : x;\n y = (y === Infinity) ? huge : (y === -Infinity) ? -huge : y;\n\n // Difference p2 - p1\n dx = p2[1] - p1[1];\n dy = p2[2] - p1[2];\n dx = (dx === Infinity) ? huge : (dx === -Infinity) ? -huge : dx;\n dy = (dy === Infinity) ? huge : (dy === -Infinity) ? -huge : dy;\n\n // If den==0 then p1 and p2 are identical\n // In this case the distance to p1 is returned\n den = dx * dx + dy * dy;\n if (den > eps) {\n lbda = (x * dx + y * dy) / den;\n if (lbda < 0.0) {\n lbda = 0.0;\n } else if (lbda > 1.0) {\n lbda = 1.0;\n }\n x -= lbda * dx;\n y -= lbda * dy;\n }\n\n return Mat.hypot(x, y);\n },\n\n /* ***************************************/\n /* *** 3D CALCULATIONS ****/\n /* ***************************************/\n\n /**\n * Generate the function which computes the data of the intersection between\n * \n * Algorithm: approximate the floating point number\n * by a continued fraction and simultaneously keep track\n * of its convergents.\n * Inspired by {@link https://kevinboone.me/rationalize.html}.\n *\n * @param {Number} x Number which is to be converted\n * @param {Number} [order=0.001] Small number determining the approximation precision.\n * @returns {Array} [sign, leading, nominator, denominator] where sign is 1 or -1.\n * @see JXG.toFraction\n *\n * @example\n * JXG.Math.decToFraction(0.33333333);\n * // Result: [ 1, 0, 1, 3 ]\n *\n * JXG.Math.decToFraction(0);\n * // Result: [ 1, 0, 0, 1 ]\n *\n * JXG.Math.decToFraction(-10.66666666666667);\n * // Result: [-1, 10, 2, 3 ]\n */\n decToFraction: function (x, order) {\n var lead, sign, a,\n n, n1, n2,\n d, d1, d2,\n it = 0,\n maxit = 20;\n\n order = Type.def(order, 0.001);\n\n // Round the number.\n // Otherwise, 0.999999999 would result in [0, 1, 1].\n x = Math.round(x * 1.e12) * 1.e-12;\n\n // Negative numbers:\n // The minus sign is handled in sign.\n sign = (x < 0) ? -1 : 1;\n x = Math.abs(x);\n\n // From now on we consider x to be nonnegative.\n lead = Math.floor(x);\n x -= Math.floor(x);\n a = 0.0;\n n2 = 1.0;\n n = n1 = a;\n d2 = 0.0;\n d = d1 = 1.0;\n\n while (x - Math.floor(x) > order && it < maxit) {\n x = 1 / (x - a);\n a = Math.floor(x);\n n = n2 + a * n1;\n d = d2 + a * d1;\n n2 = n1;\n d2 = d1;\n n1 = n;\n d1 = d;\n it++;\n }\n return [sign, lead, n, d];\n },\n\n /* *************************** Normalize *************************** */\n\n /**\n * Normalize the standard form [c, b0, b1, a, k, r, q0, q1].\n * @private\n * @param {Array} stdform The standard form to be normalized.\n * @returns {Array} The normalized standard form.\n */\n normalize: function (stdform) {\n var n,\n signr,\n a2 = 2 * stdform[3],\n r = stdform[4] / a2;\n\n stdform[5] = r;\n stdform[6] = -stdform[1] / a2;\n stdform[7] = -stdform[2] / a2;\n\n if (!isFinite(r)) {\n n = this.hypot(stdform[1], stdform[2]);\n\n stdform[0] /= n;\n stdform[1] /= n;\n stdform[2] /= n;\n stdform[3] = 0;\n stdform[4] = 1;\n } else if (Math.abs(r) >= 1) {\n stdform[0] = (stdform[6] * stdform[6] + stdform[7] * stdform[7] - r * r) / (2 * r);\n stdform[1] = -stdform[6] / r;\n stdform[2] = -stdform[7] / r;\n stdform[3] = 1 / (2 * r);\n stdform[4] = 1;\n } else {\n signr = r <= 0 ? -1 : 1;\n stdform[0] =\n signr * (stdform[6] * stdform[6] + stdform[7] * stdform[7] - r * r) * 0.5;\n stdform[1] = -signr * stdform[6];\n stdform[2] = -signr * stdform[7];\n stdform[3] = signr / 2;\n stdform[4] = signr * r;\n }\n\n return stdform;\n },\n\n /**\n * Converts a two-dimensional array to a one-dimensional Float32Array that can be processed by WebGL.\n * @param {Array} m A matrix in a two-dimensional array.\n * @returns {Float32Array} A one-dimensional array containing the matrix in column wise notation. Provides a fall\n * back to the default JavaScript Array if Float32Array is not available.\n */\n toGL: function (m) {\n var v, i, j;\n\n if (typeof Float32Array === 'function') {\n v = new Float32Array(16);\n } else {\n v = new Array(16);\n }\n\n if (m.length !== 4 && m[0].length !== 4) {\n return v;\n }\n\n for (i = 0; i < 4; i++) {\n for (j = 0; j < 4; j++) {\n v[i + 4 * j] = m[i][j];\n }\n }\n\n return v;\n },\n\n /**\n * Theorem of Vieta: Given a set of simple zeroes x_0, ..., x_n\n * of a polynomial f, compute the coefficients s_k, (k=0,...,n-1)\n * of the polynomial of the form. See {@link https://de.wikipedia.org/wiki/Elementarsymmetrisches_Polynom}.\n * \n * f(x) = (x-x_0)*...*(x-x_n) =\n * x^n + sum_{k=1}^{n} (-1)^(k) s_{k-1} x^(n-k)\n * \n * We set\n * (e, f) := (c1_x(t1) - c2_x(t2), c1_y(t1) - c2_y(t2))\n * \n * The Jacobian J is defined by\n * \n *\n * @param {JXG.Curve} c1 Curve, Line or Circle\n * @param {JXG.Curve} c2 Curve, Line or Circle\n * @param {Number} t1ini start value for t1\n * @param {Number} t2ini start value for t2\n * @returns {JXG.Coords} intersection point\n * @memberof JXG.Math.Numerics\n */\n generalizedNewton: function (c1, c2, t1ini, t2ini) {\n var t1, t2,\n a, b, c, d, e, f,\n disc,\n F,\n D00, D01, D10, D11,\n count = 0;\n\n // if (this.generalizedNewton.t1memo) {\n // t1 = this.generalizedNewton.t1memo;\n // t2 = this.generalizedNewton.t2memo;\n // } else {\n t1 = t1ini;\n t2 = t2ini;\n // }\n\n e = c1.X(t1) - c2.X(t2);\n f = c1.Y(t1) - c2.Y(t2);\n F = e * e + f * f;\n\n D00 = this.D(c1.X, c1);\n D01 = this.D(c2.X, c2);\n D10 = this.D(c1.Y, c1);\n D11 = this.D(c2.Y, c2);\n\n while (F > Mat.eps && count < 10) {\n a = D00(t1);\n b = -D01(t2);\n c = D10(t1);\n d = -D11(t2);\n disc = a * d - b * c;\n t1 -= (d * e - b * f) / disc;\n t2 -= (a * f - c * e) / disc;\n e = c1.X(t1) - c2.X(t2);\n f = c1.Y(t1) - c2.Y(t2);\n F = e * e + f * f;\n count += 1;\n }\n\n // this.generalizedNewton.t1memo = t1;\n // this.generalizedNewton.t2memo = t2;\n\n if (Math.abs(t1) < Math.abs(t2)) {\n return [c1.X(t1), c1.Y(t1)];\n }\n\n return [c2.X(t2), c2.Y(t2)];\n },\n\n /**\n * Apply damped Newton-Raphson algorithm to determine the intersection\n * between the curve elements c1 and c2. Transformations of the curves\n * are already taken into regard.\n * \n * We use a very high accuracy: Mat.eps**3\n *\n * @deprecated\n * @param {JXG.Curve} c1 Curve, Line or Circle\n * @param {JXG.Curve} c2 Curve, Line or Circle\n * @param {Number} t1ini Start value for curve c1\n * @param {Number} t2ini Start value for curve c2\n * @param {Number} gamma Damping factor, should be in the open interval (0, 1)\n * @param {Number} eps Stop if function value is smaller than eps\n * @returns {Array} [t1, t2, F2], where t1 and t2 are the parameters of the intersection for both curves, F2 is ||c1[t1]-c2[t2]||**2.\n */\n generalizedDampedNewtonCurves: function (c1, c2, t1ini, t2ini, gamma, eps) {\n var t1, t2,\n a, b, c, d, e, f,\n disc,\n F2,\n f1, f2,\n D, Dt,\n max_it = 40,\n count = 0;\n\n t1 = t1ini;\n t2 = t2ini;\n\n f1 = c1.Ft(t1);\n f2 = c2.Ft(t2);\n e = f1[1] - f2[1];\n f = f1[2] - f2[2];\n F2 = e * e + f * f;\n\n D = function(t1, t2) {\n var h = Mat.eps,\n f1_1 = c1.Ft(t1 - h),\n f1_2 = c1.Ft(t1 + h),\n f2_1 = c2.Ft(t2 - h),\n f2_2 = c2.Ft(t2 + h);\n return [\n [ (f1_2[1] - f1_1[1]) / (2 * h),\n -(f2_2[1] - f2_1[1]) / (2 * h)],\n [ (f1_2[2] - f1_1[2]) / (2 * h),\n -(f2_2[2] - f2_1[2]) / (2 * h)]\n ];\n };\n\n while (F2 > eps && count < max_it) {\n Dt = D(t1, t2);\n a = Dt[0][0];\n b = Dt[0][1];\n c = Dt[1][0];\n d = Dt[1][1];\n\n disc = a * d - b * c;\n t1 -= gamma * (d * e - b * f) / disc;\n t2 -= gamma * (a * f - c * e) / disc;\n f1 = c1.Ft(t1);\n f2 = c2.Ft(t2);\n\n e = f1[1] - f2[1];\n f = f1[2] - f2[2];\n F2 = e * e + f * f;\n count += 1;\n }\n\n return [t1, t2, F2];\n },\n\n /**\n * Apply the damped Newton-Raphson algorithm to determine to find a root of a\n * function F: R^n to R^n.\n *\n * @param {Function} F Function with n parameters, returns a vactor of length n.\n * @param {Function} D Function returning the Jacobian matrix (n \\times n) of F\n * @param {Number} n\n * @param {Array} t_ini Array of length n, containing start values\n * @param {Number} gamma Damping factor should be between 0 and 1. If equal to 1,\n * the algorithm is Newton-Raphson.\n * @param {Number} eps The algorithm stops if the square norm of the root is less than this eps\n * or if the maximum number of steps is reached.\n * @param {Number} [max_steps=40] maximum number of steps\n * @returns {Array} [t, F2] array of length, containing t, the approximation of the root (array of length n),\n * and the square norm of F(t).\n */\n generalizedDampedNewton: function (F, D, n, t_ini, gamma, eps, max_steps) {\n var i,\n t = [],\n a, b, c, d, e, f,\n disc,\n Ft, Dt,\n F2, vec,\n count = 0;\n\n max_steps = max_steps || 40;\n\n t = t_ini.slice(0, n);\n Ft = F(t, n);\n\n if (n === 2) {\n // Special case n = 2\n Ft = F(t, n);\n e = Ft[0];\n f = Ft[1];\n F2 = e * e + f * f;\n\n while (F2 > eps && count < max_steps) {\n Dt = D(t, n);\n\n a = Dt[0][0];\n b = Dt[0][1];\n c = Dt[1][0];\n d = Dt[1][1];\n\n disc = a * d - b * c;\n t[0] -= gamma * (d * e - b * f) / disc;\n t[1] -= gamma * (a * f - c * e) / disc;\n\n Ft = F(t, n);\n e = Ft[0];\n f = Ft[1];\n F2 = e * e + f * f;\n\n count += 1;\n }\n\n return [t, F2];\n } else {\n // General case, arbitrary n\n Ft = F(t, n);\n F2 = Mat.innerProduct(Ft, Ft, n);\n\n while (F2 > eps && count < max_steps) {\n Dt = Mat.inverse(D(t, n));\n\n vec = Mat.matVecMult(Dt, Ft);\n for (i = 0; i < n; i++) {\n t[i] -= gamma * vec[i];\n }\n\n Ft = F(t, n);\n F2 = Mat.innerProduct(Ft, Ft, n);\n\n count += 1;\n }\n\n return [t, F2];\n }\n },\n\n /**\n * Returns the Lagrange polynomials for curves with equidistant nodes, see\n * Jean-Paul Berrut, Lloyd N. Trefethen: Barycentric Lagrange Interpolation,\n * SIAM Review, Vol 46, No 3, (2004) 501-517.\n * The graph of the parametric curve [x(t),y(t)] runs through the given points.\n * @param {Array} p Array of JXG.Points\n * @returns {Array} An array consisting of two functions x(t), y(t) which define a parametric curve\n * f(t) = (x(t), y(t)), a number x1 (which equals 0) and a function x2 defining the curve's domain.\n * That means the curve is defined between x1 and x2(). x2 returns the (length of array p minus one).\n * @memberof JXG.Math.Numerics\n *\n * @example\n * var p = [];\n *\n * p[0] = board.create('point', [0, -2], {size:2, name: 'C(a)'});\n * p[1] = board.create('point', [-1.5, 5], {size:2, name: ''});\n * p[2] = board.create('point', [1, 4], {size:2, name: ''});\n * p[3] = board.create('point', [3, 3], {size:2, name: 'C(b)'});\n *\n * // Curve\n * var fg = JXG.Math.Numerics.Neville(p);\n * var graph = board.create('curve', fg, {strokeWidth:3, strokeOpacity:0.5});\n *\n * \n * It possesses the method getTerm() which returns the string containing the function term of the polynomial and\n * the method getCoefficients() which returns an array containing the coefficients of the polynomial.\n * @param {Array} p Array of JXG.Points\n * @returns {function} A function of one parameter which returns the value of the polynomial, whose graph runs through the given points.\n * @memberof JXG.Math.Numerics\n *\n * @example\n * var p = [];\n * p[0] = board.create('point', [-1,2], {size:4});\n * p[1] = board.create('point', [0,3], {size:4});\n * p[2] = board.create('point', [1,1], {size:4});\n * p[3] = board.create('point', [3,-1], {size:4});\n * var f = JXG.Math.Numerics.lagrangePolynomial(p);\n * var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});\n *\n * \n * In case of type \"simpson\" and \"trapezoidal\", the horizontal line approximating the function value\n * is replaced by a parabola or a secant. IN case of \"simpson\",\n * the parabola is approximated visually by a polygonal chain of fixed step width.\n *\n * @param {Function|Array} f Function or array of two functions.\n * If f is a function the integral of this function is approximated by the Riemann sum.\n * If f is an array consisting of two functions the area between the two functions is filled\n * by the Riemann sum bars.\n * @param {Number} n number of rectangles.\n * @param {String} type Type of approximation. Possible values are: 'left', 'right', 'middle', 'lower', 'upper', 'random', 'simpson', or 'trapezoidal'.\n * \"simpson\" is Simpson's 1/3 rule.\n * @param {Number} start Left border of the approximation interval\n * @param {Number} end Right border of the approximation interval\n * @returns {Array} An array of two arrays containing the x and y coordinates for the rectangles showing the Riemann sum. This\n * array may be used as parent array of a {@link JXG.Curve}. The third parameteris the riemann sum, i.e. the sum of the volumes of all\n * rectangles.\n * @memberof JXG.Math.Numerics\n */\n riemann: function (gf, n, type, start, end) {\n var i, delta,\n k, a, b, c, f0, f1, f2, xx, h,\n steps = 30, // Constant step width for Simpson's rule\n xarr = [],\n yarr = [],\n x = start,\n sum = 0,\n y, f, g;\n\n if (Type.isArray(gf)) {\n g = gf[0];\n f = gf[1];\n } else {\n f = gf;\n }\n\n n = Math.floor(n);\n\n if (n <= 0) {\n return [xarr, yarr, sum];\n }\n\n delta = (end - start) / n;\n\n // Horizontal lines defined by function\n // Go forward\n for (i = 0; i < n; i++) {\n if (type === 'simpson') {\n sum += this._riemannValue(x, f, type, delta) * delta;\n\n h = delta * 0.5;\n f0 = f(x);\n f1 = f(x + h);\n f2 = f(x + 2 * h);\n\n a = (f2 + f0 - 2 * f1) / (h * h) * 0.5;\n b = (f2 - f0) / (2 * h);\n c = f1;\n for (k = 0; k < steps; k++) {\n xx = k * delta / steps - h;\n xarr.push(x + xx + h);\n yarr.push(a * xx * xx + b * xx + c);\n }\n x += delta;\n y = f2;\n } else {\n y = this._riemannValue(x, f, type, delta);\n xarr.push(x);\n yarr.push(y);\n\n x += delta;\n if (type === 'trapezoidal') {\n f2 = f(x);\n sum += (y + f2) * 0.5 * delta;\n y = f2;\n } else {\n sum += y * delta;\n }\n }\n xarr.push(x);\n yarr.push(y);\n }\n\n // Horizontal lines defined by x-axis or second function\n // Go backwards\n for (i = 0; i < n; i++) {\n if (type === \"simpson\" && g) {\n sum -= this._riemannValue(x, g, type, -delta) * delta;\n\n h = delta * 0.5;\n f0 = g(x);\n f1 = g(x - h);\n f2 = g(x - 2 * h);\n\n a = (f2 + f0 - 2 * f1) / (h * h) * 0.5;\n b = (f2 - f0) / (2 * h);\n c = f1;\n for (k = 0; k < steps; k++) {\n xx = k * delta / steps - h;\n xarr.push(x - xx - h);\n yarr.push(a * xx * xx + b * xx + c);\n }\n x -= delta;\n y = f2;\n } else {\n if (g) {\n y = this._riemannValue(x, g, type, -delta);\n } else {\n y = 0.0;\n }\n xarr.push(x);\n yarr.push(y);\n\n x -= delta;\n if (g) {\n if (type === 'trapezoidal') {\n f2 = g(x);\n sum -= (y + f2) * 0.5 * delta;\n y = f2;\n } else {\n sum -= y * delta;\n }\n }\n }\n xarr.push(x);\n yarr.push(y);\n\n // Close rectangle\n xarr.push(x);\n if (type === 'simpson') {\n yarr.push(f(x));\n } else {\n y = this._riemannValue(x, f, type, delta);\n yarr.push(y);\n }\n }\n\n return [xarr, yarr, sum];\n },\n\n /**\n * Approximate the integral by Riemann sums.\n * Compute the area described by the riemann sum rectangles.\n *\n * If there is an element of type {@link Riemannsum}, then it is more efficient\n * to use the method JXG.Curve.Value() of this element instead.\n *\n * @param {Function_Array} f Function or array of two functions.\n * If f is a function the integral of this function is approximated by the Riemann sum.\n * If f is an array consisting of two functions the area between the two functions is approximated\n * by the Riemann sum.\n * @param {Number} n number of rectangles.\n * @param {String} type Type of approximation. Possible values are: 'left', 'right', 'middle', 'lower', 'upper', 'random', 'simpson' or 'trapezoidal'.\n *\n * @param {Number} start Left border of the approximation interval\n * @param {Number} end Right border of the approximation interval\n * @returns {Number} The sum of the areas of the rectangles.\n * @memberof JXG.Math.Numerics\n */\n riemannsum: function (f, n, type, start, end) {\n JXG.deprecated(\"Numerics.riemannsum()\", \"Numerics.riemann()[2]\");\n return this.riemann(f, n, type, start, end)[2];\n },\n\n /**\n * Solve initial value problems numerically using explicit Runge-Kutta methods.\n * See {@link https://en.wikipedia.org/wiki/Runge-Kutta_methods} for more information on the algorithm.\n * @param {object|String} butcher Butcher tableau describing the Runge-Kutta method to use. This can be either a string describing\n * a Runge-Kutta method with a Butcher tableau predefined in JSXGraph like 'euler', 'heun', 'rk4' or an object providing the structure\n * \n * This is a helper function which is used in {@link JXG.Math.Numerics.fminbr},\n * {@link JXG.Math.Numerics.fzero}, and {@link JXG.Curve.getLabelPosition}\n * to avoid search in an interval where the function is mostly undefined.\n *\n * @param {function} f\n * @param {Array} x0 Start interval\n * @param {Object} context Parent object in case f is method of it\n * @param {Boolean} [outer=true] if true take a proper enclosing array. If false return the domain such that the function is defined\n * at its borders.\n * @returns Array\n *\n * @example\n * var f = (x) => Math.sqrt(x);\n * console.log(JXG.Math.Numerics.findDomain(f, [-5, 5]));\n *\n * // Output: [ -0.00020428174445492973, 5 ]\n *\n * @example\n * var f = (x) => Math.sqrt(x);\n * console.log(JXG.Math.Numerics.findDomain(f, [-5, 5], null, false));\n *\n * // Output: [ 0.00020428174562965915, 5 ]\n */\n findDomain: function (f, x0, context, outer) {\n var a, b, c, fc,\n x,\n gr = 1 - 1 / 1.61803398875,\n eps = 0.001,\n cnt,\n max_cnt = 20;\n\n if (outer === undefined) {\n outer = true;\n }\n\n if (!Type.isArray(x0) || x0.length < 2) {\n throw new Error(\n \"JXG.Math.Numerics.findDomain: length of array x0 has to be at least two.\"\n );\n }\n\n x = x0.slice();\n a = x[0];\n b = x[1];\n fc = f.call(context, a);\n if (isNaN(fc)) {\n // Divide the interval with the golden ratio\n // and keep a such that f(a) = NaN\n cnt = 0;\n while (b - a > eps && cnt < max_cnt) {\n c = (b - a) * gr + a;\n fc = f.call(context, c);\n if (isNaN(fc)) {\n a = c;\n } else {\n b = c;\n }\n cnt++;\n }\n if (outer) {\n x[0] = a;\n } else {\n x[0] = b;\n }\n // x[0] = a;\n }\n\n a = x[0];\n b = x[1];\n fc = f.call(context, b);\n if (isNaN(fc)) {\n // Divide the interval with the golden ratio\n // and keep b such that f(b) = NaN\n cnt = 0;\n while (b - a > eps && cnt < max_cnt) {\n c = b - (b - a) * gr;\n fc = f.call(context, c);\n if (isNaN(fc)) {\n b = c;\n } else {\n a = c;\n }\n cnt++;\n }\n if (outer) {\n x[1] = b;\n } else {\n x[1] = a;\n }\n // x[1] = b;\n }\n\n return x;\n },\n\n /**\n *\n * Find minimum of an univariate function f.\n * \n * Algorithm:\n * G.Forsythe, M.Malcolm, C.Moler, Computer methods for mathematical\n * computations. M., Mir, 1980, p.180 of the Russian edition\n *\n * @param {function} f Function, whose minimum is to be found\n * @param {Array} x0 Start interval enclosing the minimum\n * @param {Object} [context] Parent object in case f is method of it\n * @returns {Number} the approximation of the minimum value position\n * @memberof JXG.Math.Numerics\n **/\n fminbr: function (f, x0, context) {\n var a, b, x, v, w,\n fx, fv, fw,\n x00,\n range, middle_range, tol_act, new_step,\n p, q, t, ft,\n r = (3.0 - Math.sqrt(5.0)) * 0.5, // Golden section ratio\n tol = Mat.eps,\n sqrteps = Mat.eps, // Math.sqrt(Mat.eps),\n maxiter = this.maxIterationsMinimize,\n niter = 0;\n // nfev = 0;\n\n if (!Type.isArray(x0) || x0.length < 2) {\n throw new Error(\n \"JXG.Math.Numerics.fminbr: length of array x0 has to be at least two.\"\n );\n }\n\n x00 = this.findDomain(f, x0, context);\n a = x00[0];\n b = x00[1];\n v = a + r * (b - a);\n fv = f.call(context, v);\n\n // First step - always gold section\n // nfev += 1;\n x = v;\n w = v;\n fx = fv;\n fw = fv;\n\n while (niter < maxiter) {\n // Range over the interval in which we are looking for the minimum\n range = b - a;\n middle_range = (a + b) * 0.5;\n\n // Actual tolerance\n tol_act = sqrteps * Math.abs(x) + tol / 3.0;\n\n if (Math.abs(x - middle_range) + range * 0.5 <= 2.0 * tol_act) {\n // Acceptable approx. is found\n return x;\n }\n\n // Obtain the golden section step\n new_step = r * (x < middle_range ? b - x : a - x);\n\n // Decide if the interpolation can be tried. If x and w are distinct, interpolatiom may be tried\n if (Math.abs(x - w) >= tol_act) {\n // Interpolation step is calculated as p/q;\n // division operation is delayed until last moment\n t = (x - w) * (fx - fv);\n q = (x - v) * (fx - fw);\n p = (x - v) * q - (x - w) * t;\n q = 2 * (q - t);\n\n if (q > 0) {\n p = -p; // q was calculated with the opposite sign; make q positive\n } else {\n q = -q; // // and assign possible minus to p\n }\n if (\n Math.abs(p) < Math.abs(new_step * q) && // If x+p/q falls in [a,b]\n p > q * (a - x + 2 * tol_act) && // not too close to a and\n p < q * (b - x - 2 * tol_act)\n ) {\n // b, and isn't too large\n new_step = p / q; // it is accepted\n }\n // If p / q is too large then the\n // golden section procedure can\n // reduce [a,b] range to more\n // extent\n }\n\n // Adjust the step to be not less than tolerance\n if (Math.abs(new_step) < tol_act) {\n if (new_step > 0) {\n new_step = tol_act;\n } else {\n new_step = -tol_act;\n }\n }\n\n // Obtain the next approximation to min\n // and reduce the enveloping range\n\n // Tentative point for the min\n t = x + new_step;\n ft = f.call(context, t);\n // nfev += 1;\n\n // t is a better approximation\n if (ft <= fx) {\n // Reduce the range so that t would fall within it\n if (t < x) {\n b = x;\n } else {\n a = x;\n }\n\n // Assign the best approx to x\n v = w;\n w = x;\n x = t;\n\n fv = fw;\n fw = fx;\n fx = ft;\n // x remains the better approx\n } else {\n // Reduce the range enclosing x\n if (t < x) {\n a = t;\n } else {\n b = t;\n }\n\n if (ft <= fw || w === x) {\n v = w;\n w = t;\n fv = fw;\n fw = ft;\n } else if (ft <= fv || v === x || v === w) {\n v = t;\n fv = ft;\n }\n }\n niter += 1;\n }\n\n return x;\n },\n\n /**\n * GLOMIN seeks a global minimum of a function F(X) in an interval [A,B]\n * and is the adaption of the algorithm GLOMIN by Richard Brent.\n *\n * Here is the original documentation:\n * \n * The returned roots are sorted with respect to their real values.\n * This method makes use of the JSXGraph classes {@link JXG.Complex} and {@link JXG.C} to handle\n * complex numbers.\n *\n * @param {Array} a Array of coefficients of the polynomial a[0] + a[1]*x+ a[2]*x**2...\n * The coefficients are of type Number or JXG.Complex.\n * @param {Number} [deg] Optional degree of the polynomial. Otherwise all entries are taken, with\n * leading zeros removed.\n * @param {Number} [tol=Number.EPSILON] Approximation tolerance\n * @param {Number} [max_it=30] Maximum number of iterations\n * @param {Array} [initial_values=null] Array of initial values for the roots. If not given,\n * starting values are determined by the method of Ozawa.\n * @returns {Array} Array of complex numbers (of JXG.Complex) approximating the roots of the polynomial.\n * @memberof JXG.Math.Numerics\n * @see JXG.Complex\n * @see JXG.C\n *\n * @example\n * // Polynomial p(z) = -1 + 1z^2\n * var i, roots,\n * p = [-1, 0, 1];\n *\n * roots = JXG.Math.Numerics.polzeros(p);\n * for (i = 0; i < roots.length; i++) {\n * console.log(i, roots[i].toString());\n * }\n * // Output:\n * 0 -1 + -3.308722450212111e-24i\n * 1 1 + 0i\n *\n * @example\n * // Polynomial p(z) = -1 + 3z - 9z^2 + z^3 - 8z^6 + 9z^7 - 9z^8 + z^9\n * var i, roots,\n * p = [-1, 3, -9, 1, 0, 0, -8, 9, -9, 1];\n *\n * roots = JXG.Math.Numerics.polzeros(p);\n * for (i = 0; i < roots.length; i++) {\n * console.log(i, roots[i].toString());\n * }\n * // Output:\n * 0 -0.7424155888401961 + 0.4950476539211721i\n * 1 -0.7424155888401961 + -0.4950476539211721i\n * 2 0.16674869833354108 + 0.2980502714610669i\n * 3 0.16674869833354108 + -0.29805027146106694i\n * 4 0.21429002063640837 + 1.0682775088132996i\n * 5 0.21429002063640842 + -1.0682775088132999i\n * 6 0.861375497926218 + -0.6259177003583295i\n * 7 0.8613754979262181 + 0.6259177003583295i\n * 8 8.000002743888055 + -1.8367099231598242e-40i\n *\n */\n polzeros: function (coeffs, deg, tol, max_it, initial_values) {\n var i, le, off, it,\n debug = false,\n cc = [],\n obvious = [],\n roots = [],\n\n /**\n * Horner method to evaluate polynomial or the derivative thereof for complex numbers,\n * i.e. coefficients and variable are complex.\n * @function\n * @param {Array} a Array of complex coefficients of the polynomial a[0] + a[1]*x+ a[2]*x**2...\n * @param {JXG.Complex} z Value for which the polynomial will be evaluated.\n * @param {Boolean} [derivative=false] If true the derivative will be evaluated.\n * @ignore\n */\n hornerComplex = function (a, z, derivative) {\n var i, s,\n n = a.length - 1;\n\n derivative = derivative || false;\n if (derivative) {\n // s = n * a_n\n s = JXG.C.mult(n, a[n]);\n for (i = n - 1; i > 0; i--) {\n // s = s * z + i * a_i\n s.mult(z);\n s.add(JXG.C.mult(a[i], i));\n }\n } else {\n // s = a_n\n s = JXG.C.copy(a[n]);\n for (i = n - 1; i >= 0; i--) {\n // s = s * z + a_i\n s.mult(z);\n s.add(a[i]);\n }\n }\n return s;\n },\n\n /**\n * Horner method to evaluate reciprocal polynomial or the derivative thereof for complex numbers,\n * i.e. coefficients and variable are complex.\n * @function\n * @param {Array} a Array of complex coefficients of the polynomial a[0] + a[1]*x+ a[2]*x**2...\n * @param {JXG.Complex} z Value for which the reciprocal polynomial will be evaluated.\n * @param {Boolean} [derivative=false] If true the derivative will be evaluated.\n * @ignore\n */\n hornerRec = function (a, x, derivative) {\n var i, s,\n n = a.length - 1;\n\n derivative = derivative || false;\n if (derivative) {\n // s = n * a_0\n s = JXG.C.mult(n, a[0]);\n for (i = n - 1; i > 0; i--) {\n // s = s * x + i * a_{n-i}\n s.mult(x);\n s.add(JXG.C.mult(a[n - i], i));\n }\n } else {\n // s = a_0\n s = JXG.C.copy(a[0]);\n for (i = n - 1; i >= 0; i--) {\n // s = s * x + a_{n-i}\n s.mult(x);\n s.add(a[n - i]);\n }\n }\n return s;\n },\n\n /**\n * Horner method to evaluate real polynomial at a real value.\n * @function\n * @param {Array} a Array of real coefficients of the polynomial a[0] + a[1]*x+ a[2]*x**2...\n * @param {Number} z Value for which the polynomial will be evaluated.\n * @ignore\n */\n horner = function (a, x) {\n var i, s,\n n = a.length - 1;\n\n s = a[n];\n for (i = n - 1; i >= 0; i--) {\n s = s * x + a[i];\n }\n return s;\n },\n\n /**\n * Determine start values for the Aberth iteration, see\n * Ozawa, \"An experimental study of the starting values\n * of the Durand-Kerner-Aberth iteration\" (1995).\n *\n * @function\n * @param {Array} a Array of complex coefficients of the polynomial a[0] + a[1]*x+ a[2]*x**2...\n * @returns {Array} Array Initial values for the roots.\n * @ignore\n */\n initial_guess = function (a) {\n var i, r,\n n = a.length - 1, // degree\n alpha1 = Math.PI * 2 / n,\n alpha0 = Math.PI / n * 0.5,\n b, z,\n init = [];\n\n\n // From Ozawa, \"An experimental study of the starting values\n // of the Durand-Kerner-Aberth iteration\" (1995)\n\n // b is the arithmetic mean of the roots.\n // With is Vieta's formula \n * Naive implementation with runtime O(samples).\n *\n * @param {Number} good ways to make a good selection\n * @param {Number} bad ways to make a bad selection\n * @param {Number} samples number of items sampled\n * @returns\n * @memberof JXG.Math.Statistics\n */\n randomHypergeometric: function (good, bad, k) {\n var i, u,\n x = 0,\n // kk,\n // n = good + bad,\n d1 = good + bad - k,\n d2 = Math.min(good, bad),\n y = d2;\n\n if (good < 1 || bad < 1 || k > good + bad) {\n return NaN;\n }\n\n // Naive method\n // kk = Math.min(k, n - k);\n // for (i = 0; i < k; i ++) {\n // u = Math.random();\n // if (n * u <= good) {\n // x += 1;\n // if (x === good) {\n // return x;\n // }\n // good -= 1;\n // }\n // n -= 1;\n // }\n // return x;\n\n // Implementation from\n // Monte Carlo by George S. Fishman\n // https://link.springer.com/book/10.1007/978-1-4757-2553-7\n // page 218\n //\n i = k;\n while (y * i > 0) {\n u = Math.random();\n y -= Math.floor(u + y / (d1 + i));\n i -= 1;\n }\n x = d2 - y;\n if (good <= bad) {\n return x;\n } else {\n return k - x;\n }\n },\n\n /**\n * Compute the histogram of a dataset.\n * Optional parameters can be supplied through a JavaScript object\n * with the following default values:\n * \n * The second array contains the counts of each bin.\n * @param {Array} x\n * @param {Object} opt Optional parameters\n * @returns Array [bin, counts] Array bins contains start values of bins, array counts contains\n * the number of entries of x which are contained in each bin.\n * @memberof JXG.Math.Statistics\n *\n * @example\n * let board = JXG.JSXGraph.initBoard('jxgbox',\n * { boundingbox: [-1.7, .5, 20, -.03], axis: true});\n * let board2 = JXG.JSXGraph.initBoard('jxgbox2',\n * { boundingbox: [-1.6, 1.1, 20, -.06], axis: true});\n *\n * let runs = [\n * [0.5, 1.0, 'brown'],\n * [1.0, 2.0, 'red'],\n * [2.0, 2.0, 'orange'],\n * [3.0, 2.0, 'yellow'],\n * [5.0, 1.0, 'green'],\n * [9.0, 0.5, 'black'],\n * [7.5, 1.0, 'purple'],\n * ]\n *\n * let labelY = .4\n * runs.forEach((run,i) => {\n * board.create('segment',[[7,labelY-(i/50)],[9,labelY-(i/50)]],{strokeColor:run[2]})\n * board.create('text',[10,labelY-(i/50),`k=${run[0]}, θ=${run[1]}`])\n *\n * // density\n * let x = Array(50000).fill(0).map(() => JXG.Math.Statistics.randomGamma(run[0],run[1]))\n * let res = JXG.Math.Statistics.histogram(x, { bins: 50, density: true, cumulative: false, range: [0, 20] });\n * board.create('curve', [res[1], res[0]], { strokeColor: run[2], strokeWidth:2});\n *\n * // cumulative density\n * res = JXG.Math.Statistics.histogram(x, { bins: 50, density: true, cumulative: true, range: [0, 20] });\n * res[0].unshift(0) // add zero to front so cumulative starts at zero\n * res[1].unshift(0)\n * board2.create('curve', [res[1], res[0]], { strokeColor: run[2], strokeWidth:2 });\n * })\n *\n *\n * \n * In case of {@link JXG.Board#dblClickSuppressClick} being false, this attribute is used\n * to clear the list of clicked elements after the time specified by this attribute.\n * \n * Recommendation: if {@link JXG.Board#dblClickSuppressClick} is true, use a value of approx. 300,\n * otherwise stay with the default 600.\n *\n * @name JXG.Board#clickDelay\n * @type Number\n * @default 600\n * @see JXG.Board#dblClickSuppressClick\n */\n clickDelay: 600,\n\n /**\n * CSS attributes for the JSXGraph div element.\n *\n * @name JXG.Board#cssStyle\n * @type String\n * @default ''\n */\n cssStyle: '',\n\n /**\n * If false (default), JSXGraph follows the JavaScript standard and fires before a dblclick event two\n * click events.\n * \n * If true, the click events are suppressed if there is a dblclick event.\n * The consequence is that in this case any click event is fired with a delay specified by\n * {@link JXG.Board#clickDelay}.\n *\n * @name JXG.Board#dblClickSuppressClick\n * @type Boolean\n * @default false\n * @see JXG.Board#clickDelay\n *\n */\n dblClickSuppressClick: false,\n\n /**\n * Attributes for the default axes in case of the attribute\n * axis:true in {@link JXG.JSXGraph#initBoard}.\n *\n * @name JXG.Board#defaultAxes\n * @type Object\n * @default {x: {name:'x'}, y: {name: 'y'}}\n *\n * @example\n * const board = JXG.JSXGraph.initBoard('id', {\n * boundingbox: [-5, 5, 5, -5], axis:true,\n * defaultAxes: {\n * x: {\n * name: 'Distance (mi)',\n * withLabel: true,\n * label: {\n * position: 'rt',\n * offset: [-5, 15],\n * anchorX: 'right'\n * }\n * },\n * y: {\n * withLabel: true,\n * name: 'Y',\n * label: {\n * position: 'rt',\n * offset: [-20, -5],\n * anchorY: 'top'\n * }\n * }\n * }\n * });\n *\n * \n * If set false and hasPoint() is true for both an element and it's label,\n * the label is taken (if it is on a higher layer than the element)\n * \n * Meanwhile, this feature might be irrelevant.\n * @name JXG.Board#ignoreLabels\n * @type Booelan\n * @default true\n */\n ignoreLabels: true,\n\n /**\n * Support for internationalization of number formatting. This affects\n * \n * User generated texts consisting of texts AND numbers have to be internationalized by the user, see\n * {@link Text#intl}.\n * Language locale and options can be individually controlled for each element by its intl attribute.\n * If no locale is set, the default language of the browser is used.\n *\n * @name JXG.Board#intl\n * @type Object\n * @default {enabled: false}\n * @see Integral#label\n * @see Slider#intl\n * @see Text#intl\n * @see Ticks#intl\n * @see JXG.Board.infobox\n *\n * @example\n * // Set the board-wide locale and use individual\n * // options for a text.\n * const board = JXG.JSXGraph.initBoard(BOARDID, {\n * axis: true,\n * intl: {\n * enabled: true,\n * locale: 'de-DE'\n * },\n * boundingbox:[-0.5, 0.5, 0.5, -0.5]\n * });\n *\n * var t = board.create('text', [0.05, 0.2, -Math.PI*100], {\n * formatNumber: true,\n * digits: 2,\n * intl: {\n * enabled: true,\n * options: {\n * style: 'unit',\n * unit: 'celsius'\n * }\n * }\n * });\n *\n * \n * If the aspect ration of the hosting div changes, JSXGraphs will change\n * the user supplied bounding box accordingly.\n * This is necessary if circles should look like circles and not\n * like ellipses. It is recommended to set keepAspectRatio = true\n * for geometric applets.\n * \n * For function plotting keepAspectRatio = false\n * might be the better choice.\n *\n * @name JXG.Board#keepAspectRatio\n * @see JXG.Board#boundingBox\n * @see JXG.Board#maxBoundingBox\n * @see JXG.Board#setBoundingBox\n * @type Boolean\n * @default false\n */\n keepAspectRatio: false,\n\n /**\n * Control using the keyboard to change the construction.\n * \n * This optimization seems to be obsolete in newer browsers (from 2021 on, at least)\n * and even slow down the constructions. Therefore, the default is set to 'none' since v1.2.4.\n * \n * If set to 'svg', before every redrawing of the JSXGraph construction\n * the SVG sub-tree of the DOM tree is taken out of the DOM.\n *\n * If set to 'all', before every redrawing of the JSXGraph construction the\n * complete DOM tree is taken out of the DOM.\n * If set to 'none' the redrawing is done in-place.\n *\n * Using 'svg' or 'all' speeds up the update process considerably. The risk\n * is that if there is an exception, only a white div or window is left.\n *\n *\n * @name JXG.Board#minimizeReflow\n * @type String\n * @default 'none'\n */\n minimizeReflow: 'none',\n\n /**\n * Maximal bounding box of the visible area in user coordinates.\n * It is an array consisting of four values:\n * [x1, y1, x2, y2]\n *\n * The bounding box of the canvas must be inside of this maximal\n * bounding box.\n *\n * @name JXG.Board#maxBoundingBox\n * @type Array\n * @see JXG.Board#boundingBox\n * @default [-Infinity, Infinity, Infinity, -Infinity]\n *\n * @example\n * var board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingBox: [-5, 5, 5, -5],\n * maxBoundingBox: [-8, 8, 8, -8],\n * pan: {enabled: true},\n * axis: true\n * });\n *\n * \n * A situation where dragging outside of the board is uncritical is for example if\n * only sliders are used to interact with the construction.\n * \n * Possible values for this attributes are:\n * \n * Since the introduction of this attribute \"moveTarget\", the value \"document\" has become sort of\n * default on touch devices like smartphones. However, it is no longer the case that the document listens to\n * move events, but there is the new feature \"setPointerCapture\", which is also implicitly enabled on certain devices.\n * In future versions, JSXGraph may adopt this new standard and distinguish only two cases:\n * \n * This attribute is immutable.\n * It can be changed as follows:\n *\n * @example\n * board.setAttribute({moveTarget: null});\n * board.removeEventHandlers();\n * board.addEventHandlers();\n *\n * @name JXG.Board#moveTarget\n * @type Object\n * @description HTML node or document\n * @default null\n *\n * @example\n * var board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-5,5,5,-5],\n * axis: true,\n * moveTarget: document\n * });\n *\n * \n * Using a Boolean value turns on all events (or not), supplying an object of\n * the form\n * This attribute is immutable. Please use\n * {@link JXG.Board#addEventHandlers()} and\n * {@link JXG.Board#removeEventHandlers()} directly.\n *\n * @name JXG.Board.registerEvents\n * @see JXG.Board#keyboard\n * @see JXG.Board.registerResizeEvent\n * @see JXG.Board.registerFullscreenEvent\n * @type Boolean\n * @default true\n */\n registerEvents: true,\n\n // /**\n // * Listen to fullscreen event.\n // *\n // * This attribute is immutable. Please use\n // * {@link JXG.Board#addFullscreenEventHandlers()} and\n // * {@link JXG.Board#removeEventHandlers()} directly.\n // *\n // * @name JXG.Board#registerFullscreenEvent\n // * @see JXG.Board#registerEvents\n // * @see JXG.Board#registerResizeEvent\n // * @type Boolean\n // * @default true\n // */\n // registerFullscreenEvent: true,\n\n // /**\n // * Listen to resize events, i.e. start \"resizeObserver\" or handle the resize event with\n // * \"resizeListener\". This is independent from the mouse, touch, pointer events.\n // *\n // * This attribute is immutable. Please use\n // * {@link JXG.Board#addResizeEventHandlers()} and\n // * {@link JXG.Board#removeEventHandlers()} directly.\n // * \n // * This attribute just starts a resizeObserver. If the resizeObserver reacts\n // * to size changed is controlled with {@link JXG.Board#resize}.\n // *\n // * @name JXG.Board#registerResizeEvent\n // * @see JXG.Board#resize\n // * @see JXG.Board#registerEvents\n // * @see JXG.Board#registerFullscreenEvent\n // * @type Boolean\n // * @default true\n // */\n // registerResizeEvent: true,\n\n /**\n * Default rendering engine. Possible values are 'svg', 'canvas', 'vml', 'no', or 'auto'.\n * If the rendering engine is not available JSXGraph tries to detect a different engine.\n *\n * \n * In case of 'canvas' it is advisable to call 'board.update()' after all elements have been\n * constructed. This ensures that all elements are drawn with their intended visual appearance.\n *\n * \n * This attribute is immutable.\n *\n * @name JXG.Board#renderer\n * @type String\n * @default 'auto'\n */\n renderer: 'auto',\n\n /**\n * Control if JSXGraph reacts to resizing of the JSXGraph container element\n * by the user / browser.\n * The attribute \"throttle\" determines the minimal time in msec between to\n * resize calls.\n * \n * Attention: if the JSXGraph container has no CSS property like width or height and max-width or max-height set, but\n * has a property like box-sizing:content-box, then the interplay between CSS and the resize attribute may result in an\n * infinite loop with ever increasing JSXGraph container.\n *\n * @see JXG.Board#startResizeObserver\n * @see JXG.Board#resizeListener\n *\n * @name JXG.Board#resize\n * @type Object\n * @default {enabled: true, throttle: 10}\n *\n * @example\n * var board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-5,5,5,-5],\n * keepAspectRatio: true,\n * axis: true,\n * resize: {enabled: true, throttle: 200}\n * });\n *\n * \n * So far it works in SVG renderer only.\n * \n * Possible sub-attributes with default values are:\n * \n * Board events triggered by selection manipulation:\n * 'startselecting', 'stopselecting', 'mousestartselecting', 'mousestopselecting',\n * 'pointerstartselecting', 'pointerstopselecting', 'touchstartselecting', 'touchstopselecting'.\n *\n * @example\n * board.on('stopselecting', function(){\n * var box = board.stopSelectionMode(),\n * // bbox has the coordinates of the selectionr rectangle.\n * // Attention: box[i].usrCoords have the form [1, x, y], i.e.\n * // are homogeneous coordinates.\n * bbox = box[0].usrCoords.slice(1).concat(box[1].usrCoords.slice(1));\n * // Set a new bounding box\n * board.setBoundingBox(bbox, false);\n * });\n *\n * @name JXG.Board#selection\n *\n * @see JXG.Board#startSelectionMode\n * @see JXG.Board#stopSelectionMode\n *\n * @type Object\n * @default\n */\n selection: {\n enabled: false,\n name: 'selectionPolygon',\n needShift: false,\n needCtrl: true,\n fillColor: '#ffff00',\n\n // immutable:\n visible: false,\n withLines: false,\n vertices: {\n visible: false\n }\n },\n\n /**\n * Control the sketchcurves for pointer device or first and second finger.\n * @name JXG.Board#sketches\n * @type Object\n * @default \n * If {@link JXG.Board#showCopyright} is false, the logo can be shown anyhow\n * by setting showLogo to true.\n *\n * @name JXG.Board#showLogo\n * @type Boolean\n * @default false\n * @see JXG.Board#showCopyright\n */\n showLogo: false,\n\n /**\n * Display of navigation arrows and zoom buttons in the navigation bar.\n * \n * The navigation bar has the\n * the ID \"{board_id}_navigation\" and the CSS class\n * JXG_navigation\".\n * The individual buttons can be accessed by JavaScript or CSS with\n * the ID \"{board_id}_navigation_button_{type}\" or by the CSS classes\n * JXG_navigation_button\" or\n * JXG_navigation_button_{type}\", where {type}\n * is one of left, right, or up, down,\n * in, 100, or out,\n * fullscreen, screenshot, cleartraces, reload.\n *\n * @name JXG.Board#showNavigation\n * @type Boolean\n * @default true\n * @see JXG.AbstractRenderer#drawNavigationBar\n */\n showNavigation: true,\n\n /**\n * Show a button in the navigation bar to force reload of a construction.\n * Works only with the JessieCode tag.\n * This button can be accessed by JavaScript or CSS with\n * the ID \"{board_id}_navigation_button_reload\" or by the CSS classes\n * JXG_navigation_button\" or\n * JXG_navigation_button_reload\".\n *\n * @name JXG.Board#showReload\n * @type Boolean\n * @default false\n * @see JXG.AbstractRenderer#drawNavigationBar\n */\n showReload: false,\n\n /**\n * Show a button in the navigation bar to enable screenshots.\n * This button can be accessed by JavaScript or CSS with\n * the ID \"{board_id}_navigation_button_screenshot\" or by the CSS classes\n * JXG_navigation_button\" or\n * JXG_navigation_button_screenshot\".\n *\n * @name JXG.Board#showScreenshot\n * @type Boolean\n * @default false\n * @see JXG.AbstractRenderer#drawNavigationBar\n */\n showScreenshot: false,\n\n /**\n * Display of zoom buttons in the navigation bar. To show zoom buttons, additionally\n * showNavigation has to be set to true.\n * \n * The individual buttons can be accessed by JavaScript or CSS with\n * the ID \"{board_id}_navigation_button_{type}\" or by the CSS classes\n * JXG_navigation_button\" or\n * JXG_navigation_button_{type}\", where {type}\n * is in, 100, or out.\n *\n * @name JXG.Board#showZoom\n * @type Boolean\n * @default true\n * @see JXG.AbstractRenderer#drawNavigationBar\n */\n showZoom: true,\n\n /**\n * If true the first element of the set JXG.board.objects having hasPoint==true is taken as drag element.\n *\n * @name JXG.Board#takeFirst\n * @type Boolean\n * @default false\n */\n takeFirst: false,\n\n /**\n * If true, when read from a file or string - the size of the div can be changed by the construction text.\n *\n * @name JXG.Board#takeSizeFromFile\n * @type Boolean\n * @default false\n */\n takeSizeFromFile: false,\n\n /**\n * Set a visual theme for a board. At the moment this attribute is immutable.\n * Available themes are\n * \n * For non-text and non-image elements, this feature is available for the SVG renderer, only.\n * \n * For text and image elements the specificity (priority) of JSXGraph attributes is higher than the CSS class properties, see\n * {@link Text#cssDefaultStyle}\n * For other elements, however, the specificity of a CSS class is higher than the corresponding JSXGraph attribute, see the example below.\n * The fill-properties of a CSS class will be set only if the corresponding JSXGraph attributes are set (to a dummy value).\n *\n * @example\n * // CSS class\n * .line {\n * stroke: blue;\n * stroke-width: 10px;\n * fill: yellow;\n * }\n *\n * // JavaScript\n * var line = board.create('line', [[0, 0], [3, 3]], {\n * cssClass: 'line',\n * strokeColor: 'black',\n * strokeWidth: 2,\n * fillColor: '' // Necessary to enable the yellow fill color of the CSS class\n * });\n *\n * // The line is blue and has stroke-width 10px;\n *\n *\n * @name cssClass\n * @memberOf JXG.GeometryElement.prototype\n * @type String\n * @default ''\n * @see Text#cssClass\n * @see JXG.GeometryElement#highlightCssClass\n */\n cssClass: '',\n\n /**\n * Apply CSS classes to an element in highlighted view. It is possible to supply one or more\n * CSS classes separated by blanks.\n * \n * For non-text and non-image elements, this feature is available for the SVG renderer, only.\n *\n * @name highlightCssClass\n * @memberOf JXG.GeometryElement.prototype\n * @type String\n * @default ''\n * @see Text#highlightCssClass\n * @see JXG.GeometryElement#cssClass\n */\n highlightCssClass: '',\n\n /**\n * Determines the elements border-style.\n * Possible values are:\n * \n * In case the element is a polygon or line and it has the attribute \"rotatable:false\",\n * moving the element with two fingers results in a rotation or translation.\n * \n * If an element is set to be neither scalable nor rotatable, it can only be translated.\n * \n * In case of a polygon, scaling is only possible if no vertex has snapToGrid or snapToPoints\n * enabled and no vertex is fixed by some other constraint. Also, the polygon itself has to have\n * snapToGrid disabled.\n *\n * @type Boolean\n * @default true\n * @name JXG.GeometryElement#rotatable\n * @see JXG.GeometryElement#scalable\n */\n rotatable: true,\n\n /**\n * Determines whether two-finger manipulation of this object may change its size.\n * If set to false, the object is only rotated and translated.\n * \n * In case the element is a horizontal or vertical line having ticks, \"scalable:true\"\n * enables zooming of the board by dragging ticks lines. This feature is enabled,\n * for the ticks element of the line element the attribute \"fixed\" has to be false\n * and the line element's scalable attribute has to be true.\n * \n * In case the element is a polygon or line and it has the attribute \"scalable:false\",\n * moving the element with two fingers results in a rotation or translation.\n * \n * If an element is set to be neither scalable nor rotatable, it can only be translated.\n * \n * In case of a polygon, scaling is only possible if no vertex has snapToGrid or snapToPoints\n * enabled and no vertex is fixed by some other constraint. Also, the polygon itself has to have\n * snapToGrid disabled.\n *\n * @type Boolean\n * @default true\n * @name JXG.GeometryElement#scalable\n * @see JXG.Ticks#fixed\n * @see JXG.GeometryElement#rotatable\n */\n scalable: true,\n\n /**\n * If enabled:true the (stroke) element will get a customized shadow.\n * \n * Customize color and opacity:\n * If the object's RGB stroke color is [r,g,b] and its opacity is op, and\n * the shadow parameters color is given as [r', g', b'] and opacity as op'\n * the shadow will receive the RGB color\n * \n * This attribute is only available with SVG, not with canvas.\n *\n * @type Object\n * @name JXG.GeometryElement#shadow\n * @default shadow: {\n * enabled: false,\n * color: [0, 0, 0],\n * opacity: 1,\n * blur: 3,\n * blend: 0.1,\n * offset: [5, 5]\n * }\n *\n * @example\n * board.options.line.strokeWidth = 2\n * // No shadow\n * var li1 = board.create('line', [[-2, 5], [2, 6]], {strokeColor: 'red', shadow: false});\n *\n * // Default shadow\n * var li2 = board.create('line', [[-2, 3], [2, 4]], {strokeColor: 'red', shadow: true});\n *\n * // No shadow\n * var li3 = board.create('line', [[-2, 1], [2, 2]], {strokeColor: 'blue', shadow: {enabled: false}});\n *\n * // Shadow uses same color as line\n * var li4 = board.create('line', [[-2, -1], [2, 0]], {strokeColor: 'blue',\n * shadow: {enabled: true, color: '#000000', blend: 1}\n * });\n *\n * // Shadow color as a mixture between black and the line color, additionally set opacity\n * var li5 = board.create('line', [[-2, -3], [2, -2]], {strokeColor: 'blue',\n * shadow: {enabled: true, color: '#000000', blend: 0.5, opacity: 0.5}\n * });\n *\n * // Use different value for blur and offset [dx, dy]\n * var li6 = board.create('line', [[-2, -5], [2, -4]], {strokeColor: 'blue',\n * shadow: {enabled: true, offset:[0, 25], blur: 6}\n * });\n *\n * \n * If the attribute 'selection' is set to 'minor' or 'major' and\n * \"the other\" angle sector is to be taken, the orientation of the angle switches, too.\n * \n * Apart from 'selection' having value 'minor' or 'major', the value of the angle\n * is always the (positive) angle value of the visible sector - independent of\n * orientation.\n *\n * @type {String}\n * @name Angle#orientation\n * @default 'counterclockwise'\n * @visprop\n * @example\n *\n * var p1, p2, p3, a;\n * p1 = board.create('point', [0, 0]);\n * p2 = board.create('point', [4, 0]);\n * p3 = board.create('point', [3, 3]);\n * a = board.create('angle', [p2, p1, p3], {\n * name: 'φ',\n * radius: 2,\n * // selection: 'minor',\n * orientation: 'clockwise',\n * arc: {\n * visible: true,\n * strokeWidth: 4,\n * lastArrow: true,\n * }\n * });\n *\n * \n * If the attribute 'selection' is set to 'minor' or 'major' and\n * \"the other\" arc is to be taken, the orientation of the arc switches, too.\n *\n * @type {String}\n * @name Arc#orientation\n * @default 'counterclockwise'\n *\n * @example\n * var p1, p2, p3, a;\n * p1 = board.create('point', [0, 0]);\n * p2 = board.create('point', [4, 0]);\n * p3 = board.create('point', [3, 3]);\n * board.create('arc', [p1, p2, p3], {\n * dash: 3,\n * name: 'a',\n * withLabel: true,\n * strokeColor: 'black',\n * strokeWidth: 3,\n * orientation: 'clockwise',\n * lastArrow: true\n * });\n *\n * \n * This attribute is immutable (by purpose).\n * This attribute is necessary for circumCircleArcs\n *\n * @type Boolean\n * @name Arc#useDirection\n * @default false\n * @private\n */\n useDirection: false,\n\n /**\n * Attributes for center point.\n *\n * @type Point\n * @name Arc#center\n * @default {}\n */\n center: {\n },\n\n /**\n * Attributes for radius point.\n *\n * @type Point\n * @name Arc#radiusPoint\n * @default {}\n */\n radiusPoint: {\n },\n\n /**\n * Attributes for angle point.\n *\n * @type Point\n * @name Arc#anglePoint\n * @default {}\n */\n anglePoint: {\n }\n\n /**#@-*/\n },\n\n /* special arrow options */\n arrow: {\n /**#@+\n * @visprop\n */\n\n firstArrow: false,\n\n lastArrow: {\n type: 1,\n highlightSize: 6,\n size: 6\n }\n\n /**#@-*/\n },\n\n /* special arrowparallel options */\n arrowparallel: {\n /**#@+\n * @visprop\n */\n\n firstArrow: false,\n\n lastArrow: {\n type: 1,\n highlightSize: 6,\n size: 6\n }\n\n /**#@-*/\n },\n\n /* special axis options */\n axis: {\n /**#@+\n * @visprop\n */\n\n name: '', // By default, do not generate names for axes.\n needsRegularUpdate: false, // Axes only updated after zooming and moving of the origin.\n strokeWidth: 1,\n lastArrow: {\n type: 1,\n highlightSize: 8,\n size: 8\n },\n strokeColor: '#666666',\n highlightStrokeWidth: 1,\n highlightStrokeColor: '#888888',\n\n /**\n * Is used to define the behavior of the axis.\n * Settings in this attribute only have an effect if the axis is exactly horizontal or vertical.\n * Possible values are:\n * \n * In certain cases this attribute causes problems, like for\n * conic elements, curve intersection/union/difference\n * \n * Implements the Ramer-Douglas-Peucker algorithm.\n *\n * @name Curve#RDPsmoothing\n * @type Boolean\n * @default false\n * @see Curve#RDPthreshold\n *\n */\n RDPsmoothing: false,\n\n /**\n * Threshold when to stop eliminating points in polyline simplification with the Ramer-Douglas-Peucker algorithm.\n * This number affects simplification with user coordinates, but corresponds to the distance of a point to a\n * line in pixel if the JSXGraph board has size 800x800 pixel and the pixel per unit both horizontally and vertically\n * are roughly equal (For the latter, the geometric mean is taken).\n *\n * @name Curve#RDPthreshold\n * @type Number\n * @default 0.2\n * @see Curve#RDPsmoothing\n */\n RDPthreshold: 0.2,\n\n /**\n * Configure arrow head at the start position for curve.\n * Recommended arrow head type is 7.\n *\n * @name Curve#recursionDepthHigh\n * @see Curve#doAdvancedPlot\n * @type Number\n * @default 17\n */\n recursionDepthHigh: 17,\n\n /**\n * Number of points used for plotting triggered by move events in case\n * (i.e. lower quality plotting but fast)\n * {@link Curve#doAdvancedPlot} is true.\n *\n * @name Curve#recursionDepthLow\n * @see Curve#doAdvancedPlot\n * @type Number\n * @default 13\n */\n recursionDepthLow: 15\n\n /**#@-*/\n },\n\n /* special foreignObject options */\n foreignobject: {\n /**#@+\n * @visprop\n */\n\n fixed: true,\n visible: true,\n needsRegularUpdate: false,\n\n /**\n * List of attractor elements. If the distance of the foreignobject is less than\n * attractorDistance the foreignobject is made to glider of this element.\n *\n * @name ForeignObject#attractors\n *\n * @type Array\n * @default empty\n */\n attractors: [],\n\n /**\n * If set to true, this object is only evaluated once and not re-evaluated on update.\n * This is necessary if you want to have a board within a foreignObject of another board.\n *\n * @name ForeignObject#evaluateOnlyOnce\n *\n * @type Boolean\n * @default false\n */\n evaluateOnlyOnce: false\n\n /**#@-*/\n },\n\n /* special functiongraph options */\n functiongraph: {\n /**#@+\n * @visprop\n */\n\n /**\n * Attributes for functiongraph label.\n *\n * @type Label\n * @name Functiongraph#label\n */\n label: {\n position: 'rt'\n },\n\n /**\n * Remove data points from the function graph which do not influence\n * its appearance. In some cases this makes JSXGraph run much faster,\n * especially if this function graph has glider points or has dependent\n * curves like inequality or curve intersection/union/difference.\n * \n * Implements the Ramer-Douglas-Peucker algorithm.\n *\n * @name Functiongraph#RDPsmoothing\n * @type Boolean\n * @default true\n * @see Curve#RDPsmoothing\n * @see Curve#RDPthreshold\n */\n RDPsmoothing: true\n\n /**#@-*/\n },\n\n /* special glider options */\n glider: {\n /**#@+\n * @visprop\n */\n\n label: {}\n /**#@-*/\n },\n\n /* special grid options */\n grid: {\n /**#@+\n * @visprop\n */\n\n needsRegularUpdate: false,\n hasGrid: false, // Used in standardoptions\n highlight: false,\n\n /**\n * Deprecated. Use {@link Grid#majorStep} instead.\n *\n * @deprecated\n * @type {Number|String}\n * @name Grid#gridX\n * @default null\n */\n gridX: null,\n\n /**\n * Deprecated. Use {@link Grid#majorStep} instead.\n *\n * @deprecated\n * @type {Number|String}\n * @name Grid#gridY\n * @default null\n */\n gridY: null,\n\n /**\n * Distance of major grid elements. There are three possibilities:\n * This attribute can be set individually for major and minor grid as a sub-entry of {@link Grid#major} or {@link Grid#minor},\n * e.g. major: {size: ...}\n * For default values have a look there. This attribute can be set individually for major and minor grid as a sub-entry of {@link Grid#major} or {@link Grid#minor},\n * e.g. major: {face: ...}\n * For default values have a look there. This attribute can be set individually for major and minor grid as a sub-entry of {@link Grid#major} or {@link Grid#minor},\n * e.g. major: {margin: ...}\n * For default values have a look there. This attribute can be set individually for major and minor grid as a sub-entry of {@link Grid#major} or {@link Grid#minor},\n * e.g. major: {drawZero: ...}\n * For default values have a look there. This attribute can be set individually for major and minor grid as a sub-entry of {@link Grid#major} or {@link Grid#minor},\n * e.g. major: {polygonVertices: ...}\n * For default values have a look there. \n * Here, JSXGraph distinguishes whether the object is a segment or a line wlement that\n * is displayed as a segment (with staightFirst = straightLast = true).\n * In the latter case, the object is always treated like an infinite line, regardless if\n * it appears like a segment or an infinite line.\n *\n * @name Intersection.alwaysIntersect\n * @type Boolean\n * @default true\n */\n alwaysIntersect: true\n\n /**#@-*/\n },\n\n /* special label options */\n label: {\n /**#@+\n * @visprop\n */\n\n visible: 'inherit',\n clip: 'inherit',\n strokeColor: '#000000',\n strokeOpacity: 1,\n highlightStrokeOpacity: 0.666666,\n highlightStrokeColor: '#000000',\n\n fixed: true,\n tabindex: null,\n\n /**\n * Point labels are positioned by setting {@link Point#anchorX}, {@link Point#anchorY}\n * and {@link Label#offset}.\n * For line, circle and curve elements (and their derived objects)\n * there are two possibilities to position labels.\n * \n * An arrow head can be turned off with line.setAttribute({firstArrow: false}).\n *\n * @example\n * board.options.line.lastArrow = false;\n * board.options.line.firstArrow = {size: 10, highlightSize: 10};\n * board.options.line.point1 = {visible: false, withLabel: true, label: {visible: true, anchorX: 'right'}};\n * board.options.line.strokeWidth = 4;\n * board.options.line.highlightStrokeWidth = 4;\n *\n * board.create('segment', [[-5,4], [3,4]], {firstArrow: {type: 1}, point1: {name: 'type:1'}});\n * board.create('segment', [[-5,3], [3,3]], {firstArrow: {type: 2}, point1: {name: 'type:2'}});\n * board.create('segment', [[-5,2], [3,2]], {firstArrow: {type: 3}, point1: {name: 'type:3'}});\n * board.create('segment', [[-5,1], [3,1]], {firstArrow: {type: 4}, point1: {name: 'type:4'}});\n * board.create('segment', [[-5,0], [3,0]], {firstArrow: {type: 5}, point1: {name: 'type:5'}});\n * board.create('segment', [[-5,-1], [3,-1]], {firstArrow: {type: 6}, point1: {name: 'type:6'}});\n * board.create('segment', [[-5,-2], [3,-2]], {firstArrow: {type: 7}, point1: {name: 'type:7'}});\n *\n * \n * An arrow head can be turned off with line.setAttribute({lastArrow: false}).\n *\n * @example\n * var p1 = board.create('point', [-5, 2], {size:1});\n * var p2 = board.create('point', [5, 2], {size:10});\n * var li = board.create('segment', ['A','B'],\n * {name:'seg',\n * strokeColor:'#000000',\n * strokeWidth:1,\n * highlightStrokeWidth: 5,\n * lastArrow: {type: 2, size: 8, highlightSize: 6},\n * touchLastPoint: true,\n * firstArrow: {type: 3, size: 8}\n * });\n *\n * \n * The coordinates of the grid points are either integer multiples of snapSizeX and snapSizeY\n * (given in user coordinates, not pixels) or are the intersection points\n * of the major ticks of the boards default axes in case that snapSizeX, snapSizeY are negative.\n *\n * @name Point#snapToGrid\n *\n * @see Point#snapSizeX\n * @see Point#snapSizeY\n * @type Boolean\n * @default false\n */\n snapToGrid: false,\n\n /**\n * If set to true, the point will only snap to (possibly invisibly) grid points\n * when within {@link Point#attractorDistance} of such a grid point.\n * \n * The coordinates of the grid points are either integer multiples of snapSizeX and snapSizeY\n * (given in user coordinates, not pixels) or are the intersection points\n * of the major ticks of the boards default axes in case that snapSizeX, snapSizeY are negative.\n *\n * @name Point#attractToGrid\n *\n * @see Point#attractorDistance\n * @see Point#attractorUnit\n * @see Point#snapToGrid\n * @see Point#snapSizeX\n * @see Point#snapSizeY\n * @type Boolean\n * @default false\n *\n * @example\n * board.create('point', [3, 3], { attractToGrid: true, attractorDistance: 10, attractorunit: 'screen' });\n *\n * \n * With this attribute set to true, also the borders change strokeWidth if the polygon itself gets the focus.\n *\n * @type Boolean\n * @name Polygon#highlightByStrokeWidth\n * @default false\n */\n highlightByStrokeWidth: false,\n\n /**\n * Attributes for the polygon vertices.\n *\n * @type Point\n * @name Polygon#vertices\n */\n vertices: {\n layer: 9,\n withLabel: false,\n name: '',\n strokeColor: Color.palette.red,\n fillColor: Color.palette.red,\n fixed: false,\n visible: 'inherit'\n },\n\n /**\n * Attributes for the polygon label.\n *\n * @type Label\n * @name Polygon#label\n */\n label: {\n offset: [0, 0]\n }\n\n /**#@-*/\n },\n\n /* special polygonal chain options\n */\n polygonalchain: {\n /**#@+\n * @visprop\n */\n\n fillColor: 'none',\n highlightFillColor: 'none'\n\n /**#@-*/\n },\n\n /* special prescribed angle options\n * Not yet implemented. But angle.setAngle(val) is implemented.\n\n */\n prescribedangle: {\n /**#@+\n * @visprop\n */\n\n /**\n * Attributes for the helper point of the prescribed angle.\n *\n * @type Point\n * @name Prescribedangle#anglePoint\n * @ignore\n */\n anglePoint: {\n size: 2,\n visible: false,\n withLabel: false\n }\n\n /**#@-*/\n },\n\n /* special reflection options */\n reflection: {\n /**#@+\n * @visprop\n */\n\n fixed: true,\n\n /**\n * Attributes of circle center, i.e. the center of the circle,\n * if a circle is the mirror element and the transformation type is 'Euclidean'\n *\n * @type center\n * @name Reflection#center\n */\n center: {},\n\n /**\n * Type of transformation. Possible values are 'Euclidean', 'projective'.\n *\n * If the value is 'Euclidean', the reflected element of a circle is again a circle,\n * otherwise it is a conic section.\n *\n * @type String\n * @name Reflection#type\n * @default 'Euclidean'\n */\n type: 'Euclidean'\n\n /**#@-*/\n },\n\n /* special reflexangle options */\n reflexangle: {\n /**#@+\n * @visprop\n */\n\n /**#@-*/\n },\n\n /* special regular polygon options */\n regularpolygon: {\n /**#@+\n * @visprop\n */\n\n /**\n * If true, moving the mouse over inner points triggers hasPoint.\n * @see JXG.GeometryElement#hasPoint\n *\n * @name RegularPolygon#hasInnerPoints\n * @type Boolean\n * @default false\n */\n hasInnerPoints: false,\n fillColor: Color.palette.yellow,\n highlightFillColor: Color.palette.yellow,\n fillOpacity: 0.3,\n highlightFillOpacity: 0.2,\n\n /**\n * Is the polygon bordered by lines?\n *\n * @type Boolean\n * @name RegularPolygon#withLines\n * @default true\n */\n withLines: true,\n\n /**\n * Attributes for the polygon border lines.\n *\n * @type Line\n * @name RegularPolygon#borders\n */\n borders: {\n withLabel: false,\n strokeWidth: 1,\n highlightStrokeWidth: 1,\n // Polygon layer + 1\n layer: 5,\n label: {\n position: 'top'\n }\n },\n\n /**\n * Attributes for the polygon vertices.\n *\n * @type Point\n * @name RegularPolygon#vertices\n */\n vertices: {\n layer: 9,\n withLabel: true,\n strokeColor: Color.palette.red,\n fillColor: Color.palette.red,\n fixed: false\n },\n\n /**\n * Attributes for the polygon label.\n *\n * @type Label\n * @name RegularPolygon#label\n */\n label: {\n offset: [0, 0]\n }\n\n /**#@-*/\n },\n\n /* special options for riemann sums */\n riemannsum: {\n /**#@+\n * @visprop\n */\n\n withLabel: false,\n fillOpacity: 0.3,\n fillColor: Color.palette.yellow\n\n /**#@-*/\n },\n\n /* special sector options */\n sector: {\n /**#@+\n * @visprop\n */\n\n fillColor: Color.palette.yellow,\n highlightFillColor: Color.palette.yellow,\n // fillColor: '#00ff00',\n // highlightFillColor: '#00ff00',\n\n fillOpacity: 0.3,\n highlightFillOpacity: 0.3,\n highlightOnSector: false,\n highlightStrokeWidth: 0,\n\n /**\n * If true, there is a fourth parent point, i.e. the parents are [center, p1, p2, p3].\n * p1 is still the radius point, p2 the angle point. The sector will be that part of the\n * the circle with center 'center' which starts at p1, ends at the ray between center\n * and p2, and passes p3.\n * \n * This attribute is immutable (by purpose).\n * This attribute is necessary for circumCircleSectors\n *\n * @type Boolean\n * @name Arc#useDirection\n * @default false\n * @private\n */\n useDirection: false,\n\n /**\n * Type of sector. Possible values are 'minor', 'major', and 'auto'.\n *\n * @type String\n * @name Sector#selection\n * @default 'auto'\n */\n selection: 'auto',\n\n /**\n * Orientation of the sector: 'clockwise' or 'counterclockwise' (default).\n * \n * If the attribute 'selection' is set to 'minor' or 'major' and\n * \"the other\" angle sector is to be taken, the orientation of the angle switches, too.\n *\n * @type {String}\n * @name Sector#orientation\n * @default 'counterclockwise'\n *\n * @example\n * var p1, p2, p3, a;\n * p1 = board.create('point', [0, 0]);\n * p2 = board.create('point', [4, 0]);\n * p3 = board.create('point', [3, 3]);\n * a = board.create('sector', [p1, p2, p3], {\n * name: 'φ',\n * // selection: 'minor',\n * orientation: 'clockwise',\n * arc: {\n * visible: true,\n * strokeWidth: 4,\n * lastArrow: true,\n * }\n * });\n *\n * \n * Otherwise, display the raw number.\n *\n * @name formatNumber\n * @memberOf Text.prototype\n * @default false\n * @type Boolean\n * @see Text#toFraction\n * @see Text#digits\n */\n formatNumber: false,\n\n /**\n * Used to round texts consisting solely of a number. Needs the attribute formatNumber:true.\n *\n * @name digits\n * @memberOf Text.prototype\n * @default 2\n * @type Number\n * @see Text#formatNumber\n */\n digits: 2,\n\n //draft: false,\n\n /**\n * Internationalization support for texts consisting of a number only.\n * \n * Setting the local overwrites the board-wide locale set in the board attributes.\n * The JSXGraph attribute digits is overruled by the\n * Intl attributes \"minimumFractionDigits\" and \"maximumFractionDigits\".\n * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Intl/NumberFormat/NumberFormat\n * for more information about possible options.\n * \n * See below for an example where the text is composed from a string and a locale formatted number.\n *\n * @name intl\n * @memberOf Text.prototype\n * @type object\n * @default \n * The CSS properties which are set here, are handed over to the style property\n * of the HTML text element. That means, they have higher property than any\n * CSS class.\n * \n * If a property which is set here should be overruled by a CSS class\n * then this property should be removed here.\n * \n * The reason, why this attribute should be kept to its default value at all,\n * is that screen dumps of SVG boards with board.renderer.dumpToCanvas()\n * will ignore the font-family if it is set in a CSS class.\n * It has to be set explicitly as style attribute.\n * \n * In summary, the order of priorities (specificity) from high to low is\n * \n * The CSS properties which are set here, are handed over to the style property\n * of the HTML text element. That means, they have higher property than any\n * CSS class.\n * @example\n * If all texts should get its font-family from the default CSS class\n * before initializing the board\n * \n * The CSS properties which are set here, are handed over to the style property\n * of the HTML text element. That means, they have higher property (specificity) han any\n * CSS class.\n *\n * @name cssStyle\n * @memberOf Text.prototype\n * @default ''\n * @type String\n * @see Text#cssDefaultStyle\n * @see Text#highlightCssDefaultStyle\n * @see Text#highlightCssStyle\n */\n cssStyle: '',\n\n /**\n * CSS properties of the HTML text element in case of highlighting.\n * \n * The CSS properties which are set here, are handed over to the style property\n * of the HTML text element. That means, they have higher property (specificity) than any\n * CSS class.\n *\n * @name highlightCssStyle\n * @memberOf Text.prototype\n * @default ''\n * @type String\n * @see Text#cssDefaultStyle\n * @see Text#highlightCssDefaultStyle\n * @see Text#cssStyle\n */\n highlightCssStyle: '',\n\n transitionProperties: ['color', 'opacity'],\n\n /**\n * If true, the input will be given to ASCIIMathML before rendering.\n *\n * @name useASCIIMathML\n * @memberOf Text.prototype\n * @default false\n * @type Boolean\n */\n useASCIIMathML: false,\n\n /**\n * If true, MathJax will be used to render the input string.\n * Supports MathJax 2 and above.\n * It is recommended to use this option together with the option\n * \"parse: false\". Otherwise, 4 backslashes (e.g. \\\\alpha) are needed\n * instead of two (e.g. \\alpha).\n *\n * @name useMathJax\n * @memberOf Text.prototype\n * @default false\n * @type Boolean\n * @see Text#parse\n *\n * @example\n * // Before loading MathJax, it can be configured like this:\n * <script>\n * MathJax = {\n * tex: {\n * inlineMath: {'[+]': [['$', '$']]},\n * displayMath: {'[+]': [['$$', '$$']]},\n * packages: ['base', 'ams']\n * }\n * };\n * </script>\n * // Then, MathJax is loaded:\n * <script src=\"https://cdn.jsdelivr.net/npm/mathjax@4/tex-svg.js\" id=\"MathJax-script\"></script>\n *\n * // Here is the JSXGraph part:\n * // Display style\n * board.create('text',[ 2,2, function(){return '$$X=\\\\frac{2}{x}$$'}], {\n * fontSize: 15, color:'green', useMathJax: true});\n *\n * // Inline style\n * board.create('text',[-2,2, function(){return '$X_A=\\\\frac{2}{x}$'}], {\n * fontSize: 15, color:'green', useMathJax: true});\n *\n * var A = board.create('point', [-2, 0]);\n * var B = board.create('point', [1, 0]);\n * var C = board.create('point', [0, 1]);\n *\n * var graph = board.create('ellipse', [A, B, C], {\n * fixed: true,\n * withLabel: true,\n * strokeColor: 'black',\n * strokeWidth: 2,\n * fillColor: '#cccccc',\n * fillOpacity: 0.3,\n * highlightStrokeColor: 'red',\n * highlightStrokeWidth: 3,\n * name: '$1=\\\\frac{(x-h)^2}{a^2}+\\\\frac{(y-k)^2}{b^2}$',\n * label: {useMathJax: true}\n * });\n *\n * var nvect1 = board.create('text', [-4, -3, '\\\\[\\\\overrightarrow{V}\\\\]'],\n * {\n * fontSize: 24, parse: false, useMathJax: true\n * });\n * var nvect1 = board.create('text', [-2, -4, function() {return '$\\\\overrightarrow{G}$';}],\n * {\n * fontSize: 24, useMathJax: true\n * });\n *\n * \n * The example below does not work, because there is a conflict with\n * the MathJax library which is used below.\n * \n *\n * @private\n */\n maxScreenCoord: 16777215, // = (2**24 - 1),\n // Too large: 2147483647 = Math.pow(2, 31) - 1,\n // 5000,\n\n /**\n * Determines whether evt is a touch event.\n * @param evt {Event}\n * @returns {Boolean}\n */\n isTouchEvent: function (evt) {\n return JXG.exists(evt['touches']); // Old iOS touch events\n },\n\n /**\n * Determines whether evt is a pointer event.\n * @param evt {Event}\n * @returns {Boolean}\n */\n isPointerEvent: function (evt) {\n return JXG.exists(evt.pointerId);\n },\n\n /**\n * Determines whether evt is neither a touch event nor a pointer event.\n * @param evt {Event}\n * @returns {Boolean}\n */\n isMouseEvent: function (evt) {\n return !JXG.isTouchEvent(evt) && !JXG.isPointerEvent(evt);\n },\n\n /**\n * Determines the number of touch points in a touch event.\n * For other events, -1 is returned.\n * @param evt {Event}\n * @returns {Number}\n */\n getNumberOfTouchPoints: function (evt) {\n var n = -1;\n\n if (JXG.isTouchEvent(evt)) {\n n = evt['touches'].length;\n }\n\n return n;\n },\n\n /**\n * Checks whether an mouse, pointer or touch event evt is the first event of a multitouch event.\n * Attention: When two or more pointer device types are being used concurrently,\n * it is only checked whether the passed event is the first one of its type!\n * @param evt {Event}\n * @returns {boolean}\n */\n isFirstTouch: function (evt) {\n var touchPoints = JXG.getNumberOfTouchPoints(evt);\n\n if (JXG.isPointerEvent(evt)) {\n return evt.isPrimary;\n }\n\n return touchPoints === 1;\n },\n\n /**\n * A document/window environment is available.\n * @type Boolean\n * @default false\n */\n // isBrowser: Type.exists(window) && Type.exists(document) &&\n // typeof window === \"object\" && typeof document === \"object\",\n isBrowser: typeof window !== 'undefined' && typeof document !== 'undefined' &&\n typeof window === \"object\" && typeof document === \"object\",\n\n /**\n * Features of ECMAScript 6+ are available.\n * @type Boolean\n * @default false\n */\n supportsES6: function () {\n // var testMap;\n /* jshint ignore:start */\n try {\n // This would kill the old uglifyjs: testMap = (a = 0) => a;\n new Function(\"(a = 0) => a\");\n return true;\n } catch (err) {\n return false;\n }\n /* jshint ignore:end */\n },\n\n /**\n * Detect browser support for VML.\n * @returns {Boolean} True, if the browser supports VML.\n */\n supportsVML: function () {\n // From stackoverflow.com\n return this.isBrowser && !!document.namespaces;\n },\n\n /**\n * Detect browser support for SVG.\n * @returns {Boolean} True, if the browser supports SVG.\n */\n supportsSVG: function () {\n var svgSupport;\n if (!this.isBrowser) {\n return false;\n }\n svgSupport = !!document.createElementNS && !!document.createElementNS('http://www.w3.org/2000/svg', 'svg').createSVGRect;\n return svgSupport;\n },\n\n /**\n * Detect browser support for Canvas.\n * @returns {Boolean} True, if the browser supports HTML canvas.\n */\n supportsCanvas: function () {\n var hasCanvas = false;\n\n // if (this.isNode()) {\n // try {\n // // c = typeof module === \"object\" ? module.require('canvas') : $__canvas;\n // c = typeof module === \"object\" ? module.require('canvas') : import('canvas');\n // hasCanvas = !!c;\n // } catch (err) {}\n // }\n\n if (this.isNode()) {\n //try {\n // JXG.createCanvas(500, 500);\n hasCanvas = true;\n // } catch (err) {\n // throw new Error('JXG.createCanvas not available.\\n' +\n // 'Install the npm package `canvas`\\n' +\n // 'and call:\\n' +\n // ' import { createCanvas } from 'canvas.js'\\n' +\n // ' JXG.createCanvas = createCanvas;\\n');\n // }\n }\n\n return (\n hasCanvas || (this.isBrowser && !!document.createElement('canvas').getContext)\n );\n },\n\n /**\n * True, if run inside a node.js environment.\n * @returns {Boolean}\n */\n isNode: function () {\n // This is not a 100% sure but should be valid in most cases\n // We are not inside a browser\n /* eslint-disable no-undef */\n return (\n !this.isBrowser &&\n (typeof process !== 'undefined') &&\n (process.release.name.search(/node|io.js/) !== -1)\n /* eslint-enable no-undef */\n\n // there is a module object (plain node, no requirejs)\n // ((typeof module === \"object\" && !!module.exports) ||\n // // there is a global object and requirejs is loaded\n // (typeof global === \"object\" &&\n // global.requirejsVars &&\n // !global.requirejsVars.isBrowser)\n // )\n );\n },\n\n /**\n * True if run inside a webworker environment.\n * @returns {Boolean}\n */\n isWebWorker: function () {\n return (\n !this.isBrowser &&\n typeof self === \"object\" &&\n typeof self.postMessage === \"function\"\n );\n },\n\n /**\n * Checks if the environments supports the W3C Pointer Events API {@link https://www.w3.org/TR/pointerevents/}\n * @returns {Boolean}\n */\n supportsPointerEvents: function () {\n return !!(\n (\n this.isBrowser &&\n window.navigator &&\n (window.PointerEvent || // Chrome/Edge/IE11+\n window.navigator.pointerEnabled || // IE11+\n window.navigator.msPointerEnabled)\n ) // IE10-\n );\n },\n\n /**\n * Determine if the current browser supports touch events\n * @returns {Boolean} True, if the browser supports touch events.\n */\n isTouchDevice: function () {\n return this.isBrowser && window.ontouchstart !== undefined;\n },\n\n /**\n * Detects if the user is using an Android powered device.\n * @returns {Boolean}\n * @deprecated\n */\n isAndroid: function () {\n return (\n Type.exists(navigator) &&\n navigator.userAgent.toLowerCase().indexOf('android') > -1\n );\n },\n\n /**\n * Detects if the user is using the default Webkit browser on an Android powered device.\n * @returns {Boolean}\n * @deprecated\n */\n isWebkitAndroid: function () {\n return this.isAndroid() && navigator.userAgent.indexOf(\" AppleWebKit/\") > -1;\n },\n\n /**\n * Detects if the user is using a Apple iPad / iPhone.\n * @returns {Boolean}\n * @deprecated\n */\n isApple: function () {\n return (\n Type.exists(navigator) &&\n (navigator.userAgent.indexOf('iPad') > -1 ||\n navigator.userAgent.indexOf('iPhone') > -1)\n );\n },\n\n /**\n * Detects if the user is using Safari on an Apple device.\n * See https://evilmartians.com/chronicles/how-to-detect-safari-and-ios-versions-with-ease (2025)\n * @returns {Boolean}\n * @deprecated\n */\n isWebkitApple: function () {\n var is = ('GestureEvent' in window) && // Desktop and mobile\n (\n ('ongesturechange' in window) || // mobile webkit browsers and webview iOS\n (window !== undefined && // Desktop Safari\n 'safari' in window &&\n 'pushNotification' in window.safari)\n );\n return is;\n\n // return (\n // this.isApple() && navigator.userAgent.search(/Mobile\\/[0-9A-Za-z.]*Safari/) > -1\n // );\n },\n\n /**\n * Returns true if the run inside a Windows 8 \"Metro\" App.\n * @returns {Boolean}\n * @deprecated\n */\n isMetroApp: function () {\n return (\n typeof window === \"object\" &&\n window.clientInformation &&\n window.clientInformation.appVersion &&\n window.clientInformation.appVersion.indexOf('MSAppHost') > -1\n );\n },\n\n /**\n * Detects if the user is using a Mozilla browser\n * @returns {Boolean}\n * @deprecated\n */\n isMozilla: function () {\n return (\n Type.exists(navigator) &&\n navigator.userAgent.toLowerCase().indexOf('mozilla') > -1 &&\n navigator.userAgent.toLowerCase().indexOf('apple') === -1\n );\n },\n\n /**\n * Detects if the user is using a firefoxOS powered device.\n * @returns {Boolean}\n * @deprecated\n */\n isFirefoxOS: function () {\n return (\n Type.exists(navigator) &&\n navigator.userAgent.toLowerCase().indexOf('android') === -1 &&\n navigator.userAgent.toLowerCase().indexOf('apple') === -1 &&\n navigator.userAgent.toLowerCase().indexOf('mobile') > -1 &&\n navigator.userAgent.toLowerCase().indexOf('mozilla') > -1\n );\n },\n\n /**\n * Detects if the user is using a desktop device, see https://stackoverflow.com/a/61073480.\n * @returns {boolean}\n *\n * @deprecated\n */\n isDesktop: function () {\n return true;\n // console.log(\"isDesktop\", screen.orientation);\n // const navigatorAgent =\n // navigator.userAgent || navigator.vendor || window.opera;\n // return !(\n // /(android|bb\\d+|meego).+mobile|avantgo|bada\\/|blackberry|blazer|compal|elaine|fennec|hiptop|iemobile|ip(hone|od)|iris|kindle|lge |maemo|midp|mmp|mobile.+firefox|netfront|opera m(ob|in)i|palm( os)?|phone|p(ixi|re)\\/|plucker|pocket|psp|series([46])0|symbian|treo|up\\.(browser|link)|vodafone|wap|windows ce|xda|xiino|android|ipad|playbook|silk/i.test(\n // navigatorAgent\n // ) ||\n // /1207|6310|6590|3gso|4thp|50[1-6]i|770s|802s|a wa|abac|ac(er|oo|s-)|ai(ko|rn)|al(av|ca|co)|amoi|an(ex|ny|yw)|aptu|ar(ch|go)|as(te|us)|attw|au(di|-m|r |s )|avan|be(ck|ll|nq)|bi(lb|rd)|bl(ac|az)|br([ev])w|bumb|bw-([nu])|c55\\/|capi|ccwa|cdm-|cell|chtm|cldc|cmd-|co(mp|nd)|craw|da(it|ll|ng)|dbte|dc-s|devi|dica|dmob|do([cp])o|ds(12|-d)|el(49|ai)|em(l2|ul)|er(ic|k0)|esl8|ez([4-7]0|os|wa|ze)|fetc|fly([-_])|g1 u|g560|gene|gf-5|g-mo|go(\\.w|od)|gr(ad|un)|haie|hcit|hd-([mpt])|hei-|hi(pt|ta)|hp( i|ip)|hs-c|ht(c([- _agpst])|tp)|hu(aw|tc)|i-(20|go|ma)|i230|iac([ \\-/])|ibro|idea|ig01|ikom|im1k|inno|ipaq|iris|ja([tv])a|jbro|jemu|jigs|kddi|keji|kgt([ /])|klon|kpt |kwc-|kyo([ck])|le(no|xi)|lg( g|\\/([klu])|50|54|-[a-w])|libw|lynx|m1-w|m3ga|m50\\/|ma(te|ui|xo)|mc(01|21|ca)|m-cr|me(rc|ri)|mi(o8|oa|ts)|mmef|mo(01|02|bi|de|do|t([- ov])|zz)|mt(50|p1|v )|mwbp|mywa|n10[0-2]|n20[2-3]|n30([02])|n50([025])|n7(0([01])|10)|ne(([cm])-|on|tf|wf|wg|wt)|nok([6i])|nzph|o2im|op(ti|wv)|oran|owg1|p800|pan([adt])|pdxg|pg(13|-([1-8]|c))|phil|pire|pl(ay|uc)|pn-2|po(ck|rt|se)|prox|psio|pt-g|qa-a|qc(07|12|21|32|60|-[2-7]|i-)|qtek|r380|r600|raks|rim9|ro(ve|zo)|s55\\/|sa(ge|ma|mm|ms|ny|va)|sc(01|h-|oo|p-)|sdk\\/|se(c([-01])|47|mc|nd|ri)|sgh-|shar|sie([-m])|sk-0|sl(45|id)|sm(al|ar|b3|it|t5)|so(ft|ny)|sp(01|h-|v-|v )|sy(01|mb)|t2(18|50)|t6(00|10|18)|ta(gt|lk)|tcl-|tdg-|tel([im])|tim-|t-mo|to(pl|sh)|ts(70|m-|m3|m5)|tx-9|up(\\.b|g1|si)|utst|v400|v750|veri|vi(rg|te)|vk(40|5[0-3]|-v)|vm40|voda|vulc|vx(52|53|60|61|70|80|81|83|85|98)|w3c([- ])|webc|whit|wi(g |nc|nw)|wmlb|wonu|x700|yas-|your|zeto|zte-/i.test(\n // navigatorAgent.substr(0, 4)\n // )\n // );\n },\n\n /**\n * Detects if the user is using a mobile device, see https://stackoverflow.com/questions/25542814/html5-detecting-if-youre-on-mobile-or-pc-with-javascript.\n * @returns {boolean}\n *\n * @deprecated\n *\n */\n isMobile: function () {\n return true;\n // return Type.exists(navigator) && /Android|webOS|iPhone|iPad|iPod|BlackBerry|IEMobile|Opera Mini/i.test(navigator.userAgent);\n },\n\n /**\n * Internet Explorer version. Works only for IE > 4.\n * @type Number\n * @deprecated\n */\n ieVersion: (function () {\n var div,\n all,\n v = 3;\n\n if (typeof document === 'undefined' || document === null || typeof document !== 'object') {\n return 0;\n }\n\n div = document.createElement('div');\n all = div.getElementsByTagName('i');\n\n do {\n div.innerHTML = \"\";\n } while (all[0]);\n\n return v > 4 ? v : undefined;\n })(),\n\n /**\n * Reads the width and height of an HTML element.\n * @param {String|Object} elementId id of or reference to an HTML DOM node.\n * @returns {Object} An object with the two properties width and height.\n */\n getDimensions: function (elementId, doc) {\n var element,\n display,\n els,\n originalVisibility,\n originalPosition,\n originalDisplay,\n originalWidth,\n originalHeight,\n style,\n pixelDimRegExp = /\\d+(\\.\\d*)?px/;\n\n if (!this.isBrowser || elementId === null) {\n return {\n width: 500,\n height: 500\n };\n }\n\n doc = doc || document;\n // Borrowed from prototype.js\n element = (Type.isString(elementId)) ? doc.getElementById(elementId) : elementId;\n if (!Type.exists(element)) {\n throw new Error(\n \"\\nJSXGraph: HTML container element '\" + elementId + \"' not found.\"\n );\n }\n\n display = element.style.display;\n\n // Work around a bug in Safari\n if (display !== \"none\" && display !== null) {\n if (element.clientWidth > 0 && element.clientHeight > 0) {\n return { width: element.clientWidth, height: element.clientHeight };\n }\n\n // A parent might be set to display:none; try reading them from styles\n style = window.getComputedStyle ? window.getComputedStyle(element) : element.style;\n return {\n width: pixelDimRegExp.test(style.width) ? parseFloat(style.width) : 0,\n height: pixelDimRegExp.test(style.height) ? parseFloat(style.height) : 0\n };\n }\n\n // All *Width and *Height properties give 0 on elements with display set to none,\n // hence we show the element temporarily\n els = element.style;\n\n // store style\n originalVisibility = els.visibility;\n originalPosition = els.position;\n originalDisplay = els.display;\n\n // show element\n els.visibility = 'hidden';\n els.position = 'absolute';\n els.display = 'block';\n\n // read the dimension\n originalWidth = element.clientWidth;\n originalHeight = element.clientHeight;\n\n // restore original css values\n els.display = originalDisplay;\n els.position = originalPosition;\n els.visibility = originalVisibility;\n\n return {\n width: originalWidth,\n height: originalHeight\n };\n },\n\n /**\n * Adds an event listener to a DOM element.\n * @param {Object} obj Reference to a DOM node.\n * @param {String} type The event to catch, without leading 'on', e.g. 'mousemove' instead of 'onmousemove'.\n * @param {Function} fn The function to call when the event is triggered.\n * @param {Object} owner The scope in which the event trigger is called.\n * @param {Object|Boolean} [options=false] This parameter is passed as the third parameter to the method addEventListener. Depending on the data type it is either\n * an options object or the useCapture Boolean.\n *\n */\n addEvent: function (obj, type, fn, owner, options) {\n var el = function () {\n return fn.apply(owner, arguments);\n };\n\n el.origin = fn;\n // Check if owner is a board\n if (typeof owner === 'object' && Type.exists(owner.BOARD_MODE_NONE)) {\n owner['x_internal' + type] = owner['x_internal' + type] || [];\n owner['x_internal' + type].push(el);\n }\n\n // Non-IE browser\n if (Type.exists(obj) && Type.exists(obj.addEventListener)) {\n options = options || false; // options or useCapture\n obj.addEventListener(type, el, options);\n }\n\n // IE\n if (Type.exists(obj) && Type.exists(obj.attachEvent)) {\n obj.attachEvent(\"on\" + type, el);\n }\n },\n\n /**\n * Removes an event listener from a DOM element.\n * @param {Object} obj Reference to a DOM node.\n * @param {String} type The event to catch, without leading 'on', e.g. 'mousemove' instead of 'onmousemove'.\n * @param {Function} fn The function to call when the event is triggered.\n * @param {Object} owner The scope in which the event trigger is called.\n */\n removeEvent: function (obj, type, fn, owner) {\n var i;\n\n if (!Type.exists(owner)) {\n JXG.debug(\"no such owner\");\n return;\n }\n\n if (!Type.exists(owner[\"x_internal\" + type])) {\n JXG.debug(\"removeEvent: no such type: \" + type);\n return;\n }\n\n if (!Type.isArray(owner[\"x_internal\" + type])) {\n JXG.debug(\"owner[x_internal + \" + type + \"] is not an array\");\n return;\n }\n\n i = Type.indexOf(owner[\"x_internal\" + type], fn, 'origin');\n\n if (i === -1) {\n JXG.debug(\"removeEvent: no such event function in internal list: \" + fn);\n return;\n }\n\n try {\n // Non-IE browser\n if (Type.exists(obj) && Type.exists(obj.removeEventListener)) {\n obj.removeEventListener(type, owner[\"x_internal\" + type][i], false);\n }\n\n // IE\n if (Type.exists(obj) && Type.exists(obj.detachEvent)) {\n obj.detachEvent(\"on\" + type, owner[\"x_internal\" + type][i]);\n }\n } catch (e) {\n JXG.debug(\"removeEvent: event not registered in browser: (\" + type + \" -- \" + fn + \")\");\n }\n\n owner[\"x_internal\" + type].splice(i, 1);\n },\n\n /**\n * Removes all events of the given type from a given DOM node; Use with caution and do not use it on a container div\n * of a {@link JXG.Board} because this might corrupt the event handling system.\n * @param {Object} obj Reference to a DOM node.\n * @param {String} type The event to catch, without leading 'on', e.g. 'mousemove' instead of 'onmousemove'.\n * @param {Object} owner The scope in which the event trigger is called.\n */\n removeAllEvents: function (obj, type, owner) {\n var i, len;\n if (owner[\"x_internal\" + type]) {\n len = owner[\"x_internal\" + type].length;\n\n for (i = len - 1; i >= 0; i--) {\n JXG.removeEvent(obj, type, owner[\"x_internal\" + type][i].origin, owner);\n }\n\n if (owner[\"x_internal\" + type].length > 0) {\n JXG.debug(\"removeAllEvents: Not all events could be removed.\");\n }\n }\n },\n\n /**\n * Cross browser mouse / pointer / touch coordinates retrieval relative to the documents's top left corner.\n * This method might be a bit outdated today, since pointer events and clientX/Y are omnipresent.\n *\n * @param {Object} [e] The browsers event object. If omitted, window.event will be used.\n * @param {Number} [index] If e is a touch event, this provides the index of the touch coordinates, i.e. it determines which finger.\n * @param {Object} [doc] The document object.\n * @returns {Array} Contains the position as x,y-coordinates in the first resp. second component.\n */\n getPosition: function (e, index, doc) {\n var i,\n len,\n evtTouches,\n posx = 0,\n posy = 0;\n\n if (!e) {\n e = window.event;\n }\n\n doc = doc || document;\n evtTouches = e['touches']; // iOS touch events\n\n // touchend events have their position in \"changedTouches\"\n if (Type.exists(evtTouches) && evtTouches.length === 0) {\n evtTouches = e.changedTouches;\n }\n\n if (Type.exists(index) && Type.exists(evtTouches)) {\n if (index === -1) {\n len = evtTouches.length;\n\n for (i = 0; i < len; i++) {\n if (evtTouches[i]) {\n e = evtTouches[i];\n break;\n }\n }\n } else {\n e = evtTouches[index];\n }\n }\n\n // Scrolling is ignored.\n // e.clientX is supported since IE6\n if (e.clientX) {\n posx = e.clientX;\n posy = e.clientY;\n }\n\n return [posx, posy];\n },\n\n /**\n * Calculates recursively the offset of the DOM element in which the board is stored.\n * @param {Object} obj A DOM element\n * @returns {Array} An array with the elements left and top offset.\n */\n getOffset: function (obj) {\n var cPos,\n o = obj,\n o2 = obj,\n l = o.offsetLeft - o.scrollLeft,\n t = o.offsetTop - o.scrollTop;\n\n cPos = this.getCSSTransform([l, t], o);\n l = cPos[0];\n t = cPos[1];\n\n /*\n * In Mozilla and Webkit: offsetParent seems to jump at least to the next iframe,\n * if not to the body. In IE and if we are in an position:absolute environment\n * offsetParent walks up the DOM hierarchy.\n * In order to walk up the DOM hierarchy also in Mozilla and Webkit\n * we need the parentNode steps.\n */\n o = o.offsetParent;\n while (o) {\n l += o.offsetLeft;\n t += o.offsetTop;\n\n if (o.offsetParent) {\n l += o.clientLeft - o.scrollLeft;\n t += o.clientTop - o.scrollTop;\n }\n\n cPos = this.getCSSTransform([l, t], o);\n l = cPos[0];\n t = cPos[1];\n\n o2 = o2.parentNode;\n\n while (o2 !== o) {\n l += o2.clientLeft - o2.scrollLeft;\n t += o2.clientTop - o2.scrollTop;\n\n cPos = this.getCSSTransform([l, t], o2);\n l = cPos[0];\n t = cPos[1];\n\n o2 = o2.parentNode;\n }\n o = o.offsetParent;\n }\n\n return [l, t];\n },\n\n /**\n * Access CSS style sheets.\n * @param {Object} obj A DOM element\n * @param {String} stylename The CSS property to read.\n * @returns The value of the CSS property and undefined if it is not set.\n */\n getStyle: function (obj, stylename) {\n var r,\n doc = obj.ownerDocument;\n\n // Non-IE\n if (doc.defaultView && doc.defaultView.getComputedStyle) {\n r = doc.defaultView.getComputedStyle(obj, null).getPropertyValue(stylename);\n // IE\n } else if (obj.currentStyle && JXG.ieVersion >= 9) {\n r = obj.currentStyle[stylename];\n } else {\n if (obj.style) {\n // make stylename lower camelcase\n stylename = stylename.replace(/-([a-z]|[0-9])/gi, function (all, letter) {\n return letter.toUpperCase();\n });\n r = obj.style[stylename];\n }\n }\n\n return r;\n },\n\n /**\n * Reads css style sheets of a given element. This method is a getStyle wrapper and\n * defaults the read value to 0 if it can't be parsed as an integer value.\n * @param {DOMElement} el\n * @param {string} css\n * @returns {number}\n */\n getProp: function (el, css) {\n var n = parseInt(this.getStyle(el, css), 10);\n return isNaN(n) ? 0 : n;\n },\n\n /**\n * Correct position of upper left corner in case of\n * a CSS transformation. Here, only translations are\n * extracted. All scaling transformations are corrected\n * in {@link JXG.Board#getMousePosition}.\n * @param {Array} cPos Previously determined position\n * @param {Object} obj A DOM element\n * @returns {Array} The corrected position.\n */\n getCSSTransform: function (cPos, obj) {\n var i,\n j,\n str,\n arrStr,\n start,\n len,\n len2,\n arr,\n t = [\n \"transform\",\n \"webkitTransform\",\n \"MozTransform\",\n \"msTransform\",\n \"oTransform\"\n ];\n\n // Take the first transformation matrix\n len = t.length;\n\n for (i = 0, str = \"\"; i < len; i++) {\n if (Type.exists(obj.style[t[i]])) {\n str = obj.style[t[i]];\n break;\n }\n }\n\n /**\n * Extract the coordinates and apply the transformation\n * to cPos\n */\n if (str !== \"\") {\n start = str.indexOf(\"(\");\n\n if (start > 0) {\n len = str.length;\n arrStr = str.substring(start + 1, len - 1);\n arr = arrStr.split(\",\");\n\n for (j = 0, len2 = arr.length; j < len2; j++) {\n arr[j] = parseFloat(arr[j]);\n }\n\n if (str.indexOf('matrix') === 0) {\n cPos[0] += arr[4];\n cPos[1] += arr[5];\n } else if (str.indexOf('translateX') === 0) {\n cPos[0] += arr[0];\n } else if (str.indexOf('translateY') === 0) {\n cPos[1] += arr[0];\n } else if (str.indexOf('translate') === 0) {\n cPos[0] += arr[0];\n cPos[1] += arr[1];\n }\n }\n }\n\n // Zoom is used by reveal.js\n if (Type.exists(obj.style.zoom)) {\n str = obj.style.zoom;\n if (str !== \"\") {\n cPos[0] *= parseFloat(str);\n cPos[1] *= parseFloat(str);\n }\n }\n\n return cPos;\n },\n\n /**\n * Scaling CSS transformations applied to the div element containing the JSXGraph constructions\n * are determined. In IE prior to 9, 'rotate', 'skew', 'skewX', 'skewY' are not supported.\n * @returns {Array} 3x3 transformation matrix without translation part. See {@link JXG.Board#updateCSSTransforms}.\n */\n getCSSTransformMatrix: function (obj) {\n var i, j, str, arrstr, arr,\n start, len, len2, st,\n doc = obj.ownerDocument,\n t = [\n \"transform\",\n \"webkitTransform\",\n \"MozTransform\",\n \"msTransform\",\n \"oTransform\"\n ],\n mat = [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1]\n ];\n\n // This should work on all browsers except IE 6-8\n if (doc.defaultView && doc.defaultView.getComputedStyle) {\n st = doc.defaultView.getComputedStyle(obj, null);\n str =\n st.getPropertyValue(\"-webkit-transform\") ||\n st.getPropertyValue(\"-moz-transform\") ||\n st.getPropertyValue(\"-ms-transform\") ||\n st.getPropertyValue(\"-o-transform\") ||\n st.getPropertyValue('transform');\n } else {\n // Take the first transformation matrix\n len = t.length;\n for (i = 0, str = \"\"; i < len; i++) {\n if (Type.exists(obj.style[t[i]])) {\n str = obj.style[t[i]];\n break;\n }\n }\n }\n\n // Convert and reorder the matrix for JSXGraph\n if (str !== \"\") {\n start = str.indexOf(\"(\");\n\n if (start > 0) {\n len = str.length;\n arrstr = str.substring(start + 1, len - 1);\n arr = arrstr.split(\",\");\n\n for (j = 0, len2 = arr.length; j < len2; j++) {\n arr[j] = parseFloat(arr[j]);\n }\n\n if (str.indexOf('matrix') === 0) {\n mat = [\n [1, 0, 0],\n [0, arr[0], arr[1]],\n [0, arr[2], arr[3]]\n ];\n } else if (str.indexOf('scaleX') === 0) {\n mat[1][1] = arr[0];\n } else if (str.indexOf('scaleY') === 0) {\n mat[2][2] = arr[0];\n } else if (str.indexOf('scale') === 0) {\n mat[1][1] = arr[0];\n mat[2][2] = arr[1];\n }\n }\n }\n\n // CSS style zoom is used by reveal.js\n // Recursively search for zoom style entries.\n // This is necessary for reveal.js on webkit.\n // It fails if the user does zooming\n if (Type.exists(obj.style.zoom)) {\n str = obj.style.zoom;\n if (str !== \"\") {\n mat[1][1] *= parseFloat(str);\n mat[2][2] *= parseFloat(str);\n }\n }\n\n return mat;\n },\n\n /**\n * Process data in timed chunks. Data which takes long to process, either because it is such\n * a huge amount of data or the processing takes some time, causes warnings in browsers about\n * irresponsive scripts. To prevent these warnings, the processing is split into smaller pieces\n * called chunks which will be processed in serial order.\n * Copyright 2009 Nicholas C. Zakas. All rights reserved. MIT Licensed\n * @param {Array} items to do\n * @param {Function} process Function that is applied for every array item\n * @param {Object} context The scope of function process\n * @param {Function} callback This function is called after the last array element has been processed.\n */\n timedChunk: function (items, process, context, callback) {\n //create a clone of the original\n var todo = items.slice(),\n timerFun = function () {\n var start = +new Date();\n\n do {\n process.call(context, todo.shift());\n } while (todo.length > 0 && +new Date() - start < 300);\n\n if (todo.length > 0) {\n window.setTimeout(timerFun, 1);\n } else {\n callback(items);\n }\n };\n\n window.setTimeout(timerFun, 1);\n },\n\n /**\n * Scale and vertically shift a DOM element (usually a JSXGraph div)\n * inside of a parent DOM\n * element which is set to fullscreen.\n * This is realized with a CSS transformation.\n *\n * @param {String} wrap_id id of the parent DOM element which is in fullscreen mode\n * @param {String} inner_id id of the DOM element which is scaled and shifted\n * @param {Object} doc document object or shadow root\n * @param {Number} scale Relative size of the JSXGraph board in the fullscreen window.\n *\n * @private\n * @see JXG.Board#toFullscreen\n * @see JXG.Board#fullscreenListener\n *\n */\n scaleJSXGraphDiv: function (wrap_id, inner_id, doc, scale) {\n var w, h, b,\n wi, hi,\n wo, ho, inner,\n scale_l, vshift_l,\n f = scale,\n ratio,\n pseudo_keys = [\n \":fullscreen\",\n \":-webkit-full-screen\",\n \":-moz-full-screen\",\n \":-ms-fullscreen\"\n ],\n len_pseudo = pseudo_keys.length,\n i;\n\n b = doc.getElementById(wrap_id).getBoundingClientRect();\n h = b.height;\n w = b.width;\n\n inner = doc.getElementById(inner_id);\n wo = inner._cssFullscreenStore.w;\n ho = inner._cssFullscreenStore.h;\n ratio = ho / wo;\n\n // Scale the div such that fits into the fullscreen.\n if (wo > w * f) {\n wo = w * f;\n ho = wo * ratio;\n }\n if (ho > h * f) {\n ho = h * f;\n wo = ho / ratio;\n }\n\n wi = wo;\n hi = ho;\n // Compare the code in this.setBoundingBox()\n if (ratio > 1) {\n // h > w\n if (ratio < h / w) {\n scale_l = w * f / wo;\n } else {\n scale_l = h * f / ho;\n }\n } else {\n // h <= w\n if (ratio < h / w) {\n scale_l = w * f / wo;\n } else {\n scale_l = h * f / ho;\n }\n }\n vshift_l = (h - hi) * 0.5;\n\n // Set a CSS properties to center the JSXGraph div horizontally and vertically\n // at the first position of the fullscreen pseudo classes.\n for (i = 0; i < len_pseudo; i++) {\n try {\n inner.style.width = wi + 'px !important';\n inner.style.height = hi + 'px !important';\n inner.style.margin = '0 auto';\n // Add the transform to a possibly already existing transform\n inner.style.transform = inner._cssFullscreenStore.transform +\n ' matrix(' + scale_l + ',0,0,' + scale_l + ',0,' + vshift_l + ')';\n break;\n } catch (err) {\n JXG.debug(\"JXG.scaleJSXGraphDiv:\\n\" + err);\n }\n }\n if (i === len_pseudo) {\n JXG.debug(\"JXG.scaleJSXGraphDiv: Could not set any CSS property.\");\n }\n }\n\n }\n);\n\nexport default JXG;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * In contrast to method JXG.mergeAttr, merge recurses into any kind of object, e.g. DOM object and JSXGraph objects.\n * So, please be careful.\n * @param {Object} obj1\n * @param {Object} obj2\n * @returns {Object}\n * @see JXG.mergeAttr\n *\n * @example\n * JXG.Options = JXG.merge(JXG.Options, {\n * board: {\n * showNavigation: false,\n * showInfobox: true\n * },\n * point: {\n * face: 'o',\n * size: 4,\n * fillColor: '#eeeeee',\n * highlightFillColor: '#eeeeee',\n * strokeColor: 'white',\n * highlightStrokeColor: 'white',\n * showInfobox: 'inherit'\n * }\n * });\n *\n * \n * In contrast to method JXG.merge, mergeAttr does not recurse into DOM objects and JSXGraph objects. Instead\n * handles (pointers) to these objects are used.\n *\n * @param {Object} attr Object with attributes - usually containing default options - that will be changed in-place.\n * @param {Object} special Special option values which overwrite (recursively) the default options\n * @param {Boolean} [toLower=true] If true the keys are converted to lower case.\n * @param {Boolean} [ignoreUndefinedSpecials=false] If true the values in special that are undefined are not used.\n *\n * @see JXG.merge\n *\n */\n mergeAttr: function (attr, special, toLower, ignoreUndefinedSpecials) {\n var e, e2, o;\n\n toLower = toLower || true;\n ignoreUndefinedSpecials = ignoreUndefinedSpecials || false;\n\n for (e in special) {\n if (special.hasOwnProperty(e)) {\n e2 = (toLower) ? e.toLowerCase(): e;\n // Key already exists, but not in lower case\n if (e2 !== e && attr.hasOwnProperty(e)) {\n if (attr.hasOwnProperty(e2)) {\n // Lower case key already exists - this should not happen\n // We have to unify the two key-value pairs\n // It is not clear which has precedence.\n this.mergeAttr(attr[e2], attr[e], toLower);\n } else {\n attr[e2] = attr[e];\n }\n delete attr[e];\n }\n\n o = special[e];\n if (this.isObject(o) && o !== null &&\n // Do not recurse into a document object or a JSXGraph object\n !this.isDocumentOrFragment(o) && !this.exists(o.board) &&\n // Do not recurse if a string is provided as \"new String(...)\"\n typeof o.valueOf() !== 'string') {\n if (attr[e2] === undefined || attr[e2] === null || !this.isObject(attr[e2])) {\n // The last test handles the case:\n // attr.draft = false;\n // special.draft = { strokewidth: 4}\n attr[e2] = {};\n }\n this.mergeAttr(attr[e2], o, toLower);\n } else if(!ignoreUndefinedSpecials || this.exists(o)) {\n // Flat copy\n // This is also used in the cases\n // attr.shadow = { enabled: true ...}\n // special.shadow = false;\n // and\n // special.anchor is a JSXGraph element\n attr[e2] = o;\n }\n }\n }\n },\n\n /**\n * Convert an object to a new object containing only\n * lower case properties.\n *\n * @param {Object} obj\n * @returns Object\n * @example\n * var attr = JXG.keysToLowerCase({radiusPoint: {visible: false}});\n *\n * // return {radiuspoint: {visible: false}}\n */\n keysToLowerCase: function (obj) {\n var key, val,\n keys = Object.keys(obj),\n n = keys.length,\n newObj = {};\n\n if (typeof obj !== 'object') {\n return obj;\n }\n\n while (n--) {\n key = keys[n];\n if (obj.hasOwnProperty(key)) {\n // We recurse into an object only if it is\n // neither a DOM node nor an JSXGraph object\n val = obj[key];\n if (typeof val === 'object' && val !== null &&\n !this.isArray(val) &&\n !this.exists(val.nodeType) &&\n !this.exists(val.board)) {\n newObj[key.toLowerCase()] = this.keysToLowerCase(val);\n } else {\n newObj[key.toLowerCase()] = val;\n }\n }\n }\n return newObj;\n },\n\n /**\n * Generates an attributes object that is filled with default values from the Options object\n * and overwritten by the user specified attributes.\n * @param {Object} attributes user specified attributes\n * @param {Object} options defaults options\n * @param {String} s variable number of strings, e.g. 'slider', subtype 'point1'. Must be provided in lower case!\n * @returns {Object} The resulting attributes object\n */\n copyAttributes: function (attributes, options, s) {\n var a, arg, i, len, o, isAvail,\n primitives = {\n circle: 1,\n curve: 1,\n foreignobject: 1,\n image: 1,\n line: 1,\n point: 1,\n polygon: 1,\n text: 1,\n ticks: 1,\n integral: 1\n };\n\n len = arguments.length;\n // Old code: if (len < 3 || primitives[s]) {\n // If len > 3, the element is certainly not a primitive object,\n // e.g. copyAttributes(attributes, JXG.Options, 'line', 'point1').\n // That is, a later create('point', ...) will be the primitive call.\n // This will not yet cover all cases of inheritance.\n if (len < 3 || (len === 3 && primitives[s])) {\n // Default options from Options.elements\n a = JXG.deepCopy(options.elements, null, true);\n } else {\n a = {};\n }\n\n // Only the layer of the main element is set.\n if (len < 4 && this.exists(s) && this.exists(options.layer[s])) {\n a.layer = options.layer[s];\n }\n\n // Default options from the specific element like 'line' in\n // copyAttribute(attributes, board.options, 'line')\n // but also like in\n // Type.copyAttributes(attributes, board.options, 'view3d', 'az', 'slider');\n o = options;\n isAvail = true;\n for (i = 2; i < len; i++) {\n arg = arguments[i];\n if (this.exists(o[arg])) {\n o = o[arg];\n } else {\n isAvail = false;\n break;\n }\n }\n if (isAvail) {\n a = JXG.deepCopy(a, o, true);\n }\n\n // Merge the specific options given in the parameter 'attributes'\n // into the default options.\n // Additionally, we step into a sub-element of attribute like line.point1 -\n // in case it is supplied as in\n // copyAttribute(attributes, board.options, 'line', 'point1')\n // In this case we would merge attributes.point1 into the global line.point1 attributes.\n o = (typeof attributes === 'object') ? this.keysToLowerCase(attributes) : {};\n isAvail = true;\n for (i = 3; i < len; i++) {\n arg = arguments[i].toLowerCase();\n if (this.exists(o[arg])) {\n o = o[arg];\n } else {\n isAvail = false;\n break;\n }\n }\n if (isAvail) {\n this.mergeAttr(a, o, true);\n }\n\n if (arguments[2] === 'board') {\n // For board attributes we are done now.\n return a;\n }\n\n // Special treatment of labels\n o = options;\n isAvail = true;\n for (i = 2; i < len; i++) {\n arg = arguments[i];\n if (this.exists(o[arg])) {\n o = o[arg];\n } else {\n isAvail = false;\n break;\n }\n }\n if (isAvail && this.exists(o.label)) {\n a.label = JXG.deepCopy(o.label, a.label, true);\n }\n a.label = JXG.deepCopy(options.label, a.label, true);\n\n return a;\n },\n\n /**\n * Copy all prototype methods from object \"superObject\" to object\n * \"subObject\". The constructor of superObject will be available\n * in subObject as subObject.constructor[constructorName].\n * @param {Object} subObject A JavaScript object which receives new methods.\n * @param {Object} superObject A JavaScript object which lends its prototype methods to subObject\n * @param {String} constructorName Under this name the constructor of superObj will be available\n * in subObject.\n * @private\n */\n copyPrototypeMethods: function (subObject, superObject, constructorName) {\n var key;\n\n subObject.prototype[constructorName] = superObject.prototype.constructor;\n for (key in superObject.prototype) {\n if (superObject.prototype.hasOwnProperty(key)) {\n if (key === 'methodMap') {\n JXG.copyMethodMap(subObject, superObject.prototype.methodMap);\n } else {\n subObject.prototype[key] = superObject.prototype[key];\n }\n }\n }\n },\n\n /**\n * Create a copy of methodMap in \"objectClass.prototype\" and optional extend it.\n * If objectClass.prototype.methodMap does not exist, it will be initialized.\n *\n * The methodMap determines which methods can be called from within JessieCode and under which name it\n * can be used. The map is saved in an object, the name of a property is the name of the method used in JessieCode,\n * the value of a property is the name of the method in JavaScript.\n *\n * @param {Object} objectClass\n * @param {Object} [extension]\n * @private\n */\n copyMethodMap: function (objectClass, extension) {\n extension = extension || {};\n\n objectClass.prototype.methodMap = objectClass.prototype.methodMap || {};\n objectClass.prototype.methodMap = this.deepCopy(objectClass.prototype.methodMap, extension);\n },\n\n /**\n * Copy methodMap of \"object.prototype\" to objects instance and optional extend it.\n * If extension is of type String and extensionValue is defined, a key-value-pair is added.\n *\n * The methodMap determines which methods can be called from within JessieCode and under which name it\n * can be used. The map is saved in an object, the name of a property is the name of the method used in JessieCode,\n * the value of a property is the name of the method in JavaScript.\n *\n * @param {Object} object\n * @param {Object|String} [extension]\n * @param {String} [extensionValue]\n * @private\n */\n extendInstanceMethodMap: function (object, extension, extensionValue) {\n extension = extension || {};\n\n // Create own copy only if instance still uses prototype version\n if (!object.hasOwnProperty(\"methodMap\")) {\n object.methodMap = Object.assign({}, object.methodMap);\n }\n\n if (this.isObject(extension)) {\n object.methodMap = this.deepCopy(object.methodMap, extension);\n } else if (this.isString(extension) && this.exists(extensionValue)) {\n object.methodMap[extension] = extensionValue;\n }\n },\n\n /**\n * Create a stripped down version of a JSXGraph element for cloning to the background.\n * Used in {JXG.GeometryElement#cloneToBackground} for creating traces.\n *\n * @param {JXG.GeometryElement} el Element to be cloned\n * @returns Object Cloned element\n * @private\n */\n getCloneObject: function(el) {\n var obj, key,\n copy = {};\n\n copy.id = el.id + \"T\" + el.numTraces;\n el.numTraces += 1;\n\n copy.coords = el.coords;\n obj = this.deepCopy(el.visProp, el.visProp.traceattributes, true);\n copy.visProp = {};\n for (key in obj) {\n if (obj.hasOwnProperty(key)) {\n if (\n key.indexOf('aria') !== 0 &&\n key.indexOf('highlight') !== 0 &&\n key.indexOf('attractor') !== 0 &&\n key !== 'label' &&\n key !== 'needsregularupdate' &&\n key !== 'infoboxdigits'\n ) {\n copy.visProp[key] = el.eval(obj[key]);\n }\n }\n }\n copy.evalVisProp = function(val) {\n return copy.visProp[val];\n };\n copy.eval = function(val) {\n return val;\n };\n\n copy.visProp.layer = el.board.options.layer.trace;\n copy.visProp.tabindex = null;\n copy.visProp.highlight = false;\n copy.board = el.board;\n copy.elementClass = el.elementClass;\n\n this.clearVisPropOld(copy);\n copy.visPropCalc = {\n visible: el.evalVisProp('visible')\n };\n\n return copy;\n },\n\n /**\n * Converts a JavaScript object into a JSON string.\n * @param {Object} obj A JavaScript object, functions will be ignored.\n * @param {Boolean} [noquote=false] No quotes around the name of a property.\n * @returns {String} The given object stored in a JSON string.\n * @deprecated\n */\n toJSON: function (obj, noquote) {\n var list, prop, i, s, val;\n\n noquote = JXG.def(noquote, false);\n\n // check for native JSON support:\n if (JSON !== undefined && JSON.stringify && !noquote) {\n try {\n s = JSON.stringify(obj);\n return s;\n } catch (e) {\n // if something goes wrong, e.g. if obj contains functions we won't return\n // and use our own implementation as a fallback\n }\n }\n\n switch (typeof obj) {\n case \"object\":\n if (obj) {\n list = [];\n\n if (this.isArray(obj)) {\n for (i = 0; i < obj.length; i++) {\n list.push(JXG.toJSON(obj[i], noquote));\n }\n\n return \"[\" + list.join(\",\") + \"]\";\n }\n\n for (prop in obj) {\n if (obj.hasOwnProperty(prop)) {\n try {\n val = JXG.toJSON(obj[prop], noquote);\n } catch (e2) {\n val = \"\";\n }\n\n if (noquote) {\n list.push(prop + \":\" + val);\n } else {\n list.push('\"' + prop + '\":' + val);\n }\n }\n }\n\n return \"{\" + list.join(\",\") + \"} \";\n }\n return 'null';\n case \"string\":\n return \"'\" + obj.replace(/([\"'])/g, \"\\\\$1\") + \"'\";\n case \"number\":\n case \"boolean\":\n return obj.toString();\n }\n\n return '0';\n },\n\n /**\n * Resets visPropOld.\n * @param {JXG.GeometryElement} el\n * @returns {GeometryElement}\n */\n clearVisPropOld: function (el) {\n el.visPropOld = {\n cssclass: \"\",\n cssdefaultstyle: \"\",\n cssstyle: \"\",\n fillcolor: \"\",\n fillopacity: \"\",\n firstarrow: false,\n fontsize: -1,\n lastarrow: false,\n left: -100000,\n linecap: \"\",\n shadow: false,\n strokecolor: \"\",\n strokeopacity: \"\",\n strokewidth: \"\",\n tabindex: -100000,\n transitionduration: 0,\n top: -100000,\n visible: null\n };\n\n return el;\n },\n\n /**\n * Checks if an object contains a key, whose value equals to val.\n * @param {Object} obj\n * @param val\n * @returns {Boolean}\n */\n isInObject: function (obj, val) {\n var el;\n\n for (el in obj) {\n if (obj.hasOwnProperty(el)) {\n if (obj[el] === val) {\n return true;\n }\n }\n }\n\n return false;\n },\n\n /**\n * Replaces all occurences of & by &, > by >, and < by <.\n * @param {String} str\n * @returns {String}\n */\n escapeHTML: function (str) {\n return str.replace(/&/g, \"&\").replace(//g, \">\");\n },\n\n /**\n * Eliminates all substrings enclosed by < and > and replaces all occurences of\n * & by &, > by >, and < by <.\n * @param {String} str\n * @returns {String}\n */\n unescapeHTML: function (str) {\n // This regex is NOT insecure. We are replacing everything found with ''\n /*jslint regexp:true*/\n return str\n .replace(/<\\/?[^>]+>/gi, \"\")\n .replace(/&/g, \"&\")\n .replace(/</g, \"<\")\n .replace(/>/g, \">\");\n },\n\n /**\n * Makes a string lower case except for the first character which will be upper case.\n * @param {String} str Arbitrary string\n * @returns {String} The capitalized string.\n */\n capitalize: function (str) {\n return str.charAt(0).toUpperCase() + str.substring(1).toLowerCase();\n },\n\n /**\n * Make numbers given as strings nicer by removing all unnecessary leading and trailing zeroes.\n * @param {String} str\n * @returns {String}\n */\n trimNumber: function (str) {\n str = str.replace(/^0+/, \"\");\n str = str.replace(/0+$/, \"\");\n\n if (str[str.length - 1] === \".\" || str[str.length - 1] === \",\") {\n str = str.slice(0, -1);\n }\n\n if (str[0] === \".\" || str[0] === \",\") {\n str = \"0\" + str;\n }\n\n return str;\n },\n\n /**\n * Filter an array of elements.\n * @param {Array} list\n * @param {Object|function} filter\n * @returns {Array}\n */\n filterElements: function (list, filter) {\n var i,\n f,\n item,\n flower,\n value,\n visPropValue,\n pass,\n l = list.length,\n result = [];\n\n if (this.exists(filter) && typeof filter !== \"function\" && typeof filter !== 'object') {\n return result;\n }\n\n for (i = 0; i < l; i++) {\n pass = true;\n item = list[i];\n\n if (typeof filter === 'object') {\n for (f in filter) {\n if (filter.hasOwnProperty(f)) {\n flower = f.toLowerCase();\n\n if (typeof item[f] === 'function') {\n value = item[f]();\n } else {\n value = item[f];\n }\n\n if (item.visProp && typeof item.visProp[flower] === 'function') {\n visPropValue = item.visProp[flower]();\n } else {\n visPropValue = item.visProp && item.visProp[flower];\n }\n\n if (typeof filter[f] === 'function') {\n pass = filter[f](value) || filter[f](visPropValue);\n } else {\n pass = value === filter[f] || visPropValue === filter[f];\n }\n\n if (!pass) {\n break;\n }\n }\n }\n } else if (typeof filter === 'function') {\n pass = filter(item);\n }\n\n if (pass) {\n result.push(item);\n }\n }\n\n return result;\n },\n\n /**\n * Remove all leading and trailing whitespaces from a given string.\n * @param {String} str\n * @returns {String}\n */\n trim: function (str) {\n // str = str.replace(/^\\s+/, '');\n // str = str.replace(/\\s+$/, '');\n //\n // return str;\n return str.replace(/^[\\s\\uFEFF\\xA0]+|[\\s\\uFEFF\\xA0]+$/g, \"\");\n },\n\n /**\n * Convert a floating point number to a string integer + fraction.\n * Returns either a string of the form '3 1/3' (in case of useTeX=false)\n * or '3 \\\\frac{1}{3}' (in case of useTeX=true).\n *\n * @param {Number} x\n * @param {Boolean} [useTeX=false]\n * @param {Number} [order=0.001]\n * @returns {String}\n * @see JXG.Math.decToFraction\n */\n toFraction: function (x, useTeX, order) {\n var arr = Mat.decToFraction(x, order),\n str = '';\n\n if (arr[1] === 0 && arr[2] === 0) {\n // 0\n str += '0';\n } else {\n // Sign\n if (arr[0] < 0) {\n str += '-';\n }\n if (arr[2] === 0) {\n // Integer\n str += arr[1];\n } else if (!(arr[2] === 1 && arr[3] === 1)) {\n // Proper fraction\n if (arr[1] !== 0) {\n // Absolute value larger than 1\n str += arr[1] + ' ';\n }\n // Add fractional part\n if (useTeX === true) {\n str += '\\\\frac{' + arr[2] + '}{' + arr[3] + '}';\n } else {\n str += arr[2] + '/' + arr[3];\n }\n }\n }\n return str;\n },\n\n /**\n * Concat array src to array dest.\n * Uses push instead of JavaScript concat, which is much\n * faster.\n * The array dest is changed in place.\n * Attention: if \"dest\" is an anonymous array, the correct result is returned from the function.\n *\n * @param {Array} dest\n * @param {Array} src\n * @returns Array\n */\n concat: function(dest, src) {\n var i,\n le = src.length;\n for (i = 0; i < le; i++) {\n dest.push(src[i]);\n }\n return dest;\n },\n\n /**\n * Convert HTML tags to entities or use html_sanitize if the google caja html sanitizer is available.\n * @param {String} str\n * @param {Boolean} caja\n * @returns {String} Sanitized string\n */\n sanitizeHTML: function (str, caja) {\n if (typeof html_sanitize === \"function\" && caja) {\n return html_sanitize(\n str,\n function () {\n return undefined;\n },\n function (id) {\n return id;\n }\n );\n }\n\n if (str && typeof str === 'string') {\n str = str.replace(//g, \">\");\n }\n\n return str;\n },\n\n /**\n * If s is a slider, it returns the sliders value, otherwise it just returns the given value.\n * @param {*} s\n * @returns {*} s.Value() if s is an element of type slider, s otherwise\n */\n evalSlider: function (s) {\n if (s && s.type === Const.OBJECT_TYPE_GLIDER && typeof s.Value === 'function') {\n return s.Value();\n }\n\n return s;\n },\n\n /**\n * Convert a string containing a MAXIMA /STACK expression into a JSXGraph / JessieCode string\n * or an array of JSXGraph / JessieCode strings.\n * \n * This function is meanwhile superseded by stack_jxg.stack2jsxgraph.\n *\n * @deprecated\n *\n * @example\n * console.log( JXG.stack2jsxgraph(\"%e**x\") );\n * // Output:\n * // \"EULER**x\"\n *\n * @example\n * console.log( JXG.stack2jsxgraph(\"[%pi*(x**2 - 1), %phi*(x - 1), %gamma*(x+1)]\") );\n * // Output:\n * // [ \"PI*(x**2 - 1)\", \"1.618033988749895*(x - 1)\", \"0.5772156649015329*(x+1)\" ]\n *\n * @param {String} str\n * @returns String\n */\n stack2jsxgraph: function(str) {\n var t;\n\n t = str.\n replace(/%pi/g, 'PI').\n replace(/%e/g, 'EULER').\n replace(/%phi/g, '1.618033988749895').\n replace(/%gamma/g, '0.5772156649015329').\n trim();\n\n // String containing array -> array containing strings\n if (t[0] === '[' && t[t.length - 1] === ']') {\n t = t.slice(1, -1).split(/\\s*,\\s*/);\n }\n\n return t;\n }\n }\n);\n\nexport default JXG;\n","// The module cache\nconst __webpack_module_cache__ = {};\n\n// The require function\nfunction __webpack_require__(moduleId) {\n\t// Check if module is in cache\n\tconst cachedModule = __webpack_module_cache__[moduleId];\n\tif (cachedModule !== undefined) {\n\t\treturn cachedModule.exports;\n\t}\n\t// Create a new module (and put it into the cache)\n\tconst module = __webpack_module_cache__[moduleId] = {\n\t\t// no module.id needed\n\t\t// no module.loaded needed\n\t\texports: {}\n\t};\n\n\t// Execute the module function\n\t__webpack_modules__[moduleId](module, module.exports, __webpack_require__);\n\n\t// Return the exports of the module\n\treturn module.exports;\n}\n\n","// define getter/value functions for harmony exports\n__webpack_require__.d = (exports, definition) => {\n\tif(Array.isArray(definition)) {\n\t\tvar i = 0;\n\t\twhile(i < definition.length) {\n\t\t\tvar key = definition[i++];\n\t\t\tvar binding = definition[i++];\n\t\t\tif(!__webpack_require__.o(exports, key)) {\n\t\t\t\tif(binding === 0) {\n\t\t\t\t\tObject.defineProperty(exports, key, { enumerable: true, value: definition[i++] });\n\t\t\t\t} else {\n\t\t\t\t\tObject.defineProperty(exports, key, { enumerable: true, get: binding });\n\t\t\t\t}\n\t\t\t} else if(binding === 0) { i++; }\n\t\t}\n\t} else {\n\t\tfor(var key in definition) {\n\t\t\tif(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {\n\t\t\t\tObject.defineProperty(exports, key, { enumerable: true, get: definition[key] });\n\t\t\t}\n\t\t}\n\t}\n};","__webpack_require__.o = (obj, prop) => (Object.prototype.hasOwnProperty.call(obj, prop))","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * This method is necessary to restrict the recursive plotting algorithm\n * {@link JXG.Curve._plotRecursive} to the visible area and not waste\n * recursion to areas far outside of the visible area.\n * \n * This method can also be used to find the last visible point\n * by reversing the input parameters.\n *\n * @param {JXG.Curve} curve JSXGraph curve element\n * @param {Array} ta Curve parameter of a.\n * @param {Array} b Screen coordinates of the end point of the segment (unused)\n * @param {Array} tb Curve parameter of b\n * @return {Array} Array of length two containing the screen ccordinates of\n * the starting point and the curve parameter at this point.\n * @private\n */\n _findStartPoint: function (curve, a, ta, b, tb) {\n // The code below is too unstable.\n // E.g. [function(t) { return Math.pow(t, 2) * (t + 5) * Math.pow(t - 5, 2); }, -8, 8]\n // Therefore, we return here.\n return [a, ta];\n\n // var i,\n // delta,\n // tc,\n // td,\n // z,\n // isFound,\n // w2,\n // h2,\n // pnt = new Coords(Const.COORDS_BY_USER, [0, 0], curve.board, false),\n // steps = 40,\n // eps = 0.01,\n // fnX1,\n // fnX2,\n // fnY1,\n // fnY2,\n // bbox = curve.board.getBoundingBox();\n\n // if (true || !this._isOutsidePoint(a, curve.board)) {\n // return [a, ta];\n // }\n // w2 = (bbox[2] - bbox[0]) * 0.3;\n // h2 = (bbox[1] - bbox[3]) * 0.3;\n // bbox[0] -= w2;\n // bbox[1] += h2;\n // bbox[2] += w2;\n // bbox[3] -= h2;\n\n // delta = (tb - ta) / steps;\n // tc = ta + delta;\n // isFound = false;\n\n // fnX1 = function (t) {\n // return curve.X(t, true) - bbox[0];\n // };\n // fnY1 = function (t) {\n // return curve.Y(t, true) - bbox[1];\n // };\n // fnX2 = function (t) {\n // return curve.X(t, true) - bbox[2];\n // };\n // fnY2 = function (t) {\n // return curve.Y(t, true) - bbox[3];\n // };\n // for (i = 0; i < steps; ++i) {\n // // Left border\n // z = bbox[0];\n // td = Numerics.root(fnX1, [tc - delta, tc], curve);\n // // td = Numerics.fzero(fnX1, [tc - delta, tc], this);\n // // console.log(\"A\", tc - delta, tc, td, Math.abs(this.X(td, true) - z));\n // if (Math.abs(curve.X(td, true) - z) < eps) {\n // //} * Math.abs(z)) {\n // isFound = true;\n // break;\n // }\n // // Top border\n // z = bbox[1];\n // td = Numerics.root(fnY1, [tc - delta, tc], curve);\n // // td = Numerics.fzero(fnY1, [tc - delta, tc], this);\n // // console.log(\"B\", tc - delta, tc, td, Math.abs(this.Y(td, true) - z));\n // if (Math.abs(curve.Y(td, true) - z) < eps) {\n // // * Math.abs(z)) {\n // isFound = true;\n // break;\n // }\n // // Right border\n // z = bbox[2];\n // td = Numerics.root(fnX2, [tc - delta, tc], curve);\n // // td = Numerics.fzero(fnX2, [tc - delta, tc], this);\n // // console.log(\"C\", tc - delta, tc, td, Math.abs(this.X(td, true) - z));\n // if (Math.abs(curve.X(td, true) - z) < eps) {\n // // * Math.abs(z)) {\n // isFound = true;\n // break;\n // }\n // // Bottom border\n // z = bbox[3];\n // td = Numerics.root(fnY2, [tc - delta, tc], curve);\n // // td = Numerics.fzero(fnY2, [tc - delta, tc], this);\n // // console.log(\"D\", tc - delta, tc, td, Math.abs(this.Y(td, true) - z));\n // if (Math.abs(curve.Y(td, true) - z) < eps) {\n // // * Math.abs(z)) {\n // isFound = true;\n // break;\n // }\n // tc += delta;\n // }\n // if (isFound) {\n // pnt.setCoordinates(\n // Const.COORDS_BY_USER,\n // [curve.X(td, true), curve.Y(td, true)],\n // false\n // );\n // return [pnt.scrCoords, td];\n // }\n // console.log(\"TODO _findStartPoint\", curve.Y.toString(), tc);\n // pnt.setCoordinates(Const.COORDS_BY_USER, [curve.X(ta, true), curve.Y(ta, true)], false);\n // return [pnt.scrCoords, ta];\n },\n\n /**\n * Investigate a function term at the bounds of intervals where\n * the function is not defined, e.g. log(x) at x = 0.\n *\n * c is inbetween a and b\n *\n * @param {JXG.Curve} curve JSXGraph curve element\n * @param {Array} a Screen coordinates of the left interval bound\n * @param {Array} b Screen coordinates of the right interval bound\n * @param {Array} c Screen coordinates of the bisection point at (ta + tb) / 2\n * @param {Number} ta Parameter which evaluates to a, i.e. [1, X(ta), Y(ta)] = a in screen coordinates\n * @param {Number} tb Parameter which evaluates to b, i.e. [1, X(tb), Y(tb)] = b in screen coordinates\n * @param {Number} tc (ta + tb) / 2 = tc. Parameter which evaluates to b, i.e. [1, X(tc), Y(tc)] = c in screen coordinates\n * @param {Number} depth Actual recursion depth. The recursion stops if depth is equal to 0.\n * @returns {JXG.Boolean} true if the point is inserted and the recursion should stop, false otherwise.\n *\n * @private\n */\n _getBorderPos: function (curve, ta, a, tc, c, tb, b) {\n var t, pnt, p, j,\n max_it = 30,\n is_undef = false,\n t_good, t_bad;\n\n pnt = new Coords(Const.COORDS_BY_USER, [0, 0], curve.board, false);\n j = 0;\n // Bisect a, b and c until the point t_real is inside of the definition interval\n // and as close as possible at the boundary.\n // (t_real2 is/was the second closest point).\n // There are four cases:\n // a | c | b\n // ---------------\n // inf | R | R\n // R | R | inf\n // inf | inf | R\n // R | inf | inf\n //\n if (isNaN(a[1] + a[2]) && !isNaN(c[1] + c[2])) {\n t_bad = ta;\n t_good = tc;\n } else if (isNaN(b[1] + b[2]) && !isNaN(c[1] + c[2])) {\n t_bad = tb;\n t_good = tc;\n } else if (isNaN(c[1] + c[2]) && !isNaN(b[1] + b[2])) {\n t_bad = tc;\n t_good = tb;\n } else if (isNaN(c[1] + c[2]) && !isNaN(a[1] + a[2])) {\n t_bad = tc;\n t_good = ta;\n } else {\n return false;\n }\n do {\n t = 0.5 * (t_good + t_bad);\n pnt.setCoordinates(\n Const.COORDS_BY_USER,\n [curve.X(t, true), curve.Y(t, true)],\n false\n );\n p = pnt.usrCoords;\n is_undef = isNaN(p[1] + p[2]);\n if (is_undef) {\n t_bad = t;\n } else {\n t_good = t;\n }\n ++j;\n } while (j < max_it && Math.abs(t_good - t_bad) > Mat.eps);\n return t;\n },\n\n /**\n *\n * @param {JXG.Curve} curve JSXGraph curve element\n * @param {Number} ta\n * @param {Number} tb\n */\n _getCuspPos: function (curve, ta, tb) {\n var a = [curve.X(ta, true), curve.Y(ta, true)],\n b = [curve.X(tb, true), curve.Y(tb, true)],\n max_func = function (t) {\n var c = [curve.X(t, true), curve.Y(t, true)];\n return -(\n Mat.hypot(a[0] - c[0], a[1] - c[1]) +\n Mat.hypot(b[0] - c[0], b[1] - c[1])\n );\n };\n\n return Numerics.fminbr(max_func, [ta, tb], curve);\n },\n\n /**\n *\n * @param {JXG.Curve} curve JSXGraph curve element\n * @param {Number} ta\n * @param {Number} tb\n */\n _getJumpPos: function (curve, ta, tb) {\n var max_func = function (t) {\n var e = Mat.eps * Mat.eps,\n c1 = [curve.X(t, true), curve.Y(t, true)],\n c2 = [curve.X(t + e, true), curve.Y(t + e, true)];\n return -Math.abs((c2[1] - c1[1]) / (c2[0] - c1[0]));\n };\n\n return Numerics.fminbr(max_func, [ta, tb], curve);\n },\n\n /**\n *\n * @param {JXG.Curve} curve JSXGraph curve element\n * @param {Number} t\n * @private\n */\n _getLimits: function (curve, t) {\n var res,\n step = 2 / (curve.maxX() - curve.minX()),\n x_l,\n x_r,\n y_l,\n y_r;\n\n // From left\n res = Extrapolate.limit(t, -step, curve.X);\n x_l = res[0];\n if (res[1] === 'infinite') {\n x_l = Math.sign(x_l) * Infinity;\n }\n\n res = Extrapolate.limit(t, -step, curve.Y);\n y_l = res[0];\n if (res[1] === 'infinite') {\n y_l = Math.sign(y_l) * Infinity;\n }\n\n // From right\n res = Extrapolate.limit(t, step, curve.X);\n x_r = res[0];\n if (res[1] === 'infinite') {\n x_r = Math.sign(x_r) * Infinity;\n }\n\n res = Extrapolate.limit(t, step, curve.Y);\n y_r = res[0];\n if (res[1] === 'infinite') {\n y_r = Math.sign(y_r) * Infinity;\n }\n\n return {\n left_x: x_l,\n left_y: y_l,\n right_x: x_r,\n right_y: y_r,\n t: t\n };\n },\n\n /**\n *\n * @param {JXG.Curve} curve JSXGraph curve element\n * @param {Array} a\n * @param {Number} tc\n * @param {Array} c\n * @param {Number} tb\n * @param {Array} b\n * @param {String} may_be_special\n * @param {Number} depth\n * @private\n */\n _getLimes: function (curve, ta, a, tc, c, tb, b, may_be_special, depth) {\n var t;\n\n if (may_be_special === 'border') {\n t = this._getBorderPos(curve, ta, a, tc, c, tb, b);\n } else if (may_be_special === 'cusp') {\n t = this._getCuspPos(curve, ta, tb);\n } else if (may_be_special === 'jump') {\n t = this._getJumpPos(curve, ta, tb);\n }\n return this._getLimits(curve, t);\n },\n\n /**\n * Recursive interval bisection algorithm for curve plotting.\n * Used in {@link JXG.Curve.updateParametricCurve}.\n * @private\n * @param {JXG.Curve} curve JSXGraph curve element\n * @param {Array} a Screen coordinates of the left interval bound\n * @param {Number} ta Parameter which evaluates to a, i.e. [1, X(ta), Y(ta)] = a in screen coordinates\n * @param {Array} b Screen coordinates of the right interval bound\n * @param {Number} tb Parameter which evaluates to b, i.e. [1, X(tb), Y(tb)] = b in screen coordinates\n * @param {Number} depth Actual recursion depth. The recursion stops if depth is equal to 0.\n * @param {Number} delta If the distance of the bisection point at (ta + tb) / 2 from the point (a + b) / 2 is less then delta,\n * the segment [a,b] is regarded as straight line.\n * @returns {JXG.Curve} Reference to the curve object.\n */\n _plotNonRecursive: function (curve, a, ta, b, tb, d) {\n var tc,\n c,\n ds,\n mindepth = 0,\n limes = null,\n a_nan,\n b_nan,\n isSmooth = false,\n may_be_special = \"\",\n x,\n y,\n oc,\n depth,\n ds0,\n stack = [],\n stack_length = 0,\n item;\n\n oc = curve.board.origin.scrCoords;\n stack[stack_length++] = [a, ta, b, tb, d, Infinity];\n while (stack_length > 0) {\n // item = stack.pop();\n item = stack[--stack_length];\n a = item[0];\n ta = item[1];\n b = item[2];\n tb = item[3];\n depth = item[4];\n ds0 = item[5];\n\n isSmooth = false;\n may_be_special = \"\";\n limes = null;\n //console.log(stack.length, item)\n\n if (curve.points.length > 65536) {\n return;\n }\n\n if (depth < this.nanLevel) {\n // Test if the function is undefined in the whole interval [ta, tb]\n if (this._isUndefined(curve, a, ta, b, tb)) {\n continue;\n }\n // Test if the graph is far outside the visible are for the interval [ta, tb]\n if (this._isOutside(a, ta, b, tb, curve.board)) {\n continue;\n }\n }\n\n tc = (ta + tb) * 0.5;\n\n // Screen coordinates of point at tc\n x = curve.X(tc, true);\n y = curve.Y(tc, true);\n c = [1, oc[1] + x * curve.board.unitX, oc[2] - y * curve.board.unitY];\n ds = this._triangleDists(a, b, c); // returns [d_ab, d_ac, d_cb, d_cd]\n\n a_nan = isNaN(a[1] + a[2]);\n b_nan = isNaN(b[1] + b[2]);\n if ((a_nan && !b_nan) || (!a_nan && b_nan)) {\n may_be_special = 'border';\n } else if (\n ds[0] > 0.66 * ds0 ||\n ds[0] < this.cusp_threshold * (ds[1] + ds[2]) ||\n ds[1] > 5 * ds[2] ||\n ds[2] > 5 * ds[1]\n ) {\n may_be_special = 'cusp';\n } else if (\n ds[2] > this.jump_threshold * ds[0] ||\n ds[1] > this.jump_threshold * ds[0] ||\n ds[0] === Infinity ||\n ds[1] === Infinity ||\n ds[2] === Infinity\n ) {\n may_be_special = 'jump';\n }\n isSmooth =\n may_be_special === \"\" &&\n depth < this.smoothLevel &&\n ds[3] < this.smooth_threshold;\n\n if (depth < this.testLevel && !isSmooth) {\n if (may_be_special === \"\") {\n isSmooth = true;\n } else {\n limes = this._getLimes(curve, ta, a, tc, c, tb, b, may_be_special, depth);\n }\n }\n\n if (limes !== null) {\n c = [1, NaN, NaN];\n this._insertPoint(curve, c, tc, depth, limes);\n } else if (depth <= mindepth || isSmooth) {\n this._insertPoint(curve, c, tc, depth, null);\n } else {\n stack[stack_length++] = [c, tc, b, tb, depth - 1, ds[0]];\n stack[stack_length++] = [a, ta, c, tc, depth - 1, ds[0]];\n }\n }\n\n return this;\n },\n\n /**\n * Updates the data points of a parametric curve. This version is used if {@link JXG.Curve#plotVersion} is 3.\n * This is an experimental plot version, not recommended to be used.\n * @param {JXG.Curve} curve JSXGraph curve element\n * @param {Number} mi Left bound of curve\n * @param {Number} ma Right bound of curve\n * @returns {JXG.Curve} Reference to the curve object.\n */\n updateParametricCurve_v3: function (curve, mi, ma) {\n var ta,\n tb,\n a,\n b,\n suspendUpdate = false,\n pa = new Coords(Const.COORDS_BY_USER, [0, 0], curve.board, false),\n pb = new Coords(Const.COORDS_BY_USER, [0, 0], curve.board, false),\n depth,\n w2, // h2,\n bbox,\n ret_arr;\n\n // console.log(\"-----------------------------------------------------------\");\n // console.time('plot');\n // if (curve.board.updateQuality === curve.board.BOARD_QUALITY_LOW) {\n // depth = curve.evalVisProp('recursiondepthlow') || 14;\n // } else {\n depth = curve.evalVisProp('recursiondepthhigh') || 17;\n // }\n\n // smoothLevel has to be small for graphs in a huge interval.\n this.smoothLevel = 7; //depth - 10;\n this.nanLevel = depth - 4;\n this.testLevel = 4;\n this.cusp_threshold = 0.5;\n this.jump_threshold = 0.99;\n this.smooth_threshold = 2;\n\n curve.points = [];\n\n if (curve.xterm === 'x') {\n // For function graphs we can restrict the plot interval\n // to the visible area +plus margin\n bbox = curve.board.getBoundingBox();\n w2 = (bbox[2] - bbox[0]) * 0.3;\n //h2 = (bbox[1] - bbox[3]) * 0.3;\n ta = Math.max(mi, bbox[0] - w2);\n tb = Math.min(ma, bbox[2] + w2);\n } else {\n ta = mi;\n tb = ma;\n }\n pa.setCoordinates(\n Const.COORDS_BY_USER,\n [curve.X(ta, suspendUpdate), curve.Y(ta, suspendUpdate)],\n false\n );\n\n // The first function calls of X() and Y() are done. We can now\n // switch `suspendUpdate` on. If supported by the functions, this\n // avoids for the rest of the plotting algorithm, evaluation of any\n // parent elements.\n suspendUpdate = true;\n\n pb.setCoordinates(\n Const.COORDS_BY_USER,\n [curve.X(tb, suspendUpdate), curve.Y(tb, suspendUpdate)],\n false\n );\n\n // Find start and end points of the visible area (plus a certain margin)\n ret_arr = this._findStartPoint(curve, pa.scrCoords, ta, pb.scrCoords, tb);\n pa.setCoordinates(Const.COORDS_BY_SCREEN, ret_arr[0], false);\n ta = ret_arr[1];\n ret_arr = this._findStartPoint(curve, pb.scrCoords, tb, pa.scrCoords, ta);\n pb.setCoordinates(Const.COORDS_BY_SCREEN, ret_arr[0], false);\n tb = ret_arr[1];\n\n // Store the visible area.\n // This can be used in Curve.hasPoint().\n this._visibleArea = [ta, tb];\n\n // Start recursive plotting algorithm\n a = pa.copy('scrCoords');\n b = pb.copy('scrCoords');\n pa._t = ta;\n curve.points.push(pa);\n this._lastScrCrds = pa.copy('scrCoords'); // Used in _insertPoint\n this._lastUsrCrds = pa.copy('usrCoords'); // Used in _insertPoint\n\n this._plotNonRecursive(curve, a, ta, b, tb, depth);\n\n pb._t = tb;\n curve.points.push(pb);\n\n curve.numberPoints = curve.points.length;\n // console.timeEnd('plot');\n // console.log(\"number of points:\", this.numberPoints);\n\n return curve;\n },\n\n //----------------------------------------------------------------------\n // Plot algorithm v4\n //----------------------------------------------------------------------\n\n /**\n * TODO\n * @param {Array} vec\n * @param {Number} le\n * @param {Number} level\n * @returns Object\n * @private\n */\n _criticalInterval: function (vec, le, level) {\n var i,\n j,\n le1,\n med,\n sgn,\n sgnChange,\n isGroup = false,\n abs_vec,\n last = -Infinity,\n very_small = false,\n smooth = false,\n group = 0,\n groups = [],\n types = [],\n positions = [];\n\n abs_vec = Statistics.abs(vec);\n med = Statistics.median(abs_vec);\n\n if (med < 1.0e-7) {\n med = 1.0e-7;\n very_small = true;\n } else {\n med *= this.criticalThreshold;\n }\n\n //console.log(\"Median\", med);\n for (i = 0; i < le; i++) {\n // Start a group if not yet done and\n // add position to group\n if (abs_vec[i] > med /*&& abs_vec[i] > 0.01*/) {\n positions.push({ i: i, v: vec[i], group: group });\n last = i;\n if (!isGroup) {\n isGroup = true;\n }\n } else {\n if (isGroup && i > last + 4) {\n // End the group\n if (positions.length > 0) {\n groups.push(positions.slice(0));\n }\n positions = [];\n isGroup = false;\n group++;\n }\n }\n }\n if (isGroup) {\n if (positions.length > 1) {\n groups.push(positions.slice(0));\n }\n }\n\n if (very_small && groups.length === 0) {\n smooth = true;\n }\n\n // Decide if there is a singular critical point\n // or if a whole interval is problematic.\n // The latter is the case if the differences have many sign changes.\n for (j = 0; j < groups.length; j++) {\n types[j] = 'point';\n le1 = groups[j].length;\n if (le1 < 64) {\n continue;\n }\n sgnChange = 0;\n sgn = Math.sign(groups[j][0].v);\n for (i = 1; i < le1; i++) {\n if (Math.sign(groups[j][i].v) !== sgn) {\n sgnChange++;\n sgn = Math.sign(groups[j][i].v);\n }\n }\n if (sgnChange * 6 > le1) {\n types[j] = 'interval';\n }\n }\n\n return { smooth: smooth, groups: groups, types: types };\n },\n\n Component: function () {\n this.left_isNaN = false;\n this.right_isNaN = false;\n this.left_t = null;\n this.right_t = null;\n this.t_values = [];\n this.x_values = [];\n this.y_values = [];\n this.len = 0;\n },\n\n findComponents: function (curve, mi, ma, steps) {\n var i, t, h,\n x, y,\n components = [],\n comp,\n comp_nr = 0,\n cnt = 0,\n cntNaNs = 0,\n comp_started = false,\n suspended = false;\n\n h = (ma - mi) / steps;\n components[comp_nr] = new this.Component();\n comp = components[comp_nr];\n\n for (i = 0, t = mi; i <= steps; i++, t += h) {\n x = curve.X(t, suspended);\n y = curve.Y(t, suspended);\n\n if (isNaN(x) || isNaN(y)) {\n cntNaNs++;\n // Wait for - at least - two consecutive NaNs\n // This avoids starting a new component if\n // the function value has infinity as intermediate value.\n if (cntNaNs > 1 && comp_started) {\n // Finalize a component\n comp.right_isNaN = true;\n comp.right_t = t - h;\n comp.len = cnt;\n\n // Prepare a new component\n comp_started = false;\n comp_nr++;\n components[comp_nr] = new this.Component();\n comp = components[comp_nr];\n cntNaNs = 0;\n }\n } else {\n // Now there is a non-NaN entry.\n if (!comp_started) {\n // Start the component\n comp_started = true;\n cnt = 0;\n if (cntNaNs > 0) {\n comp.left_t = t - h;\n comp.left_isNaN = true;\n }\n }\n cntNaNs = 0;\n // Add the value to the component\n comp.t_values[cnt] = t;\n comp.x_values[cnt] = x;\n comp.y_values[cnt] = y;\n cnt++;\n }\n if (i === 0) {\n suspended = true;\n }\n }\n if (comp_started) {\n comp.len = cnt;\n } else {\n components.pop();\n }\n\n return components;\n },\n\n getPointType: function (curve, pos, t_approx, t_values, x_table, y_table, len) {\n var x_values = x_table[0],\n y_values = y_table[0],\n full_len = t_values.length,\n result = {\n idx: pos,\n t: t_approx, //t_values[pos],\n x: x_values[pos],\n y: y_values[pos],\n type: \"other\"\n };\n\n if (pos < 5) {\n result.type = 'borderleft';\n result.idx = 0;\n result.t = t_values[0];\n result.x = x_values[0];\n result.y = y_values[0];\n\n // console.log('Border left', result.t);\n return result;\n }\n if (pos > len - 6) {\n result.type = 'borderright';\n result.idx = full_len - 1;\n result.t = t_values[full_len - 1];\n result.x = x_values[full_len - 1];\n result.y = y_values[full_len - 1];\n\n // console.log('Border right', result.t, full_len - 1);\n return result;\n }\n\n return result;\n },\n\n newtonApprox: function (idx, t, h, level, table) {\n var i,\n s = 0.0;\n for (i = level; i > 0; i--) {\n s = ((s + table[i][idx]) * (t - (i - 1) * h)) / i;\n }\n return s + table[0][idx];\n },\n\n // Thiele's interpolation formula,\n // https://en.wikipedia.org/wiki/Thiele%27s_interpolation_formula\n // unused\n thiele: function (t, recip, t_values, idx, degree) {\n var i,\n v = 0.0;\n for (i = degree; i > 1; i--) {\n v = (t - t_values[idx + i]) / (recip[i][idx + 1] - recip[i - 2][idx + 1] + v);\n }\n return recip[0][idx + 1] + (t - t_values[idx + 1]) / (recip[1][idx + 1] + v);\n },\n\n differenceMethodExperiments: function (component, curve) {\n var i,\n level,\n le,\n up,\n t_values = component.t_values,\n x_values = component.x_values,\n y_values = component.y_values,\n x_diffs = [],\n y_diffs = [],\n x_slopes = [],\n y_slopes = [],\n x_table = [],\n y_table = [],\n x_recip = [],\n y_recip = [],\n h,\n numerator,\n // x_med, y_med,\n foundCriticalPoint = 0,\n pos,\n ma,\n j,\n v,\n groups,\n criticalPoints = [];\n\n h = t_values[1] - t_values[0];\n x_table.push([]);\n y_table.push([]);\n x_recip.push([]);\n y_recip.push([]);\n le = y_values.length;\n for (i = 0; i < le; i++) {\n x_table[0][i] = x_values[i];\n y_table[0][i] = y_values[i];\n x_recip[0][i] = x_values[i];\n y_recip[0][i] = y_values[i];\n }\n\n x_table.push([]);\n y_table.push([]);\n x_recip.push([]);\n y_recip.push([]);\n numerator = h;\n le = y_values.length - 1;\n for (i = 0; i < le; i++) {\n x_diffs[i] = x_values[i + 1] - x_values[i];\n y_diffs[i] = y_values[i + 1] - y_values[i];\n x_slopes[i] = x_diffs[i];\n y_slopes[i] = y_diffs[i];\n x_table[1][i] = x_diffs[i];\n y_table[1][i] = y_diffs[i];\n x_recip[1][i] = numerator / x_diffs[i];\n y_recip[1][i] = numerator / y_diffs[i];\n }\n le--;\n\n up = Math.min(8, y_values.length - 1);\n for (level = 1; level < up; level++) {\n x_table.push([]);\n y_table.push([]);\n x_recip.push([]);\n y_recip.push([]);\n numerator *= h;\n for (i = 0; i < le; i++) {\n x_diffs[i] = x_diffs[i + 1] - x_diffs[i];\n y_diffs[i] = y_diffs[i + 1] - y_diffs[i];\n x_table[level + 1][i] = x_diffs[i];\n y_table[level + 1][i] = y_diffs[i];\n x_recip[level + 1][i] =\n numerator / (x_recip[level][i + 1] - x_recip[level][i]) +\n x_recip[level - 1][i + 1];\n y_recip[level + 1][i] =\n numerator / (y_recip[level][i + 1] - y_recip[level][i]) +\n y_recip[level - 1][i + 1];\n }\n\n // if (level == 1) {\n // console.log(\"bends level=\", level, y_diffs.toString());\n // }\n\n // Store point location which may be centered around\n // critical points.\n // If the level is suitable, step out of the loop.\n groups = this._criticalPoints(y_diffs, le, level);\n if (groups === false) {\n // Its seems, the degree of the polynomial is equal to level\n console.log(\"Polynomial of degree\", level);\n groups = [];\n break;\n }\n if (groups.length > 0) {\n foundCriticalPoint++;\n if (foundCriticalPoint > 1 && level % 2 === 0) {\n break;\n }\n }\n le--;\n }\n\n // console.log(\"Last diffs\", y_diffs, \"level\", level);\n\n // Analyze the groups which have been found.\n for (i = 0; i < groups.length; i++) {\n // console.log(\"Group\", i, groups[i])\n // Identify the maximum difference, i.e. the center of the \"problem\"\n ma = -Infinity;\n for (j = 0; j < groups[i].length; j++) {\n v = Math.abs(groups[i][j].v);\n if (v > ma) {\n ma = v;\n pos = j;\n }\n }\n pos = Math.floor(groups[i][pos].i + level / 2);\n // Analyze the critical point\n criticalPoints.push(\n this.getPointType(\n curve,\n pos,\n t_values,\n x_values,\n y_values,\n x_slopes,\n y_slopes,\n le + 1\n )\n );\n }\n\n return [criticalPoints, x_table, y_table, x_recip, y_recip];\n },\n\n getCenterOfCriticalInterval: function (group, degree, t_values) {\n var ma,\n j,\n pos,\n v,\n num = 0.0,\n den = 0.0,\n h = t_values[1] - t_values[0],\n pos_mean,\n range = [];\n\n // Identify the maximum difference, i.e. the center of the \"problem\"\n // If there are several equal maxima, store the positions\n // in the array range and determine the center of the array.\n\n ma = -Infinity;\n range = [];\n for (j = 0; j < group.length; j++) {\n v = Math.abs(group[j].v);\n if (v > ma) {\n range = [j];\n ma = v;\n pos = j;\n } else if (ma === v) {\n range.push(j);\n }\n }\n if (range.length > 0) {\n pos_mean =\n range.reduce(function (total, val) {\n return total + val;\n }, 0) / range.length;\n pos = Math.floor(pos_mean);\n pos_mean += group[0].i;\n }\n\n if (ma < Infinity) {\n for (j = 0; j < group.length; j++) {\n num += Math.abs(group[j].v) * group[j].i;\n den += Math.abs(group[j].v);\n }\n pos_mean = num / den;\n }\n pos_mean += degree / 2;\n return [\n group[pos].i + degree / 2,\n pos_mean,\n t_values[Math.floor(pos_mean)] + h * (pos_mean - Math.floor(pos_mean))\n ];\n },\n\n differenceMethod: function (component, curve) {\n var i,\n level,\n le,\n up,\n t_values = component.t_values,\n x_values = component.x_values,\n y_values = component.y_values,\n x_table = [],\n y_table = [],\n foundCriticalPoint = 0,\n degree_x = -1,\n degree_y = -1,\n pos,\n res,\n res_x,\n res_y,\n t_approx,\n groups = [],\n types,\n criticalPoints = [];\n\n le = y_values.length;\n // x_table.push([]);\n // y_table.push([]);\n // for (i = 0; i < le; i++) {\n // x_table[0][i] = x_values[i];\n // y_table[0][i] = y_values[i];\n // }\n x_table.push(new Float64Array(x_values));\n y_table.push(new Float64Array(y_values));\n\n le--;\n up = Math.min(12, le);\n for (level = 0; level < up; level++) {\n // Old style method:\n // x_table.push([]);\n // y_table.push([]);\n // for (i = 0; i < le; i++) {\n // x_table[level + 1][i] = x_table[level][i + 1] - x_table[level][i];\n // y_table[level + 1][i] = y_table[level][i + 1] - y_table[level][i];\n // }\n // New method:\n x_table.push(new Float64Array(le));\n y_table.push(new Float64Array(le));\n x_table[level + 1] = x_table[level].map(function (v, idx, arr) {\n return arr[idx + 1] - v;\n });\n y_table[level + 1] = y_table[level].map(function (v, idx, arr) {\n return arr[idx + 1] - v;\n });\n\n // Store point location which may be centered around critical points.\n // If the level is suitable, step out of the loop.\n res_y = this._criticalInterval(y_table[level + 1], le, level);\n if (res_y.smooth === true) {\n // Its seems, the degree of the polynomial is equal to level\n // If the values in level + 1 are zero, it might be a polynomial of degree level.\n // Seems to work numerically stable until degree 6.\n degree_y = level;\n groups = [];\n }\n res_x = this._criticalInterval(x_table[level + 1], le, level);\n if (degree_x === -1 && res_x.smooth === true) {\n // Its seems, the degree of the polynomial is equal to level\n // If the values in level + 1 are zero, it might be a polynomial of degree level.\n // Seems to work numerically stable until degree 6.\n degree_x = level;\n }\n if (degree_y >= 0) {\n break;\n }\n\n if (res_y.groups.length > 0) {\n foundCriticalPoint++;\n if (foundCriticalPoint > 2 && (level + 1) % 2 === 0) {\n groups = res_y.groups;\n types = res_y.types;\n break;\n }\n }\n le--;\n }\n\n // console.log(\"Last diffs\", y_table[Math.min(level + 1, up)], \"level\", level + 1);\n // Analyze the groups which have been found.\n for (i = 0; i < groups.length; i++) {\n if (types[i] === 'interval') {\n continue;\n }\n // console.log(\"Group\", i, groups[i], types[i], level + 1)\n res = this.getCenterOfCriticalInterval(groups[i], level + 1, t_values);\n pos = res_y[0];\n pos = Math.floor(res[1]);\n t_approx = res[2];\n // console.log(\"Critical points:\", groups, res, pos)\n\n // Analyze the type of the critical point\n // Result is of type 'borderleft', borderright', 'other'\n criticalPoints.push(\n this.getPointType(curve, pos, t_approx, t_values, x_table, y_table, le + 1)\n );\n }\n\n // if (level === up) {\n // console.log(\"No convergence!\");\n // } else {\n // console.log(\"Convergence level\", level);\n // }\n return [criticalPoints, x_table, y_table, degree_x, degree_y];\n },\n\n _insertPoint_v4: function (curve, crds, t, doLog) {\n var p,\n prev = null,\n x,\n y,\n near = 0.8;\n\n if (curve.points.length > 0) {\n prev = curve.points[curve.points.length - 1].scrCoords;\n }\n\n // Add regular point\n p = new Coords(Const.COORDS_BY_USER, crds, curve.board);\n\n if (prev !== null) {\n x = p.scrCoords[1] - prev[1];\n y = p.scrCoords[2] - prev[2];\n if (x * x + y * y < near * near) {\n // Math.abs(p.scrCoords[1] - prev[1]) < near &&\n // Math.abs(p.scrCoords[2] - prev[2]) < near) {\n return;\n }\n }\n\n p._t = t;\n curve.points.push(p);\n },\n\n getInterval: function (curve, ta, tb) {\n var t_int,\n // x_int,\n y_int;\n\n //console.log('critical point', ta, tb);\n IntervalArithmetic.disable();\n\n t_int = IntervalArithmetic.Interval(ta, tb);\n curve.board.mathLib = IntervalArithmetic;\n curve.board.mathLibJXG = IntervalArithmetic;\n // x_int = curve.X(t_int, true);\n y_int = curve.Y(t_int, true);\n curve.board.mathLib = Math;\n curve.board.mathLibJXG = JXG.Math;\n\n //console.log(x_int, y_int);\n return y_int;\n },\n\n sign: function (v) {\n if (v < 0) {\n return -1;\n }\n if (v > 0) {\n return 1;\n }\n return 0;\n },\n\n handleBorder: function (curve, comp, group, x_table, y_table) {\n var idx = group.idx,\n t,\n t1,\n t2,\n size = 32,\n y_int,\n x,\n y,\n lo,\n hi,\n i,\n components2,\n le,\n h;\n\n // console.log(\"HandleBorder at t =\", t_approx);\n // console.log(\"component:\", comp)\n // console.log(\"Group:\", group);\n\n h = comp.t_values[1] - comp.t_values[0];\n if (group.type === 'borderleft') {\n t = comp.left_isNaN ? comp.left_t : group.t - h;\n t1 = t;\n t2 = t1 + h;\n } else if (group.type === 'borderright') {\n t = comp.right_isNaN ? comp.right_t : group.t + h;\n t2 = t;\n t1 = t2 - h;\n } else {\n console.log(\"No bordercase!!!\");\n }\n\n components2 = this.findComponents(curve, t1, t2, size);\n if (components2.length === 0) {\n return;\n }\n if (group.type === 'borderleft') {\n t1 = components2[0].left_t;\n t2 = components2[0].t_values[0];\n h = components2[0].t_values[1] - components2[0].t_values[0];\n t1 = t1 === null ? t2 - h : t1;\n t = t1;\n y_int = this.getInterval(curve, t1, t2);\n if (Type.isObject(y_int)) {\n lo = y_int.lo;\n hi = y_int.hi;\n\n x = curve.X(t, true);\n y = y_table[1][idx] < 0 ? hi : lo;\n this._insertPoint_v4(curve, [1, x, y], t);\n }\n }\n\n le = components2[0].t_values.length;\n for (i = 0; i < le; i++) {\n t = components2[0].t_values[i];\n x = components2[0].x_values[i];\n y = components2[0].y_values[i];\n this._insertPoint_v4(curve, [1, x, y], t);\n }\n\n if (group.type === 'borderright') {\n t1 = components2[0].t_values[le - 1];\n t2 = components2[0].right_t;\n h = components2[0].t_values[1] - components2[0].t_values[0];\n t2 = t2 === null ? t1 + h : t2;\n\n t = t2;\n y_int = this.getInterval(curve, t1, t2);\n if (Type.isObject(y_int)) {\n lo = y_int.lo;\n hi = y_int.hi;\n x = curve.X(t, true);\n y = y_table[1][idx] > 0 ? hi : lo;\n this._insertPoint_v4(curve, [1, x, y], t);\n }\n }\n },\n\n _seconditeration_v4: function (curve, comp, group, x_table, y_table) {\n var i, t1, t2, ret, components2, comp2, idx, groups2, g, x_table2, y_table2, start, le;\n\n // Look at two points, hopefully left and right from the critical point\n t1 = comp.t_values[group.idx - 2];\n t2 = comp.t_values[group.idx + 2];\n components2 = this.findComponents(curve, t1, t2, 64);\n for (idx = 0; idx < components2.length; idx++) {\n comp2 = components2[idx];\n ret = this.differenceMethod(comp2, curve);\n groups2 = ret[0];\n x_table2 = ret[1];\n y_table2 = ret[2];\n start = 0;\n for (g = 0; g <= groups2.length; g++) {\n if (g === groups2.length) {\n le = comp2.len;\n } else {\n le = groups2[g].idx;\n }\n\n // Insert all uncritical points until next critical point\n for (i = start; i < le; i++) {\n if (!isNaN(comp2.x_values[i]) && !isNaN(comp2.y_values[i])) {\n this._insertPoint_v4(\n curve,\n [1, comp2.x_values[i], comp2.y_values[i]],\n comp2.t_values[i]\n );\n }\n }\n // Handle next critical point\n if (g < groups2.length) {\n this.handleSingularity(curve, comp2, groups2[g], x_table2, y_table2);\n start = groups2[g].idx + 1;\n }\n }\n le = comp2.len;\n if (idx < components2.length - 1) {\n this._insertPoint_v4(curve, [1, NaN, NaN], comp2.right_t);\n }\n }\n return this;\n },\n\n _recurse_v4: function (curve, t1, t2, x1, y1, x2, y2, level) {\n var tol = 2,\n t = (t1 + t2) * 0.5,\n x = curve.X(t, true),\n y = curve.Y(t, true),\n dx,\n dy;\n\n //console.log(\"Level\", level)\n if (level === 0) {\n this._insertPoint_v4(curve, [1, NaN, NaN], t);\n return;\n }\n // console.log(\"R\", t1, t2)\n dx = (x - x1) * curve.board.unitX;\n dy = (y - y1) * curve.board.unitY;\n // console.log(\"D1\", Math.sqrt(dx * dx + dy * dy))\n if (Mat.hypot(dx, dy) > tol) {\n this._recurse_v4(curve, t1, t, x1, y1, x, y, level - 1);\n } else {\n this._insertPoint_v4(curve, [1, x, y], t);\n }\n dx = (x - x2) * curve.board.unitX;\n dy = (y - y2) * curve.board.unitY;\n // console.log(\"D2\", Math.sqrt(dx * dx + dy * dy), x-x2, y-y2)\n if (Mat.hypot(dx, dy) > tol) {\n this._recurse_v4(curve, t, t2, x, y, x2, y2, level - 1);\n } else {\n this._insertPoint_v4(curve, [1, x, y], t);\n }\n },\n\n handleSingularity: function (curve, comp, group, x_table, y_table) {\n var idx = group.idx,\n t,\n t1,\n t2,\n y_int,\n i1,\n i2,\n x,\n // y,\n lo,\n hi,\n d_lft,\n d_rgt,\n d_thresh = 100,\n // d1,\n // d2,\n di1 = 5,\n di2 = 3;\n\n t = group.t;\n console.log(\"HandleSingularity at t =\", t);\n // console.log(comp.t_values[idx - 1], comp.y_values[idx - 1], comp.t_values[idx + 1], comp.y_values[idx + 1]);\n // console.log(group);\n\n // Look at two points, hopefully left and right from the critical point\n t1 = comp.t_values[idx - di1];\n t2 = comp.t_values[idx + di1];\n\n y_int = this.getInterval(curve, t1, t2);\n if (Type.isObject(y_int)) {\n lo = y_int.lo;\n hi = y_int.hi;\n } else {\n if (y_table[0][idx - 1] < y_table[0][idx + 1]) {\n lo = y_table[0][idx - 1];\n hi = y_table[0][idx + 1];\n } else {\n lo = y_table[0][idx + 1];\n hi = y_table[0][idx - 1];\n }\n }\n\n x = curve.X(t, true);\n\n d_lft =\n (y_table[0][idx - di2] - y_table[0][idx - di1]) /\n (comp.t_values[idx - di2] - comp.t_values[idx - di1]);\n d_rgt =\n (y_table[0][idx + di2] - y_table[0][idx + di1]) /\n (comp.t_values[idx + di2] - comp.t_values[idx + di1]);\n\n console.log(\":::\", d_lft, d_rgt);\n\n //this._insertPoint_v4(curve, [1, NaN, NaN], 0);\n\n if (d_lft < -d_thresh) {\n // Left branch very steep downwards -> add the minimum\n this._insertPoint_v4(curve, [1, x, lo], t, true);\n if (d_rgt <= d_thresh) {\n // Right branch not very steep upwards -> interrupt the curve\n // I.e. it looks like -infty / (finite or infty) and not like -infty / -infty\n this._insertPoint_v4(curve, [1, NaN, NaN], t);\n }\n } else if (d_lft > d_thresh) {\n // Left branch very steep upwards -> add the maximum\n this._insertPoint_v4(curve, [1, x, hi], t);\n if (d_rgt >= -d_thresh) {\n // Right branch not very steep downwards -> interrupt the curve\n // I.e. it looks like infty / (finite or -infty) and not like infty / infty\n this._insertPoint_v4(curve, [1, NaN, NaN], t);\n }\n } else {\n if (lo === -Infinity) {\n this._insertPoint_v4(curve, [1, x, lo], t, true);\n this._insertPoint_v4(curve, [1, NaN, NaN], t);\n }\n if (hi === Infinity) {\n this._insertPoint_v4(curve, [1, NaN, NaN], t);\n this._insertPoint_v4(curve, [1, x, hi], t, true);\n }\n\n if (group.t < comp.t_values[idx]) {\n i1 = idx - 1;\n i2 = idx;\n } else {\n i1 = idx;\n i2 = idx + 1;\n }\n t1 = comp.t_values[i1];\n t2 = comp.t_values[i2];\n this._recurse_v4(\n curve,\n t1,\n t2,\n x_table[0][i1],\n y_table[0][i1],\n x_table[0][i2],\n y_table[0][i2],\n 10\n );\n\n // x = (x_table[0][idx] - x_table[0][idx - 1]) * curve.board.unitX;\n // y = (y_table[0][idx] - y_table[0][idx - 1]) * curve.board.unitY;\n // d1 = Math.sqrt(x * x + y * y);\n // x = (x_table[0][idx + 1] - x_table[0][idx]) * curve.board.unitX;\n // y = (y_table[0][idx + 1] - y_table[0][idx]) * curve.board.unitY;\n // d2 = Math.sqrt(x * x + y * y);\n\n // console.log(\"end\", t1, t2, t);\n // if (true || (d1 > 2 || d2 > 2)) {\n\n // console.log(d1, d2, y_table[0][idx])\n // // Finite jump\n // this._insertPoint_v4(curve, [1, NaN, NaN], t);\n // } else {\n // if (lo !== -Infinity && hi !== Infinity) {\n // // Critical point which can be ignored\n // this._insertPoint_v4(curve, [1, x_table[0][idx], y_table[0][idx]], comp.t_values[idx]);\n // } else {\n // if (lo === -Infinity) {\n // this._insertPoint_v4(curve, [1, x, lo], t, true);\n // this._insertPoint_v4(curve, [1, NaN, NaN], t);\n // }\n // if (hi === Infinity) {\n // this._insertPoint_v4(curve, [1, NaN, NaN], t);\n // this._insertPoint_v4(curve, [1, x, hi], t, true);\n // }\n // }\n // }\n }\n if (d_rgt < -d_thresh) {\n // Right branch very steep downwards -> add the maximum\n this._insertPoint_v4(curve, [1, x, hi], t);\n } else if (d_rgt > d_thresh) {\n // Right branch very steep upwards -> add the minimum\n this._insertPoint_v4(curve, [1, x, lo], t);\n }\n },\n\n /**\n * Number of equidistant points where the function is evaluated\n */\n steps: 1021, //2053, // 1021,\n\n /**\n * If the absolute maximum of the set of differences is larger than\n * criticalThreshold * median of these values, it is regarded as critical point.\n * @see JXG.Math.Plot._criticalInterval\n */\n criticalThreshold: 1000,\n\n plot_v4: function (curve, ta, tb, steps) {\n var i,\n // j,\n le,\n components,\n idx,\n comp,\n groups,\n g,\n start,\n ret,\n x_table, y_table,\n t, t1, t2,\n // good,\n // bad,\n // x_int,\n y_int,\n // degree_x,\n // degree_y,\n h = (tb - ta) / steps,\n Ypl = function (x) {\n return curve.Y(x, true);\n },\n Ymi = function (x) {\n return -curve.Y(x, true);\n },\n h2 = h * 0.5;\n\n components = this.findComponents(curve, ta, tb, steps);\n for (idx = 0; idx < components.length; idx++) {\n comp = components[idx];\n ret = this.differenceMethod(comp, curve);\n groups = ret[0];\n x_table = ret[1];\n y_table = ret[2];\n\n // degree_x = ret[3];\n // degree_y = ret[4];\n // if (degree_x >= 0) {\n // console.log(\"x polynomial of degree\", degree_x);\n // }\n // if (degree_y >= 0) {\n // console.log(\"y polynomial of degree\", degree_y);\n // }\n if (groups.length === 0 || groups[0].type !== 'borderleft') {\n groups.unshift({\n idx: 0,\n t: comp.t_values[0],\n x: comp.x_values[0],\n y: comp.y_values[0],\n type: \"borderleft\"\n });\n }\n if (groups[groups.length - 1].type !== 'borderright') {\n le = comp.t_values.length;\n groups.push({\n idx: le - 1,\n t: comp.t_values[le - 1],\n x: comp.x_values[le - 1],\n y: comp.y_values[le - 1],\n type: \"borderright\"\n });\n }\n\n start = 0;\n for (g = 0; g <= groups.length; g++) {\n if (g === groups.length) {\n le = comp.len;\n } else {\n le = groups[g].idx - 1;\n }\n\n // good = 0;\n // bad = 0;\n // Insert all uncritical points until next critical point\n for (i = start; i < le - 2; i++) {\n this._insertPoint_v4(\n curve,\n [1, comp.x_values[i], comp.y_values[i]],\n comp.t_values[i]\n );\n // j = Math.max(0, i - 2);\n // Add more points in critical intervals\n if (\n //degree_y === -1 && // No polynomial\n i >= start + 3 &&\n i < le - 3 && // Do not do this if too close to a critical point\n y_table.length > 3 &&\n Math.abs(y_table[2][i]) > 0.2 * Math.abs(y_table[0][i])\n ) {\n t = comp.t_values[i];\n h2 = h * 0.25;\n y_int = this.getInterval(curve, t, t + h);\n if (Type.isObject(y_int)) {\n if (y_table[2][i] > 0) {\n this._insertPoint_v4(curve, [1, t + h2, y_int.lo], t + h2);\n } else {\n this._insertPoint_v4(\n curve,\n [1, t + h - h2, y_int.hi],\n t + h - h2\n );\n }\n } else {\n t1 = Numerics.fminbr(Ypl, [t, t + h]);\n t2 = Numerics.fminbr(Ymi, [t, t + h]);\n if (t1 < t2) {\n this._insertPoint_v4(\n curve,\n [1, curve.X(t1, true), curve.Y(t1, true)],\n t1\n );\n this._insertPoint_v4(\n curve,\n [1, curve.X(t2, true), curve.Y(t2, true)],\n t2\n );\n } else {\n this._insertPoint_v4(\n curve,\n [1, curve.X(t2, true), curve.Y(t2, true)],\n t2\n );\n this._insertPoint_v4(\n curve,\n [1, curve.X(t1, true), curve.Y(t1, true)],\n t1\n );\n }\n }\n // bad++;\n // } else {\n // good++;\n }\n }\n // console.log(\"GOOD\", good, \"BAD\", bad);\n\n // Handle next critical point\n if (g < groups.length) {\n //console.log(\"critical point / interval\", groups[g]);\n\n i = groups[g].idx;\n if (groups[g].type === \"borderleft\" || groups[g].type === 'borderright') {\n this.handleBorder(curve, comp, groups[g], x_table, y_table);\n } else {\n this._seconditeration_v4(curve, comp, groups[g], x_table, y_table);\n }\n\n start = groups[g].idx + 1 + 1;\n }\n }\n\n le = comp.len;\n if (idx < components.length - 1) {\n this._insertPoint_v4(curve, [1, NaN, NaN], comp.right_t);\n }\n }\n },\n\n /**\n * Updates the data points of a parametric curve, plotVersion 4. This version is used if {@link JXG.Curve#plotVersion} is 4.\n * @param {JXG.Curve} curve JSXGraph curve element\n * @param {Number} mi Left bound of curve\n * @param {Number} ma Right bound of curve\n * @returns {JXG.Curve} Reference to the curve object.\n */\n updateParametricCurve_v4: function (curve, mi, ma) {\n var ta, tb, w2, bbox;\n\n if (curve.xterm === 'x') {\n // For function graphs we can restrict the plot interval\n // to the visible area +plus margin\n bbox = curve.board.getBoundingBox();\n w2 = (bbox[2] - bbox[0]) * 0.3;\n // h2 = (bbox[1] - bbox[3]) * 0.3;\n ta = Math.max(mi, bbox[0] - w2);\n tb = Math.min(ma, bbox[2] + w2);\n } else {\n ta = mi;\n tb = ma;\n }\n\n curve.points = [];\n\n //console.log(\"--------------------\");\n this.plot_v4(curve, ta, tb, this.steps);\n\n curve.numberPoints = curve.points.length;\n //console.log(curve.numberPoints);\n },\n\n //----------------------------------------------------------------------\n // Plot algorithm alias\n //----------------------------------------------------------------------\n\n /**\n * Updates the data points of a parametric curve, alias for {@link JXG.Curve#updateParametricCurve_v2}.\n * This is needed for backwards compatibility, if this method has been\n * used directly in an application.\n * @param {JXG.Curve} curve JSXGraph curve element\n * @param {Number} mi Left bound of curve\n * @param {Number} ma Right bound of curve\n * @returns {JXG.Curve} Reference to the curve object.\n *\n * @see JXG.Curve#updateParametricCurve_v2\n */\n updateParametricCurve: function (curve, mi, ma) {\n return this.updateParametricCurve_v2(curve, mi, ma);\n }\n};\n\nexport default Mat.Plot;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * The main class initializes a new implicit plot instance.\n * \n * The algorithm should be able to plot most implicit curves as long as the equations\n * are not too complex. We are aware of the paper by Oliver Labs,\n * A List of Challenges for Real Algebraic Plane Curve Visualization Software\n * which contains many equations where this algorithm may fail.\n * For example, at the time being there is no attempt to detect solitary points.\n * Also, it is always a trade off to find all components of the curve and\n * keep the construction responsive.\n *\n * @name JXG.Math.ImplicitPlot\n * @exports Mat.ImplicitPlot as JXG.Math.ImplicitPlot\n * @param {Array} bbox Bounding box of the area in which solutions of the equation\n * are determined.\n * @param {Object} config Configuration object. Default:\n * \n * The method is a predictor / corrector method consisting of Euler and Newton steps\n * together with step width adaption.\n * \n * The algorithm is an adaption of the algorithm in\n * Eugene L. Allgower, Kurt Georg: Introduction to Numerical Continuation methods.\n *\n * @param {Array} u0 Starting point in homogenous coordinates [1, x, y].\n * @param {Number} direction 1 or -1\n * @returns Array [pathX, pathY, loop_closed] or []\n * @private\n */\n tracing: function (u0, direction) {\n var u = [],\n ulast = [],\n len,\n v = [],\n v_start = [],\n w = [],\n t_u, t_v, t_u_0, tloc,\n A,\n grad,\n nrm,\n dir,\n steps = 0,\n k = 0,\n loop_closed = false,\n k0, k1, denom, dist, progress,\n kappa, delta, alpha,\n factor,\n point_added = false,\n\n quasi = false,\n cusp_or_bifurc = false,\n kappa_0 = this.config.kappa_0, // Inverse of planned number of Newton steps\n delta_0 = this.config.delta_0, // Distance of predictor point to curve\n alpha_0 = this.config.alpha_0, // Angle between two successive tangents\n h = this.config.h_initial,\n max_steps = this.config.max_steps,\n\n omega = direction,\n pathX = [],\n pathY = [],\n\n T = [], // Gosper's loop detector table\n n, m, i, e;\n\n u = u0.slice(1);\n pathX.push(u[0]);\n pathY.push(u[1]);\n\n t_u = this.tangent(u);\n if (t_u === false) {\n // We don't want to start at a singularity.\n // Get out of here and search for another starting point.\n return [];\n }\n A = [this.dfx(u[0], u[1]), this.dfy(u[0], u[1])];\n\n do {\n\n if (quasi) {\n t_u = this.tangent_A(A);\n } else {\n t_u = this.tangent(u);\n }\n if (t_u === false) {\n u = v.slice();\n pathX.push(u[0]);\n pathY.push(u[1]);\n // console.log(\"-> Bail out: t_u undefined.\");\n break;\n }\n\n if (pathX.length === 1) {\n // Store first point\n t_u_0 = t_u.slice();\n } else if (pathX.length === 2) {\n T.push(pathX.length - 1); // Put first point into Gosper table T\n\n } else if (point_added && pathX.length > 2 && !cusp_or_bifurc) {\n\n // Detect if loop has been closed\n dist = Geometry.distPointSegment(\n [1, u[0], u[1]],\n [1, pathX[0], pathY[0]],\n [1, pathX[1], pathY[1]]\n );\n\n if (dist < this.config.loop_dist * h &&\n Mat.innerProduct(t_u, t_u_0, 2) > this.config.loop_dir\n ) {\n\n // console.log(\"Loop detected after\", steps, 'steps');\n // console.log(\"\\t\", \"v\", v, \"u0:\", u0)\n // console.log(\"\\t\", \"Dist(v, path0)\", dist, config.loop_dist * h)\n // console.log(\"\\t\", \"t_u\", t_u);\n // console.log(\"\\t\", \"inner:\", Mat.innerProduct(t_u, t_u_0, 2));\n // console.log(\"\\t\", \"h\", h);\n\n u = u0.slice(1);\n pathX.push(u[0]);\n pathY.push(u[1]);\n\n loop_closed = true;\n break;\n }\n\n // Gosper's loop detector\n if (this.config.loop_detection) {\n n = pathX.length - 1;\n // console.log(\"Check Gosper\", n);\n m = Math.floor(Mat.log2(n));\n\n for (i = 0; i <= m; i++) {\n dist = Geometry.distPointSegment(\n [1, u[0], u[1]],\n [1, pathX[T[i] - 1], pathY[T[i] - 1]],\n [1, pathX[T[i]], pathY[T[i]]]\n );\n\n if (dist < this.config.loop_dist * h) {\n // console.log(\"!!!!!!!!!!!!!!! GOSPER LOOP CLOSED !!!!\", i, n + 1,\n // this.config.loop_dist * h\n // );\n\n t_v = this.tangent([pathX[T[i]], pathY[T[i]]]);\n if (Mat.innerProduct(t_u, t_v, 2) > this.config.loop_dir) {\n // console.log(\"!!!!!!!!!!!!!!! angle is good enough\");\n break;\n }\n }\n }\n if (i <= m) {\n loop_closed = true;\n break;\n }\n\n m = 1;\n e = 0;\n for (i = 0; i < 100; i++) {\n if ((n + 1) % m !== 0) {\n break;\n }\n m *= 2;\n e++;\n }\n // console.log(\"Add at e\", e);\n T[e] = n;\n }\n\n }\n\n // Predictor step\n // if (true /*h < 2 * this.config.h_initial*/) {\n // Euler\n // console.log('euler')\n v[0] = u[0] + h * omega * t_u[0];\n v[1] = u[1] + h * omega * t_u[1];\n // } else {\n // // Heun\n // // console.log('heun')\n // v[0] = u[0] + h * omega * t_u[0];\n // v[1] = u[1] + h * omega * t_u[1];\n\n // t_v = this.tangent(v);\n // v[0] = 0.5 * u[0] + 0.5 * (v[0] + h * omega * t_v[0]);\n // v[1] = 0.5 * u[1] + 0.5 * (v[1] + h * omega * t_v[1]);\n // }\n if (quasi) {\n A = this.updateA(A, u, v);\n v_start = v.slice();\n }\n\n // Corrector step: Newton\n k = 0;\n do {\n if (quasi) {\n grad = A;\n } else {\n grad = [this.dfx(v[0], v[1]), this.dfy(v[0], v[1])];\n }\n\n // Compute w = v - A(v) * f(v),\n // grad: row vector and A(v) is the Moore-Penrose inverse:\n // grad^T * (grad * grad^T)^(-1)\n denom = grad[0] * grad[0] + grad[1] * grad[1];\n nrm = this.f(v[0], v[1]) / denom;\n\n w[0] = v[0] - grad[0] * nrm;\n w[1] = v[1] - grad[1] * nrm;\n if (k === 0) {\n k0 = Math.abs(nrm) * Math.sqrt(denom);\n } else if (k === 1) {\n k1 = Math.abs(nrm) * Math.sqrt(denom);\n }\n\n v[0] = w[0];\n v[1] = w[1];\n k++;\n } while (k < 20 &&\n Math.abs(this.f(v[0], v[1])) > this.config.tol_newton\n );\n\n delta = k0;\n if (k > 1) {\n kappa = k1 / k0;\n } else {\n kappa = 0.0;\n }\n\n if (quasi) {\n A = this.updateA(A, v_start, v);\n t_v = this.tangent_A(A);\n } else {\n t_v = this.tangent(v);\n }\n\n dir = Mat.innerProduct(t_u, t_v, 2);\n dir = Math.max(-1, Math.min(1, dir));\n alpha = Math.acos(dir);\n\n // Look for simple bifurcation points and cusps\n cusp_or_bifurc = false;\n progress = Geometry.distance(u, v, 2);\n if (progress < this.config.tol_progress) {\n u = v.slice();\n pathX.push(u[0]);\n pathY.push(u[1]);\n // console.log(\"-> Bail out, no progress\", progress, steps);\n break;\n\n } else if (dir < 0.0) {\n if (h > this.config.h_critical) {\n // console.log(\"Critical point at [\", u[0].toFixed(4), u[1].toFixed(4), \"], v: [\", v[0].toFixed(4), v[1].toFixed(4), \"], but large h:\", h);\n\n } else {\n\n cusp_or_bifurc = true;\n if (this.isBifurcation(u, this.config.tol_cusp)) {\n // console.log(steps, \"bifurcation point between\", u, \"and\", v, \":\", dir, \"h\", h, \"alpha\", alpha);\n // A = [dfx(v[0], v[1]), dfy(v[0], v[1])];\n omega *= (-1);\n // If there is a bifurcation point, we\n // ignore the angle alpha for subsequent step length\n // adaption. Because then we might be able to\n // \"jump over the critical point\"\n alpha = 0;\n } else {\n // Cusp or something more weird\n u = v.slice();\n pathX.push(u[0]);\n pathY.push(u[1]);\n // console.log(\"-> Bail out, cusp\")\n break;\n }\n }\n }\n\n // Adapt stepwidth\n if (!cusp_or_bifurc) {\n factor = Math.max(\n Math.sqrt(kappa / kappa_0),\n Math.sqrt(delta / delta_0),\n alpha / alpha_0\n );\n if (isNaN(factor)) {\n factor = 1;\n }\n factor = Math.max(Math.min(factor, 2), 0.5);\n h /= factor;\n h = Math.min(this.config.h_max, h);\n\n if (factor >= 2) {\n steps++;\n if (steps >= 3 * max_steps) {\n break;\n }\n\n point_added = false;\n continue;\n }\n }\n\n u = v.slice();\n pathX.push(u[0]);\n pathY.push(u[1]);\n point_added = true;\n\n steps++;\n } while (\n steps < max_steps &&\n u[0] >= this.bbox[0] &&\n u[1] <= this.bbox[1] &&\n u[0] <= this.bbox[2] &&\n u[1] >= this.bbox[3]\n );\n\n // Clipping to bounding box, last may be outside, interpolate between second last und last point\n len = pathX.length;\n ulast = [pathX[len - 2], pathY[len - 2]];\n\n // If u[0] is outside x-interval in bounding box, interpolate to the box.\n if (u[0] < this.bbox[0]) {\n if (u[0] !== ulast[0]) {\n tloc = (this.bbox[0] - ulast[0]) / (u[0] - ulast[0]);\n if (u[1] !== ulast[1]) {\n u[1] = ulast[1] + tloc * (u[1] - ulast[1]);\n }\n }\n u[0] = this.bbox[0];\n }\n if (u[0] > this.bbox[2]) {\n if (u[0] !== ulast[0]) {\n tloc = (this.bbox[2] - ulast[0]) / (u[0] - ulast[0]);\n if (u[1] !== ulast[1]) {\n u[1] = ulast[1] + tloc * (u[1] - ulast[1]);\n }\n }\n u[0] = this.bbox[2];\n }\n\n // If u[1] is outside y-interval in bounding box, interpolate to the box.\n if (u[1] < this.bbox[3]) {\n if (u[1] !== ulast[1]) {\n tloc = (this.bbox[3] - ulast[1]) / (u[1] - ulast[1]);\n if (u[0] !== ulast[0]) {\n u[0] = ulast[0] + tloc * (u[0] - ulast[0]);\n }\n }\n u[1] = this.bbox[3];\n }\n if (u[1] > this.bbox[1]) {\n if (u[1] !== ulast[1]) {\n tloc = (this.bbox[1] - ulast[1]) / (u[1] - ulast[1]);\n if (u[0] !== ulast[0]) {\n u[0] = ulast[0] + tloc * (u[0] - ulast[0]);\n }\n }\n u[1] = this.bbox[1];\n }\n\n // Update last point\n pathX[len - 1] = u[0];\n pathY[len - 1] = u[1];\n\n // if (!loop_closed) {\n // console.log(\"No loop\", steps);\n // } else {\n // console.log(\"Loop\", steps);\n // }\n\n return [pathX, pathY, loop_closed];\n },\n\n /**\n * If both eigenvalues of the Hessian are different from zero, the critical point at u\n * is a simple bifurcation point.\n *\n * @param {Array} u Critical point [x, y]\n * @param {Number} tol Tolerance of the eigenvalues to be zero.\n * @returns Boolean True if the point is a simple bifurcation point.\n * @private\n */\n isBifurcation: function (u, tol) {\n // Former experiments:\n // If the Hessian has exactly one zero eigenvalue,\n // we claim that there is a cusp.\n // Otherwise, we decide that there is a bifurcation point.\n // In the latter case, if both eigenvalues are zero\n // this is a somewhat crude decision.\n //\n var h = Mat.eps * Mat.eps * 100,\n x, y, a, b, c, d, ad,\n lbda1, lbda2,\n dis;\n\n x = u[0];\n y = u[1];\n a = 0.5 * (this.dfx(x + h, y) - this.dfx(x - h, y)) / h;\n b = 0.5 * (this.dfx(x, y + h) - this.dfx(x, y - h)) / h;\n c = 0.5 * (this.dfy(x + h, y) - this.dfy(x - h, y)) / h;\n d = 0.5 * (this.dfy(x, y + h) - this.dfy(x, y - h)) / h;\n\n // c = b\n ad = a + d;\n dis = ad * ad - 4 * (a * d - b * c);\n lbda1 = 0.5 * (ad + Math.sqrt(dis));\n lbda2 = 0.5 * (ad - Math.sqrt(dis));\n\n // console.log(a, b, c, d)\n // console.log(\"Eigenvals u:\", lbda1, lbda2, tol);\n\n if (Math.abs(lbda1) > tol && Math.abs(lbda2) > tol) {\n // if (lbda1 * lbda2 > 0) {\n // console.log(\"Seems to be isolated singularity at\", u);\n // }\n return true;\n }\n\n return false;\n },\n\n /**\n * Search in an arc around a critical point for a further point on the curve.\n * Unused for the moment.\n *\n * @param {Array} u Critical point [x, y]\n * @param {Array} t_u Tangent at u\n * @param {Number} r Radius\n * @param {Number} omega angle\n * @returns {Array} Coordinates [x, y] of a new point.\n * @private\n */\n handleCriticalPoint: function (u, t_u, r, omega) {\n var a = Math.atan2(omega * t_u[1], omega * t_u[0]),\n // s = a - 0.75 * Math.PI,\n // e = a + 0.75 * Math.PI,\n f_circ = function (t) {\n var x = u[0] + r * Math.cos(t),\n y = u[1] + r * Math.sin(t);\n return this.f(x, y);\n },\n x, y, t0;\n\n // t0 = Numerics.fzero(f_circ, [s, e]);\n t0 = Numerics.root(f_circ, a);\n\n x = u[0] + r * Math.cos(t0);\n y = u[1] + r * Math.sin(t0);\n // console.log(\"\\t\", \"result\", x, y, \"f\", f(x, y));\n\n return [x, y];\n },\n\n /**\n * Quasi-Newton update of the Moore-Penrose inverse.\n * See (7.2.3) in Allgower, Georg.\n *\n * @param {Array} A\n * @param {Array} u0\n * @param {Array} u1\n * @returns Array\n * @private\n */\n updateA: function (A, u0, u1) {\n var s = [u1[0] - u0[0], u1[1] - u0[1]],\n y = this.f(u1[0], u1[1]) - this.f(u0[0], u0[1]),\n nom, denom;\n\n denom = s[0] * s[0] + s[1] * s[1];\n nom = y - (A[0] * s[0] + A[1] * s[1]);\n nom /= denom;\n A[0] += nom * s[0];\n A[1] += nom * s[1];\n\n return A;\n },\n\n /**\n * Approximate tangent (of norm 1) with Quasi-Newton method\n * @param {Array} A\n * @returns Array\n * @private\n */\n tangent_A: function (A) {\n var t = [-A[1], A[0]],\n nrm = Mat.norm(t, 2);\n\n if (nrm < Mat.eps) {\n // console.log(\"Approx. Singularity\", t, \"is zero\", nrm);\n }\n return [t[0] / nrm, t[1] / nrm];\n },\n\n /**\n * Tangent of norm 1 at point u.\n * @param {Array} u Point [x, y]\n * @returns Array\n * @private\n */\n tangent: function (u) {\n var t = [-this.dfy(u[0], u[1]), this.dfx(u[0], u[1])],\n nrm = Mat.norm(t, 2);\n\n if (nrm < Mat.eps * Mat.eps) {\n // console.log(\"Singularity\", t, \"is zero\", \"at\", u, \":\", nrm);\n return false;\n }\n return [t[0] / nrm, t[1] / nrm];\n }\n }\n\n);\n\nexport default Mat.ImplicitPlot;\n\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * If all four determinants are zero, we add random noise to the point.\n *\n * @param {JXG.Math.Clip.Vertex} P Start of path\n * @private\n * @see JXG.Math.Clip.markEntryExit\n * @see JXG.Math.Clip._handleIntersectionChains\n */\n _classifyDegenerateIntersections: function (P) {\n var Pp, Pm, Qp, Qm, Q,\n side, cnt, tmp, det,\n oppositeDir,\n s1, s2, s3, s4,\n endless = true,\n DEBUG = false;\n\n if (DEBUG) {\n console.log(\n \"\\n-------------- _classifyDegenerateIntersections()\",\n Type.exists(P.data) ? P.data.pathname : \" \"\n );\n }\n det = Geometry.det3p;\n cnt = 0;\n P._tours = 0;\n while (endless) {\n if (DEBUG) {\n console.log(\"Inspect P:\", P.coords.usrCoords, P.data ? P.data.type : \" \");\n }\n if (P.intersection && P.data.type === 'T') {\n // Handle the degenerate cases\n // Decide if they are (delayed) bouncing or crossing intersections\n Pp = P._next.coords.usrCoords; // P+\n Pm = P._prev.coords.usrCoords; // P-\n\n // If the intersection point is degenerated and\n // equal to the start and end of one component,\n // then there will be two adjacent points with\n // the same coordinate.\n // In that case, we proceed to the next node.\n if (Geometry.distance(P.coords.usrCoords, Pp, 3) < Mat.eps) {\n Pp = P._next._next.coords.usrCoords;\n }\n if (Geometry.distance(P.coords.usrCoords, Pm, 3) < Mat.eps) {\n Pm = P._prev._prev.coords.usrCoords;\n }\n\n Q = P.neighbour;\n Qm = Q._prev.coords.usrCoords; // Q-\n Qp = Q._next.coords.usrCoords; // Q+\n if (Geometry.distance(Q.coords.usrCoords, Qp, 3) < Mat.eps) {\n Qp = Q._next._next.coords.usrCoords;\n }\n if (Geometry.distance(Q.coords.usrCoords, Qm, 3) < Mat.eps) {\n Qm = Q._prev._prev.coords.usrCoords;\n }\n\n if (DEBUG) {\n console.log(\"P chain:\", Pm, P.coords.usrCoords, Pp);\n console.log(\"Q chain:\", Qm, P.neighbour.coords.usrCoords, Qp);\n console.log(\"Pm\", this._getPosition(Pm, Qm, Q.coords.usrCoords, Qp));\n console.log(\"Pp\", this._getPosition(Pp, Qm, Q.coords.usrCoords, Qp));\n }\n\n s1 = det(P.coords.usrCoords, Pm, Qm);\n s2 = det(P.coords.usrCoords, Pp, Qp);\n s3 = det(P.coords.usrCoords, Pm, Qp);\n s4 = det(P.coords.usrCoords, Pp, Qm);\n\n if (s1 === 0 && s2 === 0 && s3 === 0 && s4 === 0) {\n P.coords.usrCoords[1] *= 1 + Math.random() * Mat.eps;\n P.coords.usrCoords[2] *= 1 + Math.random() * Mat.eps;\n Q.coords.usrCoords[1] = P.coords.usrCoords[1];\n Q.coords.usrCoords[2] = P.coords.usrCoords[2];\n s1 = det(P.coords.usrCoords, Pm, Qm);\n s2 = det(P.coords.usrCoords, Pp, Qp);\n s3 = det(P.coords.usrCoords, Pm, Qp);\n s4 = det(P.coords.usrCoords, Pp, Qm);\n if (DEBUG) {\n console.log(\"Random shift\", P.coords.usrCoords);\n console.log(s1, s2, s3, s4, s2 === 0);\n console.log(\n this._getPosition(Pm, Qm, Q.coords.usrCoords, Qp),\n this._getPosition(Pp, Qm, Q.coords.usrCoords, Qp)\n );\n }\n }\n oppositeDir = false;\n if (s1 === 0) {\n // Q-, Q=P, P- on straight line\n if (Geometry.affineRatio(P.coords.usrCoords, Pm, Qm) < 0) {\n oppositeDir = true;\n }\n } else if (s2 === 0) {\n if (Geometry.affineRatio(P.coords.usrCoords, Pp, Qp) < 0) {\n oppositeDir = true;\n }\n } else if (s3 === 0) {\n if (Geometry.affineRatio(P.coords.usrCoords, Pm, Qp) > 0) {\n oppositeDir = true;\n }\n } else if (s4 === 0) {\n if (Geometry.affineRatio(P.coords.usrCoords, Pp, Qm) > 0) {\n oppositeDir = true;\n }\n }\n if (oppositeDir) {\n // Swap Qm and Qp\n // Then Qm Q Qp has the same direction as Pm P Pp\n tmp = Qm;\n Qm = Qp;\n Qp = tmp;\n tmp = s1;\n s1 = s3;\n s3 = tmp;\n tmp = s2;\n s2 = s4;\n s4 = tmp;\n }\n\n if (DEBUG) {\n console.log(s1, s2, s3, s4, oppositeDir);\n }\n\n if (!Type.exists(P.delayedStatus)) {\n P.delayedStatus = [];\n }\n\n if (s1 === 0 && s2 === 0) {\n // Line [P-,P] equals [Q-,Q] and line [P,P+] equals [Q,Q+]\n // Interior of delayed crossing / bouncing\n P.delayedStatus = [\"on\", \"on\"];\n } else if (s1 === 0) {\n // P- on line [Q-,Q], P+ not on line [Q,Q+]\n // Begin / end of delayed crossing / bouncing\n side = this._getPosition(Pp, Qm, Q.coords.usrCoords, Qp);\n P.delayedStatus = [\"on\", side];\n } else if (s2 === 0) {\n // P+ on line [Q,Q+], P- not on line [Q-,Q]\n // Begin / end of delayed crossing / bouncing\n side = this._getPosition(Pm, Qm, Q.coords.usrCoords, Qp);\n P.delayedStatus = [side, \"on\"];\n } else {\n // Neither P+ on line [Q,Q+], nor P- on line [Q-,Q]\n // No delayed crossing / bouncing\n if (P.delayedStatus.length === 0) {\n if (\n this._getPosition(Pm, Qm, Q.coords.usrCoords, Qp) !==\n this._getPosition(Pp, Qm, Q.coords.usrCoords, Qp)\n ) {\n P.data.type = 'X';\n } else {\n P.data.type = 'B';\n }\n }\n }\n\n if (DEBUG) {\n console.log(\n \">>>> P:\",\n P.coords.usrCoords,\n \"delayedStatus:\",\n P.delayedStatus.toString(),\n P.data ? P.data.type : \" \",\n \"\\n---\"\n );\n }\n }\n\n if (Type.exists(P._tours)) {\n P._tours++;\n }\n\n if (P._tours > 3 || P._end || cnt > 1000) {\n // Jump out if either\n // - we reached the end\n // - there are more than 1000 intersection points\n // - P._tours > 3: We went already 4 times through this path.\n if (cnt > 1000) {\n console.log(\"Clipping: _classifyDegenerateIntersections exit\");\n }\n if (Type.exists(P._tours)) {\n delete P._tours;\n }\n break;\n }\n if (P.intersection) {\n cnt++;\n }\n P = P._next;\n }\n if (DEBUG) {\n console.log(\"------------------------\");\n }\n },\n\n /**\n * At this point the degenerated intersections have been classified.\n * Now we decide if the intersection chains of the given path\n * ultimatively cross the other path or bounce.\n *\n * @param {JXG.Math.Clip.Vertex} P Start of path\n *\n * @see JXG.Math.Clip.markEntryExit\n * @see JXG.Math.Clip._classifyDegenerateIntersections\n * @private\n */\n _handleIntersectionChains: function (P) {\n var cnt = 0,\n start_status = \"Null\",\n P_start,\n endless = true,\n intersection_chain = false,\n wait_for_exit = false,\n DEBUG = false;\n\n if (DEBUG) {\n console.log(\n \"\\n-------------- _handleIntersectionChains()\",\n Type.exists(P.data) ? P.data.pathname : \" \"\n );\n }\n while (endless) {\n if (P.intersection === true) {\n if (DEBUG) {\n if (P.data.type === 'T') {\n console.log(\n \"Degenerate point\",\n P.coords.usrCoords,\n P.data.type,\n P.data.type === \"T\" ? P.delayedStatus : \" \"\n );\n } else {\n console.log(\"Intersection point\", P.coords.usrCoords, P.data.type);\n }\n }\n if (P.data.type === 'T') {\n if (P.delayedStatus[0] !== \"on\" && P.delayedStatus[1] === 'on') {\n // First point of intersection chain\n intersection_chain = true;\n P_start = P;\n start_status = P.delayedStatus[0];\n } else if (\n intersection_chain &&\n P.delayedStatus[0] === \"on\" &&\n P.delayedStatus[1] === \"on\"\n ) {\n // Interior of intersection chain\n P.data.type = 'B';\n if (DEBUG) {\n console.log(\"Interior\", P.coords.usrCoords);\n }\n } else if (\n intersection_chain &&\n P.delayedStatus[0] === \"on\" &&\n P.delayedStatus[1] !== \"on\"\n ) {\n // Last point of intersection chain\n intersection_chain = false;\n if (start_status === P.delayedStatus[1]) {\n // Intersection chain is delayed bouncing\n P_start.data.type = 'DB';\n P.data.type = 'DB';\n if (DEBUG) {\n console.log(\n \"Chain: delayed bouncing\",\n P_start.coords.usrCoords,\n \"...\",\n P.coords.usrCoords\n );\n }\n } else {\n // Intersection chain is delayed crossing\n P_start.data.type = 'DX';\n P.data.type = 'DX';\n if (DEBUG) {\n console.log(\n \"Chain: delayed crossing\",\n P_start.coords.usrCoords,\n \"...\",\n P.coords.usrCoords\n );\n }\n }\n }\n }\n cnt++;\n }\n if (P._end) {\n wait_for_exit = true;\n }\n if (wait_for_exit && !intersection_chain) {\n break;\n }\n if (cnt > 1000) {\n console.log(\n \"Warning: _handleIntersectionChains: intersection chain reached maximum numbers of iterations\"\n );\n break;\n }\n P = P._next;\n }\n },\n\n /**\n * Handle the case that all vertices of one path are contained\n * in the other path. In this case we search for a midpoint of an edge\n * which is not contained in the other path and add it to the path.\n * It will be used as starting point for the entry/exit algorithm.\n *\n * @private\n * @param {Array} S Subject path\n * @param {Array} C Clip path\n * @param {JXG.board} board JSXGraph board object. It is needed to convert between\n * user coordinates and screen coordinates.\n */\n _handleFullyDegenerateCase: function (S, C, board) {\n var P, Q, l, M, crds,\n q1, q2, node, i, j,\n leP, leQ, is_on_Q,\n tmp, is_fully_degenerated,\n arr = [S, C];\n\n for (l = 0; l < 2; l++) {\n P = arr[l];\n leP = P.length;\n for (i = 0, is_fully_degenerated = true; i < leP; i++) {\n if (!P[i].intersection) {\n is_fully_degenerated = false;\n break;\n }\n }\n\n if (is_fully_degenerated) {\n // All nodes of P are also on the other path.\n Q = arr[(l + 1) % 2];\n leQ = Q.length;\n\n // We search for a midpoint of one edge of P which is not the other path and\n // we add that midpoint to P.\n for (i = 0; i < leP; i++) {\n q1 = P[i].coords.usrCoords;\n q2 = P[i]._next.coords.usrCoords;\n\n // M is the midpoint\n M = [(q1[0] + q2[0]) * 0.5, (q1[1] + q2[1]) * 0.5, (q1[2] + q2[2]) * 0.5];\n\n // Test if M is on path Q. If this is not the case,\n // we take M as additional point of P.\n for (j = 0, is_on_Q = false; j < leQ; j++) {\n if (\n Math.abs(\n Geometry.det3p(\n Q[j].coords.usrCoords,\n Q[(j + 1) % leQ].coords.usrCoords,\n M\n )\n ) < Mat.eps\n ) {\n is_on_Q = true;\n break;\n }\n }\n if (!is_on_Q) {\n // The midpoint is added to the doubly-linked list.\n crds = new Coords(Const.COORDS_BY_USER, M, board);\n node = {\n pos: i,\n intersection: false,\n coords: crds,\n elementClass: Const.OBJECT_CLASS_POINT\n };\n\n tmp = P[i]._next;\n P[i]._next = node;\n node._prev = P[i];\n node._next = tmp;\n tmp._prev = node;\n\n if (P[i]._end) {\n P[i]._end = false;\n node._end = true;\n }\n\n break;\n }\n }\n }\n }\n },\n\n _getStatus: function (P, path) {\n var status;\n while (P.intersection) {\n if (P._end) {\n break;\n }\n P = P._next;\n }\n if (Geometry.windingNumber(P.coords.usrCoords, path) === 0) {\n // Outside\n status = 'entry';\n // console.log(P.coords.usrCoords, ' is outside')\n } else {\n // Inside\n status = 'exit';\n // console.log(P.coords.usrCoords, ' is inside')\n }\n\n return [P, status];\n },\n\n /**\n * Mark the intersection vertices of path1 as entry points or as exit points\n * in respect to path2.\n * \n * This is the simple algorithm as in\n * Greiner, Günther; Kai Hormann (1998). \"Efficient clipping of arbitrary polygons\".\n * ACM Transactions on Graphics. 17 (2): 71–83\n * \n * The algorithm handles also \"delayed crossings\" from\n * Erich, L. Foster, and Kai Hormann, Kai, and Romeo Traaian Popa (2019),\n * \"Clipping simple polygons with degenerate intersections\", Computers & Graphics:X, 2.\n * and - as an additional improvement -\n * handles self intersections of delayed crossings (A.W. 2021).\n *\n * @private\n * @param {Array} path1 First path\n * @param {Array} path2 Second path\n */\n markEntryExit: function (path1, path2, starters) {\n var status, P, cnt, res,\n i, len, start,\n endless = true,\n chain_start = null,\n intersection_chain = 0,\n DEBUG = false;\n\n len = starters.length;\n for (i = 0; i < len; i++) {\n start = starters[i];\n if (DEBUG) {\n console.log(\n \"\\n;;;;;;;;;; Labelling phase\",\n Type.exists(path1[start].data) ? path1[start].data.pathname : \" \",\n path1[start].coords.usrCoords\n );\n }\n this._classifyDegenerateIntersections(path1[start]);\n this._handleIntersectionChains(path1[start]);\n if (DEBUG) {\n console.log(\"\\n---- back to markEntryExit\");\n }\n\n // Decide if the first point of the component is inside or outside\n // of the other path.\n res = this._getStatus(path1[start], path2);\n P = res[0];\n status = res[1];\n if (DEBUG) {\n console.log(\"Start node:\", P.coords.usrCoords, status);\n }\n\n P._starter = true;\n\n // Greiner-Hormann entry/exit algorithm\n // with additional handling of delayed crossing / bouncing\n cnt = 0;\n chain_start = null;\n intersection_chain = 0;\n\n while (endless) {\n if (P.intersection === true) {\n if (P.data.type === \"X\" && intersection_chain === 1) {\n // While we are in an intersection chain, i.e. a delayed crossing,\n // we stumble on a crossing intersection.\n // Probably, the other path is self intersecting.\n // We end the intersection chain here and\n // mark this event by setting intersection_chain = 2.\n chain_start.entry_exit = status;\n if (status === 'exit') {\n chain_start.data.type = 'X';\n }\n intersection_chain = 2;\n }\n\n if (P.data.type === \"X\" || P.data.type === 'DB') {\n P.entry_exit = status;\n status = status === \"entry\" ? \"exit\" : 'entry';\n if (DEBUG) {\n console.log(\"mark:\", P.coords.usrCoords, P.data.type, P.entry_exit);\n }\n }\n\n if (P.data.type === 'DX') {\n if (intersection_chain === 0) {\n // Start of intersection chain.\n // No active intersection chain yet,\n // i.e. we did not pass a the first node of a delayed crossing.\n chain_start = P;\n intersection_chain = 1;\n if (DEBUG) {\n console.log(\n \"Start intersection chain:\",\n P.coords.usrCoords,\n P.data.type,\n status\n );\n }\n } else if (intersection_chain === 1) {\n // Active intersection chain (intersection_chain===1)!\n // End of delayed crossing chain reached\n P.entry_exit = status;\n chain_start.entry_exit = status;\n if (status === 'exit') {\n chain_start.data.type = 'X';\n } else {\n P.data.type = 'X';\n }\n status = status === \"entry\" ? \"exit\" : 'entry';\n\n if (DEBUG) {\n console.log(\n \"mark':\",\n chain_start.coords.usrCoords,\n chain_start.data.type,\n chain_start.entry_exit\n );\n console.log(\n \"mark:\",\n P.coords.usrCoords,\n P.data.type,\n P.entry_exit\n );\n }\n chain_start = null;\n intersection_chain = 0;\n } else if (intersection_chain === 2) {\n // The delayed crossing had been interrupted by a crossing intersection.\n // Now we treat the end of the delayed crossing as regular crossing.\n P.entry_exit = status;\n P.data.type = 'X';\n status = status === \"entry\" ? \"exit\" : 'entry';\n chain_start = null;\n intersection_chain = 0;\n }\n }\n }\n\n P = P._next;\n if (Type.exists(P._starter) || cnt > 10000) {\n break;\n }\n\n cnt++;\n }\n }\n },\n\n /**\n *\n * @private\n * @param {Array} P\n * @param {Boolean} isBackward\n * @returns {Boolean} True, if the node is an intersection and is of type 'X'\n */\n _stayOnPath: function (P, status) {\n var stay = true;\n\n if (P.intersection && P.data.type !== 'B') {\n stay = status === P.entry_exit;\n }\n return stay;\n },\n\n /**\n * Add a point to the clipping path and returns if the algorithms\n * arrived at an intersection point which has already been visited.\n * In this case, true is returned.\n *\n * @param {Array} path Resulting path\n * @param {JXG.Math.Clip.Vertex} vertex Point to be added\n * @param {Boolean} DEBUG if true, write debug output to console.log\n * @returns {Boolean} true: point has been visited before, false otherwise\n * @private\n */\n _addVertex: function (path, vertex, DEBUG) {\n if (!isNaN(vertex.coords.usrCoords[1]) && !isNaN(vertex.coords.usrCoords[2])) {\n path.push(vertex);\n }\n if (vertex.intersection && vertex.data.done) {\n if (DEBUG) {\n console.log(\n \"Add last intersection point\",\n vertex.coords.usrCoords,\n \"on\",\n vertex.data.pathname,\n vertex.entry_exit,\n vertex.data.type\n );\n }\n return true;\n }\n if (vertex.intersection) {\n vertex.data.done = true;\n\n if (DEBUG) {\n console.log(\n \"Add intersection point\",\n vertex.coords.usrCoords,\n \"on\",\n vertex.data.pathname,\n vertex.entry_exit,\n vertex.data.type\n );\n }\n }\n return false;\n },\n\n /**\n * Tracing phase of the Greiner-Hormann algorithm, see\n * Greiner, Günther; Kai Hormann (1998).\n * \"Efficient clipping of arbitrary polygons\". ACM Transactions on Graphics. 17 (2): 71–83\n *\n * Boolean operations on polygons are distinguished: 'intersection', 'union', 'difference'.\n *\n * @private\n * @param {Array} S Subject path\n * @param {Array} S_intersect Array containing the intersection vertices of the subject path\n * @param {String} clip_type contains the Boolean operation: 'intersection', 'union', or 'difference'\n * @return {Array} Array consisting of two arrays containing the x-coordinates and the y-coordintaes of\n * the resulting path.\n */\n tracing: function (S, S_intersect, clip_type) {\n var P, status, current, start,\n cnt = 0,\n maxCnt = 10000,\n S_idx = 0,\n path = [],\n done = false,\n DEBUG = false;\n\n if (DEBUG) {\n console.log(\"\\n------ Start Phase 3\");\n }\n\n // reverse = (clip_type === 'difference' || clip_type === 'union') ? true : false;\n while (S_idx < S_intersect.length && cnt < maxCnt) {\n // Take the first intersection node of the subject path\n // which is not yet included as start point.\n current = S_intersect[S_idx];\n if (\n current.data.done ||\n current.data.type !== \"X\" /*|| !this._isCrossing(current, reverse)*/\n ) {\n S_idx++;\n continue;\n }\n\n if (DEBUG) {\n console.log(\n \"\\nStart\",\n current.data.pathname,\n current.coords.usrCoords,\n current.data.type,\n current.entry_exit,\n S_idx\n );\n }\n if (path.length > 0) {\n // Add a new path\n path.push([NaN, NaN]);\n }\n\n // Start now the tracing with that node of the subject path\n start = current.data.idx;\n P = S;\n\n done = this._addVertex(path, current, DEBUG);\n status = current.entry_exit;\n do {\n if (done) {\n break;\n }\n //\n // Decide if we follow the current path forward or backward.\n // for example, in case the clipping is of type \"intersection\"\n // and the current intersection node is of type entry, we go forward.\n //\n if (\n (clip_type === \"intersection\" && current.entry_exit === 'entry') ||\n (clip_type === \"union\" && current.entry_exit === 'exit') ||\n (clip_type === \"difference\" &&\n (P === S) === (current.entry_exit === 'exit'))\n ) {\n if (DEBUG) {\n console.log(\"Go forward on\", current.data.pathname, current.entry_exit);\n }\n\n //\n // Take the next nodes and add them to the path\n // as long as they are not intersection nodes of type 'X'.\n //\n do {\n current = current._next;\n done = this._addVertex(path, current, DEBUG);\n if (done) {\n break;\n }\n } while (this._stayOnPath(current, status));\n cnt++;\n } else {\n if (DEBUG) {\n console.log(\"Go backward on\", current.data.pathname);\n }\n //\n // Here, we go backward:\n // Take the previous nodes and add them to the path\n // as long as they are not intersection nodes of type 'X'.\n //\n do {\n current = current._prev;\n done = this._addVertex(path, current, DEBUG);\n if (done) {\n break;\n }\n } while (this._stayOnPath(current, status));\n cnt++;\n }\n\n if (done) {\n break;\n }\n\n if (!current.neighbour) {\n console.log(\n \"Tracing: emergency break - no neighbour!!!!!!!!!!!!!!!!!\",\n cnt\n );\n return [[0], [0]];\n }\n //\n // We stopped the forward or backward loop, because we've\n // arrived at a crossing intersection node, i.e. we have to\n // switch to the other path now.\n if (DEBUG) {\n console.log(\n \"Switch from\",\n current.coords.usrCoords,\n current.data.pathname,\n \"to\",\n current.neighbour.coords.usrCoords,\n \"on\",\n current.neighbour.data.pathname\n );\n }\n current = current.neighbour;\n if (current.data.done) {\n break;\n }\n current.data.done = true;\n status = current.entry_exit;\n\n // if (current.data.done) {\n // // We arrived at an intersection node which is already\n // // added to the clipping path.\n // // We add it again to close the clipping path and jump out of the\n // // loop.\n // path.push(current);\n // if (DEBUG) {\n // console.log(\"Push last\", current.coords.usrCoords);\n // }\n // break;\n // }\n P = current.data.path;\n\n // Polygon closed:\n // if (DEBUG) {\n // console.log(\"End of loop:\", \"start=\", start, \"idx=\", current.data.idx);\n // }\n // } while (!(current.data.pathname === 'S' && current.data.idx === start) && cnt < maxCnt);\n } while (current.data.idx !== start && cnt < maxCnt);\n\n if (cnt >= maxCnt) {\n console.log(\"Tracing: stopping an infinite loop!\", cnt);\n }\n\n S_idx++;\n }\n return this._getCoordsArrays(path, false);\n },\n\n /**\n * Handle path clipping if one of the two paths is empty.\n * @private\n * @param {Array} S First path, array of JXG.Coords\n * @param {Array} C Second path, array of JXG.Coords\n * @param {String} clip_type Type of Boolean operation: 'intersection', 'union', 'differrence'.\n * @return {Boolean} true, if one of the input paths is empty, false otherwise.\n */\n isEmptyCase: function (S, C, clip_type) {\n if (clip_type === \"intersection\" && (S.length === 0 || C.length === 0)) {\n return true;\n }\n if (clip_type === \"union\" && S.length === 0 && C.length === 0) {\n return true;\n }\n if (clip_type === \"difference\" && S.length === 0) {\n return true;\n }\n\n return false;\n },\n\n _getCoordsArrays: function (path, doClose) {\n var pathX = [],\n pathY = [],\n i,\n le = path.length;\n\n for (i = 0; i < le; i++) {\n if (path[i].coords) {\n pathX.push(path[i].coords.usrCoords[1]);\n pathY.push(path[i].coords.usrCoords[2]);\n } else {\n pathX.push(path[i][0]);\n pathY.push(path[i][1]);\n }\n }\n if (doClose && le > 0) {\n if (path[0].coords) {\n pathX.push(path[0].coords.usrCoords[1]);\n pathY.push(path[0].coords.usrCoords[2]);\n } else {\n pathX.push(path[0][0]);\n pathY.push(path[0][1]);\n }\n }\n\n return [pathX, pathY];\n },\n\n /**\n * Handle cases when there are no intersection points of the two paths. This is the case if the\n * paths are disjoint or one is contained in the other.\n * @private\n * @param {Array} S First path, array of JXG.Coords\n * @param {Array} C Second path, array of JXG.Coords\n * @param {String} clip_type Type of Boolean operation: 'intersection', 'union', 'differrence'.\n * @return {Array} Array consisting of two arrays containing the x-coordinates and the y-coordinates of\n * the resulting path.\n */\n handleEmptyIntersection: function (S, C, clip_type) {\n var P,\n Q,\n doClose = false,\n path = [];\n\n // Handle trivial cases\n if (S.length === 0) {\n if (clip_type === 'union') {\n // S cup C = C\n path = C;\n } else {\n // S cap C = S \\ C = {}\n path = [];\n }\n return this._getCoordsArrays(path, true);\n }\n if (C.length === 0) {\n if (clip_type === 'intersection') {\n // S cap C = {}\n path = [];\n } else {\n // S cup C = S \\ C = S\n path = S;\n }\n return this._getCoordsArrays(path, true);\n }\n\n // From now on, both paths have non-zero length.\n // The two paths have no crossing intersections,\n // but there might be bouncing intersections.\n\n // First, we find -- if possible -- on each path a point which is not an intersection point.\n if (S.length > 0) {\n P = S[0];\n while (P.intersection) {\n P = P._next;\n if (P._end) {\n break;\n }\n }\n }\n if (C.length > 0) {\n Q = C[0];\n while (Q.intersection) {\n Q = Q._next;\n if (Q._end) {\n break;\n }\n }\n }\n\n // Test if one curve is contained by the other\n if (Geometry.windingNumber(P.coords.usrCoords, C) === 0) {\n // P is outside of C:\n // Either S is disjoint from C or C is inside of S\n if (Geometry.windingNumber(Q.coords.usrCoords, S) !== 0) {\n // C is inside of S, i.e. C subset of S\n\n if (clip_type === 'union') {\n Type.concat(path, S);\n path.push(S[0]);\n } else if (clip_type === 'difference') {\n Type.concat(path, S);\n path.push(S[0]);\n if (Geometry.signedPolygon(S) * Geometry.signedPolygon(C) > 0) {\n // Pathes have same orientation, we have to revert one.\n path.reverse();\n }\n path.push([NaN, NaN]);\n }\n if (clip_type === \"difference\" || clip_type === 'intersection') {\n Type.concat(path, C);\n path.push(C[0]);\n doClose = false;\n }\n } else {\n // The curves are disjoint\n if (clip_type === 'difference') {\n Type.concat(path, S);\n doClose = true;\n } else if (clip_type === 'union') {\n Type.concat(path, S);\n path.push(S[0]);\n path.push([NaN, NaN]);\n Type.concat(path, C);\n path.push(C[0]);\n }\n }\n } else {\n // S inside of C, i.e. S subset of C\n if (clip_type === 'intersection') {\n Type.concat(path, S);\n doClose = true;\n } else if (clip_type === 'union') {\n Type.concat(path, C);\n path.push(C[0]);\n }\n\n // 'difference': path is empty\n }\n\n return this._getCoordsArrays(path, doClose);\n },\n\n /**\n * Count intersection points of type 'X'.\n * @param {JXG.Mat.Clip.Vertex} intersections\n * @returns Number\n * @private\n */\n _countCrossingIntersections: function (intersections) {\n var i,\n le = intersections.length,\n sum = 0;\n\n for (i = 0; i < le; i++) {\n if (intersections[i].data.type === 'X') {\n sum++;\n }\n }\n return sum;\n },\n\n /**\n * Create path from all sorts of input elements and convert it\n * to a suitable input path for greinerHormann().\n *\n * @private\n * @param {Object} obj Maybe curve, arc, sector, circle, polygon, array of points, array of JXG.Coords,\n * array of coordinate pairs.\n * @param {JXG.Board} board JSXGraph board object. It is needed to convert between\n * user coordinates and screen coordinates.\n * @returns {Array} Array of JXG.Coords elements containing a path.\n * @see JXG.Math.Clip.greinerHormann\n */\n _getPath: function (obj, board) {\n var i, len, r,\n rad, angle, alpha, steps,\n S = [];\n\n // Collect all points into path array S\n if (\n obj.elementClass === Const.OBJECT_CLASS_CURVE &&\n (obj.type === Const.OBJECT_TYPE_ARC || obj.type === Const.OBJECT_TYPE_SECTOR)\n ) {\n angle = Geometry.rad(obj.radiuspoint, obj.center, obj.anglepoint);\n steps = Math.floor((angle * 180) / Math.PI);\n r = obj.Radius();\n rad = angle / steps;\n alpha = Math.atan2(\n obj.radiuspoint.coords.usrCoords[2] - obj.center.coords.usrCoords[2],\n obj.radiuspoint.coords.usrCoords[1] - obj.center.coords.usrCoords[1]\n );\n\n if (obj.type === Const.OBJECT_TYPE_SECTOR) {\n this._addToList(S, obj.center.coords, 0);\n }\n for (i = 0; i <= steps; i++) {\n this._addToList(\n S,\n new Coords(\n Const.COORDS_BY_USER,\n [\n obj.center.coords.usrCoords[0],\n obj.center.coords.usrCoords[1] + Math.cos(i * rad + alpha) * r,\n obj.center.coords.usrCoords[2] + Math.sin(i * rad + alpha) * r\n ],\n board\n ),\n i + 1\n );\n }\n if (obj.type === Const.OBJECT_TYPE_SECTOR) {\n this._addToList(S, obj.center.coords, steps + 2);\n }\n } else if (obj.elementClass === Const.OBJECT_CLASS_CURVE && Type.exists(obj.points)) {\n len = obj.numberPoints;\n for (i = 0; i < len; i++) {\n this._addToList(S, obj.points[i], i);\n }\n } else if (obj.type === Const.OBJECT_TYPE_POLYGON) {\n for (i = 0; i < obj.vertices.length; i++) {\n this._addToList(S, obj.vertices[i].coords, i);\n }\n } else if (obj.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n steps = 359;\n r = obj.Radius();\n rad = (2 * Math.PI) / steps;\n for (i = 0; i <= steps; i++) {\n this._addToList(\n S,\n new Coords(\n Const.COORDS_BY_USER,\n [\n obj.center.coords.usrCoords[0],\n obj.center.coords.usrCoords[1] + Math.cos(i * rad) * r,\n obj.center.coords.usrCoords[2] + Math.sin(i * rad) * r\n ],\n board\n ),\n i\n );\n }\n } else if (Type.isArray(obj)) {\n len = obj.length;\n for (i = 0; i < len; i++) {\n if (Type.exists(obj[i].coords)) {\n // Point type\n this._addToList(S, obj[i].coords, i);\n } else if (Type.isArray(obj[i])) {\n // Coordinate pair\n this._addToList(S, new Coords(Const.COORDS_BY_USER, obj[i], board), i);\n } else if (Type.exists(obj[i].usrCoords)) {\n // JXG.Coordinates\n this._addToList(S, obj[i], i);\n }\n }\n }\n\n return S;\n },\n\n /**\n * Determine the intersection, union or difference of two closed paths.\n * \n * This is an implementation of the Greiner-Hormann algorithm, see\n * Günther Greiner and Kai Hormann (1998).\n * \"Efficient clipping of arbitrary polygons\". ACM Transactions on Graphics. 17 (2): 71–83.\n * and\n * Erich, L. Foster, and Kai Hormann, Kai, and Romeo Traaian Popa (2019),\n * \"Clipping simple polygons with degenerate intersections\", Computers & Graphics:X, 2.\n * \n * It is assumed that the pathes are closed, whereby it does not matter if the last point indeed\n * equals the first point. In contrast to the original Greiner-Hormann algorithm,\n * this algorithm can cope with many degenerate cases. A degenerate case is a vertext of one path\n * which is contained in the other path.\n * \n *\n * Problematic are:\n * This class defines the interface to the graphics part of JSXGraph. This class is an abstract class, it\n * actually does not render anything. This is up to the {@link JXG.SVGRenderer}, {@link JXG.VMLRenderer},\n * and {@link JXG.CanvasRenderer} classes. We strongly discourage you from using the methods in these classes\n * directly. Only the methods which are defined in this class and are not marked as private are guaranteed\n * to exist in any renderer instance you can access via {@link JXG.Board#renderer}. But not all methods may\n * work as expected. The methods of this renderer can be divided into different categories:\n * \n * The returned object also contains the types of the arrow heads.\n *\n * @param {JXG.GeometryElement} el JSXGraph line or curve element\n * @param {Number} strokewidth strokewidth of the element\n * @param {String} hl Ither 'highlight' or empty string\n * @returns {Object} object containing the data\n *\n * @private\n */\n getArrowHeadData: function (el, strokewidth, hl) {\n var minlen = Mat.eps,\n typeFirst,\n typeLast,\n offFirst = 0,\n offLast = 0,\n sizeFirst = 0,\n sizeLast = 0,\n ev_fa = el.evalVisProp('firstarrow'),\n ev_la = el.evalVisProp('lastarrow'),\n off,\n size;\n\n /*\n Handle arrow heads.\n\n The default arrow head is an isosceles triangle with base length 10 units and height 10 units.\n These 10 units are scaled to strokeWidth * arrowSize pixels.\n */\n if (ev_fa || ev_la) {\n if (Type.exists(ev_fa.type)) {\n typeFirst = el.eval(ev_fa.type);\n } else {\n if (el.elementClass === Const.OBJECT_CLASS_LINE) {\n typeFirst = 1;\n } else {\n typeFirst = 7;\n }\n }\n if (Type.exists(ev_la.type)) {\n typeLast = el.eval(ev_la.type);\n } else {\n if (el.elementClass === Const.OBJECT_CLASS_LINE) {\n typeLast = 1;\n } else {\n typeLast = 7;\n }\n }\n\n if (ev_fa) {\n size = 6;\n if (Type.exists(ev_fa.size)) {\n size = el.eval(ev_fa.size);\n }\n if (hl !== \"\" && Type.exists(ev_fa[hl + \"size\"])) {\n size = el.eval(ev_fa[hl + \"size\"]);\n }\n\n off = strokewidth * size;\n if (typeFirst === 2) {\n off *= 0.5;\n minlen += strokewidth * size;\n } else if (typeFirst === 3) {\n off = (strokewidth * size) / 3;\n minlen += strokewidth;\n } else if (typeFirst === 4 || typeFirst === 5 || typeFirst === 6) {\n off = (strokewidth * size) / 1.5;\n minlen += strokewidth * size;\n } else if (typeFirst === 7) {\n off = 0;\n size = 10;\n minlen += strokewidth;\n } else {\n minlen += strokewidth * size;\n }\n offFirst += off;\n sizeFirst = size;\n }\n\n if (ev_la) {\n size = 6;\n if (Type.exists(ev_la.size)) {\n size = el.eval(ev_la.size);\n }\n if (hl !== \"\" && Type.exists(ev_la[hl + \"size\"])) {\n size = el.eval(ev_la[hl + \"size\"]);\n }\n off = strokewidth * size;\n if (typeLast === 2) {\n off *= 0.5;\n minlen += strokewidth * size;\n } else if (typeLast === 3) {\n off = (strokewidth * size) / 3;\n minlen += strokewidth;\n } else if (typeLast === 4 || typeLast === 5 || typeLast === 6) {\n off = (strokewidth * size) / 1.5;\n minlen += strokewidth * size;\n } else if (typeLast === 7) {\n off = 0;\n size = 10;\n minlen += strokewidth;\n } else {\n minlen += strokewidth * size;\n }\n offLast += off;\n sizeLast = size;\n }\n }\n el.visPropCalc.typeFirst = typeFirst;\n el.visPropCalc.typeLast = typeLast;\n\n return {\n evFirst: ev_fa,\n evLast: ev_la,\n typeFirst: typeFirst,\n typeLast: typeLast,\n offFirst: offFirst,\n offLast: offLast,\n sizeFirst: sizeFirst,\n sizeLast: sizeLast,\n showFirst: 1, // Show arrow head. 0 if the distance is too small\n showLast: 1, // Show arrow head. 0 if the distance is too small\n minLen: minlen,\n strokeWidth: strokewidth\n };\n },\n\n /**\n * Corrects the line length if there are arrow heads, such that\n * the arrow ends exactly at the intended position.\n * Calls the renderer method to draw the line.\n *\n * @param {JXG.Line} el Reference to a line object, that has to be drawn\n * @param {Object} arrowData Data concerning possible arrow heads\n *\n * @returns {JXG.AbstractRenderer} Reference to the renderer\n *\n * @private\n * @see Line\n * @see JXG.Line\n * @see JXG.AbstractRenderer#updateLine\n * @see JXG.AbstractRenderer#getPositionArrowHead\n *\n */\n updateLineWithEndings: function (el, arrowData) {\n var c1,\n c2,\n // useTotalLength = true,\n margin = null;\n\n c1 = new Coords(Const.COORDS_BY_USER, el.point1.coords.usrCoords, el.board);\n c2 = new Coords(Const.COORDS_BY_USER, el.point2.coords.usrCoords, el.board);\n margin = el.evalVisProp('margin');\n if (!el.evalVisProp('clip')) {\n margin += 4096;\n }\n Geometry.calcStraight(el, c1, c2, margin);\n\n this.handleTouchpoints(el, c1, c2, arrowData);\n this.getPositionArrowHead(el, c1, c2, arrowData);\n\n this.updateLinePrim(\n el.rendNode,\n c1.scrCoords[1],\n c1.scrCoords[2],\n c2.scrCoords[1],\n c2.scrCoords[2],\n el.board\n );\n\n return this;\n },\n\n /**\n *\n * Calls the renderer method to draw a curve.\n *\n * @param {JXG.GeometryElement} el Reference to a line object, that has to be drawn.\n * @returns {JXG.AbstractRenderer} Reference to the renderer\n *\n * @private\n * @see Curve\n * @see JXG.Curve\n * @see JXG.AbstractRenderer#updateCurve\n *\n */\n updatePath: function (el) {\n if (el.evalVisProp('handdrawing')) {\n this.updatePathPrim(el.rendNode, this.updatePathStringBezierPrim(el), el.board);\n } else {\n this.updatePathPrim(el.rendNode, this.updatePathStringPrim(el), el.board);\n }\n\n return this;\n },\n\n /**\n * Shorten the length of a line element such that the arrow head touches\n * the start or end point and such that the arrow head ends exactly\n * at the start / end position of the line.\n * \n * The Coords objects c1 and c2 are changed in place. In object a, the Boolean properties\n * 'showFirst' and 'showLast' are set.\n *\n * @param {JXG.Line} el Reference to the line object that gets arrow heads.\n * @param {JXG.Coords} c1 Coords of the first point of the line (after {@link JXG.Math.Geometry#calcStraight}).\n * @param {JXG.Coords} c2 Coords of the second point of the line (after {@link JXG.Math.Geometry#calcStraight}).\n * @param {Object} a Object { evFirst: Boolean, evLast: Boolean} containing information about arrow heads.\n * @see JXG.AbstractRenderer#getArrowHeadData\n *\n */\n getPositionArrowHead: function (el, c1, c2, a) {\n var d, d1x, d1y, d2x, d2y;\n\n // Handle arrow heads.\n\n // The default arrow head (type==1) is an isosceles triangle with base length 10 units and height 10 units.\n // These 10 units are scaled to strokeWidth * arrowSize pixels.\n if (a.evFirst || a.evLast) {\n // Correct the position of the arrow heads\n d1x = d1y = d2x = d2y = 0.0;\n d = c1.distance(Const.COORDS_BY_SCREEN, c2);\n\n if (a.evFirst && el.board.renderer.type !== 'vml') {\n if (d >= a.minLen) {\n d1x = ((c2.scrCoords[1] - c1.scrCoords[1]) * a.offFirst) / d;\n d1y = ((c2.scrCoords[2] - c1.scrCoords[2]) * a.offFirst) / d;\n } else {\n a.showFirst = 0;\n }\n }\n\n if (a.evLast && el.board.renderer.type !== 'vml') {\n if (d >= a.minLen) {\n d2x = ((c2.scrCoords[1] - c1.scrCoords[1]) * a.offLast) / d;\n d2y = ((c2.scrCoords[2] - c1.scrCoords[2]) * a.offLast) / d;\n } else {\n a.showLast = 0;\n }\n }\n c1.setCoordinates(\n Const.COORDS_BY_SCREEN,\n [c1.scrCoords[1] + d1x, c1.scrCoords[2] + d1y],\n false,\n true\n );\n c2.setCoordinates(\n Const.COORDS_BY_SCREEN,\n [c2.scrCoords[1] - d2x, c2.scrCoords[2] - d2y],\n false,\n true\n );\n }\n\n return this;\n },\n\n /**\n * Handle touchlastpoint / touchfirstpoint\n *\n * @param {JXG.GeometryElement} el\n * @param {JXG.Coords} c1 Coordinates of the start of the line. The coordinates are changed in place.\n * @param {JXG.Coords} c2 Coordinates of the end of the line. The coordinates are changed in place.\n * @param {Object} a\n * @see JXG.AbstractRenderer#getArrowHeadData\n */\n handleTouchpoints: function (el, c1, c2, a) {\n var s1, s2, d, d1x, d1y, d2x, d2y;\n\n if (a.evFirst || a.evLast) {\n d = d1x = d1y = d2x = d2y = 0.0;\n\n s1 = el.point1.evalVisProp('size') +\n el.point1.evalVisProp('strokewidth');\n\n s2 = el.point2.evalVisProp('size') +\n el.point2.evalVisProp('strokewidth');\n\n // Handle touchlastpoint /touchfirstpoint\n if (a.evFirst && el.evalVisProp('touchfirstpoint') &&\n el.point1.evalVisProp('visible')) {\n d = c1.distance(Const.COORDS_BY_SCREEN, c2);\n //if (d > s) {\n d1x = ((c2.scrCoords[1] - c1.scrCoords[1]) * s1) / d;\n d1y = ((c2.scrCoords[2] - c1.scrCoords[2]) * s1) / d;\n //}\n }\n if (a.evLast && el.evalVisProp('touchlastpoint') &&\n el.point2.evalVisProp('visible')) {\n d = c1.distance(Const.COORDS_BY_SCREEN, c2);\n //if (d > s) {\n d2x = ((c2.scrCoords[1] - c1.scrCoords[1]) * s2) / d;\n d2y = ((c2.scrCoords[2] - c1.scrCoords[2]) * s2) / d;\n //}\n }\n c1.setCoordinates(\n Const.COORDS_BY_SCREEN,\n [c1.scrCoords[1] + d1x, c1.scrCoords[2] + d1y],\n false,\n true\n );\n c2.setCoordinates(\n Const.COORDS_BY_SCREEN,\n [c2.scrCoords[1] - d2x, c2.scrCoords[2] - d2y],\n false,\n true\n );\n }\n\n return this;\n },\n\n /**\n * Set the arrow head size.\n *\n * @param {JXG.GeometryElement} el Reference to a line or curve object that has to be drawn.\n * @param {Object} arrowData Data concerning possible arrow heads\n * @returns {JXG.AbstractRenderer} Reference to the renderer\n *\n * @private\n * @see Line\n * @see JXG.Line\n * @see Curve\n * @see JXG.Curve\n * @see JXG.AbstractRenderer#updatePathWithArrowHeads\n * @see JXG.AbstractRenderer#getArrowHeadData\n */\n setArrowSize: function (el, a) {\n if (a.evFirst) {\n this._setArrowWidth(\n el.rendNodeTriangleStart,\n a.showFirst * a.strokeWidth,\n el.rendNode,\n a.sizeFirst\n );\n }\n if (a.evLast) {\n this._setArrowWidth(\n el.rendNodeTriangleEnd,\n a.showLast * a.strokeWidth,\n el.rendNode,\n a.sizeLast\n );\n }\n return this;\n },\n\n /**\n * Update the line endings (linecap) of a straight line from its attribute\n * 'linecap'.\n * Possible values for the attribute 'linecap' are: 'butt', 'round', 'square'.\n * The default value is 'butt'. Not available for VML renderer.\n *\n * @param {JXG.Line} element A arbitrary line.\n * @see Line\n * @see JXG.Line\n * @see JXG.AbstractRenderer#updateLine\n */\n setLineCap: function (el) { /* stub */ },\n\n /* ********* Ticks related stuff *********** */\n\n /**\n * Creates a rendering node for ticks added to a line.\n * @param {JXG.Line} el A arbitrary line.\n * @see Line\n * @see Ticks\n * @see JXG.Line\n * @see JXG.Ticks\n * @see JXG.AbstractRenderer#updateTicks\n */\n drawTicks: function (el) {\n el.rendNode = this.appendChildPrim(\n this.createPrim(\"path\", el.id),\n el.evalVisProp('layer')\n );\n this.appendNodesToElement(el, 'path');\n },\n\n /**\n * Update {@link Ticks} on a {@link JXG.Line}. This method is only a stub and has to be implemented\n * in any descendant renderer class.\n * @param {JXG.Ticks} el Reference of a ticks object that has to be updated.\n * @see Line\n * @see Ticks\n * @see JXG.Line\n * @see JXG.Ticks\n * @see JXG.AbstractRenderer#drawTicks\n */\n updateTicks: function (el) { /* stub */ },\n\n /* ********* Circle related stuff *********** */\n\n /**\n * Draws a {@link JXG.Circle}\n * @param {JXG.Circle} el Reference to a {@link JXG.Circle} object that has to be drawn.\n * @see Circle\n * @see JXG.Circle\n * @see JXG.AbstractRenderer#updateEllipse\n */\n drawEllipse: function (el) {\n el.rendNode = this.appendChildPrim(\n this.createPrim(\"ellipse\", el.id),\n el.evalVisProp('layer')\n );\n this.appendNodesToElement(el, 'ellipse');\n this.updateEllipse(el);\n },\n\n /**\n * Updates visual appearance of a given {@link JXG.Circle} on the {@link JXG.Board}.\n * @param {JXG.Circle} el Reference to a {@link JXG.Circle} object, that has to be updated.\n * @see Circle\n * @see JXG.Circle\n * @see JXG.AbstractRenderer#drawEllipse\n */\n updateEllipse: function (el) {\n this._updateVisual(el);\n\n var radius = el.Radius();\n\n if (\n /*radius > 0.0 &&*/\n Math.abs(el.center.coords.usrCoords[0]) > Mat.eps &&\n !isNaN(radius + el.center.coords.scrCoords[1] + el.center.coords.scrCoords[2]) &&\n radius * el.board.unitX < 2000000\n ) {\n this.updateEllipsePrim(\n el.rendNode,\n el.center.coords.scrCoords[1],\n el.center.coords.scrCoords[2],\n radius * el.board.unitX,\n radius * el.board.unitY\n );\n }\n this.setLineCap(el);\n },\n\n /* ********* Polygon related stuff *********** */\n\n /**\n * Draws a {@link JXG.Polygon} on the {@link JXG.Board}.\n * @param {JXG.Polygon} el Reference to a Polygon object, that is to be drawn.\n * @see Polygon\n * @see JXG.Polygon\n * @see JXG.AbstractRenderer#updatePolygon\n */\n drawPolygon: function (el) {\n el.rendNode = this.appendChildPrim(\n this.createPrim(\"polygon\", el.id),\n el.evalVisProp('layer')\n );\n this.appendNodesToElement(el, 'polygon');\n this.updatePolygon(el);\n },\n\n /**\n * Updates properties of a {@link JXG.Polygon}'s rendering node.\n * @param {JXG.Polygon} el Reference to a {@link JXG.Polygon} object, that has to be updated.\n * @see Polygon\n * @see JXG.Polygon\n * @see JXG.AbstractRenderer#drawPolygon\n */\n updatePolygon: function (el) {\n // Here originally strokecolor wasn't updated but strokewidth was.\n // But if there's no strokecolor i don't see why we should update strokewidth.\n this._updateVisual(el, { stroke: true, dash: true });\n this.updatePolygonPrim(el.rendNode, el);\n },\n\n /* ********* Text related stuff *********** */\n\n /**\n * Shows a small copyright notice in the top left corner of the board.\n * @param {String} str The copyright notice itself\n * @param {Number} fontsize Size of the font the copyright notice is written in\n * @see JXG.AbstractRenderer#displayLogo\n * @see Text#fontSize\n */\n displayCopyright: function (str, fontsize) { /* stub */ },\n\n /**\n * Shows a small JSXGraph logo in the top left corner of the board.\n * @param {String} str The data-URL of the logo\n * @param {Number} fontsize Size of the font the copyright notice is written in\n * @see JXG.AbstractRenderer#displayCopyright\n * @see Text#fontSize\n */\n displayLogo: function (str, fontsize) { /* stub */ },\n\n /**\n * An internal text is a {@link JXG.Text} element which is drawn using only\n * the given renderer but no HTML. This method is only a stub, the drawing\n * is done in the special renderers.\n * @param {JXG.Text} el Reference to a {@link JXG.Text} object\n * @see Text\n * @see JXG.Text\n * @see JXG.AbstractRenderer#updateInternalText\n * @see JXG.AbstractRenderer#drawText\n * @see JXG.AbstractRenderer#updateText\n * @see JXG.AbstractRenderer#updateTextStyle\n */\n drawInternalText: function (el) { /* stub */ },\n\n /**\n * Updates visual properties of an already existing {@link JXG.Text} element.\n * @param {JXG.Text} el Reference to an {@link JXG.Text} object, that has to be updated.\n * @see Text\n * @see JXG.Text\n * @see JXG.AbstractRenderer#drawInternalText\n * @see JXG.AbstractRenderer#drawText\n * @see JXG.AbstractRenderer#updateText\n * @see JXG.AbstractRenderer#updateTextStyle\n */\n updateInternalText: function (el) { /* stub */ },\n\n /**\n * Displays a {@link JXG.Text} on the {@link JXG.Board} by putting a HTML div over it.\n * @param {JXG.Text} el Reference to an {@link JXG.Text} object, that has to be displayed\n * @see Text\n * @see JXG.Text\n * @see JXG.AbstractRenderer#drawInternalText\n * @see JXG.AbstractRenderer#updateText\n * @see JXG.AbstractRenderer#updateInternalText\n * @see JXG.AbstractRenderer#updateTextStyle\n */\n drawText: function (el) {\n var node, z, level, ev_visible;\n\n if (\n el.evalVisProp('display') === \"html\" &&\n Env.isBrowser &&\n this.type !== \"no\"\n ) {\n node = this.container.ownerDocument.createElement('div');\n //node = this.container.ownerDocument.createElementNS('http://www.w3.org/1999/xhtml', 'div'); //\n node.style.position = 'absolute';\n node.className = el.evalVisProp('cssclass');\n\n level = el.evalVisProp('layer');\n if (!Type.exists(level)) {\n // trace nodes have level not set\n level = 0;\n }\n\n if (this.container.style.zIndex === \"\") {\n z = 0;\n } else {\n z = parseInt(this.container.style.zIndex, 10);\n }\n\n node.style.zIndex = z + level;\n this.container.appendChild(node);\n\n node.setAttribute(\"id\", this.container.id + \"_\" + el.id);\n } else {\n node = this.drawInternalText(el);\n }\n\n el.rendNode = node;\n el.htmlStr = \"\";\n\n // Set el.visPropCalc.visible\n if (el.visProp.islabel && Type.exists(el.visProp.anchor)) {\n ev_visible = el.visProp.anchor.evalVisProp('visible');\n el.prepareUpdate().updateVisibility(ev_visible);\n } else {\n el.prepareUpdate().updateVisibility();\n }\n this.updateText(el);\n },\n\n /**\n * Update CSS property clip-path to HTML texts if `overflow:hidden`\n * has to be avoided.\n *\n * TODO clipping for transformed texts\n *\n * @param {JXG.Text} el Reference to an {@link JXG.Text} object that has to be clipped.\n * @param {Boolean} [val=undefined] Set an explicit value, overwrites the element's attribute 'clip'. This is useful for handling the value 'inherit'.\n * @see Text\n * @see JXG.Text\n */\n updateClipPath: function(el, val) {\n var x, y, x2, y2,\n w = el.rendNode.offsetWidth,\n h = el.rendNode.offsetHeight,\n is = el.rendNode.style.inset.split(' '),\n cw = el.board.canvasWidth,\n ch = el.board.canvasHeight;\n\n if (val === undefined) {\n val = el.evalVisProp('clip');\n }\n\n if (!val) {\n el.rendNode.style.removeProperty('clip-path');\n return;\n }\n if (is[3] !== 'auto') {\n x = parseFloat(is[3]);\n x2 = cw - x;\n } else {\n x2 = parseFloat(is[1]) + w;\n x = cw - x2;\n }\n\n if (is[0] !== 'auto') {\n y = parseFloat(is[0]);\n y2 = ch - y;\n } else {\n y2 = parseFloat(is[2]) + h;\n y = ch - y2;\n }\n\n el.rendNode.style.clipPath = 'rect(' + (-y) + 'px ' // top\n + (x2) + 'px ' // right\n + (y2) + 'px ' // bottom\n + (-x) + 'px)'; // left\n },\n\n /**\n * Updates visual properties of an already existing {@link JXG.Text} element.\n * @param {JXG.Text} el Reference to an {@link JXG.Text} object that has to be updated.\n * @see Text\n * @see JXG.Text\n * @see JXG.AbstractRenderer#drawText\n * @see JXG.AbstractRenderer#drawInternalText\n * @see JXG.AbstractRenderer#updateInternalText\n * @see JXG.AbstractRenderer#updateTextStyle\n */\n updateText: function (el) {\n var content = el.plaintext,\n v, c,\n parentNode, node,\n // scale, vshift,\n // id, wrap_id,\n ax, ay, angle, co, si,\n to_h, to_v;\n\n if (el.visPropCalc.visible) {\n this.updateTextStyle(el, false);\n\n if (el.evalVisProp('display') === \"html\" && this.type !== 'no') {\n // Set the position\n if (!isNaN(el.coords.scrCoords[1] + el.coords.scrCoords[2])) {\n // Horizontal\n c = el.coords.scrCoords[1];\n // webkit seems to fail for extremely large values for c.\n c = Math.abs(c) < 1000000 ? c : 1000000;\n ax = el.getAnchorX();\n\n if (ax === 'right') {\n // v = Math.floor(el.board.canvasWidth - c);\n v = el.board.canvasWidth - c;\n to_h = 'right';\n } else if (ax === 'middle') {\n // v = Math.floor(c - 0.5 * el.size[0]);\n v = c - 0.5 * el.size[0];\n to_h = 'center';\n } else {\n // 'left'\n // v = Math.floor(c);\n v = c;\n to_h = 'left';\n }\n\n // This may be useful for foreignObj.\n //if (window.devicePixelRatio !== undefined) {\n //v *= window.devicePixelRatio;\n //}\n\n if (el.visPropOld.left !== ax + v) {\n if (ax === 'right') {\n el.rendNode.style.right = v + 'px';\n el.rendNode.style.left = 'auto';\n } else {\n el.rendNode.style.left = v + 'px';\n el.rendNode.style.right = 'auto';\n }\n el.visPropOld.left = ax + v;\n }\n\n // Vertical\n c = el.coords.scrCoords[2] + this.vOffsetText;\n c = Math.abs(c) < 1000000 ? c : 1000000;\n ay = el.getAnchorY();\n\n if (ay === 'bottom') {\n // v = Math.floor(el.board.canvasHeight - c);\n v = el.board.canvasHeight - c;\n to_v = 'bottom';\n } else if (ay === 'middle') {\n // v = Math.floor(c - 0.5 * el.size[1]);\n v = c - 0.5 * el.size[1];\n to_v = 'center';\n } else {\n // top\n // v = Math.floor(c);\n v = c;\n to_v = 'top';\n }\n\n // This may be useful for foreignObj.\n //if (window.devicePixelRatio !== undefined) {\n //v *= window.devicePixelRatio;\n //}\n\n if (el.visPropOld.top !== ay + v) {\n if (ay === 'bottom') {\n el.rendNode.style.top = 'auto';\n el.rendNode.style.bottom = v + 'px';\n } else {\n el.rendNode.style.bottom = 'auto';\n el.rendNode.style.top = v + 'px';\n }\n el.visPropOld.top = ay + v;\n }\n }\n\n // Set the content\n if (el.htmlStr !== content) {\n try {\n if (el.type === Type.OBJECT_TYPE_BUTTON) {\n el.rendNodeButton.innerHTML = content;\n } else if (\n el.type === Type.OBJECT_TYPE_CHECKBOX ||\n el.type === Type.OBJECT_TYPE_INPUT\n ) {\n el.rendNodeLabel.innerHTML = content;\n } else {\n el.rendNode.innerHTML = content;\n }\n } catch (e) {\n // Setting innerHTML sometimes fails in IE8.\n // A workaround is to take the node off the DOM, assign innerHTML,\n // then append back.\n // Works for text elements as they are absolutely positioned.\n parentNode = el.rendNode.parentNode;\n el.rendNode.parentNode.removeChild(el.rendNode);\n el.rendNode.innerHTML = content;\n parentNode.appendChild(el.rendNode);\n }\n el.htmlStr = content;\n\n if (el.evalVisProp('usemathjax')) {\n // Typesetting directly might not work because MathJax was not yet loaded completely\n try {\n if (MathJax.typeset) {\n // Version 3\n MathJax.typeset([el.rendNode]);\n } else {\n // Version 2\n MathJax.Hub.Queue([\"Typeset\", MathJax.Hub, el.rendNode]);\n }\n\n // Obsolete:\n // // Restore the transformation necessary for fullscreen mode\n // // MathJax removes it when handling dynamic content\n // id = el.board.container;\n // wrap_id = \"fullscreenwrap_\" + id;\n // if (document.getElementById(wrap_id)) {\n // scale = el.board.containerObj._cssFullscreenStore.scale;\n // vshift = el.board.containerObj._cssFullscreenStore.vshift;\n // Env.scaleJSXGraphDiv(\n // \"#\" + wrap_id,\n // \"#\" + id,\n // scale,\n // vshift\n // );\n // }\n } catch (e) {\n JXG.debug(\"MathJax (not yet) loaded\");\n }\n } else if (el.evalVisProp('usekatex')) {\n try {\n // Checkboxes et. al. do not possess rendNodeLabel during the first update.\n // In this case node will be undefined and not rendered by KaTeX.\n if (el.rendNode.innerHTML.indexOf(' \n * Only affine transformation are supported, no proper projective transformations. This means, the\n * respective entries of the transformation matrix are simply ignored.\n *\n * @param {JXG.Image|JXG.Text} el A {@link JXG.Image} or {@link JXG.Text} object.\n * @param {Array} transformations An array of {@link JXG.Transformation} objects. This is usually the\n * transformations property of the given element el.\n */\n transformRect: function (el, transformations) { /* stub */ },\n\n /**\n * If the URL of the image is provided by a function the URL has to be updated during updateImage()\n * @param {JXG.Image} el Reference to an image object.\n * @see JXG.AbstractRenderer#updateImage\n */\n updateImageURL: function (el) { /* stub */ },\n\n /**\n * Updates CSS style properties of a {@link JXG.Image} node.\n * In SVGRenderer opacity is the only available style element.\n * This function is called by highlight() and nohighlight().\n * This function works for VML.\n * It does not work for Canvas.\n * SVGRenderer overwrites this method.\n * @param {JXG.Text} el Reference to the {@link JXG.Image} object, that has to be updated.\n * @param {Boolean} doHighlight\n * @see Image\n * @see JXG.Image\n * @see JXG.AbstractRenderer#highlight\n * @see JXG.AbstractRenderer#noHighlight\n */\n updateImageStyle: function (el, doHighlight) {\n el.rendNode.className = el.evalVisProp(\n doHighlight ? 'highlightcssclass' : 'cssclass'\n );\n },\n\n drawForeignObject: function (el) { /* stub */ },\n\n updateForeignObject: function (el) {\n /* stub */\n },\n\n /* ********* Render primitive objects *********** */\n\n /**\n * Appends a node to a specific layer level. This is just an abstract method and has to be implemented\n * in all renderers that want to use the createPrim model to draw.\n * @param {Node} node A DOM tree node.\n * @param {Number} level The layer the node is attached to. This is the index of the layer in\n * {@link JXG.SVGRenderer#layer} or the z-index style property of the node in VMLRenderer.\n */\n appendChildPrim: function (node, level) { /* stub */ },\n\n /**\n * Stores the rendering nodes. This is an abstract method which has to be implemented in all renderers that use\n * the createPrim method.\n * @param {JXG.GeometryElement} el A JSXGraph element.\n * @param {String} type The XML node name. Only used in VMLRenderer.\n */\n appendNodesToElement: function (el, type) { /* stub */ },\n\n /**\n * Creates a node of a given type with a given id.\n * @param {String} type The type of the node to create.\n * @param {String} id Set the id attribute to this.\n * @returns {Node} Reference to the created node.\n */\n createPrim: function (type, id) { /* stub */ return null; },\n\n /**\n * Removes an element node. Just a stub.\n * @param {Node} node The node to remove.\n */\n remove: function (node) { /* stub */ },\n\n /**\n * Can be used to create the nodes to display arrows. This is an abstract method which has to be implemented\n * in any descendant renderer.\n * @param {JXG.GeometryElement} el The element the arrows are to be attached to.\n * @param {Object} arrowData Data concerning possible arrow heads\n *\n */\n makeArrows: function (el, arrowData) { /* stub */ },\n\n /**\n * Updates width of an arrow DOM node. Used in\n * @param {Node} node The arrow node.\n * @param {Number} width\n * @param {Node} parentNode Used in IE only\n */\n _setArrowWidth: function (node, width, parentNode) { /* stub */ },\n\n /**\n * Updates an ellipse node primitive. This is an abstract method which has to be implemented in all renderers\n * that use the createPrim method.\n * @param {Node} node Reference to the node.\n * @param {Number} x Centre X coordinate\n * @param {Number} y Centre Y coordinate\n * @param {Number} rx The x-axis radius.\n * @param {Number} ry The y-axis radius.\n */\n updateEllipsePrim: function (node, x, y, rx, ry) { /* stub */ },\n\n /**\n * Refreshes a line node. This is an abstract method which has to be implemented in all renderers that use\n * the createPrim method.\n * @param {Node} node The node to be refreshed.\n * @param {Number} p1x The first point's x coordinate.\n * @param {Number} p1y The first point's y coordinate.\n * @param {Number} p2x The second point's x coordinate.\n * @param {Number} p2y The second point's y coordinate.\n * @param {JXG.Board} board\n */\n updateLinePrim: function (node, p1x, p1y, p2x, p2y, board) { /* stub */ },\n\n /**\n * Updates a path element. This is an abstract method which has to be implemented in all renderers that use\n * the createPrim method.\n * @param {Node} node The path node.\n * @param {String} pathString A string formatted like e.g. 'M 1,2 L 3,1 L5,5'. The format of the string\n * depends on the rendering engine.\n * @param {JXG.Board} board Reference to the element's board.\n */\n updatePathPrim: function (node, pathString, board) { /* stub */ },\n\n /**\n * Builds a path data string to draw a point with a face other than rect and circle. Since\n * the format of such a string usually depends on the renderer this method\n * is only an abstract method. Therefore, it has to be implemented in the descendant renderer itself unless\n * the renderer does not use the createPrim interface but the draw* interfaces to paint.\n * @param {JXG.Point} el The point element\n * @param {Number} size A positive number describing the size. Usually the half of the width and height of\n * the drawn point.\n * @param {String} type A string describing the point's face. This method only accepts the shortcut version of\n * each possible face: x, +, |, -, [], <>, <<>>,^, v, >, < \n */\n updatePathStringPoint: function (el, size, type) { /* stub */ },\n\n /**\n * Builds a path data string from a {@link JXG.Curve} element. Since the path data strings heavily depend on the\n * underlying rendering technique this method is just a stub. Although such a path string is of no use for the\n * CanvasRenderer, this method is used there to draw a path directly.\n * @param {JXG.GeometryElement} el\n */\n updatePathStringPrim: function (el) { /* stub */ },\n\n /**\n * Builds a path data string from a {@link JXG.Curve} element such that the curve looks like hand drawn. Since\n * the path data strings heavily depend on the underlying rendering technique this method is just a stub.\n * Although such a path string is of no use for the CanvasRenderer, this method is used there to draw a path\n * directly.\n * @param {JXG.GeometryElement} el\n */\n updatePathStringBezierPrim: function (el) { /* stub */ },\n\n /**\n * Update a polygon primitive.\n * @param {Node} node\n * @param {JXG.Polygon} el A JSXGraph element of type {@link JXG.Polygon}\n */\n updatePolygonPrim: function (node, el) { /* stub */ },\n\n /**\n * Update a rectangle primitive. This is used only for points with face of type 'rect'.\n * @param {Node} node The node yearning to be updated.\n * @param {Number} x x coordinate of the top left vertex.\n * @param {Number} y y coordinate of the top left vertex.\n * @param {Number} w Width of the rectangle.\n * @param {Number} h The rectangle's height.\n */\n updateRectPrim: function (node, x, y, w, h) { /* stub */ },\n\n /* ********* Set attributes *********** */\n\n /**\n * Shows or hides an element on the canvas; Only a stub, requires implementation in the derived renderer.\n * @param {JXG.GeometryElement} el Reference to the object that has to appear.\n * @param {Boolean} value true to show the element, false to hide the element.\n */\n display: function (el, value) {\n if (el) {\n el.visPropOld.visible = value;\n }\n },\n\n /**\n * Hides an element on the canvas; Only a stub, requires implementation in the derived renderer.\n *\n * Please use JXG.AbstractRenderer#display instead\n * @param {JXG.GeometryElement} el Reference to the geometry element that has to disappear.\n * @see JXG.AbstractRenderer#show\n * @deprecated\n */\n hide: function (el) { /* stub */ },\n\n /**\n * Highlights an object, i.e. changes the current colors of the object to its highlighting colors\n * and highlighting strokewidth.\n * @param {JXG.GeometryElement} el Reference of the object that will be highlighted.\n * @param {Boolean} [suppressHighlightStrokeWidth=undefined] If undefined or false, highlighting also changes strokeWidth. This might not be\n * the cases for polygon borders. Thus, if a polygon is highlighted, its polygon borders change strokeWidth only if the polygon attribute\n * highlightByStrokeWidth == true.\n * @returns {JXG.AbstractRenderer} Reference to the renderer\n * @see JXG.AbstractRenderer#updateTextStyle\n */\n highlight: function (el, suppressHighlightStrokeWidth) {\n var i, do_hl, sw;\n\n this.setObjectTransition(el);\n if (!el.visProp.draft) {\n if (el.type === Const.OBJECT_TYPE_POLYGON) {\n this.setObjectFillColor(el, el.evalVisProp('highlightfillcolor'), el.evalVisProp('highlightfillopacity'));\n do_hl = el.evalVisProp('highlightbystrokewidth');\n for (i = 0; i < el.borders.length; i++) {\n this.highlight(el.borders[i], !do_hl);\n }\n } else {\n if (el.elementClass === Const.OBJECT_CLASS_TEXT) {\n this.updateTextStyle(el, true);\n } else if (el.type === Const.OBJECT_TYPE_IMAGE) {\n this.updateImageStyle(el, true);\n this.setObjectFillColor(\n el,\n el.evalVisProp('highlightfillcolor'),\n el.evalVisProp('highlightfillopacity')\n );\n } else {\n this.setObjectStrokeColor(\n el,\n el.evalVisProp('highlightstrokecolor'),\n el.evalVisProp('highlightstrokeopacity')\n );\n this.setObjectFillColor(\n el,\n el.evalVisProp('highlightfillcolor'),\n el.evalVisProp('highlightfillopacity')\n );\n }\n }\n\n // Highlight strokeWidth is suppressed if\n // parameter suppressHighlightStrokeWidth is false or undefined.\n // suppressHighlightStrokeWidth is false if polygon attribute\n // highlightbystrokewidth is true.\n if (!suppressHighlightStrokeWidth && el.evalVisProp('highlightstrokewidth')) {\n sw = Math.max(\n el.evalVisProp('highlightstrokewidth'),\n el.evalVisProp('strokewidth')\n );\n this.setObjectStrokeWidth(el, sw);\n if (\n el.elementClass === Const.OBJECT_CLASS_LINE ||\n el.elementClass === Const.OBJECT_CLASS_CURVE\n ) {\n this.updatePathWithArrowHeads(el, true);\n }\n }\n }\n this.setCssClass(el, el.evalVisProp('highlightcssclass'));\n\n return this;\n },\n\n /**\n * Uses the normal colors of an object, i.e. the opposite of {@link JXG.AbstractRenderer#highlight}.\n * @param {JXG.GeometryElement} el Reference of the object that will get its normal colors.\n * @returns {JXG.AbstractRenderer} Reference to the renderer\n * @see JXG.AbstractRenderer#updateTextStyle\n */\n noHighlight: function (el) {\n var i, sw;\n\n this.setObjectTransition(el);\n if (!el.evalVisProp('draft')) {\n if (el.type === Const.OBJECT_TYPE_POLYGON) {\n this.setObjectFillColor(el, el.evalVisProp('fillcolor'), el.evalVisProp('fillopacity'));\n for (i = 0; i < el.borders.length; i++) {\n this.noHighlight(el.borders[i]);\n }\n } else {\n if (el.elementClass === Const.OBJECT_CLASS_TEXT) {\n this.updateTextStyle(el, false);\n } else if (el.type === Const.OBJECT_TYPE_IMAGE) {\n this.updateImageStyle(el, false);\n this.setObjectFillColor(el, el.evalVisProp('fillcolor'), el.evalVisProp('fillopacity'));\n } else {\n this.setObjectStrokeColor(el, el.evalVisProp('strokecolor'), el.evalVisProp('strokeopacity'));\n this.setObjectFillColor(el, el.evalVisProp('fillcolor'), el.evalVisProp('fillopacity'));\n }\n }\n\n sw = el.evalVisProp('strokewidth');\n this.setObjectStrokeWidth(el, sw);\n if (\n el.elementClass === Const.OBJECT_CLASS_LINE ||\n el.elementClass === Const.OBJECT_CLASS_CURVE\n ) {\n this.updatePathWithArrowHeads(el, false);\n }\n }\n this.setCssClass(el, el.evalVisProp('cssclass'));\n\n return this;\n },\n\n /**\n * Puts an object from draft mode back into normal mode.\n * @param {JXG.GeometryElement} el Reference of the object that no longer is in draft mode.\n */\n removeDraft: function (el) {\n this.setObjectTransition(el);\n if (el.type === Const.OBJECT_TYPE_POLYGON) {\n this.setObjectFillColor(el, el.evalVisProp('fillcolor'), el.evalVisProp('fillopacity'));\n } else {\n if (el.type === Const.OBJECT_CLASS_POINT) {\n this.setObjectFillColor(el, el.evalVisProp('fillcolor'), el.evalVisProp('fillopacity'));\n }\n this.setObjectStrokeColor(el, el.evalVisProp('strokecolor'), el.evalVisProp('strokeopacity'));\n this.setObjectStrokeWidth(el, el.evalVisProp('strokewidth'));\n }\n },\n\n /**\n * Set ARIA related properties of an element. The attribute \"aria\" of an element contains at least the\n * properties \"enabled\", \"label\", and \"live\". Additionally, all available properties from\n * {@link https://developer.mozilla.org/en-US/docs/Web/Accessibility/ARIA} may be set.\n * \n * In JSXGraph, the available properties are used without the leading 'aria-'.\n * For example, the value of the JSXGraph attribute 'aria.label' will be set to the\n * HTML attribute 'aria-label'.\n *\n * @param {JXG.GeometryElement} el Reference of the object that wants new\n * ARIA attributes.\n */\n setARIA: function(el) { /* stub */ },\n\n /**\n * Sets the buffering as recommended by SVGWG. Until now only Opera supports this and will be ignored by other\n * browsers. Although this feature is only supported by SVG we have this method in {@link JXG.AbstractRenderer}\n * because it is called from outside the renderer.\n * @param {Node} node The SVG DOM Node which buffering type to update.\n * @param {String} type Either 'auto', 'dynamic', or 'static'. For an explanation see\n * {@link https://www.w3.org/TR/SVGTiny12/painting.html#BufferedRenderingProperty}.\n */\n setBuffering: function (node, type) { /* stub */ },\n\n /**\n * Clip element to the JSXGraph container element (div). To be precise: to the SVG node\n * in case of SVG rendering - the only renderer, where this is relevant.\n *\n * @param {JXG.GeometryElement} el Reference of the object\n * @param {Boolean} val true: clip to the JSXGraph div, false: do not clip\n * @see JXG.SVGRenderer#setClipPathRect\n */\n setClipPath: function(el, val) { /* stub */ },\n\n /**\n * Sets CSS classes for elements (relevant for SVG only).\n *\n * @param {JXG.GeometryElement} el Reference of the object that wants a\n * new set of CSS classes.\n * @param {String} cssClass String containing a space separated list of CSS classes.\n */\n setCssClass: function (el, cssClass) { /* stub */ },\n\n /**\n * Sets an element's dash style.\n * @param {JXG.GeometryElement} el An JSXGraph element.\n */\n setDashStyle: function (el) { /* stub */ },\n\n /**\n * Puts an object into draft mode, i.e. it's visual appearance will be changed. For GEONExT backwards\n * compatibility.\n * @param {JXG.GeometryElement} el Reference of the object that is in draft mode.\n */\n setDraft: function (el) {\n if (!el.evalVisProp('draft')) {\n return;\n }\n var draftColor = el.board.options.elements.draft.color,\n draftOpacity = el.board.options.elements.draft.opacity;\n\n this.setObjectTransition(el);\n if (el.type === Const.OBJECT_TYPE_POLYGON) {\n this.setObjectFillColor(el, draftColor, draftOpacity);\n } else {\n if (el.elementClass === Const.OBJECT_CLASS_POINT) {\n this.setObjectFillColor(el, draftColor, draftOpacity);\n } else {\n this.setObjectFillColor(el, \"none\", 0);\n }\n this.setObjectStrokeColor(el, draftColor, draftOpacity);\n this.setObjectStrokeWidth(el, el.board.options.elements.draft.strokeWidth);\n }\n },\n\n /**\n * Sets up nodes for rendering a gradient fill.\n * @param {JXG.GeometryElement} el Reference of the object which gets the gradient\n */\n setGradient: function (el) { /* stub */ },\n\n /**\n * Move element into new layer. This is trivial for canvas, but needs more effort in SVG.\n * Does not work dynamically, i.e. if level is a function.\n *\n * @param {JXG.GeometryElement} el Element which is put into different layer\n * @param {Number} value Layer number\n * @private\n */\n setLayer: function (el, level) { /* stub */ },\n\n /**\n * Sets an objects fill color.\n * @param {JXG.GeometryElement} el Reference of the object that wants a new fill color.\n * @param {String} color Color in a HTML/CSS compatible format. If you don't want any fill color at all, choose\n * 'none'.\n * @param {Number} opacity Opacity of the fill color. Must be between 0 and 1.\n */\n setObjectFillColor: function (el, color, opacity) { /* stub */ },\n\n /**\n * Changes an objects stroke color to the given color.\n * @param {JXG.GeometryElement} el Reference of the {@link JXG.GeometryElement} that gets a new stroke\n * color.\n * @param {String} color Color value in a HTML compatible format, e.g. #00ff00 or\n * green for green.\n * @param {Number} opacity Opacity of the fill color. Must be between 0 and 1.\n */\n setObjectStrokeColor: function (el, color, opacity) { /* stub */ },\n\n /**\n * Sets an element's stroke width.\n * @param {JXG.GeometryElement} el Reference to the geometry element.\n * @param {Number} width The new stroke width to be assigned to the element.\n */\n setObjectStrokeWidth: function (el, width) { /* stub */ },\n\n /**\n * Sets the transition duration (in milliseconds) for fill color and stroke\n * color and opacity.\n * @param {JXG.GeometryElement} el Reference of the object that wants a\n * new transition duration.\n * @param {Number} duration (Optional) duration in milliseconds. If not given,\n * element.visProp.transitionDuration is taken. This is the default.\n */\n setObjectTransition: function (el, duration) { /* stub */ },\n\n /**\n * Sets a node's attribute.\n * @param {Node} node The node that is to be updated.\n * @param {String} key Name of the attribute.\n * @param {String} val New value for the attribute.\n */\n setPropertyPrim: function (node, key, val) { /* stub */ },\n\n /**\n * Sets the shadow properties to a geometry element. This method is only a stub, it is implemented in the actual\n * renderers.\n * @param {JXG.GeometryElement} el Reference to a geometry object, that should get a shadow\n */\n setShadow: function (el) { /* stub */ },\n\n /**\n * Set the attribute `tabindex` to the attribute `tabindex` of an element.\n * This is only relevant for the SVG renderer.\n *\n * @param {JXG.GeometryElement} el\n */\n setTabindex: function (el) { /* stub */ },\n\n /**\n * Shows a hidden element on the canvas; Only a stub, requires implementation in the derived renderer.\n *\n * Please use JXG.AbstractRenderer#display instead\n * @param {JXG.GeometryElement} el Reference to the object that has to appear.\n * @see JXG.AbstractRenderer#hide\n * @deprecated\n */\n show: function (el) { /* stub */ },\n\n /**\n * Updates the gradient fill.\n * @param {JXG.GeometryElement} el An JSXGraph element with an area that can be filled.\n */\n updateGradient: function (el) { /* stub */ },\n\n /* ********* Renderer control *********** */\n\n /**\n * Stop redraw. This method is called before every update, so a non-vector-graphics based renderer can use this\n * method to delete the contents of the drawing panel. This is an abstract method every descendant renderer\n * should implement, if appropriate.\n * @see JXG.AbstractRenderer#unsuspendRedraw\n */\n suspendRedraw: function () { /* stub */ },\n\n /**\n * Restart redraw. This method is called after updating all the rendering node attributes.\n * @see JXG.AbstractRenderer#suspendRedraw\n */\n unsuspendRedraw: function () { /* stub */ },\n\n /**\n * The tiny zoom bar shown on the bottom of a board (if board attribute \"showNavigation\" is true).\n * It is a div element and gets the CSS class \"JXG_navigation\" and the id {board id}_navigationbar.\n * \n * The buttons get the CSS class \"JXG_navigation_button\" and the id {board_id}_name where name is\n * one of [top, down, left, right, out, 100, in, fullscreen, screenshot, reload, cleartraces].\n * \n * The symbols for zoom, navigation and reload are hard-coded.\n *\n * @param {JXG.Board} board Reference to a JSXGraph board.\n * @param {Object} attr Attributes of the navigation bar\n * @private\n */\n drawNavigationBar: function (board, attr) {\n var doc,\n node,\n cancelbubble = function (e) {\n if (!e) {\n e = window.event;\n }\n\n if (e.stopPropagation) {\n // Non IE<=8\n e.stopPropagation();\n } else {\n e.cancelBubble = true;\n }\n },\n createButton = function (label, handler, board_id, type) {\n var button;\n\n board_id = board_id || \"\";\n\n button = doc.createElement('span');\n button.innerHTML = label; // button.appendChild(doc.createTextNode(label));\n\n // Style settings are superseded by adding the CSS class below\n button.style.paddingLeft = '7px';\n button.style.paddingRight = '7px';\n\n if (button.classList !== undefined) {\n // classList not available in IE 9\n button.classList.add(\"JXG_navigation_button\");\n button.classList.add(\"JXG_navigation_button_\" + type);\n }\n // button.setAttribute('tabindex', 0);\n\n button.setAttribute(\"id\", board_id + '_navigation_' + type);\n button.setAttribute(\"aria-hidden\", 'true'); // navigation buttons should never appear in screen reader\n\n node.appendChild(button);\n\n Env.addEvent(\n button,\n \"click\",\n function (e) {\n Type.bind(handler, board)();\n return false;\n },\n board\n );\n // prevent the click from bubbling down to the board\n Env.addEvent(button, \"pointerup\", cancelbubble, board);\n Env.addEvent(button, \"pointerdown\", cancelbubble, board);\n Env.addEvent(button, \"pointerleave\", cancelbubble, board);\n Env.addEvent(button, \"mouseup\", cancelbubble, board);\n Env.addEvent(button, \"mousedown\", cancelbubble, board);\n Env.addEvent(button, \"touchend\", cancelbubble, board);\n Env.addEvent(button, \"touchstart\", cancelbubble, board);\n };\n\n if (Env.isBrowser && this.type !== 'no') {\n doc = board.containerObj.ownerDocument;\n node = doc.createElement('div');\n\n node.setAttribute(\"id\", board.container + \"_navigationbar\");\n\n // Style settings are superseded by adding the CSS class below\n node.style.color = attr.strokecolor;\n node.style.backgroundColor = attr.fillcolor;\n node.style.padding = attr.padding;\n node.style.position = attr.position;\n node.style.fontSize = attr.fontsize;\n node.style.cursor = attr.cursor;\n node.style.zIndex = attr.zindex;\n board.containerObj.appendChild(node);\n node.style.right = attr.right;\n node.style.bottom = attr.bottom;\n\n if (node.classList !== undefined) {\n // classList not available in IE 9\n node.classList.add(\"JXG_navigation\");\n }\n // For XHTML we need unicode instead of HTML entities\n\n if (board.attr.showfullscreen) {\n createButton(\n board.attr.fullscreen.symbol,\n function () {\n board.toFullscreen(board.attr.fullscreen.id);\n },\n board.container, \"fullscreen\"\n );\n }\n\n if (board.attr.showscreenshot) {\n createButton(\n board.attr.screenshot.symbol,\n function () {\n window.setTimeout(function () {\n board.renderer.screenshot(board, \"\", false);\n }, 330);\n },\n board.container, \"screenshot\"\n );\n }\n\n if (board.attr.showreload) {\n // full reload circle: \\u27F2\n // the board.reload() method does not exist during the creation\n // of this button. That's why this anonymous function wrapper is required.\n createButton(\n \"\\u21BB\",\n function () {\n board.reload();\n },\n board.container, \"reload\"\n );\n }\n\n if (board.attr.showcleartraces) {\n // clear traces symbol (otimes): \\u27F2\n createButton(\"\\u2297\",\n function () {\n board.clearTraces();\n },\n board.container, \"cleartraces\"\n );\n }\n\n if (board.attr.shownavigation) {\n if (board.attr.showzoom) {\n createButton(\"\\u2013\", board.zoomOut, board.container, 'out');\n createButton(\"o\", board.zoom100, board.container, '100');\n createButton(\"+\", board.zoomIn, board.container, 'in');\n }\n createButton(\"\\u2190\", board.clickLeftArrow, board.container, 'left');\n createButton(\"\\u2193\", board.clickUpArrow, board.container, 'down'); // Down arrow\n createButton(\"\\u2191\", board.clickDownArrow, board.container, 'up'); // Up arrow\n createButton(\"\\u2192\", board.clickRightArrow, board.container, 'right');\n }\n }\n },\n\n /**\n * Wrapper for getElementById for maybe other renderers which elements are not directly accessible by DOM\n * methods like document.getElementById().\n * @param {String} id Unique identifier for element.\n * @returns {Object} Reference to a JavaScript object. In case of SVG/VMLRenderer it's a reference to a SVG/VML node.\n */\n getElementById: function (id) {\n var str;\n if (Type.exists(this.container)) {\n // Use querySelector over getElementById for compatibility with both 'regular' document\n // and ShadowDOM fragments.\n str = this.container.id + '_' + id;\n // Mask special symbols like '/' and '\\' in id\n if (Type.exists(CSS) && Type.exists(CSS.escape)) {\n str = CSS.escape(str);\n }\n return this.container.querySelector('#' + str);\n }\n return \"\";\n },\n\n /**\n * Remove an element and provide a function that inserts it into its original position. This method\n * is taken from this article {@link https://developers.google.com/speed/articles/javascript-dom}.\n * @author KeeKim Heng, Google Web Developer\n * @param {Element} el The element to be temporarily removed\n * @returns {Function} A function that inserts the element into its original position\n */\n removeToInsertLater: function (el) {\n var parentNode = el.parentNode,\n nextSibling = el.nextSibling;\n\n if (parentNode === null) {\n return;\n }\n parentNode.removeChild(el);\n\n return function () {\n if (nextSibling) {\n parentNode.insertBefore(el, nextSibling);\n } else {\n parentNode.appendChild(el);\n }\n };\n },\n\n /**\n * Resizes the rendering element\n * @param {Number} w New width\n * @param {Number} h New height\n */\n resize: function (w, h) { /* stub */ },\n\n /**\n * Create crosshair elements (Fadenkreuz) for presentations.\n * @param {Number} n Number of crosshairs.\n */\n createTouchpoints: function (n) { /* stub */ },\n\n /**\n * Show a specific crosshair.\n * @param {Number} i Number of the crosshair to show\n */\n showTouchpoint: function (i) { /* stub */ },\n\n /**\n * Hide a specific crosshair.\n * @param {Number} i Number of the crosshair to show\n */\n hideTouchpoint: function (i) { /* stub */ },\n\n /**\n * Move a specific crosshair.\n * @param {Number} i Number of the crosshair to show\n * @param {Array} pos New positon in screen coordinates\n */\n updateTouchpoint: function (i, pos) { /* stub */ },\n\n /* ********* Dump related stuff *********** */\n\n /**\n * Convert SVG construction to base64 encoded SVG data URL.\n * Only available on SVGRenderer.\n *\n * @see JXG.SVGRenderer#dumpToDataURI\n */\n dumpToDataURI: function (_ignoreTexts) { /* stub */ },\n\n /**\n * Convert SVG construction to canvas.\n * Only available on SVGRenderer.\n *\n * @see JXG.SVGRenderer#dumpToCanvas\n */\n dumpToCanvas: function (canvasId, w, h, _ignoreTexts) { /* stub */ },\n\n /**\n * Display SVG image in html img-tag which enables\n * easy download for the user.\n *\n * See JXG.SVGRenderer#screenshot\n */\n screenshot: function (board) { /* stub */ }\n\n }\n);\n\nexport default JXG.AbstractRenderer;\n","/*global JXG: true, define: true, escape: true, unescape: true*/\n/*jslint nomen: true, plusplus: true, bitwise: true*/\n\nimport JXG from \"../jxg.js\";\n\n// constants\nvar UTF8_ACCEPT = 0,\n // UTF8_REJECT = 12,\n UTF8D = [\n // The first part of the table maps bytes to character classes that\n // to reduce the size of the transition table and create bitmasks.\n 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9,\n 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,\n 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 3, 3, 3, 3, 3, 3, 3,\n 3, 3, 3, 3, 3, 4, 3, 3, 11, 6, 6, 6, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,\n\n // The second part is a transition table that maps a combination\n // of a state of the automaton and a character class to a state.\n 0, 12, 24, 36, 60, 96, 84, 12, 12, 12, 48, 72, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,\n 12, 12, 12, 0, 12, 12, 12, 12, 12, 0, 12, 0, 12, 12, 12, 24, 12, 12, 12, 12, 12, 24, 12,\n 24, 12, 12, 12, 12, 12, 12, 12, 12, 12, 24, 12, 12, 12, 12, 12, 24, 12, 12, 12, 12, 12,\n 12, 12, 24, 12, 12, 12, 12, 12, 12, 12, 12, 12, 36, 12, 36, 12, 12, 12, 36, 12, 12, 12,\n 12, 12, 36, 12, 36, 12, 12, 12, 36, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12\n ];\n\n// Util namespace\nJXG.Util = JXG.Util || {};\n\n/**\n * UTF8 encoding routines\n * @namespace\n */\nJXG.Util.UTF8 = {\n /**\n * Encode a string to utf-8.\n * @param {String} string\n * @returns {String} utf8 encoded string\n */\n encode: function (string) {\n var n,\n c,\n utftext = \"\",\n len = string.length;\n\n string = string.replace(/\\r\\n/g, \"\\n\");\n\n // See\n // http://ecmanaut.blogspot.ca/2006/07/encoding-decoding-utf8-in-javascript.html\n if (typeof unescape === \"function\" && typeof encodeURIComponent === 'function') {\n return unescape(encodeURIComponent(string));\n }\n\n for (n = 0; n < len; n++) {\n c = string.charCodeAt(n);\n\n if (c < 128) {\n utftext += String.fromCharCode(c);\n } else if (c > 127 && c < 2048) {\n utftext += String.fromCharCode((c >> 6) | 192);\n utftext += String.fromCharCode((c & 63) | 128);\n } else {\n utftext += String.fromCharCode((c >> 12) | 224);\n utftext += String.fromCharCode(((c >> 6) & 63) | 128);\n utftext += String.fromCharCode((c & 63) | 128);\n }\n }\n\n return utftext;\n },\n\n /**\n * Decode a string from utf-8.\n * @param {String} utftext to decode\n * @returns {String} utf8 decoded string\n */\n decode: function (utftext) {\n /*\n The following code is a translation from C99 to JavaScript.\n\n The original C99 code can be found at\n https://bjoern.hoehrmann.de/utf-8/decoder/dfa/\n\n Original copyright note:\n\n Copyright (c) 2008-2009 Bjoern Hoehrmann 'start' and 'end' contain the amount of milliseconds elapsed between 1 January 1970 00:00:00 UTC\n * and the time the event happened.\n * \n * For the time being (i.e. v1.5.0) the only supported type is 'drag'.\n * @type Array\n */\n this.userLog = [];\n\n /**\n * Array of length two containing sketchcurves of the board. In case of mouse or pen\n * only the first entry is used. In case of finger input, sketchcurves\n * for the first and second finger are possible.\n *\n * @example\n * const board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-10, 10, 10, -10],\n * axis: true,\n * sketches: {\n * enabled: true,\n * 0: {strokeWidth: 2, visible: true, maxLength: 20},\n * 1: {strokeWidth: 3, visible: true}\n * }\n * });\n *\n * // Use event handler to access the actual curve\n * board.on('move', function(evt) {\n * console.log('JSXGraph example: move', this.sketches[0].dataX.length);\n * });\n *\n * // Use event handler to access the actual curve\n * board.on('up', function(evt) {\n * console.log('JSXGraph example: up', this.sketches[0].dataX.length);\n * });\n *\n * \n * User-supplied events might use this flag to test if sketching is active.\n * Usually, this flag is true starting with a down event and ends with the up event.\n * @type {Array}\n * @see JXG.Board#sketches\n *\n */\n this.isSketching = [false, false];\n\n /**\n *\n */\n this.mathLib = Math; // Math or JXG.Math.IntervalArithmetic\n\n /**\n *\n */\n this.mathLibJXG = JXG.Math; // JXG.Math or JXG.Math.IntervalArithmetic\n\n if (this.attr.registerevents === true) {\n this.attr.registerevents = {\n fullscreen: true,\n keyboard: true,\n pointer: true,\n resize: true,\n wheel: true\n };\n } else if (typeof this.attr.registerevents === 'object') {\n if (!Type.exists(this.attr.registerevents.fullscreen)) {\n this.attr.registerevents.fullscreen = true;\n }\n if (!Type.exists(this.attr.registerevents.keyboard)) {\n this.attr.registerevents.keyboard = true;\n }\n if (!Type.exists(this.attr.registerevents.pointer)) {\n this.attr.registerevents.pointer = true;\n }\n if (!Type.exists(this.attr.registerevents.resize)) {\n this.attr.registerevents.resize = true;\n }\n if (!Type.exists(this.attr.registerevents.wheel)) {\n this.attr.registerevents.wheel = true;\n }\n }\n if (this.attr.registerevents !== false) {\n if (this.attr.registerevents.fullscreen) {\n this.addFullscreenEventHandlers();\n }\n if (this.attr.registerevents.keyboard) {\n this.addKeyboardEventHandlers();\n }\n if (this.attr.registerevents.pointer) {\n this.addEventHandlers();\n }\n if (this.attr.registerevents.resize) {\n this.addResizeEventHandlers();\n }\n if (this.attr.registerevents.wheel) {\n this.addWheelEventHandlers();\n }\n }\n};\n\nType.copyMethodMap(JXG.Board, {\n update: 'update',\n fullUpdate: 'fullUpdate',\n on: 'on',\n off: 'off',\n trigger: 'trigger',\n setAttribute: 'setAttribute',\n setBoundingBox: 'setBoundingBox',\n setView: 'setBoundingBox',\n getBoundingBox: 'getBoundingBox',\n BoundingBox: 'getBoundingBox',\n getView: 'getBoundingBox',\n View: 'getBoundingBox',\n migratePoint: 'migratePoint',\n colorblind: 'emulateColorblindness',\n suspendUpdate: 'suspendUpdate',\n unsuspendUpdate: 'unsuspendUpdate',\n clearTraces: 'clearTraces',\n left: 'clickLeftArrow',\n right: 'clickRightArrow',\n up: 'clickUpArrow',\n down: 'clickDownArrow',\n zoomIn: 'zoomIn',\n zoomOut: 'zoomOut',\n zoom100: 'zoom100',\n zoomElements: 'zoomElements',\n remove: 'removeObject',\n removeObject: 'removeObject'\n});\n\nJXG.extend(\n JXG.Board.prototype,\n /** @lends JXG.Board.prototype */ {\n /**\n * Generates an unique name for the given object. The result depends on the objects type, if the\n * object is a {@link JXG.Point}, capital characters are used, if it is of type {@link JXG.Line}\n * only lower case characters are used. If object is of type {@link JXG.Polygon}, a bunch of lower\n * case characters prefixed with P_ are used. If object is of type {@link JXG.Circle} the name is\n * generated using lower case characters. prefixed with k_ is used. In any other case, lower case\n * chars prefixed with s_ is used.\n * @param {Object} object Reference of an JXG.GeometryElement that is to be named.\n * @returns {String} Unique name for the object.\n */\n generateName: function (object) {\n var possibleNames, i,\n maxNameLength = this.attr.maxnamelength,\n pre = '',\n post = '',\n indices = [],\n name = '';\n\n if (object.type === Const.OBJECT_TYPE_TICKS) {\n return '';\n }\n\n if (Type.isPoint(object) || Type.isPoint3D(object)) {\n // points have capital letters\n possibleNames = [\n '', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'\n ];\n } else if (object.type === Const.OBJECT_TYPE_ANGLE) {\n possibleNames = [\n '', 'α', 'β', 'γ', 'δ', 'ε', 'ζ', 'η', 'θ', 'ι', 'κ', 'λ',\n 'μ', 'ν', 'ξ', 'ο', 'π', 'ρ', 'σ', 'τ', 'υ', 'φ', 'χ', 'ψ', 'ω'\n ];\n } else {\n // all other elements get lowercase labels\n possibleNames = [\n '', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'\n ];\n }\n\n if (\n !Type.isPoint(object) &&\n !Type.isPoint3D(object) &&\n object.elementClass !== Const.OBJECT_CLASS_LINE &&\n object.type !== Const.OBJECT_TYPE_ANGLE\n ) {\n if (object.type === Const.OBJECT_TYPE_POLYGON) {\n pre = 'P_{';\n } else if (object.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n pre = 'k_{';\n } else if (object.elementClass === Const.OBJECT_CLASS_TEXT) {\n pre = 't_{';\n } else {\n pre = 's_{';\n }\n post = '}';\n }\n\n for (i = 0; i < maxNameLength; i++) {\n indices[i] = 0;\n }\n\n while (indices[maxNameLength - 1] < possibleNames.length) {\n for (indices[0] = 1; indices[0] < possibleNames.length; indices[0]++) {\n name = pre;\n\n for (i = maxNameLength; i > 0; i--) {\n name += possibleNames[indices[i - 1]];\n }\n\n if (!Type.exists(this.elementsByName[name + post])) {\n return name + post;\n }\n }\n indices[0] = possibleNames.length;\n\n for (i = 1; i < maxNameLength; i++) {\n if (indices[i - 1] === possibleNames.length) {\n indices[i - 1] = 1;\n indices[i] += 1;\n }\n }\n }\n\n return '';\n },\n\n /**\n * Generates unique id for a board. The result is randomly generated and prefixed with 'jxgBoard'.\n * @returns {String} Unique id for a board.\n */\n generateId: function () {\n var r = 1;\n\n // as long as we don't have a unique id generate a new one\n while (Type.exists(JXG.boards['jxgBoard' + r])) {\n r = Math.round(Math.random() * 16777216);\n }\n\n return 'jxgBoard' + r;\n },\n\n /**\n * Composes an id for an element. If the ID is empty ('' or null) a new ID is generated, depending on the\n * object type. As a side effect {@link JXG.Board#numObjects}\n * is updated.\n * @param {Object} obj Reference of an geometry object that needs an id.\n * @param {Number} type Type of the object.\n * @returns {String} Unique id for an element.\n */\n setId: function (obj, type) {\n var randomNumber,\n num = this.numObjects,\n elId = obj.id;\n\n this.numObjects += 1;\n\n // If no id is provided or id is empty string, a new one is chosen\n if (elId === '' || !Type.exists(elId)) {\n elId = this.id + type + num;\n while (Type.exists(this.objects[elId])) {\n randomNumber = Math.round(Math.random() * 65535);\n elId = this.id + type + num + '-' + randomNumber;\n }\n }\n\n obj.id = elId;\n this.objects[elId] = obj;\n obj._pos = this.objectsList.length;\n this.objectsList[this.objectsList.length] = obj;\n\n return elId;\n },\n\n /**\n * After construction of the object the visibility is set\n * and the label is constructed if necessary.\n * @param {Object} obj The object to add.\n */\n finalizeAdding: function (obj) {\n if (obj.evalVisProp('visible') === false) {\n this.renderer.display(obj, false);\n }\n },\n\n finalizeLabel: function (obj) {\n if (\n obj.hasLabel &&\n !obj.label.evalVisProp('islabel') &&\n obj.label.evalVisProp('visible') === false\n ) {\n this.renderer.display(obj.label, false);\n }\n },\n\n /**********************************************************\n *\n * Event Handler helpers\n *\n **********************************************************/\n\n /**\n * Returns false if the event has been triggered faster than the maximum frame rate.\n *\n * @param {Event} evt Event object given by the browser (unused)\n * @returns {Boolean} If the event has been triggered faster than the maximum frame rate, false is returned.\n * @private\n * @see JXG.Board#pointerMoveListener\n * @see JXG.Board#touchMoveListener\n * @see JXG.Board#mouseMoveListener\n */\n checkFrameRate: function (evt) {\n var handleEvt = false,\n time = new Date().getTime();\n\n if (Type.exists(evt.pointerId) && this.touchMoveLastId !== evt.pointerId) {\n handleEvt = true;\n this.touchMoveLastId = evt.pointerId;\n }\n if (!handleEvt && (time - this.touchMoveLast) * this.attr.maxframerate >= 1000) {\n handleEvt = true;\n }\n if (handleEvt) {\n this.touchMoveLast = time;\n }\n return handleEvt;\n },\n\n /**\n * Calculates mouse coordinates relative to the boards container.\n * @returns {Array} Array of coordinates relative the boards container top left corner.\n */\n getCoordsTopLeftCorner: function () {\n var cPos,\n doc,\n crect,\n // In ownerDoc we need the 'real' document object.\n // The first version is used in the case of shadowDOM,\n // the second case in the 'normal' case.\n ownerDoc = this.document.ownerDocument || this.document,\n docElement = ownerDoc.documentElement || this.document.body.parentNode,\n docBody = ownerDoc.body,\n container = this.containerObj,\n zoom,\n o;\n\n /**\n * During drags and origin moves the container element is usually not changed.\n * Check the position of the upper left corner at most every 1000 msecs\n */\n if (\n this.cPos.length > 0 &&\n (this.mode === this.BOARD_MODE_DRAG ||\n this.mode === this.BOARD_MODE_MOVE_ORIGIN ||\n new Date().getTime() - this.positionAccessLast < 1000)\n ) {\n return this.cPos;\n }\n this.positionAccessLast = new Date().getTime();\n\n // Check if getBoundingClientRect exists. If so, use this as this covers *everything*\n // even CSS3D transformations etc.\n // Supported by all browsers but IE 6, 7.\n if (container.getBoundingClientRect) {\n crect = container.getBoundingClientRect();\n\n zoom = 1.0;\n // Recursively search for zoom style entries.\n // This is necessary for reveal.js on webkit.\n // It fails if the user does zooming\n o = container;\n while (o && Type.exists(o.parentNode)) {\n if (\n Type.exists(o.style) &&\n Type.exists(o.style.zoom) &&\n o.style.zoom !== ''\n ) {\n zoom *= parseFloat(o.style.zoom);\n }\n o = o.parentNode;\n }\n cPos = [crect.left * zoom, crect.top * zoom];\n\n // add border width\n cPos[0] += Env.getProp(container, 'border-left-width');\n cPos[1] += Env.getProp(container, 'border-top-width');\n\n // vml seems to ignore paddings\n if (this.renderer.type !== 'vml') {\n // add padding\n cPos[0] += Env.getProp(container, 'padding-left');\n cPos[1] += Env.getProp(container, 'padding-top');\n }\n\n this.cPos = cPos.slice();\n return this.cPos;\n }\n\n //\n // OLD CODE\n // IE 6-7 only:\n //\n cPos = Env.getOffset(container);\n doc = this.document.documentElement.ownerDocument;\n\n if (!this.containerObj.currentStyle && doc.defaultView) {\n // Non IE\n // this is for hacks like this one used in wordpress for the admin bar:\n // html { margin-top: 28px }\n // seems like it doesn't work in IE\n\n cPos[0] += Env.getProp(docElement, 'margin-left');\n cPos[1] += Env.getProp(docElement, 'margin-top');\n\n cPos[0] += Env.getProp(docElement, 'border-left-width');\n cPos[1] += Env.getProp(docElement, 'border-top-width');\n\n cPos[0] += Env.getProp(docElement, 'padding-left');\n cPos[1] += Env.getProp(docElement, 'padding-top');\n }\n\n if (docBody) {\n cPos[0] += Env.getProp(docBody, 'left');\n cPos[1] += Env.getProp(docBody, 'top');\n }\n\n // Google Translate offers widgets for web authors. These widgets apparently tamper with the clientX\n // and clientY coordinates of the mouse events. The minified sources seem to be the only publicly\n // available version so we're doing it the hacky way: Add a fixed offset.\n // see https://groups.google.com/d/msg/google-translate-general/H2zj0TNjjpY/jw6irtPlCw8J\n if (typeof google === 'object' && google.translate) {\n cPos[0] += 10;\n cPos[1] += 25;\n }\n\n // add border width\n cPos[0] += Env.getProp(container, 'border-left-width');\n cPos[1] += Env.getProp(container, 'border-top-width');\n\n // vml seems to ignore paddings\n if (this.renderer.type !== 'vml') {\n // add padding\n cPos[0] += Env.getProp(container, 'padding-left');\n cPos[1] += Env.getProp(container, 'padding-top');\n }\n\n cPos[0] += this.attr.offsetx;\n cPos[1] += this.attr.offsety;\n\n this.cPos = cPos.slice();\n return this.cPos;\n },\n\n /**\n * This function divides the board into 9 sections and returns an array [u,v] which symbolizes the location of position.\n * Optional a margin to the inner of the board is respected. \n * If one vertex of the polygon snaps to the grid or to points or is not draggable,\n * two-finger-movement is cancelled.\n *\n * @param {Array} tar Array containing touch event objects: {JXG.Board#touches.targets}.\n * @param {object} drag The object that is dragged:\n * @param {Number} id pointerId of the event. In case of old touch event this is emulated.\n */\n twoFingerTouchObject: function (tar, drag, id) {\n var t, T,\n ar, i, len,\n snap = false;\n\n if (\n Type.exists(tar[0]) &&\n Type.exists(tar[1]) &&\n !isNaN(tar[0].Xprev + tar[0].Yprev + tar[1].Xprev + tar[1].Yprev)\n ) {\n\n T = this.getTwoFingerTransform(\n tar[0], tar[1],\n drag.evalVisProp('scalable'),\n drag.evalVisProp('rotatable'));\n t = this.create('transform', T, { type: 'generic' });\n t.update();\n\n if (drag.elementClass === Const.OBJECT_CLASS_LINE) {\n ar = [];\n if (drag.point1.draggable()) {\n ar.push(drag.point1);\n }\n if (drag.point2.draggable()) {\n ar.push(drag.point2);\n }\n t.applyOnce(ar);\n } else if (drag.type === Const.OBJECT_TYPE_POLYGON) {\n len = drag.vertices.length - 1;\n snap = drag.evalVisProp('snaptogrid') || drag.evalVisProp('snaptopoints');\n for (i = 0; i < len && !snap; ++i) {\n snap = snap || drag.vertices[i].evalVisProp('snaptogrid') || drag.vertices[i].evalVisProp('snaptopoints');\n snap = snap || (!drag.vertices[i].draggable());\n }\n if (!snap) {\n ar = [];\n for (i = 0; i < len; ++i) {\n if (drag.vertices[i].draggable()) {\n ar.push(drag.vertices[i]);\n }\n }\n t.applyOnce(ar);\n }\n }\n\n this.update();\n drag.highlight(true);\n }\n },\n\n /*\n * Moves, rotates and scales a circle with two fingers.\n * @param {Array} tar Array containing touch event objects: {JXG.Board#touches.targets}.\n * @param {object} drag The object that is dragged:\n * @param {Number} id pointerId of the event. In case of old touch event this is emulated.\n */\n twoFingerTouchCircle: function (tar, drag, id) {\n var fixEl, moveEl, np, op, fix, d, alpha, t1, t2, t3, t4;\n\n if (drag.method === 'pointCircle' || drag.method === 'pointLine') {\n return;\n }\n\n if (\n Type.exists(tar[0]) &&\n Type.exists(tar[1]) &&\n !isNaN(tar[0].Xprev + tar[0].Yprev + tar[1].Xprev + tar[1].Yprev)\n ) {\n if (id === tar[0].num) {\n fixEl = tar[1];\n moveEl = tar[0];\n } else {\n fixEl = tar[0];\n moveEl = tar[1];\n }\n\n fix = new Coords(Const.COORDS_BY_SCREEN, [fixEl.Xprev, fixEl.Yprev], this)\n .usrCoords;\n // Previous finger position\n op = new Coords(Const.COORDS_BY_SCREEN, [moveEl.Xprev, moveEl.Yprev], this)\n .usrCoords;\n // New finger position\n np = new Coords(Const.COORDS_BY_SCREEN, [moveEl.X, moveEl.Y], this).usrCoords;\n\n alpha = Geometry.rad(op.slice(1), fix.slice(1), np.slice(1));\n\n // Rotate and scale by the movement of the second finger\n t1 = this.create('transform', [-fix[1], -fix[2]], {\n type: 'translate'\n });\n t2 = this.create('transform', [alpha], { type: 'rotate' });\n t1.melt(t2);\n if (drag.evalVisProp('scalable')) {\n d = Geometry.distance(fix, np) / Geometry.distance(fix, op);\n t3 = this.create('transform', [d, d], { type: 'scale' });\n t1.melt(t3);\n }\n t4 = this.create('transform', [fix[1], fix[2]], {\n type: 'translate'\n });\n t1.melt(t4);\n\n if (drag.center.draggable()) {\n t1.applyOnce([drag.center]);\n }\n\n if (drag.method === 'twoPoints') {\n if (drag.point2.draggable()) {\n t1.applyOnce([drag.point2]);\n }\n } else if (drag.method === 'pointRadius') {\n if (Type.isNumber(drag.updateRadius.origin)) {\n drag.setRadius(drag.radius * d);\n }\n }\n\n this.update(drag.center);\n drag.highlight(true);\n }\n },\n\n highlightElements: function (x, y, evt, target) {\n var el,\n pEl,\n pId,\n overObjects = {},\n len = this.objectsList.length;\n\n // Elements below the mouse pointer which are not highlighted yet will be highlighted.\n for (el = 0; el < len; el++) {\n pEl = this.objectsList[el];\n pId = pEl.id;\n if (\n Type.exists(pEl.hasPoint) &&\n pEl.visPropCalc.visible &&\n pEl.hasPoint(x, y)\n ) {\n // this is required in any case because otherwise the box won't be shown until the point is dragged\n this.updateInfobox(pEl);\n\n if (!Type.exists(this.highlightedObjects[pId])) {\n // highlight only if not highlighted\n overObjects[pId] = pEl;\n pEl.highlight();\n // triggers board event.\n this.triggerEventHandlers(['mousehit', 'hit'], [evt, pEl, target]);\n }\n\n if (pEl.mouseover) {\n pEl.triggerEventHandlers(['mousemove', 'move'], [evt]);\n } else {\n pEl.triggerEventHandlers(['mouseover', 'over'], [evt]);\n pEl.mouseover = true;\n }\n }\n }\n\n for (el = 0; el < len; el++) {\n pEl = this.objectsList[el];\n pId = pEl.id;\n if (pEl.mouseover) {\n if (!overObjects[pId]) {\n pEl.triggerEventHandlers(['mouseout', 'out'], [evt]);\n pEl.mouseover = false;\n }\n }\n }\n },\n\n /**\n * Helper function which returns a reasonable starting point for the object being dragged.\n * Formerly known as initXYstart().\n * @private\n * @param {JXG.GeometryElement} obj The object to be dragged\n * @param {Array} targets Array of targets. It is changed by this function.\n */\n saveStartPos: function (obj, targets) {\n var xy = [],\n i,\n len;\n\n if (obj.type === Const.OBJECT_TYPE_TICKS) {\n xy.push([1, NaN, NaN]);\n } else if (obj.elementClass === Const.OBJECT_CLASS_LINE) {\n xy.push(obj.point1.coords.usrCoords);\n xy.push(obj.point2.coords.usrCoords);\n } else if (obj.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n xy.push(obj.center.coords.usrCoords);\n if (obj.method === 'twoPoints') {\n xy.push(obj.point2.coords.usrCoords);\n }\n } else if (obj.type === Const.OBJECT_TYPE_POLYGON) {\n len = obj.vertices.length - 1;\n for (i = 0; i < len; i++) {\n xy.push(obj.vertices[i].coords.usrCoords);\n }\n } else if (obj.type === Const.OBJECT_TYPE_SECTOR) {\n xy.push(obj.point1.coords.usrCoords);\n xy.push(obj.point2.coords.usrCoords);\n xy.push(obj.point3.coords.usrCoords);\n } else if (Type.isPoint(obj) || obj.type === Const.OBJECT_TYPE_GLIDER) {\n xy.push(obj.coords.usrCoords);\n } else if (obj.elementClass === Const.OBJECT_CLASS_CURVE) {\n // if (Type.exists(obj.parents)) {\n // len = obj.parents.length;\n // if (len > 0) {\n // for (i = 0; i < len; i++) {\n // xy.push(this.select(obj.parents[i]).coords.usrCoords);\n // }\n // } else\n // }\n if (obj.points.length > 0) {\n xy.push(obj.points[0].usrCoords);\n }\n } else {\n try {\n xy.push(obj.coords.usrCoords);\n } catch (e) {\n JXG.debug(\n 'JSXGraph+ saveStartPos: obj.coords.usrCoords not available: ' + e\n );\n }\n }\n\n len = xy.length;\n for (i = 0; i < len; i++) {\n targets.Zstart.push(xy[i][0]);\n targets.Xstart.push(xy[i][1]);\n targets.Ystart.push(xy[i][2]);\n }\n },\n\n mouseOriginMoveStart: function (evt) {\n var r, pos;\n\n r = this._isRequiredKeyPressed(evt, 'pan');\n if (r) {\n pos = this.getMousePosition(evt);\n this.initMoveOrigin(pos[0], pos[1]);\n }\n\n return r;\n },\n\n mouseOriginMove: function (evt) {\n var r = this.mode === this.BOARD_MODE_MOVE_ORIGIN,\n pos;\n\n if (r) {\n pos = this.getMousePosition(evt);\n this.moveOrigin(pos[0], pos[1], true);\n }\n\n return r;\n },\n\n /**\n * Start moving the origin with one finger.\n * @private\n * @param {Object} evt Event from touchStartListener\n * @return {Boolean} returns if the origin is moved.\n */\n touchStartMoveOriginOneFinger: function (evt) {\n var touches = evt['touches'],\n conditions,\n pos;\n\n conditions =\n this.attr.pan.enabled && !this.attr.pan.needtwofingers && touches.length === 1;\n\n if (conditions) {\n pos = this.getMousePosition(evt, 0);\n this.initMoveOrigin(pos[0], pos[1]);\n }\n\n return conditions;\n },\n\n /**\n * Move the origin with one finger\n * @private\n * @param {Object} evt Event from touchMoveListener\n * @return {Boolean} returns if the origin is moved.\n */\n touchOriginMove: function (evt) {\n var r = this.mode === this.BOARD_MODE_MOVE_ORIGIN,\n pos;\n\n if (r) {\n pos = this.getMousePosition(evt, 0);\n this.moveOrigin(pos[0], pos[1], true);\n }\n\n return r;\n },\n\n /**\n * Stop moving the origin with one finger\n * @return {null} null\n * @private\n */\n originMoveEnd: function () {\n this.updateQuality = this.BOARD_QUALITY_HIGH;\n this.mode = this.BOARD_MODE_NONE;\n },\n\n /**********************************************************\n *\n * Event Handler\n *\n **********************************************************/\n\n /**\n * Suppresses the default event handling.\n * Used for context menu.\n *\n * @param {Event} e\n * @returns {Boolean} false\n */\n suppressDefault: function (e) {\n if (Type.exists(e)) {\n e.preventDefault();\n }\n return false;\n },\n\n /**\n * Add all possible event handlers to the board object\n * that move objects, i.e. mouse, pointer and touch events.\n */\n addEventHandlers: function () {\n if (Env.supportsPointerEvents()) {\n this.addPointerEventHandlers();\n } else {\n this.addMouseEventHandlers();\n this.addTouchEventHandlers();\n }\n\n if (this.containerObj !== null) {\n // this.containerObj.oncontextmenu = this.suppressDefault;\n Env.addEvent(this.containerObj, 'contextmenu', this.suppressDefault, this);\n }\n\n // This one produces errors on IE\n // // Env.addEvent(this.containerObj, 'contextmenu', function (e) { e.preventDefault(); return false;}, this);\n // This one works on IE, Firefox and Chromium with default configurations. On some Safari\n // or Opera versions the user must explicitly allow the deactivation of the context menu.\n },\n\n /**\n * Remove all event handlers from the board object\n */\n removeEventHandlers: function () {\n if ((this.hasPointerHandlers || this.hasMouseHandlers || this.hasTouchHandlers) &&\n this.containerObj !== null\n ) {\n Env.removeEvent(this.containerObj, 'contextmenu', this.suppressDefault, this);\n }\n\n this.removeMouseEventHandlers();\n this.removeTouchEventHandlers();\n this.removePointerEventHandlers();\n\n this.removeFullscreenEventHandlers();\n this.removeKeyboardEventHandlers();\n this.removeResizeEventHandlers();\n\n // if (Env.isBrowser) {\n // if (Type.exists(this.resizeObserver)) {\n // this.stopResizeObserver();\n // } else {\n // Env.removeEvent(window, 'resize', this.resizeListener, this);\n // this.stopIntersectionObserver();\n // }\n // Env.removeEvent(window, 'scroll', this.scrollListener, this);\n // }\n },\n\n /**\n * Add resize related event handlers\n *\n */\n addResizeEventHandlers: function () {\n // var that = this;\n\n this.resizeHandlers = [];\n if (Env.isBrowser) {\n try {\n // Supported by all new browsers\n // resizeObserver: triggered if size of the JSXGraph div changes.\n this.startResizeObserver();\n this.resizeHandlers.push('resizeobserver');\n } catch (err) {\n // Certain Safari and edge version do not support\n // resizeObserver, but intersectionObserver.\n // resize event: triggered if size of window changes\n Env.addEvent(window, 'resize', this.resizeListener, this);\n // intersectionObserver: triggered if JSXGraph becomes visible.\n this.startIntersectionObserver();\n this.resizeHandlers.push('resize');\n }\n // Scroll event: needs to be captured since on mobile devices\n // sometimes a header bar is displayed / hidden, which triggers a\n // resize event.\n Env.addEvent(window, 'scroll', this.scrollListener, this);\n this.resizeHandlers.push('scroll');\n\n // On browser print:\n // we need to call the listener when having @media: print.\n try {\n // window.matchMedia('print').addEventListener('change', this.printListenerMatch.apply(this, arguments));\n this.printListenerMatchBound = this.printListenerMatch.bind(this);\n this.printMediaQuery = window.matchMedia('print');\n this.screenMediaQuery = window.matchMedia('screen');\n this.printMediaQuery.addEventListener('change', this.printListenerMatchBound);\n this.screenMediaQuery.addEventListener('change', this.printListenerMatchBound);\n this.resizeHandlers.push('print');\n } catch (err) {\n JXG.debug(\"Error adding printListener\", err);\n }\n // if (Type.isFunction(MediaQueryList.prototype.addEventListener)) {\n // window.matchMedia('print').addEventListener('change', function (mql) {\n // if (mql.matches) {\n // that.printListener();\n // }\n // });\n // } else if (Type.isFunction(MediaQueryList.prototype.addListener)) { // addListener might be deprecated\n // window.matchMedia('print').addListener(function (mql, ev) {\n // if (mql.matches) {\n // that.printListener(ev);\n // }\n // });\n // }\n\n // When closing the print dialog we again have to resize.\n // Env.addEvent(window, 'afterprint', this.printListener, this);\n // this.resizeHandlers.push('afterprint');\n }\n },\n\n /**\n * Remove resize related event handlers\n *\n */\n removeResizeEventHandlers: function () {\n var i, e;\n if (this.resizeHandlers.length > 0 && Env.isBrowser) {\n for (i = 0; i < this.resizeHandlers.length; i++) {\n e = this.resizeHandlers[i];\n switch (e) {\n case 'resizeobserver':\n if (Type.exists(this.resizeObserver)) {\n this.stopResizeObserver();\n }\n break;\n case 'resize':\n Env.removeEvent(window, 'resize', this.resizeListener, this);\n if (Type.exists(this.intersectionObserver)) {\n this.stopIntersectionObserver();\n }\n break;\n case 'scroll':\n Env.removeEvent(window, 'scroll', this.scrollListener, this);\n break;\n case 'print':\n this.printMediaQuery.removeEventListener('change', this.printListenerMatchBound, false);\n this.screenMediaQuery.removeEventListener('change', this.printListenerMatchBound, false);\n this.printMediaQuery = null;\n this.screenMediaQuery = null;\n this.printListenerMatchBound = null;\n break;\n // case 'afterprint':\n // Env.removeEvent(window, 'afterprint', this.printListener, this);\n // break;\n }\n }\n this.resizeHandlers = [];\n }\n },\n\n\n /**\n * Registers pointer event handlers.\n */\n addPointerEventHandlers: function () {\n if (!this.hasPointerHandlers && Env.isBrowser) {\n var moveTarget = this.attr.movetarget || this.containerObj;\n\n if (window.navigator.msPointerEnabled) {\n // IE10-\n // Env.addEvent(this.containerObj, 'MSPointerDown', this.pointerDownListener, this);\n Env.addEvent(moveTarget, 'MSPointerDown', this.pointerDownListener, this);\n Env.addEvent(moveTarget, 'MSPointerMove', this.pointerMoveListener, this);\n } else {\n // Env.addEvent(this.containerObj, 'pointerdown', this.pointerDownListener, this);\n Env.addEvent(moveTarget, 'pointerdown', this.pointerDownListener, this);\n Env.addEvent(moveTarget, 'pointermove', this.pointerMoveListener, this);\n Env.addEvent(moveTarget, 'pointerleave', this.pointerLeaveListener, this);\n Env.addEvent(moveTarget, 'click', this.pointerClickListener, this);\n Env.addEvent(moveTarget, 'dblclick', this.pointerDblClickListener, this);\n }\n\n if (this.containerObj !== null) {\n // This is needed for capturing touch events.\n // It is in jsxgraph.css, for ms-touch-action...\n this.containerObj.style.touchAction = 'none';\n // this.containerObj.style.touchAction = 'auto';\n }\n\n this.hasPointerHandlers = true;\n }\n },\n\n /**\n * Registers mouse move, down and wheel event handlers.\n */\n addMouseEventHandlers: function () {\n if (!this.hasMouseHandlers && Env.isBrowser) {\n var moveTarget = this.attr.movetarget || this.containerObj;\n\n // Env.addEvent(this.containerObj, 'mousedown', this.mouseDownListener, this);\n Env.addEvent(moveTarget, 'mousedown', this.mouseDownListener, this);\n Env.addEvent(moveTarget, 'mousemove', this.mouseMoveListener, this);\n Env.addEvent(moveTarget, 'click', this.mouseClickListener, this);\n Env.addEvent(moveTarget, 'dblclick', this.mouseDblClickListener, this);\n\n this.hasMouseHandlers = true;\n }\n },\n\n /**\n * Register touch start and move and gesture start and change event handlers.\n * @param {Boolean} appleGestures If set to false the gesturestart and gesturechange event handlers\n * will not be registered.\n *\n * Since iOS 13, touch events were abandoned in favour of pointer events\n */\n addTouchEventHandlers: function (appleGestures) {\n if (!this.hasTouchHandlers && Env.isBrowser) {\n var moveTarget = this.attr.movetarget || this.containerObj;\n\n // Env.addEvent(this.containerObj, 'touchstart', this.touchStartListener, this);\n Env.addEvent(moveTarget, 'touchstart', this.touchStartListener, this);\n Env.addEvent(moveTarget, 'touchmove', this.touchMoveListener, this);\n\n /*\n if (!Type.exists(appleGestures) || appleGestures) {\n // Gesture listener are called in touchStart and touchMove.\n //Env.addEvent(this.containerObj, 'gesturestart', this.gestureStartListener, this);\n //Env.addEvent(this.containerObj, 'gesturechange', this.gestureChangeListener, this);\n }\n */\n\n this.hasTouchHandlers = true;\n }\n },\n\n /**\n * Registers pointer event handlers.\n */\n addWheelEventHandlers: function () {\n if (!this.hasWheelHandlers && Env.isBrowser) {\n Env.addEvent(this.containerObj, 'mousewheel', this.mouseWheelListener, this);\n Env.addEvent(this.containerObj, 'DOMMouseScroll', this.mouseWheelListener, this);\n this.hasWheelHandlers = true;\n }\n },\n\n /**\n * Add fullscreen events which update the CSS transformation matrix to correct\n * the mouse/touch/pointer positions in case of CSS transformations.\n */\n addFullscreenEventHandlers: function () {\n var i,\n // standard/Edge, firefox, chrome/safari, IE11\n events = [\n 'fullscreenchange',\n 'mozfullscreenchange',\n 'webkitfullscreenchange',\n 'msfullscreenchange'\n ],\n le = events.length;\n\n if (!this.hasFullscreenEventHandlers && Env.isBrowser) {\n for (i = 0; i < le; i++) {\n Env.addEvent(this.document, events[i], this.fullscreenListener, this);\n }\n this.hasFullscreenEventHandlers = true;\n }\n },\n\n /**\n * Register keyboard event handlers.\n */\n addKeyboardEventHandlers: function () {\n if (this.attr.keyboard.enabled && !this.hasKeyboardHandlers && Env.isBrowser) {\n Env.addEvent(this.containerObj, 'keydown', this.keyDownListener, this);\n Env.addEvent(this.containerObj, 'focusin', this.keyFocusInListener, this);\n Env.addEvent(this.containerObj, 'focusout', this.keyFocusOutListener, this);\n this.hasKeyboardHandlers = true;\n }\n },\n\n /**\n * Remove all registered touch event handlers.\n */\n removeKeyboardEventHandlers: function () {\n if (this.hasKeyboardHandlers && Env.isBrowser) {\n Env.removeEvent(this.containerObj, 'keydown', this.keyDownListener, this);\n Env.removeEvent(this.containerObj, 'focusin', this.keyFocusInListener, this);\n Env.removeEvent(this.containerObj, 'focusout', this.keyFocusOutListener, this);\n this.hasKeyboardHandlers = false;\n }\n },\n\n /**\n * Remove all registered event handlers regarding fullscreen mode.\n */\n removeFullscreenEventHandlers: function () {\n var i,\n // standard/Edge, firefox, chrome/safari, IE11\n events = [\n 'fullscreenchange',\n 'mozfullscreenchange',\n 'webkitfullscreenchange',\n 'msfullscreenchange'\n ],\n le = events.length;\n\n if (this.hasFullscreenEventHandlers && Env.isBrowser) {\n for (i = 0; i < le; i++) {\n Env.removeEvent(this.document, events[i], this.fullscreenListener, this);\n }\n this.hasFullscreenEventHandlers = false;\n }\n },\n\n /**\n * Remove MSPointer* Event handlers.\n */\n removePointerEventHandlers: function () {\n if (this.hasPointerHandlers && Env.isBrowser) {\n var moveTarget = this.attr.movetarget || this.containerObj;\n\n if (window.navigator.msPointerEnabled) {\n // IE10-\n // Env.removeEvent(this.containerObj, 'MSPointerDown', this.pointerDownListener, this);\n Env.removeEvent(moveTarget, 'MSPointerDown', this.pointerDownListener, this);\n Env.removeEvent(moveTarget, 'MSPointerMove', this.pointerMoveListener, this);\n } else {\n // Env.removeEvent(this.containerObj, 'pointerdown', this.pointerDownListener, this);\n Env.removeEvent(moveTarget, 'pointerdown', this.pointerDownListener, this);\n Env.removeEvent(moveTarget, 'pointermove', this.pointerMoveListener, this);\n Env.removeEvent(moveTarget, 'pointerleave', this.pointerLeaveListener, this);\n Env.removeEvent(moveTarget, 'click', this.pointerClickListener, this);\n Env.removeEvent(moveTarget, 'dblclick', this.pointerDblClickListener, this);\n }\n\n if (this.hasWheelHandlers) {\n Env.removeEvent(this.containerObj, 'mousewheel', this.mouseWheelListener, this);\n Env.removeEvent(this.containerObj, 'DOMMouseScroll', this.mouseWheelListener, this);\n }\n\n if (this.hasPointerUp) {\n if (window.navigator.msPointerEnabled) {\n // IE10-\n Env.removeEvent(this.document, 'MSPointerUp', this.pointerUpListener, this);\n } else {\n Env.removeEvent(this.document, 'pointerup', this.pointerUpListener, this);\n Env.removeEvent(this.document, 'pointercancel', this.pointerUpListener, this);\n }\n this.hasPointerUp = false;\n }\n\n this.hasPointerHandlers = false;\n }\n },\n\n /**\n * De-register mouse event handlers.\n */\n removeMouseEventHandlers: function () {\n if (this.hasMouseHandlers && Env.isBrowser) {\n var moveTarget = this.attr.movetarget || this.containerObj;\n\n // Env.removeEvent(this.containerObj, 'mousedown', this.mouseDownListener, this);\n Env.removeEvent(moveTarget, 'mousedown', this.mouseDownListener, this);\n Env.removeEvent(moveTarget, 'mousemove', this.mouseMoveListener, this);\n Env.removeEvent(moveTarget, 'click', this.mouseClickListener, this);\n Env.removeEvent(moveTarget, 'dblclick', this.mouseDblClickListener, this);\n\n if (this.hasMouseUp) {\n Env.removeEvent(this.document, 'mouseup', this.mouseUpListener, this);\n this.hasMouseUp = false;\n }\n\n if (this.hasWheelHandlers) {\n Env.removeEvent(this.containerObj, 'mousewheel', this.mouseWheelListener, this);\n Env.removeEvent(\n this.containerObj,\n 'DOMMouseScroll',\n this.mouseWheelListener,\n this\n );\n }\n\n this.hasMouseHandlers = false;\n }\n },\n\n /**\n * Remove all registered touch event handlers.\n */\n removeTouchEventHandlers: function () {\n if (this.hasTouchHandlers && Env.isBrowser) {\n var moveTarget = this.attr.movetarget || this.containerObj;\n\n // Env.removeEvent(this.containerObj, 'touchstart', this.touchStartListener, this);\n Env.removeEvent(moveTarget, 'touchstart', this.touchStartListener, this);\n Env.removeEvent(moveTarget, 'touchmove', this.touchMoveListener, this);\n\n if (this.hasTouchEnd) {\n Env.removeEvent(this.document, 'touchend', this.touchEndListener, this);\n this.hasTouchEnd = false;\n }\n\n this.hasTouchHandlers = false;\n }\n },\n\n /**\n * Handler for click on left arrow in the navigation bar\n * @returns {JXG.Board} Reference to the board\n */\n clickLeftArrow: function () {\n this.moveOrigin(\n this.origin.scrCoords[1] + this.canvasWidth * 0.1,\n this.origin.scrCoords[2]\n );\n return this;\n },\n\n /**\n * Handler for click on right arrow in the navigation bar\n * @returns {JXG.Board} Reference to the board\n */\n clickRightArrow: function () {\n this.moveOrigin(\n this.origin.scrCoords[1] - this.canvasWidth * 0.1,\n this.origin.scrCoords[2]\n );\n return this;\n },\n\n /**\n * Handler for click on up arrow in the navigation bar\n * @returns {JXG.Board} Reference to the board\n */\n clickUpArrow: function () {\n this.moveOrigin(\n this.origin.scrCoords[1],\n this.origin.scrCoords[2] - this.canvasHeight * 0.1\n );\n return this;\n },\n\n /**\n * Handler for click on down arrow in the navigation bar\n * @returns {JXG.Board} Reference to the board\n */\n clickDownArrow: function () {\n this.moveOrigin(\n this.origin.scrCoords[1],\n this.origin.scrCoords[2] + this.canvasHeight * 0.1\n );\n return this;\n },\n\n /**\n * Triggered on iOS/Safari while the user inputs a gesture (e.g. pinch) and is used to zoom into the board.\n * Works on iOS/Safari and Android.\n * @param {Event} evt Browser event object\n * @returns {Boolean}\n */\n gestureChangeListener: function (evt) {\n var c,\n dir1 = [],\n dir2 = [],\n angle,\n mi = 10,\n isPinch = false,\n // Save zoomFactors\n zx = this.attr.zoom.factorx,\n zy = this.attr.zoom.factory,\n factor, dist, theta, bound,\n zoomCenter,\n doZoom = false,\n dx, dy, cx, cy;\n\n if (this.mode !== this.BOARD_MODE_ZOOM) {\n return true;\n }\n evt.preventDefault();\n\n dist = Geometry.distance(\n [evt.touches[0].clientX, evt.touches[0].clientY],\n [evt.touches[1].clientX, evt.touches[1].clientY],\n 2\n );\n\n // Android pinch to zoom\n // evt.scale was available in iOS touch events (pre iOS 13)\n // evt.scale is undefined in Android\n if (evt.scale === undefined) {\n evt.scale = dist / this.prevDist;\n }\n\n if (!Type.exists(this.prevCoords)) {\n return false;\n }\n // Compute the angle of the two finger directions\n dir1 = [\n evt.touches[0].clientX - this.prevCoords[0][0],\n evt.touches[0].clientY - this.prevCoords[0][1]\n ];\n dir2 = [\n evt.touches[1].clientX - this.prevCoords[1][0],\n evt.touches[1].clientY - this.prevCoords[1][1]\n ];\n\n if (\n dir1[0] * dir1[0] + dir1[1] * dir1[1] < mi * mi &&\n dir2[0] * dir2[0] + dir2[1] * dir2[1] < mi * mi\n ) {\n return false;\n }\n\n angle = Geometry.rad(dir1, [0, 0], dir2);\n if (\n this.isPreviousGesture !== 'pan' &&\n Math.abs(angle) > Math.PI * 0.2 &&\n Math.abs(angle) < Math.PI * 1.8\n ) {\n isPinch = true;\n }\n\n if (this.isPreviousGesture !== 'pan' && !isPinch) {\n if (Math.abs(evt.scale) < 0.77 || Math.abs(evt.scale) > 1.3) {\n isPinch = true;\n }\n }\n\n factor = evt.scale / this.prevScale;\n this.prevScale = evt.scale;\n this.prevCoords = [\n [evt.touches[0].clientX, evt.touches[0].clientY],\n [evt.touches[1].clientX, evt.touches[1].clientY]\n ];\n\n c = new Coords(Const.COORDS_BY_SCREEN, this.getMousePosition(evt, 0), this);\n\n if (this.attr.pan.enabled && this.attr.pan.needtwofingers && !isPinch) {\n // Pan detected\n this.isPreviousGesture = 'pan';\n this.moveOrigin(c.scrCoords[1], c.scrCoords[2], true);\n\n } else if (this.attr.zoom.enabled && Math.abs(factor - 1.0) < 0.5) {\n doZoom = false;\n zoomCenter = this.attr.zoom.center;\n // Pinch detected\n if (this.attr.zoom.pinchhorizontal || this.attr.zoom.pinchvertical) {\n dx = Math.abs(evt.touches[0].clientX - evt.touches[1].clientX);\n dy = Math.abs(evt.touches[0].clientY - evt.touches[1].clientY);\n theta = Math.abs(Math.atan2(dy, dx));\n bound = (Math.PI * this.attr.zoom.pinchsensitivity) / 90.0;\n }\n\n if (!this.keepaspectratio &&\n this.attr.zoom.pinchhorizontal &&\n theta < bound) {\n this.attr.zoom.factorx = factor;\n this.attr.zoom.factory = 1.0;\n cx = 0;\n cy = 0;\n doZoom = true;\n } else if (!this.keepaspectratio &&\n this.attr.zoom.pinchvertical &&\n Math.abs(theta - Math.PI * 0.5) < bound\n ) {\n this.attr.zoom.factorx = 1.0;\n this.attr.zoom.factory = factor;\n cx = 0;\n cy = 0;\n doZoom = true;\n } else if (this.attr.zoom.pinch) {\n this.attr.zoom.factorx = factor;\n this.attr.zoom.factory = factor;\n cx = c.usrCoords[1];\n cy = c.usrCoords[2];\n doZoom = true;\n }\n\n if (doZoom) {\n if (zoomCenter === 'board') {\n this.zoomIn();\n } else { // including zoomCenter === 'auto'\n this.zoomIn(cx, cy);\n }\n\n // Restore zoomFactors\n this.attr.zoom.factorx = zx;\n this.attr.zoom.factory = zy;\n }\n }\n\n return false;\n },\n\n /**\n * Called by iOS/Safari as soon as the user starts a gesture. Works natively on iOS/Safari,\n * on Android we emulate it.\n * @param {Event} evt\n * @returns {Boolean}\n */\n gestureStartListener: function (evt) {\n var pos;\n\n evt.preventDefault();\n this.prevScale = 1.0;\n // Android pinch to zoom\n this.prevDist = Geometry.distance(\n [evt.touches[0].clientX, evt.touches[0].clientY],\n [evt.touches[1].clientX, evt.touches[1].clientY],\n 2\n );\n this.prevCoords = [\n [evt.touches[0].clientX, evt.touches[0].clientY],\n [evt.touches[1].clientX, evt.touches[1].clientY]\n ];\n this.isPreviousGesture = 'none';\n\n // If pinch-to-zoom is interpreted as panning\n // we have to prepare move origin\n pos = this.getMousePosition(evt, 0);\n this.initMoveOrigin(pos[0], pos[1]);\n\n this.mode = this.BOARD_MODE_ZOOM;\n this._change3DView = false;\n return false;\n },\n\n /**\n * Test if the required key combination is pressed for wheel zoom, move origin and\n * selection\n * @private\n * @param {Object} evt Mouse or pen event\n * @param {String} action String containing the action: 'zoom', 'pan', 'selection'.\n * Corresponds to the attribute subobject.\n * @return {Boolean} true or false.\n */\n _isRequiredKeyPressed: function (evt, action) {\n var obj = this.attr[action];\n if (!obj.enabled) {\n return false;\n }\n\n if (\n ((obj.needshift && evt.shiftKey) || (!obj.needshift && !evt.shiftKey)) &&\n ((obj.needctrl && evt.ctrlKey) || (!obj.needctrl && !evt.ctrlKey))\n ) {\n return true;\n }\n\n return false;\n },\n\n /*\n * Pointer events\n */\n\n /**\n *\n * Check if pointer event is already registered in {@link JXG.Board#_board_touches}.\n *\n * @param {Object} evt Event object\n * @return {Boolean} true if down event has already been sent.\n * @private\n */\n _isPointerRegistered: function (evt) {\n var i,\n len = this._board_touches.length;\n\n for (i = 0; i < len; i++) {\n if (this._board_touches[i].pointerId === evt.pointerId) {\n return true;\n }\n }\n return false;\n },\n\n /**\n *\n * Store the position of a pointer event.\n * If not yet done, registers a pointer event in {@link JXG.Board#_board_touches}.\n * Allows to follow the path of that finger on the screen.\n * Only two simultaneous touches are supported.\n *\n * @param {Object} evt Event object\n * @returns {JXG.Board} Reference to the board\n * @private\n */\n _pointerStorePosition: function (evt) {\n var i, found;\n\n for (i = 0, found = false; i < this._board_touches.length; i++) {\n if (this._board_touches[i].pointerId === evt.pointerId) {\n this._board_touches[i].clientX = evt.clientX;\n this._board_touches[i].clientY = evt.clientY;\n found = true;\n break;\n }\n }\n\n // Restrict the number of simultaneous touches to 2\n if (!found && this._board_touches.length < 2) {\n this._board_touches.push({\n pointerId: evt.pointerId,\n clientX: evt.clientX,\n clientY: evt.clientY\n });\n }\n\n return this;\n },\n\n /**\n * Deregisters a pointer event in {@link JXG.Board#_board_touches}.\n * It happens if a finger has been lifted from the screen.\n *\n * @param {Object} evt Event object\n * @returns {JXG.Board} Reference to the board\n * @private\n */\n _pointerRemoveTouches: function (evt) {\n var i;\n for (i = 0; i < this._board_touches.length; i++) {\n if (this._board_touches[i].pointerId === evt.pointerId) {\n this._board_touches.splice(i, 1);\n break;\n }\n }\n\n return this;\n },\n\n /**\n * Remove all registered fingers from {@link JXG.Board#_board_touches}.\n * This might be necessary if too many fingers have been registered.\n * @returns {JXG.Board} Reference to the board\n * @private\n */\n _pointerClearTouches: function (pId) {\n // var i;\n // if (pId) {\n // for (i = 0; i < this._board_touches.length; i++) {\n // if (pId === this._board_touches[i].pointerId) {\n // this._board_touches.splice(i, i);\n // break;\n // }\n // }\n // } else {\n // }\n if (this._board_touches.length > 0) {\n this.dehighlightAll();\n }\n this.updateQuality = this.BOARD_QUALITY_HIGH;\n this.mode = this.BOARD_MODE_NONE;\n this._board_touches = [];\n this.touches = [];\n },\n\n /**\n * Determine which input device is used for this action.\n * Possible devices are 'touch', 'pen' and 'mouse'.\n * This affects the precision and certain events.\n * In case of no browser, 'mouse' is used.\n *\n * @see JXG.Board#pointerDownListener\n * @see JXG.Board#pointerMoveListener\n * @see JXG.Board#initMoveObject\n * @see JXG.Board#moveObject\n *\n * @param {Event} evt The browsers event object.\n * @returns {String} 'mouse', 'pen', or 'touch'\n * @private\n */\n _getPointerInputDevice: function (evt) {\n if (Env.isBrowser) {\n if (\n evt.pointerType === 'touch' || // New\n (window.navigator.msMaxTouchPoints && // Old\n window.navigator.msMaxTouchPoints > 1)\n ) {\n return 'touch';\n }\n if (evt.pointerType === 'mouse') {\n return 'mouse';\n }\n if (evt.pointerType === 'pen') {\n return 'pen';\n }\n }\n return 'mouse';\n },\n\n /**\n * This method is called by the browser when a pointing device is pressed on the screen.\n * @param {Event} evt The browsers event object.\n * @param {Object} object If the object to be dragged is already known, it can be submitted via this parameter\n * @param {Boolean} [allowDefaultEventHandling=false] If true event is not canceled, i.e. prevent call of evt.preventDefault()\n * @returns {Boolean} false if the first finger event is sent twice, or not a browser, or in selection mode. Otherwise returns true.\n */\n pointerDownListener: function (evt, object, allowDefaultEventHandling) {\n var i, j, k, pos,\n elements, sel, target_obj,\n type = 'mouse', // Used in case of no browser\n found, target, ta;\n\n // Fix for Firefox browser: When using a second finger, the\n // touch event for the first finger is sent again.\n if (!object && this._isPointerRegistered(evt)) {\n return false;\n }\n\n if (Type.evaluate(this.attr.movetarget) === null &&\n Type.exists(evt.target) && Type.exists(evt.target.releasePointerCapture)) {\n evt.target.releasePointerCapture(evt.pointerId);\n }\n\n if (!object && evt.isPrimary) {\n // First finger down. To be on the safe side this._board_touches is cleared.\n // this._pointerClearTouches();\n }\n\n if (!this.hasPointerUp) {\n if (window.navigator.msPointerEnabled) {\n // IE10-\n Env.addEvent(this.document, 'MSPointerUp', this.pointerUpListener, this);\n } else {\n // 'pointercancel' is fired e.g. if the finger leaves the browser and drags down the system menu on Android\n Env.addEvent(this.document, 'pointerup', this.pointerUpListener, this);\n Env.addEvent(this.document, 'pointercancel', this.pointerUpListener, this);\n }\n this.hasPointerUp = true;\n }\n\n if (this.hasMouseHandlers) {\n this.removeMouseEventHandlers();\n }\n\n if (this.hasTouchHandlers) {\n this.removeTouchEventHandlers();\n }\n\n // Prevent accidental selection of text\n if (this.document.selection && Type.isFunction(this.document.selection.empty)) {\n this.document.selection.empty();\n } else if (window.getSelection) {\n sel = window.getSelection();\n if (sel.removeAllRanges) {\n try {\n sel.removeAllRanges();\n } catch (e) { }\n }\n }\n\n // Mouse, touch or pen device\n this._inputDevice = this._getPointerInputDevice(evt);\n type = this._inputDevice;\n this.options.precision.hasPoint = this.options.precision[type];\n\n // Handling of multi touch with pointer events should be easier than with touch events.\n // Every pointer device has its own pointerId, e.g. the mouse\n // always has id 1 or 0, fingers and pens get unique ids every time a pointerDown event is fired and they will\n // keep this id until a pointerUp event is fired. What we have to do here is:\n // 1. collect all elements under the current pointer\n // 2. run through the touches control structure\n // a. look for the object collected in step 1.\n // b. if an object is found, check the number of pointers. If appropriate, add the pointer.\n pos = this.getMousePosition(evt);\n\n // Handle selection rectangle\n this._testForSelection(evt);\n if (this.selectingMode) {\n this._startSelecting(pos);\n this.triggerEventHandlers(\n ['touchstartselecting', 'pointerstartselecting', 'startselecting'],\n [evt]\n );\n return; // don't continue as a normal click\n }\n\n if (this.attr.drag.enabled && object) {\n elements = [object];\n this.mode = this.BOARD_MODE_DRAG;\n } else {\n elements = this.initMoveObject(pos[0], pos[1], evt, type);\n }\n\n target_obj = {\n num: evt.pointerId,\n X: pos[0],\n Y: pos[1],\n Xprev: NaN,\n Yprev: NaN,\n Xstart: [],\n Ystart: [],\n Zstart: []\n };\n\n // If no draggable object can be found, get out here immediately\n if (elements.length > 0) {\n // check touches structure\n target = elements[elements.length - 1];\n found = false;\n\n // Reminder: this.touches is the list of elements which\n // currently 'possess' a pointer (mouse, pen, finger)\n for (i = 0; i < this.touches.length; i++) {\n // An element receives a further touch, i.e.\n // the target is already in our touches array, add the pointer to the existing touch\n if (this.touches[i].obj === target) {\n j = i;\n k = this.touches[i].targets.push(target_obj) - 1;\n found = true;\n break;\n }\n }\n if (!found) {\n // A new element has been touched.\n k = 0;\n j =\n this.touches.push({\n obj: target,\n targets: [target_obj]\n }) - 1;\n }\n\n this.dehighlightAll();\n target.highlight(true);\n\n this.saveStartPos(target, this.touches[j].targets[k]);\n\n // Prevent accidental text selection\n // this could get us new trouble: input fields, links and drop down boxes placed as text\n // on the board don't work anymore.\n if (evt && evt.preventDefault && !allowDefaultEventHandling) {\n // All browser supporting pointer events know preventDefault()\n evt.preventDefault();\n }\n }\n\n if (this.touches.length > 0 && !allowDefaultEventHandling) {\n evt.preventDefault();\n evt.stopPropagation();\n }\n\n if (!Env.isBrowser) {\n return false;\n }\n if (this._getPointerInputDevice(evt) !== 'touch') {\n if (this.mode === this.BOARD_MODE_NONE) {\n this.mouseOriginMoveStart(evt);\n }\n } else {\n this._pointerStorePosition(evt);\n evt.touches = this._board_touches;\n\n // Touch events on empty areas of the board are handled here, see also touchStartListener\n // 1. case: one finger. If allowed, this triggers pan with one finger\n if (\n evt.touches.length === 1 &&\n this.mode === this.BOARD_MODE_NONE &&\n this.touchStartMoveOriginOneFinger(evt)\n ) {\n // Empty by purpose\n } else if (\n evt.touches.length === 2 &&\n (this.mode === this.BOARD_MODE_NONE ||\n this.mode === this.BOARD_MODE_MOVE_ORIGIN)\n ) {\n // 2. case: two fingers: pinch to zoom or pan with two fingers needed.\n // This happens when the second finger hits the device. First, the\n // 'one finger pan mode' has to be cancelled.\n if (this.mode === this.BOARD_MODE_MOVE_ORIGIN) {\n this.originMoveEnd();\n }\n\n this.gestureStartListener(evt);\n }\n }\n\n this.initSketchCurve(evt);\n\n // Allow browser scrolling\n // For this: pan by one finger has to be disabled\n\n ta = 'none'; // JSXGraph catches all user touch events\n if (this.mode === this.BOARD_MODE_NONE &&\n (Type.evaluate(this.attr.browserpan) === true || Type.evaluate(this.attr.browserpan.enabled) === true) &&\n // One-finger pan has priority over browserPan\n (Type.evaluate(this.attr.pan.enabled) === false || Type.evaluate(this.attr.pan.needtwofingers) === true)\n ) {\n // ta = 'pan-x pan-y'; // JSXGraph allows browser scrolling\n ta = 'auto'; // JSXGraph allows browser scrolling\n }\n this.containerObj.style.touchAction = ta;\n\n this.triggerEventHandlers(['touchstart', 'down', 'pointerdown', 'MSPointerDown'], [evt]);\n\n return true;\n },\n\n /**\n * Internal handling of click events for pointers and mouse.\n *\n * @param {Event} evt The browsers event object.\n * @param {Array} evtArray list of event names\n * @private\n */\n _handleClicks: function(evt, evtArray) {\n var that = this,\n el, delay, suppress;\n\n if (this.selectingMode) {\n evt.stopPropagation();\n return;\n }\n\n delay = Type.evaluate(this.attr.clickdelay);\n suppress = Type.evaluate(this.attr.dblclicksuppressclick);\n\n if (suppress) {\n // dblclick suppresses previous click events\n this._preventSingleClick = false;\n\n // Wait if there is a dblclick event.\n // If not fire a click event\n this._singleClickTimer = setTimeout(function() {\n if (!that._preventSingleClick) {\n // Fire click event and remove element from click list\n that.triggerEventHandlers(evtArray, [evt]);\n for (el in that.clickObjects) {\n if (that.clickObjects.hasOwnProperty(el)) {\n that.clickObjects[el].triggerEventHandlers(evtArray, [evt]);\n delete that.clickObjects[el];\n }\n }\n }\n }, delay);\n } else {\n // dblclick is preceded by two click events\n\n // Fire click events\n that.triggerEventHandlers(evtArray, [evt]);\n for (el in that.clickObjects) {\n if (that.clickObjects.hasOwnProperty(el)) {\n that.clickObjects[el].triggerEventHandlers(evtArray, [evt]);\n }\n }\n\n // Clear list of clicked elements with a delay\n setTimeout(function() {\n for (el in that.clickObjects) {\n if (that.clickObjects.hasOwnProperty(el)) {\n delete that.clickObjects[el];\n }\n }\n }, delay);\n }\n evt.stopPropagation();\n },\n\n /**\n * Internal handling of dblclick events for pointers and mouse.\n *\n * @param {Event} evt The browsers event object.\n * @param {Array} evtArray list of event names\n * @private\n */\n _handleDblClicks: function(evt, evtArray) {\n var el;\n\n if (this.selectingMode) {\n evt.stopPropagation();\n return;\n }\n\n // Notify that a dblclick has happened\n this._preventSingleClick = true;\n clearTimeout(this._singleClickTimer);\n\n // Fire dblclick event\n this.triggerEventHandlers(evtArray, [evt]);\n for (el in this.clickObjects) {\n if (this.clickObjects.hasOwnProperty(el)) {\n this.clickObjects[el].triggerEventHandlers(evtArray, [evt]);\n delete this.clickObjects[el];\n }\n }\n\n evt.stopPropagation();\n },\n\n /**\n * This method is called by the browser when a pointer device clicks on the screen.\n * @param {Event} evt The browsers event object.\n */\n pointerClickListener: function (evt) {\n this._handleClicks(evt, ['click', 'pointerclick']);\n },\n\n /**\n * This method is called by the browser when a pointer device double clicks on the screen.\n * @param {Event} evt The browsers event object.\n */\n pointerDblClickListener: function (evt) {\n this._handleDblClicks(evt, ['dblclick', 'pointerdblclick']);\n },\n\n /**\n * This method is called by the browser when the mouse device clicks on the screen.\n * @param {Event} evt The browsers event object.\n */\n mouseClickListener: function (evt) {\n this._handleClicks(evt, ['click', 'mouseclick']);\n },\n\n /**\n * This method is called by the browser when the mouse device double clicks on the screen.\n * @param {Event} evt The browsers event object.\n */\n mouseDblClickListener: function (evt) {\n this._handleDblClicks(evt, ['dblclick', 'mousedblclick']);\n },\n\n // /**\n // * Called if pointer leaves an HTML tag. It is called by the inner-most tag.\n // * That means, if a JSXGraph text, i.e. an HTML div, is placed close\n // * to the border of the board, this pointerout event will be ignored.\n // * @param {Event} evt\n // * @return {Boolean}\n // */\n // pointerOutListener: function (evt) {\n // if (evt.target === this.containerObj ||\n // (this.renderer.type === 'svg' && evt.target === this.renderer.foreignObjLayer)) {\n // this.pointerUpListener(evt);\n // }\n // return this.mode === this.BOARD_MODE_NONE;\n // },\n\n /**\n * Called periodically by the browser while the user moves a pointing device across the screen.\n * @param {Event} evt\n * @returns {Boolean}\n */\n pointerMoveListener: function (evt) {\n var i, j, pos,\n eps,\n touchTargets,\n type = 'mouse'; // in case of no browser\n\n if (\n this._getPointerInputDevice(evt) === 'touch' &&\n !this._isPointerRegistered(evt)\n ) {\n // Test, if there was a previous down event of this _getPointerId\n // (in case it is a touch event).\n // Otherwise this move event is ignored. This is necessary e.g. for sketchometry.\n return this.BOARD_MODE_NONE;\n }\n\n if (!this.checkFrameRate(evt)) {\n return false;\n }\n\n if (this.mode !== this.BOARD_MODE_DRAG) {\n this.dehighlightAll();\n this.displayInfobox(false);\n }\n\n if (this.mode !== this.BOARD_MODE_NONE) {\n evt.preventDefault();\n evt.stopPropagation();\n }\n\n this.updateQuality = this.BOARD_QUALITY_LOW;\n // Mouse, touch or pen device\n this._inputDevice = this._getPointerInputDevice(evt);\n type = this._inputDevice;\n this.options.precision.hasPoint = this.options.precision[type];\n eps = this.options.precision.hasPoint * 0.3333;\n\n pos = this.getMousePosition(evt);\n // Ignore pointer move event if too close at the border\n // and setPointerCapture is off\n if (Type.evaluate(this.attr.movetarget) === null &&\n (pos[0] <= eps || pos[1] <= eps ||\n pos[0] >= this.canvasWidth - eps ||\n pos[1] >= this.canvasHeight - eps)\n ) {\n return this.mode === this.BOARD_MODE_NONE;\n }\n\n // selection\n if (this.selectingMode) {\n this._moveSelecting(pos);\n this.triggerEventHandlers(\n ['touchmoveselecting', 'moveselecting', 'pointermoveselecting'],\n [evt, this.mode]\n );\n } else if (!this.mouseOriginMove(evt)) {\n\n this.addToSketchCurve(evt);\n\n if (this.mode === this.BOARD_MODE_DRAG) {\n // Run through all jsxgraph elements which are touched by at least one finger.\n for (i = 0; i < this.touches.length; i++) {\n touchTargets = this.touches[i].targets;\n // Run through all touch events which have been started on this jsxgraph element.\n for (j = 0; j < touchTargets.length; j++) {\n if (touchTargets[j].num === evt.pointerId) {\n touchTargets[j].X = pos[0];\n touchTargets[j].Y = pos[1];\n\n if (touchTargets.length === 1) {\n // Touch by one finger: this is possible for all elements that can be dragged\n this.moveObject(pos[0], pos[1], this.touches[i], evt, type);\n } else if (touchTargets.length === 2) {\n // Touch by two fingers: e.g. moving lines\n this.twoFingerMove(this.touches[i], evt.pointerId, evt);\n\n touchTargets[j].Xprev = pos[0];\n touchTargets[j].Yprev = pos[1];\n }\n\n // There is only one pointer in the evt object, so there's no point in looking further\n break;\n }\n }\n }\n } else {\n if (this._getPointerInputDevice(evt) === 'touch') {\n this._pointerStorePosition(evt);\n\n if (this._board_touches.length === 2) {\n evt.touches = this._board_touches;\n this.gestureChangeListener(evt);\n }\n }\n\n // Move event without dragging an element\n this.highlightElements(pos[0], pos[1], evt, -1);\n }\n }\n\n // Hiding the infobox is commented out, since it prevents showing the infobox\n // on IE 11+ on 'over'\n //if (this.mode !== this.BOARD_MODE_DRAG) {\n //this.displayInfobox(false);\n //}\n this.triggerEventHandlers(['pointermove', 'MSPointerMove', 'move'], [evt, this.mode]);\n this.updateQuality = this.BOARD_QUALITY_HIGH;\n\n return this.mode === this.BOARD_MODE_NONE;\n },\n\n /**\n * Triggered as soon as the user stops touching the device with at least one finger.\n *\n * @param {Event} evt\n * @returns {Boolean}\n */\n pointerUpListener: function (evt) {\n var i, j, found, eh,\n touchTargets,\n updateNeeded = false;\n\n this.triggerEventHandlers(['touchend', 'up', 'pointerup', 'MSPointerUp'], [evt]);\n this.displayInfobox(false);\n\n if (evt) {\n for (i = 0; i < this.touches.length; i++) {\n touchTargets = this.touches[i].targets;\n for (j = 0; j < touchTargets.length; j++) {\n if (touchTargets[j].num === evt.pointerId) {\n touchTargets.splice(j, 1);\n if (touchTargets.length === 0) {\n this.touches.splice(i, 1);\n }\n break;\n }\n }\n }\n }\n\n this.finalizeSketchCurve(evt);\n this.originMoveEnd();\n this.update();\n\n // selection\n if (this.selectingMode) {\n this._stopSelecting(evt);\n this.triggerEventHandlers(\n ['touchstopselecting', 'pointerstopselecting', 'stopselecting'],\n [evt]\n );\n this.stopSelectionMode();\n } else {\n for (i = this.downObjects.length - 1; i > -1; i--) {\n found = false;\n for (j = 0; j < this.touches.length; j++) {\n if (this.touches[j].obj.id === this.downObjects[i].id) {\n found = true;\n }\n }\n if (!found) {\n this.downObjects[i].triggerEventHandlers(\n ['touchend', 'up', 'pointerup', 'MSPointerUp'],\n [evt]\n );\n if (!Type.exists(this.downObjects[i].coords)) {\n // snapTo methods have to be called e.g. for line elements here.\n // For coordsElements there might be a conflict with\n // attractors, see commit from 2022.04.08, 11:12:18.\n this.downObjects[i].snapToGrid();\n this.downObjects[i].snapToPoints();\n updateNeeded = true;\n }\n\n // Check if we have to keep the element for a click or dblclick event\n // Otherwise remove it from downObjects\n eh = this.downObjects[i].eventHandlers;\n if ((Type.exists(eh.click) && eh.click.length > 0) ||\n (Type.exists(eh.pointerclick) && eh.pointerclick.length > 0) ||\n (Type.exists(eh.dblclick) && eh.dblclick.length > 0) ||\n (Type.exists(eh.pointerdblclick) && eh.pointerdblclick.length > 0)\n ) {\n this.clickObjects[this.downObjects[i].id] = this.downObjects[i];\n }\n this.downObjects.splice(i, 1);\n }\n }\n }\n\n if (this.hasPointerUp) {\n if (window.navigator.msPointerEnabled) {\n // IE10-\n Env.removeEvent(this.document, 'MSPointerUp', this.pointerUpListener, this);\n } else {\n Env.removeEvent(this.document, 'pointerup', this.pointerUpListener, this);\n Env.removeEvent(this.document, 'pointercancel', this.pointerUpListener, this);\n }\n this.hasPointerUp = false;\n }\n\n // After one finger leaves the screen the gesture is stopped.\n this._pointerClearTouches(evt.pointerId);\n if (this._getPointerInputDevice(evt) !== 'touch') {\n this.dehighlightAll();\n }\n\n if (updateNeeded) {\n this.update();\n }\n\n return true;\n },\n\n /**\n * Triggered by the pointerleave event. This is needed in addition to\n * {@link JXG.Board#pointerUpListener} in the situation that a pen is used\n * and after an up event the pen leaves the hover range vertically. Here, it happens that\n * after the pointerup event further pointermove events are fired and elements get highlighted.\n * This highlighting has to be cancelled.\n *\n * @param {Event} evt\n * @returns {Boolean}\n */\n pointerLeaveListener: function (evt) {\n this.displayInfobox(false);\n this.dehighlightAll();\n\n return true;\n },\n\n /**\n * Touch-Events\n */\n\n /**\n * This method is called by the browser when a finger touches the surface of the touch-device.\n * @param {Event} evt The browsers event object.\n * @returns {Boolean} ...\n */\n touchStartListener: function (evt) {\n var i, j, k,\n pos, elements, obj,\n eps = this.options.precision.touch,\n evtTouches = evt['touches'],\n found,\n targets, target,\n touchTargets;\n\n if (!this.hasTouchEnd) {\n Env.addEvent(this.document, 'touchend', this.touchEndListener, this);\n this.hasTouchEnd = true;\n }\n\n // Do not remove mouseHandlers, since Chrome on win tablets sends mouseevents if used with pen.\n //if (this.hasMouseHandlers) { this.removeMouseEventHandlers(); }\n\n // prevent accidental selection of text\n if (this.document.selection && Type.isFunction(this.document.selection.empty)) {\n this.document.selection.empty();\n } else if (window.getSelection) {\n window.getSelection().removeAllRanges();\n }\n\n // multitouch\n this._inputDevice = 'touch';\n this.options.precision.hasPoint = this.options.precision.touch;\n\n // This is the most critical part. first we should run through the existing touches and collect all targettouches that don't belong to our\n // previous touches. once this is done we run through the existing touches again and watch out for free touches that can be attached to our existing\n // touches, e.g. we translate (parallel translation) a line with one finger, now a second finger is over this line. this should change the operation to\n // a rotational translation. or one finger moves a circle, a second finger can be attached to the circle: this now changes the operation from translation to\n // stretching. as a last step we're going through the rest of the targettouches and initiate new move operations:\n // * points have higher priority over other elements.\n // * if we find a targettouch over an element that could be transformed with more than one finger, we search the rest of the targettouches, if they are over\n // this element and add them.\n // ADDENDUM 11/10/11:\n // (1) run through the touches control object,\n // (2) try to find the targetTouches for every touch. on touchstart only new touches are added, hence we can find a targettouch\n // for every target in our touches objects\n // (3) if one of the targettouches was bound to a touches targets array, mark it\n // (4) run through the targettouches. if the targettouch is marked, continue. otherwise check for elements below the targettouch:\n // (a) if no element could be found: mark the target touches and continue\n // --- in the following cases, 'init' means:\n // (i) check if the element is already used in another touches element, if so, mark the targettouch and continue\n // (ii) if not, init a new touches element, add the targettouch to the touches property and mark it\n // (b) if the element is a point, init\n // (c) if the element is a line, init and try to find a second targettouch on that line. if a second one is found, add and mark it\n // (d) if the element is a circle, init and try to find TWO other targettouches on that circle. if only one is found, mark it and continue. otherwise\n // add both to the touches array and mark them.\n for (i = 0; i < evtTouches.length; i++) {\n evtTouches[i].jxg_isused = false;\n }\n\n for (i = 0; i < this.touches.length; i++) {\n touchTargets = this.touches[i].targets;\n for (j = 0; j < touchTargets.length; j++) {\n touchTargets[j].num = -1;\n eps = this.options.precision.touch;\n\n do {\n for (k = 0; k < evtTouches.length; k++) {\n // find the new targettouches\n if (\n Math.abs(\n Math.pow(evtTouches[k].screenX - touchTargets[j].X, 2) +\n Math.pow(evtTouches[k].screenY - touchTargets[j].Y, 2)\n ) <\n eps * eps\n ) {\n touchTargets[j].num = k;\n touchTargets[j].X = evtTouches[k].screenX;\n touchTargets[j].Y = evtTouches[k].screenY;\n evtTouches[k].jxg_isused = true;\n break;\n }\n }\n\n eps *= 2;\n } while (\n touchTargets[j].num === -1 &&\n eps < this.options.precision.touchMax\n );\n\n if (touchTargets[j].num === -1) {\n JXG.debug(\n \"i couldn't find a targettouches for target no \" +\n j +\n ' on ' +\n this.touches[i].obj.name +\n ' (' +\n this.touches[i].obj.id +\n '). Removed the target.'\n );\n JXG.debug(\n 'eps = ' + eps + ', touchMax = ' + Options.precision.touchMax\n );\n touchTargets.splice(i, 1);\n }\n }\n }\n\n // we just re-mapped the targettouches to our existing touches list.\n // now we have to initialize some touches from additional targettouches\n for (i = 0; i < evtTouches.length; i++) {\n if (!evtTouches[i].jxg_isused) {\n pos = this.getMousePosition(evt, i);\n // selection\n // this._testForSelection(evt); // we do not have shift or ctrl keys yet.\n if (this.selectingMode) {\n this._startSelecting(pos);\n this.triggerEventHandlers(\n ['touchstartselecting', 'startselecting'],\n [evt]\n );\n evt.preventDefault();\n evt.stopPropagation();\n this.options.precision.hasPoint = this.options.precision.mouse;\n return this.touches.length > 0; // don't continue as a normal click\n }\n\n elements = this.initMoveObject(pos[0], pos[1], evt, 'touch');\n if (elements.length !== 0) {\n obj = elements[elements.length - 1];\n target = {\n num: i,\n X: evtTouches[i].screenX,\n Y: evtTouches[i].screenY,\n Xprev: NaN,\n Yprev: NaN,\n Xstart: [],\n Ystart: [],\n Zstart: []\n };\n\n if (\n Type.isPoint(obj) ||\n obj.elementClass === Const.OBJECT_CLASS_TEXT ||\n obj.type === Const.OBJECT_TYPE_TICKS ||\n obj.type === Const.OBJECT_TYPE_IMAGE\n ) {\n // It's a point, so it's single touch, so we just push it to our touches\n targets = [target];\n\n // For the UNDO/REDO of object moves\n this.saveStartPos(obj, targets[0]);\n\n this.touches.push({ obj: obj, targets: targets });\n obj.highlight(true);\n } else if (\n obj.elementClass === Const.OBJECT_CLASS_LINE ||\n obj.elementClass === Const.OBJECT_CLASS_CIRCLE ||\n obj.elementClass === Const.OBJECT_CLASS_CURVE ||\n obj.type === Const.OBJECT_TYPE_POLYGON\n ) {\n found = false;\n\n // first check if this geometric object is already captured in this.touches\n for (j = 0; j < this.touches.length; j++) {\n if (obj.id === this.touches[j].obj.id) {\n found = true;\n // only add it, if we don't have two targets in there already\n if (this.touches[j].targets.length === 1) {\n // For the UNDO/REDO of object moves\n this.saveStartPos(obj, target);\n this.touches[j].targets.push(target);\n }\n\n evtTouches[i].jxg_isused = true;\n }\n }\n\n // we couldn't find it in touches, so we just init a new touches\n // IF there is a second touch targetting this line, we will find it later on, and then add it to\n // the touches control object.\n if (!found) {\n targets = [target];\n\n // For the UNDO/REDO of object moves\n this.saveStartPos(obj, targets[0]);\n this.touches.push({ obj: obj, targets: targets });\n obj.highlight(true);\n }\n }\n }\n\n evtTouches[i].jxg_isused = true;\n }\n }\n\n if (this.touches.length > 0) {\n evt.preventDefault();\n evt.stopPropagation();\n }\n\n // Touch events on empty areas of the board are handled here:\n // 1. case: one finger. If allowed, this triggers pan with one finger\n if (\n evtTouches.length === 1 &&\n this.mode === this.BOARD_MODE_NONE &&\n this.touchStartMoveOriginOneFinger(evt)\n ) {\n } else if (\n evtTouches.length === 2 &&\n (this.mode === this.BOARD_MODE_NONE ||\n this.mode === this.BOARD_MODE_MOVE_ORIGIN)\n ) {\n // 2. case: two fingers: pinch to zoom or pan with two fingers needed.\n // This happens when the second finger hits the device. First, the\n // 'one finger pan mode' has to be cancelled.\n if (this.mode === this.BOARD_MODE_MOVE_ORIGIN) {\n this.originMoveEnd();\n }\n this.gestureStartListener(evt);\n }\n\n this.initSketchCurve(evt);\n\n this.options.precision.hasPoint = this.options.precision.mouse;\n this.triggerEventHandlers(['touchstart', 'down'], [evt]);\n\n return false;\n //return this.touches.length > 0;\n },\n\n /**\n * Called periodically by the browser while the user moves his fingers across the device.\n * @param {Event} evt\n * @returns {Boolean}\n */\n touchMoveListener: function (evt) {\n var i,\n pos1, pos2,\n touchTargets,\n evtTouches = evt['touches'];\n\n if (!this.checkFrameRate(evt)) {\n return false;\n }\n\n if (this.mode !== this.BOARD_MODE_NONE) {\n evt.preventDefault();\n evt.stopPropagation();\n }\n\n if (this.mode !== this.BOARD_MODE_DRAG) {\n this.dehighlightAll();\n this.displayInfobox(false);\n }\n\n this._inputDevice = 'touch';\n this.options.precision.hasPoint = this.options.precision.touch;\n this.updateQuality = this.BOARD_QUALITY_LOW;\n\n // selection\n if (this.selectingMode) {\n for (i = 0; i < evtTouches.length; i++) {\n if (!evtTouches[i].jxg_isused) {\n pos1 = this.getMousePosition(evt, i);\n this._moveSelecting(pos1);\n this.triggerEventHandlers(\n ['touchmoves', 'moveselecting'],\n [evt, this.mode]\n );\n break;\n }\n }\n } else {\n if (!this.touchOriginMove(evt)) {\n\n this.addToSketchCurve(evt);\n\n if (this.mode === this.BOARD_MODE_DRAG) {\n // Runs over through all elements which are touched\n // by at least one finger.\n for (i = 0; i < this.touches.length; i++) {\n touchTargets = this.touches[i].targets;\n if (touchTargets.length === 1) {\n // Touch by one finger: this is possible for all elements that can be dragged\n if (evtTouches[touchTargets[0].num]) {\n pos1 = this.getMousePosition(evt, touchTargets[0].num);\n if (\n pos1[0] < 0 ||\n pos1[0] > this.canvasWidth ||\n pos1[1] < 0 ||\n pos1[1] > this.canvasHeight\n ) {\n return;\n }\n touchTargets[0].X = pos1[0];\n touchTargets[0].Y = pos1[1];\n this.moveObject(\n pos1[0],\n pos1[1],\n this.touches[i],\n evt,\n 'touch'\n );\n }\n } else if (\n touchTargets.length === 2 &&\n touchTargets[0].num > -1 &&\n touchTargets[1].num > -1\n ) {\n // Touch by two fingers: moving lines, ...\n if (\n evtTouches[touchTargets[0].num] &&\n evtTouches[touchTargets[1].num]\n ) {\n // Get coordinates of the two touches\n pos1 = this.getMousePosition(evt, touchTargets[0].num);\n pos2 = this.getMousePosition(evt, touchTargets[1].num);\n if (\n pos1[0] < 0 ||\n pos1[0] > this.canvasWidth ||\n pos1[1] < 0 ||\n pos1[1] > this.canvasHeight ||\n pos2[0] < 0 ||\n pos2[0] > this.canvasWidth ||\n pos2[1] < 0 ||\n pos2[1] > this.canvasHeight\n ) {\n return;\n }\n\n touchTargets[0].X = pos1[0];\n touchTargets[0].Y = pos1[1];\n touchTargets[1].X = pos2[0];\n touchTargets[1].Y = pos2[1];\n\n this.twoFingerMove(\n this.touches[i],\n touchTargets[0].num,\n evt\n );\n\n touchTargets[0].Xprev = pos1[0];\n touchTargets[0].Yprev = pos1[1];\n touchTargets[1].Xprev = pos2[0];\n touchTargets[1].Yprev = pos2[1];\n }\n }\n }\n } else {\n if (evtTouches.length === 2) {\n this.gestureChangeListener(evt);\n }\n // Move event without dragging an element\n pos1 = this.getMousePosition(evt, 0);\n this.highlightElements(pos1[0], pos1[1], evt, -1);\n }\n }\n }\n\n if (this.mode !== this.BOARD_MODE_DRAG) {\n this.displayInfobox(false);\n }\n\n this.triggerEventHandlers(['touchmove', 'move'], [evt, this.mode]);\n this.options.precision.hasPoint = this.options.precision.mouse;\n this.updateQuality = this.BOARD_QUALITY_HIGH;\n\n return this.mode === this.BOARD_MODE_NONE;\n },\n\n /**\n * Triggered as soon as the user stops touching the device with at least one finger.\n * @param {Event} evt\n * @returns {Boolean}\n */\n touchEndListener: function (evt) {\n var i,\n j,\n k,\n eps = this.options.precision.touch,\n tmpTouches = [],\n found,\n foundNumber,\n evtTouches = evt && evt['touches'],\n touchTargets,\n updateNeeded = false;\n\n this.triggerEventHandlers(['touchend', 'up'], [evt]);\n this.displayInfobox(false);\n\n this.finalizeSketchCurve(evt);\n\n // selection\n if (this.selectingMode) {\n this._stopSelecting(evt);\n this.triggerEventHandlers(['touchstopselecting', 'stopselecting'], [evt]);\n this.stopSelectionMode();\n } else if (evtTouches && evtTouches.length > 0) {\n for (i = 0; i < this.touches.length; i++) {\n tmpTouches[i] = this.touches[i];\n }\n this.touches.length = 0;\n\n // try to convert the operation, e.g. if a lines is rotated and translated with two fingers and one finger is lifted,\n // convert the operation to a simple one-finger-translation.\n // ADDENDUM 11/10/11:\n // see addendum to touchStartListener from 11/10/11\n // (1) run through the tmptouches\n // (2) check the touches.obj, if it is a\n // (a) point, try to find the targettouch, if found keep it and mark the targettouch, else drop the touch.\n // (b) line with\n // (i) one target: try to find it, if found keep it mark the targettouch, else drop the touch.\n // (ii) two targets: if none can be found, drop the touch. if one can be found, remove the other target. mark all found targettouches\n // (c) circle with [proceed like in line]\n\n // init the targettouches marker\n for (i = 0; i < evtTouches.length; i++) {\n evtTouches[i].jxg_isused = false;\n }\n\n for (i = 0; i < tmpTouches.length; i++) {\n // could all targets of the current this.touches.obj be assigned to targettouches?\n found = false;\n foundNumber = 0;\n touchTargets = tmpTouches[i].targets;\n\n for (j = 0; j < touchTargets.length; j++) {\n touchTargets[j].found = false;\n for (k = 0; k < evtTouches.length; k++) {\n if (\n Math.abs(\n Math.pow(evtTouches[k].screenX - touchTargets[j].X, 2) +\n Math.pow(evtTouches[k].screenY - touchTargets[j].Y, 2)\n ) <\n eps * eps\n ) {\n touchTargets[j].found = true;\n touchTargets[j].num = k;\n touchTargets[j].X = evtTouches[k].screenX;\n touchTargets[j].Y = evtTouches[k].screenY;\n foundNumber += 1;\n break;\n }\n }\n }\n\n if (Type.isPoint(tmpTouches[i].obj)) {\n found = touchTargets[0] && touchTargets[0].found;\n } else if (tmpTouches[i].obj.elementClass === Const.OBJECT_CLASS_LINE) {\n found =\n (touchTargets[0] && touchTargets[0].found) ||\n (touchTargets[1] && touchTargets[1].found);\n } else if (tmpTouches[i].obj.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n found = foundNumber === 1 || foundNumber === 3;\n }\n\n // if we found this object to be still dragged by the user, add it back to this.touches\n if (found) {\n this.touches.push({\n obj: tmpTouches[i].obj,\n targets: []\n });\n\n for (j = 0; j < touchTargets.length; j++) {\n if (touchTargets[j].found) {\n this.touches[this.touches.length - 1].targets.push({\n num: touchTargets[j].num,\n X: touchTargets[j].screenX,\n Y: touchTargets[j].screenY,\n Xprev: NaN,\n Yprev: NaN,\n Xstart: touchTargets[j].Xstart,\n Ystart: touchTargets[j].Ystart,\n Zstart: touchTargets[j].Zstart\n });\n }\n }\n } else {\n tmpTouches[i].obj.noHighlight();\n }\n }\n } else {\n this.touches.length = 0;\n }\n\n for (i = this.downObjects.length - 1; i > -1; i--) {\n found = false;\n for (j = 0; j < this.touches.length; j++) {\n if (this.touches[j].obj.id === this.downObjects[i].id) {\n found = true;\n }\n }\n if (!found) {\n this.downObjects[i].triggerEventHandlers(['touchup', 'up'], [evt]);\n if (!Type.exists(this.downObjects[i].coords)) {\n // snapTo methods have to be called e.g. for line elements here.\n // For coordsElements there might be a conflict with\n // attractors, see commit from 2022.04.08, 11:12:18.\n this.downObjects[i].snapToGrid();\n this.downObjects[i].snapToPoints();\n updateNeeded = true;\n }\n this.downObjects.splice(i, 1);\n }\n }\n\n if (!evtTouches || evtTouches.length === 0) {\n if (this.hasTouchEnd) {\n Env.removeEvent(this.document, 'touchend', this.touchEndListener, this);\n this.hasTouchEnd = false;\n }\n\n this.dehighlightAll();\n this.updateQuality = this.BOARD_QUALITY_HIGH;\n\n this.originMoveEnd();\n if (updateNeeded) {\n this.update();\n }\n }\n\n return true;\n },\n\n /**\n * This method is called by the browser when the mouse button is clicked.\n * @param {Event} evt The browsers event object.\n * @returns {Boolean} True if no element is found under the current mouse pointer, false otherwise.\n */\n mouseDownListener: function (evt) {\n var pos, elements, result;\n\n // prevent accidental selection of text\n if (this.document.selection && Type.isFunction(this.document.selection.empty)) {\n this.document.selection.empty();\n } else if (window.getSelection) {\n window.getSelection().removeAllRanges();\n }\n\n if (!this.hasMouseUp) {\n Env.addEvent(this.document, 'mouseup', this.mouseUpListener, this);\n this.hasMouseUp = true;\n } else {\n // In case this.hasMouseUp==true, it may be that there was a\n // mousedown event before which was not followed by an mouseup event.\n // This seems to happen with interactive whiteboard pens sometimes.\n return;\n }\n\n this._inputDevice = 'mouse';\n this.options.precision.hasPoint = this.options.precision.mouse;\n pos = this.getMousePosition(evt);\n\n // selection\n this._testForSelection(evt);\n if (this.selectingMode) {\n this._startSelecting(pos);\n this.triggerEventHandlers(['mousestartselecting', 'startselecting'], [evt]);\n return; // don't continue as a normal click\n }\n\n elements = this.initMoveObject(pos[0], pos[1], evt, 'mouse');\n\n // if no draggable object can be found, get out here immediately\n if (elements.length === 0) {\n this.mode = this.BOARD_MODE_NONE;\n result = true;\n } else {\n this.mouse = {\n obj: null,\n targets: [\n {\n X: pos[0],\n Y: pos[1],\n Xprev: NaN,\n Yprev: NaN\n }\n ]\n };\n this.mouse.obj = elements[elements.length - 1];\n\n this.dehighlightAll();\n this.mouse.obj.highlight(true);\n\n this.mouse.targets[0].Xstart = [];\n this.mouse.targets[0].Ystart = [];\n this.mouse.targets[0].Zstart = [];\n\n this.saveStartPos(this.mouse.obj, this.mouse.targets[0]);\n\n // prevent accidental text selection\n // this could get us new trouble: input fields, links and drop down boxes placed as text\n // on the board don't work anymore.\n if (evt && evt.preventDefault) {\n evt.preventDefault();\n } else if (window.event) {\n window.event.returnValue = false;\n }\n }\n\n if (this.mode === this.BOARD_MODE_NONE) {\n result = this.mouseOriginMoveStart(evt);\n }\n\n this.initSketchCurve(evt);\n this.triggerEventHandlers(['mousedown', 'down'], [evt]);\n\n return result;\n },\n\n /**\n * This method is called by the browser when the mouse is moved.\n * @param {Event} evt The browsers event object.\n */\n mouseMoveListener: function (evt) {\n var pos;\n\n if (!this.checkFrameRate(evt)) {\n return false;\n }\n\n pos = this.getMousePosition(evt);\n\n this.updateQuality = this.BOARD_QUALITY_LOW;\n\n if (this.mode !== this.BOARD_MODE_DRAG) {\n this.dehighlightAll();\n this.displayInfobox(false);\n }\n\n // we have to check for four cases:\n // * user moves origin\n // * user drags an object\n // * user just moves the mouse, here highlight all elements at\n // the current mouse position\n // * the user is selecting\n\n // selection\n if (this.selectingMode) {\n this._moveSelecting(pos);\n this.triggerEventHandlers(\n ['mousemoveselecting', 'moveselecting'],\n [evt, this.mode]\n );\n } else if (!this.mouseOriginMove(evt)) {\n\n this.addToSketchCurve(evt);\n\n if (this.mode === this.BOARD_MODE_DRAG) {\n this.moveObject(pos[0], pos[1], this.mouse, evt, 'mouse');\n } else {\n // BOARD_MODE_NONE\n // Move event without dragging an element\n this.highlightElements(pos[0], pos[1], evt, -1);\n }\n this.triggerEventHandlers(['mousemove', 'move'], [evt, this.mode]);\n }\n this.updateQuality = this.BOARD_QUALITY_HIGH;\n },\n\n /**\n * This method is called by the browser when the mouse button is released.\n * @param {Event} evt\n */\n mouseUpListener: function (evt) {\n var i;\n\n if (this.selectingMode === false) {\n this.triggerEventHandlers(['mouseup', 'up'], [evt]);\n }\n\n // redraw with high precision\n this.updateQuality = this.BOARD_QUALITY_HIGH;\n\n if (this.mouse && this.mouse.obj) {\n if (!Type.exists(this.mouse.obj.coords)) {\n // snapTo methods have to be called e.g. for line elements here.\n // For coordsElements there might be a conflict with\n // attractors, see commit from 2022.04.08, 11:12:18.\n // The parameter is needed for lines with snapToGrid enabled\n this.mouse.obj.snapToGrid(this.mouse.targets[0]);\n this.mouse.obj.snapToPoints();\n }\n }\n\n this.finalizeSketchCurve(evt);\n this.originMoveEnd();\n this.dehighlightAll();\n this.update();\n\n // selection\n if (this.selectingMode) {\n this._stopSelecting(evt);\n this.triggerEventHandlers(['mousestopselecting', 'stopselecting'], [evt]);\n this.stopSelectionMode();\n } else {\n for (i = 0; i < this.downObjects.length; i++) {\n this.downObjects[i].triggerEventHandlers(['mouseup', 'up'], [evt]);\n }\n }\n\n this.downObjects.length = 0;\n\n if (this.hasMouseUp) {\n Env.removeEvent(this.document, 'mouseup', this.mouseUpListener, this);\n this.hasMouseUp = false;\n }\n\n // release dragged mouse object\n this.mouse = null;\n },\n\n /**\n * Handler for mouse wheel events. Used to zoom in and out of the board.\n * @param {Event} evt\n * @returns {Boolean}\n */\n mouseWheelListener: function (evt) {\n var wd, zoomCenter, pos;\n\n if (!this.attr.zoom.enabled ||\n !this.attr.zoom.wheel ||\n !this._isRequiredKeyPressed(evt, 'zoom')) {\n\n return true;\n }\n\n evt = evt || window.event;\n wd = evt.detail ? -evt.detail : evt.wheelDelta / 40;\n zoomCenter = this.attr.zoom.center;\n\n if (zoomCenter === 'board') {\n pos = [];\n } else { // including zoomCenter === 'auto'\n pos = new Coords(Const.COORDS_BY_SCREEN, this.getMousePosition(evt), this).usrCoords;\n }\n\n // pos == [] does not throw an error\n if (wd > 0) {\n this.zoomIn(pos[1], pos[2]);\n } else {\n this.zoomOut(pos[1], pos[2]);\n }\n\n this.triggerEventHandlers(['mousewheel'], [evt]);\n\n evt.preventDefault();\n return false;\n },\n\n /**\n * Allow moving of JSXGraph elements with arrow keys.\n * The selection of the element is done with the tab key. For this,\n * the attribute 'tabindex' of the element has to be set to some number (default=0).\n * tabindex corresponds to the HTML and SVG attribute of the same name.\n * \n * Panning of the construction is done with arrow keys\n * if the pan key (shift or ctrl - depending on the board attributes) is pressed.\n * \n * Zooming is triggered with the keys +, o, -, if\n * the pan key (shift or ctrl - depending on the board attributes) is pressed.\n * \n * Keyboard control (move, pan, and zoom) is disabled if an HTML element of type input or textarea has received focus.\n *\n * @param {Event} evt The browser's event object\n *\n * @see JXG.Board#keyboard\n * @see JXG.Board#keyFocusInListener\n * @see JXG.Board#keyFocusOutListener\n *\n */\n keyDownListener: function (evt) {\n var id_node = evt.target.id,\n id, el, res, doc,\n sX = 0,\n sY = 0,\n // dx, dy are provided in screen units and\n // are converted to user coordinates\n dx = Type.evaluate(this.attr.keyboard.dx) / this.unitX,\n dy = Type.evaluate(this.attr.keyboard.dy) / this.unitY,\n // u = 100,\n doZoom = false,\n done = true,\n dir,\n actPos;\n\n if (!this.attr.keyboard.enabled || id_node === '') {\n return false;\n }\n\n // Tab key should be handled by the browser\n if (evt.keyCode === 9) {\n return false;\n }\n\n // dx = Math.round(dx * u) / u;\n // dy = Math.round(dy * u) / u;\n\n // An element of type input or textarea has focus, get out of here.\n doc = this.containerObj.shadowRoot || document;\n if (doc.activeElement) {\n el = doc.activeElement;\n if (el.tagName === 'INPUT' || el.tagName === 'textarea') {\n return false;\n }\n }\n\n // Get the JSXGraph id from the id of the SVG node.\n id = id_node.replace(this.containerObj.id + '_', '');\n el = this.select(id);\n\n if (Type.exists(el.coords)) {\n actPos = el.coords.usrCoords.slice(1);\n }\n\n if (\n (Type.evaluate(this.attr.keyboard.panshift) && evt.shiftKey) ||\n (Type.evaluate(this.attr.keyboard.panctrl) && evt.ctrlKey)\n ) {\n // Pan key has been pressed\n\n if (Type.evaluate(this.attr.zoom.enabled) === true) {\n doZoom = true;\n }\n\n // Arrow keys\n if (evt.keyCode === 38) {\n // up\n this.clickUpArrow();\n } else if (evt.keyCode === 40) {\n // down\n this.clickDownArrow();\n } else if (evt.keyCode === 37) {\n // left\n this.clickLeftArrow();\n } else if (evt.keyCode === 39) {\n // right\n this.clickRightArrow();\n\n // Zoom keys\n } else if (doZoom && evt.keyCode === 171) {\n // +\n this.zoomIn();\n } else if (doZoom && evt.keyCode === 173) {\n // -\n this.zoomOut();\n } else if (doZoom && evt.keyCode === 79) {\n // o\n this.zoom100();\n } else {\n done = false;\n }\n } else if (!evt.shiftKey && !evt.ctrlKey) { // Move an element if neither shift or ctrl are pressed\n // Adapt dx, dy to snapToGrid and attractToGrid.\n // snapToGrid has priority.\n if (Type.exists(el.visProp)) {\n if (\n Type.exists(el.visProp.snaptogrid) &&\n el.visProp.snaptogrid &&\n el.evalVisProp('snapsizex') &&\n el.evalVisProp('snapsizey')\n ) {\n // Adapt dx, dy such that snapToGrid is possible\n res = el.getSnapSizes();\n sX = res[0];\n sY = res[1];\n // If snaptogrid is true,\n // we can only jump from grid point to grid point.\n dx = sX;\n dy = sY;\n } else if (\n Type.exists(el.visProp.attracttogrid) &&\n el.visProp.attracttogrid &&\n el.evalVisProp('attractordistance') &&\n el.evalVisProp('attractorunit')\n ) {\n // Adapt dx, dy such that attractToGrid is possible\n sX = 1.1 * el.evalVisProp('attractordistance');\n sY = sX;\n\n if (el.evalVisProp('attractorunit') === 'screen') {\n sX /= this.unitX;\n sY /= this.unitX;\n }\n dx = Math.max(sX, dx);\n dy = Math.max(sY, dy);\n }\n }\n\n if (evt.keyCode === 38) {\n // up\n dir = [0, dy];\n } else if (evt.keyCode === 40) {\n // down\n dir = [0, -dy];\n } else if (evt.keyCode === 37) {\n // left\n dir = [-dx, 0];\n } else if (evt.keyCode === 39) {\n // right\n dir = [dx, 0];\n } else {\n done = false;\n }\n\n if (dir && el.isDraggable &&\n el.visPropCalc.visible &&\n ((this.geonextCompatibilityMode &&\n (Type.isPoint(el) ||\n el.elementClass === Const.OBJECT_CLASS_TEXT)\n ) || !this.geonextCompatibilityMode) &&\n !el.evalVisProp('fixed')\n ) {\n this.mode = this.BOARD_MODE_DRAG;\n if (Type.exists(el.coords)) {\n dir[0] += actPos[0];\n dir[1] += actPos[1];\n }\n // For coordsElement setPosition has to call setPositionDirectly.\n // Otherwise the position is set by a translation.\n if (Type.exists(el.coords)) {\n el.setPosition(JXG.COORDS_BY_USER, dir);\n this.updateInfobox(el);\n } else {\n this.displayInfobox(false);\n el.setPositionDirectly(\n Const.COORDS_BY_USER,\n dir,\n [0, 0]\n );\n }\n\n this.triggerEventHandlers(['keymove', 'move'], [evt, this.mode]);\n el.triggerEventHandlers(['keydrag', 'drag'], [evt]);\n this.mode = this.BOARD_MODE_NONE;\n }\n }\n\n this.update();\n\n if (done && Type.exists(evt.preventDefault)) {\n evt.preventDefault();\n }\n return done;\n },\n\n /**\n * Event listener for SVG elements getting focus.\n * This is needed for highlighting when using keyboard control.\n * Only elements having the attribute 'tabindex' can receive focus.\n *\n * @see JXG.Board#keyFocusOutListener\n * @see JXG.Board#keyDownListener\n * @see JXG.Board#keyboard\n *\n * @param {Event} evt The browser's event object\n */\n keyFocusInListener: function (evt) {\n var id_node = evt.target.id,\n id,\n el;\n\n if (!this.attr.keyboard.enabled || id_node === '') {\n return false;\n }\n\n // Get JSXGraph id from node id\n id = id_node.replace(this.containerObj.id + '_', '');\n el = this.select(id);\n if (Type.exists(el.highlight)) {\n el.highlight(true);\n this.focusObjects = [id];\n el.triggerEventHandlers(['hit'], [evt]);\n }\n if (Type.exists(el.coords)) {\n this.updateInfobox(el);\n }\n },\n\n /**\n * Event listener for SVG elements losing focus.\n * This is needed for dehighlighting when using keyboard control.\n * Only elements having the attribute 'tabindex' can receive focus.\n *\n * @see JXG.Board#keyFocusInListener\n * @see JXG.Board#keyDownListener\n * @see JXG.Board#keyboard\n *\n * @param {Event} evt The browser's event object\n */\n keyFocusOutListener: function (evt) {\n if (!this.attr.keyboard.enabled) {\n return false;\n }\n this.focusObjects = []; // This has to be before displayInfobox(false)\n this.dehighlightAll();\n this.displayInfobox(false);\n },\n\n /**\n * Update the width and height of the JSXGraph container div element.\n * If width and height are not supplied, read actual values with offsetWidth/Height,\n * and call board.resizeContainer() with this values.\n * \n * If necessary, also call setBoundingBox().\n * @param {Number} [width=this.containerObj.offsetWidth] Width of the container element\n * @param {Number} [height=this.containerObj.offsetHeight] Height of the container element\n * @returns {JXG.Board} Reference to the board\n *\n * @see JXG.Board#startResizeObserver\n * @see JXG.Board#resizeListener\n * @see JXG.Board#resizeContainer\n * @see JXG.Board#setBoundingBox\n *\n */\n updateContainerDims: function (width, height) {\n var w = width,\n h = height,\n // bb,\n css,\n width_adjustment, height_adjustment;\n\n if (width === undefined) {\n // Get size of the board's container div\n //\n // offsetWidth/Height ignores CSS transforms,\n // getBoundingClientRect includes CSS transforms\n //\n // bb = this.containerObj.getBoundingClientRect();\n // w = bb.width;\n // h = bb.height;\n w = this.containerObj.offsetWidth;\n h = this.containerObj.offsetHeight;\n }\n\n if (width === undefined && window && window.getComputedStyle) {\n // Subtract the border size\n css = window.getComputedStyle(this.containerObj, null);\n width_adjustment = parseFloat(css.getPropertyValue('border-left-width')) + parseFloat(css.getPropertyValue('border-right-width'));\n if (!isNaN(width_adjustment)) {\n w -= width_adjustment;\n }\n height_adjustment = parseFloat(css.getPropertyValue('border-top-width')) + parseFloat(css.getPropertyValue('border-bottom-width'));\n if (!isNaN(height_adjustment)) {\n h -= height_adjustment;\n }\n }\n\n // If div is invisible - do nothing\n if (w <= 0 || h <= 0 || isNaN(w) || isNaN(h)) {\n return this;\n }\n\n // If bounding box is not yet initialized, do it now.\n if (isNaN(this.getBoundingBox()[0])) {\n this.setBoundingBox(this.attr.boundingbox, this.keepaspectratio, 'keep');\n }\n\n // Do nothing if the dimension did not change since being visible\n // the last time. Note that if the div had display:none in the mean time,\n // we did not store this._prevDim.\n if (Type.exists(this._prevDim) && this._prevDim.w === w && this._prevDim.h === h) {\n return this;\n }\n // Set the size of the SVG or canvas element\n this.resizeContainer(w, h, true);\n this._prevDim = {\n w: w,\n h: h\n };\n return this;\n },\n\n /**\n * Start observer which reacts to size changes of the JSXGraph\n * container div element. Calls updateContainerDims().\n * If not available, an event listener for the window-resize event is started.\n * On mobile devices also scrolling might trigger resizes.\n * However, resize events triggered by scrolling events should be ignored.\n * Therefore, also a scrollListener is started.\n * Resize can be controlled with the board attribute resize.\n *\n * @see JXG.Board#updateContainerDims\n * @see JXG.Board#resizeListener\n * @see JXG.Board#scrollListener\n * @see JXG.Board#resize\n *\n */\n startResizeObserver: function () {\n var that = this;\n\n if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {\n return;\n }\n\n this.resizeObserver = new ResizeObserver(function (entries) {\n var bb;\n if (!that._isResizing) {\n that._isResizing = true;\n bb = entries[0].contentRect;\n window.setTimeout(function () {\n try {\n that.updateContainerDims(bb.width, bb.height);\n } catch (e) {\n JXG.debug(e); // Used to log errors during board.update()\n that.stopResizeObserver();\n } finally {\n that._isResizing = false;\n }\n }, that.attr.resize.throttle);\n }\n });\n this.resizeObserver.observe(this.containerObj);\n },\n\n /**\n * Stops the resize observer.\n * @see JXG.Board#startResizeObserver\n *\n */\n stopResizeObserver: function () {\n if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {\n return;\n }\n\n if (Type.exists(this.resizeObserver)) {\n this.resizeObserver.unobserve(this.containerObj);\n }\n },\n\n /**\n * Fallback solutions if there is no resizeObserver available in the browser.\n * Reacts to resize events of the window (only). Otherwise similar to\n * startResizeObserver(). To handle changes of the visibility\n * of the JSXGraph container element, additionally an intersection observer is used.\n * which watches changes in the visibility of the JSXGraph container element.\n * This is necessary e.g. for register tabs or dia shows.\n *\n * @see JXG.Board#startResizeObserver\n * @see JXG.Board#startIntersectionObserver\n */\n resizeListener: function () {\n var that = this;\n\n if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {\n return;\n }\n if (!this._isScrolling && !this._isResizing) {\n this._isResizing = true;\n window.setTimeout(function () {\n that.updateContainerDims();\n that._isResizing = false;\n }, this.attr.resize.throttle);\n }\n },\n\n /**\n * Listener to watch for scroll events. Sets board._isScrolling = true\n * @param {Event} evt The browser's event object\n *\n * @see JXG.Board#startResizeObserver\n * @see JXG.Board#resizeListener\n *\n */\n scrollListener: function (evt) {\n var that = this;\n\n if (!Env.isBrowser) {\n return;\n }\n if (!this._isScrolling) {\n this._isScrolling = true;\n window.setTimeout(function () {\n that._isScrolling = false;\n }, 66);\n }\n },\n\n /**\n * Watch for changes of the visibility of the JSXGraph container element.\n *\n * @see JXG.Board#startResizeObserver\n * @see JXG.Board#resizeListener\n *\n */\n startIntersectionObserver: function () {\n var that = this,\n options = {\n root: null,\n rootMargin: '0px',\n threshold: 0.8\n };\n\n try {\n this.intersectionObserver = new IntersectionObserver(function (entries) {\n // If bounding box is not yet initialized, do it now.\n if (isNaN(that.getBoundingBox()[0])) {\n that.updateContainerDims();\n }\n }, options);\n this.intersectionObserver.observe(that.containerObj);\n } catch (err) {\n JXG.debug('JSXGraph: IntersectionObserver not available in this browser.');\n }\n },\n\n /**\n * Stop the intersection observer\n *\n * @see JXG.Board#startIntersectionObserver\n *\n */\n stopIntersectionObserver: function () {\n if (Type.exists(this.intersectionObserver)) {\n this.intersectionObserver.unobserve(this.containerObj);\n }\n },\n\n /**\n * Update the container before and after printing.\n * @param {Event} [evt]\n */\n printListener: function(evt) {\n this.updateContainerDims();\n },\n\n /**\n * Wrapper for printListener to be used in mediaQuery matches.\n * @param {MediaQueryList} mql\n */\n printListenerMatch: function (mql) {\n if (mql.matches) {\n this.printListener();\n }\n },\n\n /**********************************************************\n *\n * End of Event Handlers\n *\n **********************************************************/\n\n /**\n * Initialize the info box object which is used to display\n * the coordinates of points near the mouse pointer,\n * @returns {JXG.Board} Reference to the board\n */\n initInfobox: function (attributes) {\n var attr = Type.copyAttributes(attributes, this.options, 'infobox');\n\n attr.id = this.id + '_infobox';\n\n /**\n * Infobox close to points in which the points' coordinates are displayed.\n * This is simply a JXG.Text element. Access through board.infobox.\n * Uses CSS class .JXGinfobox.\n *\n * @namespace\n * @name JXG.Board.infobox\n * @type JXG.Text\n *\n * @example\n * const board = JXG.JSXGraph.initBoard(BOARDID, {\n * boundingbox: [-0.5, 0.5, 0.5, -0.5],\n * intl: {\n * enabled: false,\n * locale: 'de-DE'\n * },\n * keepaspectratio: true,\n * axis: true,\n * infobox: {\n * distanceY: 40,\n * intl: {\n * enabled: true,\n * options: {\n * minimumFractionDigits: 1,\n * maximumFractionDigits: 2\n * }\n * }\n * }\n * });\n * var p = board.create('point', [0.1, 0.1], {});\n *\n * \n * Performance hints: It is recommended to use the JSXGraph object's id.\n * If many elements are removed, it is best to either\n * \\n';\n for (el in this.objects) {\n if (this.objects.hasOwnProperty(el)) {\n i = 0;\n for (c in this.objects[el].childElements) {\n if (this.objects[el].childElements.hasOwnProperty(c)) {\n i += 1;\n }\n }\n if (i >= 0) {\n t += '' + this.objects[el].id + ':<' + '/strong> ';\n }\n\n for (c in this.objects[el].childElements) {\n if (this.objects[el].childElements.hasOwnProperty(c)) {\n t +=\n this.objects[el].childElements[c].id +\n '(' +\n this.objects[el].childElements[c].name +\n ')' +\n ', ';\n }\n }\n t += ' \\n';\n }\n }\n t += '<' + '/p>\\n';\n f = window.open();\n f.document.open();\n f.document.write(t);\n f.document.close();\n return this;\n },\n\n /**\n * Lists the XML code of the construction in a new HTML-window.\n * @returns {JXG.Board} Reference to the board\n */\n showXML: function () {\n var f = window.open('');\n f.document.open();\n f.document.write(' \n * Sets board.isSketching[i] = true where i depends on the finger (1st or 2nd).\n *\n * @private\n * @param {Object} evt Event object\n * @see JXG.Board#addToSketchCurve\n * @see JXG.Board#finalizeSketchCurve\n */\n initSketchCurve: function(evt) {\n var i, c;\n // Init sketchcurves\n if (this.mode !== this.BOARD_MODE_MOVE_ORIGIN) {\n // Add coords to sketch curves\n // Only first and second finger are stored\n c = this.getUsrCoordsOfMouse(evt);\n i = (evt.isPrimary) ? 0 : 1;\n if (Type.exists(this.sketches[i])) {\n this.sketches[i].dataX = [c[0]];\n this.sketches[i].dataY = [c[1]];\n this.isSketching[i] = true;\n }\n }\n },\n\n /**\n * Add the position of the event to the sketchcurve i in board.sketches[].\n * Called at move events.\n * Point is only added if board.isSketching[i] = true.\n *\n * @private\n * @param {Object} evt Event object\n * @see JXG.Board#initSketchCurve\n * @see JXG.Board#finalizeSketchCurve\n */\n addToSketchCurve: function(evt) {\n var i, c, len;\n\n // Add coords to sketchcurves\n // Only first and second finger are stored\n i = (evt.isPrimary) ? 0 : 1;\n if (this.attr.sketches.enabled && this.isSketching[i] === true) {\n if (Type.exists(this.sketches[i])) {\n c = this.getUsrCoordsOfMouse(evt);\n this.sketches[i].dataX.push(c[0]);\n this.sketches[i].dataY.push(c[1]);\n\n len = this.sketches[i].evalVisProp('maxlength');\n if (len !== null && this.sketches[i].dataX.length > len) {\n this.sketches[i].dataX = this.sketches[i].dataX.slice(-len);\n this.sketches[i].dataY = this.sketches[i].dataY.slice(-len);\n }\n if (this.sketches[i].evalVisProp('visible')) {\n this.update();\n }\n }\n }\n },\n\n /**\n * Ends adding points to the sketchcurve i in board.sketches[].\n * Called at up events.\n * Sets board.isSketching[i] = false.\n * Empties the curve if deleteOnUp==true;\n *\n * @private\n * @param {Object} evt Event object\n * @see JXG.Board#initSketchCurve\n * @see JXG.Board#addToSketchCurve\n */\n finalizeSketchCurve: function(evt) {\n var i;\n\n // Stop sketching into this.sketches\n i = (evt.isPrimary) ? 0 : 1;\n if (this.attr.sketches.enabled) {\n if (Type.exists(this.sketches[i])) {\n this.isSketching[i] = false;\n if (this.sketches[i].evalVisProp('deleteOnUp')) {\n this.sketches[i].dataX = [];\n this.sketches[i].dataY = [];\n }\n }\n }\n },\n\n /* **************************\n * EVENT DEFINITION\n * for documentation purposes\n * ************************** */\n\n //region Event handler documentation\n\n /**\n * @event\n * @description Whenever the {@link JXG.Board#setAttribute} is called.\n * @name JXG.Board#attribute\n * @param {Event} e The browser's event object.\n */\n __evt__attribute: function (e) { },\n\n /**\n * @event\n * @description Whenever the user starts to touch or click the board.\n * @name JXG.Board#down\n * @param {Event} e The browser's event object.\n */\n __evt__down: function (e) { },\n\n /**\n * @event\n * @description Whenever the user starts to click on the board.\n * @name JXG.Board#mousedown\n * @param {Event} e The browser's event object.\n */\n __evt__mousedown: function (e) { },\n\n /**\n * @event\n * @description Whenever the user taps the pen on the board.\n * @name JXG.Board#pendown\n * @param {Event} e The browser's event object.\n */\n __evt__pendown: function (e) { },\n\n /**\n * @event\n * @description Whenever the user starts to click on the board with a\n * device sending pointer events.\n * @name JXG.Board#pointerdown\n * @param {Event} e The browser's event object.\n */\n __evt__pointerdown: function (e) { },\n\n /**\n * @event\n * @description Whenever the user starts to touch the board.\n * @name JXG.Board#touchstart\n * @param {Event} e The browser's event object.\n */\n __evt__touchstart: function (e) { },\n\n /**\n * @event\n * @description Whenever the user stops to touch or click the board.\n * @name JXG.Board#up\n * @param {Event} e The browser's event object.\n */\n __evt__up: function (e) { },\n\n /**\n * @event\n * @description Whenever the user releases the mousebutton over the board.\n * @name JXG.Board#mouseup\n * @param {Event} e The browser's event object.\n */\n __evt__mouseup: function (e) { },\n\n /**\n * @event\n * @description Whenever the user releases the mousebutton over the board with a\n * device sending pointer events.\n * @name JXG.Board#pointerup\n * @param {Event} e The browser's event object.\n */\n __evt__pointerup: function (e) { },\n\n /**\n * @event\n * @description Whenever the user stops touching the board.\n * @name JXG.Board#touchend\n * @param {Event} e The browser's event object.\n */\n __evt__touchend: function (e) { },\n\n /**\n * @event\n * @description Whenever the user clicks on the board.\n * @name JXG.Board#click\n * @see JXG.Board#clickDelay\n * @param {Event} e The browser's event object.\n */\n __evt__click: function (e) { },\n\n /**\n * @event\n * @description Whenever the user double clicks on the board.\n * This event works on desktop browser, but is undefined\n * on mobile browsers.\n * @name JXG.Board#dblclick\n * @see JXG.Board#clickDelay\n * @see JXG.Board#dblClickSuppressClick\n * @param {Event} e The browser's event object.\n */\n __evt__dblclick: function (e) { },\n\n /**\n * @event\n * @description Whenever the user clicks on the board with a mouse device.\n * @name JXG.Board#mouseclick\n * @param {Event} e The browser's event object.\n */\n __evt__mouseclick: function (e) { },\n\n /**\n * @event\n * @description Whenever the user double clicks on the board with a mouse device.\n * @name JXG.Board#mousedblclick\n * @see JXG.Board#clickDelay\n * @param {Event} e The browser's event object.\n */\n __evt__mousedblclick: function (e) { },\n\n /**\n * @event\n * @description Whenever the user clicks on the board with a pointer device.\n * @name JXG.Board#pointerclick\n * @param {Event} e The browser's event object.\n */\n __evt__pointerclick: function (e) { },\n\n /**\n * @event\n * @description Whenever the user double clicks on the board with a pointer device.\n * This event works on desktop browser, but is undefined\n * on mobile browsers.\n * @name JXG.Board#pointerdblclick\n * @see JXG.Board#clickDelay\n * @param {Event} e The browser's event object.\n */\n __evt__pointerdblclick: function (e) { },\n\n /**\n * @event\n * @description This event is fired whenever the user is moving the finger or mouse pointer over the board.\n * @name JXG.Board#move\n * @param {Event} e The browser's event object.\n * @param {Number} mode The mode the board currently is in\n * @see JXG.Board#mode\n */\n __evt__move: function (e, mode) { },\n\n /**\n * @event\n * @description This event is fired whenever the user is moving the mouse over the board.\n * @name JXG.Board#mousemove\n * @param {Event} e The browser's event object.\n * @param {Number} mode The mode the board currently is in\n * @see JXG.Board#mode\n */\n __evt__mousemove: function (e, mode) { },\n\n /**\n * @event\n * @description This event is fired whenever the user is moving the pen over the board.\n * @name JXG.Board#penmove\n * @param {Event} e The browser's event object.\n * @param {Number} mode The mode the board currently is in\n * @see JXG.Board#mode\n */\n __evt__penmove: function (e, mode) { },\n\n /**\n * @event\n * @description This event is fired whenever the user is moving the mouse over the board with a\n * device sending pointer events.\n * @name JXG.Board#pointermove\n * @param {Event} e The browser's event object.\n * @param {Number} mode The mode the board currently is in\n * @see JXG.Board#mode\n */\n __evt__pointermove: function (e, mode) { },\n\n /**\n * @event\n * @description This event is fired whenever the user is moving the finger over the board.\n * @name JXG.Board#touchmove\n * @param {Event} e The browser's event object.\n * @param {Number} mode The mode the board currently is in\n * @see JXG.Board#mode\n */\n __evt__touchmove: function (e, mode) { },\n\n /**\n * @event\n * @description This event is fired whenever the user is moving an element over the board by\n * pressing arrow keys on a keyboard.\n * @name JXG.Board#keymove\n * @param {Event} e The browser's event object.\n * @param {Number} mode The mode the board currently is in\n * @see JXG.Board#mode\n */\n __evt__keymove: function (e, mode) { },\n\n /**\n * @event\n * @description Whenever an element is highlighted this event is fired.\n * @name JXG.Board#hit\n * @param {Event} e The browser's event object.\n * @param {JXG.GeometryElement} el The hit element.\n * @param target\n *\n * @example\n * var c = board.create('circle', [[1, 1], 2]);\n * board.on('hit', function(evt, el) {\n * console.log('JSXGraph example: Hit element', el);\n * });\n *\n * \n * The wrapping div has the CSS class 'jxgbox_wrap_private' which is\n * defined in the file 'jsxgraph.css'\n * \n * This feature is not available on iPhones (as of December 2021).\n *\n * @param {String} id (Optional) id of the div element which is brought to fullscreen.\n * If not provided, this defaults to the JSXGraph div. However, it may be necessary for the aspect ratio trick\n * which using padding-bottom/top and an out div element. Then, the id of the outer div has to be supplied.\n *\n * @return {JXG.Board} Reference to the board\n *\n * @example\n * <div id='jxgbox' class='jxgbox' style='width:500px; height:200px;'></div>\n * <button onClick='board.toFullscreen()'>Fullscreen</button>\n *\n * <script language='Javascript' type='text/javascript'>\n * var board = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-5,5,5,-5]});\n * var p = board.create('point', [0, 1]);\n * </script>\n *\n * \n * Might fail if any text element or foreign object element contains SVG. This\n * is the case e.g. for the default fullscreen symbol.\n * \n * For IE, it is realized as function.\n * It works from version 9, with the exception that HTML texts\n * are ignored on IE. The drawing is done with a delay of\n * 200 ms. Otherwise there would be problems with IE.\n *\n * @param {String} canvasId Id of an HTML canvas element\n * @param {Number} w Width in pixel of the dumped image, i.e. of the canvas tag.\n * @param {Number} h Height in pixel of the dumped image, i.e. of the canvas tag.\n * @param {Boolean} ignoreTexts If true, the foreignObject tag is taken out from the SVG root.\n * This is necessary for older versions of Safari. Default: false\n * @returns {Promise} Promise object\n *\n * @example\n * \tboard.renderer.dumpToCanvas('canvas').then(function() { console.log('done'); });\n *\n * @example\n * // IE 11 example:\n * \tboard.renderer.dumpToCanvas('canvas');\n * \tsetTimeout(function() { console.log('done'); }, 400);\n */\n dumpToCanvas: function (canvasId, w, h, ignoreTexts) {\n var svg, tmpImg,\n cv, ctx,\n doc = this.container.ownerDocument;\n\n // Prepare the canvas element\n cv = doc.getElementById(canvasId);\n\n // Clear the canvas\n /* eslint-disable no-self-assign */\n cv.width = cv.width;\n /* eslint-enable no-self-assign */\n\n ctx = cv.getContext('2d');\n if (w !== undefined && h !== undefined) {\n cv.style.width = parseFloat(w) + 'px';\n cv.style.height = parseFloat(h) + 'px';\n // Scale twice the CSS size to make the image crisp\n // cv.setAttribute('width', 2 * parseFloat(wOrg));\n // cv.setAttribute('height', 2 * parseFloat(hOrg));\n // ctx.scale(2 * wOrg / w, 2 * hOrg / h);\n cv.setAttribute(\"width\", parseFloat(w));\n cv.setAttribute(\"height\", parseFloat(h));\n }\n\n // Display the SVG string as data-uri in an HTML img.\n /**\n * @type {Image}\n * @ignore\n * {ignore}\n */\n tmpImg = new Image();\n svg = this.dumpToDataURI(ignoreTexts);\n tmpImg.src = svg;\n\n // Finally, draw the HTML img in the canvas.\n if (!(\"Promise\" in window)) {\n /**\n * @function\n * @ignore\n */\n tmpImg.onload = function () {\n // IE needs a pause...\n // Seems to be broken\n window.setTimeout(function () {\n try {\n ctx.drawImage(tmpImg, 0, 0, w, h);\n } catch (err) {\n console.log(\"screenshots not longer supported on IE\");\n }\n }, 200);\n };\n return this;\n }\n\n return new Promise(function (resolve, reject) {\n try {\n tmpImg.onload = function () {\n ctx.drawImage(tmpImg, 0, 0, w, h);\n resolve();\n };\n } catch (e) {\n reject(e);\n }\n });\n },\n\n /**\n * Display SVG image in html img-tag which enables\n * easy download for the user.\n *\n * Support:\n * \n * Additionally, a line can be created by providing a line and a transformation (or an array of transformations).\n * Then, the result is a line which is the transformation of the supplied line.\n * @example\n * // Create a line using point and coordinates/\n * // The second point will be fixed and invisible.\n * var p1 = board.create('point', [4.5, 2.0]);\n * var l1 = board.create('line', [p1, [1.0, 1.0]]);\n * \n * If the point is not on the object (line, circle, conic, curve, turtle) the output depends on the type of the object.\n * For conics and circles, the polar line will be constructed. For function graphs,\n * the tangent of the vertical projection of the point to the function graph is constructed. For all other objects, the tangent\n * in the orthogonal projection of the point to the object will be constructed.\n * @pseudo\n * @name Tangent\n * @augments JXG.Line\n * @constructor\n * @type JXG.Line\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Glider} g A glider on a line, circle, or curve.\n * @param {JXG.GeometryElement} [c] Optional element for which the tangent is constructed\n * @example\n * // Create a tangent providing a glider on a function graph\n * var c1 = board.create('curve', [function(t){return t},function(t){return t*t*t;}]);\n * var g1 = board.create('glider', [0.6, 1.2, c1]);\n * var t1 = board.create('tangent', [g1]);\n * \n * Attention: from a technical point of view, the point from which the tangent to the conic/circle is constructed is not an element of\n * the tangent line.\n * @name TangentTo\n * @augments JXG.Line\n * @constructor\n * @type JXG.Line\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Conic,JXG.Circle_JXG.Point_Number} conic,point,[number=0] The result will be the tangent line through\n * the point with respect to the conic or circle.\n *\n * @example\n * var c = board.create('circle', [[3, 0], [3, 4]]);\n * var p = board.create('point', [0, 6]);\n * var t0 = board.create('tangentto', [c, p, 0], { color: 'black', polar: {visible: true}, point: {visible: true} });\n * var t1 = board.create('tangentto', [c, p, 1], { color: 'black' });\n *\n * \n * If the radius is supplied as number or output of a function, its absolute value is taken.\n *\n * @example\n * // Create a circle providing two points\n * var p1 = board.create('point', [2.0, 2.0]),\n * p2 = board.create('point', [2.0, 0.0]),\n * c1 = board.create('circle', [p1, p2]);\n *\n * // Create another circle using the above circle\n * var p3 = board.create('point', [3.0, 2.0]),\n * c2 = board.create('circle', [p3, c1]);\n * Ax2+ Bxy+Cy2 + Dx + Ey + F = 0 \n * An alternative is to use the methods from {@link JXG.Math.Clip}, where the algorithm by Greiner and Hormann\n * is used.\n *\n * @param {JXG.Polygon} polygon Polygon which will be clipped.\n *\n * @returns {Array} of (normalized homogeneous user) coordinates (i.e. [z, x, y], where z==1 in most cases,\n * representing the vertices of the intersection polygon.\n *\n * @example\n * // Static intersection of two polygons pol1 and pol2\n * var pol1 = board.create('polygon', [[-2, 3], [-4, -3], [2, 0], [4, 4]], {\n * name:'pol1', withLabel: true,\n * fillColor: 'yellow'\n * });\n * var pol2 = board.create('polygon', [[-2, -3], [-4, 1], [0, 4], [5, 1]], {\n * name:'pol2', withLabel: true\n * });\n *\n * // Static version:\n * // the intersection polygon does not adapt to changes of pol1 or pol2.\n * var pol3 = board.create('polygon', pol1.intersect(pol2), {fillColor: 'blue'});\n * \n * The points of the curve are either the elements of the properties dataX and dataY or\n * the result of the plotting algorithm. In any case, the points are stored in the private\n * property \"points\".\n * @returns {Array}\n */\n getCoords: function() {\n var len, i,\n arr = [];\n\n len = this.numberPoints;\n for (i = 0; i < len; i++) {\n arr.push(this.points[i].usrCoords.slice());\n }\n return arr;\n }\n\n\n }\n);\n\n/**\n * @class Curves can be defined by mappings or by discrete data sets.\n * In general, a curve is a mapping from R to R^2, where t maps to (x(t),y(t)). The graph is drawn for t in the interval [a,b].\n * \n * The following types of curves can be plotted:\n * \n * x describes the x-coordinate of the curve. It may be a function term in one variable, e.g. x(t).\n * In case of x being of type number, x(t) is set to a constant function.\n * this function at the values of the array.\n * \n * y describes the y-coordinate of the curve. In case of a number, y(t) is set to the constant function\n * returning this number.\n * \n * Further parameters are an optional number or function for the left interval border a,\n * and an optional number or function for the right interval border b.\n * \n * Default values are a=-10 and b=10.\n * \n * x and y are arrays contining the x and y coordinates of the data points which are connected by\n * line segments. The individual entries of x and y may also be functions.\n * In case of x being an array the curve type is data plot, regardless of the second parameter and\n * if additionally the second parameter y is a function term the data plot evaluates.\n * \n * The first parameter is a function term r(phi) describing the polar curve.\n * \n * The second parameter is the offset of the curve. It has to be\n * an array containing numbers or functions describing the offset. Default value is the origin [0,0].\n * \n * Further parameters are an optional number or function for the left interval border a,\n * and an optional number or function for the right interval border b.\n * \n * Default values are a=-10 and b=10.\n * \n * Additionally, a curve can be created by providing a curve and a transformation (or an array of transformations).\n * The result is a curve which is the transformation of the supplied curve.\n *\n * @see JXG.Curve\n * @example\n * // Parametric curve\n * // Create a curve of the form (t-sin(t), 1-cos(t), i.e.\n * // the cycloid curve.\n * var graph = board.create('curve',\n * [function(t){ return t-Math.sin(t);},\n * function(t){ return 1-Math.cos(t);},\n * 0, 2*Math.PI]\n * );\n * \n * Further, an optional number or function for the left interval border a,\n * and an optional number or function for the right interval border b.\n * \n * Default values are a=-10 and b=10.\n * @see JXG.Curve\n * @example\n * // Create a function graph for f(x) = 0.5*x*x-2*x\n * var graph = board.create('functiongraph',\n * [function(x){ return 0.5*x*x-2*x;}, -2, 4]\n * );\n * \n * First entry: Array of points the spline interpolates. This can be\n * \n * Second entry: JavaScript object containing the control values like tension, direction, curl.\n * @param {Object} attributes Define color, width, ... of the metapost spline\n * @returns {JXG.Curve} Returns reference to an object of type JXG.Curve.\n * @see JXG.Curve\n * @example\n * var po = [],\n * attr = {\n * size: 5,\n * color: 'red'\n * },\n * controls;\n *\n * var tension = board.create('slider', [[-3, 6], [3, 6], [0, 1, 20]], {name: 'tension'});\n * var curl = board.create('slider', [[-3, 5], [3, 5], [0, 1, 30]], {name: 'curl A, D'});\n * var dir = board.create('slider', [[-3, 4], [3, 4], [-180, 0, 180]], {name: 'direction B'});\n *\n * po.push(board.create('point', [-3, -3]));\n * po.push(board.create('point', [0, -3]));\n * po.push(board.create('point', [4, -5]));\n * po.push(board.create('point', [6, -2]));\n *\n * var controls = {\n * tension: function() {return tension.Value(); },\n * direction: { 1: function() {return dir.Value(); } },\n * curl: { 0: function() {return curl.Value(); },\n * 3: function() {return curl.Value(); }\n * },\n * isClosed: false\n * };\n *\n * // Plot a metapost curve\n * var cu = board.create('metapostspline', [po, controls], {strokeColor: 'blue', strokeWidth: 2});\n *\n *\n * \n * In case of type \"simpson\" and \"trapezoidal\", the horizontal line approximating the function value\n * is replaced by a parabola or a secant. IN case of \"simpson\",\n * the parabola is approximated visually by a polygonal chain of fixed step width.\n *\n * @pseudo\n * @name Riemannsum\n * @augments JXG.Curve\n * @constructor\n * @type Curve\n * @param {function,array_number,function_string,function_function,number_function,number} f,n,type_,a_,b_ Parent elements of Riemannsum are a\n * Either a function term f(x) describing the function graph which is filled by the Riemann bars, or\n * an array consisting of two functions and the area between is filled by the Riemann bars.\n * \n * n determines the number of bars, it is either a fixed number or a function.\n * \n * type is a string or function returning one of the values: 'left', 'right', 'middle', 'lower', 'upper', 'random', 'simpson', or 'trapezoidal'.\n * Default value is 'left'. \"simpson\" is Simpson's 1/3 rule.\n * \n * Further parameters are an optional number or function for the left interval border a,\n * and an optional number or function for the right interval border b.\n * \n * Default values are a=-10 and b=10.\n * @see JXG.Curve\n * @example\n * // Create Riemann sums for f(x) = 0.5*x*x-2*x.\n * var s = board.create('slider',[[0,4],[3,4],[0,4,10]],{snapWidth:1});\n * var f = function(x) { return 0.5*x*x-2*x; };\n * var r = board.create('riemannsum',\n * [f, function(){return s.Value();}, 'upper', -2, 5],\n * {fillOpacity:0.4}\n * );\n * var g = board.create('functiongraph',[f, -2, 5]);\n * var t = board.create('text',[-2,-2, function(){ return 'Sum=' + JXG.toFixed(r.Value(), 4); }]);\n * \n * Given a data set, the input array Q for the boxplot can be computed e.g. with the method {@link JXG.Math.Statistics.boxplot}.\n *\n * @example\n * var data = [57, 57, 57, 58, 63, 66, 66, 67, 67, 68, 69, 70, 70, 70, 70, 72, 73, 75, 75, 76, 76, 78, 79, 81];\n * var Q = JXG.Math.Statistics.boxplot(data);\n * var b = board.create('boxplot', [Q, 2, 4]);\n *\n * @pseudo\n * @name Boxplot\n * @param {Array} quantiles Array containing five quantiles (e.g. min, first quartile, median, third quartile, maximum) and an optional array with outlier values. The elements of this array can be of type number, function or string. The optional aub-array outlier is an array of numbers or a function returning an array of numbers.\n * @param {Number|Function} axis Axis position of the boxplot\n * @param {Number|Function} width Width of the rectangle part of the boxplot. The width of the first and 3th quartile\n * is relative to this width and can be controlled by the attribute \"smallWidth\".\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n * @see JXG.Math.Statistics#boxplot\n *\n * @example\n * var Q = [ -1, 2, 3, 3.5, 5 ];\n *\n * var b = board.create('boxplot', [Q, 2, 4], {strokeWidth: 3});\n *\n * \n * The partial derivatives for f are optional. If not given, numerical\n * derivatives are used instead. This is good enough for most practical use cases.\n * But if supplied, both partial derivatives must be supplied.\n * \n * The most effective attributes to tinker with if the implicit curve algorithm fails are\n * {@link ImplicitCurve#resolution_outer},\n * {@link ImplicitCurve#resolution_inner},\n * {@link ImplicitCurve#alpha_0},\n * {@link ImplicitCurve#h_initial},\n * {@link ImplicitCurve#h_max}, and\n * {@link ImplicitCurve#qdt_box}.\n *\n * @pseudo\n * @name ImplicitCurve\n * @param {Function|String} f Function of two variables for the left side of the equation f(x,y)=0.\n * If f is supplied as string, it has to use the variables 'x' and 'y'.\n * @param {Function|String} [dfx=null] Optional partial derivative in respect to the first variable\n * If dfx is supplied as string, it has to use the variables 'x' and 'y'.\n * @param {Function|String} [dfy=null] Optional partial derivative in respect to the second variable\n * If dfy is supplied as string, it has to use the variables 'x' and 'y'.\n * @param {Array|Function} [rangex=boundingbox] Optional array of length 2\n * of the form [x_min, x_max] setting the domain of the x coordinate of the implicit curve.\n * If not supplied, the board's boundingbox (+ the attribute 'margin') is taken.\n * @param {Array|Function} [rangey=boundingbox] Optional array of length 2\n * of the form [y_min, y_max] setting the domain of the y coordinate of the implicit curve.\n * If not supplied, the board's boundingbox (+ the attribute 'margin') is taken.\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n *\n * @example\n * var f, c;\n * f = (x, y) => 1 / 16 * x ** 2 + y ** 2 - 1;\n * c = board.create('implicitcurve', [f], {\n * strokeWidth: 3,\n * strokeColor: JXG.palette.red,\n * strokeOpacity: 0.8\n * });\n *\n * \n * As a curve the arc has curve length 6.\n * @pseudo\n * @name Arc\n * @augments Curve\n * @constructor\n * @type JXG.Curve\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The result will be an arc of a circle around p1 through p2. The arc is drawn\n * counter-clockwise from p2 to p3.\n * @example\n * // Create an arc out of three free points\n * var p1 = board.create('point', [2.0, 2.0]);\n * var p2 = board.create('point', [1.0, 0.5]);\n * var p3 = board.create('point', [3.5, 1.0]);\n *\n * var a = board.create('arc', [p1, p2, p3]);\n * board.create('text',[1,6,function(){return 'arclength: '+Math.round(a.Value()*100)/100}])\n * \n * The sector as curve consists of two legs and an arc. The curve length is 6. That means, a point with coordinates\n * [sector.X(t), sector.Y(t)] is on\n * \n * In this case, the sector will have an arc as sub-object.\n * \n * Second possibility of input parameters are:\n * @param {JXG.Line_JXG.Line_array,number_array,number_number,function} line, line2, coords1 or direction1, coords2 or direction2, radius The sector is defined by two lines.\n * The two legs which define the sector are given by two coordinates arrays which are projected initially to the two lines or by\n * two directions (+/- 1). If the two lines are parallel, two of the defining points on different lines have to coincide.\n * This will be the center of the sector.\n * The last parameter is the radius of the sector.\n * In this case, the sector will not have an arc as sub-object.\n *\n * @example\n * // Create a sector out of three free points\n * var p1 = board.create('point', [1.5, 5.0]),\n * p2 = board.create('point', [1.0, 0.5]),\n * p3 = board.create('point', [5.0, 3.0]),\n *\n * a = board.create('sector', [p1, p2, p3]);\n * \n * If no name is provided the angle label is automatically set to a lower greek letter. If no label should be displayed use\n * the attribute withLabel:false or set the name attribute to the empty string.\n *\n * @pseudo\n * @name Angle\n * @augments Sector\n * @constructor\n * @type Sector\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * First possibility of input parameters are:\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 An angle is always drawn counterclockwise from p1 to\n * p3 around p2.\n *\n * Second possibility of input parameters are:\n * @param {JXG.Line_JXG.Line_array|number_array|number} line, line2, coords1 or direction1, coords2 or direction2, radius The angle is defined by two lines.\n * The two legs which define the angle are given by two coordinate arrays.\n * The points given by these coordinate arrays are projected initially (i.e. only once) onto the two lines.\n * The other possibility is to supply directions (+/- 1).\n *\n * @example\n * // Create an angle out of three free points\n * var p1 = board.create('point', [5.0, 3.0]),\n * p2 = board.create('point', [1.0, 0.5]),\n * p3 = board.create('point', [1.5, 5.0]),\n *\n * a = board.create('angle', [p1, p2, p3]),\n * t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);\n * \n * If original line is given as a JSXGraph line object, the resulting parallel line will be defined by the given point and an\n * infinitely far away point (an ideal point). That means, the line can not be shortened to a segment.\n * \n * If the original line is given as two points, the resulting parallel line can be shortened to a a segment.\n * @pseudo\n * @name Parallel\n * @augments Line\n * @constructor\n * @type JXG.Line\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Line_JXG.Point} l,p The constructed line contains p and has the same slope as l. Alternative parameters are p1, p2, p: The\n * constructed line contains p and has the same slope as the line through p1 and p2.\n * @example\n * // Create a parallel\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n * var l1 = board.create('line', [p1, p2]);\n *\n * var p3 = board.create('point', [3.0, 3.0]);\n * var pl1 = board.create('parallel', [l1, p3]);\n * \n * @pseudo\n * @constructor\n * @name Arrowparallel\n * @type Parallel\n * @augments Parallel\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The constructed arrow contains p3 and has the same slope as the line through p1 and p2.\n * @example\n * // Create a parallel\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n * var l1 = board.create('segment', [p1, p2]);\n *\n * var p3 = board.create('point', [3.0, 3.0]);\n * var pl1 = board.create('arrowparallel', [p1, p2, p3]);\n * \n * For function graphs the area below the function graph is filled, i.e. the\n * area of the inequality y <= f(x).\n * With the attribute inverse:true the area of the inequality y >= f(x) is filled.\n *\n * @param {JXG.Line} l The area drawn will be the area below this line. With the attribute\n * inverse:true, the inequality 'greater than or equal to' is shown.\n * @constructor\n * @name Inequality\n * @type JXG.Curve\n * @augments JXG.Curve\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @example\n * var p = board.create('point', [1, 3]),\n * q = board.create('point', [-2, -4]),\n * l = board.create('line', [p, q]),\n * ineq = board.create('inequality', [l]);\n * ineq = board.create('inequality', [l]);\n * \n * The array size defines the image's width and height in user coordinates.\n * @example\n * var im = board.create('image', ['https://jsxgraph.org/jsxgraph/distrib/images/uccellino.jpg', [-3,-2], [3,3]]);\n *\n * \n * Possible operands are:\n * \n * Possible operators are:\n * \n * Possible operands are:\n * \n * ['+', ['Area', obj1], ['L', obj2]] will retrun NaN, because the two\n * operands have conflicting dimensions.\n * \n * If an element is a measurement element, then it's dimension can be set as attribute.\n * This overrules the computed dimension.\n *\n * @param {Array|Number} term Prefix expression\n * @returns Number\n */\n dimension: function (term) {\n var method, i, le, res, fun, d, v, unit;\n\n if (Type.isNumber(term)) {\n return 0;\n }\n if (!Type.isArray(term) || term.length < 2) {\n throw new Error('PrefixParser.dimension: term is not an array');\n }\n\n method = term[0];\n le = term.length;\n\n if (Type.isInArray(['+', '-', '*', '/'], method)) {\n\n res = this.dimension(term[1]);\n for (i = 2; i < le; i++) {\n v = this.dimension(term[i]);\n switch (method) {\n case '+':\n if (v !== res) {\n res = NaN;\n }\n break;\n case '-':\n if (v !== res) {\n res = NaN;\n }\n break;\n case '*':\n res += v;\n break;\n case '/':\n res -= v;\n break;\n default:\n }\n }\n\n } else if (method === 'exec') {\n if (term[2].type === Type.OBJECT_TYPE_MEASUREMENT) {\n res = term[2].Dimension();\n // If attribute \"dim\" is set, this overrules anything else.\n if (Type.exists(term[2].visProp.dim)) {\n d = term[2].evalVisProp('dim');\n if (d !== null) {\n res = d;\n }\n }\n } else {\n res = 0;\n }\n } else {\n // Allow shortcut 'V' for 'Value'\n fun = term[0];\n\n switch (fun) {\n case 'Slope':\n case 'Angle':\n res = 0;\n break;\n case 'L':\n case 'Length':\n case 'Perimeter':\n case 'Diameter':\n case 'Radius':\n case 'R':\n case 'DeltaX':\n case 'DeltaY':\n res = 1;\n break;\n case 'Area':\n case 'A':\n res = 2;\n break;\n default: // 'V', 'Value'\n if (term[1].type === Type.OBJECT_TYPE_MEASUREMENT) {\n res = term[1].Dimension();\n // If attribute \"dim\" is set, this overrules anything else.\n if (Type.exists(term[1].visProp.dim)) {\n d = term[1].evalVisProp('dim');\n if (d !== null) {\n res = d;\n }\n }\n } else {\n res = 0;\n\n if (fun === 'Value' || fun === 'V') {\n // The Value method of sector, angle and arc does not have the same dimension\n // for all units.\n if ([Const.OBJECT_TYPE_ARC, Const.OBJECT_TYPE_SECTOR, Const.OBJECT_TYPE_ANGLE].indexOf(term[1].type) >= 0) {\n unit = '';\n if (term.length === 3 && Type.isString(term[2])) {\n unit = term[2].toLowerCase();\n }\n if (unit === '') {\n // Default values:\n if (term[1].type === Const.OBJECT_TYPE_ANGLE) {\n // Default for angle.Value() is radians, i.e. dim 0\n res = 0;\n } else {\n // Default for sector|arc.Value() is length, i.e. dim 1\n res = 1;\n }\n } else if (unit.indexOf('len') === 0) {\n // Length has dim 1\n res = 1;\n } else {\n // Angles in various units has dimension 0\n res = 0;\n }\n }\n }\n }\n }\n }\n\n return res;\n },\n\n /**\n * Convert a prefix expression into a new prefix expression in which\n * JSXGraph elements have been replaced by their ids.\n *\n * @param {Array|Number} term\n * @returns {Array|Number}\n */\n toPrefix: function (term) {\n var method, i, le, res;\n\n if (Type.isNumber(term)) {\n return term;\n }\n if (!Type.isArray(term) || term.length < 2) {\n throw new Error('PrefixParser.toPrefix: term is not an array');\n }\n\n method = term[0];\n le = term.length;\n res = [method];\n\n for (i = 1; i < le; i++) {\n if (Type.isInArray(['+', '-', '*', '/'], method)) {\n res.push(this.toPrefix(term[i]));\n } else {\n if (method === 'V' && term[i].type === Type.OBJECT_TYPE_MEASUREMENT) {\n res = term[i].toPrefix();\n } else if (method === 'exec') {\n if (i === 1) {\n res.push(term[i]);\n } else {\n res.push(this.toPrefix(term[i]));\n }\n } else {\n res = [method, term[i].id];\n }\n }\n }\n\n return res;\n },\n\n /**\n * Determine parent elements of a prefix expression.\n * @param {Array|Number} term prefix expression\n * @returns Array\n * @private\n */\n getParents: function (term) {\n var method, i, le, res;\n\n if (Type.isNumber(term)) {\n return [];\n }\n if (!Type.isArray(term) || term.length < 2) {\n throw new Error('PrefixParser.getParents: term is not an array');\n }\n\n method = term[0];\n le = term.length;\n res = [];\n\n for (i = 1; i < le; i++) {\n if (Type.isInArray(['+', '-', '*', '/'], method)) {\n Type.concat(res, this.getParents(term[i]));\n } else {\n if (method === 'V' && term[i].type === Type.OBJECT_TYPE_MEASUREMENT) {\n Type.concat(res, term[i].getParents());\n } else if (method === 'exec') {\n if (i > 1) {\n Type.concat(res, this.getParents(term[i]));\n }\n } else {\n res.push(term[i]);\n }\n }\n }\n\n return res;\n }\n};\n\nexport default JXG.PrefixParser;","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * The two defining points of the tape measure (which is a segment) do not inherit by default the attribute \"visible\" from\n * the segment. Otherwise the tape meassure would be inaccessible if the two points coincide and the segment is hidden.\n *\n * @pseudo\n * @name Tapemeasure\n * @augments Segment\n * @constructor\n * @type JXG.Segment\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Array_Array} start,end, The two arrays give the initial position where the tape measure\n * is drawn on the board.\n * @example\n * // Create a tape measure\n * var p1 = board.create('point', [0,0]);\n * var p2 = board.create('point', [1,1]);\n * var p3 = board.create('point', [3,1]);\n * var tape = board.create('tapemeasure', [[1, 2], [4, 2]], {name:'dist'});\n * \n * The purpose of this element is to display values of measurements of geometric objects, like the radius of a circle,\n * as well as expressions consisting of measurements.\n *\n * @pseudo\n * @name Measurement\n * @augments Text\n * @constructor\n * @type JXG.Text\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Point|Array_Point|Array_Array} x,y,expression\n * Here, expression is a prefix expression, see {@link JXG.PrefixParser}.\n * @example\n * var p1 = board.create('point', [1, 1]);\n * var p2 = board.create('point', [1, 3]);\n * var ci1 = board.create('circle', [p1, p2]);\n *\n * var m1 = board.create('measurement', [1, -2, ['Area', ci1]], {\n * visible: true,\n * prefix: 'area: ',\n * baseUnit: 'cm'\n * });\n *\n * var m2 = board.create('measurement', [1, -4, ['Radius', ci1]], {\n * prefix: 'radius: ',\n * baseUnit: 'cm'\n * });\n *\n * \n * The parent array may be of one of the following forms:\n * \n * The legend object consists of segements with labels. These lines can be\n * accessed with the property \"lines\" of the element.\n * @constructor\n * @augments JXG.GeometryElement\n * @param {String|JXG.Board} board The board the new legend is drawn on.\n * @param {Array} coords Coordinates of the left top point of the legend.\n * @param {Object} attributes Attributes of the legend\n */\nJXG.Legend = function (board, coords, attributes) {\n var attr;\n\n /* Call the constructor of GeometryElement */\n this.constructor();\n\n attr = Type.copyAttributes(attributes, board.options, 'legend');\n\n this.board = board;\n this.coords = new Coords(Const.COORDS_BY_USER, coords, this.board);\n this.myAtts = {};\n this.label_array = attr.labelarray || attr.labels;\n this.color_array = attr.colorarray || attr.colors;\n this.opacy_array = attr.strokeopacity || [1];\n this.lines = [];\n this.myAtts.strokewidth = attr.strokewidth || 5;\n this.myAtts.straightfirst = false;\n this.myAtts.straightlast = false;\n this.myAtts.withlabel = true;\n this.myAtts.fixed = true;\n this.myAtts.frozen = attr.frozen || false ;\n this.style = attr.legendstyle || attr.style;\n\n if (this.style === 'vertical') {\n this.drawVerticalLegend(board, attr);\n } else {\n throw new Error(\"JSXGraph: Unknown legend style: \" + this.style);\n }\n\n this.id = this.board.setId(this, 'Leg');\n\n};\n\nJXG.Legend.prototype = new GeometryElement();\n\n/**\n * Draw a vertical legend.\n *\n * @private\n * @param {String|JXG.Board} board The board the legend is drawn on\n * @param {Object} attributes Attributes of the legend\n */\nJXG.Legend.prototype.drawVerticalLegend = function (board, attributes) {\n var i,\n line_length = attributes.linelength || 1,\n offy = (attributes.rowheight || 20) / this.board.unitY,\n getLabelAnchor = function () {\n this.setLabelRelativeCoords(this.visProp.label.offset);\n return new Coords(\n Const.COORDS_BY_USER,\n [this.point2.X(), this.point2.Y()],\n this.board\n );\n };\n\n for (i = 0; i < this.label_array.length; i++) {\n this.myAtts.name = this.label_array[i];\n this.myAtts.strokecolor = this.color_array[i % this.color_array.length];\n this.myAtts.highlightstrokecolor = this.color_array[i % this.color_array.length];\n this.myAtts.strokeopacity = this.opacy_array[i % this.opacy_array.length];\n this.myAtts.highlightstrokeopacity = this.opacy_array[i % this.opacy_array.length];\n this.myAtts.label = {\n offset: [10, 0],\n strokeColor: this.color_array[i % this.color_array.length],\n strokeWidth: this.myAtts.strokewidth\n };\n\n this.lines[i] = board.create(\n \"line\",\n [\n [this.coords.usrCoords[1], this.coords.usrCoords[2] - i * offy],\n [this.coords.usrCoords[1] + line_length, this.coords.usrCoords[2] - i * offy]\n ],\n this.myAtts\n );\n\n if (this.myAtts.frozen){\n this.lines[i].setAttribute({ point1: { frozen: true }, point2: { frozen: true } });\n }\n\n this.lines[i].getLabelAnchor = getLabelAnchor;\n this.lines[i]\n .prepareUpdate()\n .update()\n .updateVisibility(this.lines[i].evalVisProp('visible'))\n .updateRenderer();\n\n this.addChild(this.lines[i]);\n }\n};\n\n/**\n * @class Creates a legend for a chart element.\n * Parameter is a pair of coordinates. The label names and the label colors are\n * supplied in the attributes:\n * \n * Translation matrix:\n * \n * Scale matrix:\n * \n * A rotation matrix with angle a (in Radians)\n * \n * Shear matrix:\n * Generic affine transformation (4 parameters):\n * Affine 2x2 matrix:\n * Generic transformation (9 parameters):\n * 3x3 Matrix:\n * A transformation with a generic matrix looks like:\n * \n * Translation matrix:\n * \n * Scale matrix:\n * \n * A rotation matrix with angle a (in Radians)\n * \n * Shear matrix:\n * Generic affine transformation (4 parameters):\n * Affine 2x2 matrix:\n * Generic transformation (9 parameters):\n * 3x3 Matrix:\n * A transformation with a generic matrix looks like:\n * \n * Translation matrix:\n * \n * Scale matrix:\n * \n * rotateX: a rotation matrix with angle a (in Radians)\n * \n * rotateY: a rotation matrix with angle a (in Radians)\n * \n * rotateZ: a rotation matrix with angle a (in Radians)\n * \n * rotate: a rotation matrix with angle a (in Radians)\n * and normal n.\n *\n * Generic affine transformation (9 parameters):\n * Affine 3x3 matrix:\n * Generic transformation (16 parameters):\n * Generic 4x4 matrix:\n * \n * Restricted to 2D transformations.\n *\n * @private\n * @param {JXG.GeometryElement} p element which is transformed\n * @param {String} 'self' Apply the transformation to the initialCoords instead of the coords if this is set.\n * @returns {Array}\n */\n apply: function (p, self) {\n var c;\n\n this.update();\n if (this.is3D) {\n c = p.coords;\n } else if (Type.exists(self)) {\n c = p.initialCoords.usrCoords;\n } else {\n c = p.coords.usrCoords;\n }\n\n return Mat.matVecMult(this.matrix, c);\n },\n\n /**\n * Applies a transformation once to a point element, that are: {@link Point}, {@link Text}, {@link Image}, {@link Point3D} or to an array of such elements.\n * If it is a free 2D point, then it can be dragged around later\n * and will overwrite the transformed coordinates.\n * @param {JXG.Point|Array} p\n */\n applyOnce: function (p) {\n var c, len, i;\n\n if (!Type.isArray(p)) {\n p = [p];\n }\n\n len = p.length;\n for (i = 0; i < len; i++) {\n this.update();\n if (this.is3D) {\n p[i].coords = Mat.matVecMult(this.matrix, p[i].coords);\n } else {\n c = Mat.matVecMult(this.matrix, p[i].coords.usrCoords);\n p[i].coords.setCoordinates(Const.COORDS_BY_USER, c);\n }\n }\n },\n\n /**\n * Binds a transformation to a GeometryElement or an array of elements. In every update of the\n * GeometryElement(s), the transformation is executed. That means, in order to immediately\n * apply the transformation after calling bindTo, a call of board.update() has to follow.\n * \n * The transformation is simply appended to the existing list of transformations of the object.\n * It is not fused (melt) with an existing transformation.\n *\n * @param {Array|JXG.Object} el JXG.Object or array of JXG.Object to\n * which the transformation is bound to.\n * @see JXG.Transformation.meltTo\n */\n bindTo: function (el) {\n var i, len;\n if (Type.isArray(el)) {\n len = el.length;\n\n for (i = 0; i < len; i++) {\n el[i].transformations.push(this);\n }\n } else {\n el.transformations.push(this);\n }\n },\n\n /**\n * Binds a transformation to a GeometryElement or an array of elements. In every update of the\n * GeometryElement(s), the transformation is executed. That means, in order to immediately\n * apply the transformation after calling meltTo, a call of board.update() has to follow.\n * \n * In case the last transformation of the element and this transformation are static,\n * i.e. the transformation matrices do not depend on other elements,\n * the transformation will be fused into (multiplied with) the last transformation of\n * the element. Thus, the list of transformations is kept small.\n * If the transformation will be the first transformation of the element, it will be cloned\n * to prevent side effects.\n *\n * @param {Array|JXG.Object} el JXG.Object or array of JXG.Objects to\n * which the transformation is bound to.\n *\n * @see JXG.Transformation#bindTo\n */\n meltTo: function (el) {\n var i, elt, t;\n\n if (Type.isArray(el)) {\n for (i = 0; i < el.length; i++) {\n this.meltTo(el[i]);\n }\n } else {\n elt = el.transformations;\n\n if (elt.length > 0 &&\n elt[elt.length - 1].isNumericMatrix &&\n this.isNumericMatrix\n ) {\n elt[elt.length - 1].melt(this);\n } else {\n // Use a clone of the transformation.\n // Otherwise, if the transformation is meltTo twice\n // the transformation will be changed.\n t = this.clone();\n elt.push(t);\n }\n }\n },\n\n /**\n * Create a copy of the transformation in case it is static, i.e.\n * if the transformation matrix does not depend on other elements.\n * \n * If the transformation matrix is not static, null will be returned.\n *\n * @returns {JXG.Transformation}\n */\n clone: function () {\n var t = null;\n\n this.update();\n if (this.isNumericMatrix) {\n t = new JXG.Transformation(this.board, 'none', []);\n t.matrix = this.matrix.slice();\n t.transformationType = this.transformationType;\n }\n\n return t;\n },\n\n /**\n * Unused\n * @deprecated Use setAttribute\n * @param term\n */\n setProperty: function (term) {\n JXG.deprecated(\"Transformation.setProperty()\", \"Transformation.setAttribute()\");\n },\n\n /**\n * Empty method. Unused.\n * @param {Object} term Key-value pairs of the attributes.\n */\n setAttribute: function (term) {},\n\n /**\n * Combine two transformations to one transformation. This only works if\n * both of transformation matrices consist of numbers solely, and do not\n * contain functions.\n *\n * Multiplies the transformation with a transformation t from the left.\n * i.e. (this) = (t) join (this)\n * @param {JXG.Transform} t Transformation which is the left multiplicand\n * @returns {JXG.Transform} the transformation object.\n */\n melt: function (t) {\n var res = [];\n\n this.update();\n t.update();\n\n res = Mat.matMatMult(t.matrix, this.matrix);\n\n this.update = function () {\n this.matrix = res;\n };\n\n return this;\n },\n\n // Documented in element.js\n // Not yet, since transformations are not listed in board.objects.\n getParents: function () {\n var p = [[].concat.apply([], this.matrix)];\n\n if (this.parents.length !== 0) {\n p = this.parents;\n }\n\n return p;\n }\n }\n);\n\n/**\n * @class Define projective 2D transformations like translation, rotation, reflection.\n * @pseudo\n * @description A transformation consists of a 3x3 matrix, i.e. it is a projective transformation.\n * \n * Internally, a transformation is applied to an element by multiplying the 3x3 matrix from the left to\n * the homogeneous coordinates of the element. JSXGraph represents homogeneous coordinates in the order\n * (z, x, y). The matrix has the form\n * \n * Transformations acting on texts and images are considered to be affine, i.e. b and c are ignored.\n *\n * @name Transformation\n * @augments JXG.Transformation\n * @constructor\n * @type JXG.Transformation\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {number|function|JXG.GeometryElement} parameters The parameters depend on the transformation type, supplied as attribute 'type'.\n * Possible transformation types are\n * Valid parameters for these types are:\n * \n * Internally, a transformation is applied to an element by multiplying the 4x4 matrix from the left to\n * the homogeneous coordinates of the element. JSXGraph represents homogeneous coordinates in the order\n * (w, x, y, z). If the coordinate is a finite point, w=1. The matrix has the form\n * \n *\n * @name Transformation3D\n * @augments JXG.Transformation\n * @constructor\n * @type JXG.Transformation\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {number|function|JXG.GeometryElement3D} parameters The parameters depend on the transformation type, supplied as attribute 'type'.\n * Possible transformation types are\n * Valid parameters for these types are:\n * \n * There are the following ways to position the tick lines:\n * \n * For arbitrary lines (and not axes) a \"zero coordinate\" is determined\n * which defines where the first tick is positioned. This zero coordinate\n * can be altered with the attribute anchor. Possible values are \"left\", \"middle\", \"right\" or a number.\n * The default value is \"left\".\n *\n * @pseudo\n * @name Ticks\n * @augments JXG.Ticks\n * @constructor\n * @type JXG.Ticks\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Line|JXG.Curve} line The parents consist of the line or curve the ticks are going to be attached to.\n * @param {Array} [ticks] Optional array of numbers. If given, a fixed number of static ticks is created\n * at these user-supplied positions.\n * \n * Deprecated: Alternatively, a number defining the distance between two major ticks\n * can be specified. However, this is meanwhile ignored. Use attribute ticksDistance instead.\n *\n * @example\n * // Add ticks to line 'l1' through 'p1' and 'p2'. The major ticks are\n * // two units apart and 40 px long.\n * var p1 = board.create('point', [0, 3]);\n * var p2 = board.create('point', [1, 3]);\n * var l1 = board.create('line', [p1, p2]);\n * var t = board.create('ticks', [l1], {\n * ticksDistance: 2,\n * majorHeight: 40\n * });\n * Setting a CSS class: The attribute cssClass affects the HTML div element that contains the checkbox element. To change the CSS properties of the HTML checkbox element a selector of the form\n * .mycheck > checkbox { ... } has to be used. See the analog example for buttons:\n * {@link Button}.\n *\n * Access the checkbox element with JavaScript:\n * The underlying HTML checkbox element can be accessed through the sub-object 'rendNodeCheck', e.g. to\n * add event listeners.\n *\n * @pseudo\n * @name Checkbox\n * @augments Text\n * @constructor\n * @type JXG.Text\n *\n * @param {number,function_number,function_String,function} x,y,label Parent elements for checkbox elements.\n * \n * x and y are the coordinates of the lower left corner of the text box.\n * The position of the text is fixed,\n * x and y are numbers. The position is variable if x or y are functions.\n * \n * The label of the input element may be given as string or function.\n * \n * The value of the checkbox can be controlled with the attribute checked\n * The HTML node can be accessed with element.rendNodeCheckbox\n *\n * @example\n * // Create a checkbox element at position [0,3].\n * var checkbox = board.create('checkbox', [0, 3, 'Change Y'], {});\n * var p = board.create('point', [\n * function(){ return 0.5;}, // X-coordinate\n * function() {\n * y = 0.5;\n * if (checkbox.Value()) {\n * y += 0.5;\n * }\n * return y;\n * }]);\n * Setting a CSS class: The attribute cssClass affects the HTML div element that contains the input element. To change the CSS properties of the HTML input element a selector of the form\n * .myinput > input { ... } has to be used. See the analog example for buttons:\n * {@link Button}.\n *\n * Access the input element with JavaScript:\n * The underlying HTML button element can be accessed through the sub-object 'rendNodeInput', e.g. to\n * add event listeners.\n *\n * @pseudo\n * @name Input\n * @augments Text\n * @constructor\n * @type JXG.Text\n *\n * @param {number,function_number,function_String_String,function} x,y,value,label Parent elements for input elements.\n * \n * x and y are the coordinates of the lower left corner of the text box. The position of the text is fixed,\n * x and y are numbers. The position is variable if x or y are functions.\n * \n * The default value of the input element must be given as string.\n * \n * The label of the input element may be given as string or function.\n *\n * @example\n * // Create an input element at position [1,4].\n * var input = board.create('input', [0, 1, 'sin(x)*x', 'f(x)='], {cssStyle: 'width: 100px'});\n * var f = board.jc.snippet(input.Value(), true, 'x', false);\n * var graph = board.create('functiongraph',[f,\n * function() {\n * var c = new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],board);\n * return c.usrCoords[1];\n * },\n * function() {\n * var c = new JXG.Coords(JXG.COORDS_BY_SCREEN,[board.canvasWidth,0],board);\n * return c.usrCoords[1];\n * }\n * ]);\n *\n * board.create('text', [1, 3, '<button onclick=\"updateGraph()\">Update graph</button>']);\n *\n * var updateGraph = function() {\n * graph.Y = board.jc.snippet(input.Value(), true, 'x', false);\n * graph.updateCurve();\n * board.update();\n * }\n * Setting a CSS class: The attribute cssClass affects the HTML div element that contains the button element. To change the CSS properties of the HTML button element a selector of the form\n * .mybutton > button { ... } has to be used. See the example below.\n *\n * Access the button element with JavaScript:\n * The underlying HTML button element can be accessed through the sub-object 'rendNodeButton', e.g. to\n * add event listeners.\n *\n * @pseudo\n * @name Button\n * @augments Text\n * @constructor\n * @type JXG.Text\n *\n * @param {number,function_number,function_String,function_function} x,y,label,handler Parent elements for button elements.\n * \n * x and y are the coordinates of the lower left corner of the text box.\n * The position of the text is fixed,\n * x and y are numbers. The position is variable if x or y are functions.\n * \n * The label of the input element may be given as string.\n * \n * The (optional) handler function which is called when the button is pressed.\n *\n * @example\n * var p = board.create('point', [0.5, 0.5], {id: 'p1'});\n *\n * // Create a button element at position [1,2].\n * var button1 = board.create('button', [1, 2, 'Change Y with JavaScript', function() {\n * p.moveTo([p.X(), p.Y() + 0.5], 100);\n * }], {});\n *\n * // Create a button element at position [1,4].\n * var button2 = board.create('button', [1, 4, 'Change Y with JessieCode',\n * \"$('p1').Y = $('p1').Y() - 0.5;\"\n * ], {});\n *\n * \n * Plot a vector field either given by two functions f1(x, y) and f2(x,y) or by a function f(x, y) returning an array of size 2.\n *\n * @pseudo\n * @name Vectorfield\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * Parameter options:\n * @param {Array|Function|String} F Either an array containing two functions f1(x, y) and f2(x, y) or function f(x, y) returning an array of length 2.\n * @param {Array} xData Array of length 3 containing start value for x, number of steps, end value of x. The vector field will contain\n * (number of steps) + 1 vectors in direction of x.\n * @param {Array} yData Array of length 3 containing start value for y, number of steps, end value of y. The vector field will contain\n * (number of steps) + 1 vectors in direction of y.\n *\n * @example\n * // Defining functions\n * var fx = (x, y) => Math.sin(y);\n * var fy = (x, y) => Math.cos(x);\n *\n * var field = board.create('vectorfield', [\n * [fx, fy], // Defining function\n * [-6, 25, 6], // Horizontal mesh\n * [-5, 20, 5], // Vertical mesh\n * ]);\n *\n * \n * Plot a slope field given by a function f(x, y) returning a number.\n *\n * @pseudo\n * @name Slopefield\n * @augments Vectorfield\n * @constructor\n * @type JXG.Curve\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * Parameter options:\n * @param {Function|String} F Function f(x, y) returning a number.\n * @param {Array} xData Array of length 3 containing start value for x, number of steps, end value of x. The slope field will contain\n * (number of steps) + 1 vectors in direction of x.\n * @param {Array} yData Array of length 3 containing start value for y, number of steps, end value of y. The slope field will contain\n * (number of steps) + 1 vectors in direction of y.\n * @example\n * var field = board.create('slopefield', [\n * (x, y) => x * x - x - 2,\n * [-6, 25, 6], // Horizontal mesh\n * [-5, 20, 5] // Vertical mesh\n * ]);\n *\n * \n * If additionally a text, or a function is supplied and the content is not the empty string,\n * that text is displayed instead of the measurement.\n * \n * Smartlabels use custom made CSS layouts defined in jsxgraph.css. Therefore, the inclusion of the file jsxgraph.css is mandatory or\n * the CSS classes have to be replaced by other classes.\n * \n * The default attributes for smartlabels are defined for each type of measured element in the following sub-objects.\n * This is a deviation from the usual JSXGraph attribute usage.\n * \n * Instead of board.create('foreignobject') the shortcut board.create('fo') may be used.\n *\n * NOTE: In Safari up to version 15, a foreignObject does not obey the layer structure\n * if it contains <video> or <iframe> tags, as well as elements which are\n * positioned with position:absolute|relative|fixed. In this case, the foreignobject will be\n * \"above\" the JSXGraph construction.\n * \n * Note that shading needs a lot of computing resources, in particular for\n * SVG rendering. Setting `renderer:'canvas'` will allow to rotate the viewport\n * much faster.\n *\n * @type Object\n * @name Face3D#shader\n * @see View3D#depthOrder\n * @default \n * In case of `tiling:'triangle'` or `tiling:'rectangle'` a polyhedron3d element is displayed, using the\n * attributes `stepsU` and `stepsV`. In case of `triangle`, equilateral triangles are created if stepsV==0.\n * \n * All other attributes of the polyhedron3d have to be set inside of `polyhedron`, including `strokeWidth`\n * and `strokeColor`. The wireframe settings for these attributes are ignored.\n * \n * At the time being (v1.13+), this attribute is immutable.\n *\n * @type String\n * @name ParametricSurface3D#tiling\n * @default 'wireframe'\n * @see ParametricSurface3D#polyhedron\n *\n * @example\n *\n * var view = board.create('view3d',\n * [\n * [-6, -3], [8, 8],\n * [[-5, 5], [-5, 5], [-5, 5]]\n * ],\n * {\n * xPlaneRear: {visible: false},\n * yPlaneRear: {visible: false},\n * });\n *\n * // Function F to be plotted\n * var F = (x, y) => Math.cos(x * y / 4);\n *\n * // 3D surface\n * var c = view.create('functiongraph3d', [\n * F,\n * [-5, 5],\n * [-5, 5],\n * ], {\n * strokeWidth: 0.5,\n * stepsU: 70,\n * stepsV: 70,\n * tiling:'wireframe'\n * });\n *\n * \n * For each layer this depth ordering is done independently.\n * Sub-attributes:\n * \n * Possible values for attribute key: 'shift' or 'ctrl'.\n *\n * @name View3D#verticalDrag\n * @type Object\n * @default {enabled: true, key: 'shift'}\n */\n verticalDrag: {\n enabled: true,\n key: 'shift'\n },\n\n /**\n * Specify the user handling of the azimuth.\n * \n * After a call of view.setView(az, el, r), view.nextView(),\n * view.previousView(), or view.setCurrentView()\n * with an optional r,\n * the camera distance is set to this value of r until a call of view.freeR().\n *\n * @type {Number|String}\n * @default 'auto'\n * @see View3D#setView\n * @see View3D#freeR\n * @see View3D#nextView\n * @see View3D#previousView\n * @see View3D#setCurrentView\n */\n r: 'auto',\n\n /**\n * Enable user handling by a virtual trackball that allows to move the 3D scene\n * with 3 degrees of freedom. If not enabled, direct user dragging (i.e. in the JSXGraph board, not manipulating the sliders) will only have\n * two degrees of freedom. This means, the z-axis will always be projected to a vertical 2D line.\n * \n * Sub-attributes:\n * \n * Used in View3d.project2DTo3DVertical() and\n * Line3d.projectScreenCoords().\n *\n * @param {Array} pScr The screen coordinates of the point to project.\n * @param {Array} end0 The world space coordinates of one end of the\n * line segment (array of length 4).\n * @param {Array} end1 The world space coordinates of the other end of\n * the line segment (array of length 4).\n *\n * @returns {Array} Homogeneous coordinates of the projection\n */\n projectScreenToSegment: function (pScr, end0, end1) {\n var end0_2d = this.project3DTo2D(end0).slice(1, 3),\n end1_2d = this.project3DTo2D(end1).slice(1, 3),\n dir_2d = [\n end1_2d[0] - end0_2d[0],\n end1_2d[1] - end0_2d[1]\n ],\n dir_2d_norm_sq = Mat.innerProduct(dir_2d, dir_2d),\n diff = [\n pScr[0] - end0_2d[0],\n pScr[1] - end0_2d[1]\n ],\n s = Mat.innerProduct(diff, dir_2d) / dir_2d_norm_sq, // screen-space affine parameter\n mid, mid_2d, mid_diff, m,\n\n t, // view-space affine parameter\n t_clamped, // affine parameter clamped to range\n t_clamped_co;\n\n if (this.projectionType === 'central') {\n mid = [\n 1,\n 0.5 * (end0[1] + end1[1]),\n 0.5 * (end0[2] + end1[2]),\n 0.5 * (end0[3] + end1[3])\n ];\n mid_2d = this.project3DTo2D(mid).slice(1, 3);\n mid_diff = [\n mid_2d[0] - end0_2d[0],\n mid_2d[1] - end0_2d[1]\n ];\n m = Mat.innerProduct(mid_diff, dir_2d) / dir_2d_norm_sq;\n\n // the view-space affine parameter s is related to the\n // screen-space affine parameter t by a Möbius transformation,\n // which is determined by the following relations:\n //\n // s | t\n // -----\n // 0 | 0\n // m | 1/2\n // 1 | 1\n //\n t = (1 - m) * s / ((1 - 2 * m) * s + m);\n } else {\n t = s;\n }\n\n t_clamped = Math.min(Math.max(t, 0), 1);\n t_clamped_co = 1 - t_clamped;\n return [\n 1,\n t_clamped_co * end0[1] + t_clamped * end1[1],\n t_clamped_co * end0[2] + t_clamped * end1[2],\n t_clamped_co * end0[3] + t_clamped * end1[3]\n ];\n },\n\n /**\n * Project a 2D coordinate to a new 3D position by keeping\n * the 3D x, y coordinates and changing only the z coordinate.\n * All horizontal moves of the 2D point are ignored.\n *\n * @param {JXG.Point} point2d\n * @param {Array} base_c3d\n * @returns {Array} of length 4 containing the projected\n * point in homogeneous coordinates.\n */\n project2DTo3DVertical: function (point2d, base_c3d) {\n var pScr = point2d.coords.usrCoords.slice(1, 3),\n end0 = [1, base_c3d[1], base_c3d[2], this.bbox3D[2][0]],\n end1 = [1, base_c3d[1], base_c3d[2], this.bbox3D[2][1]];\n\n return this.projectScreenToSegment(pScr, end0, end1);\n },\n\n /**\n * Limit 3D coordinates to the bounding cube.\n *\n * @param {Array} c3d 3D coordinates [x,y,z]\n * @returns Array [Array, Boolean] containing [coords, corrected]. coords contains the updated 3D coordinates,\n * correct is true if the coords have been changed.\n */\n project3DToCube: function (c3d) {\n var cube = this.bbox3D,\n isOut = false;\n\n if (c3d[1] < cube[0][0]) {\n c3d[1] = cube[0][0];\n isOut = true;\n }\n if (c3d[1] > cube[0][1]) {\n c3d[1] = cube[0][1];\n isOut = true;\n }\n if (c3d[2] < cube[1][0]) {\n c3d[2] = cube[1][0];\n isOut = true;\n }\n if (c3d[2] > cube[1][1]) {\n c3d[2] = cube[1][1];\n isOut = true;\n }\n if (c3d[3] <= cube[2][0]) {\n c3d[3] = cube[2][0];\n isOut = true;\n }\n if (c3d[3] >= cube[2][1]) {\n c3d[3] = cube[2][1];\n isOut = true;\n }\n\n return [c3d, isOut];\n },\n\n /**\n * Intersect a ray with the bounding cube of the 3D view.\n * @param {Array} p 3D coordinates [w,x,y,z]\n * @param {Array} dir 3D direction vector of the line (array of length 3 or 4)\n * @param {Number} r direction of the ray (positive if r > 0, negative if r < 0).\n * @returns Affine ratio of the intersection of the line with the cube.\n */\n intersectionLineCube: function (p, dir, r) {\n var r_n, i, r0, r1, d;\n\n d = (dir.length === 3) ? dir : dir.slice(1);\n\n r_n = r;\n for (i = 0; i < 3; i++) {\n if (d[i] !== 0) {\n r0 = (this.bbox3D[i][0] - p[i + 1]) / d[i];\n r1 = (this.bbox3D[i][1] - p[i + 1]) / d[i];\n if (r < 0) {\n r_n = Math.max(r_n, Math.min(r0, r1));\n } else {\n r_n = Math.min(r_n, Math.max(r0, r1));\n }\n }\n }\n return r_n;\n },\n\n /**\n * Test if coordinates are inside of the bounding cube.\n * @param {array} p 3D coordinates [[w],x,y,z] of a point.\n * @returns Boolean\n */\n isInCube: function (p, polyhedron) {\n var q;\n if (p.length === 4) {\n if (p[0] === 0) {\n return false;\n }\n q = p.slice(1);\n }\n return (\n q[0] > this.bbox3D[0][0] - Mat.eps &&\n q[0] < this.bbox3D[0][1] + Mat.eps &&\n q[1] > this.bbox3D[1][0] - Mat.eps &&\n q[1] < this.bbox3D[1][1] + Mat.eps &&\n q[2] > this.bbox3D[2][0] - Mat.eps &&\n q[2] < this.bbox3D[2][1] + Mat.eps\n );\n },\n\n /**\n *\n * @param {JXG.Plane3D} plane1\n * @param {JXG.Plane3D} plane2\n * @param {Number} d Right hand side of Hesse normal for plane2 (it can be adjusted)\n * @returns {Array} of length 2 containing the coordinates of the defining points of\n * of the intersection segment, or false if there is no intersection\n */\n intersectionPlanePlane: function (plane1, plane2, d) {\n var ret = [false, false],\n p, q, r, w,\n dir;\n\n d = d || plane2.d;\n\n // Get one point of the intersection of the two planes\n w = Mat.crossProduct(plane1.normal.slice(1), plane2.normal.slice(1));\n w.unshift(0);\n\n p = Mat.Geometry.meet3Planes(\n plane1.normal,\n plane1.d,\n plane2.normal,\n d,\n w,\n 0\n );\n\n // Get the direction of the intersecting line of the two planes\n dir = Mat.Geometry.meetPlanePlane(\n plane1.vec1,\n plane1.vec2,\n plane2.vec1,\n plane2.vec2\n );\n\n // Get the bounding points of the intersecting segment\n r = this.intersectionLineCube(p, dir, Infinity);\n q = Mat.axpy(r, dir, p);\n if (this.isInCube(q)) {\n ret[0] = q;\n }\n r = this.intersectionLineCube(p, dir, -Infinity);\n q = Mat.axpy(r, dir, p);\n if (this.isInCube(q)) {\n ret[1] = q;\n }\n\n return ret;\n },\n\n intersectionPlaneFace: function (plane, face) {\n var ret = [],\n j, t,\n p, crds,\n p1, p2, c,\n f, le, x1, y1, x2, y2,\n dir, vec, w,\n mat = [], b = [], sol;\n\n w = Mat.crossProduct(plane.normal.slice(1), face.normal.slice(1));\n w.unshift(0);\n\n // Get one point of the intersection of the two planes\n p = Geometry.meet3Planes(\n plane.normal,\n plane.d,\n face.normal,\n face.d,\n w,\n 0\n );\n\n // Get the direction the intersecting line of the two planes\n dir = Geometry.meetPlanePlane(\n plane.vec1,\n plane.vec2,\n face.vec1,\n face.vec2\n );\n\n f = face.polyhedron.faces[face.faceNumber];\n crds = face.polyhedron.coords;\n le = f.length;\n for (j = 1; j <= le; j++) {\n p1 = crds[f[j - 1]];\n p2 = crds[f[j % le]];\n vec = [0, p2[1] - p1[1], p2[2] - p1[2], p2[3] - p1[3]];\n\n x1 = Math.random();\n y1 = Math.random();\n x2 = Math.random();\n y2 = Math.random();\n mat = [\n [x1 * dir[1] + y1 * dir[3], x1 * (-vec[1]) + y1 * (-vec[3])],\n [x2 * dir[2] + y2 * dir[3], x2 * (-vec[2]) + y2 * (-vec[3])]\n ];\n b = [\n x1 * (p1[1] - p[1]) + y1 * (p1[3] - p[3]),\n x2 * (p1[2] - p[2]) + y2 * (p1[3] - p[3])\n ];\n\n sol = Numerics.Gauss(mat, b);\n t = sol[1];\n if (t > -Mat.eps && t < 1 + Mat.eps) {\n c = [1, p1[1] + t * vec[1], p1[2] + t * vec[2], p1[3] + t * vec[3]];\n ret.push(c);\n }\n }\n\n return ret;\n },\n\n // TODO:\n // - handle non-closed polyhedra\n // - handle intersections in vertex, edge, plane\n intersectionPlanePolyhedron: function(plane, phdr) {\n var i, j, seg,\n p, first, pos, pos_akt,\n eps = 1e-12,\n points = [],\n x = [],\n y = [],\n z = [];\n\n for (i = 0; i < phdr.numberFaces; i++) {\n if (phdr.def.faces[i].length < 3) {\n // We skip intersection with points or lines\n continue;\n }\n\n // seg will be an array consisting of two points\n // that span the intersecting segment of the plane\n // and the face.\n seg = this.intersectionPlaneFace(plane, phdr.faces[i]);\n\n // Plane intersects the face in less than 2 points\n if (seg.length < 2) {\n continue;\n }\n\n if (seg[0].length === 4 && seg[1].length === 4) {\n // This test is necessary to filter out intersection lines which are\n // identical to intersections of axis planes (they would occur twice),\n // i.e. edges of bbox3d.\n for (j = 0; j < points.length; j++) {\n if (\n (Geometry.distance(seg[0], points[j][0], 4) < eps &&\n Geometry.distance(seg[1], points[j][1], 4) < eps) ||\n (Geometry.distance(seg[0], points[j][1], 4) < eps &&\n Geometry.distance(seg[1], points[j][0], 4) < eps)\n ) {\n break;\n }\n }\n if (j === points.length) {\n points.push(seg.slice());\n }\n }\n }\n\n // Handle the case that the intersection is the empty set.\n if (points.length === 0) {\n return { X: x, Y: y, Z: z };\n }\n\n // Concatenate the intersection points to a polygon.\n // If all went well, each intersection should appear\n // twice in the list.\n // __Attention:__ each face has to be planar!!!\n // Otherwise the algorithm will fail.\n first = 0;\n pos = first;\n i = 0;\n do {\n p = points[pos][i];\n if (p.length === 4) {\n x.push(p[1]);\n y.push(p[2]);\n z.push(p[3]);\n }\n i = (i + 1) % 2;\n p = points[pos][i];\n\n pos_akt = pos;\n for (j = 0; j < points.length; j++) {\n if (j !== pos && Geometry.distance(p, points[j][0]) < eps) {\n pos = j;\n i = 0;\n break;\n }\n if (j !== pos && Geometry.distance(p, points[j][1]) < eps) {\n pos = j;\n i = 1;\n break;\n }\n }\n if (pos === pos_akt) {\n console.log('Error face3d intersection update: did not find next', pos, i);\n break;\n }\n } while (pos !== first);\n x.push(x[0]);\n y.push(y[0]);\n z.push(z[0]);\n\n return { X: x, Y: y, Z: z };\n },\n\n /**\n * Generate mesh for a surface / plane.\n * Returns array [dataX, dataY] for a JSXGraph curve's updateDataArray function.\n * @param {Array|Function} func\n * @param {Array} interval_u\n * @param {Array} interval_v\n * @returns Array\n * @private\n *\n * @example\n * var el = view.create('curve', [[], []]);\n * el.updateDataArray = function () {\n * var steps_u = this.evalVisProp('stepsu'),\n * steps_v = this.evalVisProp('stepsv'),\n * r_u = Type.evaluate(this.range_u),\n * r_v = Type.evaluate(this.range_v),\n * func, ret;\n *\n * if (this.F !== null) {\n * func = this.F;\n * } else {\n * func = [this.X, this.Y, this.Z];\n * }\n * ret = this.view.getMesh(func,\n * r_u.concat([steps_u]),\n * r_v.concat([steps_v]));\n *\n * this.dataX = ret[0];\n * this.dataY = ret[1];\n * };\n *\n */\n getMesh: function (func, interval_u, interval_v) {\n var i_u, i_v, u, v,\n c2d, delta_u, delta_v,\n p = [0, 0, 0],\n steps_u = Type.evaluate(interval_u[2]),\n steps_v = Type.evaluate(interval_v[2]),\n dataX = [],\n dataY = [];\n\n delta_u = (Type.evaluate(interval_u[1]) - Type.evaluate(interval_u[0])) / steps_u;\n delta_v = (Type.evaluate(interval_v[1]) - Type.evaluate(interval_v[0])) / steps_v;\n\n for (i_u = 0; i_u <= steps_u; i_u++) {\n u = interval_u[0] + delta_u * i_u;\n for (i_v = 0; i_v <= steps_v; i_v++) {\n v = interval_v[0] + delta_v * i_v;\n if (Type.isFunction(func)) {\n p = func(u, v);\n } else {\n p = [func[0](u, v), func[1](u, v), func[2](u, v)];\n }\n c2d = this.project3DTo2D(p);\n dataX.push(c2d[1]);\n dataY.push(c2d[2]);\n }\n dataX.push(NaN);\n dataY.push(NaN);\n }\n\n for (i_v = 0; i_v <= steps_v; i_v++) {\n v = interval_v[0] + delta_v * i_v;\n for (i_u = 0; i_u <= steps_u; i_u++) {\n u = interval_u[0] + delta_u * i_u;\n if (Type.isFunction(func)) {\n p = func(u, v);\n } else {\n p = [func[0](u, v), func[1](u, v), func[2](u, v)];\n }\n c2d = this.project3DTo2D(p);\n dataX.push(c2d[1]);\n dataY.push(c2d[2]);\n }\n dataX.push(NaN);\n dataY.push(NaN);\n }\n\n return [dataX, dataY];\n },\n\n /**\n *\n */\n animateAzimuth: function () {\n var s = this.az_slide._smin,\n e = this.az_slide._smax,\n sdiff = e - s,\n newVal = this.az_slide.Value() + 0.1;\n\n this.az_slide.position = (newVal - s) / sdiff;\n if (this.az_slide.position > 1) {\n this.az_slide.position = 0.0;\n }\n this.board._change3DView = true;\n this.board.update();\n this.board._change3DView = false;\n\n this.timeoutAzimuth = setTimeout(function () {\n this.animateAzimuth();\n }.bind(this), 200);\n },\n\n /**\n *\n */\n stopAzimuth: function () {\n clearTimeout(this.timeoutAzimuth);\n this.timeoutAzimuth = null;\n },\n\n /**\n * Check if vertical dragging is enabled and which action is needed.\n * Default is shiftKey.\n *\n * @returns Boolean\n * @private\n */\n isVerticalDrag: function () {\n var b = this.board,\n key;\n if (!this.evalVisProp('verticaldrag.enabled')) {\n return false;\n }\n key = '_' + this.evalVisProp('verticaldrag.key') + 'Key';\n return b[key];\n },\n\n /**\n * Stop ignoring attribute r. After a call of view3d.setView, view3d.nextView,\n * view3d.previousView, or view3d.setCurrentView this attribute is ignored.\n * Call of view3d.freeR() will end this.\n * @see View3D#setView\n */\n freeR: function() {\n this.r = null;\n },\n\n /**\n * Sets camera view to the given values.\n * If the optional value r is supplied that value has priority until the next call of\n * view3d.setView or until a call of view3d.freeR().\n * In particular, the attribute r is ignored until a call of view3d.freeR().\n * @param {Number} az Value of azimuth.\n * @param {Number} el Value of elevation.\n * @param {Number} [r] Value of radius.\n *\n * @returns {Object} Reference to the view.\n * @see View3D#freeR\n * @see View3D#r\n * @see View3D#nextView\n * @see View3D#previousView\n * @see View3D#setCurrentView\n */\n setView: function (az, el, r) {\n // Set the distance to a fixed value.\n if (r !== undefined) {\n this.r = r;\n }\n r = this.getCameraDistance();\n\n this.az_slide.setValue(az);\n this.el_slide.setValue(el);\n this.board.update();\n\n return this;\n },\n\n /**\n * Changes view to the next view stored in the attribute `values`.\n *\n * @see View3D#values\n * @see View3D#setView\n * @see View3D#previousView\n * @see View3D#setCurrentView\n * @see View3D#freeR\n *\n * @returns {Object} Reference to the view.\n */\n nextView: function () {\n var views = this.evalVisProp('values'),\n n = this.visProp._currentview;\n\n n = (n + 1) % views.length;\n this.setCurrentView(n);\n\n return this;\n },\n\n /**\n * Changes view to the previous view stored in the attribute `values`.\n *\n * @see View3D#values\n * @see View3D#setView\n * @see View3D#nextView\n * @see View3D#setCurrentView\n * @see View3D#freeR\n *\n * @returns {Object} Reference to the view.\n */\n previousView: function () {\n var views = this.evalVisProp('values'),\n n = this.visProp._currentview;\n\n n = (n + views.length - 1) % views.length;\n this.setCurrentView(n);\n\n return this;\n },\n\n /**\n * Changes view to the determined view stored in the attribute `values`.\n *\n * @see View3D#values\n * @see View3D#nextView\n * @see View3D#previousView\n * @see View3D#setCurrentView\n * @see View3D#freeR\n *\n * @param {Number} n Index of view in attribute `values`.\n * @returns {Object} Reference to the view.\n */\n setCurrentView: function (n) {\n var views = this.evalVisProp('values');\n\n if (n < 0 || n >= views.length) {\n n = ((n % views.length) + views.length) % views.length;\n }\n\n this.setView(views[n][0], views[n][1], views[n][2]);\n this.visProp._currentview = n;\n\n return this;\n },\n\n /**\n * Controls 2-degree navigation in az direction using pointer.\n *\n * @private\n *\n * @param {event} evt the pointer event\n * @returns view\n */\n _az_elEventHandler: function (evt) {\n var smax = this.az_slide._smax,\n smin = this.az_slide._smin,\n speed = (smax - smin) / this.board.canvasWidth * (this.evalVisProp('az.pointer.speed')),\n deltaX, // = evt.movementX,\n deltaY, // = evt.movementY\n az = this.az_slide.Value(),\n el = this.el_slide.Value();\n\n deltaX = evt.screenX - this._lastPos.x;\n this._lastPos.x = evt.screenX;\n deltaY = evt.screenY - this._lastPos.y;\n this._lastPos.y = evt.screenY;\n\n // Doesn't allow navigation if another moving event is triggered\n if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) {\n return this;\n }\n\n if (this.evalVisProp('az.pointer.enabled') && (deltaX !== 0) && evt.key == null) {\n // delta *= (Math.abs(delta) > 100) ? 0.03 : 1;\n az += deltaX * speed;\n }\n if (this.evalVisProp('el.pointer.enabled') && (deltaY !== 0) && evt.key == null) {\n el += deltaY * speed;\n }\n\n // Project the calculated az value to a usable value in the interval [smin,smax]\n // Use modulo if continuous is true\n if (this.evalVisProp('az.continuous')) {\n az = Mat.wrap(az, smin, smax);\n } else {\n if (az > 0) {\n az = Math.min(smax, az);\n } else if (az < 0) {\n az = Math.max(smin, az);\n }\n }\n // Project the calculated el value to a usable value in the interval [smin,smax]\n // Use modulo if continuous is true and the trackball is disabled\n smax = this.el_slide._smax;\n smin = this.el_slide._smin;\n if (this.evalVisProp('el.continuous') && !this.trackballEnabled) {\n el = Mat.wrap(el, smin, smax);\n } else {\n if (el > 0) {\n el = Math.min(smax, el);\n } else if (el < 0) {\n el = Math.max(smin, el);\n }\n }\n\n this.setView(az, el);\n return this;\n },\n\n /**\n * Controls the navigation in az direction using either the keyboard or a pointer.\n *\n * @private\n *\n * @param {event} evt either the keydown or the pointer event\n * @returns view\n */\n _azEventHandler: function (evt) {\n var smax = this.az_slide._smax,\n smin = this.az_slide._smin,\n speed = (smax - smin) / this.board.canvasWidth * (this.evalVisProp('az.pointer.speed')),\n delta, // = evt.movementX,\n az = this.az_slide.Value(),\n el = this.el_slide.Value();\n\n delta = evt.screenX - this._lastPos.x;\n this._lastPos.x = evt.screenX;\n\n // Doesn't allow navigation if another moving event is triggered\n if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) {\n return this;\n }\n\n // Calculate new az value if keyboard events are triggered\n // Plus if right-button, minus if left-button\n if (this.evalVisProp('az.keyboard.enabled')) {\n if (evt.key === 'ArrowRight') {\n az = az + this.evalVisProp('az.keyboard.step') * Math.PI / 180;\n } else if (evt.key === 'ArrowLeft') {\n az = az - this.evalVisProp('az.keyboard.step') * Math.PI / 180;\n }\n }\n\n if (this.evalVisProp('az.pointer.enabled') && (delta !== 0) && evt.key == null) {\n // delta *= (Math.abs(delta) > 100) ? 0.03 : 1;\n az += delta * speed;\n }\n\n // Project the calculated az value to a usable value in the interval [smin,smax]\n // Use modulo if continuous is true\n if (this.evalVisProp('az.continuous')) {\n az = Mat.wrap(az, smin, smax);\n } else {\n if (az > 0) {\n az = Math.min(smax, az);\n } else if (az < 0) {\n az = Math.max(smin, az);\n }\n }\n\n this.setView(az, el);\n return this;\n },\n\n /**\n * Controls the navigation in el direction using either the keyboard or a pointer.\n *\n * @private\n *\n * @param {event} evt either the keydown or the pointer event\n * @returns view\n */\n _elEventHandler: function (evt) {\n var smax = this.el_slide._smax,\n smin = this.el_slide._smin,\n speed = (smax - smin) / this.board.canvasHeight * this.evalVisProp('el.pointer.speed'),\n delta, // = evt.movementY,\n az = this.az_slide.Value(),\n el = this.el_slide.Value();\n\n delta = evt.screenY - this._lastPos.y;\n this._lastPos.y = evt.screenY;\n\n // Doesn't allow navigation if another moving event is triggered\n if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) {\n return this;\n }\n\n // Calculate new az value if keyboard events are triggered\n // Plus if down-button, minus if up-button\n if (this.evalVisProp('el.keyboard.enabled')) {\n if (evt.key === 'ArrowUp') {\n el = el - this.evalVisProp('el.keyboard.step') * Math.PI / 180;\n } else if (evt.key === 'ArrowDown') {\n el = el + this.evalVisProp('el.keyboard.step') * Math.PI / 180;\n }\n }\n\n if (this.evalVisProp('el.pointer.enabled') && (delta !== 0) && evt.key == null) {\n // delta *= (Math.abs(delta) > 100) ? 0.05 : 1;\n el += delta * speed;\n }\n\n // Project the calculated el value to a usable value in the interval [smin,smax]\n // Use modulo if continuous is true and the trackball is disabled\n if (this.evalVisProp('el.continuous') && !this.trackballEnabled) {\n el = Mat.wrap(el, smin, smax);\n } else {\n if (el > 0) {\n el = Math.min(smax, el);\n } else if (el < 0) {\n el = Math.max(smin, el);\n }\n }\n\n this.setView(az, el);\n\n return this;\n },\n\n /**\n * Controls the navigation in bank direction using either the keyboard or a pointer.\n *\n * @private\n *\n * @param {event} evt either the keydown or the pointer event\n * @returns view\n */\n _bankEventHandler: function (evt) {\n var smax = this.bank_slide._smax,\n smin = this.bank_slide._smin,\n step, speed,\n delta = evt.deltaY, // Wheel event\n bank = this.bank_slide.Value();\n\n // Doesn't allow navigation if another moving event is triggered\n if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) {\n return this;\n }\n\n // Calculate new bank value if keyboard events are triggered\n // Plus if down-button, minus if up-button\n if (this.evalVisProp('bank.keyboard.enabled')) {\n step = this.evalVisProp('bank.keyboard.step') * Math.PI / 180;\n if (evt.key === '.' || evt.key === '<') {\n bank -= step;\n } else if (evt.key === ',' || evt.key === '>') {\n bank += step;\n }\n }\n\n if (this.evalVisProp('bank.pointer.enabled') && (delta !== 0) && evt.key == null) {\n speed = (smax - smin) / this.board.canvasHeight * this.evalVisProp('bank.pointer.speed');\n bank += delta * speed;\n\n // prevent the pointer wheel from scrolling the page\n evt.preventDefault();\n }\n\n // Project the calculated bank value to a usable value in the interval [smin,smax]\n if (this.evalVisProp('bank.continuous')) {\n // in continuous mode, wrap value around slider range\n bank = Mat.wrap(bank, smin, smax);\n } else {\n // in non-continuous mode, clamp value to slider range\n bank = Mat.clamp(bank, smin, smax);\n }\n\n this.bank_slide.setValue(bank);\n this.board.update();\n return this;\n },\n\n /**\n * Controls the navigation using either virtual trackball.\n *\n * @private\n *\n * @param {event} evt either the keydown or the pointer event\n * @returns view\n */\n _trackballHandler: function (evt) {\n var pos = this.board.getMousePosition(evt),\n x, y, dx, dy, center;\n\n center = new Coords(Const.COORDS_BY_USER, [this.llftCorner[0] + this.size[0] * 0.5, this.llftCorner[1] + this.size[1] * 0.5], this.board);\n x = pos[0] - center.scrCoords[1];\n y = pos[1] - center.scrCoords[2];\n\n dx = evt.screenX - this._lastPos.x;\n dy = evt.screenY - this._lastPos.y;\n this._lastPos.x = evt.screenX;\n this._lastPos.y = evt.screenY;\n\n this._trackball = {\n dx: dx,\n dy: -dy,\n x: x,\n y: -y\n };\n this.board.update();\n return this;\n },\n\n /**\n * Event handler for pointer down event. Triggers handling of all 3D navigation.\n *\n * @private\n * @param {event} evt\n * @returns view\n */\n pointerDownHandler: function (evt) {\n var neededButton, neededKey, target;\n\n this._hasMoveAzEl = false;\n this._hasMoveAz = false;\n this._hasMoveEl = false;\n this._hasMoveBank = false;\n this._hasMoveTrackball = false;\n\n if (this.board.mode !== this.board.BOARD_MODE_NONE) {\n return;\n }\n\n this.board._change3DView = true;\n\n this._lastPos.x = evt.screenX;\n this._lastPos.y = evt.screenY;\n\n if (this.evalVisProp('trackball.enabled')) {\n neededButton = this.evalVisProp('trackball.button');\n neededKey = this.evalVisProp('trackball.key');\n\n // Move events for virtual trackball\n if (\n (neededButton === -1 || neededButton === evt.button) &&\n (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))\n ) {\n // If outside is true then the event listener is bound to the document, otherwise to the div\n target = (this.evalVisProp('trackball.outside')) ? document : this.board.containerObj;\n Env.addEvent(target, 'pointermove', this._trackballHandler, this);\n this._hasMoveTrackball = true;\n }\n } else {\n if (this.evalVisProp('az.pointer.enabled') && this.evalVisProp('el.pointer.enabled')) {\n neededButton = this.evalVisProp('az.pointer.button');\n neededKey = this.evalVisProp('az.pointer.key');\n if (neededButton === this.evalVisProp('el.pointer.button') &&\n neededKey === this.evalVisProp('el.pointer.key')) {\n\n // Move events for azimuth and elevation\n if (\n (neededButton === -1 || neededButton === evt.button) &&\n (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) ||\n (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))\n ) {\n // If outside is true then the event listener is bound to the document, otherwise to the div\n target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj;\n\n if (target === ((this.evalVisProp('el.pointer.outside')) ? document : this.board.containerObj)) {\n Env.addEvent(target, 'pointermove', this._az_elEventHandler, this);\n this._hasMoveAzEl = true;\n }\n }\n }\n }\n if (!this._hasMoveAzEl) {\n if (this.evalVisProp('az.pointer.enabled')) {\n neededButton = this.evalVisProp('az.pointer.button');\n neededKey = this.evalVisProp('az.pointer.key');\n\n // Move events for azimuth\n if (\n (neededButton === -1 || neededButton === evt.button) &&\n (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))\n ) {\n // If outside is true then the event listener is bound to the document, otherwise to the div\n target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj;\n Env.addEvent(target, 'pointermove', this._azEventHandler, this);\n this._hasMoveAz = true;\n }\n }\n\n if (this.evalVisProp('el.pointer.enabled')) {\n neededButton = this.evalVisProp('el.pointer.button');\n neededKey = this.evalVisProp('el.pointer.key');\n\n // Events for elevation\n if (\n (neededButton === -1 || neededButton === evt.button) &&\n (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))\n ) {\n // If outside is true then the event listener is bound to the document, otherwise to the div\n target = (this.evalVisProp('el.pointer.outside')) ? document : this.board.containerObj;\n Env.addEvent(target, 'pointermove', this._elEventHandler, this);\n this._hasMoveEl = true;\n }\n }\n }\n if (this.evalVisProp('bank.pointer.enabled')) {\n neededButton = this.evalVisProp('bank.pointer.button');\n neededKey = this.evalVisProp('bank.pointer.key');\n\n // Events for bank\n if (\n (neededButton === -1 || neededButton === evt.button) &&\n (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))\n ) {\n // If `outside` is true, we bind the event listener to\n // the document. otherwise, we bind it to the div. we\n // register the event listener as active so it can\n // prevent the pointer wheel from scrolling the page\n target = (this.evalVisProp('bank.pointer.outside')) ? document : this.board.containerObj;\n Env.addEvent(target, 'wheel', this._bankEventHandler, this, { passive: false });\n this._hasMoveBank = true;\n }\n }\n }\n Env.addEvent(document, 'pointerup', this.pointerUpHandler, this);\n },\n\n /**\n * Event handler for pointer up event. Triggers handling of all 3D navigation.\n *\n * @private\n * @param {event} evt\n * @returns view\n */\n pointerUpHandler: function (evt) {\n var target;\n\n if (this._hasMoveAzEl) {\n target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj;\n Env.removeEvent(target, 'pointermove', this._az_elEventHandler, this);\n this._hasMoveAzEl = false;\n }\n if (this._hasMoveAz) {\n target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj;\n Env.removeEvent(target, 'pointermove', this._azEventHandler, this);\n this._hasMoveAz = false;\n }\n if (this._hasMoveEl) {\n target = (this.evalVisProp('el.pointer.outside')) ? document : this.board.containerObj;\n Env.removeEvent(target, 'pointermove', this._elEventHandler, this);\n this._hasMoveEl = false;\n }\n if (this._hasMoveBank) {\n target = (this.evalVisProp('bank.pointer.outside')) ? document : this.board.containerObj;\n Env.removeEvent(target, 'wheel', this._bankEventHandler, this);\n this._hasMoveBank = false;\n }\n if (this._hasMoveTrackball) {\n target = (this.evalVisProp('trackball.outside')) ? document : this.board.containerObj;\n Env.removeEvent(target, 'pointermove', this._trackballHandler, this);\n this._hasMoveTrackball = false;\n }\n Env.removeEvent(document, 'pointerup', this.pointerUpHandler, this);\n this.board._change3DView = false;\n this.board.mode = this.board.BOARD_MODE_NONE;\n }\n});\n\n/**\n * @class A View3D element provides the container and the methods to create and display 3D elements.\n * @pseudo\n * @description A View3D element provides the container and the methods to create and display 3D elements.\n * It is contained in a JSXGraph board.\n * \n * It is advisable to disable panning of the board by setting the board attribute \"pan\":\n * \n * The start position of the camera can be adjusted by the attributes {@link View3D#az}, {@link View3D#el}, and {@link View3D#bank}.\n *\n * @name View3D\n * @augments JXG.View3D\n * @constructor\n * @type Object\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Array_Array_Array} lower,dim,cube Here, lower is an array of the form [x, y] and\n * dim is an array of the form [w, h].\n * The arrays [x, y] and [w, h] define the 2D frame into which the 3D cube is\n * (roughly) projected. If the view's azimuth=0 and elevation=0, the 3D view will cover a rectangle with lower left corner\n * [x,y] and side lengths [w, h] of the board.\n * The array 'cube' is of the form [[x1, x2], [y1, y2], [z1, z2]]\n * which determines the coordinate ranges of the 3D cube.\n *\n * @example\n * var bound = [-4, 6];\n * var view = board.create('view3d',\n * [[-4, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'parallel',\n * trackball: {enabled:true},\n * });\n *\n * var curve = view.create('curve3d', [\n * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),\n * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),\n * (t) => Math.sin(3 * t),\n * [-Math.PI, Math.PI]\n * ], { strokeWidth: 4 });\n *\n * \n * At the time being, the input arrays are NOT dynamic, i.e. can not be given as functions.\n *\n * @name Axis3D\n * @augments Arrow\n * @constructor\n * @type Object\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Array_Array} start,end Two arrays of length 3 for the start point and the end point of the axis.\n *\n */\nJXG.createAxis3D = function (board, parents, attributes) {\n var view = parents[0],\n attr = Type.copyAttributes(attributes, board.options, 'axis3d');\n\n return view.create('line3d', parents.slice(1), attr);\n};\nJXG.registerElement('axis3d', JXG.createAxis3D);\n\n// JXG.createAxis3DOld = function (board, parents, attributes) {\n// var view = parents[0],\n// attr,\n// start = parents[1],\n// end = parents[2],\n// el_start,\n// el_end,\n// el;\n//\n// // Use 2D points to create axis\n// attr = Type.copyAttributes(attributes.point1, board.options, \"axis3d\", 'point1');\n// attr.element3d = true; // Needed to avoid update during change of view\n// el_start = view.create(\n// \"point\",\n// [\n// (function (xx, yy, zz) {\n// return function () {\n// return view.project3DTo2D(xx, yy, zz)[1];\n// };\n// })(start[0], start[1], start[2]),\n// (function (xx, yy, zz) {\n// return function () {\n// return view.project3DTo2D(xx, yy, zz)[2];\n// };\n// })(start[0], start[1], start[2])\n// ],\n// attr\n// );\n//\n// attr = Type.copyAttributes(attributes.point2, board.options, \"axis3d\", 'point2');\n// attr.element3d = true; // Needed to avoid update during change of view\n// el_end = view.create(\n// \"point\",\n// [\n// (function (xx, yy, zz) {\n// return function () {\n// return view.project3DTo2D(xx, yy, zz)[1];\n// };\n// })(end[0], end[1], end[2]),\n// (function (xx, yy, zz) {\n// return function () {\n// return view.project3DTo2D(xx, yy, zz)[2];\n// };\n// })(end[0], end[1], end[2])\n// ],\n// attr\n// );\n//\n// attr = Type.copyAttributes(attributes, board.options, 'axis3d');\n// attr.element3d = true; // Needed to avoid update during change of view\n// el = view.create(\"arrow\", [el_start, el_end], attr);\n//\n// return el;\n// };\n\n/**\n * @class Display a rectangular mesh on a 3D plane element.\n * @pseudo\n * @description Create a (rectangular) mesh - i.e. grid lines - on a plane3D element.\n * \n * At the time being, the mesh is not connected to the plane. The connecting element is simply the\n * parameter point.\n *\n * @name Mesh3D\n * @augments Curve\n * @constructor\n * @type Object\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Array_Array_Array_Array_Array} point,direction1,direction2,range1,range2 point is an array of length 3\n * determining the starting point of the grid. direction1 and direction2 are arrays of length 3 for the directions of the grid.\n * range1 and range2 (arrays of length 2) give the respective ranges.\n * All parameters can be supplied as functions returning an appropriate data type.\n *\n */\nJXG.createMesh3D = function (board, parents, attributes) {\n var view = parents[0],\n attr, el;\n\n attr = Type.copyAttributes(attributes, board.options, 'mesh3d');\n attr.element3d = true; // Needed to avoid update during change of view\n el = view.create(\"curve\", [[], []], attr);\n\n el.point = parents[1];\n el.direction1 = parents[2];\n el.direction2 = parents[3];\n el.range1 = parents[4];\n el.range2 = parents[5];\n\n /**\n * @ignore\n */\n el.updateDataArray = function () {\n var range1 = Type.evaluate(this.range1),\n range2 = Type.evaluate(this.range2),\n s1 = range1[0],\n e1 = range1[1],\n s2 = range2[0],\n e2 = range2[1],\n l1, l2, res, i,\n v1 = [0, 0, 0],\n v2 = [0, 0, 0],\n step_u = this.evalVisProp('stepwidthu'),\n step_v = this.evalVisProp('stepwidthv'),\n q = [0, 0, 0];\n\n this.dataX = [];\n this.dataY = [];\n\n if (Type.isFunction(this.point)) {\n q = this.point();\n } else {\n if (Type.isPoint3D(this.point)) {\n q = this.point.coords;\n } else {\n for (i = 0; i < this.point.length; i++) {\n q[i] = Type.evaluate(this.point[i]);\n }\n }\n }\n if (Type.isFunction(this.direction1)) {\n v1 = Type.evaluate(this.direction1);\n } else {\n for (i = 0; i < this.direction1.length; i++) {\n v1[i] = Type.evaluate(this.direction1[i]);\n }\n }\n if (Type.isFunction(this.direction2)) {\n v2 = Type.evaluate(this.direction2);\n } else {\n for (i = 0; i < this.direction2.length; i++) {\n v2[i] = Type.evaluate(this.direction2[i]);\n }\n }\n if (q.length === 4) {\n q = q.slice(1);\n }\n if (v1.length === 4) {\n v1 = v1.slice(1);\n }\n if (v2.length === 4) {\n v2 = v2.slice(1);\n }\n\n l1 = JXG.Math.norm(v1, 3);\n l2 = JXG.Math.norm(v2, 3);\n for (i = 0; i < 3; i++) {\n v1[i] /= l1;\n v2[i] /= l2;\n }\n\n // sol = Mat.Geometry.getPlaneBounds(v1, v2, q, s1, e1);\n // if (sol !== null) {\n // s1 = sol[0];\n // e1 = sol[1];\n // s2 = sol[2];\n // e2 = sol[3];\n // }\n\n res = view.getMesh(\n [\n function (u, v) {\n return q[0] + u * v1[0] + v * v2[0];\n },\n function (u, v) {\n return q[1] + u * v1[1] + v * v2[1];\n },\n function (u, v) {\n return q[2] + u * v1[2] + v * v2[2];\n }\n ],\n [Math.ceil(s1), Math.floor(e1), (Math.ceil(e1) - Math.floor(s1)) / step_u],\n [Math.ceil(s2), Math.floor(e2), (Math.ceil(e2) - Math.floor(s2)) / step_v]\n );\n this.dataX = res[0];\n this.dataY = res[1];\n };\n\n return el;\n};\n\nJXG.registerElement(\"mesh3d\", JXG.createMesh3D);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Aaron Fenyes,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * If the radius has a negative value, its absolute value is taken. If the radius evaluates to NaN,\n * the circle is not displayed. This is convenient for constructing an intersection circle, which is empty when its parents do not intersect.\n * @name Circle3D\n * @augments JXG.Circle3D\n * @constructor\n * @type JXG.Circle3D\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point,Array,Function_Array,Function_Number,Function} center,normal,radius The center must be given as a {@link JXG.Point}, array or function (see {@link JXG.providePoints}).\n * The normal vector can be given as an array of four numbers (i.e. homogeneous coordinates [0, x, y, z]) or a function returning an array of length 4\n * and the radius can be given as a number (which will create a circle with a fixed radius) or a function.\n * \n * If the radius is supplied as a number or the output of a function, its absolute value is taken. When the radius evaluates to NaN, the circle does not display.\n */\nJXG.createCircle3D = function (board, parents, attributes) {\n var view = parents[0],\n attr = Type.copyAttributes(attributes, board.options, 'circle3d'),\n center = Type.providePoints3D(view, [parents[1]], attributes, 'circle3d', ['point'])[0],\n normal = parents[2],\n radius = parents[3],\n el;\n\n if (Type.isArray(normal) && normal.length === 3) {\n normal.unshift(0);\n }\n // Create element\n el = new JXG.Circle3D(view, center, normal, radius, attr);\n\n // Update scene tree\n el.curve.addParents([el]);\n el.addChild(el.curve);\n\n el.update();\n return el;\n};\n\nJXG.registerElement(\"circle3d\", JXG.createCircle3D);\n\n/**\n * @class The circle that is the intersection of two elements (plane3d or sphere3d) in 3D.\n *\n * @pseudo\n * @name IntersectionCircle3D\n * @augments JXG.Circle3D\n * @constructor\n * @type JXG.Circle3D\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Sphere3D_JXG.Sphere3D|JXG.Plane3D} el1,el2 The result will be the intersection of el1 and el2.\n * @example\n * // Create the intersection circle of two spheres\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[0, 3], [0, 3], [0, 3]]],\n * {\n * xPlaneRear: {fillOpacity: 0.2, gradient: null},\n * yPlaneRear: {fillOpacity: 0.2, gradient: null},\n * zPlaneRear: {fillOpacity: 0.2, gradient: null}\n * }\n * );\n * var a1 = view.create('point3d', [-1, 0, 0]);\n * var a2 = view.create('point3d', [1, 0, 0]);\n *\n * var s1 = view.create(\n * 'sphere3d',\n * [a1, 2],\n * {fillColor: '#00ff80'}\n * );\n * var s2 = view.create(\n * 'sphere3d',\n * [a2, 2],\n * {fillColor: '#ff0000'}\n * );\n *\n * var i = view.create('intersectioncircle3d', [s1, s2]);\n *\n * \n * Plot a vector field either given by three functions\n * f1(x, y, z), f2(x, y, z), and f3(x, y, z) or by a function f(x, y, z)\n * returning an array of size 3.\n *\n * @pseudo\n * @name Vectorfield3D\n * @augments JXG.Curve3D\n * @constructor\n * @type JXG.Curve3D\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * Parameter options:\n * @param {Array|Function|String} F Either an array containing three functions f1(x, y, z), f2(x, y, z),\n * and f3(x, y) or function f(x, y, z) returning an array of length 3.\n * @param {Array} xData Array of length 3 containing start value for x, number of steps,\n * end value of x. The vector field will contain (number of steps) + 1 vectors in direction of x.\n * @param {Array} yData Array of length 3 containing start value for y, number of steps,\n * end value of y. The vector field will contain (number of steps) + 1 vectors in direction of y.\n * @param {Array} zData Array of length 3 containing start value for z, number of steps,\n * end value of z. The vector field will contain (number of steps) + 1 vectors in direction of z.\n *\n * @example\n * const view = board.create('view3d',\n * [\n * [-6, -3],\n * [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]\n * ], {});\n *\n * var vf = view.create('vectorfield3d', [\n * [(x, y, z) => Math.cos(y), (x, y, z) => Math.sin(x), (x, y, z) => z],\n * [-2, 5, 2], // x from -2 to 2 in 5 steps\n * [-2, 5, 2], // y\n * [-2, 5, 2] // z\n * ], {\n * strokeColor: 'red',\n * scale: 0.5\n * });\n *\n * The 3D line is defined by a point (or coordinate array [x, y, z])\n * a direction given as array [x, y, z] and an optional range\n * given as array [s, e]. The default value for the range is [-Infinity, Infinity].\n * \n * All coordinate arrays can be supplied as functions returning a coordinate array.\n *\n * @pseudo\n * @name Plane3D\n * @augments JXG.GeometryElement3D\n * @constructor\n * @throws {Exception} If the element cannot be constructed with the given parent\n * objects an exception is thrown.\n *\n * @param {JXG.Point3D,array,function_JXG.Line3D,array,function_JXG.Line3D,array,function_array,function_array,function} point,direction1,direction2,[range1],[range2] The plane is defined by point, direction1, direction2, range1, and range2.\n * \n * That is, all numbers can also be provided as functions returning a number.\n * \n * At the time being, text display is independent from the camera view.\n *\n * @name Text3D\n * @augments JXG.Text3D\n * @augments Text\n * @constructor\n * @throws {Exception} If the element cannot be constructed with the given parent\n * objects an exception is thrown.\n * @param {number,function_number,function_number,function_String,function_JXG.GeometryElement3D} x,y,z,txt,[slide=undefined]\n * The coordinates are given as x, y, z consisting of numbers of functions and the text.\n * If an optional 3D element \"slide\" is supplied, the point is a glider on that element.\n * @param {array,function_string_JXG.GeometryElement3D}} F,txt,[slide=undefined] Alternatively, the coordinates can be supplied as array or function returning an array.\n * If an optional 3D element \"slide\" is supplied, the point is a glider on that element.\n *\n * @example\n * var bound = [-4, 6];\n * var view = board.create('view3d',\n * [[-4, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'central'\n * });\n *\n * var txt1 = view.create('text3d', [[1, 2, 1], 'hello'], {\n * fontSize: 20,\n * });\n *\n * \n * At the time being, the ticks are not connected to the line or axis. The connecting element is simply the\n * parameter point.\n *\n * @name Ticks3D\n * @augments Curve\n * @constructor\n * @type Object\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Array_Array_Number_Array} point,direction1,length,direction2 point is an array of length 3\n * determining the starting point of the grid. direction1 and direction2 are arrays of length 3. Here, direction1 is the direction\n * of the 3D line, direction2 is the direction of the ticks.\n * \"length\" is the length of the line.\n * All parameters can be supplied as functions returning an appropriate data type.\n * \n * The step width of the ticks is determined by the attribute \"ticksDistance\".\n *\n */\nJXG.createTicks3D = function (board, parents, attributes) {\n var view = parents[0],\n point = parents[1],\n dir1 = parents[2],\n length = parents[3],\n dir2 = parents[4],\n el, attr;\n\n attr = Type.copyAttributes(attributes, board.options, 'ticks3d');\n el = view.create(\"curve\", [[], []], attr);\n\n el.point = point;\n el.direction1 = dir1;\n el.len = length;\n el.direction2 = dir2;\n\n el.drawLabels = function(attr) {\n var s1 = 0,\n e1 = this.len,\n step = this.evalVisProp('ticksdistance'),\n range2 = this.evalVisProp('tickendings'),\n mh = this.evalVisProp('majorheight'),\n e2,\n l1, l2,\n i,\n u, val, p,\n v1 = [0, 0, 0],\n v2 = [0, 0, 0],\n q = [0, 0, 0],\n labels = [];\n\n mh /= Math.sqrt(board.unitX * board.unitY); // Very crude estimation of tick length\n e2 = mh * range2[1] * 2;\n\n this.dataX = [];\n this.dataY = [];\n\n if (Type.isFunction(this.point)) {\n q = this.point().slice(1);\n } else {\n for (i = 0; i < 3; i++) {\n q[i] = Type.evaluate(this.point[i]);\n }\n }\n for (i = 0; i < 3; i++) {\n v1[i] = Type.evaluate(this.direction1[i]);\n v2[i] = Type.evaluate(this.direction2[i]);\n }\n\n l1 = JXG.Math.norm(v1, 3);\n l2 = JXG.Math.norm(v2, 3);\n for (i = 0; i < 3; i++) {\n v1[i] /= l1;\n v2[i] /= l2;\n }\n\n if (Math.abs(step) < Mat.eps) {\n return;\n }\n for (u = s1; u <= e1; u += step) {\n // Label\n p = [\n q[0] + u * v1[0] + e2 * v2[0],\n q[1] + u * v1[1] + e2 * v2[1],\n q[2] + u * v1[2] + e2 * v2[2]\n ];\n for (i = 0; i < 3; i++) {\n if (v1[i] !== 0) {\n val = q[i] + u * v1[i];\n }\n }\n labels.push(view.create('text3d', [p, val], attr));\n }\n return labels;\n };\n\n if (el.evalVisProp('drawlabels')) {\n el.labels = el.drawLabels(attr.label);\n }\n\n /**\n * @ignore\n */\n el.updateDataArray = function () {\n var s1 = 0,\n e1 = this.len,\n step = this.evalVisProp('ticksdistance'),\n range2 = this.evalVisProp('tickendings'),\n mh = this.evalVisProp('majorheight'),\n s2, e2,\n l1, l2,\n i,\n u, c2d, p,\n v1 = [0, 0, 0],\n v2 = [0, 0, 0],\n q = [0, 0, 0];\n\n mh /= Math.sqrt(board.unitX * board.unitY); // Very crude estimation of tick length\n s2 = mh * (-range2[0]);\n e2 = mh * range2[1];\n\n this.dataX = [];\n this.dataY = [];\n\n if (Type.isFunction(this.point)) {\n q = this.point().slice(1);\n } else {\n for (i = 0; i < 3; i++) {\n q[i] = Type.evaluate(this.point[i]);\n }\n }\n for (i = 0; i < 3; i++) {\n v1[i] = Type.evaluate(this.direction1[i]);\n v2[i] = Type.evaluate(this.direction2[i]);\n }\n\n l1 = JXG.Math.norm(v1, 3);\n l2 = JXG.Math.norm(v2, 3);\n for (i = 0; i < 3; i++) {\n v1[i] /= l1;\n v2[i] /= l2;\n }\n\n if (Math.abs(step) < Mat.eps) {\n return;\n }\n for (u = s1; u <= e1; u += step) {\n p = [\n q[0] + u * v1[0] + s2 * v2[0],\n q[1] + u * v1[1] + s2 * v2[1],\n q[2] + u * v1[2] + s2 * v2[2]\n ];\n c2d = view.project3DTo2D(p);\n this.dataX.push(c2d[1]);\n this.dataY.push(c2d[2]);\n p = [\n q[0] + u * v1[0] + e2 * v2[0],\n q[1] + u * v1[1] + e2 * v2[1],\n q[2] + u * v1[2] + e2 * v2[2]\n ];\n c2d = view.project3DTo2D(p);\n this.dataX.push(c2d[1]);\n this.dataY.push(c2d[2]);\n this.dataX.push(NaN);\n this.dataY.push(NaN);\n }\n };\n\n return el;\n};\n\nJXG.registerElement(\"ticks3d\", JXG.createTicks3D);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Aaron Fenyes,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * JSXGraph does not require and does not check planarity of the polygon.\n *\n * @pseudo\n * @constructor\n * @name Polygon3D\n * @type JXG.Polygon3D\n * @augments JXG.Polygon3D\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Array} vertices The polygon's vertices.\n */\nJXG.createPolygon3D = function (board, parents, attributes) {\n var view = parents[0],\n el, i, le, obj,\n points = [],\n points2d = [],\n attr,\n attr_points,\n is_transform = false;\n\n attr = Type.copyAttributes(attributes, board.options, 'polygon3d');\n obj = board.select(parents[1]);\n if (obj === null) {\n // This is necessary if the original polygon is defined in another board.\n obj = parents[1];\n }\n // TODO: Number of points? Is the last point equal to the first point?\n if (\n Type.isObject(obj) &&\n obj.type === Const.OBJECT_TYPE_POLYGON3D &&\n Type.isTransformationOrArray(parents[2])\n ) {\n is_transform = true;\n le = obj.vertices.length - 1;\n attr_points = Type.copyAttributes(attributes, board.options, 'polygon3d', 'vertices');\n for (i = 0; i < le; i++) {\n if (attr_points.withlabel) {\n attr_points.name =\n obj.vertices[i].name === '' ? '' : obj.vertices[i].name + \"'\";\n }\n points.push(board.create('point3d', [obj.vertices[i], parents[2]], attr_points));\n }\n } else if (Type.isArray(parents[1]) && parents[1].every((x) => Type.isPoint3D(x))) {\n // array of points [A, B, C]\n // TODO mixing points and coords arrays\n points = parents[1];\n } else {\n points = Type.providePoints3D(view, parents.slice(1), attributes, 'polygon3d', ['vertices']);\n if (points === false) {\n throw new Error(\n \"JSXGraph: Can't create polygon3d with parent types other than 'point' and 'coordinate arrays' or a function returning an array of coordinates. Alternatively, a polygon3d and a transformation can be supplied\"\n );\n }\n }\n\n el = new JXG.Polygon3D(view, points, attr);\n el.isDraggable = true;\n\n attr = el.setAttr2D(attr);\n for (i = 0; i < points.length; i++) {\n points2d.push(points[i].element2D);\n }\n el.element2D = board.create('polygon', points2d, attr);\n el.element2D.view = view;\n el.element2D.dump = false;\n el.addChild(el.element2D);\n el.inherits.push(el.element2D);\n el.element2D.setParents(el);\n\n // Put the points in their positions\n if (is_transform) {\n el.prepareUpdate().update().updateVisibility().updateRenderer();\n le = obj.vertices.length - 1;\n for (i = 0; i < le; i++) {\n points[i].prepareUpdate().update().updateVisibility().updateRenderer();\n }\n }\n\n return el;\n};\nJXG.registerElement('polygon3d', JXG.createPolygon3D);","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * Sets the fillColor of the adjoint 2D curve.\n * @name shader\n * @memberOf Face3D\n * @function\n * @returns {Number} zIndex of the face\n */\n shader: function() {\n var hue, sat, light, angle, hsl,\n sun, angles,\n abs,\n lightObj,\n minFace, maxFace,\n minLight, maxLight;\n\n if (this.evalVisProp('shader.enabled')) {\n hue = this.evalVisProp('shader.hue');\n sat = this.evalVisProp('shader.saturation');\n minLight = this.evalVisProp('shader.minlightness');\n maxLight = this.evalVisProp('shader.maxlightness');\n\n if (this.evalVisProp('shader.type').toLowerCase() === 'angle') {\n lightObj = this.evalVisProp('shader.light');\n\n switch (lightObj.type) {\n // 1: lighting==camera (default),\n // 2: Fixed: angle(object, camera),\n // 3: Fixed: angle(lighting, camera)\n case 2: // Fixed: angle(object, camera)\n angles = {\n az: lightObj.az * Math.PI / 180,\n el: lightObj.el * Math.PI / 180,\n bank: lightObj.bank * Math.PI / 180\n };\n sun = this.getRotationFromAngles(angles)[3];\n abs = lightObj.dir;\n break;\n case 3: // Fixed: angle(lighting, camera)\n angles = {\n az: this.view.angles.az + lightObj.az * Math.PI / 180,\n el: this.view.angles.el + lightObj.el * Math.PI / 180,\n bank: this.view.angles.bank\n };\n sun = this.getRotationFromAngles(angles)[3];\n abs = lightObj.dir;\n break;\n default: // Fixed: angle(lighting, camera) = 0\n sun = this.view.matrix3DRotShift[3];\n abs = lightObj.dir;\n }\n\n // angle = Mat.innerProduct(this.view.matrix3DRotShift[3], this.normal);\n angle = Mat.innerProduct(sun, this.normal);\n angle = (abs === 0) ? Math.abs(angle) : ((abs < 0) ? -angle : angle);\n light = minLight + (maxLight - minLight) * angle;\n } else {\n // zIndex\n maxFace = this.view.zIndexMax;\n minFace = this.view.zIndexMin;\n light = minLight + (maxLight - minLight) * ((this.zIndex - minFace) / (maxFace - minFace));\n }\n\n // hsl = `hsl(${hue}, ${sat}%, ${light}%)`;\n hsl = 'hsl(' + hue + ',' + sat +'%,' + light + '%)';\n\n this.element2D.visProp.fillcolor = hsl;\n this._shadingDone = true;\n return this.zIndex;\n }\n }\n }\n);\n\n/**\n * @class This element creates a 3D face.\n * @pseudo\n * @description A 3D faces is TODO\n *\n * @name Face3D\n * @augments Curve\n * @constructor\n * @type Object\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n */\nJXG.createFace3D = function (board, parents, attributes) {\n var view = parents[0],\n polyhedron = parents[1],\n faceNumber = parents[2],\n attr, el;\n\n // TODO Throw new Error\n attr = Type.copyAttributes(attributes, board.options, 'face3d');\n el = new JXG.Face3D(view, polyhedron, faceNumber, attr);\n\n attr = el.setAttr2D(attr);\n el.element2D = view.create(\"curve\", [[], []], attr);\n el.element2D.view = view;\n el.element2D.dump = false;\n\n /**\n * @class\n * @ignore\n */\n el.element2D.updateDataArray = function () {\n var ret = el.updateDataArray2D();\n this.dataX = ret.X;\n this.dataY = ret.Y;\n };\n // Deactivate hasPoint to increase speed.\n // This is be too agressive, e.g. for the upcoming\n // rotation3D circles (SoftwarePraktikum)\n // We may enable have to enable hasPoint() for\n // click events.\n el.element2D.hasPoint = function() {};\n\n el.addChild(el.element2D);\n el.inherits.push(el.element2D);\n el.element2D.setParents(el);\n\n el.element2D.prepareUpdate().update();\n if (!board.isSuspendedUpdate) {\n el.element2D.updateVisibility().updateRenderer();\n }\n\n return el;\n};\n\nJXG.registerElement(\"face3d\", JXG.createFace3D);\n\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * If the radius is supplied as number or the output of a function, its absolute value is taken.\n *\n * @example\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[0, 3], [0, 3], [0, 3]]],\n * {\n * xPlaneRear: {fillOpacity: 0.2, gradient: null},\n * yPlaneRear: {fillOpacity: 0.2, gradient: null},\n * zPlaneRear: {fillOpacity: 0.2, gradient: null}\n * }\n * );\n *\n * // Two points\n * var center = view.create(\n * 'point3d',\n * [1.5, 1.5, 1.5],\n * {\n * withLabel: false,\n * size: 5,\n * }\n * );\n * var point = view.create(\n * 'point3d',\n * [2, 1.5, 1.5],\n * {\n * withLabel: false,\n * size: 5\n * }\n * );\n *\n * // Sphere\n * var sphere = view.create(\n * 'sphere3d',\n * [center, point],\n * {}\n * );\n *\n * \n *
\n *\n * @private\n * @param {Number} x x-coordinate of the center (screen coordinates)\n * @param {Number} y y-coordinate of the center (screen coordinates)\n * @param {Number} w width of the box in pixel\n * @param {Number} h width of the box in pixel\n * @param {Array} [whiteList] array of ids which should be ignored\n * @return {Number} Number of overlapping elements\n */\n getNumberOfConflicts: function(x, y, w, h, whiteList) {\n whiteList = whiteList || [];\n var count = 0,\n i, obj,\n coords,\n saveHasInnerPoints,\n savePointPrecision = this.board.options.precision.hasPoint,\n objCenterX, objCenterY,\n objWidth, objHeight;\n\n // set a new precision for hasPoint\n // this.board.options.precision.hasPoint = Math.max(w, h) * 0.5;\n this.board.options.precision.hasPoint = (w + h) * 0.3;\n\n // loop over all objects\n for (i = 0; i < this.board.objectsList.length; i++) {\n obj = this.board.objectsList[i];\n\n //Skip the object if it is not meant to influence label position\n if (\n obj.visPropCalc.visible &&\n obj !== this &&\n whiteList.indexOf(obj.id) === -1 &&\n obj.evalVisProp('ignoreforlabelautoposition') !== true\n ) {\n // Save hasinnerpoints and temporarily disable to handle polygon areas\n saveHasInnerPoints = obj.visProp.hasinnerpoints;\n obj.visProp.hasinnerpoints = false;\n\n // If is label or point use other conflict detection\n if (\n obj.visProp.islabel ||\n obj.elementClass === Const.OBJECT_CLASS_POINT\n ) {\n // get coords and size of the object\n coords = obj.coords.scrCoords;\n objCenterX = coords[1];\n objCenterY = coords[2];\n objWidth = obj.size[0];\n objHeight = obj.size[1];\n\n // move coords to the center of the label\n if (obj.visProp.islabel) {\n // Vertical adjustment\n if (obj.visProp.anchory === 'top') {\n objCenterY = objCenterY + objHeight / 2;\n } else {\n objCenterY = objCenterY - objHeight / 2;\n }\n\n // Horizontal adjustment\n if (obj.visProp.anchorx === 'left') {\n objCenterX = objCenterX + objWidth / 2;\n } else {\n objCenterX = objCenterX - objWidth / 2;\n }\n } else {\n // Points are treated dimensionless\n objWidth = 0;\n objHeight = 0;\n }\n\n // Check for overlap\n if (\n Math.abs(objCenterX - x) < (w + objWidth) / 2 &&\n Math.abs(objCenterY - y) < (h + objHeight) / 2\n ) {\n count++;\n }\n\n //if not label or point check conflict with hasPoint\n } else if (obj.hasPoint(x, y)) {\n count++;\n }\n\n // Restore original hasinnerpoints\n obj.visProp.hasinnerpoints = saveHasInnerPoints;\n }\n }\n\n // Restore original precision\n this.board.options.precision.hasPoint = savePointPrecision;\n\n return count;\n },\n /**\n * Calculates the score of a label position with a given radius and angle. The score is calculated by the following rules:\n * \n *
\n *\n * @param {number} radius radius in pixels\n * @param {number} angle angle in radians\n * @returns {number} Position score, higher values indicate better positions\n */\n calculateScore: function(radius, angle) {\n var x, y, co, si, angleCurrentOffset, angleDifference,\n score = 0,\n cornerPoint = [0,0],\n w = this.getSize()[0],\n h = this.getSize()[1],\n anchorCoords,\n currentOffset = this.evalVisProp('offset'),\n boundingBox = this.board.getBoundingBox();\n\n if (this.evalVisProp('islabel') && Type.exists(this.element)) {\n anchorCoords = this.element.getLabelAnchor().scrCoords;\n } else {\n return 0;\n }\n co = Math.cos(angle);\n si = Math.sin(angle);\n\n // calculate new position with srccoords, radius and angle\n x = anchorCoords[1] + radius * co;\n y = anchorCoords[2] - radius * si;\n\n // if the label was placed on the left side of the element, the anchorx is set to \"right\"\n if (co < 0) {\n cornerPoint[0] = x - w;\n x -= w / 2;\n } else {\n cornerPoint[0] = x + w;\n x += w / 2;\n }\n\n // If the label was placed on the bottom side of the element, so the anchory is set to \"top\"\n if (si < 0) {\n cornerPoint[1] = y + h;\n y += h / 2;\n } else {\n cornerPoint[1] = y - h;\n y -= h / 2;\n }\n\n // If label was not in bounding box, score is reduced by 1\n if(\n cornerPoint[0] < 0 ||\n cornerPoint[0] > (boundingBox[2] - boundingBox[0]) * this.board.unitX ||\n cornerPoint[1] < 0 ||\n cornerPoint[1] > (boundingBox[1] - boundingBox[3]) * this.board.unitY\n ) {\n score -= 1;\n }\n\n // Per conflict, score is reduced by 1\n score -= this.getNumberOfConflicts(x, y, w, h, Type.evaluate(this.visProp.autopositionwhitelist));\n\n // Calculate displacement, minimum score is 0 if radius is minRadius, maximum score is < 1 when radius is maxRadius\n score -= radius / this.evalVisProp('autopositionmindistance') / 10 - 0.1;\n\n // Calculate angle between current offset and new offset\n angleCurrentOffset = Math.atan2(currentOffset[1], currentOffset[0]);\n\n // If angle is negative, add 2*PI to get positive angle\n if (angleCurrentOffset < 0) {\n angleCurrentOffset += 2 * Math.PI;\n }\n\n // Calculate displacement by angle between original label position and new label position,\n // use cos to check if angle is on the right side.\n // If both angles are on the right side and more than 180° apart, add 2*PI. e.g. 0.1 and 6.1 are near each other\n if (co > 0 && Math.cos(angleCurrentOffset) > 0 && Math.abs(angle - angleCurrentOffset) > Math.PI) {\n angleDifference = Math.abs(angle - angleCurrentOffset - 2 * Math.PI);\n } else {\n angleDifference = Math.abs(angle - angleCurrentOffset);\n }\n\n // Minimum score is 0 if angle difference is 0, maximum score is pi / 10\n score -= angleDifference / 10;\n\n return score;\n },\n\n /**\n * Automatically positions the label by finding the optimal position.\n * Aims to minimize conflicts while maintaining readability.\n * \n *
\n * @pseudo\n * @name Text\n * @augments JXG.Text\n * @constructor\n * @type JXG.Text\n *\n * @param {number,function_number,function_number,function_String,function} z_,x,y,str Parent elements for text elements.\n * \n * @example\n * // Create a variable text at a variable position.\n * var s = board.create('slider',[[0,4],[3,4],[-2,0,2]]);\n * var graph = board.create('text',\n * [function(x){ return s.Value();}, 1,\n * function(){return \"The value of s is\"+JXG.toFixed(s.Value(), 2);}\n * ]\n * );\n * \n * \n * @example\n * // Create a text bound to the point A\n * var p = board.create('point',[0, 1]),\n * t = board.create('text',[0, -1,\"Hello World\"], {anchor: p});\n *\n * \n * \n *\n */\nJXG.createText = function (board, parents, attributes) {\n var t,\n attr = Type.copyAttributes(attributes, board.options, 'text'),\n coords = parents.slice(0, -1),\n content = parents[parents.length - 1];\n\n // Backwards compatibility\n attr.anchor = attr.parent || attr.anchor;\n t = CoordsElement.create(JXG.Text, board, coords, attr, content);\n\n if (!t) {\n throw new Error(\n \"JSXGraph: Can't create text with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [x,y], [z,x,y], [element,transformation]\"\n );\n }\n\n if (attr.rotate !== 0) {\n // This is the default value, i.e. no rotation\n t.addRotation(attr.rotate);\n }\n\n return t;\n};\n\nJXG.registerElement(\"text\", JXG.createText);\n\n/**\n * @class Labels are text objects tied to other elements like points, lines and curves.\n * Labels are handled internally by JSXGraph, only. There is NO constructor \"board.create('label', ...)\".\n *\n * @description\n * Labels for points are positioned with the attributes {@link Text#anchorX}, {@link Text#anchorX} and {@link Label#offset}.\n * \n *
\n *\n * @pseudo\n * @name Label\n * @augments JXG.Text\n * @constructor\n * @type JXG.Text\n */\n// See element.js#createLabel\n\n/**\n * [[x,y], [w px, h px], [range]\n */\nJXG.createHTMLSlider = function (board, parents, attributes) {\n var t,\n par,\n attr = Type.copyAttributes(attributes, board.options, 'htmlslider');\n\n if (parents.length !== 2 || parents[0].length !== 2 || parents[1].length !== 3) {\n throw new Error(\n \"JSXGraph: Can't create htmlslider with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parents are: [[x,y], [min, start, max]]\"\n );\n }\n\n // Backwards compatibility\n attr.anchor = attr.parent || attr.anchor;\n attr.fixed = attr.fixed || true;\n\n par = [\n parents[0][0],\n parents[0][1],\n '\"\n ];\n\n t = JXG.createText(board, par, attr);\n t.type = Type.OBJECT_TYPE_HTMLSLIDER;\n\n t.rendNodeForm = t.rendNode.childNodes[0];\n\n t.rendNodeRange = t.rendNodeForm.childNodes[0];\n t.rendNodeRange.min = parents[1][0];\n t.rendNodeRange.max = parents[1][2];\n t.rendNodeRange.step = attr.step;\n t.rendNodeRange.value = parents[1][1];\n\n t.rendNodeLabel = t.rendNodeForm.childNodes[1];\n t.rendNodeLabel.id = t.rendNode.id + \"_label\";\n\n if (attr.withlabel) {\n t.rendNodeLabel.innerText = t.name + \"=\";\n }\n\n t.rendNodeOut = t.rendNodeForm.childNodes[2];\n t.rendNodeOut.value = parents[1][1];\n\n try {\n t.rendNodeForm.id = t.rendNode.id + \"_form\";\n t.rendNodeRange.id = t.rendNode.id + \"_range\";\n t.rendNodeOut.id = t.rendNode.id + \"_out\";\n } catch (e) {\n JXG.debug(e);\n }\n\n t.rendNodeRange.style.width = attr.widthrange + 'px';\n t.rendNodeRange.style.verticalAlign = 'middle';\n t.rendNodeOut.style.width = attr.widthout + 'px';\n\n t._val = parents[1][1];\n\n if (JXG.supportsVML()) {\n /*\n * OnChange event is used for IE browsers\n * The range element is supported since IE10\n */\n Env.addEvent(t.rendNodeForm, \"change\", priv.HTMLSliderInputEventHandler, t);\n } else {\n /*\n * OnInput event is used for non-IE browsers\n */\n Env.addEvent(t.rendNodeForm, \"input\", priv.HTMLSliderInputEventHandler, t);\n }\n\n t.Value = function () {\n return this._val;\n };\n\n return t;\n};\n\nJXG.registerElement(\"htmlslider\", JXG.createHTMLSlider);\n\nexport default JXG.Text;\n// export default {\n// Text: JXG.Text,\n// createText: JXG.createText,\n// createHTMLSlider: JXG.createHTMLSlider\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Andreas Walter,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph and JSXCompressor.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n JSXCompressor is free software dual licensed under the GNU LGPL or Apache License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n OR\n * Apache License Version 2.0\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License, Apache\n License, and the MIT License along with JSXGraph. If not, see\n \n *\n *\n * @example\n * const board = JXG.board('jxgbox', {\n * boundingbox: [-10, 10, 10, -10],\n * axis: true,\n * showCopyright: true,\n * showFullscreen: true,\n * showScreenshot: false,\n * showClearTraces: false,\n * showInfobox: false,\n * showNavigation: true,\n * grid: false,\n * defaultAxes: {\n * x: {\n * withLabel: true,\n * label: {\n * position: '95% left',\n * offset: [-10, 10]\n * },\n * lastArrow: {\n * type: 4,\n * size: 10\n * }\n * },\n * y: {\n * withLabel: true,\n * label: {\n * position: '0.90fr right',\n * offset: [6, -6]\n * },\n * lastArrow: {\n * type: 4,\n * size: 10\n * }\n * }\n * }\n * });\n *\n * \n * \n * @example\n * const board = JXG.board('jxgbox', {\n * boundingbox: [-5, 5, 5, -5],\n * intl: {\n * enabled: false,\n * locale: 'en-EN'\n * },\n * keepaspectratio: true,\n * axis: true,\n * defaultAxes: {\n * x: {\n * ticks: {\n * intl: {\n * enabled: true,\n * options: {\n * style: 'unit',\n * unit: 'kilometer-per-hour',\n * unitDisplay: 'narrow'\n * }\n * }\n * }\n * },\n * y: {\n * ticks: {\n * }\n * }\n * },\n * infobox: {\n * fontSize: 20,\n * intl: {\n * enabled: true,\n * options: {\n * minimumFractionDigits: 4,\n * maximumFractionDigits: 5\n * }\n * }\n * }\n * });\n *\n * \n * \n *\n */\n board: function (box, attributes) {\n return this.JSXGraph.initBoard(box, attributes);\n },\n\n /**\n * Create a JSXGraph div element containing a JSXGraph board inside of a user supplied div.\n * \n * \n * \n * \n * jxgbox: {\n * cssStyle: 'width:640px; aspect-ratio:2/1; background-color: white',\n * cssClass: '',\n * id: 'jxgbox'\n * }\n * \n * i.e. the div's style-attribute and a list of classes (separated by blanks) can be given.\n * \n *\n */\n appBox: function (box, attributes) {\n var node, id, jxg_id, innerdiv,\n obb, bb, w, h,\n attr, board;\n\n if (!JXG.isBrowser) {\n throw new Error(\"JSXGraph: JXG.appBox needs a browser\");\n }\n if (JXG.isString(box)) {\n // Hosting div is given as string\n node = document.getElementById(box);\n id = box;\n } else {\n // Hosting div is given as object pointer\n node = box;\n id = box.getAttribute('id');\n }\n\n innerdiv = document.createElement(\"div\");\n\n attr = JXG.copyAttributes(attributes, JXG.Options, 'board').jxgbox;\n\n jxg_id = ((id !== null) ? id + '_' : '') + attr.id;\n innerdiv.setAttribute('id', jxg_id);\n innerdiv.className += 'jxgbox ';\n innerdiv.className += attr.cssclass;\n innerdiv.style = attr.cssstyle;\n\n obb = attr.outerbox;\n if (obb !== null && JXG.isArray(obb)) {\n bb = JXG.copyAttributes(attributes, JXG.Options, 'board').boundingbox;\n node.style.position = 'relative';\n w = obb[2] - obb[0];\n h = obb[1] - obb[3];\n innerdiv.style.position = 'absolute';\n innerdiv.style.left = (100 * (bb[0] - obb[0]) / w) + '%';\n innerdiv.style.top = (100 * (obb[1] - bb[1]) / h) + '%';\n innerdiv.style.width = (100 * (bb[2] - bb[0]) / w) + '%';\n innerdiv.style.height = (100 * (bb[1] - bb[3]) / h) + '%';\n\n // rect = node.getBoundingClientRect();\n // innerdiv.style.left = ((bb[0] - obb[0]) / w * rect.width) + 'px';\n // innerdiv.style.top = ((obb[1] - bb[1]) / h * rect.height) + 'px';\n // innerdiv.style.width = ((bb[2] - bb[0]) / w * rect.width) + 'px';\n // innerdiv.style.height = ((bb[1] - bb[3]) / h * rect.height) + 'px';\n }\n\n node.appendChild(innerdiv);\n attributes.moveTarget = node;\n\n board = this.board(innerdiv, attributes);\n\n innerdiv.style.overflow = 'visible';\n if (board.renderer.type === 'svg') {\n board.renderer.svgRoot.style.overflow = 'visible';\n } else {\n throw new Error(\"JSXGraph: JXG.appBox needs SVG renderer\");\n }\n\n return board;\n },\n\n themes: {}\n }\n);\n\nexport default jxg;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Andreas Walter,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n *\n * @param {JXG.Point|JXG.Coords|Array} p1\n * @param {JXG.Point|JXG.Coords|Array} p2\n * @param {JXG.Point|JXG.Coords|Array} p3\n *\n * @returns {Number}\n */\n signedTriangle: function (p1, p2, p3) {\n var A = Expect.coordsArray(p1),\n B = Expect.coordsArray(p2),\n C = Expect.coordsArray(p3);\n return 0.5 * ((B[1] - A[1]) * (C[2] - A[2]) - (B[2] - A[2]) * (C[1] - A[1]));\n },\n\n /**\n * Determine the signed area of a non-self-intersecting polygon.\n * Surveyor's Formula\n *\n * @param {Array} p An array containing {@link JXG.Point}, {@link JXG.Coords}, and/or arrays.\n * @param {Boolean} [sort=true]\n *\n * @returns {Number}\n */\n signedPolygon: function (p, sort) {\n var i,\n N,\n A = 0,\n ps = Expect.each(p, Expect.coordsArray);\n\n if (sort === undefined) {\n sort = true;\n }\n\n if (!sort) {\n ps = this.sortVertices(ps);\n } else {\n // Make sure the polygon is closed. If it is already closed this won't change the sum because the last\n // summand will be 0.\n ps.unshift(ps[ps.length - 1]);\n }\n\n N = ps.length;\n\n for (i = 1; i < N; i++) {\n A += ps[i - 1][1] * ps[i][2] - ps[i][1] * ps[i - 1][2];\n }\n\n return 0.5 * A;\n },\n\n /**\n * Calculate the complex hull of a point cloud by the Graham scan algorithm.\n *\n * @param {Array} points An array containing {@link JXG.Point}, {@link JXG.Coords}, and/or arrays.\n *\n * @returns {Array} List of objects {i: index, c: coords} containing the convex hull points\n * in form of the index in the original input array and a coords array.\n *\n * @example\n * // Static example\n *\n * var i, hull,\n * p = [],\n * q = [];\n *\n * p.push( board.create('point', [4, 0], {withLabel:false }) );\n * p.push( board.create('point', [0, 4], {withLabel:false }) );\n * p.push( board.create('point', [0, 0], {withLabel:false }) );\n * p.push([-1, 0]);\n * p.push([-3, -3]);\n *\n * hull = JXG.Math.Geometry.GrahamScan(p);\n * for (i = 0; i < hull.length; i++) {\n * console.log(\"JSXGraph example:\", hull[i]);\n * q.push(hull[i].c);\n * }\n * board.create('polygon', q);\n * // Output:\n * // { i: 4, c: [1, -3, 3]}\n * // { i: 0, c: [1, 4, 0]}\n * // { i: 1, c: [1, 0, 4]}\n *\n * \n * \n *\n */\n GrahamScan: function (points) {\n var i, M, o,\n mi_idx,\n mi_x, mi_y, ma_x, ma_y,\n mi_xpy, mi_xmy, ma_xpy, ma_xmy,\n mi_x_i, ma_x_i, mi_y_i, ma_y_i,\n mi_xpy_i, mi_xmy_i, ma_xpy_i, ma_xmy_i,\n v, c,\n eps = Mat.eps * Mat.eps,\n that = this,\n ps_idx = [],\n stack = [],\n ps = Expect.each(points, Expect.coordsArray), // New array object, i.e. a copy of the input array.\n N,\n AklToussaint = 1024; // This is a rough threshold where the heuristic pays off.\n\n N = ps.length;\n if (N === 0) {\n return [];\n }\n\n if (N > AklToussaint) {\n //\n // Akl-Toussaint heuristic\n // Determine an irregular convex octagon whose inside can be discarded.\n //\n mi_x = ps[0][1];\n ma_x = mi_x;\n mi_y = ps[0][2];\n ma_y = mi_y;\n\n mi_xmy = ps[0][1] - ps[0][2];\n ma_xmy = mi_xmy;\n mi_xpy = ps[0][1] + ps[0][2];\n ma_xpy = mi_xpy;\n\n mi_x_i = 0;\n ma_x_i = 0;\n mi_y_i = 0;\n ma_y_i = 0;\n\n mi_xmy_i = 0;\n ma_xmy_i = 0;\n mi_xpy_i = 0;\n ma_xpy_i = 0;\n for (i = 1; i < N; i++) {\n v = ps[i][1];\n if (v < mi_x) {\n mi_x = v;\n mi_x_i = i;\n } else if (v > ma_x) {\n ma_x = v;\n ma_x_i = i;\n }\n\n v = ps[i][2];\n if (v < mi_y) {\n mi_y = v;\n mi_y_i = i;\n } else if (v > ma_y) {\n ma_y = v;\n ma_y_i = i;\n }\n\n v = ps[i][1] - ps[i][2];\n if (v < mi_xmy) {\n mi_xmy = v;\n mi_xmy_i = i;\n } else if (v > ma_xmy) {\n ma_xmy = v;\n ma_xmy_i = i;\n }\n\n v = ps[i][1] + ps[i][2];\n if (v < mi_xpy) {\n mi_xpy = v;\n mi_xpy_i = i;\n } else if (v > ma_xpy) {\n ma_xpy = v;\n ma_xpy_i = i;\n }\n }\n }\n\n // Keep track of the indices of the input points.\n for (i = 0; i < N; i++) {\n c = ps[i];\n if (N <= AklToussaint ||\n // Discard inside of the octagon according to the Akl-Toussaint heuristic\n // [mi_x_i, ma_x_i, mi_y_i, ma_y_i, mi_xpy_i, mi_xmy_i, ma_xpy_i, ma_xmy_i].includes(i) ||\n [mi_x_i, ma_x_i, mi_y_i, ma_y_i, mi_xpy_i, mi_xmy_i, ma_xpy_i, ma_xmy_i].indexOf(i) >= 0||\n (mi_x_i !== mi_xmy_i && this.signedTriangle(ps[mi_x_i], ps[mi_xmy_i], c) >= -eps) ||\n (mi_xmy_i !== ma_y_i && this.signedTriangle(ps[mi_xmy_i], ps[ma_y_i], c) >= -eps) ||\n (ma_y_i !== ma_xpy_i && this.signedTriangle(ps[ma_y_i], ps[ma_xpy_i], c) >= -eps) ||\n (ma_xpy_i !== ma_x_i && this.signedTriangle(ps[ma_xpy_i], ps[ma_x_i], c) >= -eps) ||\n (ma_x_i !== ma_xmy_i && this.signedTriangle(ps[ma_x_i], ps[ma_xmy_i], c) >= -eps) ||\n (ma_xmy_i !== mi_y_i && this.signedTriangle(ps[ma_xmy_i], ps[mi_y_i], c) >= -eps) ||\n (mi_y_i !== mi_xpy_i && this.signedTriangle(ps[mi_y_i], ps[mi_xpy_i], c) >= -eps) ||\n (mi_xpy_i !== mi_x_i && this.signedTriangle(ps[mi_xpy_i], ps[mi_x_i], c) >= -eps)\n ) {\n ps_idx.push({\n i: i,\n c: c\n });\n }\n }\n N = ps_idx.length;\n\n // Find the point with the lowest y value\n mi_idx = 0;\n mi_x = ps_idx[0].c[1];\n mi_y = ps_idx[0].c[2];\n for (i = 1; i < N; i++) {\n if ((ps_idx[i].c[2] < mi_y) || (ps_idx[i].c[2] === mi_y && ps_idx[i].c[1] < mi_x)) {\n mi_x = ps_idx[i].c[1];\n mi_y = ps_idx[i].c[2];\n mi_idx = i;\n }\n }\n ps_idx = Type.swap(ps_idx, mi_idx, 0);\n\n // Our origin o, i.e. the first point.\n o = ps_idx[0].c;\n\n // Sort according to the angle around o.\n ps_idx.sort(function(a_obj, b_obj) {\n var a = a_obj.c,\n b = b_obj.c,\n v = that.signedTriangle(o, a, b);\n\n if (v === 0) {\n // if o, a, b are collinear, the point which is further away\n // from o is considered greater.\n return Mat.hypot(a[1] - o[1], a[2] - o[2]) - Mat.hypot(b[1] - o[1], b[2] - o[2]);\n }\n\n // if v < 0, a is to the left of [o, b], i.e. angle(a) > angle(b)\n return -v;\n });\n\n // Do the Graham scan.\n M = 0;\n for (i = 0; i < N; i++) {\n while (M > 1 && this.signedTriangle(stack[M - 2].c, stack[M - 1].c, ps_idx[i].c) <= 0) {\n // stack[M - 1] is to the left of stack[M - 1], ps[i]: discard it\n stack.pop();\n M--;\n }\n stack.push(ps_idx[i]);\n M++;\n }\n\n return stack;\n },\n\n // Original method\n // GrahamScan: function (points, indices) {\n // var i,\n // M = 1,\n // ps = Expect.each(points, Expect.coordsArray),\n // N = ps.length;\n // ps = this.sortVertices(ps);\n // N = ps.length;\n // for (i = 2; i < N; i++) {\n // while (this.signedTriangle(ps[M - 1], ps[M], ps[i]) <= 0) {\n // if (M > 1) {\n // M -= 1;\n // } else if (i === N - 1) {\n // break;\n // }\n // i += 1;\n // }\n // M += 1;\n // ps = Type.swap(ps, M, i);\n // indices = Type.swap(indices, M, i);\n // }\n // return ps.slice(0, M);\n // },\n\n /**\n * Calculate the complex hull of a point cloud by the Graham scan algorithm.\n *\n * @param {Array} points An array containing {@link JXG.Point}, {@link JXG.Coords}, and/or arrays.\n * @param {Boolean} [returnCoords=false] If true, return an array of coords. Otherwise return a list of pointers\n * to the input list elements. That is, if the input is a list of {@link JXG.Point} elements, the returned list\n * will contain the points that form the convex hull.\n * @returns {Array} List containing the convex hull. Format depends on returnCoords.\n * @see JXG.Math.Geometry.GrahamScan\n *\n * @example\n * // Static example\n * var i, hull,\n * p = [];\n *\n * p.push( board.create('point', [4, 0], {withLabel:false }) );\n * p.push( board.create('point', [0, 4], {withLabel:false }) );\n * p.push( board.create('point', [0, 0], {withLabel:false }) );\n * p.push( board.create('point', [1, 1], {withLabel:false }) );\n * hull = JXG.Math.Geometry.convexHull(p);\n * for (i = 0; i < hull.length; i++) {\n * hull[i].setAttribute({color: 'blue'});\n * }\n *\n * \n * \n *\n * @example\n * // Dynamic version using returnCoords==true: drag the points\n * var p = [];\n *\n * p.push( board.create('point', [4, 0], {withLabel:false }) );\n * p.push( board.create('point', [0, 4], {withLabel:false }) );\n * p.push( board.create('point', [0, 0], {withLabel:false }) );\n * p.push( board.create('point', [1, 1], {withLabel:false }) );\n *\n * var c = board.create('curve', [[], []], {fillColor: 'yellow', fillOpacity: 0.3});\n * c.updateDataArray = function() {\n * var i,\n * hull = JXG.Math.Geometry.convexHull(p, true);\n *\n * this.dataX = [];\n * this.dataY = [];\n *\n * for (i = 0; i < hull.length; i ++) {\n * this.dataX.push(hull[i][1]);\n * this.dataY.push(hull[i][2]);\n * }\n * this.dataX.push(hull[0][1]);\n * this.dataY.push(hull[0][2]);\n * };\n * board.update();\n *\n * \n * \n *\n */\n convexHull: function(points, returnCoords) {\n var i, hull,\n res = [];\n\n hull = this.GrahamScan(points);\n for (i = 0; i < hull.length; i++) {\n if (returnCoords) {\n res.push(hull[i].c);\n } else {\n res.push(points[hull[i].i]);\n }\n }\n return res;\n },\n\n // /**\n // * Determine if a polygon or a path element is convex, non-convex or complex which are defined like this:\n // * \n // *
\n // * A path element might be specified as an array of coordinate arrays or {@link JXG.Coords}.\n // *\n // * @param {Array|Polygon|PolygonalChain} points Polygon or list of coordinates\n // * @returns {Number} -1: if complex, 0: if non-convex, 1: if convex\n // */\n /**\n * Determine if a polygon or a path element is convex:\n * \n *\n */\n isConvex: function(points) {\n var ps, le, i,\n eps = Mat.eps * Mat.eps,\n old_x, old_y, old_dir,\n new_x, new_y, new_dir,\n angle,\n orient,\n angle_sum = 0.0;\n\n if (Type.isArray(points)) {\n ps = Expect.each(points, Expect.coordsArray);\n } else if (Type.exists(points.type) && points.type === Const.OBJECT_TYPE_POLYGON) {\n ps = Expect.each(points.vertices, Expect.coordsArray);\n }\n le = ps.length;\n if (le === 0) {\n // Empty set is convex\n return true;\n }\n if (le < 3) {\n // Segments and points are convex\n return true;\n }\n\n orient = null;\n old_x = ps[le - 2][1];\n old_y = ps[le - 2][2];\n new_x = ps[le - 1][1];\n new_y = ps[le - 1][2];\n new_dir = Math.atan2(new_y - old_y, new_x - old_x);\n for (i = 0; i < le; i++) {\n old_x = new_x;\n old_y = new_y;\n old_dir = new_dir;\n new_x = ps[i][1];\n new_y = ps[i][2];\n if (old_x === new_x && old_y === new_y) {\n // Repeated consecutive points are ignored\n continue;\n }\n new_dir = Math.atan2(new_y - old_y, new_x - old_x);\n angle = new_dir - old_dir;\n if (angle <= -Math.PI) {\n angle += 2 * Math.PI;\n } else if (angle > Math.PI) {\n angle -= 2 * Math.PI;\n }\n if (orient === null) {\n if (angle === 0.0) {\n continue;\n }\n orient = (angle > 0) ? 1 : -1;\n } else {\n if (orient * angle < -eps) {\n return false;\n }\n }\n angle_sum += angle;\n }\n\n if ((Math.abs(angle_sum / (2 * Math.PI)) - 1) < eps) {\n return true;\n }\n return false;\n },\n\n /**\n * A line can be a segment, a straight, or a ray. So it is not always delimited by point1 and point2\n * calcStraight determines the visual start point and end point of the line. A segment is only drawn\n * from start to end point, a straight line is drawn until it meets the boards boundaries.\n * @param {JXG.Line} el Reference to a line object, that needs calculation of start and end point.\n * @param {JXG.Coords} point1 Coordinates of the point where line drawing begins. This value is calculated and\n * set by this method.\n * @param {JXG.Coords} point2 Coordinates of the point where line drawing ends. This value is calculated and set\n * by this method.\n * @param {Number} margin Optional margin, to avoid the display of the small sides of lines.\n * @returns null\n * @see Line\n * @see JXG.Line\n */\n calcStraight: function (el, point1, point2, margin) {\n var takePoint1,\n takePoint2,\n intersection,\n intersect1,\n intersect2,\n straightFirst,\n straightLast,\n c, p1, p2;\n\n if (!Type.exists(margin)) {\n // Enlarge the drawable region slightly. This hides the small sides\n // of thick lines in most cases.\n margin = 10;\n }\n\n straightFirst = el.evalVisProp('straightfirst');\n straightLast = el.evalVisProp('straightlast');\n\n // If one of the point is an ideal point in homogeneous coordinates\n // drawing of line segments or rays are not possible.\n if (Math.abs(point1.scrCoords[0]) < Mat.eps) {\n straightFirst = true;\n }\n if (Math.abs(point2.scrCoords[0]) < Mat.eps) {\n straightLast = true;\n }\n\n // Do nothing in case of line segments (inside or outside of the board)\n if (!straightFirst && !straightLast) {\n return;\n }\n\n // Compute the stdform of the line in screen coordinates.\n c = [];\n c[0] =\n el.stdform[0] -\n (el.stdform[1] * el.board.origin.scrCoords[1]) / el.board.unitX +\n (el.stdform[2] * el.board.origin.scrCoords[2]) / el.board.unitY;\n c[1] = el.stdform[1] / el.board.unitX;\n c[2] = -el.stdform[2] / el.board.unitY;\n\n // If p1=p2\n if (isNaN(c[0] + c[1] + c[2])) {\n return;\n }\n\n takePoint1 = false;\n takePoint2 = false;\n\n // Line starts at point1 and point1 is inside the board\n takePoint1 =\n !straightFirst &&\n Math.abs(point1.usrCoords[0]) >= Mat.eps &&\n point1.scrCoords[1] >= 0.0 &&\n point1.scrCoords[1] <= el.board.canvasWidth &&\n point1.scrCoords[2] >= 0.0 &&\n point1.scrCoords[2] <= el.board.canvasHeight;\n\n // Line ends at point2 and point2 is inside the board\n takePoint2 =\n !straightLast &&\n Math.abs(point2.usrCoords[0]) >= Mat.eps &&\n point2.scrCoords[1] >= 0.0 &&\n point2.scrCoords[1] <= el.board.canvasWidth &&\n point2.scrCoords[2] >= 0.0 &&\n point2.scrCoords[2] <= el.board.canvasHeight;\n\n // Intersect the line with the four borders of the board.\n intersection = this.meetLineBoard(c, el.board, margin);\n intersect1 = intersection[0];\n intersect2 = intersection[1];\n\n /**\n * At this point we have four points:\n * point1 and point2 are the first and the second defining point on the line,\n * intersect1, intersect2 are the intersections of the line with border around the board.\n */\n\n /*\n * Here we handle rays where both defining points are outside of the board.\n */\n // If both points are outside and the complete ray is outside we do nothing\n if (!takePoint1 && !takePoint2) {\n // Ray starting at point 1\n if (\n !straightFirst &&\n straightLast &&\n !this.isSameDirection(point1, point2, intersect1) &&\n !this.isSameDirection(point1, point2, intersect2)\n ) {\n return;\n }\n\n // Ray starting at point 2\n if (\n straightFirst &&\n !straightLast &&\n !this.isSameDirection(point2, point1, intersect1) &&\n !this.isSameDirection(point2, point1, intersect2)\n ) {\n return;\n }\n }\n\n /*\n * If at least one of the defining points is outside of the board\n * we take intersect1 or intersect2 as one of the end points\n * The order is also important for arrows of axes\n */\n if (!takePoint1) {\n if (!takePoint2) {\n // Two border intersection points are used\n if (this.isSameDir(point1, point2, intersect1, intersect2)) {\n p1 = intersect1;\n p2 = intersect2;\n } else {\n p2 = intersect1;\n p1 = intersect2;\n }\n } else {\n // One border intersection points is used\n if (this.isSameDir(point1, point2, intersect1, intersect2)) {\n p1 = intersect1;\n } else {\n p1 = intersect2;\n }\n }\n } else {\n if (!takePoint2) {\n // One border intersection points is used\n if (this.isSameDir(point1, point2, intersect1, intersect2)) {\n p2 = intersect2;\n } else {\n p2 = intersect1;\n }\n }\n }\n\n if (p1) {\n //point1.setCoordinates(Const.COORDS_BY_USER, p1.usrCoords.slice(1));\n point1.setCoordinates(Const.COORDS_BY_USER, p1.usrCoords);\n }\n\n if (p2) {\n //point2.setCoordinates(Const.COORDS_BY_USER, p2.usrCoords.slice(1));\n point2.setCoordinates(Const.COORDS_BY_USER, p2.usrCoords);\n }\n },\n\n /**\n * A line can be a segment, a straight, or a ray. so it is not always delimited by point1 and point2.\n *\n * This method adjusts the line's delimiting points taking into account its nature, the viewport defined\n * by the board.\n *\n * A segment is delimited by start and end point, a straight line or ray is delimited until it meets the\n * boards boundaries. However, if the line has infinite ticks, it will be delimited by the projection of\n * the boards vertices onto itself.\n *\n * @param {JXG.Line} el Reference to a line object, that needs calculation of start and end point.\n * @param {JXG.Coords} point1 Coordinates of the point where line drawing begins. This value is calculated and\n * set by this method.\n * @param {JXG.Coords} point2 Coordinates of the point where line drawing ends. This value is calculated and set\n * by this method.\n * @see Line\n * @see JXG.Line\n */\n calcLineDelimitingPoints: function (el, point1, point2) {\n var distP1P2,\n boundingBox,\n lineSlope,\n intersect1,\n intersect2,\n straightFirst,\n straightLast,\n c,\n p1,\n p2,\n takePoint1 = false,\n takePoint2 = false;\n\n straightFirst = el.evalVisProp('straightfirst');\n straightLast = el.evalVisProp('straightlast');\n\n // If one of the point is an ideal point in homogeneous coordinates\n // drawing of line segments or rays are not possible.\n if (Math.abs(point1.scrCoords[0]) < Mat.eps) {\n straightFirst = true;\n }\n if (Math.abs(point2.scrCoords[0]) < Mat.eps) {\n straightLast = true;\n }\n\n // Compute the stdform of the line in screen coordinates.\n c = [];\n c[0] =\n el.stdform[0] -\n (el.stdform[1] * el.board.origin.scrCoords[1]) / el.board.unitX +\n (el.stdform[2] * el.board.origin.scrCoords[2]) / el.board.unitY;\n c[1] = el.stdform[1] / el.board.unitX;\n c[2] = -el.stdform[2] / el.board.unitY;\n\n // p1=p2\n if (isNaN(c[0] + c[1] + c[2])) {\n return;\n }\n\n takePoint1 = !straightFirst;\n takePoint2 = !straightLast;\n // Intersect the board vertices on the line to establish the available visual space for the infinite ticks\n // Based on the slope of the line we can optimise and only project the two outer vertices\n\n // boundingBox = [x1, y1, x2, y2] upper left, lower right vertices\n boundingBox = el.board.getBoundingBox();\n lineSlope = el.getSlope();\n if (lineSlope >= 0) {\n // project vertices (x2,y1) (x1, y2)\n intersect1 = this.projectPointToLine(\n { coords: { usrCoords: [1, boundingBox[2], boundingBox[1]] } },\n el,\n el.board\n );\n intersect2 = this.projectPointToLine(\n { coords: { usrCoords: [1, boundingBox[0], boundingBox[3]] } },\n el,\n el.board\n );\n } else {\n // project vertices (x1, y1) (x2, y2)\n intersect1 = this.projectPointToLine(\n { coords: { usrCoords: [1, boundingBox[0], boundingBox[1]] } },\n el,\n el.board\n );\n intersect2 = this.projectPointToLine(\n { coords: { usrCoords: [1, boundingBox[2], boundingBox[3]] } },\n el,\n el.board\n );\n }\n\n /**\n * we have four points:\n * point1 and point2 are the first and the second defining point on the line,\n * intersect1, intersect2 are the intersections of the line with border around the board.\n */\n\n /*\n * Here we handle rays/segments where both defining points are outside of the board.\n */\n if (!takePoint1 && !takePoint2) {\n // Segment, if segment does not cross the board, do nothing\n if (!straightFirst && !straightLast) {\n distP1P2 = point1.distance(Const.COORDS_BY_USER, point2);\n // if intersect1 not between point1 and point2\n if (\n Math.abs(\n point1.distance(Const.COORDS_BY_USER, intersect1) +\n intersect1.distance(Const.COORDS_BY_USER, point2) -\n distP1P2\n ) > Mat.eps\n ) {\n return;\n }\n // if insersect2 not between point1 and point2\n if (\n Math.abs(\n point1.distance(Const.COORDS_BY_USER, intersect2) +\n intersect2.distance(Const.COORDS_BY_USER, point2) -\n distP1P2\n ) > Mat.eps\n ) {\n return;\n }\n }\n\n // If both points are outside and the complete ray is outside we do nothing\n // Ray starting at point 1\n if (\n !straightFirst &&\n straightLast &&\n !this.isSameDirection(point1, point2, intersect1) &&\n !this.isSameDirection(point1, point2, intersect2)\n ) {\n return;\n }\n\n // Ray starting at point 2\n if (\n straightFirst &&\n !straightLast &&\n !this.isSameDirection(point2, point1, intersect1) &&\n !this.isSameDirection(point2, point1, intersect2)\n ) {\n return;\n }\n }\n\n /*\n * If at least one of the defining points is outside of the board\n * we take intersect1 or intersect2 as one of the end points\n * The order is also important for arrows of axes\n */\n if (!takePoint1) {\n if (!takePoint2) {\n // Two border intersection points are used\n if (this.isSameDir(point1, point2, intersect1, intersect2)) {\n p1 = intersect1;\n p2 = intersect2;\n } else {\n p2 = intersect1;\n p1 = intersect2;\n }\n } else {\n // One border intersection points is used\n if (this.isSameDir(point1, point2, intersect1, intersect2)) {\n p1 = intersect1;\n } else {\n p1 = intersect2;\n }\n }\n } else {\n if (!takePoint2) {\n // One border intersection points is used\n if (this.isSameDir(point1, point2, intersect1, intersect2)) {\n p2 = intersect2;\n } else {\n p2 = intersect1;\n }\n }\n }\n\n if (p1) {\n //point1.setCoordinates(Const.COORDS_BY_USER, p1.usrCoords.slice(1));\n point1.setCoordinates(Const.COORDS_BY_USER, p1.usrCoords);\n }\n\n if (p2) {\n //point2.setCoordinates(Const.COORDS_BY_USER, p2.usrCoords.slice(1));\n point2.setCoordinates(Const.COORDS_BY_USER, p2.usrCoords);\n }\n },\n\n /**\n * Calculates the visProp.position corresponding to a given angle.\n * @param {number} angle angle in radians. Must be in range (-2pi,2pi).\n */\n calcLabelQuadrant: function (angle) {\n var q;\n if (angle < 0) {\n angle += 2 * Math.PI;\n }\n q = Math.floor((angle + Math.PI / 8) / (Math.PI / 4)) % 8;\n return [\"rt\", \"urt\", \"top\", \"ulft\", \"lft\", \"llft\", \"bot\", \"lrt\"][q];\n },\n\n /**\n * The vectors p2-p1 and i2-i1 are supposed to be collinear. If their cosine is positive\n * they point into the same direction otherwise they point in opposite direction.\n * @param {JXG.Coords} p1\n * @param {JXG.Coords} p2\n * @param {JXG.Coords} i1\n * @param {JXG.Coords} i2\n * @returns {Boolean} True, if p2-p1 and i2-i1 point into the same direction\n */\n isSameDir: function (p1, p2, i1, i2) {\n var dpx = p2.usrCoords[1] - p1.usrCoords[1],\n dpy = p2.usrCoords[2] - p1.usrCoords[2],\n dix = i2.usrCoords[1] - i1.usrCoords[1],\n diy = i2.usrCoords[2] - i1.usrCoords[2];\n\n if (Math.abs(p2.usrCoords[0]) < Mat.eps) {\n dpx = p2.usrCoords[1];\n dpy = p2.usrCoords[2];\n }\n\n if (Math.abs(p1.usrCoords[0]) < Mat.eps) {\n dpx = -p1.usrCoords[1];\n dpy = -p1.usrCoords[2];\n }\n\n return dpx * dix + dpy * diy >= 0;\n },\n\n /**\n * If you're looking from point \"start\" towards point \"s\" and you can see the point \"p\", return true.\n * Otherwise return false.\n * @param {JXG.Coords} start The point you're standing on.\n * @param {JXG.Coords} p The point in which direction you're looking.\n * @param {JXG.Coords} s The point that should be visible.\n * @returns {Boolean} True, if from start the point p is in the same direction as s is, that means s-start = k*(p-start) with k>=0.\n */\n isSameDirection: function (start, p, s) {\n var dx,\n dy,\n sx,\n sy,\n r = false;\n\n dx = p.usrCoords[1] - start.usrCoords[1];\n dy = p.usrCoords[2] - start.usrCoords[2];\n\n sx = s.usrCoords[1] - start.usrCoords[1];\n sy = s.usrCoords[2] - start.usrCoords[2];\n\n if (Math.abs(dx) < Mat.eps) {\n dx = 0;\n }\n\n if (Math.abs(dy) < Mat.eps) {\n dy = 0;\n }\n\n if (Math.abs(sx) < Mat.eps) {\n sx = 0;\n }\n\n if (Math.abs(sy) < Mat.eps) {\n sy = 0;\n }\n\n if (dx >= 0 && sx >= 0) {\n r = (dy >= 0 && sy >= 0) || (dy <= 0 && sy <= 0);\n } else if (dx <= 0 && sx <= 0) {\n r = (dy >= 0 && sy >= 0) || (dy <= 0 && sy <= 0);\n }\n\n return r;\n },\n\n /**\n * Determinant of three points in the Euclidean plane.\n * Zero, if the points are collinear. Used to determine of a point q is left or\n * right to a segment defined by points p1 and p2.\n * \n * \n *\n */\n pnpoly: function (x_in, y_in, path, coord_type, board) {\n var i, j, vi, vj, len,\n x, y, crds,\n v = path,\n isIn = false;\n\n if (coord_type === Const.COORDS_BY_USER) {\n crds = new Coords(Const.COORDS_BY_USER, [x_in, y_in], board);\n x = crds.scrCoords[1];\n y = crds.scrCoords[2];\n } else {\n x = x_in;\n y = y_in;\n }\n\n len = path.length;\n for (i = 0, j = len - 2; i < len - 1; j = i++) {\n vi = Type.exists(v[i].coords) ? v[i].coords : v[i];\n vj = Type.exists(v[j].coords) ? v[j].coords : v[j];\n\n if (\n vi.scrCoords[2] > y !== vj.scrCoords[2] > y &&\n x <\n ((vj.scrCoords[1] - vi.scrCoords[1]) * (y - vi.scrCoords[2])) /\n (vj.scrCoords[2] - vi.scrCoords[2]) +\n vi.scrCoords[1]\n ) {\n isIn = !isIn;\n }\n }\n\n return isIn;\n },\n\n /****************************************/\n /**** INTERSECTIONS ****/\n /****************************************/\n\n /**\n * Generate the function which computes the coordinates of the intersection point.\n * Primarily used in {@link JXG.Point.createIntersectionPoint}.\n * @param {JXG.Board} board object\n * @param {JXG.Line,JXG.Circle_JXG.Line,JXG.Circle_Number|Function} el1,el2,i The result will be a intersection point on el1 and el2.\n * i determines the intersection point if two points are available: \n *
\n * @param {Boolean} alwaysintersect. Flag that determines if segments and arc can have an outer intersection point\n * on their defining line or circle.\n * @returns {Function} Function returning a {@link JXG.Coords} object that determines\n * the intersection point.\n *\n * @see JXG.Point.createIntersectionPoint\n */\n intersectionFunction: function (board, el1, el2, i, j, alwaysintersect) {\n var func,\n that = this,\n el1_isArcType = false,\n el2_isArcType = false;\n\n el1_isArcType =\n el1.elementClass === Const.OBJECT_CLASS_CURVE &&\n (el1.type === Const.OBJECT_TYPE_ARC || el1.type === Const.OBJECT_TYPE_SECTOR)\n ? true\n : false;\n el2_isArcType =\n el2.elementClass === Const.OBJECT_CLASS_CURVE &&\n (el2.type === Const.OBJECT_TYPE_ARC || el2.type === Const.OBJECT_TYPE_SECTOR)\n ? true\n : false;\n\n if (\n (el1.elementClass === Const.OBJECT_CLASS_CURVE ||\n el2.elementClass === Const.OBJECT_CLASS_CURVE) &&\n (el1.elementClass === Const.OBJECT_CLASS_CURVE ||\n el1.elementClass === Const.OBJECT_CLASS_CIRCLE) &&\n (el2.elementClass === Const.OBJECT_CLASS_CURVE ||\n el2.elementClass === Const.OBJECT_CLASS_CIRCLE) /*&&\n !(el1_isArcType && el2_isArcType)*/\n ) {\n // curve - curve\n // with the exception that both elements are arc types\n /** @ignore */\n func = function () {\n return that.meetCurveCurve(el1, el2, i, j, el1.board);\n };\n } else if (\n (el1.elementClass === Const.OBJECT_CLASS_CURVE &&\n !el1_isArcType &&\n el2.elementClass === Const.OBJECT_CLASS_LINE) ||\n (el2.elementClass === Const.OBJECT_CLASS_CURVE &&\n !el2_isArcType &&\n el1.elementClass === Const.OBJECT_CLASS_LINE)\n ) {\n // curve - line (this includes intersections between conic sections and lines)\n // with the exception that the curve is of arc type\n /** @ignore */\n func = function () {\n return that.meetCurveLine(el1, el2, i, el1.board, Type.evaluate(alwaysintersect));\n };\n } else if (\n el1.type === Const.OBJECT_TYPE_POLYGON ||\n el2.type === Const.OBJECT_TYPE_POLYGON\n ) {\n // polygon - other\n // Uses the Greiner-Hormann clipping algorithm\n // Not implemented: polygon - point\n\n if (el1.elementClass === Const.OBJECT_CLASS_LINE) {\n // line - path\n /** @ignore */\n func = function () {\n var first1 = el1.evalVisProp('straightfirst'),\n last1 = el1.evalVisProp('straightlast'),\n first2 = el2.evalVisProp('straightfirst'),\n last2 = el2.evalVisProp('straightlast'),\n a_not;\n\n a_not = (!Type.evaluate(alwaysintersect) && (!first1 || !last1 || !first2 || !last2));\n return that.meetPolygonLine(el2, el1, i, el1.board, a_not);\n };\n } else if (el2.elementClass === Const.OBJECT_CLASS_LINE) {\n // path - line\n /** @ignore */\n func = function () {\n var first1 = el1.evalVisProp('straightfirst'),\n last1 = el1.evalVisProp('straightlast'),\n first2 = el2.evalVisProp('straightfirst'),\n last2 = el2.evalVisProp('straightlast'),\n a_not;\n\n a_not = (!Type.evaluate(alwaysintersect) && (!first1 || !last1 || !first2 || !last2));\n return that.meetPolygonLine(el1, el2, i, el1.board, a_not);\n };\n } else {\n // path - path\n /** @ignore */\n func = function () {\n return that.meetPathPath(el1, el2, i, el1.board);\n };\n }\n } else if (\n el1.elementClass === Const.OBJECT_CLASS_LINE &&\n el2.elementClass === Const.OBJECT_CLASS_LINE\n ) {\n // line - line, lines may also be segments.\n /** @ignore */\n func = function () {\n var res,\n c,\n first1 = el1.evalVisProp('straightfirst'),\n last1 = el1.evalVisProp('straightlast'),\n first2 = el2.evalVisProp('straightfirst'),\n last2 = el2.evalVisProp('straightlast');\n\n /**\n * If one of the lines is a segment or ray and\n * the intersection point should disappear if outside\n * of the segment or ray we call\n * meetSegmentSegment\n */\n if (\n !Type.evaluate(alwaysintersect) &&\n (!first1 || !last1 || !first2 || !last2)\n ) {\n res = that.meetSegmentSegment(\n el1.point1.coords.usrCoords,\n el1.point2.coords.usrCoords,\n el2.point1.coords.usrCoords,\n el2.point2.coords.usrCoords\n );\n\n if (\n (!first1 && res[1] < 0) ||\n (!last1 && res[1] > 1) ||\n (!first2 && res[2] < 0) ||\n (!last2 && res[2] > 1)\n ) {\n // Non-existent\n c = [0, NaN, NaN];\n } else {\n c = res[0];\n }\n\n return new Coords(Const.COORDS_BY_USER, c, el1.board);\n }\n\n return that.meet(el1.stdform, el2.stdform, i, el1.board);\n };\n } else {\n // All other combinations of circles and lines,\n // Arc types are treated as circles.\n /** @ignore */\n func = function () {\n var res = that.meet(el1.stdform, el2.stdform, i, el1.board),\n has = true,\n first,\n last,\n r;\n\n if (Type.evaluate(alwaysintersect)) {\n return res;\n }\n if (el1.elementClass === Const.OBJECT_CLASS_LINE) {\n first = el1.evalVisProp('straightfirst');\n last = el1.evalVisProp('straightlast');\n if (!first || !last) {\n r = that.affineRatio(el1.point1.coords, el1.point2.coords, res);\n if ((!last && r > 1 + Mat.eps) || (!first && r < 0 - Mat.eps)) {\n return new Coords(JXG.COORDS_BY_USER, [0, NaN, NaN], el1.board);\n }\n }\n }\n if (el2.elementClass === Const.OBJECT_CLASS_LINE) {\n first = el2.evalVisProp('straightfirst');\n last = el2.evalVisProp('straightlast');\n if (!first || !last) {\n r = that.affineRatio(el2.point1.coords, el2.point2.coords, res);\n if ((!last && r > 1 + Mat.eps) || (!first && r < 0 - Mat.eps)) {\n return new Coords(JXG.COORDS_BY_USER, [0, NaN, NaN], el1.board);\n }\n }\n }\n if (el1_isArcType) {\n has = that.coordsOnArc(el1, res);\n if (has && el2_isArcType) {\n has = that.coordsOnArc(el2, res);\n }\n if (!has) {\n return new Coords(JXG.COORDS_BY_USER, [0, NaN, NaN], el1.board);\n }\n }\n return res;\n };\n }\n\n return func;\n },\n\n otherIntersectionFunction: function (input, others, alwaysintersect, precision) {\n var func, board,\n el1, el2,\n that = this;\n\n el1 = input[0];\n el2 = input[1];\n board = el1.board;\n /** @ignore */\n func = function () {\n var i, k, c, d,\n isClose,\n le = others.length,\n eps = Type.evaluate(precision);\n\n for (i = le; i >= 0; i--) {\n if (el1.elementClass === Const.OBJECT_CLASS_CIRCLE &&\n [Const.OBJECT_CLASS_CIRCLE, Const.OBJECT_CLASS_LINE].indexOf(el2.elementClass) >= 0) {\n // circle, circle|line\n c = that.meet(el1.stdform, el2.stdform, i, board);\n } else if (el1.elementClass === Const.OBJECT_CLASS_CURVE &&\n [Const.OBJECT_CLASS_CURVE, Const.OBJECT_CLASS_CIRCLE].indexOf(el2.elementClass) >= 0) {\n // curve, circle|curve\n c = that.meetCurveCurve(el1, el2, i, 0, board);\n } else if (el1.elementClass === Const.OBJECT_CLASS_CURVE && el2.elementClass === Const.OBJECT_CLASS_LINE) {\n // curve, line\n if (Type.exists(el1.dataX)) {\n c = JXG.Math.Geometry.meetCurveLine(el1, el2, i, el1.board, Type.evaluate(alwaysintersect));\n } else {\n c = JXG.Math.Geometry.meetCurveLineContinuous(el1, el2, i, el1.board);\n }\n }\n\n if (c === undefined) {\n // Intersection point does not exist\n continue;\n }\n\n // If the intersection is close to one of the points in other\n // we have to search for another intersection point.\n isClose = false;\n for (k = 0; !isClose && k < le; k++) {\n if (Type.exists(c) && Type.exists(c.distance)) {\n d = c.distance(JXG.COORDS_BY_USER, others[k].coords);\n if (d < eps) {\n isClose = true;\n }\n }\n }\n if (!isClose) {\n // We are done, the intersection is away from any other\n // intersection point.\n return c;\n }\n }\n // Otherwise we return the last intersection point\n return c;\n };\n return func;\n },\n\n /**\n * Returns true if the coordinates are on the arc element,\n * false otherwise. Usually, coords is an intersection\n * on the circle line. Now it is decided if coords are on the\n * circle restricted to the arc line.\n * @param {Arc} arc arc or sector element\n * @param {JXG.Coords} coords Coords object of an intersection\n * @returns {Boolean}\n * @private\n */\n coordsOnArc: function (arc, coords) {\n var angle = this.rad(arc.radiuspoint, arc.center, coords.usrCoords.slice(1)),\n alpha = 0.0,\n beta = this.rad(arc.radiuspoint, arc.center, arc.anglepoint),\n ev_s = arc.evalVisProp('selection');\n\n if (arc.evalVisProp('orientation') === 'clockwise') {\n angle = 2 * Math.PI - angle;\n beta = 2 * Math.PI - beta;\n }\n\n if ((ev_s === \"minor\" && beta > Math.PI) || (ev_s === \"major\" && beta < Math.PI)) {\n alpha = beta;\n beta = 2 * Math.PI;\n }\n if (angle < alpha || angle > beta) {\n return false;\n }\n return true;\n },\n\n /**\n * Computes the intersection of a pair of lines, circles or both.\n * It uses the internal data array stdform of these elements.\n * @param {Array} el1 stdform of the first element (line or circle)\n * @param {Array} el2 stdform of the second element (line or circle)\n * @param {Number|Function} i Index of the intersection point that should be returned.\n * @param board Reference to the board.\n * @returns {JXG.Coords} Coordinates of one of the possible two or more intersection points.\n * Which point will be returned is determined by i.\n */\n meet: function (el1, el2, i, board) {\n var result,\n eps = Mat.eps;\n\n if (Math.abs(el1[3]) < eps && Math.abs(el2[3]) < eps) {\n // line line\n result = this.meetLineLine(el1, el2, i, board);\n } else if (Math.abs(el1[3]) >= eps && Math.abs(el2[3]) < eps) {\n // circle line\n result = this.meetLineCircle(el2, el1, i, board);\n } else if (Math.abs(el1[3]) < eps && Math.abs(el2[3]) >= eps) {\n // line circle\n result = this.meetLineCircle(el1, el2, i, board);\n } else {\n // circle circle\n result = this.meetCircleCircle(el1, el2, i, board);\n }\n\n return result;\n },\n\n /**\n * Intersection of the line with the board\n * @param {Array} line stdform of the line in screen coordinates\n * @param {JXG.Board} board reference to a board.\n * @param {Number} margin optional margin, to avoid the display of the small sides of lines.\n * @returns {Array} [intersection coords 1, intersection coords 2]\n */\n meetLineBoard: function (line, board, margin) {\n // Intersect the line with the four borders of the board.\n var s = [],\n intersect1,\n intersect2,\n i, j;\n\n if (!Type.exists(margin)) {\n margin = 0;\n }\n\n // top\n s[0] = Mat.crossProduct(line, [margin, 0, 1]);\n // left\n s[1] = Mat.crossProduct(line, [margin, 1, 0]);\n // bottom\n s[2] = Mat.crossProduct(line, [-margin - board.canvasHeight, 0, 1]);\n // right\n s[3] = Mat.crossProduct(line, [-margin - board.canvasWidth, 1, 0]);\n\n // Normalize the intersections\n for (i = 0; i < 4; i++) {\n if (Math.abs(s[i][0]) > Mat.eps) {\n for (j = 2; j > 0; j--) {\n s[i][j] /= s[i][0];\n }\n s[i][0] = 1.0;\n }\n }\n\n // line is parallel to \"left\", take \"top\" and \"bottom\"\n if (Math.abs(s[1][0]) < Mat.eps) {\n intersect1 = s[0]; // top\n intersect2 = s[2]; // bottom\n // line is parallel to \"top\", take \"left\" and \"right\"\n } else if (Math.abs(s[0][0]) < Mat.eps) {\n intersect1 = s[1]; // left\n intersect2 = s[3]; // right\n // left intersection out of board (above)\n } else if (s[1][2] < 0) {\n intersect1 = s[0]; // top\n\n // right intersection out of board (below)\n if (s[3][2] > board.canvasHeight) {\n intersect2 = s[2]; // bottom\n } else {\n intersect2 = s[3]; // right\n }\n // left intersection out of board (below)\n } else if (s[1][2] > board.canvasHeight) {\n intersect1 = s[2]; // bottom\n\n // right intersection out of board (above)\n if (s[3][2] < 0) {\n intersect2 = s[0]; // top\n } else {\n intersect2 = s[3]; // right\n }\n } else {\n intersect1 = s[1]; // left\n\n // right intersection out of board (above)\n if (s[3][2] < 0) {\n intersect2 = s[0]; // top\n // right intersection out of board (below)\n } else if (s[3][2] > board.canvasHeight) {\n intersect2 = s[2]; // bottom\n } else {\n intersect2 = s[3]; // right\n }\n }\n\n return [\n new Coords(Const.COORDS_BY_SCREEN, intersect1.slice(1), board),\n new Coords(Const.COORDS_BY_SCREEN, intersect2.slice(1), board)\n ];\n },\n\n /**\n * Intersection of two lines.\n * @param {Array} l1 stdform of the first line\n * @param {Array} l2 stdform of the second line\n * @param {number} i unused\n * @param {JXG.Board} board Reference to the board.\n * @returns {JXG.Coords} Coordinates of the intersection point.\n */\n meetLineLine: function (l1, l2, i, board) {\n var s = isNaN(l1[5] + l2[5]) ? [0, 0, 0] : Mat.crossProduct(l1, l2);\n\n // Make intersection of parallel lines more robust:\n if (Math.abs(s[0]) < 1.0e-14) {\n s[0] = 0;\n }\n return new Coords(Const.COORDS_BY_USER, s, board);\n },\n\n /**\n * Intersection of line and circle.\n * @param {Array} lin stdform of the line\n * @param {Array} circ stdform of the circle\n * @param {number|function} i number of the returned intersection point.\n * i==0: use the positive square root,\n * i==1: use the negative square root.\n * @param {JXG.Board} board Reference to a board.\n * @returns {JXG.Coords} Coordinates of the intersection point\n */\n meetLineCircle: function (lin, circ, i, board) {\n var a, b, c, d, n, A, B, C, k, t;\n\n // Radius is zero, return center of circle\n if (circ[4] < Mat.eps) {\n if (Math.abs(Mat.innerProduct([1, circ[6], circ[7]], lin, 3)) < Mat.eps) {\n return new Coords(Const.COORDS_BY_USER, circ.slice(6, 8), board);\n }\n\n return new Coords(Const.COORDS_BY_USER, [NaN, NaN], board);\n }\n c = circ[0];\n b = circ.slice(1, 3);\n a = circ[3];\n d = lin[0];\n n = lin.slice(1, 3);\n\n // Line is assumed to be normalized. Therefore, nn==1 and we can skip some operations:\n /*\n var nn = n[0]*n[0]+n[1]*n[1];\n A = a*nn;\n B = (b[0]*n[1]-b[1]*n[0])*nn;\n C = a*d*d - (b[0]*n[0]+b[1]*n[1])*d + c*nn;\n */\n A = a;\n B = b[0] * n[1] - b[1] * n[0];\n C = a * d * d - (b[0] * n[0] + b[1] * n[1]) * d + c;\n\n k = B * B - 4 * A * C;\n if (k > -Mat.eps * Mat.eps) {\n k = Math.sqrt(Math.abs(k));\n t = [(-B + k) / (2 * A), (-B - k) / (2 * A)];\n\n return Type.evaluate(i) === 0\n ? new Coords(\n Const.COORDS_BY_USER,\n [-t[0] * -n[1] - d * n[0], -t[0] * n[0] - d * n[1]],\n board\n )\n : new Coords(\n Const.COORDS_BY_USER,\n [-t[1] * -n[1] - d * n[0], -t[1] * n[0] - d * n[1]],\n board\n );\n }\n\n return new Coords(Const.COORDS_BY_USER, [0, 0, 0], board);\n },\n\n /**\n * Intersection of two circles.\n * @param {Array} circ1 stdform of the first circle\n * @param {Array} circ2 stdform of the second circle\n * @param {number|function} i number of the returned intersection point.\n * i==0: use the positive square root,\n * i==1: use the negative square root.\n * @param {JXG.Board} board Reference to the board.\n * @returns {JXG.Coords} Coordinates of the intersection point\n */\n meetCircleCircle: function (circ1, circ2, i, board) {\n var radicalAxis;\n\n // Radius is zero, return center of circle, if on other circle\n if (circ1[4] < Mat.eps) {\n if (\n Math.abs(this.distance(circ1.slice(6, 8), circ2.slice(6, 8)) - circ2[5]) <\n Mat.eps\n ) {\n return new Coords(Const.COORDS_BY_USER, circ1.slice(6, 8), board);\n }\n\n return new Coords(Const.COORDS_BY_USER, [0, 0, 0], board);\n }\n\n // Radius is zero, return center of circle, if on other circle\n if (circ2[4] < Mat.eps) {\n if (\n Math.abs(this.distance(circ2.slice(6, 8), circ1.slice(6, 8)) - circ1[5]) <\n Mat.eps\n ) {\n return new Coords(Const.COORDS_BY_USER, circ2.slice(6, 8), board);\n }\n\n return new Coords(Const.COORDS_BY_USER, [0, 0, 0], board);\n }\n\n radicalAxis = [\n circ2[3] * circ1[0] - circ1[3] * circ2[0],\n circ2[3] * circ1[1] - circ1[3] * circ2[1],\n circ2[3] * circ1[2] - circ1[3] * circ2[2],\n 0,\n 1,\n Infinity,\n Infinity,\n Infinity\n ];\n radicalAxis = Mat.normalize(radicalAxis);\n\n return this.meetLineCircle(radicalAxis, circ1, i, board);\n },\n\n /**\n * Segment-wise search for the nr-th intersection of two curves.\n * testSegment is always assumed to be true.\n *\n * @param {JXG.Curve} c1 Curve, Line or Circle\n * @param {JXG.Curve} c2 Curve, Line or Circle\n * @param {Number} nr the nr-th intersection point will be returned\n * @param {JXG.Board} [board=c1.board] Reference to a board object\n * @returns {JXG.Coords} intersection as Coords object\n *\n * @private\n * @see JXG.Math.Geometry.meetCurveCurve\n */\n meetCurveCurveDiscrete: function (c1, c2, nr, board) {\n var co,\n i = Type.evaluate(nr);\n\n if (c1.bezierDegree === 3 || c2.bezierDegree === 3) {\n co = this.meetBezierCurveRedBlueSegments(c1, c2, i);\n } else {\n co = this.meetCurveRedBlueSegments(c1, c2, i);\n }\n return new Coords(Const.COORDS_BY_USER, co, board);\n },\n\n /**\n * Apply Newton-Raphson to search for an intersection of two curves\n * in a given range of the first curve.\n *\n * @param {JXG.Curve} c1 Curve, Line or Circle\n * @param {JXG.Curve} c2 Curve, Line or Circle\n * @param {Array} range Domain for the search of an intersection. The start value\n * for the search is chosen to be inside of that range.\n * @param {Boolean} testSegment If true require that t1 and t2 are inside of the allowed bounds.\n * @returns {Array} [[z, x, y], t1, t2, t, ||c1[t1]-c2[t2]||**2]. The last entry is set to\n * 10000 if the intersection is outside of the given domain (range) for the first curve.\n * @private\n * @see JXG.Math.Geometry._meetCurveCurveIterative\n * @see JXG.Math.Numerics.generalizedDampedNewton\n * @see JXG.Math.Geometry.meetCurveCurveCobyla\n */\n meetCurveCurveNewton: function (c1, c2, range1, range2, testSegment) {\n var t1, t2,\n co, r,\n inphi = (Math.sqrt(5) - 1) * 0.5,\n damp = 0.85, // (\n eps3 = Mat.eps * Mat.eps * Mat.eps,\n eps2 = Mat.eps * Mat.eps,\n\n ma1 = c1.maxX(),\n mi1 = c1.minX(),\n ma2 = c2.maxX(),\n mi2 = c2.minX(),\n\n F = function(t, n) {\n var f1 = c1.Ft(t[0]),\n f2 = c2.Ft(t[1]),\n e = f1[1] - f2[1],\n f = f1[2] - f2[2];\n\n return [e, f];\n },\n D = function(t, n) {\n var h = Mat.eps,\n h2 = 2 * h,\n f1_1 = c1.Ft(t[0] - h),\n f1_2 = c1.Ft(t[0] + h),\n f2_1 = c2.Ft(t[1] - h),\n f2_2 = c2.Ft(t[1] + h);\n return [\n [ (f1_2[1] - f1_1[1]) / h2,\n -(f2_2[1] - f2_1[1]) / h2],\n [ (f1_2[2] - f1_1[2]) / h2,\n -(f2_2[2] - f2_1[2]) / h2]\n ];\n };\n\n t1 = range1[0] + (range1[1] - range1[0]) * (1 - inphi);\n t2 = range2[0] + (range2[1] - range2[0]) * (1 - inphi);\n\n // Use damped Newton\n // r = Numerics.generalizedDampedNewtonCurves(c1, c2, t1, t2, damp, eps3);\n r = Numerics.generalizedDampedNewton(F, D, 2, [t1, t2], damp, eps3, 40);\n // r: [t1, t2, F2]\n\n t1 = r[0][0];\n t2 = r[0][1];\n co = c1.Ft(t1);\n\n if (\n t1 < range1[0] - Mat.eps || t1 > range1[1] + Mat.eps ||\n t2 < range2[0] - Mat.eps || t2 > range2[1] + Mat.eps ||\n (testSegment &&\n (t1 < mi1 - eps2 || t1 > ma1 + eps2 ||\n t2 < mi2 - eps2 || t2 > ma2 + eps2)\n )\n ) {\n // Damped-Newton found solution outside of range\n return [co, t1, t2, 10000];\n }\n// console.log(t1, r[3])\n\n return [co, t1, t2, r[1]];\n },\n\n /**\n * Return a list of the (at most) first i intersection points of two curves.\n * Computed iteratively.\n *\n * @param {JXG.Curve} c1 Curve, Line or Circle\n * @param {JXG.Curve} c2 Curve, Line or Circle\n * @param {Number} low Lower bound of the search domain (between [0, 1])\n * @param {Number} up Upper bound of the search domain (between [0, 1])\n * @param {Number} i Return a list of the first i intersection points\n * @param {Boolean} testSegment If true require that t1 and t2 are inside of the allowed bounds.\n * @returns {Array} List of the first i intersection points, given by the parameter t.\n * @private\n * @see JXG.Math.Geometry.meetCurveCurveNewton\n * @see JXG.Math.Geometry.meetCurveCurve\n */\n _meetCurveCurveIterative: function(c1, c2, range1, range2, i, testSegment) {\n var ret,\n t1,// t2,\n low1, low2, up1, up2,\n eps = Mat.eps * 100, // Minimum difference between zeros\n j1, j2,\n steps = 20,\n d1, d2,\n zeros = [];\n\n low1 = range1[0];\n up1 = range1[1];\n low2 = range2[0];\n up2 = range2[1];\n if (up1 < low1 || up2 < low2) {\n return [];\n }\n\n // console.log('DO iterative', [low1, up1], [low2, up2])\n\n d1 = (up1 - low1) / steps;\n d2 = (up2 - low2) / steps;\n for (j1 = 0; j1 < steps; j1++) {\n for (j2 = 0; j2 < steps; j2++) {\n\n ret = this.meetCurveCurveNewton(c1, c2,\n [low1 + j1 * d1, low1 + (j1 + 1) * d1],\n [low2 + j2 * d2, low2 + (j2 + 1) * d2],\n testSegment);\n\n if (ret[3] < Mat.eps) {\n t1 = ret[1];\n // t2 = ret[2];\n // console.log(\"\\tFOUND\", t1, t2, c1.Ft(t1)[2])\n zeros = zeros.concat([t1]);\n zeros = Type.toUniqueArrayFloat(zeros, eps);\n // console.log(zeros, i)\n if (zeros.length > i) {\n return zeros;\n }\n }\n }\n }\n\n return zeros;\n },\n\n /**\n * Compute an intersection of the curves c1 and c2.\n * We want to find values t1, t2 such that\n * c1(t1) = c2(t2), i.e. (c1_x(t1) - c2_x(t2), c1_y(t1) - c2_y(t2)) = (0, 0).\n *\n * Available methods:\n * \n *
\n *\n * Segment-wise intersection is more stable, but has problems with tangent points.\n * Damped Newton-Raphson converges very rapidly but sometimes behaves chaotic.\n *\n * @param {JXG.Curve} c1 Curve, Line or Circle\n * @param {JXG.Curve} c2 Curve, Line or Circle\n * @param {Number|Function} nr the nr-th intersection point will be returned. For backwards compatibility:\n * if method='newton' and nr is not an integer, {@link JXG.Math.Numerics.generalizedNewton} is called\n * directly with nr as start value (not recommended).\n * @param {Number} t2ini not longer used. Must be supplied and is ignored.\n * @param {JXG.Board} [board=c1.board] Reference to a board object.\n * @param {String} [method] Intersection method, possible values are 'newton' and 'segment'.\n * If both curves are given by functions (assumed to be continuous), 'newton' is the default, otherwise\n * 'segment' is the default.\n * @parame {Boolean} testSegment If true require that the intersection is inside of the allowed bounds for both elements (in _meetCurveCurveIterative)\n * @returns {JXG.Coords} intersection point\n *\n * @see JXG.Math.Geometry.meetCurveCurveDiscrete\n * @see JXG.Math.Geometry._meetCurveCurveIterative\n */\n meetCurveCurve: function (c1, c2, nr, t2ini, board, method, testSegment) {\n var co,\n zeros,\n mi1, ma1, mi2, ma2,\n i = Type.evaluate(nr);\n\n board = board || c1.board;\n if (method === 'segment' || Type.exists(c1.dataX) || Type.exists(c2.dataX)) {\n // Discrete data points, i.e. x-coordinates of c1 or c2 are given in an array)\n return this.meetCurveCurveDiscrete(c1, c2, i, board);\n }\n\n // Outdated:\n // Backwards compatibility if nr is not a positive integer then\n // generalizedNewton is still used.\n if (Type.exists(method) && method === 'newton' && i < 0 || parseInt(i) !== i) {\n co = Numerics.generalizedNewton(c1, c2, i, t2ini);\n return new Coords(Const.COORDS_BY_USER, co, board);\n }\n\n // Method 'newton'\n mi1 = c1.minX();\n ma1 = c1.maxX();\n mi2 = c2.minX();\n ma2 = c2.maxX();\n\n // console.time('curvecurve')\n zeros = this._meetCurveCurveIterative(c1, c2, [mi1, ma1], [mi2, ma2], i, testSegment);\n // console.timeEnd('curvecurve')\n\n if (zeros.length > i) {\n co = c1.Ft(zeros[i]);\n } else {\n return [0, NaN, NaN];\n }\n\n return new Coords(Const.COORDS_BY_USER, co, board);\n },\n\n /**\n * Intersection of curve with line,\n * Order of input does not matter for el1 and el2.\n * From version 0.99.7 on this method calls\n * {@link JXG.Math.Geometry.meetCurveLineDiscrete}.\n * If higher precision is needed, {@link JXG.Math.Geometry.meetCurveLineContinuous}\n * has to be used.\n *\n * @param {JXG.Curve|JXG.Line} el1 Curve or Line\n * @param {JXG.Curve|JXG.Line} el2 Curve or Line\n * @param {Number|Function} nr the nr-th intersection point will be returned.\n * @param {JXG.Board} [board=el1.board] Reference to a board object.\n * @param {Boolean} alwaysIntersect If false just the segment between the two defining points are tested for intersection\n * @returns {JXG.Coords} Intersection point. In case no intersection point is detected,\n * the ideal point [0,1,0] is returned.\n */\n meetCurveLine: function (el1, el2, nr, board, alwaysIntersect) {\n var v = [0, NaN, NaN],\n cu,\n li;\n\n if (!Type.exists(board)) {\n board = el1.board;\n }\n\n if (el1.elementClass === Const.OBJECT_CLASS_CURVE) {\n cu = el1;\n li = el2;\n } else {\n cu = el2;\n li = el1;\n }\n\n if (Type.exists(cu.dataX)) {\n // We use the discrete version if\n // the curve is not a parametric curve, e.g. implicit plots\n v = this.meetCurveLineDiscrete(cu, li, nr, board, !alwaysIntersect);\n } else {\n v = this.meetCurveLineContinuous(cu, li, nr, board, !alwaysIntersect);\n // v = this.meetCurveCurve(cu, li, nr, 0, board, 'newton', !alwaysIntersect);\n }\n\n return v;\n },\n\n /**\n * Intersection of line and curve, continuous case.\n * Finds the nr-th intersection point\n * Uses {@link JXG.Math.Geometry.meetCurveLineDiscrete} as a first approximation.\n * A more exact solution is then found with {@link JXG.Math.Numerics.root}.\n *\n * @param {JXG.Curve} cu Curve\n * @param {JXG.Line} li Line\n * @param {NumberFunction} nr Will return the nr-th intersection point.\n * @param {JXG.Board} board\n * @param {Boolean} testSegment Test if intersection has to be inside of the segment or somewhere on the\n * line defined by the segment\n * @returns {JXG.Coords} Coords object containing the intersection.\n */\n meetCurveLineContinuous: function (cu, li, nr, board, testSegment) {\n var func0, func1,\n t, v, x, y, z,\n eps = Mat.eps,\n epsLow = Mat.eps,\n steps,\n delta,\n tnew, tmin, fmin,\n i, ft;\n\n v = this.meetCurveLineDiscrete(cu, li, nr, board, testSegment);\n x = v.usrCoords[1];\n y = v.usrCoords[2];\n\n func0 = function (t) {\n var c1, c2;\n\n if (t > cu.maxX() || t < cu.minX()) {\n return Infinity;\n }\n c1 = cu.X(t) - x;\n c2 = cu.Y(t) - y;\n return c1 * c1 + c2 * c2;\n // return c1 * (cu.X(t + h) - cu.X(t - h)) + c2 * (cu.Y(t + h) - cu.Y(t - h)) / h;\n };\n\n func1 = function (t) {\n var v = li.stdform[0] + li.stdform[1] * cu.X(t) + li.stdform[2] * cu.Y(t);\n return v * v;\n };\n\n // Find t\n steps = 50;\n delta = (cu.maxX() - cu.minX()) / steps;\n tnew = cu.minX();\n fmin = 0.0001; //eps;\n tmin = NaN;\n for (i = 0; i < steps; i++) {\n t = Numerics.root(func0, [\n Math.max(tnew, cu.minX()),\n Math.min(tnew + delta, cu.maxX())\n ]);\n ft = Math.abs(func0(t));\n if (ft <= fmin) {\n fmin = ft;\n tmin = t;\n if (fmin < eps) {\n break;\n }\n }\n\n tnew += delta;\n }\n t = tmin;\n // Compute \"exact\" t\n t = Numerics.root(func1, [\n Math.max(t - delta, cu.minX()),\n Math.min(t + delta, cu.maxX())\n ]);\n\n ft = func1(t);\n // Is the point on the line?\n if (isNaN(ft) || Math.abs(ft) > epsLow) {\n z = 0.0; //NaN;\n } else {\n z = 1.0;\n }\n\n return new Coords(Const.COORDS_BY_USER, [z, cu.X(t), cu.Y(t)], board);\n },\n\n /**\n * Intersection of line and curve, discrete case.\n * Segments are treated as lines.\n * Finding the nr-th intersection point should work for all nr.\n * @param {JXG.Curve} cu\n * @param {JXG.Line} li\n * @param {Number|Function} nr\n * @param {JXG.Board} board\n * @param {Boolean} testSegment Test if intersection has to be inside of the segment or somewhere on the\n * line defined by the segment\n *\n * @returns {JXG.Coords} Intersection point. In case no intersection point is detected,\n * the ideal point [0,1,0] is returned.\n */\n meetCurveLineDiscrete: function (cu, li, nr, board, testSegment) {\n var i, j,\n n = Type.evaluate(nr),\n p1, p2,\n p, q,\n lip1 = li.point1.coords.usrCoords,\n lip2 = li.point2.coords.usrCoords,\n d, res,\n cnt = 0,\n len = cu.numberPoints,\n ev_sf = li.evalVisProp('straightfirst'),\n ev_sl = li.evalVisProp('straightlast');\n\n // In case, no intersection will be found we will take this\n q = new Coords(Const.COORDS_BY_USER, [0, NaN, NaN], board);\n\n if (lip1[0] === 0.0) {\n lip1 = [1, lip2[1] + li.stdform[2], lip2[2] - li.stdform[1]];\n } else if (lip2[0] === 0.0) {\n lip2 = [1, lip1[1] + li.stdform[2], lip1[2] - li.stdform[1]];\n }\n\n p2 = cu.points[0].usrCoords;\n for (i = 1; i < len; i += cu.bezierDegree) {\n p1 = p2.slice(0);\n p2 = cu.points[i].usrCoords;\n d = this.distance(p1, p2);\n\n // The defining points are not identical\n if (d > Mat.eps) {\n if (cu.bezierDegree === 3) {\n res = this.meetBeziersegmentBeziersegment(\n [\n cu.points[i - 1].usrCoords.slice(1),\n cu.points[i].usrCoords.slice(1),\n cu.points[i + 1].usrCoords.slice(1),\n cu.points[i + 2].usrCoords.slice(1)\n ],\n [lip1.slice(1), lip2.slice(1)],\n testSegment\n );\n } else {\n res = [this.meetSegmentSegment(p1, p2, lip1, lip2)];\n }\n\n for (j = 0; j < res.length; j++) {\n p = res[j];\n if (0 <= p[1] && p[1] <= 1) {\n if (cnt === n) {\n /**\n * If the intersection point is not part of the segment,\n * this intersection point is set to non-existent.\n * This prevents jumping behavior of the intersection points.\n * But it may be discussed if it is the desired behavior.\n */\n if (\n testSegment &&\n ((!ev_sf && p[2] < 0) || (!ev_sl && p[2] > 1))\n ) {\n return q; // break;\n }\n\n q = new Coords(Const.COORDS_BY_USER, p[0], board);\n return q; // break;\n }\n cnt += 1;\n }\n }\n }\n }\n\n return q;\n },\n\n /**\n * Find the n-th intersection point of two curves named red (first parameter) and blue (second parameter).\n * We go through each segment of the red curve and search if there is an intersection with a segment of the blue curve.\n * This double loop, i.e. the outer loop runs along the red curve and the inner loop runs along the blue curve, defines\n * the n-th intersection point. The segments are either line segments or Bezier curves of degree 3. This depends on\n * the property bezierDegree of the curves.\n * \n *
\n *\n * @param {JXG.GeometryElement3D} el1 Plane or sphere element\n * @param {JXG.GeometryElement3D} el2 Plane or sphere element\n * @returns {Array} of functions needed as input to create the intersecting line or circle.\n *\n */\n intersectionFunction3D: function (view, el1, el2) {\n var func,\n that = this;\n\n if (el1.type === Const.OBJECT_TYPE_PLANE3D) {\n if (el2.type === Const.OBJECT_TYPE_PLANE3D) {\n // func = () => view.intersectionPlanePlane(el1, el2)[i];\n func = view.intersectionPlanePlane(el1, el2);\n } else if (el2.type === Const.OBJECT_TYPE_SPHERE3D) {\n func = that.meetPlaneSphere(el1, el2);\n }\n } else if (el1.type === Const.OBJECT_TYPE_SPHERE3D) {\n if (el2.type === Const.OBJECT_TYPE_PLANE3D) {\n func = that.meetPlaneSphere(el2, el1);\n } else if (el2.type === Const.OBJECT_TYPE_SPHERE3D) {\n func = that.meetSphereSphere(el1, el2);\n }\n }\n\n return func;\n },\n\n /**\n * Intersecting point of three planes in 3D. The planes\n * are given in Hesse normal form.\n *\n * @param {Array} n1 Hesse normal form vector of plane 1\n * @param {Number} d1 Hesse normal form right hand side of plane 1\n * @param {Array} n2 Hesse normal form vector of plane 2\n * @param {Number} d2 Hesse normal form right hand side of plane 2\n * @param {Array} n3 Hesse normal form vector of plane 1\n * @param {Number} d3 Hesse normal form right hand side of plane 3\n * @returns {Array} Coordinates array of length 4 of the intersecting point\n */\n meet3Planes: function (n1, d1, n2, d2, n3, d3) {\n var p = [1, 0, 0, 0],\n n31, n12, n23,\n denom,\n i;\n\n n31 = Mat.crossProduct(n3.slice(1), n1.slice(1));\n n12 = Mat.crossProduct(n1.slice(1), n2.slice(1));\n n23 = Mat.crossProduct(n2.slice(1), n3.slice(1));\n\n denom = Mat.innerProduct(n1.slice(1), n23, 3);\n for (i = 0; i < 3; i++) {\n p[i + 1] = (d1 * n23[i] + d2 * n31[i] + d3 * n12[i]) / denom;\n }\n\n return p;\n },\n\n /**\n * Direction of intersecting line of two planes in 3D.\n *\n * @param {Array} v11 First vector spanning plane 1 (homogeneous coordinates)\n * @param {Array} v12 Second vector spanning plane 1 (homogeneous coordinates)\n * @param {Array} v21 First vector spanning plane 2 (homogeneous coordinates)\n * @param {Array} v22 Second vector spanning plane 2 (homogeneous coordinates)\n * @returns {Array} Coordinates array of length 4 of the direction (homogeneous coordinates)\n */\n meetPlanePlane: function (v11, v12, v21, v22) {\n var no1,\n no2,\n v, w;\n\n v = v11.slice(1);\n w = v12.slice(1);\n no1 = Mat.crossProduct(v, w);\n\n v = v21.slice(1);\n w = v22.slice(1);\n no2 = Mat.crossProduct(v, w);\n\n w = Mat.crossProduct(no1, no2);\n w.unshift(0);\n return w;\n },\n\n meetPlaneSphere: function (el1, el2) {\n var dis = function () {\n return Mat.innerProduct(el1.normal, el2.center.coords, 4) - el1.d;\n };\n\n return [\n // Center\n function() {\n return Mat.axpy(-dis(), el1.normal, el2.center.coords);\n },\n // Normal\n el1.normal,\n // Radius\n function () {\n // Radius (returns NaN if spheres don't touch)\n var r = el2.Radius(),\n s = dis();\n return Math.sqrt(r * r - s * s);\n }\n ];\n },\n\n meetSphereSphere: function (el1, el2) {\n var skew = function () {\n var dist = el1.center.distance(el2.center),\n r1 = el1.Radius(),\n r2 = el2.Radius();\n return (r1 - r2) * (r1 + r2) / (dist * dist);\n };\n return [\n // Center\n function () {\n var s = skew();\n return [\n 1,\n 0.5 * ((1 - s) * el1.center.coords[1] + (1 + s) * el2.center.coords[1]),\n 0.5 * ((1 - s) * el1.center.coords[2] + (1 + s) * el2.center.coords[2]),\n 0.5 * ((1 - s) * el1.center.coords[3] + (1 + s) * el2.center.coords[3])\n ];\n },\n // Normal\n function() {\n return Stat.subtract(el2.center.coords, el1.center.coords);\n },\n // Radius\n function () {\n // Radius (returns NaN if spheres don't touch)\n var dist = el1.center.distance(el2.center),\n r1 = el1.Radius(),\n r2 = el2.Radius(),\n s = skew(),\n rIxnSq = 0.5 * (r1 * r1 + r2 * r2 - 0.5 * dist * dist * (1 + s * s));\n return Math.sqrt(rIxnSq);\n }\n ];\n },\n\n /**\n * Test if parameters are inside of allowed ranges\n *\n * @param {Array} params Array of length 1 or 2\n * @param {Array} r_u First range\n * @param {Array} [r_v] Second range\n * @returns Boolean\n * @private\n */\n _paramsOutOfRange: function(params, r_u, r_v) {\n return params[0] < r_u[0] || params[0] > r_u[1] ||\n (params.length > 1 && (params[1] < r_v[0] || params[1] > r_v[1]));\n },\n\n /**\n * Given the 2D screen coordinates of a point, finds the nearest point on the given\n * parametric curve or surface, and returns its view-space coordinates.\n * @param {Array} p Homogeneous 3D coordinates for which the closest point on the curve point is searched.\n * @param {JXG.Curve3D|JXG.Surface3D} target Parametric curve or surface to project to.\n * @param {Number} n Dimension of the host element to which the coords are projected.\n * @param {Array} params New position of point on the target (i.e. it is a return value),\n * modified in place during the search, ending up at the nearest point.\n * Usually, point.position is supplied for params.\n *\n * @returns {Array} Array of length 4 containing the coordinates of the nearest point on the curve or surface.\n */\n projectCoordsToParametric: function (p, target, n, params) {\n // The variables and parameters for the Cobyla constrained\n // minimization algorithm are explained in the Cobyla.js comments\n var rhobeg, // initial size of simplex (Cobyla)\n rhoend, // finial size of simplex (Cobyla)\n iprint = 0, // no console output (Cobyla)\n maxfun = 200, // call objective function at most 200 times (Cobyla)\n _minFunc, // Objective function for Cobyla\n f = Math.random() * 0.01 + 0.5,\n r_u, r_v,\n m = 2 * n;\n\n // adapt simplex size to parameter range\n if (n === 1) {\n r_u = [Type.evaluate(target.range[0]), Type.evaluate(target.range[1])];\n rhobeg = 0.1 * (r_u[1] - r_u[0]);\n\n } else if (n === 2) {\n r_u = [Type.evaluate(target.range_u[0]), Type.evaluate(target.range_u[1])];\n r_v = [Type.evaluate(target.range_v[0]), Type.evaluate(target.range_v[1])];\n rhobeg = 0.1 * Math.min(\n r_u[1] - r_u[0],\n r_v[1] - r_v[0]\n );\n }\n rhoend = rhobeg / 5e6;\n\n // Minimize distance of the new position to the original position\n _minFunc = function (n, m, w, con) {\n var p_new = [\n 1,\n target.X.apply(target, w),\n target.Y.apply(target, w),\n target.Z.apply(target, w)\n ],\n xDiff = p[1] - p_new[1],\n yDiff = p[2] - p_new[2],\n zDiff = p[3] - p_new[3];\n\n if (m >= 2) {\n con[0] = w[0] - r_u[0];\n con[1] = -w[0] + r_u[1];\n }\n if (m >= 4) {\n con[2] = w[1] - r_v[0];\n con[3] = -w[1] + r_v[1];\n }\n\n return xDiff * xDiff + yDiff * yDiff + zDiff * zDiff;\n };\n\n // First optimization without range constraints to give a smooth drag experience on\n // cyclic structures.\n\n // Set the start values\n if (params.length === 0) {\n // If length > 0: take the previous position as start values for the optimization\n params[0] = f * (r_u[0] + r_u[1]);\n if (n === 2) {\n params[1] = f * (r_v[0] + r_v[1]);\n }\n } else {\n params[0] = (params[0] <= r_u[0]) ? r_u[0] + Mat.eps : params[0];\n params[0] = (params[0] >= r_u[1]) ? r_u[1] - Mat.eps : params[0];\n if (n === 2) {\n params[1] = (params[1] <= r_v[0]) ? r_v[0] + Mat.eps : params[1];\n params[1] = (params[1] >= r_v[1]) ? r_v[1] - Mat.eps : params[1];\n }\n }\n\n Mat.Nlp.FindMinimum(_minFunc, n, m, params, rhobeg, rhoend, iprint, maxfun);\n\n // Update p which is used subsequently in _minFunc\n p = [\n 1,\n target.X.apply(target, params),\n target.Y.apply(target, params),\n target.Z.apply(target, params)\n ];\n\n // If the optimal params are outside of the range:\n // Second optimization to obey the range constraints\n\n if (this._paramsOutOfRange(params, r_u, r_v)) {\n // Set the start values again\n // params[0] = f * (r_u[0] + r_u[1]);\n // if (n === 2) {\n // params[1] = f * (r_v[0] + r_v[1]);\n // }\n params[0] = (params[0] <= r_u[0]) ? r_u[0] + Mat.eps : params[0];\n params[0] = (params[0] >= r_u[1]) ? r_u[1] - Mat.eps : params[0];\n if (n === 2) {\n params[1] = (params[1] <= r_v[0]) ? r_v[0] + Mat.eps : params[1];\n params[1] = (params[1] >= r_v[1]) ? r_v[1] - Mat.eps : params[1];\n }\n Mat.Nlp.FindMinimum(_minFunc, n, m, params, rhobeg, rhoend, iprint, maxfun);\n }\n\n return [1,\n target.X.apply(target, params),\n target.Y.apply(target, params),\n target.Z.apply(target, params)\n ];\n },\n\n /**\n * Given a the screen coordinates of a point, finds the point on the\n * given parametric curve or surface which is nearest in screen space,\n * and returns its view-space coordinates.\n * @param {Array} pScr Screen coordinates to project.\n * @param {JXG.Plane3D|JXG.Curve3D|JXG.Surface3D} target Plane, parametric curve or surface to project to.\n * @param {Array} params Parameters of point on the target, initially specifying the starting point of\n * the search. The parameters are modified in place during the search, ending up at the nearest point.\n * @returns {Array} Array of length 4 containing the coordinates of the nearest point on the curve or surface.\n */\n projectScreenCoordsToParametric: function (pScr, target, params, cyclic) {\n // The variables and parameters for the Cobyla constrained\n // minimization algorithm are explained in the Cobyla.js comments\n var rhobeg, // initial size of simplex (Cobyla)\n rhoend, // finial size of simplex (Cobyla)\n iprint = 0, // no console output (Cobyla)\n maxfun = 200, // call objective function at most 200 times (Cobyla)\n dim = params.length,\n r_u, r_v,\n _minFunc; // objective function (Cobyla)\n\n // Adapt simplex size to parameter range\n if (dim === 1) {\n r_u = [Type.evaluate(target.range[0]), Type.evaluate(target.range[1])];\n rhobeg = 0.1 * (r_u[1] - r_u[0]);\n } else if (dim === 2) {\n r_u = [Type.evaluate(target.range_u[0]), Type.evaluate(target.range_u[1])];\n r_v = [Type.evaluate(target.range_v[0]), Type.evaluate(target.range_v[1])];\n\n rhobeg = 0.1 * Math.min(\n r_u[1] - r_u[0],\n r_v[1] - r_v[0]\n );\n }\n\n rhoend = rhobeg / 5e6;\n\n // Minimize screen distance to cursor\n _minFunc = function (n, m, w, con) {\n var c3d = [\n 1,\n target.X.apply(target, w),\n target.Y.apply(target, w),\n target.Z.apply(target, w)\n ],\n c2d = target.view.project3DTo2D(c3d),\n xDiff = pScr[0] - c2d[1],\n yDiff = pScr[1] - c2d[2];\n\n if (n === 1) {\n con[0] = w[0] - r_u[0];\n con[1] = -w[0] + r_u[1];\n } else if (n === 2) {\n con[0] = w[0] - r_u[0];\n con[1] = -w[0] + r_u[1];\n con[2] = w[1] - r_v[0];\n con[3] = -w[1] + r_v[1];\n }\n\n return xDiff * xDiff + yDiff * yDiff;\n };\n\n if (cyclic) {\n // Cyclic\n Mat.Nlp.FindMinimum(_minFunc, dim, 0 /*2 * dim*/, params, rhobeg, rhoend, iprint, maxfun);\n params[0] = (params[0] + 20 * r_u[1]) % (r_u[1] - r_u[0]);\n if (dim === 2) {\n params[1] = (params[1] + 20 * r_v[1]) % (r_v[1] - r_v[0]);\n }\n } else {\n Mat.Nlp.FindMinimum(_minFunc, dim, 2 * dim, params, rhobeg, rhoend, iprint, maxfun);\n }\n\n return [1, target.X.apply(target, params), target.Y.apply(target, params), target.Z.apply(target, params)];\n },\n\n project3DTo3DPlane: function (point, normal, foot) {\n // TODO: homogeneous 3D coordinates\n var sol = [0, 0, 0],\n le,\n d1,\n d2,\n lbda;\n\n foot = foot || [0, 0, 0];\n\n le = Mat.norm(normal);\n d1 = Mat.innerProduct(point, normal, 3);\n d2 = Mat.innerProduct(foot, normal, 3);\n // (point - lbda * normal / le) * normal / le == foot * normal / le\n // => (point * normal - foot * normal) == lbda * le\n lbda = (d1 - d2) / le;\n sol = Mat.axpy(-lbda, normal, point);\n\n return sol;\n },\n\n getPlaneBounds: function (v1, v2, q, s, e) {\n var s1, s2, e1, e2, mat, rhs, sol;\n\n if (v1[2] + v2[0] !== 0) {\n mat = [\n [v1[0], v2[0]],\n [v1[1], v2[1]]\n ];\n rhs = [s - q[0], s - q[1]];\n\n sol = Numerics.Gauss(mat, rhs);\n s1 = sol[0];\n s2 = sol[1];\n\n rhs = [e - q[0], e - q[1]];\n sol = Numerics.Gauss(mat, rhs);\n e1 = sol[0];\n e2 = sol[1];\n return [s1, e1, s2, e2];\n }\n return null;\n },\n\n /* ***************************************/\n /* *** Various ****/\n /* ***************************************/\n\n /**\n * Helper function to create curve which displays a Reuleaux polygons.\n * @param {Array} points Array of points which should be the vertices of the Reuleaux polygon. Typically,\n * these point list is the array vertices of a regular polygon.\n * @param {Number} nr Number of vertices\n * @returns {Array} An array containing the two functions defining the Reuleaux polygon and the two values\n * for the start and the end of the paramtric curve. array may be used as parent array of a\n * {@link JXG.Curve}.\n *\n * @example\n * var A = brd.create('point',[-2,-2]);\n * var B = brd.create('point',[0,1]);\n * var pol = brd.create('regularpolygon',[A,B,3], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});\n * var reuleauxTriangle = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol.vertices, 3),\n * {strokeWidth:6, strokeColor:'#d66d55', fillColor:'#ad5544', highlightFillColor:'#ad5544'});\n *\n * \n * \n */\n reuleauxPolygon: function (points, nr) {\n var beta,\n pi2 = Math.PI * 2,\n pi2_n = pi2 / nr,\n diag = (nr - 1) / 2,\n d = 0,\n makeFct = function (which, trig) {\n return function (t, suspendUpdate) {\n var t1 = ((t % pi2) + pi2) % pi2,\n j = Math.floor(t1 / pi2_n) % nr;\n\n if (!suspendUpdate) {\n d = points[0].Dist(points[diag]);\n beta = Mat.Geometry.rad(\n [points[0].X() + 1, points[0].Y()],\n points[0],\n points[diag % nr]\n );\n }\n\n if (isNaN(j)) {\n return j;\n }\n\n t1 = t1 * 0.5 + j * pi2_n * 0.5 + beta;\n\n return points[j][which]() + d * Math[trig](t1);\n };\n };\n\n return [makeFct(\"X\", 'cos'), makeFct(\"Y\", 'sin'), 0, pi2];\n }\n\n }\n);\n\nexport default Mat.Geometry;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n * @name JXG.Math.Interval\n * @type Object\n */\n MatInterval = function (lo, hi) {\n if (lo !== undefined && hi !== undefined) {\n // possible cases:\n // - Interval(1, 2)\n // - Interval(Interval(1, 1), Interval(2, 2)) // singletons are required\n if (Mat.IntervalArithmetic.isInterval(lo)) {\n if (!Mat.IntervalArithmetic.isSingleton(lo)) {\n throw new TypeError(\n \"JXG.Math.IntervalArithmetic: interval `lo` must be a singleton\"\n );\n }\n this.lo = lo.lo;\n } else {\n this.lo = lo;\n }\n if (Mat.IntervalArithmetic.isInterval(hi)) {\n if (!Mat.IntervalArithmetic.isSingleton(hi)) {\n throw new TypeError(\n \"JXG.Math.IntervalArithmetic: interval `hi` must be a singleton\"\n );\n }\n this.hi = hi.hi;\n } else {\n this.hi = hi;\n }\n } else if (lo !== undefined) {\n // possible cases:\n // - Interval([1, 2])\n // - Interval([Interval(1, 1), Interval(2, 2)])\n if (Array.isArray(lo)) {\n return new MatInterval(lo[0], lo[1]);\n }\n // - Interval(1)\n return new MatInterval(lo, lo);\n } else {\n // This else is necessary even if jslint declares it as redundant\n // possible cases:\n // - Interval()\n this.lo = this.hi = 0;\n }\n };\n\nJXG.extend(MatInterval.prototype, {\n print: function () {\n console.log(\"[\", this.lo, this.hi, \"]\");\n },\n\n set: function (lo, hi) {\n this.lo = lo;\n this.hi = hi;\n return this;\n },\n\n bounded: function (lo, hi) {\n return this.set(Mat.IntervalArithmetic.prev(lo), Mat.IntervalArithmetic.next(hi));\n },\n\n boundedSingleton: function (v) {\n return this.bounded(v, v);\n },\n\n assign: function (lo, hi) {\n if (typeof lo !== \"number\" || typeof hi !== 'number') {\n throw new TypeError(\"JXG.Math.Interval#assign: arguments must be numbers\");\n }\n if (isNaN(lo) || isNaN(hi) || lo > hi) {\n return this.setEmpty();\n }\n return this.set(lo, hi);\n },\n\n setEmpty: function () {\n return this.set(Number.POSITIVE_INFINITY, Number.NEGATIVE_INFINITY);\n },\n\n setWhole: function () {\n return this.set(Number.NEGATIVE_INFINITY, Number.POSITIVE_INFINITY);\n },\n\n open: function (lo, hi) {\n return this.assign(Mat.IntervalArithmetic.next(lo), Mat.IntervalArithmetic.prev(hi));\n },\n\n halfOpenLeft: function (lo, hi) {\n return this.assign(Mat.IntervalArithmetic.next(lo), hi);\n },\n\n halfOpenRight: function (lo, hi) {\n return this.assign(lo, Mat.IntervalArithmetic.prev(hi));\n },\n\n toArray: function () {\n return [this.lo, this.hi];\n },\n\n clone: function () {\n return new MatInterval().set(this.lo, this.hi);\n }\n});\n\n/**\n * Object for interval arithmetics.\n * @name JXG.Math.IntervalArithmetic\n * @namespace\n * @exports Mat.IntervalArithmetic as JXG.Math.IntervalArithmetic\n *\n * @description\n * Interval arithmetic is a technique used to mitigate rounding and measurement errors in mathematical computation\n * by computing function bounds. Instead of representing a value as a single number, interval arithmetic represents each value as a range.\n *
\n *\n * For example, we wish to calculate the area of a rectangle from direct measurements using a standard meter stick with an uncertainty\n * of 0.0005 m (half the “least count measurement” of 1 mm). We measure one side nominally as L=1,\n * so 0.9995 ≤ L ≤ 1.0005, the other nominally as W=2 so the interval is [1.9995, 2.0005].\n *\n * \n * let L = JXG.Math.IntervalArithmetic.Interval(0.9995, 1.0005)\n * let W = JXG.Math.IntervalArithmetic.Interval(1.9995, 2.0005)\n *\n * let A = JXG.Math.IntervalArithmetic.mul(L, W)\n *\n * console.log('area:', A) // {hi: 2.0015002500000003, lo: 1.99850025}\n * \n *\n */\nJXG.Math.IntervalArithmetic = {\n Interval: function (lo, hi) {\n return new MatInterval(lo, hi);\n },\n\n isInterval: function (i) {\n return (\n i !== null &&\n typeof i === \"object\" &&\n typeof i.lo === \"number\" &&\n typeof i.hi === \"number\"\n );\n },\n\n isSingleton: function (i) {\n return i.lo === i.hi;\n },\n\n /*\n * Arithmetics\n */\n\n /**\n * Addition\n *\n * @param {JXG.Math.Interval|Number} x\n * @param {JXG.Math.Interval|Number} y\n * @returns JXG.Math.Interval\n */\n add: function (x, y) {\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (Type.isNumber(y)) {\n y = this.Interval(y);\n }\n return new MatInterval(this.addLo(x.lo, y.lo), this.addHi(x.hi, y.hi));\n },\n\n /**\n * Subtraction\n *\n * @param {JXG.Math.Interval|Number} x\n * @param {JXG.Math.Interval|Number} y\n * @returns JXG.Math.Interval\n */\n sub: function (x, y) {\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (Type.isNumber(y)) {\n y = this.Interval(y);\n }\n return new MatInterval(this.subLo(x.lo, y.hi), this.subHi(x.hi, y.lo));\n },\n\n /**\n * Multiplication\n *\n * @param {JXG.Math.Interval|Number} x\n * @param {JXG.Math.Interval|Number} y\n * @returns JXG.Math.Interval\n */\n mul: function (x, y) {\n var xl, xh, yl, yh, out;\n\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (Type.isNumber(y)) {\n y = this.Interval(y);\n }\n\n if (this.isEmpty(x) || this.isEmpty(y)) {\n return this.EMPTY.clone();\n }\n xl = x.lo;\n xh = x.hi;\n yl = y.lo;\n yh = y.hi;\n out = new MatInterval();\n\n if (xl < 0) {\n if (xh > 0) {\n if (yl < 0) {\n if (yh > 0) {\n // mixed * mixed\n out.lo = Math.min(this.mulLo(xl, yh), this.mulLo(xh, yl));\n out.hi = Math.max(this.mulHi(xl, yl), this.mulHi(xh, yh));\n } else {\n // mixed * negative\n out.lo = this.mulLo(xh, yl);\n out.hi = this.mulHi(xl, yl);\n }\n } else {\n if (yh > 0) {\n // mixed * positive\n out.lo = this.mulLo(xl, yh);\n out.hi = this.mulHi(xh, yh);\n } else {\n // mixed * zero\n out.lo = 0;\n out.hi = 0;\n }\n }\n } else {\n if (yl < 0) {\n if (yh > 0) {\n // negative * mixed\n out.lo = this.mulLo(xl, yh);\n out.hi = this.mulHi(xl, yl);\n } else {\n // negative * negative\n out.lo = this.mulLo(xh, yh);\n out.hi = this.mulHi(xl, yl);\n }\n } else {\n if (yh > 0) {\n // negative * positive\n out.lo = this.mulLo(xl, yh);\n out.hi = this.mulHi(xh, yl);\n } else {\n // negative * zero\n out.lo = 0;\n out.hi = 0;\n }\n }\n }\n } else {\n if (xh > 0) {\n if (yl < 0) {\n if (yh > 0) {\n // positive * mixed\n out.lo = this.mulLo(xh, yl);\n out.hi = this.mulHi(xh, yh);\n } else {\n // positive * negative\n out.lo = this.mulLo(xh, yl);\n out.hi = this.mulHi(xl, yh);\n }\n } else {\n if (yh > 0) {\n // positive * positive\n out.lo = this.mulLo(xl, yl);\n out.hi = this.mulHi(xh, yh);\n } else {\n // positive * zero\n out.lo = 0;\n out.hi = 0;\n }\n }\n } else {\n // zero * any other value\n out.lo = 0;\n out.hi = 0;\n }\n }\n return out;\n },\n\n /**\n * Division\n *\n * @param {JXG.Math.Interval|Number} x\n * @param {JXG.Math.Interval|Number} y\n * @returns JXG.Math.Interval\n */\n div: function (x, y) {\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (Type.isNumber(y)) {\n y = this.Interval(y);\n }\n\n if (this.isEmpty(x) || this.isEmpty(y)) {\n return this.EMPTY.clone();\n }\n if (this.zeroIn(y)) {\n if (y.lo !== 0) {\n if (y.hi !== 0) {\n return this.divZero(x);\n }\n return this.divNegative(x, y.lo);\n }\n if (y.hi !== 0) {\n return this.divPositive(x, y.hi);\n }\n return this.EMPTY.clone();\n }\n return this.divNonZero(x, y);\n },\n\n /**\n * Return +x (i.e. identity)\n *\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n positive: function (x) {\n return new MatInterval(x.lo, x.hi);\n },\n\n /**\n * Return -x\n *\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n negative: function (x) {\n if (Type.isNumber(x)) {\n return new MatInterval(-x);\n }\n return new MatInterval(-x.hi, -x.lo);\n },\n\n /*\n * Utils\n */\n\n /**\n * Test if interval is empty set.\n * @param {JXG.Math.Interval} i\n * @returns Boolean\n */\n isEmpty: function (i) {\n return i.lo > i.hi;\n },\n\n /**\n * Test if interval is (-Infinity, Infinity).\n * @param {JXG.Math.Interval} i\n * @returns Boolean\n */\n isWhole: function (i) {\n return i.lo === -Infinity && i.hi === Infinity;\n },\n\n /**\n * Test if interval contains 0.\n * @param {JXG.Math.Interval} i\n * @returns Boolean\n */\n zeroIn: function (i) {\n return this.hasValue(i, 0);\n },\n\n /**\n * Test if interval contains a specific value.\n * @param {JXG.Math.Interval} i\n * @param {Number} value\n * @returns Boolean\n */\n hasValue: function (i, value) {\n if (this.isEmpty(i)) {\n return false;\n }\n return i.lo <= value && value <= i.hi;\n },\n\n /**\n * Test if interval x contains interval y.\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns Boolean\n */\n hasInterval: function (x, y) {\n if (this.isEmpty(x)) {\n return true;\n }\n return !this.isEmpty(y) && y.lo <= x.lo && x.hi <= y.hi;\n },\n\n /**\n * Test if intervals x and y have non-zero intersection.\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns Boolean\n */\n intervalsOverlap: function (x, y) {\n if (this.isEmpty(x) || this.isEmpty(y)) {\n return false;\n }\n return (x.lo <= y.lo && y.lo <= x.hi) || (y.lo <= x.lo && x.lo <= y.hi);\n },\n\n /*\n * Division\n */\n /**\n * @private\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns JXG.Math.Interval\n */\n divNonZero: function (x, y) {\n var xl = x.lo,\n xh = x.hi,\n yl = y.lo,\n yh = y.hi,\n out = new MatInterval();\n\n if (xh < 0) {\n if (yh < 0) {\n out.lo = this.divLo(xh, yl);\n out.hi = this.divHi(xl, yh);\n } else {\n out.lo = this.divLo(xl, yl);\n out.hi = this.divHi(xh, yh);\n }\n } else if (xl < 0) {\n if (yh < 0) {\n out.lo = this.divLo(xh, yh);\n out.hi = this.divHi(xl, yh);\n } else {\n out.lo = this.divLo(xl, yl);\n out.hi = this.divHi(xh, yl);\n }\n } else {\n if (yh < 0) {\n out.lo = this.divLo(xh, yh);\n out.hi = this.divHi(xl, yl);\n } else {\n out.lo = this.divLo(xl, yh);\n out.hi = this.divHi(xh, yl);\n }\n }\n return out;\n },\n\n /**\n * @private\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns JXG.Math.Interval\n */\n divPositive: function (x, v) {\n if (x.lo === 0 && x.hi === 0) {\n return x;\n }\n\n if (this.zeroIn(x)) {\n // mixed considering zero in both ends\n return this.WHOLE;\n }\n\n if (x.hi < 0) {\n // negative / v\n return new MatInterval(Number.NEGATIVE_INFINITY, this.divHi(x.hi, v));\n }\n // positive / v\n return new MatInterval(this.divLo(x.lo, v), Number.POSITIVE_INFINITY);\n },\n\n /**\n * @private\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns JXG.Math.Interval\n */\n divNegative: function (x, v) {\n if (x.lo === 0 && x.hi === 0) {\n return x;\n }\n\n if (this.zeroIn(x)) {\n // mixed considering zero in both ends\n return this.WHOLE;\n }\n\n if (x.hi < 0) {\n // negative / v\n return new MatInterval(this.divLo(x.hi, v), Number.POSITIVE_INFINITY);\n }\n // positive / v\n return new MatInterval(Number.NEGATIVE_INFINITY, this.divHi(x.lo, v));\n },\n\n /**\n * @private\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n divZero: function (x) {\n if (x.lo === 0 && x.hi === 0) {\n return x;\n }\n return this.WHOLE;\n },\n\n /*\n * Algebra\n */\n /**\n * x mod y: x - n * y\n * @param {JXG.Math.Interval|Number} x\n * @param {JXG.Math.Interval|Number} y\n * @returns JXG.Math.Interval\n */\n fmod: function (x, y) {\n var yb, n;\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (Type.isNumber(y)) {\n y = this.Interval(y);\n }\n if (this.isEmpty(x) || this.isEmpty(y)) {\n return this.EMPTY.clone();\n }\n yb = x.lo < 0 ? y.lo : y.hi;\n n = x.lo / yb;\n if (n < 0) {\n n = Math.ceil(n);\n } else {\n n = Math.floor(n);\n }\n // x mod y = x - n * y\n return this.sub(x, this.mul(y, new MatInterval(n)));\n },\n\n /**\n * 1 / x\n * @param {JXG.Math.Interval|Number} x\n * @returns JXG.Math.Interval\n */\n multiplicativeInverse: function (x) {\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n if (this.zeroIn(x)) {\n if (x.lo !== 0) {\n if (x.hi !== 0) {\n // [negative, positive]\n return this.WHOLE;\n }\n // [negative, zero]\n return new MatInterval(Number.NEGATIVE_INFINITY, this.divHi(1, x.lo));\n }\n if (x.hi !== 0) {\n // [zero, positive]\n return new MatInterval(this.divLo(1, x.hi), Number.POSITIVE_INFINITY);\n }\n // [zero, zero]\n return this.EMPTY.clone();\n }\n // [positive, positive]\n return new MatInterval(this.divLo(1, x.hi), this.divHi(1, x.lo));\n },\n\n /**\n * xpower\n * @param {JXG.Math.Interval|Number} x\n * @param {JXG.Math.Interval|Number} power\n * @returns JXG.Math.Interval\n */\n pow: function (x, power) {\n var yl, yh;\n\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n if (this.isInterval(power)) {\n if (!this.isSingleton(power)) {\n return this.EMPTY.clone();\n }\n power = power.lo;\n }\n\n if (power === 0) {\n if (x.lo === 0 && x.hi === 0) {\n // 0^0\n return this.EMPTY.clone();\n }\n // x^0\n return this.ONE.clone();\n }\n if (power < 0) {\n // compute [1 / x]^-power if power is negative\n return this.pow(this.multiplicativeInverse(x), -power);\n }\n\n // power > 0\n if (power % 1 === 0) {\n // isSafeInteger(power) as boolean) {\n // power is integer\n if (x.hi < 0) {\n // [negative, negative]\n // assume that power is even so the operation will yield a positive interval\n // if not then just switch the sign and order of the interval bounds\n yl = this.powLo(-x.hi, power);\n yh = this.powHi(-x.lo, power);\n if ((power & 1) === 1) {\n // odd power\n return new MatInterval(-yh, -yl);\n }\n // even power\n return new MatInterval(yl, yh);\n }\n if (x.lo < 0) {\n // [negative, positive]\n if ((power & 1) === 1) {\n return new MatInterval(-this.powLo(-x.lo, power), this.powHi(x.hi, power));\n }\n // even power means that any negative number will be zero (min value = 0)\n // and the max value will be the max of x.lo^power, x.hi^power\n return new MatInterval(0, this.powHi(Math.max(-x.lo, x.hi), power));\n }\n // [positive, positive]\n return new MatInterval(this.powLo(x.lo, power), this.powHi(x.hi, power));\n }\n console.warn(\n \"power is not an integer, you should use nth-root instead, returning an empty interval\"\n );\n return this.EMPTY.clone();\n },\n\n /**\n * sqrt(x)\n * @param {JXG.Math.Interval|Number} x\n * @returns JXG.Math.Interval\n */\n sqrt: function (x) {\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n return this.nthRoot(x, 2);\n },\n\n /**\n * x1/n\n * @param {JXG.Math.Interval|Number} x\n * @param {Number} n\n * @returns JXG.Math.Interval\n */\n nthRoot: function (x, n) {\n var power, yl, yh, yp, yn;\n\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (this.isEmpty(x) || n < 0) {\n // compute 1 / x^-power if power is negative\n return this.EMPTY.clone();\n }\n\n // singleton interval check\n if (this.isInterval(n)) {\n if (!this.isSingleton(n)) {\n return this.EMPTY.clone();\n }\n n = n.lo;\n }\n\n power = 1 / n;\n if (x.hi < 0) {\n // [negative, negative]\n //if ((isSafeInteger(n) as boolean) && (n & 1) === 1) {\n if (n % 1 === 0 && (n & 1) === 1) {\n // when n is odd we can always take the nth root\n yl = this.powHi(-x.lo, power);\n yh = this.powLo(-x.hi, power);\n return new MatInterval(-yl, -yh);\n }\n\n // n is not odd therefore there's no nth root\n return this.EMPTY.clone();\n }\n if (x.lo < 0) {\n // [negative, positive]\n yp = this.powHi(x.hi, power);\n // if ((isSafeInteger(n) as boolean) && (n & 1) === 1) {\n if (n % 1 === 0 && (n & 1) === 1) {\n // nth root of x.lo is possible (n is odd)\n yn = -this.powHi(-x.lo, power);\n return new MatInterval(yn, yp);\n }\n return new MatInterval(0, yp);\n }\n // [positive, positive]\n return new MatInterval(this.powLo(x.lo, power), this.powHi(x.hi, power));\n },\n\n /*\n * Misc\n */\n /**\n *\n * @param {JXG.Math.Interval|Number} x\n * @returns JXG.Math.Interval\n */\n exp: function (x) {\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n return new MatInterval(this.expLo(x.lo), this.expHi(x.hi));\n },\n\n /**\n * Natural log\n * @param {JXG.Math.Interval|Number} x\n * @returns JXG.Math.Interval\n */\n log: function (x) {\n var l;\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n l = x.lo <= 0 ? Number.NEGATIVE_INFINITY : this.logLo(x.lo);\n return new MatInterval(l, this.logHi(x.hi));\n },\n\n /**\n * Natural log, alias for {@link JXG.Math.IntervalArithmetic#log}.\n * @param {JXG.Math.Interval|Number} x\n * @returns JXG.Math.Interval\n */\n ln: function (x) {\n return this.log(x);\n },\n\n // export const LOG_EXP_10 = this.log(new MatInterval(10, 10))\n // export const LOG_EXP_2 = log(new MatInterval(2, 2))\n /**\n * Logarithm to base 10.\n * @param {JXG.Math.Interval|Number} x\n * @returns JXG.Math.Interval\n */\n log10: function (x) {\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n return this.div(this.log(x), this.log(new MatInterval(10, 10)));\n },\n\n /**\n * Logarithm to base 2.\n * @param {JXG.Math.Interval|Number} x\n * @returns JXG.Math.Interval\n */\n log2: function (x) {\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n return this.div(this.log(x), this.log(new MatInterval(2, 2)));\n },\n\n /**\n * Hull of intervals x and y\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns JXG.Math.Interval\n */\n hull: function (x, y) {\n var badX = this.isEmpty(x),\n badY = this.isEmpty(y);\n if (badX && badY) {\n return this.EMPTY.clone();\n }\n if (badX) {\n return y.clone();\n }\n if (badY) {\n return x.clone();\n }\n return new MatInterval(Math.min(x.lo, y.lo), Math.max(x.hi, y.hi));\n },\n\n /**\n * Intersection of intervals x and y\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns JXG.Math.Interval\n */\n intersection: function (x, y) {\n var lo, hi;\n if (this.isEmpty(x) || this.isEmpty(y)) {\n return this.EMPTY.clone();\n }\n lo = Math.max(x.lo, y.lo);\n hi = Math.min(x.hi, y.hi);\n if (lo <= hi) {\n return new MatInterval(lo, hi);\n }\n return this.EMPTY.clone();\n },\n\n /**\n * Union of overlapping intervals x and y\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns JXG.Math.Interval\n */\n union: function (x, y) {\n if (!this.intervalsOverlap(x, y)) {\n throw new Error(\"Interval#unions do not overlap\");\n }\n return new MatInterval(Math.min(x.lo, y.lo), Math.max(x.hi, y.hi));\n },\n\n /**\n * Difference of overlapping intervals x and y\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns JXG.Math.Interval\n */\n difference: function (x, y) {\n if (this.isEmpty(x) || this.isWhole(y)) {\n return this.EMPTY.clone();\n }\n if (this.intervalsOverlap(x, y)) {\n if (x.lo < y.lo && y.hi < x.hi) {\n // difference creates multiple subsets\n throw new Error(\"Interval.difference: difference creates multiple intervals\");\n }\n\n // handle corner cases first\n if ((y.lo <= x.lo && y.hi === Infinity) || (y.hi >= x.hi && y.lo === -Infinity)) {\n return this.EMPTY.clone();\n }\n\n // NOTE: empty interval is handled automatically\n // e.g.\n //\n // n = difference([0,1], [0,1]) // n = Interval(next(1), 1) = EMPTY\n // isEmpty(n) === true\n //\n if (y.lo <= x.lo) {\n return new MatInterval().halfOpenLeft(y.hi, x.hi);\n }\n\n // y.hi >= x.hi\n return new MatInterval().halfOpenRight(x.lo, y.lo);\n }\n return x.clone();\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n width: function (x) {\n if (this.isEmpty(x)) {\n return 0;\n }\n return this.subHi(x.hi, x.lo);\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n abs: function (x) {\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n if (x.lo >= 0) {\n return x.clone();\n }\n if (x.hi <= 0) {\n return this.negative(x);\n }\n return new MatInterval(0, Math.max(-x.lo, x.hi));\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns JXG.Math.Interval\n */\n max: function (x, y) {\n var badX = this.isEmpty(x),\n badY = this.isEmpty(y);\n if (badX && badY) {\n return this.EMPTY.clone();\n }\n if (badX) {\n return y.clone();\n }\n if (badY) {\n return x.clone();\n }\n return new MatInterval(Math.max(x.lo, y.lo), Math.max(x.hi, y.hi));\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns JXG.Math.Interval\n */\n min: function (x, y) {\n var badX = this.isEmpty(x),\n badY = this.isEmpty(y);\n if (badX && badY) {\n return this.EMPTY.clone();\n }\n if (badX) {\n return y.clone();\n }\n if (badY) {\n return x.clone();\n }\n return new MatInterval(Math.min(x.lo, y.lo), Math.min(x.hi, y.hi));\n },\n\n /*\n * Trigonometric\n */\n onlyInfinity: function (x) {\n return !isFinite(x.lo) && x.lo === x.hi;\n },\n\n _handleNegative: function (interval) {\n var n;\n if (interval.lo < 0) {\n if (interval.lo === -Infinity) {\n interval.lo = 0;\n interval.hi = Infinity;\n } else {\n n = Math.ceil(-interval.lo / this.piTwiceLow);\n interval.lo += this.piTwiceLow * n;\n interval.hi += this.piTwiceLow * n;\n }\n }\n return interval;\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n cos: function (x) {\n var cache, pi2, t, cosv, lo, hi, rlo, rhi;\n\n if (this.isEmpty(x) || this.onlyInfinity(x)) {\n return this.EMPTY.clone();\n }\n\n // create a clone of `x` because the clone is going to be modified\n cache = new MatInterval().set(x.lo, x.hi);\n this._handleNegative(cache);\n\n pi2 = this.PI_TWICE;\n t = this.fmod(cache, pi2);\n if (this.width(t) >= pi2.lo) {\n return new MatInterval(-1, 1);\n }\n\n // when t.lo > pi it's the same as\n // -cos(t - pi)\n if (t.lo >= this.piHigh) {\n cosv = this.cos(this.sub(t, this.PI));\n return this.negative(cosv);\n }\n\n lo = t.lo;\n hi = t.hi;\n rlo = this.cosLo(hi);\n rhi = this.cosHi(lo);\n // it's ensured that t.lo < pi and that t.lo >= 0\n if (hi <= this.piLow) {\n // when t.hi < pi\n // [cos(t.lo), cos(t.hi)]\n return new MatInterval(rlo, rhi);\n }\n if (hi <= pi2.lo) {\n // when t.hi < 2pi\n // [-1, max(cos(t.lo), cos(t.hi))]\n return new MatInterval(-1, Math.max(rlo, rhi));\n }\n // t.lo < pi and t.hi > 2pi\n return new MatInterval(-1, 1);\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n sin: function (x) {\n if (this.isEmpty(x) || this.onlyInfinity(x)) {\n return this.EMPTY.clone();\n }\n return this.cos(this.sub(x, this.PI_HALF));\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n tan: function (x) {\n var cache, t, pi;\n if (this.isEmpty(x) || this.onlyInfinity(x)) {\n return this.EMPTY.clone();\n }\n\n // create a clone of `x` because the clone is going to be modified\n cache = new MatInterval().set(x.lo, x.hi);\n this._handleNegative(cache);\n\n pi = this.PI;\n t = this.fmod(cache, pi);\n if (t.lo >= this.piHalfLow) {\n t = this.sub(t, pi);\n }\n if (t.lo <= -this.piHalfLow || t.hi >= this.piHalfLow) {\n return this.WHOLE.clone();\n }\n return new MatInterval(this.tanLo(t.lo), this.tanHi(t.hi));\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n asin: function (x) {\n var lo, hi;\n if (this.isEmpty(x) || x.hi < -1 || x.lo > 1) {\n return this.EMPTY.clone();\n }\n lo = x.lo <= -1 ? -this.piHalfHigh : this.asinLo(x.lo);\n hi = x.hi >= 1 ? this.piHalfHigh : this.asinHi(x.hi);\n return new MatInterval(lo, hi);\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n acos: function (x) {\n var lo, hi;\n if (this.isEmpty(x) || x.hi < -1 || x.lo > 1) {\n return this.EMPTY.clone();\n }\n lo = x.hi >= 1 ? 0 : this.acosLo(x.hi);\n hi = x.lo <= -1 ? this.piHigh : this.acosHi(x.lo);\n return new MatInterval(lo, hi);\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n acot: function (x) {\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n return new MatInterval(this.acotLo(x.lo), this.acotHi(x.hi));\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n atan: function (x) {\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n return new MatInterval(this.atanLo(x.lo), this.atanHi(x.hi));\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n sinh: function (x) {\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n return new MatInterval(this.sinhLo(x.lo), this.sinhHi(x.hi));\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n cosh: function (x) {\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n if (x.hi < 0) {\n return new MatInterval(this.coshLo(x.hi), this.coshHi(x.lo));\n }\n if (x.lo >= 0) {\n return new MatInterval(this.coshLo(x.lo), this.coshHi(x.hi));\n }\n return new MatInterval(1, this.coshHi(-x.lo > x.hi ? x.lo : x.hi));\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @returns JXG.Math.Interval\n */\n tanh: function (x) {\n if (this.isEmpty(x)) {\n return this.EMPTY.clone();\n }\n return new MatInterval(this.tanhLo(x.lo), this.tanhHi(x.hi));\n },\n\n /*\n * Relational\n */\n\n /**\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns Boolean\n */\n equal: function (x, y) {\n if (this.isEmpty(x)) {\n return this.isEmpty(y);\n }\n return !this.isEmpty(y) && x.lo === y.lo && x.hi === y.hi;\n },\n\n // almostEqual: function(x, y): void {\n // x = Array.isArray(x) ? x : x.toArray();\n // y = Array.isArray(y) ? y : y.toArray();\n // assertEps(x[0], y[0])\n // assertEps(x[1], y[1])\n // },\n\n /**\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns Boolean\n */\n notEqual: function (x, y) {\n if (this.isEmpty(x)) {\n return !this.isEmpty(y);\n }\n return this.isEmpty(y) || x.hi < y.lo || x.lo > y.hi;\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns Boolean\n */\n lt: function (x, y) {\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (Type.isNumber(y)) {\n y = this.Interval(y);\n }\n if (this.isEmpty(x) || this.isEmpty(y)) {\n return false;\n }\n return x.hi < y.lo;\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns Boolean\n */\n gt: function (x, y) {\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (Type.isNumber(y)) {\n y = this.Interval(y);\n }\n if (this.isEmpty(x) || this.isEmpty(y)) {\n return false;\n }\n return x.lo > y.hi;\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns Boolean\n */\n leq: function (x, y) {\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (Type.isNumber(y)) {\n y = this.Interval(y);\n }\n if (this.isEmpty(x) || this.isEmpty(y)) {\n return false;\n }\n return x.hi <= y.lo;\n },\n\n /**\n * @param {JXG.Math.Interval} x\n * @param {JXG.Math.Interval} y\n * @returns Boolean\n */\n geq: function (x, y) {\n if (Type.isNumber(x)) {\n x = this.Interval(x);\n }\n if (Type.isNumber(y)) {\n y = this.Interval(y);\n }\n if (this.isEmpty(x) || this.isEmpty(y)) {\n return false;\n }\n return x.lo >= y.hi;\n },\n\n /*\n * Constants\n */\n piLow: (3373259426.0 + 273688.0 / (1 << 21)) / (1 << 30),\n piHigh: (3373259426.0 + 273689.0 / (1 << 21)) / (1 << 30),\n piHalfLow: ((3373259426.0 + 273688.0 / (1 << 21)) / (1 << 30)) * 0.5,\n piHalfHigh: ((3373259426.0 + 273689.0 / (1 << 21)) / (1 << 30)) * 0.5,\n piTwiceLow: ((3373259426.0 + 273688.0 / (1 << 21)) / (1 << 30)) * 2,\n piTwiceHigh: ((3373259426.0 + 273689.0 / (1 << 21)) / (1 << 30)) * 2,\n\n /*\n * Round\n * Rounding functions for numbers\n */\n identity: function (v) {\n return v;\n },\n\n _prev: function (v) {\n if (v === Infinity) {\n return v;\n }\n return this.nextafter(v, -Infinity);\n },\n\n _next: function (v) {\n if (v === -Infinity) {\n return v;\n }\n return this.nextafter(v, Infinity);\n },\n\n prev: function (v) {\n return this._prev(v);\n },\n\n next: function (v) {\n return this._next(v);\n },\n\n toInteger: function (x) {\n return x < 0 ? Math.ceil(x) : Math.floor(x);\n },\n\n addLo: function (x, y) {\n return this.prev(x + y);\n },\n addHi: function (x, y) {\n return this.next(x + y);\n },\n subLo: function (x, y) {\n return this.prev(x - y);\n },\n subHi: function (x, y) {\n return this.next(x - y);\n },\n mulLo: function (x, y) {\n return this.prev(x * y);\n },\n mulHi: function (x, y) {\n return this.next(x * y);\n },\n divLo: function (x, y) {\n return this.prev(x / y);\n },\n divHi: function (x, y) {\n return this.next(x / y);\n },\n intLo: function (x) {\n return this.toInteger(this.prev(x));\n },\n intHi: function (x) {\n return this.toInteger(this.next(x));\n },\n logLo: function (x) {\n return this.prev(Math.log(x));\n },\n logHi: function (x) {\n return this.next(Math.log(x));\n },\n expLo: function (x) {\n return this.prev(Math.exp(x));\n },\n expHi: function (x) {\n return this.next(Math.exp(x));\n },\n sinLo: function (x) {\n return this.prev(Math.sin(x));\n },\n sinHi: function (x) {\n return this.next(Math.sin(x));\n },\n cosLo: function (x) {\n return this.prev(Math.cos(x));\n },\n cosHi: function (x) {\n return this.next(Math.cos(x));\n },\n tanLo: function (x) {\n return this.prev(Math.tan(x));\n },\n tanHi: function (x) {\n return this.next(Math.tan(x));\n },\n asinLo: function (x) {\n return this.prev(Math.asin(x));\n },\n asinHi: function (x) {\n return this.next(Math.asin(x));\n },\n acosLo: function (x) {\n return this.prev(Math.acos(x));\n },\n acosHi: function (x) {\n return this.next(Math.acos(x));\n },\n acotLo: function (x) {\n return this.prev(Mat.acot(x));\n },\n acotHi: function (x) {\n return this.next(Mat.acot(x));\n },\n atanLo: function (x) {\n return this.prev(Math.atan(x));\n },\n atanHi: function (x) {\n return this.next(Math.atan(x));\n },\n sinhLo: function (x) {\n return this.prev(Mat.sinh(x));\n },\n sinhHi: function (x) {\n return this.next(Mat.sinh(x));\n },\n coshLo: function (x) {\n return this.prev(Mat.cosh(x));\n },\n coshHi: function (x) {\n return this.next(Mat.cosh(x));\n },\n tanhLo: function (x) {\n return this.prev(Mat.tanh(x));\n },\n tanhHi: function (x) {\n return this.next(Mat.tanh(x));\n },\n sqrtLo: function (x) {\n return this.prev(Math.sqrt(x));\n },\n sqrtHi: function (x) {\n return this.next(Math.sqrt(x));\n },\n\n powLo: function (x, power) {\n var y;\n if (power % 1 !== 0) {\n // power has decimals\n return this.prev(Math.pow(x, power));\n }\n\n y = (power & 1) === 1 ? x : 1;\n power >>= 1;\n while (power > 0) {\n x = this.mulLo(x, x);\n if ((power & 1) === 1) {\n y = this.mulLo(x, y);\n }\n power >>= 1;\n }\n return y;\n },\n\n powHi: function (x, power) {\n var y;\n if (power % 1 !== 0) {\n // power has decimals\n return this.next(Math.pow(x, power));\n }\n\n y = (power & 1) === 1 ? x : 1;\n power >>= 1;\n while (power > 0) {\n x = this.mulHi(x, x);\n if ((power & 1) === 1) {\n y = this.mulHi(x, y);\n }\n power >>= 1;\n }\n return y;\n },\n\n /**\n * @ignore\n * @private\n */\n disable: function () {\n this.next = this.prev = this.identity;\n },\n\n /**\n * @ignore\n * @private\n */\n enable: function () {\n this.prev = function (v) {\n return this._prev(v);\n };\n\n this.next = function (v) {\n return this._next(v);\n };\n },\n\n /*\n * nextafter\n */\n SMALLEST_DENORM: Math.pow(2, -1074),\n UINT_MAX: -1 >>> 0,\n\n nextafter: function (x, y) {\n var lo, hi;\n\n if (isNaN(x) || isNaN(y)) {\n return NaN;\n }\n if (x === y) {\n return x;\n }\n if (x === 0) {\n if (y < 0) {\n return -this.SMALLEST_DENORM;\n }\n return this.SMALLEST_DENORM;\n }\n hi = doubleBits.hi(x);\n lo = doubleBits.lo(x);\n if (y > x === x > 0) {\n if (lo === this.UINT_MAX) {\n hi += 1;\n lo = 0;\n } else {\n lo += 1;\n }\n } else {\n if (lo === 0) {\n lo = this.UINT_MAX;\n hi -= 1;\n } else {\n lo -= 1;\n }\n }\n return doubleBits.pack(lo, hi);\n }\n};\n\nJXG.Math.IntervalArithmetic.PI = new MatInterval(\n Mat.IntervalArithmetic.piLow,\n Mat.IntervalArithmetic.piHigh\n);\nJXG.Math.IntervalArithmetic.PI_HALF = new MatInterval(\n Mat.IntervalArithmetic.piHalfLow,\n Mat.IntervalArithmetic.piHalfHigh\n);\nJXG.Math.IntervalArithmetic.PI_TWICE = new MatInterval(\n Mat.IntervalArithmetic.piTwiceLow,\n Mat.IntervalArithmetic.piTwiceHigh\n);\nJXG.Math.IntervalArithmetic.ZERO = new MatInterval(0);\nJXG.Math.IntervalArithmetic.ONE = new MatInterval(1);\nJXG.Math.IntervalArithmetic.WHOLE = new MatInterval().setWhole();\nJXG.Math.IntervalArithmetic.EMPTY = new MatInterval().setEmpty();\n\nexport default JXG.Math.IntervalArithmetic;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see x into the interval [a, b) by adding\n * a multiple of b - a.\n * @param {Number} x\n * @param {Number} a\n * @param {Number} b\n */\n wrap: function (x, a, b) {\n return a + this.mod(x - a, b - a);\n },\n\n /**\n * Clamp x within the interval [a, b]. If\n * x is below a, increase it to a. If\n * it's above b, decrease it to b.\n */\n clamp: function (x, a, b) {\n return Math.min(Math.max(x, a), b);\n },\n\n /**\n * A way of clamping a periodic variable. If x is congruent mod\n * period to a point in [a, b], return that point.\n * Otherwise, wrap it into [mid - period/2, mid + period/2],\n * where mid is the mean of a and b,\n * and then clamp it to [a, b] from there.\n */\n wrapAndClamp: function (x, a, b, period) {\n var mid = 0.5 * (a + b),\n half_period = 0.5 * period;\n\n return this.clamp(\n this.wrap(\n x,\n mid - half_period,\n mid + half_period\n ),\n a,\n b\n );\n },\n\n /**\n * Initializes a vector of size n wih coefficients set to the init value (default 0)\n * @param {Number} n Length of the vector\n * @param {Number} [init=0] Initial value for each coefficient\n * @returns {Array} An array of length n\n */\n vector: function (n, init) {\n var r, i;\n\n init = init || 0;\n r = [];\n\n for (i = 0; i < n; i++) {\n r[i] = init;\n }\n\n return r;\n },\n\n /**\n * Initializes a matrix as an array of rows with the given value.\n * @param {Number} n Number of rows\n * @param {Number} [m=n] Number of columns\n * @param {Number} [init=0] Initial value for each coefficient\n * @returns {Array} A n times m-matrix represented by a\n * two-dimensional array. The inner arrays hold the columns, the outer array holds the rows.\n */\n matrix: function (n, m, init) {\n var r, i, j;\n\n init = init || 0;\n m = m || n;\n r = [];\n\n for (i = 0; i < n; i++) {\n r[i] = [];\n\n for (j = 0; j < m; j++) {\n r[i][j] = init;\n }\n }\n\n return r;\n },\n\n /**\n * Generates an identity matrix. If n is a number and m is undefined or not a number, a square matrix is generated,\n * if n and m are both numbers, an nxm matrix is generated.\n * @param {Number} n Number of rows\n * @param {Number} [m=n] Number of columns\n * @returns {Array} A square matrix of length n with all coefficients equal to 0 except a_(i,i), i out of (1, ..., n), if m is undefined or not a number\n * or a n times m-matrix with a_(i,j) = 0 and a_(i,i) = 1 if m is a number.\n */\n identity: function (n, m) {\n var r, i;\n\n if (m === undef && typeof m !== 'number') {\n m = n;\n }\n\n r = this.matrix(n, m);\n\n for (i = 0; i < Math.min(n, m); i++) {\n r[i][i] = 1;\n }\n\n return r;\n },\n\n /**\n * Generates a 4x4 matrix for 3D to 2D projections.\n * @param {Number} l Left\n * @param {Number} r Right\n * @param {Number} t Top\n * @param {Number} b Bottom\n * @param {Number} n Near\n * @param {Number} f Far\n * @returns {Array} 4x4 Matrix\n */\n frustum: function (l, r, b, t, n, f) {\n var ret = this.matrix(4, 4);\n\n ret[0][0] = (n * 2) / (r - l);\n ret[0][1] = 0;\n ret[0][2] = (r + l) / (r - l);\n ret[0][3] = 0;\n\n ret[1][0] = 0;\n ret[1][1] = (n * 2) / (t - b);\n ret[1][2] = (t + b) / (t - b);\n ret[1][3] = 0;\n\n ret[2][0] = 0;\n ret[2][1] = 0;\n ret[2][2] = -(f + n) / (f - n);\n ret[2][3] = -(f * n * 2) / (f - n);\n\n ret[3][0] = 0;\n ret[3][1] = 0;\n ret[3][2] = -1;\n ret[3][3] = 0;\n\n return ret;\n },\n\n /**\n * Generates a 4x4 matrix for 3D to 2D projections.\n * @param {Number} fov Field of view in vertical direction, given in rad.\n * @param {Number} ratio Aspect ratio of the projection plane.\n * @param {Number} n Near\n * @param {Number} f Far\n * @returns {Array} 4x4 Projection Matrix\n */\n projection: function (fov, ratio, n, f) {\n var t = n * Math.tan(fov / 2),\n r = t * ratio;\n\n return this.frustum(-r, r, -t, t, n, f);\n },\n\n /**\n * Multiplies a vector vec to a matrix mat: mat * vec. The matrix is interpreted by this function as an array of rows.\n * Please note: This\n * function does not check if the dimensions match.\n * @param {Array} mat Two-dimensional array of numbers. The inner arrays describe the columns, the outer ones the matrix' rows.\n * @param {Array} vec Array of numbers\n * @returns {Array} Array of numbers containing the result\n * @example\n * var A = [[2, 1],\n * [2, 3]],\n * b = [4, 5],\n * c;\n * c = JXG.Math.matVecMult(A, b);\n * // c === [13, 23];\n */\n matVecMult: function (mat, vec) {\n var i, k, s,\n m = mat.length,\n n = vec.length,\n res = [];\n\n if (n === 3) {\n for (i = 0; i < m; i++) {\n res[i] = mat[i][0] * vec[0] + mat[i][1] * vec[1] + mat[i][2] * vec[2];\n }\n } else {\n for (i = 0; i < m; i++) {\n s = 0;\n for (k = 0; k < n; k++) {\n s += mat[i][k] * vec[k];\n }\n res[i] = s;\n }\n }\n return res;\n },\n\n /**\n * Multiplies a vector vec to a matrix mat from the left: vec * mat.\n * The matrix is interpreted by this function as an array of rows.\n * Please note: This function does not check if the dimensions match.\n * @param {Array} vec Array of numbers\n * @param {Array} mat Two-dimensional array of numbers. The inner arrays describe the columns,\n * the outer ones the matrix' rows.\n * @returns {Array} Array of numbers containing the result\n * @example\n * var A = [[2, 1],\n * [2, 3]],\n * b = [4, 5],\n * c;\n * c = JXG.Math.vecMatMult(b, A);\n * // c === [18, 16];\n */\n vecMatMult: function (vec, mat) {\n var i, k, s,\n m = mat.length,\n n = vec.length,\n res = [];\n\n if (n === 3) {\n for (i = 0; i < m; i++) {\n res[i] = vec[0] * mat[0][i] + vec[1] * mat[1][i] + vec[2] * mat[2][i];\n }\n } else {\n for (i = 0; i < n; i++) {\n s = 0;\n for (k = 0; k < m; k++) {\n s += vec[k] * mat[k][i];\n }\n res[i] = s;\n }\n }\n return res;\n },\n\n /**\n * Computes the product of the two matrices: mat1 * mat2.\n * Returns a new matrix array.\n *\n * @param {Array} mat1 Two-dimensional array of numbers\n * @param {Array} mat2 Two-dimensional array of numbers\n * @returns {Array} Two-dimensional Array of numbers containing result\n */\n matMatMult: function (mat1, mat2) {\n var i, j, s, k,\n m = mat1.length,\n n = m > 0 ? mat2[0].length : 0,\n m2 = mat2.length,\n res = this.matrix(m, n);\n\n for (i = 0; i < m; i++) {\n for (j = 0; j < n; j++) {\n s = 0;\n for (k = 0; k < m2; k++) {\n s += mat1[i][k] * mat2[k][j];\n }\n res[i][j] = s;\n }\n }\n return res;\n },\n\n /**\n * Multiply a matrix mat by a scalar alpha: mat * scalar\n *\n * @param {Array} mat Two-dimensional array of numbers\n * @param {Number} alpha Scalar\n * @returns {Array} Two-dimensional Array of numbers containing result\n */\n matNumberMult: function (mat, alpha) {\n var i, j,\n m = mat.length,\n n = m > 0 ? mat[0].length : 0,\n res = this.matrix(m, n);\n\n for (i = 0; i < m; i++) {\n for (j = 0; j < n; j++) {\n res[i][j] = mat[i][j] * alpha;\n }\n }\n return res;\n },\n\n /**\n * Compute the sum of two matrices: mat1 + mat2.\n * Returns a new matrix object.\n *\n * @param {Array} mat1 Two-dimensional array of numbers\n * @param {Array} mat2 Two-dimensional array of numbers\n * @returns {Array} Two-dimensional Array of numbers containing result\n */\n matMatAdd: function (mat1, mat2) {\n var i, j,\n m = mat1.length,\n n = m > 0 ? mat1[0].length : 0,\n res = this.matrix(m, n);\n\n for (i = 0; i < m; i++) {\n for (j = 0; j < n; j++) {\n res[i][j] = mat1[i][j] + mat2[i][j];\n }\n }\n return res;\n },\n\n /**\n * Transposes a matrix given as a two-dimensional array.\n * @param {Array} M The matrix to be transposed\n * @returns {Array} The transpose of M\n */\n transpose: function (M) {\n var MT, i, j, m, n;\n\n // number of rows of M\n m = M.length;\n // number of columns of M\n n = M.length > 0 ? M[0].length : 0;\n MT = this.matrix(n, m);\n\n for (i = 0; i < n; i++) {\n for (j = 0; j < m; j++) {\n MT[i][j] = M[j][i];\n }\n }\n\n return MT;\n },\n\n /**\n * Compute the inverse of an (n x n)-matrix by Gauss elimination.\n *\n * @param {Array} A matrix\n * @returns {Array} Inverse matrix of A or empty array (i.e. []) in case A is singular.\n */\n inverse: function (Ain) {\n var i, j, k, r, s,\n eps = this.eps * this.eps,\n ma, swp,\n n = Ain.length,\n A = [],\n p = [],\n hv = [];\n\n for (i = 0; i < n; i++) {\n A[i] = [];\n for (j = 0; j < n; j++) {\n A[i][j] = Ain[i][j];\n }\n p[i] = i;\n }\n\n for (j = 0; j < n; j++) {\n // Pivot search\n ma = Math.abs(A[j][j]);\n r = j;\n\n for (i = j + 1; i < n; i++) {\n if (Math.abs(A[i][j]) > ma) {\n ma = Math.abs(A[i][j]);\n r = i;\n }\n }\n\n // Singular matrix\n if (ma <= eps) {\n JXG.warn('JXG.Math.inverse: singular matrix');\n return [];\n }\n\n // swap rows:\n if (r > j) {\n for (k = 0; k < n; k++) {\n swp = A[j][k];\n A[j][k] = A[r][k];\n A[r][k] = swp;\n }\n\n swp = p[j];\n p[j] = p[r];\n p[r] = swp;\n }\n\n // transformation:\n s = 1.0 / A[j][j];\n for (i = 0; i < n; i++) {\n A[i][j] *= s;\n }\n A[j][j] = s;\n\n for (k = 0; k < n; k++) {\n if (k !== j) {\n for (i = 0; i < n; i++) {\n if (i !== j) {\n A[i][k] -= A[i][j] * A[j][k];\n }\n }\n A[j][k] = -s * A[j][k];\n }\n }\n }\n\n // swap columns:\n for (i = 0; i < n; i++) {\n for (k = 0; k < n; k++) {\n hv[p[k]] = A[i][k];\n }\n for (k = 0; k < n; k++) {\n A[i][k] = hv[k];\n }\n }\n\n return A;\n },\n\n /**\n * Trace of a square matrix, given as a two-dimensional array.\n * @param {Array} M Square matrix\n * @returns {Number} The trace of M, NaN if M is not square.\n */\n trace: function (M) {\n var i, m, n,\n t = 0.0;\n\n // number of rows of M\n m = M.length;\n // number of columns of M\n n = M.length > 0 ? M[0].length : 0;\n if (m !== n) {\n return NaN;\n }\n for (i = 0; i < n; i++) {\n t += M[i][i];\n }\n\n return t;\n },\n\n /**\n * Inner product of two vectors a and b. n is the length of the vectors.\n * @param {Array} a Vector\n * @param {Array} b Vector\n * @param {Number} [n] Length of the Vectors. If not given the length of the first vector is taken.\n * @returns {Number} The inner product of a and b.\n */\n innerProduct: function (a, b, n) {\n var i,\n s = 0;\n\n if (n === undef || !Type.isNumber(n)) {\n n = a.length;\n }\n\n for (i = 0; i < n; i++) {\n s += a[i] * b[i];\n }\n\n return s;\n },\n\n /**\n * Calculates the cross product of two vectors both of length three.\n * In case of homogeneous coordinates this is either\n * \n *
\n * @param {Array} c1 Homogeneous coordinates of line or point 1\n * @param {Array} c2 Homogeneous coordinates of line or point 2\n * @returns {Array} vector of length 3: homogeneous coordinates of the resulting point / line.\n */\n crossProduct: function (c1, c2) {\n return [\n c1[1] * c2[2] - c1[2] * c2[1],\n c1[2] * c2[0] - c1[0] * c2[2],\n c1[0] * c2[1] - c1[1] * c2[0]\n ];\n },\n\n /**\n * Euclidean norm of a vector.\n *\n * @param {Array} a Array containing a vector.\n * @param {Number} n (Optional) length of the array.\n * @returns {Number} Euclidean norm of the vector.\n */\n norm: function (a, n) {\n var i,\n sum = 0.0;\n\n if (n === undef || !Type.isNumber(n)) {\n n = a.length;\n }\n\n for (i = 0; i < n; i++) {\n sum += a[i] * a[i];\n }\n\n return Math.sqrt(sum);\n },\n\n /**\n * Compute a * x + y for a scalar a and vectors x and y.\n *\n * @param {Number} a\n * @param {Array} x\n * @param {Array} y\n * @returns {Array}\n */\n axpy: function (a, x, y) {\n var i,\n le = x.length,\n p = [];\n for (i = 0; i < le; i++) {\n p[i] = a * x[i] + y[i];\n }\n return p;\n },\n\n /**\n * Compute the factorial of a positive integer. If a non-integer value\n * is given, the fraction will be ignored.\n * @function\n * @param {Number} n\n * @returns {Number} n! = n*(n-1)*...*2*1\n */\n factorial: memoizer(function (n) {\n if (n < 0) {\n return NaN;\n }\n\n n = Math.floor(n);\n\n if (n === 0 || n === 1) {\n return 1;\n }\n\n return n * this.factorial(n - 1);\n }),\n\n /**\n * Computes the binomial coefficient n over k.\n * @function\n * @param {Number} n Fraction will be ignored\n * @param {Number} k Fraction will be ignored\n * @returns {Number} The binomial coefficient n over k\n */\n binomial: memoizer(function (n, k) {\n var b, i;\n\n if (k > n || k < 0) {\n return NaN;\n }\n\n k = Math.round(k);\n n = Math.round(n);\n\n if (k === 0 || k === n) {\n return 1;\n }\n\n b = 1;\n\n for (i = 0; i < k; i++) {\n b *= n - i;\n b /= i + 1;\n }\n\n return b;\n }),\n\n /**\n * Calculates the cosine hyperbolicus of x.\n * @function\n * @param {Number} x The number the cosine hyperbolicus will be calculated of.\n * @returns {Number} Cosine hyperbolicus of the given value.\n */\n cosh:\n Math.cosh ||\n function (x) {\n return (Math.exp(x) + Math.exp(-x)) * 0.5;\n },\n\n /**\n * Sine hyperbolicus of x.\n * @function\n * @param {Number} x The number the sine hyperbolicus will be calculated of.\n * @returns {Number} Sine hyperbolicus of the given value.\n */\n sinh:\n Math.sinh ||\n function (x) {\n return (Math.exp(x) - Math.exp(-x)) * 0.5;\n },\n\n /**\n * Hyperbolic arc-cosine of a number.\n * @function\n * @param {Number} x\n * @returns {Number}\n */\n acosh:\n Math.acosh ||\n function (x) {\n return Math.log(x + Math.sqrt(x * x - 1));\n },\n\n /**\n * Hyperbolic arcsine of a number\n * @function\n * @param {Number} x\n * @returns {Number}\n */\n asinh:\n Math.asinh ||\n function (x) {\n if (x === -Infinity) {\n return x;\n }\n return Math.log(x + Math.sqrt(x * x + 1));\n },\n\n /**\n * Computes the cotangent of x.\n * @function\n * @param {Number} x The number the cotangent will be calculated of.\n * @returns {Number} Cotangent of the given value.\n */\n cot: function (x) {\n var t = Math.tan(x);\n if (Math.abs(t) < this.eps) {\n return NaN;\n }\n return 1 / t;\n },\n\n /**\n * Computes the inverse cotangent of x.\n * @param {Number} x The number the inverse cotangent will be calculated of.\n * @returns {Number} Inverse cotangent of the given value.\n */\n acot: function (x) {\n return (x >= 0 ? 0.5 : -0.5) * Math.PI - Math.atan(x);\n },\n\n /**\n * Compute n-th real root of a real number. n must be strictly positive integer.\n * If n is odd, the real n-th root exists and is negative.\n * For n even, for negative valuees of x NaN is returned\n * @param {Number} x radicand. Must be non-negative, if n even.\n * @param {Number} n index of the root. must be strictly positive integer.\n * @returns {Number} returns real root or NaN\n *\n * @example\n * nthroot(16, 4): 2\n * nthroot(-27, 3): -3\n * nthroot(-4, 2): NaN\n */\n nthroot: function (x, n) {\n var inv;\n\n if (n <= 0 || Math.floor(n) !== n) {\n return NaN;\n }\n\n inv = 1 / n;\n\n if (x === 0.0) {\n return 0.0;\n }\n\n if (x > 0) {\n return Math.exp(inv * Math.log(x));\n }\n\n // From here on, x is negative\n if (n % 2 === 1) {\n return -Math.exp(inv * Math.log(-x));\n }\n\n // x negative, even root\n return NaN;\n },\n\n /**\n * Computes cube root of real number\n * Polyfill for Math.cbrt().\n *\n * @function\n * @param {Number} x Radicand\n * @returns {Number} Cube root of x.\n */\n cbrt:\n Math.cbrt ||\n function (x) {\n return this.nthroot(x, 3);\n },\n\n /**\n * Compute base to the power of exponent.\n * @param {Number} base\n * @param {Number} exponent\n * @returns {Number} base to the power of exponent.\n */\n pow: function (base, exponent) {\n if (base === 0) {\n if (exponent === 0) {\n return 1;\n }\n return 0;\n }\n\n // exponent is an integer\n if (Math.floor(exponent) === exponent) {\n return Math.pow(base, exponent);\n }\n\n // exponent is not an integer\n if (base > 0) {\n return Math.exp(exponent * Math.log(base));\n }\n\n return NaN;\n },\n\n /**\n * Compute base to the power of the rational exponent m / n.\n * This function first reduces the fraction m/n and then computes\n * JXG.Math.pow(base, m/n).\n *\n * This function is necessary to have the same results for e.g.\n * (-8)^(1/3) = (-8)^(2/6) = -2\n * @param {Number} base\n * @param {Number} m numerator of exponent\n * @param {Number} n denominator of exponent\n * @returns {Number} base to the power of exponent.\n */\n ratpow: function (base, m, n) {\n var g;\n if (m === 0) {\n return 1;\n }\n if (n === 0) {\n return NaN;\n }\n\n g = this.gcd(m, n);\n return this.nthroot(this.pow(base, m / g), n / g);\n },\n\n /**\n * Logarithm to base 10.\n * @param {Number} x\n * @returns {Number} log10(x) Logarithm of x to base 10.\n */\n log10: function (x) {\n return Math.log(x) / Math.log(10.0);\n },\n\n /**\n * Logarithm to base 2.\n * @param {Number} x\n * @returns {Number} log2(x) Logarithm of x to base 2.\n */\n log2: function (x) {\n return Math.log(x) / Math.log(2.0);\n },\n\n /**\n * Logarithm to arbitrary base b. If b is not given, natural log is taken, i.e. b = e.\n * @param {Number} x\n * @param {Number} b base\n * @returns {Number} log(x, b) Logarithm of x to base b, that is log(x)/log(b).\n */\n log: function (x, b) {\n if (b !== undefined && Type.isNumber(b)) {\n if (b <= 0 || Math.abs(b - 1) < this.eps) {\n return NaN;\n }\n return Math.log(x) / Math.log(b);\n }\n\n return Math.log(x);\n },\n\n /**\n * The sign() function returns the sign of a number, indicating whether the number is positive, negative or zero.\n *\n * @function\n * @param {Number} x A Number\n * @returns {Number} This function has 5 kinds of return values,\n * 1, -1, 0, -0, NaN, which represent \"positive number\", \"negative number\", \"positive zero\", \"negative zero\"\n * and NaN respectively.\n */\n sign:\n Math.sign ||\n function (x) {\n x = +x; // convert to a number\n if (x === 0 || isNaN(x)) {\n return x;\n }\n return x > 0 ? 1 : -1;\n },\n\n /**\n * A square & multiply algorithm to compute base to the power of exponent.\n * Implementated by Wolfgang Riedl.\n *\n * @param {Number} base\n * @param {Number} exponent\n * @returns {Number} Base to the power of exponent\n */\n squampow: function (base, exponent) {\n var result;\n\n if (Math.floor(exponent) === exponent) {\n // exponent is integer (could be zero)\n result = 1;\n\n if (exponent < 0) {\n // invert: base\n base = 1.0 / base;\n exponent *= -1;\n }\n\n while (exponent !== 0) {\n if (exponent & 1) {\n result *= base;\n }\n\n exponent >>= 1;\n base *= base;\n }\n return result;\n }\n\n return this.pow(base, exponent);\n },\n\n /**\n * Greatest common divisor (gcd) of two numbers.\n * See {@link rosettacode.org}.\n *\n * @param {Number} a First number\n * @param {Number} b Second number\n * @returns {Number} gcd(a, b) if a and b are numbers, NaN else.\n */\n gcd: function (a, b) {\n var tmp,\n endless = true;\n\n a = Math.abs(a);\n b = Math.abs(b);\n\n if (!(Type.isNumber(a) && Type.isNumber(b))) {\n return NaN;\n }\n if (b > a) {\n tmp = a;\n a = b;\n b = tmp;\n }\n\n while (endless) {\n a %= b;\n if (a === 0) {\n return b;\n }\n b %= a;\n if (b === 0) {\n return a;\n }\n }\n },\n\n /**\n * Least common multiple (lcm) of two numbers.\n *\n * @param {Number} a First number\n * @param {Number} b Second number\n * @returns {Number} lcm(a, b) if a and b are numbers, NaN else.\n */\n lcm: function (a, b) {\n var ret;\n\n if (!(Type.isNumber(a) && Type.isNumber(b))) {\n return NaN;\n }\n\n ret = a * b;\n if (ret !== 0) {\n return ret / this.gcd(a, b);\n }\n\n return 0;\n },\n\n /**\n * Special use of Math.round function to round not only to integers but also to chosen decimal values.\n *\n * @param {Number} value Value to be rounded.\n * @param {Number} step Distance between the values to be rounded to. (default: 1.0)\n * @param {Number} [min] If set, it will be returned the maximum of value and min.\n * @param {Number} [max] If set, it will be returned the minimum of value and max.\n * @returns {Number} Fitted value.\n */\n roundToStep: function (value, step, min, max) {\n var n = value,\n tmp, minOr0;\n\n // for performance\n if (!Type.exists(step) && !Type.exists(min) && !Type.exists(max)) {\n return n;\n }\n\n if (JXG.exists(max)) {\n n = Math.min(n, max);\n }\n if (JXG.exists(min)) {\n n = Math.max(n, min);\n }\n\n minOr0 = min || 0;\n\n if (JXG.exists(step)) {\n tmp = (n - minOr0) / step;\n if (Number.isInteger(tmp)) {\n return n;\n }\n\n tmp = Math.round(tmp);\n n = minOr0 + tmp * step;\n }\n\n if (JXG.exists(max)) {\n n = Math.min(n, max);\n }\n if (JXG.exists(min)) {\n n = Math.max(n, min);\n }\n\n return n;\n },\n\n /**\n * Error function, see {@link https://en.wikipedia.org/wiki/Error_function}.\n *\n * @see JXG.Math.ProbFuncs.erf\n * @param {Number} x\n * @returns {Number}\n */\n erf: function (x) {\n return this.ProbFuncs.erf(x);\n },\n\n /**\n * Complementary error function, i.e. 1 - erf(x).\n *\n * @see JXG.Math.erf\n * @see JXG.Math.ProbFuncs.erfc\n * @param {Number} x\n * @returns {Number}\n */\n erfc: function (x) {\n return this.ProbFuncs.erfc(x);\n },\n\n /**\n * Inverse of error function\n *\n * @see JXG.Math.erf\n * @see JXG.Math.ProbFuncs.erfi\n * @param {Number} x\n * @returns {Number}\n */\n erfi: function (x) {\n return this.ProbFuncs.erfi(x);\n },\n\n /**\n * Normal distribution function\n *\n * @see JXG.Math.ProbFuncs.ndtr\n * @param {Number} x\n * @returns {Number}\n */\n ndtr: function (x) {\n return this.ProbFuncs.ndtr(x);\n },\n\n /**\n * Inverse of normal distribution function\n *\n * @see JXG.Math.ndtr\n * @see JXG.Math.ProbFuncs.ndtri\n * @param {Number} x\n * @returns {Number}\n */\n ndtri: function (x) {\n return this.ProbFuncs.ndtri(x);\n },\n\n /**\n * Returns sqrt(a * a + b * b) for a variable number of arguments.\n * This is a naive implementation which might be faster than Math.hypot.\n * The latter is numerically more stable.\n *\n * @param {Number} a Variable number of arguments.\n * @returns Number\n */\n hypot: function () {\n var i, le, a, sum;\n\n le = arguments.length;\n for (i = 0, sum = 0.0; i < le; i++) {\n a = arguments[i];\n sum += a * a;\n }\n return Math.sqrt(sum);\n },\n\n /**\n * Heaviside unit step function. Returns 0 for x <, 1 for x > 0, and 0.5 for x == 0.\n *\n * @param {Number} x\n * @returns Number\n */\n hstep: function (x) {\n return (x > 0.0) ? 1 :\n ((x < 0.0) ? 0.0 : 0.5);\n },\n\n /**\n * Gamma function for real parameters by Lanczos approximation.\n * Implementation straight from {@link https://en.wikipedia.org/wiki/Lanczos_approximation}.\n *\n * @param {Number} z\n * @returns Number\n */\n gamma: function (z) {\n var x, y, t, i, le,\n g = 7,\n // n = 9,\n p = [\n 1.0,\n 676.5203681218851,\n -1259.1392167224028,\n 771.32342877765313,\n -176.61502916214059,\n 12.507343278686905,\n -0.13857109526572012,\n 9.9843695780195716e-6,\n 1.5056327351493116e-7\n ];\n\n if (z < 0.5) {\n y = Math.PI / (Math.sin(Math.PI * z) * this.gamma(1 - z)); // Reflection formula\n } else {\n z -= 1;\n x = p[0];\n le = p.length;\n for (i = 1; i < le; i++) {\n x += p[i] / (z + i);\n }\n t = z + g + 0.5;\n y = Math.sqrt(2 * Math.PI) * Math.pow(t, z + 0.5) * Math.exp(-t) * x;\n }\n return y;\n },\n\n /* ******************** Comparisons and logical operators ************** */\n\n /**\n * Logical test: a < b?\n *\n * @param {Number} a\n * @param {Number} b\n * @returns {Boolean}\n */\n lt: function (a, b) {\n return a < b;\n },\n\n /**\n * Logical test: a <= b?\n *\n * @param {Number} a\n * @param {Number} b\n * @returns {Boolean}\n */\n leq: function (a, b) {\n return a <= b;\n },\n\n /**\n * Logical test: a > b?\n *\n * @param {Number} a\n * @param {Number} b\n * @returns {Boolean}\n */\n gt: function (a, b) {\n return a > b;\n },\n\n /**\n * Logical test: a >= b?\n *\n * @param {Number} a\n * @param {Number} b\n * @returns {Boolean}\n */\n geq: function (a, b) {\n return a >= b;\n },\n\n /**\n * Logical test: a === b?\n *\n * @param {Number} a\n * @param {Number} b\n * @returns {Boolean}\n */\n eq: function (a, b) {\n return a === b;\n },\n\n /**\n * Logical test: a !== b?\n *\n * @param {Number} a\n * @param {Number} b\n * @returns {Boolean}\n */\n neq: function (a, b) {\n return a !== b;\n },\n\n /**\n * Logical operator: a && b?\n *\n * @param {Boolean} a\n * @param {Boolean} b\n * @returns {Boolean}\n */\n and: function (a, b) {\n return a && b;\n },\n\n /**\n * Logical operator: !a?\n *\n * @param {Boolean} a\n * @returns {Boolean}\n */\n not: function (a) {\n return !a;\n },\n\n /**\n * Logical operator: a || b?\n *\n * @param {Boolean} a\n * @param {Boolean} b\n * @returns {Boolean}\n */\n or: function (a, b) {\n return a || b;\n },\n\n /**\n * Logical operator: either a or b?\n *\n * @param {Boolean} a\n * @param {Boolean} b\n * @returns {Boolean}\n */\n xor: function (a, b) {\n return (a || b) && !(a && b);\n },\n\n /**\n *\n * Convert a floating point number to sign + integer + fraction.\n * fraction is given as nominator and denominator.\n *
\n * (c1_x(t1) - c2_x(t2), c1_y(t1) - c2_y(t2)) = (0, 0).\n * \n * J = (a, b)\n * (c, d)\n *
\n * where\n * \n *
\n * The inverse J^(-1) of J is equal to\n * \n * (d, -b) / (ad - bc)\n * (-c, a) / (ad - bc)\n *
\n *\n * Then, (t1new, t2new) := (t1,t2) - J^(-1)*(e,f).\n * \n *\n */\n Neville: function (p) {\n var w = [],\n /** @ignore */\n makeFct = function (fun) {\n return function (t, suspendedUpdate) {\n var i,\n d,\n s,\n bin = Mat.binomial,\n len = p.length,\n len1 = len - 1,\n num = 0.0,\n denom = 0.0;\n\n if (!suspendedUpdate) {\n s = 1;\n for (i = 0; i < len; i++) {\n w[i] = bin(len1, i) * s;\n s *= -1;\n }\n }\n\n d = t;\n\n for (i = 0; i < len; i++) {\n if (d === 0) {\n return p[i][fun]();\n }\n s = w[i] / d;\n d -= 1;\n num += p[i][fun]() * s;\n denom += s;\n }\n return num / denom;\n };\n },\n xfct = makeFct('X'),\n yfct = makeFct('Y');\n\n return [\n xfct,\n yfct,\n 0,\n function () {\n return p.length - 1;\n }\n ];\n },\n\n /**\n * Calculates second derivatives at the given knots.\n * @param {Array} x x values of knots\n * @param {Array} y y values of knots\n * @returns {Array} Second derivatives of the interpolated function at the knots.\n * @see JXG.Math.Numerics.splineEval\n * @memberof JXG.Math.Numerics\n */\n splineDef: function (x, y) {\n var pair,\n i,\n l,\n n = Math.min(x.length, y.length),\n diag = [],\n z = [],\n data = [],\n dx = [],\n delta = [],\n F = [];\n\n if (n === 2) {\n return [0, 0];\n }\n\n for (i = 0; i < n; i++) {\n pair = { X: x[i], Y: y[i] };\n data.push(pair);\n }\n data.sort(function (a, b) {\n return a.X - b.X;\n });\n for (i = 0; i < n; i++) {\n x[i] = data[i].X;\n y[i] = data[i].Y;\n }\n\n for (i = 0; i < n - 1; i++) {\n dx.push(x[i + 1] - x[i]);\n }\n for (i = 0; i < n - 2; i++) {\n delta.push(\n (6 * (y[i + 2] - y[i + 1])) / dx[i + 1] - (6 * (y[i + 1] - y[i])) / dx[i]\n );\n }\n\n // ForwardSolve\n diag.push(2 * (dx[0] + dx[1]));\n z.push(delta[0]);\n\n for (i = 0; i < n - 3; i++) {\n l = dx[i + 1] / diag[i];\n diag.push(2 * (dx[i + 1] + dx[i + 2]) - l * dx[i + 1]);\n z.push(delta[i + 1] - l * z[i]);\n }\n\n // BackwardSolve\n F[n - 3] = z[n - 3] / diag[n - 3];\n for (i = n - 4; i >= 0; i--) {\n F[i] = (z[i] - dx[i + 1] * F[i + 1]) / diag[i];\n }\n\n // Generate f''-Vector\n for (i = n - 3; i >= 0; i--) {\n F[i + 1] = F[i];\n }\n\n // natural cubic spline\n F[0] = 0;\n F[n - 1] = 0;\n\n return F;\n },\n\n /**\n * Evaluate points on spline.\n * @param {Number|Array} x0 A single float value or an array of values to evaluate\n * @param {Array} x x values of knots\n * @param {Array} y y values of knots\n * @param {Array} F Second derivatives at knots, calculated by {@link JXG.Math.Numerics.splineDef}\n * @see JXG.Math.Numerics.splineDef\n * @returns {Number|Array} A single value or an array, depending on what is given as x0.\n * @memberof JXG.Math.Numerics\n */\n splineEval: function (x0, x, y, F) {\n var i,\n j,\n a,\n b,\n c,\n d,\n x_,\n n = Math.min(x.length, y.length),\n l = 1,\n asArray = false,\n y0 = [];\n\n // number of points to be evaluated\n if (Type.isArray(x0)) {\n l = x0.length;\n asArray = true;\n } else {\n x0 = [x0];\n }\n\n for (i = 0; i < l; i++) {\n // is x0 in defining interval?\n if (x0[i] < x[0] || x0[i] > x[n - 1]) {\n return NaN;\n }\n\n // determine part of spline in which x0 lies\n for (j = 1; j < n; j++) {\n if (x0[i] <= x[j]) {\n break;\n }\n }\n\n j -= 1;\n\n // we're now in the j-th partial interval, i.e. x[j] < x0[i] <= x[j+1];\n // determine the coefficients of the polynomial in this interval\n a = y[j];\n b =\n (y[j + 1] - y[j]) / (x[j + 1] - x[j]) -\n ((x[j + 1] - x[j]) / 6) * (F[j + 1] + 2 * F[j]);\n c = F[j] / 2;\n d = (F[j + 1] - F[j]) / (6 * (x[j + 1] - x[j]));\n // evaluate x0[i]\n x_ = x0[i] - x[j];\n //y0.push(a + b*x_ + c*x_*x_ + d*x_*x_*x_);\n y0.push(a + (b + (c + d * x_) * x_) * x_);\n }\n\n if (asArray) {\n return y0;\n }\n\n return y0[0];\n },\n\n /**\n * Generate a string containing the function term of a polynomial.\n * @param {Array} coeffs Coefficients of the polynomial. The position i belongs to x^i.\n * @param {Number} deg Degree of the polynomial\n * @param {String} varname Name of the variable (usually 'x')\n * @param {Number} prec Precision\n * @returns {String} A string containing the function term of the polynomial.\n * @memberof JXG.Math.Numerics\n */\n generatePolynomialTerm: function (coeffs, deg, varname, prec) {\n var i,\n t = [];\n\n for (i = deg; i >= 0; i--) {\n Type.concat(t, [\"(\", coeffs[i].toPrecision(prec), \")\"]);\n\n if (i > 1) {\n Type.concat(t, [\"*\", varname, \"\", i, \"<\", \"/sup> + \"]);\n } else if (i === 1) {\n Type.concat(t, [\"*\", varname, \" + \"]);\n }\n }\n\n return t.join(\"\");\n },\n\n /**\n * Computes the polynomial through a given set of coordinates in Lagrange form.\n * Returns the Lagrange polynomials, see\n * Jean-Paul Berrut, Lloyd N. Trefethen: Barycentric Lagrange Interpolation,\n * SIAM Review, Vol 46, No 3, (2004) 501-517.\n * \n * \n *\n * @example\n * var points = [];\n * points[0] = board.create('point', [-1,2], {size:4});\n * points[1] = board.create('point', [0, 0], {size:4});\n * points[2] = board.create('point', [2, 1], {size:4});\n *\n * var f = JXG.Math.Numerics.lagrangePolynomial(points);\n * var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});\n * var txt = board.create('text', [-3, -4, () => f.getTerm(2, 't', ' * ')], {fontSize: 16});\n * var txt2 = board.create('text', [-3, -6, () => f.getCoefficients()], {fontSize: 12});\n *\n * \n * \n *\n */\n lagrangePolynomial: function (p) {\n var w = [],\n that = this,\n /** @ignore */\n fct = function (x, suspendedUpdate) {\n var i, // j,\n k,\n xi,\n s, //M,\n len = p.length,\n num = 0,\n denom = 0;\n\n if (!suspendedUpdate) {\n for (i = 0; i < len; i++) {\n w[i] = 1.0;\n xi = p[i].X();\n\n for (k = 0; k < len; k++) {\n if (k !== i) {\n w[i] *= xi - p[k].X();\n }\n }\n\n w[i] = 1 / w[i];\n }\n\n // M = [];\n // for (k = 0; k < len; k++) {\n // M.push([1]);\n // }\n }\n\n for (i = 0; i < len; i++) {\n xi = p[i].X();\n\n if (x === xi) {\n return p[i].Y();\n }\n\n s = w[i] / (x - xi);\n denom += s;\n num += s * p[i].Y();\n }\n\n return num / denom;\n };\n\n /**\n * Get the term of the Lagrange polynomial as string.\n * Calls {@link JXG.Math.Numerics#lagrangePolynomialTerm}.\n *\n * @name JXG.Math.Numerics.lagrangePolynomial#getTerm\n * @param {Number} digits Number of digits of the coefficients\n * @param {String} param Variable name\n * @param {String} dot Dot symbol\n * @returns {String} containing the term of Lagrange polynomial as string.\n * @see JXG.Math.Numerics.lagrangePolynomialTerm\n * @example\n * var points = [];\n * points[0] = board.create('point', [-1,2], {size:4});\n * points[1] = board.create('point', [0, 0], {size:4});\n * points[2] = board.create('point', [2, 1], {size:4});\n *\n * var f = JXG.Math.Numerics.lagrangePolynomial(points);\n * var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});\n * var txt = board.create('text', [-3, -4, () => f.getTerm(2, 't', ' * ')], {fontSize: 16});\n *\n * \n * \n *\n */\n fct.getTerm = function (digits, param, dot) {\n return that.lagrangePolynomialTerm(p, digits, param, dot)();\n };\n\n /**\n * Get the coefficients of the Lagrange polynomial as array. The leading\n * coefficient is at position 0.\n * Calls {@link JXG.Math.Numerics#lagrangePolynomialCoefficients}.\n *\n * @name JXG.Math.Numerics.lagrangePolynomial#getCoefficients\n * @returns {Array} containing the coefficients of the Lagrange polynomial.\n * @see JXG.Math.Numerics.lagrangePolynomial.getTerm\n * @see JXG.Math.Numerics.lagrangePolynomialTerm\n * @see JXG.Math.Numerics.lagrangePolynomialCoefficients\n * @example\n * var points = [];\n * points[0] = board.create('point', [-1,2], {size:4});\n * points[1] = board.create('point', [0, 0], {size:4});\n * points[2] = board.create('point', [2, 1], {size:4});\n *\n * var f = JXG.Math.Numerics.lagrangePolynomial(points);\n * var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});\n * var txt = board.create('text', [1, -4, () => f.getCoefficients()], {fontSize: 10});\n *\n * \n * \n *\n */\n fct.getCoefficients = function () {\n return that.lagrangePolynomialCoefficients(p)();\n };\n\n return fct;\n },\n\n /**\n * Determine the Lagrange polynomial through an array of points and\n * return the term of the polynomial as string.\n *\n * @param {Array} points Array of JXG.Points\n * @param {Number} digits Number of decimal digits of the coefficients\n * @param {String} param Name of the parameter. Default: 'x'.\n * @param {String} dot Multiplication symbol. Default: ' * '.\n * @returns {Function} returning the Lagrange polynomial term through\n * the supplied points as string\n * @memberof JXG.Math.Numerics\n *\n * @example\n * var points = [];\n * points[0] = board.create('point', [-1,2], {size:4});\n * points[1] = board.create('point', [0, 0], {size:4});\n * points[2] = board.create('point', [2, 1], {size:4});\n *\n * var f = JXG.Math.Numerics.lagrangePolynomial(points);\n * var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});\n *\n * var f_txt = JXG.Math.Numerics.lagrangePolynomialTerm(points, 2, 't', ' * ');\n * var txt = board.create('text', [-3, -4, f_txt], {fontSize: 16});\n *\n * \n * \n *\n */\n lagrangePolynomialTerm: function (points, digits, param, dot) {\n var that = this;\n\n return function () {\n var len = points.length,\n coeffs = [],\n isLeading = true,\n n, t, j, c;\n\n param = param || 'x';\n if (dot === undefined) {\n dot = \" * \";\n }\n\n n = len - 1; // (Max) degree of the polynomial\n coeffs = that.lagrangePolynomialCoefficients(points)();\n\n t = \"\";\n for (j = 0; j < coeffs.length; j++) {\n c = coeffs[j];\n if (Math.abs(c) < Mat.eps) {\n continue;\n }\n if (JXG.exists(digits)) {\n c = Env._round10(c, -digits);\n }\n if (isLeading) {\n t += c > 0 ? c : \"-\" + -c;\n isLeading = false;\n } else {\n t += c > 0 ? \" + \" + c : \" - \" + -c;\n }\n\n if (n - j > 1) {\n t += dot + param + \"^\" + (n - j);\n } else if (n - j === 1) {\n t += dot + param;\n }\n }\n return t; // board.jc.manipulate('f = map(x) -> ' + t + ';');\n };\n },\n\n /**\n * Determine the Lagrange polynomial through an array of points and\n * return the coefficients of the polynomial as array.\n * The leading coefficient is at position 0.\n *\n * @param {Array} points Array of JXG.Points\n * @returns {Function} returning the coefficients of the Lagrange polynomial through\n * the supplied points.\n * @memberof JXG.Math.Numerics\n *\n * @example\n * var points = [];\n * points[0] = board.create('point', [-1,2], {size:4});\n * points[1] = board.create('point', [0, 0], {size:4});\n * points[2] = board.create('point', [2, 1], {size:4});\n *\n * var f = JXG.Math.Numerics.lagrangePolynomial(points);\n * var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});\n *\n * var f_arr = JXG.Math.Numerics.lagrangePolynomialCoefficients(points);\n * var txt = board.create('text', [1, -4, f_arr], {fontSize: 10});\n *\n * \n * \n *\n */\n lagrangePolynomialCoefficients: function (points) {\n return function () {\n var len = points.length,\n zeroes = [],\n coeffs = [],\n coeffs_sum = [],\n i, j, c, p;\n\n // n = len - 1; // (Max) degree of the polynomial\n for (j = 0; j < len; j++) {\n coeffs_sum[j] = 0;\n }\n\n for (i = 0; i < len; i++) {\n c = points[i].Y();\n p = points[i].X();\n zeroes = [];\n for (j = 0; j < len; j++) {\n if (j !== i) {\n c /= p - points[j].X();\n zeroes.push(points[j].X());\n }\n }\n coeffs = [1].concat(Mat.Vieta(zeroes));\n for (j = 0; j < coeffs.length; j++) {\n coeffs_sum[j] += (j % 2 === 1 ? -1 : 1) * coeffs[j] * c;\n }\n }\n\n return coeffs_sum;\n };\n },\n\n /**\n * Determine the coefficients of a cardinal spline polynom, See\n * https://stackoverflow.com/questions/9489736/catmull-rom-curve-with-no-cusps-and-no-self-intersections\n * @param {Number} x1 point 1\n * @param {Number} x2 point 2\n * @param {Number} t1 tangent slope 1\n * @param {Number} t2 tangent slope 2\n * @return {Array} coefficents array c for the polynomial t maps to\n * c[0] + c[1]*t + c[2]*t*t + c[3]*t*t*t\n */\n _initCubicPoly: function (x1, x2, t1, t2) {\n return [x1, t1, -3 * x1 + 3 * x2 - 2 * t1 - t2, 2 * x1 - 2 * x2 + t1 + t2];\n },\n\n /**\n * Computes the cubic cardinal spline curve through a given set of points. The curve\n * is uniformly parametrized.\n * Two artificial control points at the beginning and the end are added.\n *\n * The implementation (especially the centripetal parametrization) is from\n * https://stackoverflow.com/questions/9489736/catmull-rom-curve-with-no-cusps-and-no-self-intersections .\n * @param {Array} points Array consisting of JXG.Points.\n * @param {Number|Function} tau The tension parameter, either a constant number or a function returning a number. This number is between 0 and 1.\n * tau=1/2 give Catmull-Rom splines.\n * @param {String} type (Optional) parameter which allows to choose between \"uniform\" (default) and\n * \"centripetal\" parameterization. Thus the two possible values are \"uniform\" or \"centripetal\".\n * @returns {Array} An Array consisting of four components: Two functions each of one parameter t\n * which return the x resp. y coordinates of the Catmull-Rom-spline curve in t, a zero value,\n * and a function simply returning the length of the points array\n * minus three.\n * @memberof JXG.Math.Numerics\n */\n CardinalSpline: function (points, tau_param, type) {\n var p,\n coeffs = [],\n makeFct,\n tau, _tau,\n that = this;\n\n if (Type.isFunction(tau_param)) {\n _tau = tau_param;\n } else {\n _tau = function () {\n return tau_param;\n };\n }\n\n if (type === undefined) {\n type = 'uniform';\n }\n\n /** @ignore */\n makeFct = function (which) {\n return function (t, suspendedUpdate) {\n var s,\n c,\n // control point at the beginning and at the end\n first,\n last,\n t1,\n t2,\n dt0,\n dt1,\n dt2,\n // dx, dy,\n len;\n\n if (points.length < 2) {\n return NaN;\n }\n\n if (!suspendedUpdate) {\n tau = _tau();\n\n // New point list p: [first, points ..., last]\n first = {\n X: function () {\n return 2 * points[0].X() - points[1].X();\n },\n Y: function () {\n return 2 * points[0].Y() - points[1].Y();\n },\n Dist: function (p) {\n var dx = this.X() - p.X(),\n dy = this.Y() - p.Y();\n return Mat.hypot(dx, dy);\n }\n };\n\n last = {\n X: function () {\n return (\n 2 * points[points.length - 1].X() -\n points[points.length - 2].X()\n );\n },\n Y: function () {\n return (\n 2 * points[points.length - 1].Y() -\n points[points.length - 2].Y()\n );\n },\n Dist: function (p) {\n var dx = this.X() - p.X(),\n dy = this.Y() - p.Y();\n return Mat.hypot(dx, dy);\n }\n };\n\n p = [first].concat(points, [last]);\n len = p.length;\n\n coeffs[which] = [];\n\n for (s = 0; s < len - 3; s++) {\n if (type === 'centripetal') {\n // The order is important, since p[0].coords === undefined\n dt0 = p[s].Dist(p[s + 1]);\n dt1 = p[s + 2].Dist(p[s + 1]);\n dt2 = p[s + 3].Dist(p[s + 2]);\n\n dt0 = Math.sqrt(dt0);\n dt1 = Math.sqrt(dt1);\n dt2 = Math.sqrt(dt2);\n\n if (dt1 < Mat.eps) {\n dt1 = 1.0;\n }\n if (dt0 < Mat.eps) {\n dt0 = dt1;\n }\n if (dt2 < Mat.eps) {\n dt2 = dt1;\n }\n\n t1 =\n (p[s + 1][which]() - p[s][which]()) / dt0 -\n (p[s + 2][which]() - p[s][which]()) / (dt1 + dt0) +\n (p[s + 2][which]() - p[s + 1][which]()) / dt1;\n\n t2 =\n (p[s + 2][which]() - p[s + 1][which]()) / dt1 -\n (p[s + 3][which]() - p[s + 1][which]()) / (dt2 + dt1) +\n (p[s + 3][which]() - p[s + 2][which]()) / dt2;\n\n t1 *= dt1;\n t2 *= dt1;\n\n coeffs[which][s] = that._initCubicPoly(\n p[s + 1][which](),\n p[s + 2][which](),\n tau * t1,\n tau * t2\n );\n } else {\n coeffs[which][s] = that._initCubicPoly(\n p[s + 1][which](),\n p[s + 2][which](),\n tau * (p[s + 2][which]() - p[s][which]()),\n tau * (p[s + 3][which]() - p[s + 1][which]())\n );\n }\n }\n }\n\n if (isNaN(t)) {\n return NaN;\n }\n\n len = points.length;\n // This is necessary for our advanced plotting algorithm:\n if (t <= 0.0) {\n return points[0][which]();\n }\n if (t >= len) {\n return points[len - 1][which]();\n }\n\n s = Math.floor(t);\n if (s === t) {\n return points[s][which]();\n }\n\n t -= s;\n c = coeffs[which][s];\n if (c === undefined) {\n return NaN;\n }\n\n return ((c[3] * t + c[2]) * t + c[1]) * t + c[0];\n };\n };\n\n return [\n makeFct('X'),\n makeFct('Y'),\n 0,\n function () {\n return points.length - 1;\n }\n ];\n },\n\n /**\n * Computes the cubic Catmull-Rom spline curve through a given set of points. The curve\n * is uniformly parametrized. The curve is the cardinal spline curve for tau=0.5.\n * Two artificial control points at the beginning and the end are added.\n * @param {Array} points Array consisting of JXG.Points.\n * @param {String} type (Optional) parameter which allows to choose between \"uniform\" (default) and\n * \"centripetal\" parameterization. Thus the two possible values are \"uniform\" or \"centripetal\".\n * @returns {Array} An Array consisting of four components: Two functions each of one parameter t\n * which return the x resp. y coordinates of the Catmull-Rom-spline curve in t, a zero value, and a function simply\n * returning the length of the points array minus three.\n * @memberof JXG.Math.Numerics\n */\n CatmullRomSpline: function (points, type) {\n return this.CardinalSpline(points, 0.5, type);\n },\n\n /**\n * Computes the regression polynomial of a given degree through a given set of coordinates.\n * Returns the regression polynomial function.\n * @param {Number|function|Slider} degree number, function or slider.\n * Either\n * @param {Array} dataX Array containing either the x-coordinates of the data set or both coordinates in\n * an array of {@link JXG.Point}s or {@link JXG.Coords}.\n * In the latter case, the dataY parameter will be ignored.\n * @param {Array} dataY Array containing the y-coordinates of the data set,\n * @returns {function} A function of one parameter which returns the value of the regression polynomial of the given degree.\n * It possesses the method getTerm() which returns the string containing the function term of the polynomial.\n * The function returned will throw an exception, if the data set is malformed.\n * @memberof JXG.Math.Numerics\n */\n regressionPolynomial: function (degree, dataX, dataY) {\n var coeffs, deg, dX, dY, inputType, fct,\n term = \"\";\n\n // Slider\n if (Type.isPoint(degree) && Type.isFunction(degree.Value)) {\n /** @ignore */\n deg = function () {\n return degree.Value();\n };\n // function\n } else if (Type.isFunction(degree)) {\n deg = degree;\n // number\n } else if (Type.isNumber(degree)) {\n /** @ignore */\n deg = function () {\n return degree;\n };\n } else {\n throw new Error(\n \"JSXGraph: Can't create regressionPolynomial from degree of type'\" +\n typeof degree +\n \"'.\"\n );\n }\n\n // Parameters degree, dataX, dataY\n if (arguments.length === 3 && Type.isArray(dataX) && Type.isArray(dataY)) {\n inputType = 0;\n // Parameters degree, point array\n } else if (\n arguments.length === 2 &&\n Type.isArray(dataX) &&\n dataX.length > 0 &&\n Type.isPoint(dataX[0])\n ) {\n inputType = 1;\n } else if (\n arguments.length === 2 &&\n Type.isArray(dataX) &&\n dataX.length > 0 &&\n dataX[0].usrCoords &&\n dataX[0].scrCoords\n ) {\n inputType = 2;\n } else {\n throw new Error(\"JSXGraph: Can't create regressionPolynomial. Wrong parameters.\");\n }\n\n /** @ignore */\n fct = function (x, suspendedUpdate) {\n var i, j,\n M, MT, y, B, c, s, d,\n // input data\n len = dataX.length;\n\n d = Math.floor(deg());\n\n if (!suspendedUpdate) {\n // point list as input\n if (inputType === 1) {\n dX = [];\n dY = [];\n\n for (i = 0; i < len; i++) {\n dX[i] = dataX[i].X();\n dY[i] = dataX[i].Y();\n }\n }\n\n if (inputType === 2) {\n dX = [];\n dY = [];\n\n for (i = 0; i < len; i++) {\n dX[i] = dataX[i].usrCoords[1];\n dY[i] = dataX[i].usrCoords[2];\n }\n }\n\n // check for functions\n if (inputType === 0) {\n dX = [];\n dY = [];\n\n for (i = 0; i < len; i++) {\n if (Type.isFunction(dataX[i])) {\n dX.push(dataX[i]());\n } else {\n dX.push(dataX[i]);\n }\n\n if (Type.isFunction(dataY[i])) {\n dY.push(dataY[i]());\n } else {\n dY.push(dataY[i]);\n }\n }\n }\n\n M = [];\n for (j = 0; j < len; j++) {\n M.push([1]);\n }\n for (i = 1; i <= d; i++) {\n for (j = 0; j < len; j++) {\n M[j][i] = M[j][i - 1] * dX[j];\n }\n }\n\n y = dY;\n MT = Mat.transpose(M);\n B = Mat.matMatMult(MT, M);\n c = Mat.matVecMult(MT, y);\n coeffs = Mat.Numerics.Gauss(B, c);\n term = Mat.Numerics.generatePolynomialTerm(coeffs, d, \"x\", 3);\n }\n\n // Horner's scheme to evaluate polynomial\n s = coeffs[d];\n for (i = d - 1; i >= 0; i--) {\n s = s * x + coeffs[i];\n }\n\n return s;\n };\n\n /** @ignore */\n fct.getTerm = function () {\n return term;\n };\n\n return fct;\n },\n\n /**\n * Computes the cubic Bezier curve through a given set of points.\n * @param {Array} points Array consisting of 3*k+1 {@link JXG.Points}.\n * The points at position k with k mod 3 = 0 are the data points,\n * points at position k with k mod 3 = 1 or 2 are the control points.\n * @returns {Array} An array consisting of two functions of one parameter t which return the\n * x resp. y coordinates of the Bezier curve in t, one zero value, and a third function accepting\n * no parameters and returning one third of the length of the points.\n * @memberof JXG.Math.Numerics\n */\n bezier: function (points) {\n var len,\n flen,\n /** @ignore */\n makeFct = function (which) {\n return function (t, suspendedUpdate) {\n var z = Math.floor(t) * 3,\n t0 = t % 1,\n t1 = 1 - t0;\n\n if (!suspendedUpdate) {\n flen = 3 * Math.floor((points.length - 1) / 3);\n len = Math.floor(flen / 3);\n }\n\n if (t < 0) {\n return points[0][which]();\n }\n\n if (t >= len) {\n return points[flen][which]();\n }\n\n if (isNaN(t)) {\n return NaN;\n }\n\n return (\n t1 * t1 * (t1 * points[z][which]() + 3 * t0 * points[z + 1][which]()) +\n (3 * t1 * points[z + 2][which]() + t0 * points[z + 3][which]()) *\n t0 *\n t0\n );\n };\n };\n\n return [\n makeFct('X'),\n makeFct('Y'),\n 0,\n function () {\n return Math.floor(points.length / 3);\n }\n ];\n },\n\n /**\n * Computes the B-spline curve of order k (order = degree+1) through a given set of points.\n * @param {Array} points Array consisting of JXG.Points.\n * @param {Number} order Order of the B-spline curve.\n * @returns {Array} An Array consisting of four components: Two functions each of one parameter t\n * which return the x resp. y coordinates of the B-spline curve in t, a zero value, and a function simply\n * returning the length of the points array minus one.\n * @memberof JXG.Math.Numerics\n */\n bspline: function (points, order) {\n var knots,\n _knotVector = function (n, k) {\n var j,\n kn = [];\n\n for (j = 0; j < n + k + 1; j++) {\n if (j < k) {\n kn[j] = 0.0;\n } else if (j <= n) {\n kn[j] = j - k + 1;\n } else {\n kn[j] = n - k + 2;\n }\n }\n\n return kn;\n },\n _evalBasisFuncs = function (t, kn, k, s) {\n var i,\n j,\n a,\n b,\n den,\n N = [];\n\n if (kn[s] <= t && t < kn[s + 1]) {\n N[s] = 1;\n } else {\n N[s] = 0;\n }\n\n for (i = 2; i <= k; i++) {\n for (j = s - i + 1; j <= s; j++) {\n if (j <= s - i + 1 || j < 0) {\n a = 0.0;\n } else {\n a = N[j];\n }\n\n if (j >= s) {\n b = 0.0;\n } else {\n b = N[j + 1];\n }\n\n den = kn[j + i - 1] - kn[j];\n\n if (den === 0) {\n N[j] = 0;\n } else {\n N[j] = ((t - kn[j]) / den) * a;\n }\n\n den = kn[j + i] - kn[j + 1];\n\n if (den !== 0) {\n N[j] += ((kn[j + i] - t) / den) * b;\n }\n }\n }\n return N;\n },\n /** @ignore */\n makeFct = function (which) {\n return function (t, suspendedUpdate) {\n var y,\n j,\n s,\n N = [],\n len = points.length,\n n = len - 1,\n k = order;\n\n if (n <= 0) {\n return NaN;\n }\n\n if (n + 2 <= k) {\n k = n + 1;\n }\n\n if (t <= 0) {\n return points[0][which]();\n }\n\n if (t >= n - k + 2) {\n return points[n][which]();\n }\n\n s = Math.floor(t) + k - 1;\n knots = _knotVector(n, k);\n N = _evalBasisFuncs(t, knots, k, s);\n\n y = 0.0;\n for (j = s - k + 1; j <= s; j++) {\n if (j < len && j >= 0) {\n y += points[j][which]() * N[j];\n }\n }\n\n return y;\n };\n };\n\n return [\n makeFct('X'),\n makeFct('Y'),\n 0,\n function () {\n return points.length - 1;\n }\n ];\n },\n\n /**\n * Numerical (symmetric) approximation of derivative. suspendUpdate is piped through,\n * see {@link JXG.Curve#updateCurve}\n * and {@link JXG.Curve#hasPoint}.\n * @param {function} f Function in one variable to be differentiated.\n * @param {object} [obj] Optional object that is treated as \"this\" in the function body. This is useful, if the function is a\n * method of an object and contains a reference to its parent object via \"this\".\n * @returns {function} Derivative function of a given function f.\n * @memberof JXG.Math.Numerics\n */\n D: function (f, obj) {\n if (!Type.exists(obj)) {\n return function (x, suspendedUpdate) {\n var h = 0.00001,\n h2 = h * 2.0;\n\n // Experiments with Richardsons rule\n /*\n var phi = (f(x + h, suspendedUpdate) - f(x - h, suspendedUpdate)) / h2;\n var phi2;\n h *= 0.5;\n h2 *= 0.5;\n phi2 = (f(x + h, suspendedUpdate) - f(x - h, suspendedUpdate)) / h2;\n\n return phi2 + (phi2 - phi) / 3.0;\n */\n return (f(x + h, suspendedUpdate) - f(x - h, suspendedUpdate)) / h2;\n };\n }\n\n return function (x, suspendedUpdate) {\n var h = 0.00001,\n h2 = h * 2.0;\n\n return (\n (f.apply(obj, [x + h, suspendedUpdate]) -\n f.apply(obj, [x - h, suspendedUpdate])) /\n h2\n );\n };\n },\n\n /**\n * Evaluate the function term for {@link JXG.Math.Numerics.riemann}.\n * @private\n * @param {Number} x function argument\n * @param {function} f JavaScript function returning a number\n * @param {String} type Name of the Riemann sum type, e.g. 'lower'.\n * @param {Number} delta Width of the bars in user coordinates\n * @returns {Number} Upper (delta > 0) or lower (delta < 0) value of the bar containing x of the Riemann sum.\n * @see JXG.Math.Numerics.riemann\n * @private\n * @memberof JXG.Math.Numerics\n */\n _riemannValue: function (x, f, type, delta) {\n var y, y1, x1, delta1;\n\n if (delta < 0) {\n // delta is negative if the lower function term is evaluated\n if (type !== 'trapezoidal') {\n x = x + delta;\n }\n delta *= -1;\n if (type === 'lower') {\n type = 'upper';\n } else if (type === 'upper') {\n type = 'lower';\n }\n }\n\n delta1 = delta * 0.01; // for 'lower' and 'upper'\n\n if (type === 'right') {\n y = f(x + delta);\n } else if (type === 'middle') {\n y = f(x + delta * 0.5);\n } else if (type === \"left\" || type === 'trapezoidal') {\n y = f(x);\n } else if (type === 'lower') {\n y = f(x);\n\n for (x1 = x + delta1; x1 <= x + delta; x1 += delta1) {\n y1 = f(x1);\n\n if (y1 < y) {\n y = y1;\n }\n }\n\n y1 = f(x + delta);\n if (y1 < y) {\n y = y1;\n }\n } else if (type === 'upper') {\n y = f(x);\n\n for (x1 = x + delta1; x1 <= x + delta; x1 += delta1) {\n y1 = f(x1);\n if (y1 > y) {\n y = y1;\n }\n }\n\n y1 = f(x + delta);\n if (y1 > y) {\n y = y1;\n }\n } else if (type === 'random') {\n y = f(x + delta * Math.random());\n } else if (type === 'simpson') {\n y = (f(x) + 4 * f(x + delta * 0.5) + f(x + delta)) / 6.0;\n } else {\n y = f(x); // default is lower\n }\n\n return y;\n },\n\n /**\n * Helper function to create curve which displays Riemann sums.\n * Compute coordinates for the rectangles showing the Riemann sum.\n * \n * \n * {\n * s: <Number>,\n * A: <matrix>,\n * b: <Array>,\n * c: <Array>\n * }\n * \n * which corresponds to the Butcher tableau structure\n * shown here: https://en.wikipedia.org/w/index.php?title=List_of_Runge%E2%80%93Kutta_methods&oldid=357796696 .\n * Default is 'euler'.\n * @param {Array} x0 Initial value vector. Even if the problem is one-dimensional, the initial value has to be given in an array.\n * @param {Array} I Interval on which to integrate.\n * @param {Number} N Number of integration intervals, i.e. there are N+1 evaluation points.\n * @param {function} f Function describing the right hand side of the first order ordinary differential equation, i.e. if the ode\n * is given by the equation dx/dt = f(t, x(t))
. So, f has to take two parameters, a number t and a\n * vector x, and has to return a vector of the same length as x has.\n * @returns {Array} An array of vectors describing the solution of the ode on the given interval I.\n * @example\n * // A very simple autonomous system dx(t)/dt = x(t);\n * var f = function(t, x) {\n * return [x[0]];\n * }\n *\n * // Solve it with initial value x(0) = 1 on the interval [0, 2]\n * // with 20 evaluation points.\n * var data = JXG.Math.Numerics.rungeKutta('heun', [1], [0, 2], 20, f);\n *\n * // Prepare data for plotting the solution of the ode using a curve.\n * var dataX = [];\n * var dataY = [];\n * var h = 0.1; // (I[1] - I[0])/N = (2-0)/20\n * var i;\n * for(i=0; i<data.length; i++) {\n * dataX[i] = i*h;\n * dataY[i] = data[i][0];\n * }\n * var g = board.create('curve', [dataX, dataY], {strokeWidth:'2px'});\n * \n * @memberof JXG.Math.Numerics\n */\n rungeKutta: function (butcher, x0, I, N, f) {\n var e,\n i, j, k, l, s,\n x = [],\n y = [],\n h = (I[1] - I[0]) / N,\n t = I[0],\n dim = x0.length,\n result = [],\n r = 0;\n\n if (Type.isString(butcher)) {\n butcher = predefinedButcher[butcher] || predefinedButcher.euler;\n }\n s = butcher.s;\n\n // Don't change x0, so copy it\n x = x0.slice();\n\n for (i = 0; i <= N; i++) {\n result[r] = x.slice();\n\n r++;\n k = [];\n\n for (j = 0; j < s; j++) {\n // Init y = 0\n for (e = 0; e < dim; e++) {\n y[e] = 0.0;\n }\n\n // Calculate linear combination of former k's and save it in y\n for (l = 0; l < j; l++) {\n for (e = 0; e < dim; e++) {\n y[e] += butcher.A[j][l] * h * k[l][e];\n }\n }\n\n // Add x(t) to y\n for (e = 0; e < dim; e++) {\n y[e] += x[e];\n }\n\n // Calculate new k and add it to the k matrix\n k.push(f(t + butcher.c[j] * h, y));\n }\n\n // Init y = 0\n for (e = 0; e < dim; e++) {\n y[e] = 0.0;\n }\n\n for (l = 0; l < s; l++) {\n for (e = 0; e < dim; e++) {\n y[e] += butcher.b[l] * k[l][e];\n }\n }\n\n for (e = 0; e < dim; e++) {\n x[e] = x[e] + h * y[e];\n }\n\n t += h;\n }\n\n return result;\n },\n\n /**\n * Maximum number of iterations in {@link JXG.Math.Numerics.fzero} and\n * {@link JXG.Math.Numerics.chandrupatla}\n * @type Number\n * @default 80\n * @memberof JXG.Math.Numerics\n */\n maxIterationsRoot: 80,\n\n /**\n * Maximum number of iterations in {@link JXG.Math.Numerics.fminbr}\n * @type Number\n * @default 500\n * @memberof JXG.Math.Numerics\n */\n maxIterationsMinimize: 500,\n\n /**\n * Given a number x_0, this function tries to find a second number x_1 such that\n * the function f has opposite signs at x_0 and x_1.\n * The return values have to be tested if the method succeeded.\n *\n * @param {Function} f Function, whose root is to be found\n * @param {Number} x0 Start value\n * @param {Object} [context] Parent object in case f is method of it\n * @returns {Array} [x_0, f(x_0), x_1, f(x_1)] in case that x_0 <= x_1\n * or [x_1, f(x_1), x_0, f(x_0)] in case that x_1 < x_0.\n *\n * @see JXG.Math.Numerics.fzero\n * @see JXG.Math.Numerics.chandrupatla\n *\n * @memberof JXG.Math.Numerics\n */\n findBracket: function (f, x0, context) {\n var a, aa, fa, blist, b, fb, u, fu, i, len;\n\n if (Type.isArray(x0)) {\n return x0;\n }\n\n a = x0;\n fa = f.call(context, a);\n // nfev += 1;\n\n // Try to get b, by trying several values related to a\n aa = a === 0 ? 1 : a;\n blist = [\n a - 0.1 * aa,\n a + 0.1 * aa,\n a - 1,\n a + 1,\n a - 0.5 * aa,\n a + 0.5 * aa,\n a - 0.6 * aa,\n a + 0.6 * aa,\n a - 1 * aa,\n a + 1 * aa,\n a - 2 * aa,\n a + 2 * aa,\n a - 5 * aa,\n a + 5 * aa,\n a - 10 * aa,\n a + 10 * aa,\n a - 50 * aa,\n a + 50 * aa,\n a - 100 * aa,\n a + 100 * aa\n ];\n len = blist.length;\n\n for (i = 0; i < len; i++) {\n b = blist[i];\n fb = f.call(context, b);\n // nfev += 1;\n\n if (fa * fb <= 0) {\n break;\n }\n }\n if (b < a) {\n u = a;\n a = b;\n b = u;\n\n fu = fa;\n fa = fb;\n fb = fu;\n }\n return [a, fa, b, fb];\n },\n\n /**\n *\n * Find zero of an univariate function f.\n * @param {function} f Function, whose root is to be found\n * @param {Array|Number} x0 Start value or start interval enclosing the root.\n * If x0 is an interval [a,b], it is required that f(a)f(b) <= 0, otherwise the minimum of f in [a, b] will be returned.\n * If x0 is a number, the algorithms tries to enclose the root by an interval [a, b] containing x0 and the root and\n * f(a)f(b) <= 0. If this fails, the algorithm falls back to Newton's method.\n * @param {Object} [context] Parent object in case f is method of it\n * @returns {Number} the approximation of the root\n * Algorithm:\n * Brent's root finder from\n * G.Forsythe, M.Malcolm, C.Moler, Computer methods for mathematical\n * computations. M., Mir, 1980, p.180 of the Russian edition\n * https://www.netlib.org/c/brent.shar\n *\n * If x0 is an array containing lower and upper bound for the zero\n * algorithm 748 is applied. Otherwise, if x0 is a number,\n * the algorithm tries to bracket a zero of f starting from x0.\n * If this fails, we fall back to Newton's method.\n *\n * @see JXG.Math.Numerics.chandrupatla\n * @see JXG.Math.Numerics.root\n * @see JXG.Math.Numerics.findBracket\n * @see JXG.Math.Numerics.Newton\n * @see JXG.Math.Numerics.fminbr\n * @memberof JXG.Math.Numerics\n */\n fzero: function (f, x0, context) {\n var a, b, c,\n fa, fb, fc,\n res, x00,\n prev_step,\n t1, t2,\n cb,\n tol_act, // Actual tolerance\n p, // Interpolation step is calculated in the form p/q; division\n q, // operations is delayed until the last moment\n new_step, // Step at this iteration\n eps = Mat.eps,\n maxiter = this.maxIterationsRoot,\n niter = 0;\n // nfev = 0;\n\n if (Type.isArray(x0)) {\n if (x0.length < 2) {\n throw new Error(\n \"JXG.Math.Numerics.fzero: length of array x0 has to be at least two.\"\n );\n }\n\n x00 = this.findDomain(f, x0, context);\n a = x00[0];\n b = x00[1];\n // a = x0[0];\n // b = x0[1];\n\n fa = f.call(context, a);\n // nfev += 1;\n fb = f.call(context, b);\n // nfev += 1;\n } else {\n res = this.findBracket(f, x0, context);\n a = res[0];\n fa = res[1];\n b = res[2];\n fb = res[3];\n }\n\n if (Math.abs(fa) <= eps) {\n return a;\n }\n if (Math.abs(fb) <= eps) {\n return b;\n }\n\n if (fa * fb > 0) {\n // Bracketing not successful, fall back to Newton's method or to fminbr\n if (Type.isArray(x0)) {\n return this.fminbr(f, [a, b], context);\n }\n\n return this.Newton(f, a, context);\n }\n\n // OK, we have enclosed a zero of f.\n // Now we can start Brent's method\n c = a;\n fc = fa;\n\n // Main iteration loop\n while (niter < maxiter) {\n // Distance from the last but one to the last approximation\n prev_step = b - a;\n\n // Swap data for b to be the best approximation\n if (Math.abs(fc) < Math.abs(fb)) {\n a = b;\n b = c;\n c = a;\n\n fa = fb;\n fb = fc;\n fc = fa;\n }\n tol_act = 2 * eps * Math.abs(b) + eps * 0.5;\n new_step = (c - b) * 0.5;\n\n if (Math.abs(new_step) <= tol_act || Math.abs(fb) <= eps) {\n // Acceptable approx. is found\n return b;\n }\n\n // Decide if the interpolation can be tried\n // If prev_step was large enough and was in true direction Interpolatiom may be tried\n if (Math.abs(prev_step) >= tol_act && Math.abs(fa) > Math.abs(fb)) {\n cb = c - b;\n\n // If we have only two distinct points linear interpolation can only be applied\n if (a === c) {\n t1 = fb / fa;\n p = cb * t1;\n q = 1.0 - t1;\n // Quadric inverse interpolation\n } else {\n q = fa / fc;\n t1 = fb / fc;\n t2 = fb / fa;\n\n p = t2 * (cb * q * (q - t1) - (b - a) * (t1 - 1.0));\n q = (q - 1.0) * (t1 - 1.0) * (t2 - 1.0);\n }\n\n // p was calculated with the opposite sign; make p positive\n if (p > 0) {\n q = -q;\n // and assign possible minus to q\n } else {\n p = -p;\n }\n\n // If b+p/q falls in [b,c] and isn't too large it is accepted\n // If p/q is too large then the bissection procedure can reduce [b,c] range to more extent\n if (\n p < 0.75 * cb * q - Math.abs(tol_act * q) * 0.5 &&\n p < Math.abs(prev_step * q * 0.5)\n ) {\n new_step = p / q;\n }\n }\n\n // Adjust the step to be not less than tolerance\n if (Math.abs(new_step) < tol_act) {\n new_step = new_step > 0 ? tol_act : -tol_act;\n }\n\n // Save the previous approx.\n a = b;\n fa = fb;\n b += new_step;\n fb = f.call(context, b);\n // Do step to a new approxim.\n // nfev += 1;\n\n // Adjust c for it to have a sign opposite to that of b\n if ((fb > 0 && fc > 0) || (fb < 0 && fc < 0)) {\n c = a;\n fc = fa;\n }\n niter++;\n } // End while\n\n return b;\n },\n\n /**\n * Find zero of an univariate function f.\n * @param {function} f Function, whose root is to be found\n * @param {Array|Number} x0 Start value or start interval enclosing the root.\n * If x0 is an interval [a,b], it is required that f(a)f(b) <= 0, otherwise the minimum of f in [a, b] will be returned.\n * If x0 is a number, the algorithms tries to enclose the root by an interval [a, b] containing x0 and the root and\n * f(a)f(b) <= 0. If this fails, the algorithm falls back to Newton's method.\n * @param {Object} [context] Parent object in case f is method of it\n * @returns {Number} the approximation of the root\n * Algorithm:\n * Chandrupatla's method, see\n * Tirupathi R. Chandrupatla,\n * \"A new hybrid quadratic/bisection algorithm for finding the zero of a nonlinear function without using derivatives\",\n * Advances in Engineering Software, Volume 28, Issue 3, April 1997, Pages 145-149.\n *\n * If x0 is an array containing lower and upper bound for the zero\n * algorithm 748 is applied. Otherwise, if x0 is a number,\n * the algorithm tries to bracket a zero of f starting from x0.\n * If this fails, we fall back to Newton's method.\n *\n * @see JXG.Math.Numerics.root\n * @see JXG.Math.Numerics.fzero\n * @see JXG.Math.Numerics.findBracket\n * @see JXG.Math.Numerics.Newton\n * @see JXG.Math.Numerics.fminbr\n * @memberof JXG.Math.Numerics\n */\n chandrupatla: function (f, x0, context) {\n var a, b, fa, fb,\n res,\n niter = 0,\n maxiter = this.maxIterationsRoot,\n rand = 1 + Math.random() * 0.001,\n t = 0.5 * rand,\n eps = Mat.eps, // 1.e-10,\n dlt = 0.00001,\n x1, x2, x3, x,\n f1, f2, f3, y,\n xm, fm,\n tol, tl,\n xi, ph, fl, fh,\n AL, A, B, C, D;\n\n if (Type.isArray(x0)) {\n if (x0.length < 2) {\n throw new Error(\n \"JXG.Math.Numerics.fzero: length of array x0 has to be at least two.\"\n );\n }\n\n a = x0[0];\n fa = f.call(context, a);\n // nfev += 1;\n b = x0[1];\n fb = f.call(context, b);\n // nfev += 1;\n } else {\n res = this.findBracket(f, x0, context);\n a = res[0];\n fa = res[1];\n b = res[2];\n fb = res[3];\n }\n\n if (fa * fb > 0) {\n // Bracketing not successful, fall back to Newton's method or to fminbr\n if (Type.isArray(x0)) {\n return this.fminbr(f, [a, b], context);\n }\n\n return this.Newton(f, a, context);\n }\n\n x1 = a;\n x2 = b;\n f1 = fa;\n f2 = fb;\n do {\n x = x1 + t * (x2 - x1);\n y = f.call(context, x);\n\n // Arrange 2-1-3: 2-1 interval, 1 middle, 3 discarded point\n if (Math.sign(y) === Math.sign(f1)) {\n x3 = x1;\n x1 = x;\n f3 = f1;\n f1 = y;\n } else {\n x3 = x2;\n x2 = x1;\n f3 = f2;\n f2 = f1;\n }\n x1 = x;\n f1 = y;\n\n xm = x1;\n fm = f1;\n if (Math.abs(f2) < Math.abs(f1)) {\n xm = x2;\n fm = f2;\n }\n tol = 2 * eps * Math.abs(xm) + 0.5 * dlt;\n tl = tol / Math.abs(x2 - x1);\n if (tl > 0.5 || fm === 0) {\n break;\n }\n // If inverse quadratic interpolation holds, use it\n xi = (x1 - x2) / (x3 - x2);\n ph = (f1 - f2) / (f3 - f2);\n fl = 1 - Math.sqrt(1 - xi);\n fh = Math.sqrt(xi);\n if (fl < ph && ph < fh) {\n AL = (x3 - x1) / (x2 - x1);\n A = f1 / (f2 - f1);\n B = f3 / (f2 - f3);\n C = f1 / (f3 - f1);\n D = f2 / (f3 - f2);\n t = A * B + C * D * AL;\n } else {\n t = 0.5 * rand;\n }\n // Adjust t away from the interval boundary\n if (t < tl) {\n t = tl;\n }\n if (t > 1 - tl) {\n t = 1 - tl;\n }\n niter++;\n } while (niter <= maxiter);\n // console.log(niter);\n\n return xm;\n },\n\n /**\n * Find a small enclosing interval of the domain of a function by\n * tightening the input interval x0.\n * \n *\n * Discussion:\n *\n * This function assumes that F(X) is twice continuously differentiable over [A,B]\n * and that |F''(X)| <= M for all X in [A,B].\n *\n * Licensing:\n * This code is distributed under the GNU LGPL license.\n *\n * Modified:\n *\n * 17 April 2008\n *\n * Author:\n *\n * Original FORTRAN77 version by Richard Brent.\n * C version by John Burkardt.\n * https://people.math.sc.edu/Burkardt/c_src/brent/brent.c\n *\n * Reference:\n *\n * Richard Brent,\n * Algorithms for Minimization Without Derivatives,\n * Dover, 2002,\n * ISBN: 0-486-41998-3,\n * LC: QA402.5.B74.\n *\n * Parameters:\n *\n * Input, double A, B, the endpoints of the interval.\n * It must be the case that A < B.\n *\n * Input, double C, an initial guess for the global\n * minimizer. If no good guess is known, C = A or B is acceptable.\n *\n * Input, double M, the bound on the second derivative.\n *\n * Input, double MACHEP, an estimate for the relative machine\n * precision.\n *\n * Input, double E, a positive tolerance, a bound for the\n * absolute error in the evaluation of F(X) for any X in [A,B].\n *\n * Input, double T, a positive error tolerance.\n *\n * Input, double F (double x ), a user-supplied\n * function whose global minimum is being sought.\n *\n * Output, double *X, the estimated value of the abscissa\n * for which F attains its global minimum value in [A,B].\n *\n * Output, double GLOMIN, the value F(X).\n *
\n *\n * In JSXGraph, some parameters of the original algorithm are set to fixed values:\n * \n *
\n * @param {function} f Function, whose global minimum is to be found\n * @param {Array} x0 Array of length 2 determining the interval [A, B] for which the global minimum is to be found\n * @returns {Array} [x, y] x is the position of the global minimum and y = f(x).\n */\n glomin: function (f, x0) {\n var a0, a2, a3, d0, d1, d2, h,\n k, m2,\n p, q, qs,\n r, s, sc,\n y, y0, y1, y2, y3, yb,\n z0, z1, z2,\n a, b, c, x,\n m = 10000000.0,\n t = Mat.eps, // * Mat.eps,\n e = Mat.eps * Mat.eps,\n machep = Mat.eps * Mat.eps * Mat.eps;\n\n a = x0[0];\n b = x0[1];\n c = (f(a) < f(b)) ? a : b;\n\n a0 = b;\n x = a0;\n a2 = a;\n y0 = f(b);\n yb = y0;\n y2 = f(a);\n y = y2;\n\n if (y0 < y) {\n y = y0;\n } else {\n x = a;\n }\n\n if (m <= 0.0 || b <= a) {\n return y;\n }\n\n m2 = 0.5 * (1.0 + 16.0 * machep) * m;\n\n if (c <= a || b <= c) {\n sc = 0.5 * (a + b);\n } else {\n sc = c;\n }\n\n y1 = f(sc);\n k = 3;\n d0 = a2 - sc;\n h = 9.0 / 11.0;\n\n if (y1 < y) {\n x = sc;\n y = y1;\n }\n\n for (; ;) {\n d1 = a2 - a0;\n d2 = sc - a0;\n z2 = b - a2;\n z0 = y2 - y1;\n z1 = y2 - y0;\n r = d1 * d1 * z0 - d0 * d0 * z1;\n p = r;\n qs = 2.0 * (d0 * z1 - d1 * z0);\n q = qs;\n\n if (k < 1000000 || y2 <= y) {\n for (; ;) {\n if (q * (r * (yb - y2) + z2 * q * ((y2 - y) + t)) <\n z2 * m2 * r * (z2 * q - r)) {\n\n a3 = a2 + r / q;\n y3 = f(a3);\n\n if (y3 < y) {\n x = a3;\n y = y3;\n }\n }\n k = ((1611 * k) % 1048576);\n q = 1.0;\n r = (b - a) * 0.00001 * k;\n\n if (z2 <= r) {\n break;\n }\n }\n } else {\n k = ((1611 * k) % 1048576);\n q = 1.0;\n r = (b - a) * 0.00001 * k;\n\n while (r < z2) {\n if (q * (r * (yb - y2) + z2 * q * ((y2 - y) + t)) <\n z2 * m2 * r * (z2 * q - r)) {\n\n a3 = a2 + r / q;\n y3 = f(a3);\n\n if (y3 < y) {\n x = a3;\n y = y3;\n }\n }\n k = ((1611 * k) % 1048576);\n q = 1.0;\n r = (b - a) * 0.00001 * k;\n }\n }\n\n r = m2 * d0 * d1 * d2;\n s = Math.sqrt(((y2 - y) + t) / m2);\n h = 0.5 * (1.0 + h);\n p = h * (p + 2.0 * r * s);\n q = q + 0.5 * qs;\n r = - 0.5 * (d0 + (z0 + 2.01 * e) / (d0 * m2));\n\n if (r < s || d0 < 0.0) {\n r = a2 + s;\n } else {\n r = a2 + r;\n }\n\n if (0.0 < p * q) {\n a3 = a2 + p / q;\n } else {\n a3 = r;\n }\n\n for (; ;) {\n a3 = Math.max(a3, r);\n\n if (b <= a3) {\n a3 = b;\n y3 = yb;\n } else {\n y3 = f(a3);\n }\n\n if (y3 < y) {\n x = a3;\n y = y3;\n }\n\n d0 = a3 - a2;\n\n if (a3 <= r) {\n break;\n }\n\n p = 2.0 * (y2 - y3) / (m * d0);\n\n if ((1.0 + 9.0 * machep) * d0 <= Math.abs(p)) {\n break;\n }\n\n if (0.5 * m2 * (d0 * d0 + p * p) <= (y2 - y) + (y3 - y) + 2.0 * t) {\n break;\n }\n a3 = 0.5 * (a2 + a3);\n h = 0.9 * h;\n }\n\n if (b <= a3) {\n break;\n }\n\n a0 = sc;\n sc = a2;\n a2 = a3;\n y0 = y1;\n y1 = y2;\n y2 = y3;\n }\n\n return [x, y];\n },\n\n /**\n * Determine all roots of a polynomial with real or complex coefficients by using the\n * iterative method attributed to Weierstrass, Durand, Kerner, Aberth, and Ehrlich. In particular,\n * the iteration method with cubic convergence is used that is usually attributed to Ehrlich-Aberth.\n * \n *\n */\n Visvalingam: function (pts, numPoints) {\n var i,\n len,\n vol,\n lastVol,\n linkedList = [],\n heap = [],\n points = [],\n lft,\n rt,\n lft2,\n rt2,\n obj;\n\n len = pts.length;\n\n // At least one intermediate point is needed\n if (len <= 2) {\n return pts;\n }\n\n // Fill the linked list\n // Add first point to the linked list\n linkedList[0] = {\n used: true,\n lft: null,\n node: null\n };\n\n // Add all intermediate points to the linked list,\n // whose triangle area is nonzero.\n lft = 0;\n for (i = 1; i < len - 1; i++) {\n vol = Math.abs(\n JXG.Math.Numerics.det([\n pts[i - 1].usrCoords,\n pts[i].usrCoords,\n pts[i + 1].usrCoords\n ])\n );\n if (!isNaN(vol)) {\n obj = {\n v: vol,\n idx: i\n };\n heap.push(obj);\n linkedList[i] = {\n used: true,\n lft: lft,\n node: obj\n };\n linkedList[lft].rt = i;\n lft = i;\n }\n }\n\n // Add last point to the linked list\n linkedList[len - 1] = {\n used: true,\n rt: null,\n lft: lft,\n node: null\n };\n linkedList[lft].rt = len - 1;\n\n // Remove points until only numPoints intermediate points remain\n lastVol = -Infinity;\n while (heap.length > numPoints) {\n // Sort the heap with the updated volume values\n heap.sort(function (a, b) {\n // descending sort\n return b.v - a.v;\n });\n\n // Remove the point with the smallest triangle\n i = heap.pop().idx;\n linkedList[i].used = false;\n lastVol = linkedList[i].node.v;\n\n // Update the pointers of the linked list\n lft = linkedList[i].lft;\n rt = linkedList[i].rt;\n linkedList[lft].rt = rt;\n linkedList[rt].lft = lft;\n\n // Update the values for the volumes in the linked list\n lft2 = linkedList[lft].lft;\n if (lft2 !== null) {\n vol = Math.abs(\n JXG.Math.Numerics.det([\n pts[lft2].usrCoords,\n pts[lft].usrCoords,\n pts[rt].usrCoords\n ])\n );\n\n linkedList[lft].node.v = vol >= lastVol ? vol : lastVol;\n }\n rt2 = linkedList[rt].rt;\n if (rt2 !== null) {\n vol = Math.abs(\n JXG.Math.Numerics.det([\n pts[lft].usrCoords,\n pts[rt].usrCoords,\n pts[rt2].usrCoords\n ])\n );\n\n linkedList[rt].node.v = vol >= lastVol ? vol : lastVol;\n }\n }\n\n // Return an array with the remaining points\n i = 0;\n points = [pts[i]];\n do {\n i = linkedList[i].rt;\n points.push(pts[i]);\n } while (linkedList[i].rt !== null);\n\n return points;\n }\n};\n\nexport default Mat.Numerics;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n * JXG.Math.Statistics.TheilSenRegression(a.map(el => el.coords));\n *
\n *\n * @param {Array} coords Array of {@link JXG.Coords}.\n * @returns {Array} A stdform array of the regression line.\n * @memberof JXG.Math.Statistics\n *\n * @example\n * var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-6,6,6,-6], axis : true });\n * var a=[];\n * a[0]=board.create('point', [0,0]);\n * a[1]=board.create('point', [3,0]);\n * a[2]=board.create('point', [0,3]);\n *\n * board.create('line', [\n * () => JXG.Math.Statistics.TheilSenRegression(a.map(el => el.coords))\n * ],\n * {strokeWidth:1, strokeColor:'black'});\n *\n * \n *\n */\n TheilSenRegression: function (coords) {\n var i,\n j,\n slopes = [],\n tmpslopes = [],\n yintercepts = [];\n\n for (i = 0; i < coords.length; i++) {\n tmpslopes.length = 0;\n\n for (j = 0; j < coords.length; j++) {\n if (Math.abs(coords[j].usrCoords[1] - coords[i].usrCoords[1]) > Mat.eps) {\n tmpslopes[j] =\n (coords[j].usrCoords[2] - coords[i].usrCoords[2]) /\n (coords[j].usrCoords[1] - coords[i].usrCoords[1]);\n }\n }\n\n slopes[i] = this.median(tmpslopes);\n yintercepts.push(coords[i].usrCoords[2] - slopes[i] * coords[i].usrCoords[1]);\n }\n\n return [this.median(yintercepts), this.median(slopes), -1];\n },\n\n /**\n * Generate values of a standard normal random variable with the Marsaglia polar method, see\n * https://en.wikipedia.org/wiki/Marsaglia_polar_method.\n * See also D. E. Knuth, The art of computer programming, vol 2, p. 117.\n *\n * @param {Number} mean mean value of the normal distribution\n * @param {Number} stdDev standard deviation of the normal distribution\n * @returns {Number} value of a standard normal random variable\n * @memberof JXG.Math.Statistics\n */\n generateGaussian: function (mean, stdDev) {\n var u, v, s;\n\n if (this.hasSpare) {\n this.hasSpare = false;\n return this.spare * stdDev + mean;\n }\n\n do {\n u = Math.random() * 2 - 1;\n v = Math.random() * 2 - 1;\n s = u * u + v * v;\n } while (s >= 1 || s === 0);\n\n s = Math.sqrt((-2.0 * Math.log(s)) / s);\n\n this.spare = v * s;\n this.hasSpare = true;\n return mean + stdDev * u * s;\n },\n\n /**\n * Generate value of a standard normal random variable with given mean and standard deviation.\n * Alias for {@link JXG.Math.Statistics#generateGaussian}\n *\n * @param {Number} mean\n * @param {Number} stdDev\n * @returns Number\n * @memberof JXG.Math.Statistics\n * @see JXG.Math.Statistics.generateGaussian\n * @example\n * let board = JXG.JSXGraph.initBoard('JXGbox',\n * { boundingbox: [-5, 1.5, 5, -.03], axis: true});\n *\n * let runs = [\n * [0, 0.2, 'blue'],\n * [0, 1.0, 'red'],\n * [0, 5.0, 'orange'],\n * [-2,0.5, 'green'],\n * ]\n *\n * let labelY = 1.2\n * runs.forEach((run,i) => {\n * board.create('segment',[[1.0,labelY-(i/20)],[2.0,labelY-(i/20)]],{strokeColor:run[2]})\n * board.create('text',[2.5,labelY-(i/20),`μ=${run[0]}, σ2=${run[1]}`])\n *\n * let x = Array(50000).fill(0).map(() => JXG.Math.Statistics.randomNormal(run[0],Math.sqrt(run[1]))) // sqrt so Std Dev, not Variance\n * let res = JXG.Math.Statistics.histogram(x, { bins: 40, density: true, cumulative: false, range: false });\n * board.create('curve', [res[1], res[0]], { strokeColor: run[2], strokeWidth:2});\n * })\n *\n * \n * \n\n */\n randomNormal: function (mean, stdDev) {\n return this.generateGaussian(mean, stdDev);\n },\n\n /**\n * Generate value of a uniform distributed random variable in the interval [a, b].\n * @param {Number} a\n * @param {Number} b\n * @returns Number\n * @memberof JXG.Math.Statistics\n */\n randomUniform: function (a, b) {\n return Math.random() * (b - a) + a;\n },\n\n /**\n * Generate value of a random variable with exponential distribution, i.e.\n * f(x; lambda) = lambda * e^(-lambda x) if x >= 0 and f(x; lambda) = 0 if x < 0.\n * See https://en.wikipedia.org/wiki/Exponential_distribution.\n * Algorithm: D.E. Knuth, TAOCP 2, p. 128.\n *\n * @param {Number} lambda > 0\n * @returns Number\n * @memberof JXG.Math.Statistics\n * @example\n * let board = JXG.JSXGraph.initBoard('JXGbox',\n * { boundingbox: [-.5, 1.5, 5, -.1], axis: true});\n *\n * let runs = [\n * [0.5, 'red'],\n * [1.0, 'green'],\n * [1.5, 'blue'],\n * ]\n *\n * let labelY = 1\n * runs.forEach((run,i) => {\n * board.create('segment',[[1.8,labelY-(i/20)],[2.3,labelY-(i/20)]],{strokeColor:run[1]})\n * board.create('text',[2.5,labelY-(i/20),`λ=${run[0]}`])\n *\n * let x = Array(50000).fill(0).map(() => JXG.Math.Statistics.randomExponential(run[0]))\n * let res = JXG.Math.Statistics.histogram(x, { bins: 40, density: true, cumulative: false, range: false });\n * board.create('curve', [res[1], res[0]], { strokeColor: run[1], strokeWidth:2});\n * })\n *\n * \n * \n\n */\n randomExponential: function (lbda) {\n var u;\n\n // Knuth, TAOCP 2, p 128\n // See https://en.wikipedia.org/wiki/Exponential_distribution\n if (lbda <= 0) {\n return NaN;\n }\n\n do {\n u = Math.random();\n } while (u === 0);\n\n return -Math.log(u) / lbda;\n },\n\n /**\n * Generate value of a random variable with gamma distribution of order alpha.\n * See https://en.wikipedia.org/wiki/Gamma_distribution.\n * Algorithm: D.E. Knuth, TAOCP 2, p. 129.\n\n * @param {Number} a shape, > 0\n * @param {Number} [b=1] scale, > 0\n * @param {Number} [t=0] threshold\n * @returns Number\n * @memberof JXG.Math.Statistics\n * @example\n * let board = JXG.JSXGraph.initBoard('jxgbox',\n * { boundingbox: [-1.7, .5, 20, -.03], axis: true});\n *\n * let runs = [\n * [0.5, 1.0, 'brown'],\n * [1.0, 2.0, 'red'],\n * [2.0, 2.0, 'orange'],\n * [3.0, 2.0, 'yellow'],\n * [5.0, 1.0, 'green'],\n * [9.0, 0.5, 'black'],\n * [7.5, 1.0, 'purple'],\n * ]\n *\n * let labelY = .4\n * runs.forEach((run,i) => {\n * board.create('segment',[[7,labelY-(i/50)],[9,labelY-(i/50)]],{strokeColor:run[2]})\n * board.create('text',[10,labelY-(i/50),`k=${run[0]}, θ=${run[1]}`])\n *\n * // density\n * let x = Array(50000).fill(0).map(() => JXG.Math.Statistics.randomGamma(run[0],run[1]))\n * let res = JXG.Math.Statistics.histogram(x, { bins: 50, density: true, cumulative: false, range: [0, 20] });\n * board.create('curve', [res[1], res[0]], { strokeColor: run[2]});\n *\n * })\n *\n *\n * \n * \n * \n *\n */\n randomGamma: function (a, b, t) {\n var u, v, x, y,\n p, q;\n\n if (a <= 0) {\n return NaN;\n }\n\n b = b || 1;\n t = t || 0;\n\n if (a === 1) {\n return b * this.randomExponential(1) + t;\n }\n\n if (a < 1) {\n // Method by Ahrens\n // Knuth, TAOCP 2, Ex. 16, p 551\n p = Math.E / (a + Math.E);\n\n do {\n u = Math.random();\n do {\n v = Math.random();\n } while (v === 0);\n if (u < p) {\n x = Math.pow(v, 1 / a);\n q = Math.exp(-x);\n } else {\n x = 1 - Math.log(v);\n q = Math.pow(x, a - 1);\n }\n u = Math.random();\n } while (u >= q);\n return b * x + t;\n }\n\n // a > 1\n // Knuth, TAOCP 2, p 129\n do {\n y = Math.tan(Math.PI * Math.random());\n x = Math.sqrt(2 * a - 1) * y + a - 1;\n if (x > 0) {\n v = Math.random();\n } else {\n continue;\n }\n } while (x <= 0.0 || v > (1 + y * y) * Math.exp((a - 1) * Math.log(x / (a - 1)) - Math.sqrt(2 * a - 1) * y));\n\n return b * x + t;\n },\n\n /**\n * Generate value of a random variable with beta distribution with shape parameters alpha and beta.\n * See https://en.wikipedia.org/wiki/Beta_distribution.\n *\n * @param {Number} alpha > 0\n * @param {Number} beta > 0\n * @returns Number\n * @memberof JXG.Math.Statistics\n */\n randomBeta: function (a, b) {\n // Knuth, TAOCP 2, p 129\n var x1, x2, x;\n\n if (a <= 0 || b <= 0) {\n return NaN;\n }\n\n x1 = this.randomGamma(a);\n x2 = this.randomGamma(b);\n x = x1 / (x1 + x2);\n return x;\n },\n\n /**\n * Generate value of a random variable with chi-square distribution with k degrees of freedom.\n * See https://en.wikipedia.org/wiki/Chi-squared_distribution.\n *\n * @param {Number} k > 0\n * @returns Number\n * @memberof JXG.Math.Statistics\n */\n randomChisquare: function (nu) {\n // Knuth, TAOCP 2, p 130\n\n if (nu <= 0) {\n return NaN;\n }\n\n return 2 * this.randomGamma(nu * 0.5);\n },\n\n /**\n * Generate value of a random variable with F-distribution with d1 and d2 degrees of freedom.\n * See https://en.wikipedia.org/wiki/F-distribution.\n * @param {Number} d1 > 0\n * @param {Number} d2 > 0\n * @returns Number\n * @memberof JXG.Math.Statistics\n */\n randomF: function (nu1, nu2) {\n // Knuth, TAOCP 2, p 130\n var y1, y2;\n\n if (nu1 <= 0 || nu2 <= 0) {\n return NaN;\n }\n\n y1 = this.randomChisquare(nu1);\n y2 = this.randomChisquare(nu2);\n\n return (y1 * nu2) / (y2 * nu1);\n },\n\n /**\n * Generate value of a random variable with Students-t-distribution with ν degrees of freedom.\n * See https://en.wikipedia.org/wiki/Student%27s_t-distribution.\n * @param {Number} nu > 0\n * @returns Number\n * @memberof JXG.Math.Statistics\n */\n randomT: function (nu) {\n // Knuth, TAOCP 2, p 130\n var y1, y2;\n\n if (nu <= 0) {\n return NaN;\n }\n\n y1 = this.randomNormal(0, 1);\n y2 = this.randomChisquare(nu);\n\n return y1 / Math.sqrt(y2 / nu);\n },\n\n /**\n * Generate values for a random variable in binomial distribution with parameters n and p.\n * See https://en.wikipedia.org/wiki/Binomial_distribution.\n * It uses algorithm BG from https://dl.acm.org/doi/pdf/10.1145/42372.42381.\n *\n * @param {Number} n Number of trials (n >= 0)\n * @param {Number} p Probability (0 <= p <= 1)\n * @returns Number Integer value of a random variable in binomial distribution\n * @memberof JXG.Math.Statistics\n *\n * @example\n * let board = JXG.JSXGraph.initBoard('jxgbox',\n * { boundingbox: [-1.7, .5, 30, -.03], axis: true });\n *\n * let runs = [\n * [0.5, 20, 'blue'],\n * [0.7, 20, 'green'],\n * [0.5, 40, 'red'],\n * ];\n *\n * let labelY = .4;\n * runs.forEach((run, i) => {\n * board.create('segment', [[7, labelY - (i / 50)], [9, labelY - (i / 50)]], { strokeColor: run[2] });\n * board.create('text', [10, labelY - (i / 50), `p=${run[0]}, n=${run[1]}`]);\n *\n * let x = Array(50000).fill(0).map(() => JXG.Math.Statistics.randomBinomial(run[1], run[0]));\n * let res = JXG.Math.Statistics.histogram(x, {\n * bins: 40,\n * density: true,\n * cumulative: false,\n * range: [0, 40]\n * });\n * board.create('curve', [res[1], res[0]], { strokeColor: run[2] });\n * });\n *\n *\n * \n * \n *\n */\n randomBinomial: function (n, p) {\n var x, y, c,\n a, b, N1;\n\n if (p < 0 || p > 1 || n < 0) {\n return NaN;\n }\n\n // Edge cases\n if (p === 0) {\n return 0;\n }\n if (p === 1) {\n return n;\n }\n\n // Now, we can assume 0 < p < 1.\n\n // Fast path for common cases\n if (n === 0) {\n return 0;\n }\n if (n === 1) {\n return ((Math.random() < p) ? 1 : 0);\n }\n\n // Exploit symmetry\n if (p > 0.5) {\n return n - this.randomBinomial(n, 1 - p);\n }\n\n // General case: n > 1, p <= 0.5\n if (n < 100) {\n // n small:\n // Algorithm BG (Devroye) from:\n // https://dl.acm.org/doi/pdf/10.1145/42372.42381\n // Time O(np) so suitable for np small only.\n x = -1;\n y = 0;\n\n c = Math.log(1 - p);\n if (c === 0) {\n return 0;\n }\n\n do {\n x += 1;\n y += Math.floor(Math.log(Math.random()) / c) + 1;\n } while (y < n);\n } else {\n // n large:\n // Knuth, TAOCP 2, p 131\n a = 1 + Math.floor(n * 0.5);\n b = n - a + 1;\n x = this.randomBeta(a, b);\n if (x >= p) {\n N1 = this.randomBinomial(a - 1, p / x);\n x = N1;\n } else {\n N1 = this.randomBinomial(b - 1, (p - x) / (1 - x));\n x = a + N1;\n }\n }\n return x;\n },\n\n /**\n * Generate values for a random variable in geometric distribution with probability p.\n * See https://en.wikipedia.org/wiki/Geometric_distribution.\n *\n * @param {Number} p (0 <= p <= 1)\n * @returns Number\n * @memberof JXG.Math.Statistics\n */\n randomGeometric: function (p) {\n var u;\n\n if (p < 0 || p > 1) {\n return NaN;\n }\n // Knuth, TAOCP 2, p 131\n u = Math.random();\n\n return Math.ceil(Math.log(u) / Math.log(1 - p));\n },\n\n /**\n * Generate values for a random variable in Poisson distribution with mean mu.\n * See https://en.wikipedia.org/wiki/Poisson_distribution.\n *\n * @param {Number} mu (0 < mu)\n * @returns Number\n * @memberof JXG.Math.Statistics\n */\n randomPoisson: function (mu) {\n var e = Math.exp(-mu),\n N,\n m = 0,\n u = 1,\n x,\n alpha = 7 / 8;\n\n if (mu <= 0) {\n return NaN;\n }\n\n // Knuth, TAOCP 2, p 132\n if (mu < 10) {\n do {\n u *= Math.random();\n m += 1;\n } while (u > e);\n N = m - 1;\n } else {\n m = Math.floor(alpha * mu);\n x = this.randomGamma(m);\n if (x < mu) {\n N = m + this.randomPoisson(mu - x);\n } else {\n N = this.randomBinomial(m - 1, mu / x);\n }\n }\n return N;\n },\n\n /**\n * Generate values for a random variable in Pareto distribution with\n * shape gamma and scale k.\n * See https://en.wikipedia.org/wiki/Pareto_distribution.\n * Method: use inverse transformation sampling.\n *\n * @param {Number} gamma shape (0 < gamma)\n * @param {Number} k scale (0 < k < x)\n * @returns Number\n * @memberof JXG.Math.Statistics\n */\n randomPareto: function (gamma, k) {\n var u = Math.random();\n\n if (gamma <= 0 || k <= 0) {\n return NaN;\n }\n return k * Math.pow(1 - u, -1 / gamma);\n },\n\n /**\n * Generate values for a random variable in hypergeometric distribution.\n * Samples are drawn from a hypergeometric distribution with specified parameters, good (ways to make a good selection),\n * bad (ways to make a bad selection), and samples (number of items sampled, which is less than or equal to good + bad).\n * \n * \n * {\n * bins: 10, // Number of bins\n * range: false, // false or array. The lower and upper range of the bins.\n * // If not provided, range is simply [min(x), max(x)].\n * // Values outside the range are ignored.\n * density: false, // If true, normalize the counts by dividing by sum(counts)\n * cumulative: false\n * }\n * \n * The function returns an array containing two arrays. The first array is of length bins+1\n * containing the start values of the bins. The last entry contains the end values of the last bin.\n * \n *\n */\n histogram: function (x, opt) {\n var i, le, k,\n mi, ma, num_bins, delta,\n range,\n s,\n counts = [],\n bins = [],\n no_bin = 0; // Count of long tail elements not in histogram range\n\n // Evaluate number of bins\n num_bins = opt.bins || 10;\n\n // Evaluate range\n range = opt.range || false;\n if (range === false) {\n mi = Math.min.apply(null, x);\n ma = Math.max.apply(null, x);\n } else {\n mi = range[0];\n ma = range[1];\n }\n\n // Set uniform delta\n if (num_bins > 0) {\n delta = (ma - mi) / (num_bins - 1);\n } else {\n delta = 0;\n }\n\n // Set the bins and init the counts array\n for (i = 0; i < num_bins; i++) {\n counts.push(0);\n bins.push(mi + i * delta);\n }\n // bins.push(ma);\n\n // Determine the counts\n le = x.length;\n for (i = 0; i < le; i++) {\n k = Math.floor((x[i] - mi) / delta);\n if (k >= 0 && k < num_bins) {\n counts[k] += 1;\n } else {\n no_bin += 1;\n }\n }\n\n // Normalize if density===true\n if (opt.density) {\n s = JXG.Math.Statistics.sum(counts) + no_bin; // Normalize including long tail\n for (i = 0; i < num_bins; i++) {\n counts[i] /= (s * delta);\n // counts[i] /= s;\n }\n }\n\n // Cumulative counts\n if (opt.cumulative) {\n if (opt.density) {\n for (i = 0; i < num_bins; i++) {\n counts[i] *= delta; // Normalize\n }\n } for (i = 1; i < num_bins; i++) {\n counts[i] += counts[i - 1];\n }\n }\n\n return [counts, bins];\n }\n};\n\nexport default Mat.Statistics;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n *\n * @name JXG.Board#browserPan\n * @see JXG.Board#pan\n * @type Boolean\n * @default false\n *\n * @example\n * const board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-5, 5, 5, -5], axis: true,\n * pan: {\n * enabled: true,\n * needTwoFingers: true,\n * },\n * browserPan: true,\n * zoom: {\n * enabled: false\n * }\n * });\n *\n * var p1 = board.create('point', [1, -1]);\n * var p2 = board.create('point', [2.5, -2]);\n * var li1 = board.create('line', [p1, p2]);\n *\n * \n * \n *\n *\n */\n browserPan: false,\n\n /**\n *\n * Maximum time delay (in msec) between two clicks to be considered\n * as double click. This attribute is used together with {@link JXG.Board#dblClickSuppressClick}.\n * The JavaScript standard is that\n * a click event is preceded by two click events,\n * see {@link https://developer.mozilla.org/en-US/docs/Web/API/Element/dblclick_event}.\n * In case of {@link JXG.Board#dblClickSuppressClick} being true, the JavaScript standard is ignored and\n * this time delay is used to suppress the two click events if they are followed by a double click event.\n * \n * \n *\n * @example\n * // Display ticks labels as fractions\n * var board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-1.2, 2.3, 1.2, -2.3],\n * axis: true,\n * defaultAxes: {\n * x: {\n * ticks: {\n * label: {\n * useMathJax: true,\n * display: 'html',\n * toFraction: true\n * }\n * }\n * },\n * y: {\n * ticks: {\n * label: {\n * useMathJax: true,\n * display: 'html',\n * toFraction: true\n * }\n * }\n * }\n * }\n * });\n *\n * \n * \n * \n *\n */\n defaultAxes: {\n x: {\n name: 'x',\n fixed: true,\n needsRegularUpdate: false,\n ticks: {\n label: {\n visible: 'inherit',\n anchorX: 'middle',\n anchorY: 'top',\n fontSize: 12,\n offset: [0, -3]\n },\n tickEndings: [0, 1],\n majorTickEndings: [1, 1],\n drawZero: false,\n visible: 'inherit'\n }\n },\n y: {\n name: 'y',\n fixed: true,\n needsRegularUpdate: false,\n ticks: {\n label: {\n visible: 'inherit',\n anchorX: 'right',\n anchorY: 'middle',\n fontSize: 12,\n offset: [-6, 0]\n },\n tickEndings: [1, 0],\n majorTickEndings: [1, 1],\n drawZero: false,\n visible: 'inherit'\n }\n }\n },\n\n /**\n * Supply the document object. Defaults to window.document\n *\n * @name JXG.Board#document\n * @type Object\n * @description DOM object\n * @default false (meaning window.document)\n */\n document: false,\n\n /**\n * Control the possibilities for dragging objects.\n *\n * Possible sub-attributes with default values are:\n * \n * drag: {\n * enabled: true // Allow dragging\n * }\n * \n *\n * @name JXG.Board#drag\n * @type Object\n * @default {enabled: true}\n */\n drag: {\n enabled: true\n },\n\n /**\n * Attribute(s) to control the fullscreen icon. The attribute \"showFullscreen\"\n * controls if the icon is shown.\n * The following attribute(s) can be set:\n * \n *
\n *\n * @example\n * var board = JXG.JSXGraph.initBoard('35bec5a2-fd4d-11e8-ab14-901b0e1b8723',\n * {boundingbox: [-8, 8, 8,-8], axis: true,\n * showcopyright: false,\n * showFullscreen: true,\n * fullscreen: {\n * symbol: '\\u22c7',\n * scale: 0.95\n * }\n * });\n * var pol = board.create('polygon', [[0, 1], [3,4], [1,-4]], {fillColor: 'yellow'});\n *\n * \n * \n *\n * @name JXG.Board#fullscreen\n * @default svg code\n * @see JXG.Board#showFullscreen\n * @see JXG.AbstractRenderer#drawNavigationBar\n * @type Object\n */\n fullscreen: {\n symbol: '',\n // symbol: '\\u26f6', // '\\u26f6' (not supported by MacOS),\n scale: 0.85,\n id: null\n },\n\n /**\n * If set true and\n * hasPoint() is true for both an element and it's label,\n * the element (and not the label) is taken as drag element.\n * \n *
\n * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Intl/NumberFormat\n * for an overview on the possibilities and the options.\n * \n *\n * @example\n * // Here, locale is disabled in general, but enabled for the horizontal\n * // axis and the infobox.\n * const board = JXG.JSXGraph.initBoard(BOARDID, {\n * boundingbox: [-0.5, 0.5, 0.5, -0.5],\n * intl: {\n * enabled: false,\n * locale: 'de-DE'\n * },\n * keepaspectratio: true,\n * axis: true,\n * defaultAxes: {\n * x: {\n * ticks: {\n * intl: {\n * enabled: true,\n * options: {\n * style: 'unit',\n * unit: 'kilometer-per-hour',\n * unitDisplay: 'narrow'\n * }\n * }\n * }\n * },\n * y: {\n * ticks: {\n * }\n * }\n * },\n * infobox: {\n * fontSize: 12,\n * intl: {\n * enabled: true,\n * options: {\n * minimumFractionDigits: 4,\n * maximumFractionDigits: 5\n * }\n * }\n * }\n * });\n *\n * var p = board.create('point', [0.1, 0.1], {});\n *\n * \n * \n *\n */\n intl: {\n enabled: false\n },\n\n /**\n * Attributes for the div containing the JSXGraph board - in case\n * the board has been constructed by `JXG.initAppBox`\n * @type {Object}\n * @name JXG.Board#jxgbox\n * @default {\n * id: 'jxgbox',\n * outerbox: null,\n * cssStyle: 'width: 500px; aspect-ratio: 1/1; overflow: visible',\n * cssClass: 'jxgbox'\n * }\n */\n jxgbox: {\n id: 'jxgbox',\n outerbox: null,\n cssStyle: 'width: 500px; aspect-ratio: 1/1; overflow: visible',\n cssClass: 'jxgbox'\n },\n\n /**\n * If set to true, the ratio between horizontal and vertical unit sizes\n * stays constant - independent of size changes of the hosting HTML div element.\n * \n *
\n *\n * @example\n * var board = JXG.JSXGraph.initBoard(\"jxgbox\", {boundingbox: [-5,5,5,-5],\n * axis: true,\n * showCopyright:true,\n * showNavigation:true,\n * keyboard: {\n * enabled: true,\n * dy: 30,\n * panShift: true,\n * panCtrl: false\n * }\n * });\n *\n * \n * \n *\n *\n * @see JXG.Board#keyDownListener\n * @see JXG.Board#keyFocusInListener\n * @see JXG.Board#keyFocusOutListener\n *\n * @name JXG.Board#keyboard\n * @type Object\n * @default {enabled: true, dx: 10, dy:10, panShift: true, panCtrl: false}\n */\n keyboard: {\n enabled: true,\n dx: 10,\n dy: 10,\n panShift: true,\n panCtrl: false\n },\n\n /**\n * If enabled, user activities are logged in array \"board.userLog\".\n *\n * @name JXG.Board#logging\n * @type Object\n * @default {enabled: false}\n *\n * @example\n * var board = JXG.JSXGraph.initBoard(BOARDID,\n * {\n * boundingbox: [-8, 8, 8,-8],\n * axis: true,\n * logging: {enabled: true},\n * showcopyright: false,\n * shownavigation: false\n * });\n * var A = board.create('point', [-4, 0], { name: 'A' });\n * var B = board.create('point', [1, 2], { name: 'B' });\n * var showUserLog = function() {\n * var txt = '';\n *\n * for (let i = 0; i < board.userLog.length; i++) {\n * txt += JSON.stringify(board.userLog[i]) + '\\n';\n * }\n * alert(txt);\n * };\n * var but = board.create('button', [4, 4, 'Show user log', showUserLog]);\n *\n * \n * \n *\n *\n * @see JXG.Board#userLog\n */\n logging: {\n enabled: false\n },\n\n /**\n * Change redraw strategy in SVG rendering engine.\n * \n * \n *\n */\n maxBoundingBox: [-Infinity, Infinity, Infinity, -Infinity],\n\n /**\n * Maximum frame rate of the board, i.e. maximum number of updates per second\n * triggered by move events.\n *\n * @name JXG.Board#maxFrameRate\n * @type Number\n * @default 40\n */\n maxFrameRate: 40,\n\n /**\n * Maximum number of digits in automatic label generation.\n * For example, if set to 1 automatic point labels end at \"Z\".\n * If set to 2, point labels end at \"ZZ\".\n *\n * @name JXG.Board#maxNameLength\n * @see JXG.Board#generateName\n * @type Number\n * @default 1\n */\n maxNameLength: 1,\n\n /**\n * Element which listens to move events of the pointing device.\n * This allows to drag elements of a JSXGraph construction outside of the board.\n * Especially, on mobile devices this enhances the user experience.\n * However, it is recommended to allow dragging outside of the JSXGraph board only\n * in certain constructions where users may not \"loose\" points outside of the board.\n * In such a case, points may become unreachable.\n *
\n *
\n * \n *
\n * \n *\n *\n */\n moveTarget: null,\n\n /**\n * A number that will be added to the absolute position of the board used in mouse coordinate\n * calculations in {@link JXG.Board#getCoordsTopLeftCorner}.\n *\n * @name JXG.Board#offsetX\n * @see JXG.Board#offsetY\n * @type Number\n * @default 0\n */\n offsetX: 0,\n\n /**\n * A number that will be added to the absolute position of the board used in mouse coordinate\n * calculations in {@link JXG.Board#getCoordsTopLeftCorner}.\n *\n * @name JXG.Board#offsetY\n * @see JXG.Board#offsetX\n * @type Number\n * @default 0\n */\n offsetY: 0,\n\n /**\n * Control the possibilities for panning interaction (i.e. moving the origin).\n *\n * Possible sub-attributes with default values are:\n * \n * \n * pan: {\n * enabled: true // Allow panning\n * needTwoFingers: false, // panning is done with two fingers on touch devices\n * needShift: true, // mouse panning needs pressing of the shift key\n * }\n * \n *\n * @name JXG.Board#pan\n * @see JXG.Board#browserPan\n *\n * @type Object\n */\n pan: {\n enabled: true,\n needShift: true,\n needTwoFingers: false\n },\n\n /**\n * Allow user interaction by registering pointer events (including mouse and\n * touch events), fullscreen, keyboard, resize, and zoom events.\n * The latter events are essentially mouse wheel events.\n * Decide if JSXGraph listens to these events.\n * \n * {\n * fullscreen: true / false,\n * keyboard: true / false,\n * pointer: true / false,\n * resize: true / false,\n * wheel: true / false\n * }\n * \n * activates individual event handlers. If an event is NOT given,\n * it will be activated.\n * \n *\n *\n */\n resize: {\n enabled: true,\n throttle: 10\n },\n\n /**\n * Attributes to control the screenshot function.\n * The following attributes can be set:\n * \n *
\n * The screenshot will fail if the board contains text elements or foreign objects\n * containing SVG again.\n *\n * @name JXG.Board#screenshot\n * @type Object\n */\n screenshot: {\n scale: 1,\n type: 'png',\n symbol: '\\u2318', //'\\u22b9', //'\\u26f6',\n css: 'background-color:#eeeeee; opacity:1.0; border:2px solid black; border-radius:10px; text-align:center',\n cssButton: 'padding: 4px 10px; border: solid #356AA0 1px; border-radius: 5px; position: absolute; right: 2ex; top: 2ex; background-color: rgba(255, 255, 255, 0.3);'\n },\n\n /**\n * Control the possibilities for a selection rectangle.\n * Starting a selection event triggers the \"startselecting\" event.\n * When the mouse pointer is released, the \"stopselecting\" event is fired.\n * The \"stopselecting\" event is supplied by the user.\n * \n * selection: {\n * enabled: false,\n * name: 'selectionPolygon',\n * needShift: false, // mouse selection needs pressing of the shift key\n * needCtrl: true, // mouse selection needs pressing of the shift key\n * fillColor: '#ffff00'\n * }\n * \n * {\n * enabled: false,\n * 0: {visible: true},\n * 1: {visible: true}\n * }\n *\n * @see SketchCurve\n */\n sketches: {\n enabled: false,\n 0: {visible: true},\n 1: {visible: true}\n },\n\n /**\n * Show a button which allows to clear all traces of a board.\n * This button can be accessed by JavaScript or CSS with\n * the ID \"{board_id}_navigation_button_cleartraces\" or by the CSS classes\n * JXG_navigation_button\" or\n * JXG_navigation_button_cleartraces\".\n *\n * @name JXG.Board#showClearTraces\n * @type Boolean\n * @default false\n * @see JXG.AbstractRenderer#drawNavigationBar\n */\n showClearTraces: false,\n\n /**\n * Show copyright string and logo in the top left corner of the board.\n *\n * @name JXG.Board#showCopyright\n * @see JXG.Board#showLogo\n * @type Boolean\n * @default true\n */\n showCopyright: true,\n\n /**\n * Show a button in the navigation bar to start fullscreen mode.\n * This button can be accessed by JavaScript or CSS with\n * the ID \"{board_id}_navigation_button_fullscreen\" or by the CSS classes\n * JXG_navigation_button\" or\n * JXG_navigation_button_fullscreen\".\n *\n * @name JXG.Board#showFullscreen\n * @type Boolean\n * @see JXG.Board#fullscreen\n * @default false\n * @see JXG.AbstractRenderer#drawNavigationBar\n * @see JXG.AbstractRenderer#drawNavigationBar\n */\n showFullscreen: false,\n\n /**\n * If true, the infobox is shown on mouse/pen over for all points\n * which have set their attribute showInfobox to 'inherit'.\n * If a point has set its attribute showInfobox to false or true,\n * that value will have priority over this value.\n *\n * @name JXG.Board#showInfobox\n * @see Point#showInfobox\n * @type Boolean\n * @default true\n */\n showInfobox: true,\n\n /**\n * The JSXGraph logo in the top left corner of the board is shown as soon as\n * {@link JXG.Board#showCopyright} is true.\n * \n *
\n *\n * @name JXG.Board#theme\n * @type String\n * @default 'default'\n * @example\n * const board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-5, 5, 5, -5], axis: true,\n * theme: 'mono_thin'\n * });\n *\n * var a = board.create('slider', [[1, 4], [3, 4], [-10, 1, 10]]);\n * var p1 = board.create('point', [1, 2]);\n * var ci1 = board.create('circle', [p1, 0.7]);\n * var cu = board.create('functiongraph', ['x^2']);\n * var l1 = board.create('line', [2, 3, -1]);\n * var l2 = board.create('line', [-5, -3, -1], { dash: 2 });\n * var i1 = board.create('intersection', [l1, l2]);\n * var pol = board.create('polygon', [[1, 0], [4, 0], [3.5, 1]]);\n * var an = board.create('angle', [pol.vertices[1], pol.vertices[0], pol.vertices[2]]);\n * var se = board.create('sector', [pol.vertices[1], pol.vertices[2], pol.vertices[0]]);\n * var ci1 = board.create('circle', [[-3, -3], 0.7], { center: { visible: true } });\n *\n * \n * \n *\n */\n theme: 'default',\n\n /**\n * Title string for the board.\n * Primarily used in an invisible text element for assistive technologies.\n * The title is implemented with the attribute 'aria-label' in the JSXGraph container.\n *\n * Content should be accessible to all users, not just to those with\n * screen readers. Consider instead adding a text element with the title and add the attribute\n * aria:{enable:true,label:\"Your Title\"}\n *\n * @name JXG.Board#title\n * @type String\n * @default ''\n *\n */\n title: '',\n\n /**\n * Control the possibilities for zoom interaction.\n *\n * Possible sub-attributes with default values are:\n * \n * zoom: {\n * enabled: true, // turns off zooming completely, if set to false.\n * factorX: 1.25, // horizontal zoom factor (multiplied to {@link JXG.Board#zoomX})\n * factorY: 1.25, // vertical zoom factor (multiplied to {@link JXG.Board#zoomY})\n * wheel: true, // allow zooming by mouse wheel\n * needShift: true, // mouse wheel zooming needs pressing of the shift key\n * min: 0.001, // minimal values of {@link JXG.Board#zoomX} and {@link JXG.Board#zoomY}, limits zoomOut\n * max: 1000.0, // maximal values of {@link JXG.Board#zoomX} and {@link JXG.Board#zoomY}, limits zoomIn\n * center: 'auto', // 'auto': the center of zoom is at the position of the mouse or at the midpoint of two fingers\n * // 'board': the center of zoom is at the board's center\n * pinch: true, // pinch-to-zoom gesture for proportional zoom\n * pinchHorizontal: true, // Horizontal pinch-to-zoom zooms horizontal axis. Only available if keepaspectratio:false\n * pinchVertical: true, // Vertical pinch-to-zoom zooms vertical axis only. Only available if keepaspectratio:false\n * pinchSensitivity: 7 // Sensitivity (in degrees) for recognizing horizontal or vertical pinch-to-zoom gestures.\n * }\n * \n *\n * If the zoom buttons are visible, zooming by clicking the buttons is still possible, regardless of zoom.enabled:true/false.\n * If this should be prevented, set showZoom:false.\n *\n * Deprecated: zoom.eps which is superseded by zoom.min\n *\n * @name JXG.Board#zoom\n * @type Object\n * @default See above\n * @see JXG.Board#showZoom\n *\n */\n zoom: {\n enabled: true,\n factorX: 1.25,\n factorY: 1.25,\n wheel: true,\n needShift: true,\n center: 'auto',\n min: 0.0001,\n max: 10000.0,\n pinch: true,\n pinchHorizontal: true,\n pinchVertical: true,\n pinchSensitivity: 7\n },\n\n // /**\n // * Additional zoom factor multiplied to {@link JXG.Board#zoomX} and {@link JXG.Board#zoomY}.\n // *\n // * @name JXG.Board#zoomFactor\n // * @type Number\n // * @default 1.0\n // */\n // zoomFactor: 1,\n\n /**\n * Zoom factor in horizontal direction.\n *\n * @name JXG.Board#zoomX\n * @see JXG.Board#zoomY\n * @type Number\n * @default 1.0\n */\n zoomX: 1,\n\n /**\n * Zoom factor in vertical direction.\n *\n * @name JXG.Board#zoomY\n * @see JXG.Board#zoomX\n * @type Number\n * @default 1.0\n */\n zoomY: 1\n\n /**#@-*/\n },\n\n /**\n * Options that are used by the navigation bar.\n *\n * Default values are\n * \n * JXG.Option.navbar: {\n * strokeColor: '#333333',\n * fillColor: 'transparent',\n * highlightFillColor: '#aaaaaa',\n * padding: '2px',\n * position: 'absolute',\n * fontSize: '14px',\n * cursor: 'pointer',\n * zIndex: '100',\n * right: '5px',\n * bottom: '5px'\n * },\n * \n * These settings are overruled by the CSS class 'JXG_navigation'.\n * @deprecated\n * @type Object\n * @name JXG.Options#navbar\n *\n */\n navbar: {\n strokeColor: '#333333', //'#aaaaaa',\n fillColor: 'transparent', //#f5f5f5',\n highlightFillColor: '#aaaaaa',\n padding: '2px',\n position: 'absolute',\n fontSize: '14px',\n cursor: 'pointer',\n zIndex: '100',\n right: '5px',\n bottom: '5px'\n //border: 'none 1px black',\n //borderRadius: '4px'\n },\n\n /*\n * Generic options used by {@link JXG.GeometryElement}\n */\n elements: {\n /**#@+\n * @visprop\n */\n // This is a meta tag: http://code.google.com/p/jsdoc-toolkit/wiki/MetaTags\n\n /**\n * ARIA settings for JSXGraph elements.\n * Besides 'label' and 'live', all available properties from\n * https://developer.mozilla.org/en-US/docs/Web/Accessibility/ARIA may be set.\n * In JSXGraph, the available properties are used without the leading 'aria-'.\n * For example, the value of the JSXGraph attribute 'aria.label' will be set to the\n * HTML attribute 'aria-label' (ignoring 'aria.enabled').\n *\n * @name aria\n * @memberOf JXG.GeometryElement.prototype\n * @type Object\n * @default {\n * enabled: false,\n * label: '',\n * live: 'assertive'\n * }\n */\n aria: {\n enabled: false,\n label: '',\n live: 'assertive' // 'assertive', 'polite', 'none'\n },\n\n /**\n * If set to false, the JSXGraph element can be dragged out of the JSXGraph board. Used in {@link JXG#appBox}.\n *\n * @name clip\n * @memberOf JXG.GeometryElement.prototype\n * @type Boolean\n * @default true\n *\n * @see JXG#appBox\n */\n clip: true,\n\n /**\n * Apply CSS classes to an element in non-highlighted view. It is possible to supply one or more\n * CSS classes separated by blanks.\n *
\n * The dash patterns are defined in {@link JXG.AbstractRenderer#dashArray}.\n *\n * @type Number\n * @name JXG.GeometryElement#dash\n * @default 0\n *\n * @see JXG.GeometryElement#lineCap\n * @see JXG.AbstractRenderer#dashArray\n */\n dash: 0,\n\n /**\n * If true, the dash pattern is multiplied by strokeWidth / 2.\n * @name JXG.GeometryElement#dashScale\n * @type Boolean\n * @default false\n *\n * @see JXG.GeometryElement#dash\n * @see JXG.AbstractRenderer#dashArray\n */\n dashScale: false,\n\n /**\n * If draft.draft: true the element will be drawn in grey scale colors (as default)\n * to visualize that it's only a draft.\n *\n * @name JXG.GeometryElement#draft\n * @type Object\n * @default {@link JXG.Options.elements.draft#draft}\n */\n draft: {\n draft: false,\n strokeColor: '#565656',\n fillColor: '#565656',\n strokeOpacity: 0.8,\n fillOpacity: 0.8,\n strokeWidth: 1\n },\n\n /**\n * If the element is dragged it will be moved on mousedown or touchstart to the\n * top of its layer. Works only for SVG renderer and for simple elements\n * consisting of one SVG node.\n * @example\n * var li1 = board.create('line', [1, 1, 1], {strokeWidth: 20, dragToTopOfLayer: true});\n * var li2 = board.create('line', [1, -1, 1], {strokeWidth: 20, strokeColor: 'red'});\n *\n * \n * \n *\n * @type Boolean\n * @default false\n * @name JXG.GeometryElement#dragToTopOfLayer\n */\n dragToTopOfLayer: false,\n\n /**\n * Links to the defining 3D element of a 2D element. Otherwise it is null.\n *\n * @name JXG.GeometryElement#element3D\n * @default null\n * @private\n */\n element3D: null,\n\n /**\n * The fill color of this geometry element.\n * @type String\n * @name JXG.GeometryElement#fillColor\n * @see JXG.GeometryElement#highlightFillColor\n * @see JXG.GeometryElement#fillOpacity\n * @see JXG.GeometryElement#highlightFillOpacity\n * @default JXG.palette.red\n */\n fillColor: 'black', //Color.palette.red,\n\n /**\n * Opacity for fill color.\n * @type Number\n * @name JXG.GeometryElement#fillOpacity\n * @see JXG.GeometryElement#fillColor\n * @see JXG.GeometryElement#highlightFillColor\n * @see JXG.GeometryElement#highlightFillOpacity\n * @default 1\n */\n fillOpacity: 1,\n\n /**\n * If true the element is fixed and can not be dragged around. The element\n * will be repositioned on zoom and moveOrigin events.\n * @type Boolean\n * @default false\n * @name JXG.GeometryElement#fixed\n */\n fixed: false,\n\n /**\n * If true the element is fixed and can not be dragged around. The element\n * will even stay at its position on zoom and moveOrigin events.\n * Only free elements like points, texts, images, curves can be frozen.\n *\n * @type Boolean\n * @default false\n * @name JXG.GeometryElement#frozen\n *\n * @example\n * var txt = board.create('text', [1, 2, 'Hello'], {frozen: true, fontSize: 24});\n * var sli = board.create('slider', [[-4, 4], [-1.5, 4], [-10, 1, 10]], {\n * name:'a',\n * frozen: true\n * });\n *\n * \n * \n *\n */\n frozen: false,\n\n /**\n * Gradient type. Possible values are 'linear'. 'radial' or null.\n *\n * @example\n * var a = board.create('slider', [[0, -0.2], [3.5, -0.2], [0, 0, 2 * Math.PI]], {name: 'angle'});\n * var b = board.create('slider', [[0, -0.4], [3.5, -0.4], [0, 0, 1]], {name: 'offset1'});\n * var c = board.create('slider', [[0, -0.6], [3.5, -0.6], [0, 1, 1]], {name: 'offset2'});\n *\n * var pol = board.create('polygon', [[0, 0], [4, 0], [4,4], [0,4]], {\n * fillOpacity: 1,\n * fillColor: 'yellow',\n * gradient: 'linear',\n * gradientSecondColor: 'blue',\n * gradientAngle: function() { return a.Value(); },\n * gradientStartOffset: function() { return b.Value(); },\n * gradientEndOffset: function() { return c.Value(); },\n * hasInnerPoints: true\n * });\n *\n * \n * \n *\n * @example\n * var cx = board.create('slider', [[0, -.2], [3.5, -.2], [0, 0.5, 1]], {name: 'cx, cy'});\n * var fx = board.create('slider', [[0, -.4], [3.5, -.4], [0, 0.5, 1]], {name: 'fx, fy'});\n * var o1 = board.create('slider', [[0, -.6], [3.5, -.6], [0, 0.0, 1]], {name: 'offset1'});\n * var o2 = board.create('slider', [[0, -.8], [3.5, -.8], [0, 1, 1]], {name: 'offset2'});\n * var r = board.create('slider', [[0, -1], [3.5, -1], [0, 0.5, 1]], {name: 'r'});\n * var fr = board.create('slider', [[0, -1.2], [3.5, -1.2], [0, 0, 1]], {name: 'fr'});\n *\n * var pol = board.create('polygon', [[0, 0], [4, 0], [4,4], [0,4]], {\n * fillOpacity: 1,\n * fillColor: 'yellow',\n * gradient: 'radial',\n * gradientSecondColor: 'blue',\n * gradientCX: function() { return cx.Value(); },\n * gradientCY: function() { return cx.Value(); },\n * gradientR: function() { return r.Value(); },\n * gradientFX: function() { return fx.Value(); },\n * gradientFY: function() { return fx.Value(); },\n * gradientFR: function() { return fr.Value(); },\n * gradientStartOffset: function() { return o1.Value(); },\n * gradientEndOffset: function() { return o2.Value(); },\n * hasInnerPoints: true\n * });\n *\n * \n * \n *\n *\n * @type String\n * @name JXG.GeometryElement#gradient\n * @see JXG.GeometryElement#gradientSecondColor\n * @see JXG.GeometryElement#gradientSecondOpacity\n * @default null\n */\n gradient: null,\n\n /**\n * Angle (in radians) of the gradiant in case the gradient is of type 'linear'.\n * If the angle is 0, the first color is on the left and the second color is on the right.\n * If the angle is π/2 the first color is on top and the second color at the\n * bottom.\n * @type Number\n * @name JXG.GeometryElement#gradientAngle\n * @see JXG.GeometryElement#gradient\n * @default 0\n */\n gradientAngle: 0,\n\n /**\n * From the SVG specification: ‘cx’, ‘cy’ and ‘r’ define the largest (i.e., outermost) circle for the radial gradient.\n * The gradient will be drawn such that the 100% gradient stop is mapped to the perimeter of this largest (i.e., outermost) circle.\n * For radial gradients in canvas this is the value 'x1'.\n * Takes a value between 0 and 1.\n * @type Number\n * @name JXG.GeometryElement#gradientCX\n * @see JXG.GeometryElement#gradient\n * @see JXG.GeometryElement#gradientCY\n * @see JXG.GeometryElement#gradientR\n * @default 0.5\n */\n gradientCX: 0.5,\n\n /**\n * From the SVG specification: ‘cx’, ‘cy’ and ‘r’ define the largest (i.e., outermost) circle for the radial gradient.\n * The gradient will be drawn such that the 100% gradient stop is mapped to the perimeter of this largest (i.e., outermost) circle.\n * For radial gradients in canvas this is the value 'y1'.\n * Takes a value between 0 and 1.\n * @type Number\n * @name JXG.GeometryElement#gradientCY\n * @see JXG.GeometryElement#gradient\n * @see JXG.GeometryElement#gradientCX\n * @see JXG.GeometryElement#gradientR\n * @default 0.5\n */\n gradientCY: 0.5,\n\n /**\n * The gradientEndOffset attribute is a number (ranging from 0 to 1) which indicates where the second gradient stop is placed,\n * see the SVG specification for more information.\n * For linear gradients, this attribute represents a location along the gradient vector.\n * For radial gradients, it represents a percentage distance from (fx,fy) to the edge of the outermost/largest circle.\n * @type Number\n * @name JXG.GeometryElement#gradientEndOffset\n * @see JXG.GeometryElement#gradient\n * @see JXG.GeometryElement#gradientStartOffset\n * @default 1.0\n */\n gradientEndOffset: 1.0,\n\n /**\n * ‘fx’ and ‘fy’ define the focal point for the radial gradient.\n * The gradient will be drawn such that the 0% gradient stop is mapped to (fx, fy).\n * For radial gradients in canvas this is the value 'x0'.\n * Takes a value between 0 and 1.\n * @type Number\n * @name JXG.GeometryElement#gradientFX\n * @see JXG.GeometryElement#gradient\n * @see JXG.GeometryElement#gradientFY\n * @see JXG.GeometryElement#gradientFR\n * @default 0.5\n */\n gradientFX: 0.5,\n\n /**\n * y-coordinate of the circle center for the second color in case of gradient 'radial'. (The attribute fy in SVG)\n * For radial gradients in canvas this is the value 'y0'.\n * Takes a value between 0 and 1.\n * @type Number\n * @name JXG.GeometryElement#gradientFY\n * @see JXG.GeometryElement#gradient\n * @see JXG.GeometryElement#gradientFX\n * @see JXG.GeometryElement#gradientFR\n * @default 0.5\n */\n gradientFY: 0.5,\n\n /**\n * This attribute defines the radius of the start circle of the radial gradient.\n * The gradient will be drawn such that the 0% <stop> is mapped to the perimeter of the start circle.\n * For radial gradients in canvas this is the value 'r0'.\n * Takes a value between 0 and 1.\n * @type Number\n * @name JXG.GeometryElement#gradientFR\n * @see JXG.GeometryElement#gradient\n * @see JXG.GeometryElement#gradientFX\n * @see JXG.GeometryElement#gradientFY\n * @default 0.0\n */\n gradientFR: 0.0,\n\n /**\n * From the SVG specification: ‘cx’, ‘cy’ and ‘r’ define the largest (i.e., outermost) circle for the radial gradient.\n * The gradient will be drawn such that the 100% gradient stop is mapped to the perimeter of this largest (i.e., outermost) circle.\n * For radial gradients in canvas this is the value 'r1'.\n * Takes a value between 0 and 1.\n * @type Number\n * @name JXG.GeometryElement#gradientR\n * @see JXG.GeometryElement#gradient\n * @see JXG.GeometryElement#gradientCX\n * @see JXG.GeometryElement#gradientCY\n * @default 0.5\n */\n gradientR: 0.5,\n\n /**\n * Second color for gradient.\n * @type String\n * @name JXG.GeometryElement#gradientSecondColor\n * @see JXG.GeometryElement#gradient\n * @see JXG.GeometryElement#gradientSecondOpacity\n * @default '#ffffff'\n */\n gradientSecondColor: '#ffffff',\n\n /**\n * Opacity of second gradient color. Takes a value between 0 and 1.\n * @type Number\n * @name JXG.GeometryElement#gradientSecondOpacity\n * @see JXG.GeometryElement#gradient\n * @see JXG.GeometryElement#gradientSecondColor\n * @default 1\n */\n gradientSecondOpacity: 1,\n\n /**\n * The gradientStartOffset attribute is a number (ranging from 0 to 1) which indicates where the first gradient stop is placed,\n * see the SVG specification for more information.\n * For linear gradients, this attribute represents a location along the gradient vector.\n * For radial gradients, it represents a percentage distance from (fx,fy) to the edge of the outermost/largest circle.\n * @type Number\n * @name JXG.GeometryElement#gradientStartOffset\n * @see JXG.GeometryElement#gradient\n * @see JXG.GeometryElement#gradientEndOffset\n * @default 0.0\n */\n gradientStartOffset: 0.0,\n\n /**\n * @type Boolean\n * @default true\n * @name JXG.GeometryElement#highlight\n */\n highlight: true,\n\n /**\n * The fill color of the given geometry element when the mouse is pointed over it.\n * @type String\n * @name JXG.GeometryElement#highlightFillColor\n * @see JXG.GeometryElement#fillColor\n * @see JXG.GeometryElement#fillOpacity\n * @see JXG.GeometryElement#highlightFillOpacity\n * @default 'none'\n */\n highlightFillColor: 'none',\n\n /**\n * Opacity for fill color when the object is highlighted.\n * @type Number\n * @name JXG.GeometryElement#highlightFillOpacity\n * @see JXG.GeometryElement#fillColor\n * @see JXG.GeometryElement#highlightFillColor\n * @see JXG.GeometryElement#fillOpacity\n * @default 1\n */\n highlightFillOpacity: 1,\n\n /**\n * The stroke color of the given geometry element when the user moves the mouse over it.\n * @type String\n * @name JXG.GeometryElement#highlightStrokeColor\n * @see JXG.GeometryElement#strokeColor\n * @see JXG.GeometryElement#strokeWidth\n * @see JXG.GeometryElement#strokeOpacity\n * @see JXG.GeometryElement#highlightStrokeOpacity\n * @default '#c3d9ff'\n */\n highlightStrokeColor: '#c3d9ff',\n\n /**\n * Opacity for stroke color when the object is highlighted.\n * @type Number\n * @name JXG.GeometryElement#highlightStrokeOpacity\n * @see JXG.GeometryElement#strokeColor\n * @see JXG.GeometryElement#highlightStrokeColor\n * @see JXG.GeometryElement#strokeWidth\n * @see JXG.GeometryElement#strokeOpacity\n * @default 1\n */\n highlightStrokeOpacity: 1,\n\n /**\n * Width of the element's stroke when the mouse is pointed over it.\n * @type Number\n * @name JXG.GeometryElement#highlightStrokeWidth\n * @see JXG.GeometryElement#strokeColor\n * @see JXG.GeometryElement#highlightStrokeColor\n * @see JXG.GeometryElement#strokeOpacity\n * @see JXG.GeometryElement#highlightStrokeOpacity\n * @see JXG.GeometryElement#highlightFillColor\n * @default 2\n */\n highlightStrokeWidth: 2,\n\n /**\n * @name JXG.GeometryElement#isLabel\n * @default false\n * @private\n */\n // By default, an element is not a label. Do not change this.\n isLabel: false,\n\n /**\n * Display layer which will contain the element.\n * @name JXG.GeometryElement#layer\n * @see JXG.Options#layer\n * @default See {@link JXG.Options#layer}\n */\n layer: 0,\n\n /**\n * Line endings (linecap) of a stroke element, i.e. line, circle, curve.\n * Possible values are:\n * \n *
\n * Not available for VML renderer.\n *\n * @name JXG.GeometryElement#lineCap\n * @type String\n * @default 'butt'\n */\n lineCap: 'butt',\n\n /**\n * If this is set to true, the element is updated in every update\n * call of the board. If set to false, the element is updated only after\n * zoom events or more generally, when the bounding box has been changed.\n * Examples for the latter behavior should be axes.\n * @type Boolean\n * @default true\n * @see JXG.GeometryElement#needsRegularUpdate\n * @name JXG.GeometryElement#needsRegularUpdate\n */\n needsRegularUpdate: true,\n\n /**\n * If some size of an element is controlled by a function, like the circle radius\n * or segments of fixed length, this attribute controls what happens if the value\n * is negative. By default, the absolute value is taken. If true, the maximum\n * of 0 and the value is used.\n *\n * @type Boolean\n * @default false\n * @name JXG.GeometryElement#nonnegativeOnly\n * @example\n * var slider = board.create('slider', [[4, -3], [4, 3], [-4, 1, 4]], { name: 'a'});\n * var circle = board.create('circle', [[-1, 0], 1], {\n * nonnegativeOnly: true\n * });\n * circle.setRadius('a'); // Use JessieCode\n * var seg = board.create('segment', [[-4, 3], [0, 3], () => slider.Value()], {\n * point1: {visible: true},\n * point2: {visible: true},\n * nonnegativeOnly: true\n * });\n *\n * \n * \n *\n */\n nonnegativeOnly: false,\n\n /**\n * Precision options for JSXGraph elements.\n * This attributes takes either the value 'inherit' or an object of the form:\n *
\n * \n * precision: {\n * touch: 30,\n * mouse: 4,\n * pen: 4\n * }\n * \n *\n * In the first case, the global, JSXGraph-wide values of JXGraph.Options.precision\n * are taken.\n *\n * @type {String|Object}\n * @name JXG.GeometryElement#precision\n * @see JXG.Options#precision\n * @default 'inherit'\n */\n precision: 'inherit',\n\n /**\n * A private element will be inaccessible in certain environments, e.g. a graphical user interface.\n *\n * @name JXG.GeometryElement#priv\n * @type Boolean\n * @default false\n */\n priv: false,\n\n /**\n * Determines whether two-finger manipulation may rotate this object.\n * If set to false, the object can only be scaled and translated.\n * \n *\n */\n shadow: {\n enabled: false,\n color: [0, 0, 0],\n opacity: 1,\n blur: 3,\n blend: 0.1,\n offset: [5, 5]\n },\n\n /**\n * Snaps the element or its parents to the grid. Currently only relevant for points, circles,\n * and lines. Points are snapped to grid directly, on circles and lines it's only the parent\n * points that are snapped\n * @type Boolean\n * @default false\n * @name JXG.GeometryElement#snapToGrid\n */\n snapToGrid: false,\n\n /**\n * The stroke color of the given geometry element.\n * @type String\n * @name JXG.GeometryElement#strokeColor\n * @see JXG.GeometryElement#highlightStrokeColor\n * @see JXG.GeometryElement#strokeWidth\n * @see JXG.GeometryElement#strokeOpacity\n * @see JXG.GeometryElement#highlightStrokeOpacity\n * @default JXG.palette.blue\n */\n strokeColor: Color.palette.blue,\n\n /**\n * Opacity for element's stroke color.\n * @type Number\n * @name JXG.GeometryElement#strokeOpacity\n * @see JXG.GeometryElement#strokeColor\n * @see JXG.GeometryElement#highlightStrokeColor\n * @see JXG.GeometryElement#strokeWidth\n * @see JXG.GeometryElement#highlightStrokeOpacity\n * @default 1\n */\n strokeOpacity: 1,\n\n /**\n * Width of the element's stroke.\n * @type Number\n * @name JXG.GeometryElement#strokeWidth\n * @see JXG.GeometryElement#strokeColor\n * @see JXG.GeometryElement#highlightStrokeColor\n * @see JXG.GeometryElement#strokeOpacity\n * @see JXG.GeometryElement#highlightStrokeOpacity\n * @default 2\n */\n strokeWidth: 2,\n\n /**\n * Controls if an element can get the focus with the tab key.\n * tabindex corresponds to the HTML attribute of the same name.\n * See description at MDN.\n * The additional value \"null\" completely disables focus of an element.\n * The value will be ignored if keyboard control of the board is not enabled or\n * if the element is not visible.\n *\n * @name JXG.GeometryElement#tabindex\n * @type Number\n * @default -1\n * @see JXG.Board#keyboard\n * @see JXG.GeometryElement#fixed\n * @see JXG.GeometryElement#visible\n */\n tabindex: -1,\n\n /**\n * If true the element will be traced, i.e. on every movement the element will be copied\n * to the background. Use {@link JXG.GeometryElement#clearTrace} to delete the trace elements.\n *\n * The calling of element.setAttribute({trace:false}) additionally\n * deletes all traces of this element. By calling\n * element.setAttribute({trace:'pause'})\n * the removal of already existing traces can be prevented.\n *\n * The visual appearance of the trace can be influenced by {@link JXG.GeometryElement#traceAttributes}.\n *\n * @see JXG.GeometryElement#clearTrace\n * @see JXG.GeometryElement#traces\n * @see JXG.GeometryElement#numTraces\n * @see JXG.GeometryElement#traceAttributes\n * @type Boolean|String\n * @default false\n * @name JXG.GeometryElement#trace\n */\n trace: false,\n\n /**\n * Extra visual properties for traces of an element\n * @type Object\n * @see JXG.GeometryElement#trace\n * @name JXG.GeometryElement#traceAttributes\n * @default {}\n *\n * @example\n * JXG.Options.elements.traceAttributes = {\n * size: 2\n * };\n *\n * const board = JXG.JSXGraph.initBoard(BOARDID, {\n * boundingbox: [-4, 4, 4, -4],\n * keepaspectratio: true\n * });\n *\n * var p = board.create('point', [0.0, 2.0], {\n * trace: true,\n * size: 10,\n * traceAttributes: {\n * color: 'black',\n * face: 'x'\n * }\n * });\n *\n * \n * \n *\n */\n traceAttributes: {},\n\n /**\n * Transition duration (in milliseconds) for certain changes of properties like color and opacity.\n * The properties can be set in the attribute transitionProperties\n * Works in SVG renderer, only.\n * @type Number\n * @name JXG.GeometryElement#transitionDuration\n * @see JXG.GeometryElement#transitionProperties\n * @see JXG.GeometryElement#strokeColor\n * @see JXG.GeometryElement#highlightStrokeColor\n * @see JXG.GeometryElement#strokeOpacity\n * @see JXG.GeometryElement#highlightStrokeOpacity\n * @see JXG.GeometryElement#fillColor\n * @see JXG.GeometryElement#highlightFillColor\n * @see JXG.GeometryElement#fillOpacity\n * @see JXG.GeometryElement#highlightFillOpacity\n * @default 100 {@link JXG.Options.elements#transitionDuration}\n */\n transitionDuration: 100,\n\n /**\n * Properties which change smoothly in the time set in transitionDuration.\n * Possible values are\n * ['fill', 'fill-opacity', 'stroke', 'stroke-opacity', 'stroke-width', 'width', 'height', 'rx', 'ry']\n * (and maybe more) for geometry elements and\n * ['color', 'opacity', 'all'] for HTML texts.\n *\n * @type Array\n * @name JXG.GeometryElement#transitionProperties\n * @see JXG.GeometryElement#transitionDuration\n *\n *\n * @example\n * var p1 = board.create(\"point\", [0, 2], {\n * name: \"A\",\n * highlightStrokeWidth: 10,\n * transitionDuration: 1000,\n * transitionProperties: ['width', 'height', 'stroke-width',\n * 'fill', 'fill-opacity', 'rx', 'ry', 'stroke', 'stroke-opacity'] });\n *\n * \n * \n *\n */\n transitionProperties: ['fill', 'fill-opacity', 'stroke', 'stroke-opacity', 'stroke-width'], // org\n // transitionProperties for points.\n //transitionProperties: ['fill', 'fill-opacity', 'stroke', 'stroke-opacity', 'stroke-width', 'width', 'height', 'rx', 'ry'],\n\n /**\n * If false the element won't be visible on the board, otherwise it is shown.\n * @type Boolean\n * @name JXG.GeometryElement#visible\n * @see JXG.GeometryElement#hideElement\n * @see JXG.GeometryElement#showElement\n * @default true\n */\n visible: true,\n\n /**\n * If true a label will display the element's name.\n * Using this to suppress labels is more efficient than visible:false.\n *\n * @name JXG.GeometryElement#withLabel\n * @type Boolean\n * @default false\n */\n withLabel: false,\n\n /**\n * Decides if the element should be ignored when using auto positioning\n * for some label.\n * @name JXG.GeometryElement#ignoreForLabelAutoposition\n * @type boolean\n * @default false\n * @see Label#autoPosition\n */\n ignoreForLabelAutoposition: false\n\n // close the meta tag\n /**#@-*/\n },\n\n /*\n * Generic options used by {@link JXG.Ticks}\n */\n ticks: {\n /**#@+\n * @visprop\n */\n\n /**\n * A function that expects two {@link JXG.Coords}, the first one representing the coordinates of the\n * tick that is to be labeled, the second one the coordinates of the center (the tick with position 0).\n * The third parameter is a null, number or a string. In the latter two cases, this value is taken.\n * Returns a string.\n *\n * @type function\n * @name Ticks#generateLabelText\n *\n * @example\n * const board = JXG.JSXGraph.initBoard('jxgbox', { boundingBox: [-10, 10, 10, -10], axis: true,\n * defaultAxes: {\n * x: {\n * margin: -4,\n * ticks: {\n * minTicksDistance: 0,\n * minorTicks:4,\n * ticksDistance: 3,\n * scale: Math.PI,\n * scaleSymbol: 'π',\n * insertTicks: true\n * }\n * },\n * y: {}\n * }\n * });\n *\n * // Generate a logarithmic labelling of the vertical axis by defining the function generateLabelText directly.\n * board.defaultAxes.y.ticks[0].generateLabelText = function (tick, zero) {\n * var value = Math.pow(10, Math.round(tick.usrCoords[2] - zero.usrCoords[2]));\n * return this.formatLabelText(value);\n * };\n *\n * \n * \n * @example\n * // Generate a logarithmic labelling of the vertical axis by setting the attribute generateLabelText.\n * const board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingBox: [-10, 10, 10, -10], axis: true,\n * defaultAxes: {\n * x: {\n * margin: -4,\n * ticks: {\n * minTicksDistance: 0,\n * minorTicks: 4,\n * ticksDistance: 3,\n * scale: Math.PI,\n * scaleSymbol: 'π',\n * insertTicks: true\n * }\n * },\n * y: {\n * ticks: {\n * // Generate a logarithmic labelling of the vertical axis.\n * generateLabelText: function (tick, zero) {\n * var value = Math.pow(10, Math.round(tick.usrCoords[2] - zero.usrCoords[2]));\n * return this.formatLabelText(value);\n * }\n * }\n * }\n * }\n * });\n *\n * \n * \n *\n *\n */\n generateLabelText: null,\n\n /**\n * A function that expects two {@link JXG.Coords}, the first one representing the coordinates of the\n * tick that is to be labeled, the second one the coordinates of the center (the tick with position 0).\n *\n * @deprecated Use {@link JGX.Options@generateLabelText}\n * @type function\n * @name Ticks#generateLabelValue\n */\n generateLabelValue: null,\n\n /**\n * Draw labels yes/no\n *\n * @type Boolean\n * @name Ticks#drawLabels\n * @default false\n */\n drawLabels: false,\n\n /**\n * Attributes for the ticks labels.\n *\n * @name Ticks#label\n * @type Object\n * @default \n * {\n * tabindex: null,\n * layer: 7, // line\n * highlight: false\n * }\n *\n */\n label: {\n tabindex: null,\n layer: 7, // line\n highlight: false,\n autoPosition: false\n },\n\n /**\n * Format tick labels that were going to have scientific notation\n * like 5.00e+6 to look like 5•10⁶.\n *\n * @example\n * var board = JXG.JSXGraph.initBoard(\"jxgbox\", {\n * boundingbox: [-500000, 500000, 500000, -500000],\n * axis: true,\n * defaultAxes: {\n * x: {\n * scalable: true,\n * ticks: {\n * beautifulScientificTickLabels: true\n * },\n * },\n * y: {\n * scalable: true,\n * ticks: {\n * beautifulScientificTickLabels: true\n * },\n * }\n * },\n * });\n *\n * \n *\n * @name Ticks#beautifulScientificTickLabels\n * @type Boolean\n * @default false\n */\n beautifulScientificTickLabels: false,\n\n /**\n * Use the unicode character 0x2212, i.e. the HTML entity − as minus sign.\n * That is −1 instead of -1.\n *\n * @type Boolean\n * @name Ticks#useUnicodeMinus\n * @default true\n */\n useUnicodeMinus: true,\n\n /**\n * Determine the position of the tick with value 0. 'left' means point1 of the line, 'right' means point2,\n * and 'middle' is equivalent to the midpoint of the defining points. This attribute is ignored if the parent\n * line is of type axis.\n *\n * @type String\n * @name Ticks#anchor\n * @default 'left'\n *\n * @example\n * var li = board.create('segment', [[-4, -3], [4, 2]]);\n * var t = board.create('ticks', [li], {\n * // drawZero: true,\n * anchor: 'left',\n * drawLabels: true,\n * minorTicks: 0,\n * label: {\n * anchorX: 'middle',\n * anchorY: 'top',\n * offset: [0, -5]\n * }\n * });\n *\n *\n * \n * \n *\n * @example\n * var li = board.create('segment', [[-4, -3], [4, 2]]);\n * var t = board.create('ticks', [li], {\n * drawZero: true,\n * anchor: 'middle',\n * drawLabels: true,\n * minorTicks: 0,\n * label: {\n * anchorX: 'middle',\n * anchorY: 'top',\n * offset: [0, -5]\n * }\n * });\n *\n * \n * \n *\n */\n anchor: 'left',\n\n /**\n * Draw the zero tick, that lies at line.point1?\n *\n * @type Boolean\n * @name Ticks#drawZero\n * @default false\n *\n * @example\n * var li = board.create('segment', [[-4, 2], [4, 2]]);\n * var t = board.create('ticks', [li], {\n * drawZero: false,\n * anchor: 'middle',\n * drawLabels: true,\n * minorTicks: 0,\n * label: {\n * anchorX: 'middle',\n * anchorY: 'top',\n * offset: [0, -5]\n * }\n * });\n *\n * var li2 = board.create('segment', [[-4, -2], [4, -2]]);\n * var t2 = board.create('ticks', [li2], {\n * drawZero: true,\n * anchor: 'middle',\n * drawLabels: true,\n * minorTicks: 0,\n * label: {\n * anchorX: 'middle',\n * anchorY: 'top',\n * offset: [0, -5]\n * }\n * });\n *\n * \n * \n *\n */\n drawZero: false,\n\n /**\n * Let JSXGraph determine the distance between ticks automatically.\n * If true, the attribute ticksDistance is ignored.\n * The distance between ticks is affected by the size of the board and\n * the attribute minTicksDistance (in pixel).\n *\n * @type Boolean\n * @name Ticks#insertTicks\n * @see Ticks#ticksDistance\n * @see Ticks#minTicksDistance\n * @default false\n * @example\n * // Create an axis providing two coord pairs.\n * var p1 = board.create('point', [0, 0]);\n * var p2 = board.create('point', [50, 25]);\n * var l1 = board.create('line', [p1, p2]);\n * var t = board.create('ticks', [l1], {\n * insertTicks: true,\n * majorHeight: -1,\n * label: {\n * offset: [4, -9]\n * },\n * drawLabels: true\n * });\n * \n * \n */\n insertTicks: false,\n\n /**\n * Minimum distance in pixel of equidistant ticks in case insertTicks==true.\n * @name Ticks#minTicksDistance\n * @type Number\n * @default 10\n * @see Ticks#insertTicks\n */\n minTicksDistance: 10,\n\n /**\n * Total height of a minor tick. If negative the full height of the board is taken.\n *\n * @type Number\n * @name Ticks#minorHeight\n * @default 4\n */\n minorHeight: 4,\n\n /**\n * Total height of a major tick. If negative the full height of the board is taken.\n *\n * @type Number\n * @name Ticks#majorHeight\n * @default 10\n */\n majorHeight: 10,\n\n /**\n * Decides in which direction minor ticks are visible. Possible values are either the constants\n * 0=false or 1=true or a function returning 0 or 1.\n *\n * In case of [0,1] the tick is only visible to the right of the line. In case of\n * [1,0] the tick is only visible to the left of the line.\n *\n * @type Array\n * @name Ticks#tickEndings\n * @see Ticks#majorTickEndings\n * @default [1, 1]\n */\n tickEndings: [1, 1],\n\n /**\n * Decides in which direction major ticks are visible. Possible values are either the constants\n * 0=false or 1=true or a function returning 0 or 1.\n *\n * In case of [0,1] the tick is only visible to the right of the line. In case of\n * [1,0] the tick is only visible to the left of the line.\n *\n * @example\n * var board = JXG.JSXGraph.initBoard(\"jxgbox\", {\n * boundingbox: [-5, 5, 5, -5],\n * axis: true,\n * defaultAxes: {\n * x: {\n * ticks: {\n * majorTickEndings: [1, 0],\n * ignoreInfiniteTickEndings: false\n * }\n * },\n * y: {\n * ticks: {\n * majorTickEndings: [0, 1],\n * ignoreInfiniteTickEndings: false\n * }\n * }\n * }\n * });\n *\n * var p = board.create('point', [1, 1]);\n * var l = board.create('line', [1, -1, 1]);\n *\n * \n * \n *\n * @type Array\n * @name Ticks#majorTickEndings\n * @see Ticks#tickEndings\n * @see Ticks#ignoreInfiniteTickEndings\n * @default [1, 1]\n */\n majorTickEndings: [1, 1],\n\n /**\n * If true, ignore the tick endings attribute for infinite (full height) ticks.\n * This affects major and minor ticks.\n *\n * @type Boolean\n * @name Ticks#ignoreInfiniteTickEndings\n * @see Ticks#tickEndings\n * @see Ticks#majorTickEndings\n * @default true\n */\n ignoreInfiniteTickEndings: true,\n\n /**\n * The number of minor ticks between two major ticks.\n * @type Number\n * @name Ticks#minorTicks\n * @default 4\n */\n minorTicks: 4,\n\n /**\n * By default, i.e. if ticksPerLabel==false, labels are generated for major ticks, only.\n * If ticksPerLabel is set to a(n integer) number, this denotes the number of minor ticks\n * between two labels.\n *\n * @type {Number|Boolean}\n * @name Ticks#ticksPerLabel\n * @default false\n *\n * @example\n * const board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-4, 4, 4, -4],\n * axis: true,\n * defaultAxes: {\n * x: {\n * ticks: {\n * minorTicks: 7,\n * ticksPerLabel: 4,\n * minorHeight: 20,\n * }\n * },\n * y: {\n * ticks: {\n * minorTicks: 3,\n * ticksPerLabel: 2,\n * minorHeight: 20\n * }\n * }\n * }\n * });\n *\n * \n * \n */\n ticksPerLabel: false,\n\n /**\n * Scale the ticks but not the tick labels.\n * @type Number\n * @default 1\n * @name Ticks#scale\n * @see Ticks#scaleSymbol\n *\n * @example\n * const board = JXG.JSXGraph.initBoard('jxgbox', { boundingBox: [-10, 10, 10, -10], axis: true,\n * defaultAxes: {\n * x : {\n * margin: -4,\n * ticks: {\n * minTicksDistance: 0,\n * minorTicks:4,\n * ticksDistance: 3,\n * scale: Math.PI,\n * scaleSymbol: 'π',\n * insertTicks: true\n * }\n * },\n * y : {}\n * }\n * });\n *\n * \n * \n */\n scale: 1,\n\n /**\n * A string that is appended to every tick, used to represent the scale\n * factor given in {@link Ticks#scale}.\n *\n * @type String\n * @default ''\n * @name Ticks#scaleSymbol\n * @see Ticks#scale\n */\n scaleSymbol: '',\n\n /**\n * User defined labels for special ticks. Instead of the i-th tick's position, the i-th string stored in this array\n * is shown. If the number of strings in this array is less than the number of special ticks, the tick's position is\n * shown as a fallback.\n *\n * @type Array\n * @name Ticks#labels\n * @default []\n */\n labels: [],\n\n /**\n * The maximum number of characters a tick label can use.\n *\n * @type Number\n * @name Ticks#maxLabelLength\n * @see Ticks#digits\n * @default 5\n */\n maxLabelLength: 5,\n\n /**\n * If a label exceeds {@link Ticks#maxLabelLength} this determines the precision used to shorten the tick label.\n * Deprecated! Replaced by the attribute digits.\n *\n * @type Number\n * @name Ticks#precision\n * @see Ticks#maxLabelLength\n * @see Ticks#digits\n * @deprecated\n * @default 3\n */\n precision: 3,\n\n /**\n * If a label exceeds {@link Ticks#maxLabelLength} this determines the number of digits used to shorten the tick label.\n *\n * @type Number\n * @name Ticks#digits\n * @see Ticks#maxLabelLength\n * @deprecated\n * @default 3\n */\n digits: 3,\n\n /**\n * The default distance (in user coordinates, not pixels) between two ticks. Please be aware that this value is overruled\n * if {@link Ticks#insertTicks} is set to true. In case, {@link Ticks#insertTicks} is false, the maximum number of ticks\n * is hard coded to be less than 2048.\n *\n * @type Number\n * @name Ticks#ticksDistance\n * @see Ticks#insertTicks\n * @default 1\n */\n ticksDistance: 1,\n\n /**\n * Tick face for major ticks of finite length. By default (face: '|') this is a straight line.\n * Possible other values are '<' and '>'. These faces are used in\n * {@link JXG.Hatch} for hatch marking parallel lines.\n * @type String\n * @name Ticks#face\n * @see hatch\n * @default '|'\n * @example\n * var p1 = board.create('point', [0, 3]);\n * var p2 = board.create('point', [1, 3]);\n * var l1 = board.create('line', [p1, p2]);\n * var t = board.create('ticks', [l1], {ticksDistance: 2, face: '>', minorTicks: 0});\n *\n * \n * \n *\n */\n face: '|',\n\n strokeOpacity: 1,\n strokeWidth: 1,\n strokeColor: '#000000',\n highlightStrokeColor: '#888888',\n fillColor: 'none',\n highlightFillColor: 'none',\n visible: 'inherit',\n\n /**\n * Whether line boundaries should be included or not in the lower and upper bounds when\n * creating ticks. In mathematical terms: if a segment considered as interval is open (includeBoundaries:false)\n * or closed (includeBoundaries:true). In case of open interval, the interval is shortened by a small\n * ε.\n *\n * @type Boolean\n * @name Ticks#includeBoundaries\n * @default false\n *\n * @example\n * var li = board.create('segment', [[-4, 2], [4, 2]]);\n * var t = board.create('ticks', [li], {\n * includeBoundaries: true,\n * drawZero: true,\n * anchor: 'middle',\n * drawLabels: true,\n * minorTicks: 0,\n * label: {\n * anchorX: 'middle',\n * anchorY: 'top',\n * offset: [0, -5]\n * }\n * });\n *\n * var li2 = board.create('segment', [[-4, -2], [4, -2]]);\n * var t2 = board.create('ticks', [li2], {\n * includeBoundaries: false,\n * drawZero: true,\n * anchor: 'middle',\n * drawLabels: true,\n * minorTicks: 0,\n * label: {\n * anchorX: 'middle',\n * anchorY: 'top',\n * offset: [0, -5]\n * }\n * });\n *\n * \n * \n *\n */\n includeBoundaries: false,\n\n /**\n * Set the ticks type.\n * Possible values are 'linear' or 'polar'.\n *\n * @type String\n * @name Ticks#type\n * @default 'linear'\n *\n * @example\n * var ax = board.create('axis', [[0,0], [1,0]], {\n * needsRegularUpdate: false,\n * ticks: {\n * type: 'linear',\n * majorHeight: 0\n * }\n * });\n * var ay = board.create('axis', [[0,0], [0,1]], {\n * ticks: {\n * type: 'polar'\n * }\n * });\n *\n * var p = board.create('point', [3, 2]);\n *\n * \n * \n *\n */\n type: 'linear',\n\n /**\n * Internationalization support for ticks labels.\n * @name intl\n * @memberOf Ticks.prototype\n * @default
\n * {\n * enabled: 'inherit',\n * options: {}\n * }\n * @see JXG.Board#intl\n * @see Text#intl\n *\n * @example\n * // Here, locale is disabled in general, but enabled for the horizontal\n * // axis and the infobox.\n * const board = JXG.JSXGraph.initBoard(BOARDID, {\n * boundingbox: [-0.5, 0.5, 0.5, -0.5],\n * intl: {\n * enabled: false,\n * locale: 'de-DE'\n * },\n * keepaspectratio: true,\n * axis: true,\n * defaultAxes: {\n * x: {\n * ticks: {\n * intl: {\n * enabled: true,\n * options: {\n * style: 'unit',\n * unit: 'kilometer-per-hour',\n * unitDisplay: 'narrow'\n * }\n * }\n * }\n * },\n * y: {\n * ticks: {\n * }\n * }\n * },\n * infobox: {\n * fontSize: 12,\n * intl: {\n * enabled: true,\n * options: {\n * minimumFractionDigits: 4,\n * maximumFractionDigits: 5\n * }\n * }\n * }\n * });\n *\n * var p = board.create('point', [0.1, 0.1], {});\n *\n * \n *\n */\n intl: {\n enabled: 'inherit',\n options: {}\n },\n\n // TODO implementation and documentation\n minorTicksInArrow: false,\n majorTicksInArrow: true,\n labelInArrow: true,\n minorTicksInMargin: false,\n majorTicksInMargin: true,\n labelInMargin: true,\n\n ignoreForLabelAutoposition: true\n\n // close the meta tag\n /**#@-*/\n },\n\n /*\n * Generic options used by {@link JXG.Hatch}\n */\n hatch: {\n drawLabels: false,\n drawZero: true,\n majorHeight: 20,\n anchor: 'middle',\n face: '|',\n strokeWidth: 2,\n strokeColor: Color.palette.blue,\n /**\n * The default distance (in user coordinates, not pixels) between two hatch symbols.\n *\n * @type Number\n * @name Hatch#ticksDistance\n * @default 0.2\n */\n ticksDistance: 0.2\n },\n\n /**\n * Precision options, defining how close a pointer device (mouse, finger, pen) has to be\n * to an object such that the object is highlighted or can be dragged.\n * These values are board-wide and can be overwritten for individual elements by\n * changing their precision attribute.\n *\n * The default values are\n * \n * \n * JXG.Options.precision: {\n * touch: 30,\n * touchMax: 100,\n * mouse: 4,\n * pen: 4,\n * epsilon: 0.0001,\n * hasPoint: 4\n * }\n * \n *\n * @type Object\n * @name JXG.Options#precision\n * @see JXG.GeometryElement#precision\n */\n precision: {\n touch: 30,\n touchMax: 100,\n mouse: 4,\n pen: 4,\n epsilon: 0.0001, // Unused\n hasPoint: 4\n },\n\n /**\n * Default ordering of the layers.\n * The numbering starts from 0 and the highest layer number is numlayers-1.\n *\n * The default values are\n * \n * JXG.Options.layer: {\n * numlayers: 20, // only important in SVG\n * text: 9,\n * point: 9,\n * glider: 9,\n * arc: 8,\n * line: 7,\n * circle: 6,\n * curve: 5,\n * turtle: 5,\n * polygon: 3,\n * sector: 3,\n * angle: 3,\n * integral: 3,\n * axis: 2,\n * ticks: 2,\n * grid: 1,\n * image: 0,\n * trace: 0\n * }\n * \n * @type Object\n * @name JXG.Options#layer\n */\n layer: {\n numlayers: 20, // only important in SVG\n unused9: 19,\n unused8: 18,\n unused7: 17,\n unused6: 16,\n unused5: 15,\n unused4: 14,\n unused3: 13,\n unused2: 12,\n unused1: 11,\n unused0: 10,\n text: 9,\n point: 9,\n glider: 9,\n arc: 8,\n line: 7,\n circle: 6,\n curve: 5,\n turtle: 5,\n polygon: 3,\n sector: 3,\n angle: 3,\n integral: 3,\n axis: 2,\n ticks: 2,\n grid: 1,\n image: 0,\n trace: 0\n },\n\n /* special angle options */\n angle: {\n /**#@+\n * @visprop\n */\n\n withLabel: true,\n\n /**\n * Radius of the sector, displaying the angle.\n * The radius can be given as number (in user coordinates)\n * or as string 'auto'. In the latter case, the angle\n * is set to an value between 20 and 50 px.\n *\n * @type {Number|String}\n * @name Angle#radius\n * @default 'auto'\n * @visprop\n */\n radius: 'auto',\n\n /**\n * Orientation of the angle: 'clockwise' or 'counterclockwise' (default).\n * \n *\n */\n orientation: 'counterclockwise',\n\n /**\n * Display type of the angle field. Possible values are\n * 'sector' or 'sectordot' or 'square' or 'none'.\n *\n * @type String\n * @default 'sector'\n * @name Angle#type\n * @visprop\n */\n type: 'sector',\n\n /**\n * Display type of the angle field in case of a right angle. Possible values are\n * 'sector' or 'sectordot' or 'square' or 'none'.\n *\n * @type String\n * @default square\n * @name Angle#orthoType\n * @see Angle#orthoSensitivity\n * @visprop\n */\n orthoType: 'square',\n\n /**\n * Sensitivity (in degrees) to declare an angle as right angle.\n * If the angle measure is inside this distance from a rigth angle, the orthoType\n * of the angle is used for display.\n *\n * @type Number\n * @default 1.0\n * @name Angle#orthoSensitivity\n * @see Angle#orthoType\n * @visprop\n */\n orthoSensitivity: 1.0,\n\n fillColor: Color.palette.orange,\n highlightFillColor: Color.palette.orange,\n strokeColor: Color.palette.orange,\n // fillColor: '#ff7f00',\n // highlightFillColor: '#ff7f00',\n // strokeColor: '#ff7f00',\n\n fillOpacity: 0.3,\n highlightFillOpacity: 0.3,\n\n /**\n * @name Angle#radiuspoint\n * @type Object\n * @deprecated\n */\n radiuspoint: {\n withLabel: false,\n visible: false,\n name: ''\n },\n\n /**\n * @name Angle#pointsquare\n * @type Object\n * @deprecated\n */\n pointsquare: {\n withLabel: false,\n visible: false,\n name: ''\n },\n\n /**\n * Attributes of the dot point marking right angles.\n * @name Angle#dot\n * @type Object\n * @default {face: 'o', size: 2}\n */\n dot: {\n visible: false,\n strokeColor: 'none',\n fillColor: '#000000',\n size: 2,\n face: 'o',\n withLabel: false,\n name: ''\n },\n\n label: {\n position: 'top',\n offset: [0, 0],\n strokeColor: Color.palette.blue\n },\n\n /**\n * Attributes for sub-element arc. In general, the arc will run through the first point and\n * thus will not have the same radius as the angle sector.\n *\n * @type Arc\n * @name Angle#arc\n * @default '{visible:false}'\n */\n arc: {\n visible: false,\n orientation: 'inherit',\n fillColor: 'none'\n }\n\n /**#@-*/\n },\n\n /* special arc options */\n arc: {\n /**#@+\n * @visprop\n */\n\n /**\n * Type of arc. Possible values are 'minor', 'major', and 'auto'.\n *\n * @type String\n * @name Arc#selection\n * @default 'auto'\n */\n selection: 'auto',\n\n /**\n * Orientation of the arc: 'clockwise' or 'counterclockwise' (default).\n * \n * \n *\n */\n orientation: 'counterclockwise',\n\n /**\n * If true, moving the mouse over inner points triggers hasPoint.\n *\n * @see JXG.GeometryElement#hasPoint\n * @name Arc#hasInnerPoints\n * @type Boolean\n * @default false\n */\n hasInnerPoints: false,\n\n label: {\n anchorX: 'auto',\n anchorY: 'auto'\n },\n firstArrow: false,\n lastArrow: false,\n fillColor: 'none',\n highlightFillColor: 'none',\n strokeColor: Color.palette.blue,\n highlightStrokeColor: '#c3d9ff',\n\n /**\n * If true, there is a fourth parent point, i.e. the parents are [center, p1, p2, p3].\n * p1 is still the radius point, p2 the angle point. The arc will be that part of the\n * the circle with center 'center' which starts at p1, ends at the ray between center\n * and p2, and passes p3.\n * \n *
\n *\n * @type {String}\n * @name Axis#position\n * @default 'static'\n * @see Axis#anchor\n * @see Axis#anchorDist\n *\n * @example // Use navigation to see effect.\n * var axis1, axis2, circle;\n *\n * board.create('axis', [[0,0],[1,0]],{\n * position: 'fixed',\n * anchor: 'right',\n * anchorDist: '0.1fr'\n * });\n *\n * board.create('axis', [[0,0],[0,1]], {\n * position: 'fixed',\n * anchor: 'left',\n * anchorDist: 1\n * });\n *\n * \n * \n *\n * @example // Use navigation to see effect.\n * board.create('axis', [[0,0],[1,0]],{\n * position: 'sticky',\n * anchor: 'right',\n * anchorDist: '0.2fr'\n * });\n *\n * board.create('axis', [[0,0],[0,1]], {\n * position: 'sticky',\n * anchor: 'right left',\n * anchorDist: '75px'\n * });\n *\n * \n * \n *\n */\n position: 'static',\n\n /**\n * Position is used in cases: position=='sticky' or position=='fixed'.\n * Possible values are 'right', 'left', 'right left'. Left and right indicate the side as seen from the axis.\n * It is used in combination with the attribute position to decide on which side of the board the axis should stick or be fixed.\n *\n * @type {String}\n * @name Axis#anchor\n * @default ''\n * @example\n * board.create('axis', [[0,0],[0,1]],{\n * position: 'fixed',\n * anchor: 'left',\n * anchorDist: 2,\n * strokeColor : 'green',\n * ticks: {\n * majorHeight: 7,\n * drawZero: true,\n * }\n * });\n *\n * board.create('axis', [[0,0],[0,1]], {\n * position: 'fixed',\n * anchor: 'right',\n * anchorDist: 2,\n * strokeColor : 'blue',\n * ticks: {\n * majorHeight: 7,\n * drawZero: true,\n * }\n * });\n *\n * board.create('axis', [[0,0],[0,-1]], {\n * position: 'fixed',\n * anchor: 'left',\n * anchorDist: 4,\n * strokeColor : 'red',\n * ticks:{\n * majorHeight: 7,\n * drawZero: true,\n * }\n * });\n *\n * \n * \n */\n anchor: '',\n\n /**\n * Used to define at which distance to the edge of the board the axis should stick or be fixed.\n * This only has an effect if position=='sticky' or position=='fixed'.\n * There are the following possibilities:\n *
\n *
\n *\n * @type {Number|String}\n * @name Axis#anchorDist\n * @default '10%'\n */\n anchorDist: '10%',\n\n /**\n * If set to true, the tick labels of the axis are automatically positioned in the narrower area between the axis and the side of the board.\n * Settings in this attribute only have an effect if the axis is exactly horizontal or vertical.\n * This option overrides offset, anchorX and anchorY of axis tick labels.\n *\n * @type {Boolean}\n * @name Axis#ticksAutoPos\n * @default false\n * @example\n * // Navigate to see an effect.\n * board.create('axis', [[0, 0], [1, 0]], {\n * position: 'sticky',\n * anchor: 'left right',\n * anchorDist: '0.1',\n * ticksAutoPos: true,\n * });\n *\n * board.create('axis', [[0, 0], [0, 1]], {\n * position: 'sticky',\n * anchor: 'left right',\n * anchorDist: '0.1',\n * ticksAutoPos: true,\n * });\n *\n * \n * \n */\n ticksAutoPos: false,\n\n /**\n * Defines, when ticksAutoPos takes effect.\n * There are the following possibilities:\n *
\n *
\n *\n * @type {Number|String}\n * @name Axis#ticksAutoPosThreshold\n * @default '5%'\n */\n ticksAutoPosThreshold: '5%',\n\n /**\n * Show / hide ticks.\n *\n * Deprecated. Suggested alternative is \"ticks: {visible: false}\"\n *\n * @type Boolean\n * @name Axis#withTicks\n * @default true\n * @deprecated\n */\n withTicks: true,\n straightFirst: true,\n straightLast: true,\n margin: -4,\n withLabel: false,\n scalable: false,\n\n /**\n * Attributes for ticks of the axis.\n *\n * @type Ticks\n * @name Axis#ticks\n */\n ticks: {\n label: {\n offset: [4, -12 + 3], // This seems to be a good offset for 12 point fonts\n parse: false,\n needsRegularUpdate: false,\n display: 'internal',\n visible: 'inherit',\n layer: 9\n },\n visible: 'inherit',\n needsRegularUpdate: false,\n strokeWidth: 1,\n strokeColor: '#666666',\n highlightStrokeColor: '#888888',\n drawLabels: true,\n drawZero: false,\n insertTicks: true,\n minTicksDistance: 5,\n minorHeight: 10, // if <0: full width and height\n majorHeight: -1, // if <0: full width and height\n tickEndings: [0, 1],\n majorTickEndings: [1, 1],\n minorTicks: 4,\n ticksDistance: 1, // TODO doc\n strokeOpacity: 0.25\n },\n\n /**\n * Attributes for first point the axis.\n *\n * @type Point\n * @name Axis#point1\n */\n point1: { // Default values for point1 if created by line\n needsRegularUpdate: false,\n visible: false\n },\n\n /**\n * Attributes for second point the axis.\n *\n * @type Point\n * @name Axis#point2\n */\n point2: { // Default values for point2 if created by line\n needsRegularUpdate: false,\n visible: false\n },\n\n tabindex: -1,\n\n /**\n * Attributes for the axis label.\n *\n * @type Label\n * @name Axis#label\n */\n label: {\n position: 'lft',\n offset: [10, 10]\n },\n\n ignoreForLabelAutoposition: true\n\n /**#@-*/\n },\n\n /* special options for angle bisector of 3 points */\n bisector: {\n /**#@+\n * @visprop\n */\n\n strokeColor: '#000000', // Bisector line\n\n /**\n * Attributes for the helper point of the bisector.\n *\n * @type Point\n * @name Bisector#point\n */\n point: { // Bisector point\n visible: false,\n fixed: false,\n withLabel: false,\n name: ''\n }\n\n /**#@-*/\n },\n\n /* special options for the 2 bisectors of 2 lines */\n bisectorlines: {\n /**#@+\n * @visprop\n */\n\n /**\n * Attributes for first line.\n *\n * @type Line\n * @name Bisectorlines#line1\n */\n line1: { //\n strokeColor: '#000000'\n },\n\n /**\n * Attributes for second line.\n *\n * @type Line\n * @name Bisectorlines#line2\n */\n line2: { //\n strokeColor: '#000000'\n }\n\n /**#@-*/\n },\n\n /* special options for boxplot curves */\n boxplot: {\n /**#@+\n * @visprop\n */\n\n /**\n * Direction of the boxplot: 'vertical' or 'horizontal'\n *\n * @type String\n * @name Boxplot#dir\n * @default 'vertical'\n */\n dir: 'vertical',\n\n /**\n * Relative width of the maximum and minimum quantile\n *\n * @type Number\n * @name Boxplot#smallWidth\n * @default 0.5\n */\n smallWidth: 0.5,\n\n /**\n * Size and face of outliers. Size is the point size in pixel.\n * Possible values for face are 'o' (default), '[]', '<>', '<<>>', '+', 'x', '-', '|'.\n * See {@link JXG.Grid} for these names ('o' here is 'regpol' of the grid).\n *\n * @type Object\n * @name Boxplot#outlier\n * @default {\n * size: 3,\n * face: 'o'\n * }\n */\n outlier: {\n size: 3,\n face: 'o'\n },\n\n strokeWidth: 2,\n strokeColor: Color.palette.blue,\n fillColor: Color.palette.blue,\n fillOpacity: 0.2,\n highlightStrokeWidth: 2,\n highlightStrokeColor: Color.palette.blue,\n highlightFillColor: Color.palette.blue,\n highlightFillOpacity: 0.1\n\n /**#@-*/\n },\n\n /* special button options */\n button: {\n /**#@+\n * @visprop\n */\n\n /**\n * Control the attribute \"disabled\" of the HTML button.\n *\n * @name disabled\n * @memberOf Button.prototype\n *\n * @type Boolean\n * @default false\n */\n disabled: false,\n\n display: 'html'\n\n /**#@-*/\n },\n\n /* special cardinal spline options */\n cardinalspline: {\n /**#@+\n * @visprop\n */\n\n /**\n * Controls if the data points of the cardinal spline when given as\n * arrays should be converted into {@link JXG.Points}.\n *\n * @name createPoints\n * @memberOf Cardinalspline.prototype\n *\n * @see Cardinalspline#points\n *\n * @type Boolean\n * @default true\n */\n createPoints: true,\n\n /**\n * If set to true, the supplied coordinates are interpreted as\n * [[x_0, y_0], [x_1, y_1], p, ...].\n * Otherwise, if the data consists of two arrays of equal length,\n * it is interpreted as\n * [[x_o x_1, ..., x_n], [y_0, y_1, ..., y_n]]\n *\n * @name isArrayOfCoordinates\n * @memberOf Cardinalspline.prototype\n * @type Boolean\n * @default true\n */\n isArrayOfCoordinates: true,\n\n /**\n * Attributes for the points generated by Cardinalspline in cases\n * {@link createPoints} is set to true\n *\n * @name points\n * @memberOf Cardinalspline.prototype\n *\n * @see Cardinalspline#createPoints\n * @type Object\n */\n points: {\n strokeOpacity: 0.05,\n fillOpacity: 0.05,\n highlightStrokeOpacity: 1.0,\n highlightFillOpacity: 1.0,\n withLabel: false,\n name: '',\n fixed: false\n }\n\n /**#@-*/\n },\n\n /* special chart options */\n chart: {\n /**#@+\n * @visprop\n */\n\n chartStyle: 'line',\n colors: ['#B02B2C', '#3F4C6B', '#C79810', '#D15600', '#FFFF88', '#c3d9ff', '#4096EE', '#008C00'],\n highlightcolors: null,\n fillcolor: null,\n highlightonsector: false,\n highlightbysize: false,\n\n fillOpacity: 0.6,\n withLines: false,\n\n label: {\n }\n /**#@-*/\n },\n\n /* special html slider options */\n checkbox: {\n /**#@+\n * @visprop\n */\n\n /**\n * Control the attribute \"disabled\" of the HTML checkbox.\n *\n * @name disabled\n * @memberOf Checkbox.prototype\n *\n * @type Boolean\n * @default false\n */\n disabled: false,\n\n /**\n * Control the attribute \"checked\" of the HTML checkbox.\n *\n * @name checked\n * @memberOf Checkbox.prototype\n *\n * @type Boolean\n * @default false\n */\n checked: false,\n\n display: 'html'\n\n /**#@-*/\n },\n\n /*special circle options */\n circle: {\n /**#@+\n * @visprop\n */\n\n /**\n * If true, moving the mouse over inner points triggers hasPoint.\n *\n * @see JXG.GeometryElement#hasPoint\n * @name Circle#hasInnerPoints\n * @type Boolean\n * @default false\n */\n hasInnerPoints: false,\n\n fillColor: 'none',\n highlightFillColor: 'none',\n strokeColor: Color.palette.blue,\n highlightStrokeColor: '#c3d9ff',\n\n /**\n * Attributes for center point.\n *\n * @type Point\n * @name Circle#center\n */\n center: {\n visible: false,\n withLabel: false,\n fixed: false,\n\n fillColor: Color.palette.red,\n strokeColor: Color.palette.red,\n highlightFillColor: '#c3d9ff',\n highlightStrokeColor: '#c3d9ff',\n layer: 9,\n\n name: ''\n },\n\n /**\n * Attributes for center point.\n *\n * @type Point\n * @name Circle#point2\n */\n point2: {\n fillColor: Color.palette.red,\n strokeColor: Color.palette.red,\n highlightFillColor: '#c3d9ff',\n highlightStrokeColor: '#c3d9ff',\n layer: 9,\n\n visible: false,\n withLabel: false,\n fixed: false,\n name: ''\n },\n\n /**\n * Attributes for circle label.\n *\n * @type Label\n * @name Circle#label\n */\n label: {\n position: 'urt'\n }\n\n /**#@-*/\n },\n\n /* special options for circumcircle of 3 points */\n circumcircle: {\n /**#@+\n * @visprop\n */\n\n fillColor: 'none',\n highlightFillColor: 'none',\n strokeColor: Color.palette.blue,\n highlightStrokeColor: '#c3d9ff',\n\n /**\n * Attributes for center point.\n *\n * @type Point\n * @name Circumcircle#center\n */\n center: { // center point\n visible: false,\n fixed: false,\n withLabel: false,\n fillColor: Color.palette.red,\n strokeColor: Color.palette.red,\n highlightFillColor: '#c3d9ff',\n highlightStrokeColor: '#c3d9ff',\n name: ''\n }\n /**#@-*/\n },\n\n circumcirclearc: {\n /**#@+\n * @visprop\n */\n\n fillColor: 'none',\n highlightFillColor: 'none',\n strokeColor: Color.palette.blue,\n highlightStrokeColor: '#c3d9ff',\n useDirection: true,\n\n /**\n * Attributes for center point.\n *\n * @type Point\n * @name CircumcircleArc#center\n */\n center: {\n visible: false,\n withLabel: false,\n fixed: false,\n name: ''\n }\n /**#@-*/\n },\n\n /* special options for circumcircle sector of 3 points */\n circumcirclesector: {\n /**#@+\n * @visprop\n */\n\n useDirection: true,\n fillColor: Color.palette.yellow,\n highlightFillColor: Color.palette.yellow,\n fillOpacity: 0.3,\n highlightFillOpacity: 0.3,\n strokeColor: Color.palette.blue,\n highlightStrokeColor: '#c3d9ff',\n\n /**\n * Attributes for center point.\n *\n * @type Point\n * @name Circle#point\n */\n point: {\n visible: false,\n fixed: false,\n withLabel: false,\n name: ''\n }\n /**#@-*/\n },\n\n /* special options for comb */\n comb: {\n /**#@+\n * @visprop\n */\n\n /**\n * Frequency of comb elements.\n *\n * @type Number\n * @name Comb#frequency\n * @default 0.2\n */\n frequency: 0.2,\n\n /**\n * Width of the comb.\n *\n * @type Number\n * @name Comb#width\n * @default 0.4\n */\n width: 0.4,\n\n /**\n * Angle - given in radians - under which comb elements are positioned.\n *\n * @type Number\n * @name Comb#angle\n * @default Math.PI / 3 (i.e. π /3 or 60^° degrees)\n */\n angle: Math.PI / 3,\n\n /**\n * Should the comb go right to left instead of left to right.\n *\n * @type Boolean\n * @name Comb#reverse\n * @default false\n */\n reverse: false,\n\n /**\n * Attributes for first defining point of the comb.\n *\n * @type Point\n * @name Comb#point1\n */\n point1: {\n visible: false,\n withLabel: false,\n fixed: false,\n name: ''\n },\n\n /**\n * Attributes for second defining point of the comb.\n *\n * @type Point\n * @name Comb#point2\n */\n point2: {\n visible: false,\n withLabel: false,\n fixed: false,\n name: ''\n },\n\n // /**\n // * Attributes for the curve displaying the comb.\n // *\n // * @type Curve\n // * @name Comb#curve\n // */\n // curve: {\n // strokeWidth: 1,\n // strokeColor: '#0000ff',\n // fillColor: 'none'\n // },\n strokeWidth: 1,\n strokeColor: '#0000ff',\n fillColor: 'none'\n },\n\n /* special conic options */\n conic: {\n /**#@+\n * @visprop\n */\n\n fillColor: 'none',\n highlightFillColor: 'none',\n strokeColor: Color.palette.blue,\n highlightStrokeColor: '#c3d9ff',\n\n /**\n * Attributes for foci points.\n *\n * @type Point\n * @name Conic#foci\n */\n foci: {\n // points\n fixed: false,\n visible: false,\n withLabel: false,\n name: ''\n },\n\n /**\n * Attributes for center point.\n *\n * @type Point\n * @name Conic#center\n */\n center: {\n visible: false,\n withLabel: false,\n name: ''\n },\n\n /**\n * Attributes for five points defining the conic, if some of them are given as coordinates.\n *\n * @type Point\n * @name Conic#point\n */\n point: {\n withLabel: false,\n name: ''\n },\n\n /**\n * Attributes for parabola line in case the line is given by two\n * points or coordinate pairs.\n *\n * @type Line\n * @name Conic#line\n */\n line: {\n visible: false\n }\n\n /**#@-*/\n },\n\n /* special curve options */\n curve: {\n /**#@+\n * @visprop\n */\n\n strokeWidth: 1,\n strokeColor: Color.palette.blue,\n fillColor: 'none',\n fixed: true,\n\n /**\n * The curveType is set in {@link JXG.Curve#generateTerm} and used in {@link JXG.Curve#updateCurve}.\n * Possible values are \n *
\n * Only parameter and plot are set directly. Polar is set with {@link JXG.GeometryElement#setAttribute} only.\n * @name Curve#curveType\n * @type String\n * @default null\n */\n curveType: null,\n\n /**\n * If true use a recursive bisection algorithm.\n * It is slower, but usually the result is better. It tries to detect jumps\n * and singularities.\n *\n * @name Curve#doAdvancedPlot\n * @type Boolean\n * @default true\n */\n doAdvancedPlot: true,\n\n /**\n * If true use the algorithm by Gillam and Hohenwarter, which was default until version 0.98.\n *\n * @name Curve#doAdvancedPlotOld\n * @see Curve#doAdvancedPlot\n * @type Boolean\n * @default false\n * @deprecated\n */\n doAdvancedPlotOld: false, // v1\n\n /**\n * Configure arrow head at the start position for curve.\n * Recommended arrow head type is 7.\n *\n * @name Curve#firstArrow\n * @type Boolean | Object\n * @default false\n * @see Line#firstArrow for options\n */\n firstArrow: false,\n\n /**\n * The data points of the curve are not connected with straight lines but with bezier curves.\n * @name Curve#handDrawing\n * @type Boolean\n * @default false\n */\n handDrawing: false,\n\n /**\n * Attributes for curve label.\n *\n * @type Label\n * @name Curve#label\n */\n label: {\n position: 'rt'\n },\n\n /**\n * Configure arrow head at the end position for curve.\n * Recommended arrow head type is 7.\n *\n * @name Curve#lastArrow\n * @see Line#lastArrow for options\n * @type Boolean | Object\n * @default false\n */\n lastArrow: false,\n\n /**\n * Line endings (linecap) of a curve stroke.\n * Possible values are:\n * \n *
\n *\n * @name JXG.Curve#lineCap\n * @type String\n * @default 'round'\n */\n lineCap: 'round',\n\n /**\n * Number of points used for plotting triggered by up events\n * (i.e. high quality plotting) in case\n * {@link Curve#doAdvancedPlot} is false.\n *\n * @name Curve#numberPointsHigh\n * @see Curve#doAdvancedPlot\n * @type Number\n * @default 1600\n */\n numberPointsHigh: 1600, // Number of points on curves after mouseUp\n\n /**\n * Number of points used for plotting triggered by move events\n * (i.e. lower quality plotting but fast) in case\n * {@link Curve#doAdvancedPlot} is false.\n *\n * @name Curve#numberPointsLow\n * @see Curve#doAdvancedPlot\n * @type Number\n * @default 400\n */\n numberPointsLow: 400, // Number of points on curves after mousemove\n\n /**\n * Select the version of the plot algorithm.\n * \n *
\n * Version 4 plots correctly logarithms if the function term is supplied as string (i.e. as JessieCode)\n *\n * @example\n * var c = board.create('functiongraph', [\"log(x)\"]);\n *\n * @name Curve#plotVersion\n * @type Number\n * @default 2\n */\n plotVersion: 2,\n\n /**\n * Polyline simplification, i.e. remove data points from the curve which do not influence\n * its appearance. In some cases this makes JSXGraph run much faster.\n * The \"smoothing\" in the name is misleading, actually it does the contrary. But\n * for historical reasons we stay with it. A better name would be\n * RDPsimplification.\n * \n *
\n * Instead of one value you can provide two values as an array [x, y] here.\n * These are used as distance in x- and y-direction.\n *\n * @type {Number|String|Array}\n * @name Grid#majorStep\n * @default 'auto'\n * @see JXG.Ticks#getDistanceMajorTicks\n */\n majorStep: 'auto',\n\n /**\n * Number of elements in minor grid between elements of the major grid. There are three possibilities:\n * \n *
\n * Instead of one value you can provide two values as an array [x, y] here.\n * These are used as number in x- and y-direction.\n *\n * @type {Number|String|Array}\n * @name Grid#minorElements\n * @default 0\n */\n minorElements: 0,\n\n /**\n * To print a quadratic grid with same distance of major grid elements in x- and y-direction.\n * 'min' or true will set both distances of major grid elements in x- and y-direction to the primarily lesser value,\n * 'max' to the primarily greater value.\n *\n * @type {Boolean|String}\n * @name Grid#forceSquare\n * @default false\n */\n forceSquare: false,\n\n /**\n * To decide whether major or minor grid elements on boundaries of the boundingBox shall be shown, half-ones as well.\n *\n * @type {Boolean}\n * @name Grid#includeBoundaries\n * @default false\n */\n includeBoundaries: false,\n\n /**\n * Size of grid elements. There are the following possibilities:\n * \n *
\n * Unused for 'line' which will use the value of strokeWidth.\n * Instead of one value you can provide two values as an array [x, y] here.\n * These are used as size in x- and y-direction.\n *\n * \n *
\n *\n * Input Output Fillable by fillColor,... point, . . no line − no cross, x x no circle, o o yes square, [] [] yes plus, + + no minus, - - no divide, | | no diamond, <> <> yes diamond2, <<>> <> (bigger) yes triangleup, ^, a, A ^ no triangledown, v v no triangleleft, < < no triangleright, > > no regularPolygon, regpol ⬡ yes \n *
\n *\n *
\n * {x: true|false, y: true|false, origin: true|false}\n * \n *
\n * Default values are:\n * {\n * size: 5,\n * face: 'line',\n * margin: 0,\n * drawZero: true,\n * polygonVertices: 6\n * }\n *\n * @name Grid#major\n * @type {Object}\n */\n major: {\n\n /**\n * Documented in Grid#size\n * @class\n * @ignore\n */\n size: 5,\n\n /**\n * Documented in Grid#face\n * @class\n * @ignore\n */\n face: 'line',\n\n /**\n * Documented in Grid#margin\n * @class\n * @ignore\n */\n margin: 0,\n\n /**\n * Documented in Grid#drawZero\n * @class\n * @ignore\n */\n drawZero: true,\n\n /**\n * Documented in Grid#polygonVertices\n * @class\n * @ignore\n */\n polygonVertices: 6\n },\n\n /**\n * This object contains the attributes for minor grid elements.\n * You can override the following grid attributes individually here:\n * \n *
\n * Default values are:\n * {\n * size: 3,\n * face: 'point',\n * margin: 0,\n * drawZero: true,\n * polygonVertices: 6\n * }\n *\n * @name Grid#minor\n * @type {Object}\n */\n minor: {\n\n /**\n * @class\n * @ignore\n */\n visible: 'inherit',\n\n /**\n * Documented in Grid#size\n * @class\n * @ignore\n */\n size: 3,\n\n /**\n * Documented in Grid#face\n * @class\n * @ignore\n */\n face: 'point',\n\n /**\n * Documented in Grid#margin\n * @class\n * @ignore\n */\n margin: 0,\n\n /**\n * Documented in Grid#drawZero\n * @class\n * @ignore\n */\n drawZero: true,\n\n /**\n * Documented in Grid#polygonVertices\n * @class\n * @ignore\n */\n polygonVertices: 6\n },\n\n /**\n * @class\n * @ignore\n * @deprecated\n */\n snapToGrid: false,\n\n strokeColor: '#c0c0c0',\n strokeWidth: 1,\n strokeOpacity: 0.5,\n dash: 0,\n\n /**\n * Use a predefined theme for grid.\n * Attributes can be overwritten by explicitly set the specific value.\n *\n * @type {Number}\n * @default 0\n * @see Grid#themes\n */\n theme: 0,\n\n /**\n * Array of theme attributes.\n * The index of the entry is the number of the theme.\n *\n * @type {Array}\n * @name Grid#themes\n * @private\n *\n * @example\n * // Theme 1\n * // quadratic grid appearance with distance of major grid elements set to the primarily greater one\n *\n * JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-4, 4, 4, -4], axis: true,\n * defaultAxes: {\n * x: { ticks: {majorHeight: 10} },\n * y: { ticks: {majorHeight: 10} }\n * },\n * grid: { theme: 1 },\n * });\n * \n * \n *\n * @example\n * // Theme 2\n * // lines and points in between\n *\n * JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-4, 4, 4, -4], axis: false,\n * grid: { theme: 2 },\n * });\n * \n * \n *\n * @example\n * // Theme 3\n * // lines and thinner lines in between\n *\n * JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-4, 4, 4, -4], axis: false,\n * grid: { theme: 3 },\n * });\n * \n * \n *\n * @example\n * // Theme 4\n * // lines with grid of '+'s plotted in between\n *\n * JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-4, 4, 4, -4], axis: false,\n * grid: { theme: 4 },\n * });\n * \n * \n *\n * @example\n * // Theme 5\n * // grid of '+'s and points in between\n *\n * JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-4, 4, 4, -4], axis: false,\n * grid: { theme: 5 },\n * });\n * \n * \n *\n * @example\n * // Theme 6\n * // grid of circles with points in between\n *\n * JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-4, 4, 4, -4], axis: false,\n * grid: { theme: 6 },\n * });\n * \n * \n */\n themes: [\n {\n // default values\n },\n\n { // Theme 1: quadratic grid appearance with distance of major grid elements in x- and y-direction set to the primarily smaller one\n forceSquare: 'min',\n major: {\n face: 'line'\n }\n },\n\n { // Theme 2: lines and points in between\n major: {\n face: 'line'\n },\n minor: {\n size: 3,\n face: 'point'\n },\n minorElements: 'auto'\n },\n\n { // Theme 3: lines and thinner lines in between\n major: {\n face: 'line'\n },\n minor: {\n face: 'line',\n strokeOpacity: 0.25\n },\n minorElements: 'auto'\n },\n\n { // Theme 4: lines with grid of '+'s plotted in between\n major: {\n face: 'line'\n },\n minor: {\n face: '+',\n size: '95%'\n },\n minorElements: 'auto'\n },\n\n { // Theme 5: grid of '+'s and more points in between\n major: {\n face: '+',\n size: 10,\n strokeOpacity: 1\n },\n minor: {\n face: 'point',\n size: 3\n },\n minorElements: 'auto'\n },\n\n { // Theme 6: grid of circles with points in between\n major: {\n face: 'circle',\n size: 8,\n fillColor: '#c0c0c0'\n },\n minor: {\n face: 'point',\n size: 3\n },\n minorElements: 'auto'\n }\n ]\n\n /**#@-*/\n },\n\n group: {\n needsRegularUpdate: true\n },\n\n /* special html slider options */\n htmlslider: {\n /**#@+\n * @visprop\n */\n\n // /**\n // *\n // * These affect the DOM element input type=\"range\".\n // * The other attributes affect the DOM element div containing the range element.\n // */\n widthRange: 100,\n widthOut: 34,\n step: 0.01,\n\n frozen: true,\n isLabel: false,\n strokeColor: '#000000',\n display: 'html',\n anchorX: 'left',\n anchorY: 'middle',\n withLabel: false\n\n /**#@-*/\n },\n\n /* special image options */\n image: {\n /**#@+\n * @visprop\n */\n\n imageString: null,\n fillOpacity: 1.0,\n highlightFillOpacity: 0.6,\n\n\n /**\n * Defines the CSS class used by the image. CSS attributes defined in\n * this class will overwrite the corresponding JSXGraph attributes, e.g.\n * opacity.\n * The default CSS class is defined in jsxgraph.css.\n *\n * @name Image#cssClass\n *\n * @see Image#highlightCssClass\n * @type String\n * @default 'JXGimage'\n * @see Image#highlightCssClass\n * @see Text#cssClass\n * @see JXG.GeometryElement#cssClass\n */\n cssClass: 'JXGimage',\n\n /**\n * Defines the CSS class used by the image when highlighted.\n * CSS attributes defined in this class will overwrite the\n * corresponding JSXGraph attributes, e.g. highlightFillOpacity.\n * The default CSS class is defined in jsxgraph.css.\n *\n * @name Image#highlightCssClass\n *\n * @see Image#cssClass\n * @type String\n * @default 'JXGimageHighlight'\n * @see Image#cssClass\n * @see Image#highlightCssClass\n * @see JXG.GeometryElement#highlightCssClass\n */\n highlightCssClass: 'JXGimageHighlight',\n\n /**\n * Image rotation in degrees.\n *\n * @name Image#rotate\n * @type Number\n * @default 0\n */\n rotate: 0,\n\n /**\n * Defines together with {@link Image#snapSizeY} the grid the image snaps on to.\n * The image will only snap on user coordinates which are\n * integer multiples to snapSizeX in x and snapSizeY in y direction.\n * If this value is equal to or less than 0, it will use the grid displayed by the major ticks\n * of the default ticks of the default x axes of the board.\n *\n * @name Image#snapSizeX\n *\n * @see Point#snapToGrid\n * @see Image#snapSizeY\n * @see JXG.Board#defaultAxes\n * @type Number\n * @default 1\n */\n snapSizeX: 1,\n\n /**\n * Defines together with {@link Image#snapSizeX} the grid the image snaps on to.\n * The image will only snap on integer multiples to snapSizeX in x and snapSizeY in y direction.\n * If this value is equal to or less than 0, it will use the grid displayed by the major ticks\n * of the default ticks of the default y axes of the board.\n *\n * @name Image#snapSizeY\n *\n * @see Point#snapToGrid\n * @see Image#snapSizeX\n * @see JXG.Board#defaultAxes\n * @type Number\n * @default 1\n */\n snapSizeY: 1,\n\n /**\n * List of attractor elements. If the distance of the image is less than\n * attractorDistance the image is made to glider of this element.\n *\n * @name Image#attractors\n *\n * @type Array\n * @default empty\n */\n attractors: []\n\n /**#@-*/\n },\n\n /* special implicitcurve options */\n implicitcurve: {\n /**#@+\n * @visprop\n */\n\n /**\n * Defines the margin (in user coordinates) around the JSXGraph board in which the\n * implicit curve is plotted.\n *\n * @name ImplicitCurve#margin\n * @type {Number|Function}\n * @default 1\n */\n margin: 1,\n\n /**\n * Horizontal resolution: distance (in pixel) between vertical lines to search for components of the implicit curve.\n * A small number increases the running time. For large number components may be missed.\n * Minimum value is 0.01.\n *\n * @name ImplicitCurve#resolution_outer\n * @type {Number|Function}\n * @default 5\n */\n resolution_outer: 5,\n\n /**\n * Vertical resolution (in pixel) to search for components of the implicit curve.\n * A small number increases the running time. For large number components may be missed.\n * Minimum value is 0.01.\n *\n * @name ImplicitCurve#resolution_inner\n * @type {Number|Function}\n * @default 5\n */\n resolution_inner: 5,\n\n /**\n * Maximum iterations for one component of the implicit curve.\n *\n * @name ImplicitCurve#max_steps\n * @type {Number|Function}\n * @default 1024\n */\n max_steps: 1024,\n\n /**\n * Angle α0 between two successive tangents: determines the smoothness of\n * the curve.\n *\n * @name ImplicitCurve#alpha_0\n * @type {Number|Function}\n * @default 0.05\n */\n alpha_0: 0.05,\n\n /**\n * Tolerance to find starting points for the tracing phase of a component.\n *\n * @name ImplicitCurve#tol_0\n * @type {Number|Function}\n * @default JXG.Math.eps\n */\n tol_u0: Mat.eps,\n\n /**\n * Tolerance for the Newton steps.\n *\n * @name ImplicitCurve#tol_newton\n * @type {Number|Function}\n * @default 1.0e-7\n */\n tol_newton: 1.0e-7,\n\n /**\n * Tolerance for cusp / bifurcation detection.\n *\n * @name ImplicitCurve#tol_cusp\n * @type {Number|Function}\n * @default 0.05\n */\n tol_cusp: 0.05,\n\n /**\n * If two points are closer than this value, we bail out of the tracing phase for that\n * component.\n *\n * @name ImplicitCurve#tol_progress\n * @type {Number|Function}\n * @default 0.0001\n */\n tol_progress: 0.0001,\n\n /**\n * Half of the box size (in user units) to search for existing line segments in the quadtree.\n *\n * @name ImplicitCurve#qdt_box\n * @type {Number|Function}\n * @default 0.2\n */\n qdt_box: 0.2,\n\n /**\n * Inverse of desired number of Newton steps.\n *\n * @name ImplicitCurve#kappa_0\n * @type {Number|Function}\n * @default 0.2\n */\n kappa_0: 0.2,\n\n /**\n * Allowed distance (in user units) of predictor point to curve.\n *\n * @name ImplicitCurve#delta_0\n * @type {Number|Function}\n * @default 0.05\n */\n delta_0: 0.05,\n\n /**\n * Initial step width (in user units).\n *\n * @name ImplicitCurve#h_initial\n * @type {Number|Function}\n * @default 0.1\n */\n h_initial: 0.1,\n\n /**\n * If h is below this threshold (in user units), we bail out\n * of the tracing phase of that component.\n *\n * @name ImplicitCurve#h_critical\n * @type {Number|Function}\n * @default 0.001\n */\n h_critical: 0.001,\n\n /**\n * Maximum step width (in user units).\n *\n * @name ImplicitCurve#h_max\n * @type {Number|Function}\n * @default 0.5\n */\n h_max: 0.5,\n\n /**\n * Allowed distance (in user units multiplied by actual step width) to detect loop.\n *\n * @name ImplicitCurve#loop_dist\n * @type {Number|Function}\n * @default 0.09\n */\n loop_dist: 0.09,\n\n /**\n * Minimum acos of angle to detect loop.\n *\n * @name ImplicitCurve#loop_dir\n * @type {Number|Function}\n * @default 0.99\n */\n loop_dir: 0.99,\n\n /**\n * Use Gosper's loop detector.\n *\n * @name ImplicitCurve#loop_detection\n * @type {Boolean|Function}\n * @default true\n */\n loop_detection: true\n\n /**#@-*/\n },\n\n /* special options for incircle of 3 points */\n incircle: {\n /**#@+\n * @visprop\n */\n\n fillColor: 'none',\n highlightFillColor: 'none',\n strokeColor: Color.palette.blue,\n highlightStrokeColor: '#c3d9ff',\n\n /**\n * Attributes of circle center.\n *\n * @type Point\n * @name Incircle#center\n */\n center: { // center point\n visible: false,\n fixed: false,\n withLabel: false,\n fillColor: Color.palette.red,\n strokeColor: Color.palette.red,\n highlightFillColor: '#c3d9ff',\n highlightStrokeColor: '#c3d9ff',\n name: ''\n }\n /**#@-*/\n },\n\n inequality: {\n /**#@+\n * @visprop\n */\n\n fillColor: Color.palette.red,\n fillOpacity: 0.2,\n strokeColor: 'none',\n\n /**\n * By default an inequality is less (or equal) than. Set inverse to true will consider the inequality\n * greater (or equal) than.\n *\n * @type Boolean\n * @default false\n * @name Inequality#inverse\n * @visprop\n */\n inverse: false\n /**#@-*/\n },\n\n infobox: {\n /**#@+\n * @visprop\n */\n\n /**\n * Horizontal offset in pixel of the infobox text from its anchor point.\n *\n * @type Number\n * @default -20\n * @name JXG.Board.infobox#distanceX\n * @visprop\n */\n distanceX: -20,\n\n /**\n * Vertical offset in pixel of the infobox text from its anchor point.\n *\n * @type Number\n * @default 25\n * @name JXG.Board.infobox#distanceY\n * @visprop\n */\n distanceY: 25,\n\n /**\n * Internationalization support for infobox text.\n *\n * @name JXG.Board.infobox#intl\n * @type object\n * @default {\n * enabled: 'inherit',\n * options: {}\n * }\n * @visprop\n * @see JXG.Board#intl\n * @see Text#intl\n */\n intl: {\n enabled: 'inherit',\n options: {}\n },\n\n fontSize: 12,\n isLabel: false,\n strokeColor: '#bbbbbb',\n display: 'html', // 'html' or 'internal'\n anchorX: 'left', // 'left', 'middle', or 'right': horizontal alignment\n // of the text.\n anchorY: 'middle', // 'top', 'middle', or 'bottom': vertical alignment\n // of the text.\n cssClass: 'JXGinfobox',\n rotate: 0, // works for non-zero values only in combination\n // with display=='internal'\n visible: true,\n parse: false,\n transitionDuration: 0,\n needsRegularUpdate: false,\n tabindex: null,\n viewport: [0, 0, 0, 0],\n\n ignoreForLabelAutoposition: true\n /**#@-*/\n },\n\n /* special options for integral */\n integral: {\n /**#@+\n * @visprop\n */\n\n axis: 'x', // 'x' or 'y'\n withLabel: true, // Show integral value as text\n fixed: true,\n strokeWidth: 0,\n strokeOpacity: 0,\n fillColor: Color.palette.red,\n fillOpacity: 0.3,\n highlightFillColor: Color.palette.red,\n highlightFillOpacity: 0.2,\n\n /**\n * Attributes of the (left) starting point of the integral.\n *\n * @type Point\n * @name Integral#curveLeft\n * @see Integral#baseLeft\n */\n curveLeft: { // Start point\n visible: true,\n withLabel: false,\n color: Color.palette.red,\n fillOpacity: 0.8,\n layer: 9\n },\n\n /**\n * Attributes of the (left) base point of the integral.\n *\n * @type Point\n * @name Integral#baseLeft\n * @see Integral#curveLeft\n */\n baseLeft: { // Start point\n visible: false,\n fixed: false,\n withLabel: false,\n name: ''\n },\n\n /**\n * Attributes of the (right) end point of the integral.\n *\n * @type Point\n * @name Integral#curveRight\n * @see Integral#baseRight\n */\n curveRight: { // End point\n visible: true,\n withLabel: false,\n color: Color.palette.red,\n fillOpacity: 0.8,\n layer: 9\n },\n\n /**\n * Attributes of the (right) base point of the integral.\n *\n * @type Point\n * @name Integral#baseRight\n * @see Integral#curveRight\n */\n baseRight: { // End point\n visible: false,\n fixed: false,\n withLabel: false,\n name: ''\n },\n\n /**\n * Attributes for integral label.\n *\n * @type Label\n * @name Integral#label\n * @default {\n * fontSize: 20,\n * digits: 4,\n * intl: {\n * enabled: false,\n * options: {}\n * }\n * }\n */\n label: {\n fontSize: 20,\n digits: 4,\n intl: {\n enabled: false,\n options: {}\n }\n }\n /**#@-*/\n },\n\n /* special input options */\n input: {\n /**#@+\n * @visprop\n */\n\n /**\n * Control the attribute \"disabled\" of the HTML input field.\n *\n * @name disabled\n * @memberOf Input.prototype\n *\n * @type Boolean\n * @default false\n */\n disabled: false,\n\n /**\n * Control the attribute \"maxlength\" of the HTML input field.\n *\n * @name maxlength\n * @memberOf Input.prototype\n *\n * @type Number\n * @default 524288 (as in HTML)\n */\n maxlength: 524288,\n\n display: 'html'\n\n /**#@-*/\n },\n\n /* special intersection point options */\n intersection: {\n /**#@+\n * @visprop\n */\n\n /**\n * Used in {@link JXG.Intersection}.\n * This flag sets the behaviour of intersection points of a segment with another object.\n * If true, the segment is treated as an (infinte) line. If false\n * the intersection point exists if the segment intersects the other object setwise.\n * \n *
\n *\n * @example\n * var l1 = board.create('segment', [[-3, 2], [3, 2]], {\n * name: 'l_1',\n * withLabel: true,\n * point1: { visible: true, name: 'A', withLabel: true },\n * point2: { visible: true, name: 'B', withLabel: true },\n * label: {\n * anchorX: 'middle',\n * anchorY: 'middle',\n * offset: [0, 0],\n * distance: 1.2,\n * position: '0.2fr left'\n * }\n * });\n *\n * \n * \n *
\n * \n *
\n * Recommended for this second possibility is to use anchorX: 'middle' and 'anchorY: 'middle'.\n * \n *
\n * If the domain of a curve is not connected, a position of the label close to the line\n * between the first and last point of the curve is chosen.\n * \n *\n * @example\n * var c1 = board.create('circle', [[0, 0], 3], {\n * name: 'c_1',\n * withLabel: true,\n * label: {\n * anchorX: 'middle',\n * anchorY: 'middle',\n * offset: [0, 0],\n * fontSize: 32,\n * distance: 1.5,\n * position: '50% right'\n * }\n * });\n *\n * \n * \n *\n * @example\n * var cu1 = board.create('functiongraph', ['3 * sin(x)', -3, 3], {\n * name: 'cu_1',\n * withLabel: true,\n * label: {\n * anchorX: 'middle',\n * anchorY: 'middle',\n * offset: [0, 0],\n * distance: 2,\n * position: '0.8fr right'\n * }\n * });\n *\n * \n * \n *\n * @example\n * var A = board.create('point', [-1, 4]);\n * var B = board.create('point', [-1, -4]);\n * var C = board.create('point', [1, 1]);\n * var cu2 = board.create('ellipse', [A, B, C], {\n * name: 'cu_2',\n * withLabel: true,\n * label: {\n * anchorX: 'middle',\n * anchorY: 'middle',\n * offset: [0, 0],\n * fontSize: 20,\n * distance: 1.5,\n * position: '75% right'\n * }\n * });\n *\n * \n * \n *\n *\n * @name Label#position\n * @type String\n * @default 'urt'\n * @see Label#distance\n * @see Label#offset\n */\n position: 'urt',\n\n /**\n * Distance of the label from a path element, like line, circle, curve.\n * The true distance is this value multiplied by 0.5 times the size of the bounding box of the label text.\n * That means, with a value of 1 the label will touch the path element.\n * @name Label#distance\n * @type Number\n * @default 1.5\n *\n * @see Label#position\n *\n */\n distance: 1.5,\n\n /**\n * Label offset from label anchor.\n * The label anchor is determined by {@link Label#position}\n *\n * @name Label#offset\n * @see Label#position\n * @type Array\n * @default [10,10]\n */\n offset: [10, 10],\n\n /**\n * Automatic position of label text. When called first, the positioning algorithm\n * starts at the position defined by offset.\n * The algorithm tries to find a position with the least number of\n * overlappings with other elements, while retaining the distance\n * to the anchor element.\n *\n * @name Label#autoPosition\n * @see Label#offset\n * @type Boolean\n * @see GeometryElement#ignoreForLabelAutoposition\n * @see Label#autoPositionMinDistance\n * @see Label#autoPositionMaxDistance\n * @see Label#autoPositionWhitelist\n * @default false\n *\n * @example\n * \tvar p1 = board.create('point', [-2, 1], {id: 'A'});\n * \tvar p2 = board.create('point', [-0.85, 1], {\n * name: 'B', id: 'B', label:{autoPosition: true, offset:[10, 10]}\n * });\n * \tvar p3 = board.create('point', [-1, 1.2], {\n * name: 'C', id: 'C', label:{autoPosition: true, offset:[10, 10]}\n * });\n * var c = board.create('circle', [p1, p2]);\n * \tvar l = board.create('line', [p1, p2]);\n *\n * \n * \n *\n *\n */\n autoPosition: false,\n\n /**\n * The auto position algorithm tries to put a label to a conflict-free\n * position around it's anchor element. For this, the algorithm tests 12 positions\n * around the anchor element starting at a distance from the anchor\n * defined here (in pixel).\n *\n * @name Label#autoPositionMinDistance\n * @see Label#autoPosition\n * @see Label#autoPositionMaxDistance\n * @see Label#autoPositionWhitelist\n * @type Number\n * @default 12\n *\n */\n autoPositionMinDistance: 12,\n\n /**\n * The auto position algorithm tries to put a label to a conflict-free\n * position around it's anchor element. For this, the algorithm tests 12 positions\n * around the anchor element up to a distance from the anchor\n * defined here (in pixel).\n *\n * @name Label#autoPositionMaxDistance\n * @see Label#autoPosition\n * @see Label#autoPositionMinDistance\n * @see Label#autoPositionWhitelist\n * @type Number\n * @default 28\n *\n */\n autoPositionMaxDistance: 28,\n\n /**\n * List of object ids which should be ignored on setting automatic position of label text.\n *\n * @name Label#autoPositionWhitelist\n * @see Label#autoPosition\n * @see Label#autoPositionMinDistance\n * @see Label#autoPositionMaxDistance\n * @type Array\n * @default []\n */\n autoPositionWhitelist: []\n\n /**#@-*/\n },\n\n /* special legend options */\n legend: {\n /**#@+\n * @visprop\n */\n\n /**\n * Default style of a legend element. The only possible value is 'vertical'.\n * @name Legend#style\n * @type String\n * @default 'vertical'\n */\n style: 'vertical',\n\n /**\n * Label names of a legend element.\n * @name Legend#labels\n * @type Array\n * @default \"['1', '2', '3', '4', '5', '6', '7', '8']\"\n */\n labels: ['1', '2', '3', '4', '5', '6', '7', '8'],\n\n /**\n * (Circular) array of label colors.\n * @name Legend#colors\n * @type Array\n * @default \"['#B02B2C', '#3F4C6B', '#C79810', '#D15600', '#FFFF88', '#c3d9ff', '#4096EE', '#008C00']\"\n */\n colors: ['#B02B2C', '#3F4C6B', '#C79810', '#D15600', '#FFFF88', '#c3d9ff', '#4096EE', '#008C00'],\n\n /**\n * Length of line in one legend entry\n * @name Legend#lineLength\n * @type Number\n * @default 1\n *\n */\n lineLength: 1,\n\n /**\n * (Circular) array of opacity for legend line stroke color for one legend entry.\n * @name Legend#strokeOpacity\n * @type Array\n * @default [1]\n *\n */\n strokeOpacity: [1],\n\n /**\n * Height (in px) of one legend entry\n * @name Legend#rowHeight\n * @type Number\n * @default 20\n *\n */\n rowHeight: 20,\n\n /**\n * Height (in px) of one legend entry\n * @name Legend#strokeWidth\n * @type Number\n * @default 5\n *\n */\n strokeWidth: 5,\n\n /**\n * The element can be fixed and may not be dragged around. If true, the legend will even stay at its position on zoom and\n * moveOrigin events.\n * @name Legend#frozen\n * @type Boolean\n * @default false\n * @see JXG.GeometryElement#frozen\n *\n */\n frozen: false\n\n /**#@-*/\n },\n\n /* special line options */\n line: {\n /**#@+\n * @visprop\n */\n\n /**\n * Configure the arrow head at the position of its first point or the corresponding\n * intersection with the canvas border\n *\n * The attribute firstArrow can be a Boolean or an object with the following sub-attributes:\n * \n * \n * {\n * type: 1, // possible values are 1, 2, ..., 7. Default value is 1.\n * size: 6, // size of the arrow head. Default value is 6.\n * // This value is multiplied with the strokeWidth of the line\n * // Exception: for type=7 size is ignored\n * highlightSize: 6, // size of the arrow head in case the element is highlighted. Default value\n * }\n * \n * type=7 is the default for curves if firstArrow: true\n * \n *\n * @name Line#firstArrow\n * @see Line#lastArrow\n * @see Line#touchFirstPoint\n * @type Boolean | Object\n * @default false\n */\n firstArrow: false,\n\n /**\n * Configure the arrow head at the position of its second point or the corresponding\n * intersection with the canvas border.\n *\n * The attribute lastArrow can be a Boolean or an object with the following sub-attributes:\n *
\n * \n *\n * @example\n * board.options.line.strokeWidth = 4;\n * board.options.line.highlightStrokeWidth = 4;\n * board.options.line.firstArrow = false;\n * board.options.line.lastArrow = {size: 10, highlightSize: 10};\n * board.options.line.point2 = {visible: false, withLabel: true, label: {visible: true}};\n *\n * board.create('segment', [[-5,4], [3,4]], {lastArrow: {type: 1}, point2: {name: 'type:1'}});\n * board.create('segment', [[-5,3], [3,3]], {lastArrow: {type: 2}, point2: {name: 'type:2'}});\n * board.create('segment', [[-5,2], [3,2]], {lastArrow: {type: 3}, point2: {name: 'type:3'}});\n * board.create('segment', [[-5,1], [3,1]], {lastArrow: {type: 4}, point2: {name: 'type:4'}});\n * board.create('segment', [[-5,0], [3,0]], {lastArrow: {type: 5}, point2: {name: 'type:5'}});\n * board.create('segment', [[-5,-1], [3,-1]], {lastArrow: {type: 6}, point2: {name: 'type:6'}});\n * board.create('segment', [[-5,-2], [3,-2]], {lastArrow: {type: 7}, point2: {name: 'type:7'}});\n *\n * \n * \n * {\n * type: 1, // possible values are 1, 2, ..., 7. Default value is 1.\n * size: 6, // size of the arrow head. Default value is 6.\n * // This value is multiplied with the strokeWidth of the line.\n * // Exception: for type=7 size is ignored\n * highlightSize: 6, // size of the arrow head in case the element is highlighted. Default value is 6.\n * }\n * \n * type=7 is the default for curves if lastArrow: true\n * \n *\n * @name Line#lastArrow\n * @see Line#firstArrow\n * @see Line#touchLastPoint\n * @type Boolean | Object\n * @default false\n */\n lastArrow: false,\n\n /**\n * This number (pixel value) controls where infinite lines end at the canvas border. If zero, the line\n * ends exactly at the border, if negative there is a margin to the inside, if positive the line\n * ends outside of the canvas (which is invisible).\n *\n * @name Line#margin\n * @type Number\n * @default 0\n */\n margin: 0,\n\n /**\n * If true, line stretches infinitely in direction of its first point.\n * Otherwise it ends at point1.\n *\n * @name Line#straightFirst\n * @see Line#straightLast\n * @type Boolean\n * @default true\n */\n straightFirst: true,\n\n /**\n * If true, line stretches infinitely in direction of its second point.\n * Otherwise it ends at point2.\n *\n * @name Line#straightLast\n * @see Line#straightFirst\n * @type Boolean\n * @default true\n */\n straightLast: true,\n\n fillColor: 'none', // Important for VML on IE\n highlightFillColor: 'none', // Important for VML on IE\n strokeColor: Color.palette.blue,\n highlightStrokeColor: '#c3d9ff',\n withTicks: false,\n\n /**\n * Attributes for first defining point of the line.\n *\n * @type Point\n * @name Line#point1\n */\n point1: { // Default values for point1 if created by line\n fillColor: Color.palette.red,\n strokeColor: Color.palette.red,\n highlightFillColor: '#c3d9ff',\n highlightStrokeColor: '#c3d9ff',\n layer: 9,\n\n visible: false,\n withLabel: false,\n fixed: false,\n name: ''\n },\n\n /**\n * Attributes for second defining point of the line.\n *\n * @type Point\n * @name Line#point2\n */\n point2: { // Default values for point2 if created by line\n fillColor: Color.palette.red,\n strokeColor: Color.palette.red,\n highlightFillColor: '#c3d9ff',\n highlightStrokeColor: '#c3d9ff',\n layer: 9,\n\n visible: false,\n withLabel: false,\n fixed: false,\n name: ''\n },\n\n /**\n * Attributes for ticks of the line.\n *\n * @name Line#ticks\n * @type Object\n * @see Ticks\n */\n ticks: {\n drawLabels: true,\n label: {\n offset: [4, -12 + 3] // This seems to be a good offset for 12 point fonts\n },\n drawZero: false,\n insertTicks: false,\n ticksDistance: 1,\n minTicksDistance: 50,\n minorHeight: 4, // if <0: full width and height\n majorHeight: -1, // if <0: full width and height\n minorTicks: 4,\n strokeOpacity: 0.3,\n visible: 'inherit'\n },\n\n /**\n * Attributes for the line label.\n *\n * @type Object\n * @name Line#label\n * @see Label\n */\n label: {\n position: 'llft'\n },\n\n /**\n * If set to true, the point will snap to a grid defined by\n * {@link Point#snapSizeX} and {@link Point#snapSizeY}.\n *\n * @see Point#snapSizeX\n * @see Point#snapSizeY\n * @type Boolean\n * @name Line#snapToGrid\n * @default false\n */\n snapToGrid: false,\n\n /**\n * Defines together with {@link Point#snapSizeY} the grid the point snaps on to.\n * The point will only snap on integer multiples to snapSizeX in x and snapSizeY in y direction.\n * If this value is equal to or less than 0, it will use the grid displayed by the major ticks\n * of the default ticks of the default x axes of the board.\n *\n * @see Point#snapToGrid\n * @see Point#snapSizeY\n * @see JXG.Board#defaultAxes\n * @type Number\n * @name Line#snapSizeX\n * @default 1\n */\n snapSizeX: 1,\n\n /**\n * Defines together with {@link Point#snapSizeX} the grid the point snaps on to.\n * The point will only snap on integer multiples to snapSizeX in x and snapSizeY in y direction.\n * If this value is equal to or less than 0, it will use the grid displayed by the major ticks\n * of the default ticks of the default y axes of the board.\n *\n * @see Point#snapToGrid\n * @see Point#snapSizeX\n * @see JXG.Board#defaultAxes\n * @type Number\n * @name Line#snapSizeY\n * @default 1\n */\n snapSizeY: 1,\n\n /**\n * If set to true, {@link Line#firstArrow} is set to true and the point is visible,\n * the arrow head will just touch the circle line of the start point of the line.\n *\n * @see Line#firstArrow\n * @type Boolean\n * @name Line#touchFirstPoint\n * @default false\n */\n touchFirstPoint: false,\n\n /**\n * If set to true, {@link Line#lastArrow} is set to true and the point is visible,\n * the arrow head will just touch the circle line of the start point of the line.\n * @see Line#firstArrow\n * @type Boolean\n * @name Line#touchLastPoint\n * @default false\n */\n touchLastPoint: false,\n\n transitionProperties: []\n\n /**#@-*/\n },\n\n /* special options for locus curves */\n locus: {\n /**#@+\n * @visprop\n */\n\n translateToOrigin: false,\n translateTo10: false,\n stretch: false,\n toOrigin: null,\n to10: null\n /**#@-*/\n },\n\n /* special measurement options */\n measurement: {\n /**#@+\n * @visprop\n */\n\n /**\n * This specifies the unit of measurement in dimension 1 (e.g. length).\n * A power is automatically added to the string.\n * If you want to use different units for each dimension, see {@link Measurement#units}.\n *\n * @example\n * var p1 = board.create(\"point\", [0,1]),\n * p2 = board.create(\"point\", [3,1]),\n * c = board.create(\"circle\", [p1, p2]);\n *\n * board.create(\"measurement\", [-2, -3, [\"Perimeter\", c]], {\n * baseUnit: \" m\"\n * });\n * board.create(\"measurement\", [1, -3, [\"Area\", c]], {\n * baseUnit: \" m\"\n * });\n *\n * \n * \n *\n * @see Measurement#units\n * @name Measurement#baseUnit\n * @type String\n * @default ''\n */\n baseUnit: '',\n\n /**\n * This attribute expects an object that has the dimension numbers as keys (as integer or in the form of 'dimxx')\n * and assigns a string to each dimension.\n * If a dimension has no specification, {@link Measurement#baseUnit} is used.\n *\n * @example\n * var p1 = board.create(\"point\", [0,1]),\n * p2 = board.create(\"point\", [3,1]),\n * c = board.create(\"circle\", [p1, p2]);\n *\n * board.create(\"measurement\", [-3, -3, [\"Perimeter\", c]], {\n * baseUnit: \" m\",\n * units: {\n * 1: \" length unit\",\n * 2: \" area unit\"\n * },\n * });\n * board.create(\"measurement\", [1, -3, [\"Area\", c]], {\n * baseUnit: \" m\",\n * units: {\n * dim1: \" length unit\",\n * dim2: \" area unit\"\n * },\n * });\n *\n * \n * \n *\n * @see Measurement#baseUnit\n * @name Measurement#units\n * @type Object\n * @default {}\n */\n units: {},\n\n /**\n * Determines whether a prefix is displayed before the measurement value and unit.\n *\n * @see Measurement#prefix\n * @name Measurement#showPrefix\n * @type Boolean\n * @default true\n */\n showPrefix: true,\n\n /**\n * Determines whether a suffix is displayed after the measurement value and unit.\n *\n * @see Measurement#suffix\n * @name Measurement#showSuffix\n * @type Boolean\n * @default true\n */\n showSuffix: true,\n\n /**\n * String that is displayed before the measurement and its unit.\n *\n * @see Measurement#showPrefix\n * @name Measurement#prefix\n * @type String\n * @default ''\n */\n prefix: '',\n\n /**\n * String that is displayed after the measurement and its unit.\n *\n * @see Measurement#showSuffix\n * @name Measurement#suffix\n * @type String\n * @default ''\n */\n suffix: '',\n\n /**\n * Dimension of the measured data. This measurement can only be combined with a measurement of a suitable dimension.\n * Overwrites the dimension returned by the Dimension() method.\n * Normally, the default value null is used here to automatically determine the dimension.\n *\n * However, if the coordinates or a direction vector are measured, the value is usually returned as an array.\n * To tell the measurement that the function {@link Measurement#formatCoords} or {@link Measurement#formatDirection} should be used\n * to display the array properly, 'coords' or 'direction' must be specified here.\n *\n * @see Measurement#formatCoords\n * @see Measurement#formatDirection\n * @name Measurement#dim\n * @type Number|'coords'|'direction'\n * @default null\n */\n dim: null,\n\n /**\n * Function to format coordinates. Does only have an effect, if {@link Measurement#dim} is set to 'coords'.\n *\n * @example\n * var p = board.create(\"point\", [-2, 0]);\n *\n * board.create(\"measurement\", [0, -3, [\"Coords\", p]], {\n * dim: 'coords',\n * formatCoords: function (_,x,y,z) {\n * if (parseFloat(z) !== 1)\n * return 'Infinit coords';\n * else\n * return '(' + x + ' | ' + y + ')';\n * }\n * });\n *\n * \n * \n *\n * @see Measurement#dim\n * @name Measurement#formatCoords\n * @type Function\n * @param {Measurement} self Pointer to the measurement object itself\n * @param {Number} x c-coordinate\n * @param {Number} y c-coordinate\n * @param {Number} z c-coordinate\n * @returns String\n */\n formatCoords: function (self, x, y, z) {\n if (parseFloat(z) !== 1)\n return 'Infinit coords';\n else\n return '(' + x + ', ' + y + ')';\n },\n\n /**\n * Function to format direction vector. Does only have an effect, if {@link Measurement#dim} is set to 'direction'.\n *\n * @example\n * var p1 = board.create(\"point\", [0,1]),\n * p2 = board.create(\"point\", [3,1]),\n * s = board.create(\"segment\", [p1, p2]);\n *\n * board.create(\"measurement\", [0, -2, [\"Direction\", s]], {\n * dim: 'direction',\n * formatDirection: function (self,x,y) {\n * return '\\\\[\\\\frac{' + y + '}{' + x + '} = ' +\n * (!isFinite(y/x) ? '\\\\infty' : JXG.toFixed(y/x, self.visProp.digits)) +\n * '\\\\]';\n * },\n * useMathJax: true\n * });\n *\n * \n * \n * \n *\n * @name Measurement#formatDirection\n * @type Function\n * @param {Measurement} self Pointer to the measurement object itself\n * @param {Number} x c-coordinate\n * @param {Number} y c-coordinate\n * @returns String\n */\n formatDirection: function (self, x, y) {\n return '(' + x + ', ' + y + ')';\n }\n\n /**#@-*/\n },\n\n /* special metapost spline options */\n metapostspline: {\n /**#@+\n * @visprop\n */\n\n /**\n * Controls if the data points of the cardinal spline when given as\n * arrays should be converted into {@link JXG.Points}.\n *\n * @name createPoints\n * @memberOf Metapostspline.prototype\n *\n * @see Metapostspline#points\n *\n * @type Boolean\n * @default true\n */\n createPoints: true,\n\n /**\n * If set to true, the supplied coordinates are interpreted as\n * [[x_0, y_0], [x_1, y_1], p, ...].\n * Otherwise, if the data consists of two arrays of equal length,\n * it is interpreted as\n * [[x_o x_1, ..., x_n], [y_0, y_1, ..., y_n]]\n *\n * @name isArrayOfCoordinates\n * @memberOf Metapostspline.prototype\n * @type Boolean\n * @default true\n */\n isArrayOfCoordinates: true,\n\n /**\n * Attributes for the points generated by Metapost spline in cases\n * {@link createPoints} is set to true\n *\n * @name points\n * @memberOf Metapostspline.prototype\n *\n * @see Metapostspline#createPoints\n * @type Object\n */\n points: {\n strokeOpacity: 0.5,\n fillOpacity: 0.5,\n highlightStrokeOpacity: 1.0,\n highlightFillOpacity: 1.0,\n withLabel: false,\n name: '',\n fixed: false\n }\n\n /**#@-*/\n },\n\n /* special mirrorelement options */\n mirrorelement: {\n /**#@+\n * @visprop\n */\n\n fixed: true,\n\n /**\n * Attributes of mirror point, i.e. the point along which the element is mirrored.\n *\n * @type Point\n * @name mirrorelement#point\n */\n point: {},\n\n /**\n * Attributes of circle center, i.e. the center of the circle,\n * if a circle is the mirror element and the transformation type is 'Euclidean'\n *\n * @type Point\n * @name mirrorelement#center\n */\n center: {},\n\n /**\n * Type of transformation. Possible values are 'Euclidean', 'projective'.\n *\n * If the value is 'Euclidean', the mirror element of a circle is again a circle,\n * otherwise it is a conic section.\n *\n * @type String\n * @name mirrorelement#type\n * @default 'Euclidean'\n */\n type: 'Euclidean'\n\n /**#@-*/\n },\n\n /* special nonreflexangle options */\n nonreflexangle: {\n /**#@+\n * @visprop\n */\n\n /**#@-*/\n },\n\n // /* special options for Msector of 3 points */\n // msector: {\n // strokeColor: '#000000', // Msector line\n // point: { // Msector point\n // visible: false,\n // fixed: false,\n // withLabel: false,\n // name: ''\n // }\n // },\n\n /* special options for normal lines */\n normal: {\n /**#@+\n * @visprop\n */\n\n strokeColor: '#000000', // normal line\n\n /**\n * Attributes of helper point of normal.\n *\n * @type Point\n * @name Normal#point\n */\n point: {\n visible: false,\n fixed: false,\n withLabel: false,\n name: ''\n }\n /**#@-*/\n },\n\n /* special options for orthogonal projection points */\n orthogonalprojection: {\n /**#@+\n * @visprop\n */\n /**#@-*/\n },\n\n /* special otherintersection point options */\n otherintersection: {\n /**#@+\n * @visprop\n */\n\n /**\n * This flag sets the behavior of other intersection points of e.g.\n * a circle and a segment. If true, the intersection is treated as intersection with a line. If false\n * the intersection point exists if the segment intersects setwise.\n *\n * @name Otherintersection.alwaysIntersect\n * @type Boolean\n * @default true\n */\n alwaysIntersect: true,\n\n /**\n * Minimum distance (in user coordinates) for points to be defined as different.\n * For implicit curves and other non approximate curves this number might have to be\n * increased.\n *\n * @name Otherintersection.precision\n * @type Number\n * @default 0.001\n */\n precision: 0.001\n\n /**#@-*/\n },\n\n /* special options for parallel lines */\n parallel: {\n /**#@+\n * @visprop\n */\n\n strokeColor: '#000000', // Parallel line\n\n /**\n * Attributes of helper point of normal.\n *\n * @type Point\n * @name Parallel#point\n */\n point: {\n visible: false,\n fixed: false,\n withLabel: false,\n name: ''\n },\n\n label: {\n position: 'llft'\n }\n /**#@-*/\n },\n\n /* special parallelogram options */\n parallelogram: {\n parallelpoint: {\n withLabel: false,\n name: ''\n }\n },\n\n /* special parallelpoint options */\n parallelpoint: {\n },\n\n /* special perpendicular options */\n perpendicular: {\n /**#@+\n * @visprop\n */\n\n strokeColor: '#000000', // Perpendicular line\n straightFirst: true,\n straightLast: true\n /**#@-*/\n },\n\n /* special perpendicular options */\n perpendicularsegment: {\n /**#@+\n * @visprop\n */\n\n strokeColor: '#000000', // Perpendicular segment\n straightFirst: false,\n straightLast: false,\n point: { // Perpendicular point\n visible: false,\n fixed: true,\n withLabel: false,\n name: ''\n }\n /**#@-*/\n },\n\n /* special point options */\n point: {\n /**#@+\n * @visprop\n */\n\n withLabel: true,\n label: {},\n\n /**\n * This attribute was used to determined the point layout. It was derived from GEONExT and was\n * replaced by {@link Point#face} and {@link Point#size}.\n *\n * @name Point#style\n *\n * @see Point#face\n * @see Point#size\n * @type Number\n * @default 5\n * @deprecated\n */\n style: 5,\n\n /**\n * There are different point styles which differ in appearance.\n * Posssible values are\n * \n *
\n *\n * @name Point#face\n *\n * @type String\n * @see JXG.Point#setStyle\n * @default circle\n */\n face: 'o',\n\n /**\n * Size of a point, either in pixel or user coordinates.\n * Means radius resp. half the width of a point (depending on the face).\n *\n * @name Point#size\n *\n * @see Point#face\n * @see JXG.Point#setStyle\n * @see Point#sizeUnit\n * @type Number\n * @default 3\n */\n size: 3,\n\n /**\n * Unit for size.\n * Possible values are 'screen' and 'user.\n *\n * @name Point#sizeUnit\n *\n * @see Point#size\n * @type String\n * @default 'screen'\n */\n sizeUnit: 'screen',\n\n strokeWidth: 2,\n\n transitionProperties: ['fill', 'fill-opacity', 'stroke', 'stroke-opacity', 'stroke-width', 'width', 'height', 'rx', 'ry'],\n fillColor: Color.palette.red,\n strokeColor: Color.palette.red,\n highlightFillColor: '#c3d9ff',\n highlightStrokeColor: '#c3d9ff',\n // strokeOpacity: 1.0,\n // fillOpacity: 1.0,\n // highlightFillOpacity: 0.5,\n // highlightStrokeOpacity: 0.5,\n\n // fillColor: '#ff0000',\n // highlightFillColor: '#eeeeee',\n // strokeWidth: 2,\n // strokeColor: '#ff0000',\n // highlightStrokeColor: '#c3d9ff',\n\n /**\n * If true, the point size changes on zoom events.\n *\n * @type Boolean\n * @name Point#zoom\n * @default false\n *\n */\n zoom: false, // Change the point size on zoom\n\n /**\n * If true, the infobox is shown on mouse/pen over, if false not.\n * If the value is 'inherit', the value of\n * {@link JXG.Board#showInfobox} is taken.\n *\n * @name Point#showInfobox\n * @see JXG.Board#showInfobox\n * @type Boolean|String\n * @description true | false | 'inherit'\n * @default true\n */\n showInfobox: 'inherit',\n\n /**\n * Truncating rule for the digits in the infobox.\n * Input Output cross x circle o square, [] [] plus + minus - divide | diamond <> diamond2 <> (bigger) triangleup ^, a, A triangledown v triangleleft < triangleright > \n *
\n *\n * @name Point#infoboxDigits\n *\n * @type String| Number\n * @default 'auto'\n * @see JXG#autoDigits\n * @see JXG#toFixed\n */\n infoboxDigits: 'auto',\n\n // draft: false,\n\n /**\n * List of attractor elements. If the distance of the point is less than\n * attractorDistance the point is made to glider of this element.\n *\n * @name Point#attractors\n *\n * @type Array\n * @default empty\n */\n attractors: [],\n\n /**\n * Unit for attractorDistance and snatchDistance, used for magnetized points and for snapToPoints.\n * Possible values are 'screen' and 'user'.\n *\n * @name Point#attractorUnit\n *\n * @see Point#attractorDistance\n * @see Point#snatchDistance\n * @see Point#snapToPoints\n * @see Point#attractors\n * @type String\n * @default 'user'\n */\n attractorUnit: 'user', // 'screen', 'user'\n\n /**\n * If the distance of the point to one of its attractors is less\n * than this number the point will be a glider on this\n * attracting element.\n * If set to zero nothing happens.\n *\n * @name Point#attractorDistance\n *\n * @type Number\n * @default 0.0\n */\n attractorDistance: 0.0,\n\n /**\n * If the distance of the point to one of its attractors is at least\n * this number the point will be released from being a glider on the\n * attracting element.\n * If set to zero nothing happens.\n *\n * @name Point#snatchDistance\n *\n * @type Number\n * @default 0.0\n */\n snatchDistance: 0.0,\n\n /**\n * If set to true, the point will snap to a grid of integer multiples of\n * {@link Point#snapSizeX} and {@link Point#snapSizeY} (in user coordinates).\n * \n *\n */\n attractToGrid: false,\n\n /**\n * Defines together with {@link Point#snapSizeY} the grid the point snaps on to.\n * It is given in user coordinates, not in pixels.\n * The point will only snap on integer multiples to snapSizeX in x and snapSizeY in y direction.\n * If this value is equal to or less than 0, it will use the grid displayed by the major ticks\n * of the default ticks of the default x axes of the board.\n *\n * @name Point#snapSizeX\n *\n * @see Point#snapToGrid\n * @see Point#snapSizeY\n * @see JXG.Board#defaultAxes\n * @type Number\n * @default 1\n */\n snapSizeX: 1,\n\n /**\n * Defines together with {@link Point#snapSizeX} the grid the point snaps on to.\n * It is given in user coordinates, not in pixels.\n * The point will only snap on integer multiples to snapSizeX in x and snapSizeY in y direction.\n * If this value is equal to or less than 0, it will use the grid displayed by the major ticks\n * of the default ticks of the default y axes of the board.\n *\n * @name Point#snapSizeY\n *\n * @see Point#snapToGrid\n * @see Point#snapSizeX\n * @see JXG.Board#defaultAxes\n * @type Number\n * @default 1\n */\n snapSizeY: 1,\n\n /**\n * If set to true, the point will snap to the nearest point in distance of\n * {@link Point#attractorDistance}.\n *\n * @name Point#snapToPoints\n *\n * @see Point#attractorDistance\n * @type Boolean\n * @default false\n */\n snapToPoints: false,\n\n /**\n * List of elements which are ignored by snapToPoints.\n * @name Point#ignoredSnapToPoints\n *\n * @type Array\n * @default empty\n */\n ignoredSnapToPoints: []\n\n /**#@-*/\n },\n\n /* special polygon options */\n polygon: {\n /**#@+\n * @visprop\n */\n\n /**\n * If true, moving the mouse over inner points triggers hasPoint.\n *\n * @see JXG.GeometryElement#hasPoint\n * @name Polygon#hasInnerPoints\n * @type Boolean\n * @default false\n */\n hasInnerPoints: false,\n\n fillColor: Color.palette.yellow,\n highlightFillColor: Color.palette.yellow,\n // fillColor: '#00ff00',\n // highlightFillColor: '#00ff00',\n fillOpacity: 0.3,\n highlightFillOpacity: 0.2,\n\n /**\n * Is the polygon bordered by lines?\n *\n * @type Boolean\n * @name Polygon#withLines\n * @default true\n */\n withLines: true,\n\n /**\n * Attributes for the polygon border lines.\n *\n * @type Line\n * @name Polygon#borders\n */\n borders: {\n withLabel: false,\n strokeWidth: 1,\n highlightStrokeWidth: 1,\n // Polygon layer + 1\n layer: 5,\n label: {\n position: 'top'\n },\n visible: 'inherit'\n },\n\n /**\n * By default, the strokewidths of the borders of a polygon are not changed during highlighting (only strokeColor and strokeOpacity are changed\n * to highlightStrokeColor, and highlightStrokeOpacity).\n * However, strokewidth is changed to highlightStrokewidth if an individual border gets the focus.\n * \n * \n *\n */\n orientation: 'counterclockwise',\n\n /**\n * Attributes for sub-element arc. It is only available, if the sector is defined by three points.\n *\n * @type Arc\n * @name Sector#arc\n * @default '{visible:false}'\n */\n arc: {\n visible: false,\n fillColor: 'none',\n withLabel: false,\n name: '',\n\n orientation: 'inherit',\n\n center: {\n visible: false,\n withLabel: false,\n name: ''\n },\n\n radiusPoint: {\n visible: false,\n withLabel: false,\n name: ''\n },\n\n anglePoint: {\n visible: false,\n withLabel: false,\n name: ''\n }\n },\n\n /**\n * Attributes for helper point radiuspoint in case it is provided by coordinates.\n *\n * @type Point\n * @name Sector#radiusPoint\n */\n radiusPoint: {\n visible: false,\n withLabel: false\n },\n\n /**\n * Attributes for helper point center in case it is provided by coordinates.\n *\n * @type Point\n * @name Sector#center\n */\n center: {\n visible: false,\n withLabel: false\n },\n\n /**\n * Attributes for helper point anglepoint in case it is provided by coordinates.\n *\n * @type Point\n * @name Sector#anglePoint\n */\n anglePoint: {\n visible: false,\n withLabel: false\n },\n\n /**\n * Attributes for the sector label.\n *\n * @type Label\n * @name Sector#label\n */\n label: {\n offset: [0, 0],\n anchorX: 'auto',\n anchorY: 'auto'\n }\n\n /**#@-*/\n },\n\n /* special segment options */\n segment: {\n /**#@+\n * @visprop\n */\n\n label: {\n position: 'top'\n }\n /**#@-*/\n },\n\n semicircle: {\n /**#@+\n * @visprop\n */\n\n /**\n * Attributes for center point of the semicircle.\n *\n * @type Point\n * @name Semicircle#center\n */\n center: {\n visible: false,\n withLabel: false,\n fixed: false,\n fillColor: Color.palette.red,\n strokeColor: Color.palette.red,\n highlightFillColor: '#eeeeee',\n highlightStrokeColor: Color.palette.red,\n name: ''\n }\n\n /**#@-*/\n },\n\n /* special sketchcurve options */\n sketchcurve: {\n /**#@+\n * @visprop\n */\n\n visible: true,\n strokeColor: JXG.palette.red,\n highlight: false,\n strokeWidth: 1,\n lineCap: 'round',\n\n // Not yet implemented:\n // gradient: 'linear',\n // gradientSecondColor: 'rgba(255, 0, 0, 0)',\n\n /**\n * On up event immediately delete sketch curve\n * @type {number}\n * @name SketchCurve#deleteOnUp\n * @default false\n */\n deleteOnUp: false,\n\n /**\n * Set max number of points of a sketch curve. No limit if set to null.\n * @type {number}\n * @name SketchCurve#maxLength\n */\n maxLength: null\n\n /**#@-*/\n },\n\n /* special slider options */\n slider: {\n /**#@+\n * @visprop\n */\n\n /**\n * The slider only returns integer multiples of this value, e.g. for discrete values set this property to 1. For\n * continuous results set this to -1.\n *\n * @memberOf Slider.prototype\n * @name snapWidth\n * @type Number\n */\n snapWidth: -1, // -1 = deactivated\n\n /**\n * List of values to snap to. If the glider is within snapValueDistance\n * (in user coordinate units) of one of these points,\n * then the glider snaps to that point.\n *\n * @memberOf Slider.prototype\n * @name snapValues\n * @type Array\n * @see Slider#snapValueDistance\n * @default empty\n *\n * @example\n * var n = board.create('slider', [[-2, 3], [4, 3], [1, 5, 100]], {\n * name: 'n',\n * snapWidth: 1,\n * snapValues: [1, 22, 77, 100],\n * snapValueDistance: 5\n * });\n *\n * var k = board.create('slider', [[-2, -1], [4, -1], [-4, 0, 4]], {\n * name: 'k',\n * snapWidth: 0.1,\n * snapValues: [-3, -1, 1, 3],\n * snapValueDistance: 0.4\n * });\n *\n * \n * \n *\n */\n snapValues: [],\n\n /**\n * If the difference between the slider value and one of the elements of snapValues is less\n * than this number (in user coordinate units), the slider will snap to that value.\n *\n * @memberOf Slider.prototype\n * @name snapValueDistance\n * @type Number\n * @see Slider#snapValues\n * @default 0.0\n */\n snapValueDistance: 0.0,\n\n /**\n * The precision of the slider value displayed in the optional text.\n * Replaced by the attribute \"digits\".\n *\n * @memberOf Slider.prototype\n * @name precision\n * @type Number\n * @deprecated\n * @see Slider#digits\n * @default 2\n */\n precision: 2,\n\n /**\n * The number of digits of the slider value displayed in the optional text.\n *\n * @memberOf Slider.prototype\n * @name digits\n * @type Number\n * @default 2\n */\n digits: 2,\n\n /**\n * Internationalization support for slider labels.\n *\n * @name intl\n * @memberOf Slider.prototype\n * @type object\n * @default
\n * {\n * enabled: 'inherit',\n * options: {}\n * }\n * @see JXG.Board#intl\n * @see Text#intl\n *\n * @example\n * var s = board.create('slider', [[-2, 3], [2, 3], [0, 1, 360]], {\n * name: 'α',\n * snapWidth: 1,\n * intl: {\n * enabled: true,\n * options: {\n * style: 'unit',\n * unit: 'degree',\n * }\n * }\n * });\n *\n * \n *\n */\n intl: {\n enabled: 'inherit',\n options: {}\n },\n\n firstArrow: false,\n lastArrow: false,\n\n /**\n * Show slider ticks.\n *\n * @type Boolean\n * @name Slider#withTicks\n * @default true\n */\n withTicks: true,\n\n /**\n * Show slider label.\n *\n * @type Boolean\n * @name Slider#withLabel\n * @default true\n */\n withLabel: true,\n\n /**\n * If not null, this replaces the part \"name = \" in the slider label.\n * Possible types: string, number or function.\n * @type String\n * @name suffixLabel\n * @memberOf Slider.prototype\n * @default null\n * @see JXG.Slider#unitLabel\n * @see JXG.Slider#postLabel\n */\n suffixLabel: null,\n\n /**\n * If not null, this is appended to the value in the slider label.\n * Possible types: string, number or function.\n * @type String\n * @name unitLabel\n * @memberOf Slider.prototype\n * @default null\n * @see JXG.Slider#suffixLabel\n * @see JXG.Slider#postLabel\n */\n unitLabel: null,\n\n /**\n * If not null, this is appended to the value and to unitLabel in the slider label.\n * Possible types: string, number or function.\n * @type String\n * @name postLabel\n * @memberOf Slider.prototype\n * @default null\n * @see JXG.Slider#suffixLabel\n * @see JXG.Slider#unitLabel\n */\n postLabel: null,\n\n layer: 9,\n showInfobox: false,\n name: '',\n visible: true,\n strokeColor: '#000000',\n highlightStrokeColor: '#888888',\n fillColor: '#ffffff',\n highlightFillColor: 'none',\n\n /**\n * Size of slider point.\n *\n * @type Number\n * @name Slider#size\n * @default 6\n * @see Point#size\n */\n size: 6,\n\n /**\n * Attributes for first (left) helper point defining the slider position.\n *\n * @type Point\n * @name Slider#point1\n */\n point1: {\n needsRegularUpdate: false,\n showInfobox: false,\n withLabel: false,\n visible: false,\n fixed: true,\n frozen: 'inherit',\n name: ''\n },\n\n /**\n * Attributes for second (right) helper point defining the slider position.\n *\n * @type Point\n * @name Slider#point2\n */\n point2: {\n needsRegularUpdate: false,\n showInfobox: false,\n withLabel: false,\n visible: false,\n fixed: true,\n frozen: 'inherit',\n name: ''\n },\n\n /**\n * Attributes for the base line of the slider.\n *\n * @type Line\n * @name Slider#baseline\n */\n baseline: {\n needsRegularUpdate: false,\n visible: 'inherit',\n clip: 'inherit',\n fixed: true,\n scalable: false,\n tabindex: null,\n name: '',\n strokeWidth: 1,\n strokeColor: '#000000',\n highlightStrokeColor: '#888888'\n },\n\n /**\n * Attributes for the ticks of the base line of the slider.\n *\n * @type Ticks\n * @name Slider#ticks\n */\n ticks: {\n needsRegularUpdate: false,\n fixed: true,\n clip: 'inherit',\n\n // Label drawing\n drawLabels: false,\n digits: 2,\n includeBoundaries: true,\n drawZero: true,\n label: {\n offset: [-4, -14],\n display: 'internal'\n },\n\n minTicksDistance: 30,\n insertTicks: true,\n ticksDistance: 1, // Not necessary, since insertTicks = true\n minorHeight: 4, // if <0: full width and height\n majorHeight: 5, // if <0: full width and height\n minorTicks: 0,\n strokeOpacity: 1,\n strokeWidth: 1,\n tickEndings: [0, 1],\n majortickEndings: [0, 1],\n strokeColor: '#000000',\n visible: 'inherit'\n },\n\n /**\n * Attributes for the highlighting line of the slider.\n *\n * @type Line\n * @name Slider#highline\n */\n highline: {\n strokeWidth: 3,\n visible: 'inherit',\n clip: 'inherit',\n fixed: true,\n tabindex: null,\n name: '',\n strokeColor: '#000000',\n highlightStrokeColor: '#888888'\n },\n\n /**\n * Attributes for the slider label.\n *\n * @type Label\n * @name Slider#label\n */\n label: {\n visible: 'inherit',\n clip: 'inherit',\n strokeColor: '#000000'\n },\n\n /**\n * If true, 'up' events on the baseline will trigger slider moves.\n *\n * @type Boolean\n * @name Slider#moveOnUp\n * @default true\n */\n moveOnUp: true\n\n /**#@-*/\n },\n\n /* special vector field options */\n slopefield: {\n /**#@+\n * @visprop\n */\n\n strokeWidth: 0.5,\n highlightStrokeWidth: 0.5,\n highlightStrokeColor: Color.palette.blue,\n highlightStrokeOpacity: 0.8,\n\n /**\n * Set length of the vectors in user coordinates. This in contrast to vector fields, where this attribute just scales the vector.\n * @name scale\n * @memberOf Slopefield.prototype\n * @type {Number|Function}\n * @see Vectorfield.scale\n * @default 1\n */\n scale: 1,\n\n /**\n * Customize arrow heads of vectors. Be careful! If enabled this will slow down the performance.\n * Fields are:\n * \n *
\n * @name arrowhead\n * @memberOf Slopefield.prototype\n * @type {Object}\n * @default {enabled: false, size: 5, angle: Math.PI * 0.125}\n */\n arrowhead: {\n enabled: false,\n size: 5,\n angle: Math.PI * 0.125\n }\n\n /**#@-*/\n },\n\n /* special options for slope triangle */\n slopetriangle: {\n /**#@+\n * @visprop\n */\n\n fillColor: Color.palette.red,\n fillOpacity: 0.4,\n highlightFillColor: Color.palette.red,\n highlightFillOpacity: 0.3,\n\n borders: {\n lastArrow: {\n type: 1,\n size: 6\n }\n },\n\n /**\n * Attributes for the gliding helper point.\n *\n * @type Point\n * @name Slopetriangle#glider\n */\n glider: {\n fixed: true,\n visible: false,\n withLabel: false\n },\n\n /**\n * Attributes for the base line.\n *\n * @type Line\n * @name Slopetriangle#baseline\n */\n baseline: {\n visible: false,\n withLabel: false,\n name: ''\n },\n\n /**\n * Attributes for the base point.\n *\n * @type Point\n * @name Slopetriangle#basepoint\n */\n basepoint: {\n visible: false,\n withLabel: false,\n name: ''\n },\n\n /**\n * Attributes for the tangent.\n * The tangent is constructed by slop triangle if the construction\n * is based on a glider, solely.\n *\n * @type Line\n * @name Slopetriangle#tangent\n */\n tangent: {\n visible: false,\n withLabel: false,\n name: ''\n },\n\n /**\n * Attributes for the top point.\n *\n * @type Point\n * @name Slopetriangle#toppoint\n */\n toppoint: {\n visible: false,\n withLabel: false,\n name: ''\n },\n\n /**\n * Attributes for the slope triangle label.\n *\n * @type Label\n * @name Slopetriangle#label\n */\n label: {\n visible: true,\n position: 'first',\n\n digits: function (self) {\n return self.slopetriangle.evalVisProp('digits');\n },\n showPrefix: function (self) {\n return self.slopetriangle.evalVisProp('showPrefix');\n },\n showSuffix: function (self) {\n return self.slopetriangle.evalVisProp('showSuffix');\n },\n prefix: function (self) {\n return self.slopetriangle.evalVisProp('prefix');\n },\n suffix: function (self) {\n return self.slopetriangle.evalVisProp('suffix');\n }\n },\n\n /**\n * Used to round texts given by a number.\n *\n * @memberOf Slopetriangle.prototype\n * @name digits\n * @type Number\n * @default 2\n */\n digits: 2,\n\n /**\n * Determines whether a prefix is displayed before the slope triangle value and unit.\n *\n * @see Slopetriangle#prefix\n * @name Slopetriangle#showPrefix\n * @type Boolean\n * @default false\n */\n showPrefix: true,\n\n /**\n * Determines whether a suffix is displayed after the slope triangle value and unit.\n *\n * @see Slopetriangle#suffix\n * @name Slopetriangle#showSuffix\n * @type Boolean\n * @default false\n */\n showSuffix: true,\n\n /**\n * String that is displayed before the slope triangle and its unit.\n *\n * @see Slopetriangle#showPrefix\n * @name Slopetriangle#prefix\n * @type String\n * @default ''\n */\n prefix: '',\n\n /**\n * String that is displayed after the slope triangle and its unit.\n *\n * @see Slopetriangle#showSuffix\n * @name Slopetriangle#suffix\n * @type String\n * @default ''\n */\n suffix: '',\n\n /**\n * Function to format the value.\n * If set to null, no formatting will happen.\n *\n * @name Slopetriangle#formatValue\n * @type Function\n * @param {Slopetriangle} self Pointer to the slopetriangle object itself\n * @param {Number} val value\n * @returns String\n * @default null\n */\n formatValue: null\n\n /**#@-*/\n },\n\n /* special general options for smartlabel */\n smartlabel: {\n /**#@+\n * @visprop\n */\n\n /**\n * CSS classes for the smart label. Available classes are:\n * \n *
\n *\n * By default, an additional class is given specific for the element type.\n * Available classes are 'smart-label-angle', 'smart-label-circle',\n * 'smart-label-line', 'smart-label-point', 'smart-label-polygon'.\n *\n * @example\n * cssClass: 'smart-label-solid smart-label-point'\n *\n * @type String\n * @name Smartlabel#cssClass\n * @see Smartlabel#highlightCssClass\n * @default \n *
\n */\n cssClass: 'smart-label-solid',\n\n /**\n * CSS classes for the smart label when highlighted.\n *\n * @type String\n * @name Smartlabel#highlightCssClass\n * @see Smartlabel#cssClass\n * @default \n *
\n */\n highlightCssClass: 'smart-label-solid',\n\n /**\n * Measurement unit appended to the output text. For areas, the unit is squared automatically.\n * Replaced by the attributes \"baseUnit\" and \"units\".\n *\n * @type {String|Function}\n * @name Smartlabel#unit\n * @default ''\n * @see Smartlabel#baseUnit\n * @see Smartlabel#units\n * @deprecated\n */\n unit: '',\n\n /**\n * This specifies the unit of measurement in dimension 1 (e.g. length).\n * A power is automatically added to the string.\n * If you want to use different units for each dimension, see {@link Smartlabel#units}.\n *\n * @see Smartlabel#units\n * @name Smartlabel#baseUnit\n * @type String\n * @default ''\n */\n baseUnit: '',\n\n /**\n * This attribute expects an object that has the dimension numbers as keys (as integer or in the form of 'dimxx')\n * and assigns a string to each dimension.\n * If a dimension has no specification, {@link Smartlabel#baseUnit} is used.\n *\n * @see Smartlabel#baseUnit\n * @name Smartlabel#units\n * @type Object\n * @default {}\n */\n units: {},\n\n /**\n * Determines whether a prefix is displayed before the measurement value and unit.\n *\n * @see Smartlabel#prefix\n * @name Smartlabel#showPrefix\n * @type Boolean\n * @default true\n */\n showPrefix: true,\n\n /**\n * Determines whether a suffix is displayed after the measurement value and unit.\n *\n * @see Smartlabel#suffix\n * @name Smartlabel#showSuffix\n * @type Boolean\n * @default true\n */\n showSuffix: true,\n /**\n * Prefix text for the smartlabel. Comes before the measurement value.\n *\n * @type {String|Function}\n * @name Smartlabel#prefix\n * @default ''\n */\n prefix: '',\n\n /**\n * Suffix text for the smartlabel. Comes after unit.\n *\n * @type {String|Function}\n * @name Smartlabel#suffix\n * @default ''\n */\n suffix: '',\n\n /**\n * Function to format the value.\n * If set to null, no formatting will happen.\n *\n * @name Smartlabel#formatValue\n * @type Function\n * @param {Smartlabel} self Pointer to the smartlabel object itself\n * @param {Number|Array} val value (array, if coords)\n * @returns String\n * @default null\n */\n formatValue: null,\n\n /**\n * Type of measurement.\n * Available values are:\n * \n *
\n * Dependent on this value, i.e. the type of measurement, the label is\n * positioned differently on the object.\n *\n * @type String\n * @name Smartlabel#measure\n * @default \n *
\n */\n measure: '',\n\n useMathJax: true\n\n /**#@-*/\n },\n\n /* special options for smartlabel of angle */\n smartlabelangle: {\n cssClass: 'smart-label-solid smart-label-angle',\n highlightCssClass:'smart-label-solid smart-label-angle',\n anchorX: 'left',\n anchorY: 'middle'\n },\n\n /* special options for smartlabel of circle */\n smartlabelcircle: {\n cssClass: 'smart-label-solid smart-label-circle',\n highlightCssClass:'smart-label-solid smart-label-circle',\n anchorX: 'middle',\n\n measure: 'radius',\n\n visibleThreshold: 0.6\n },\n\n /* special options for smartlabel of line */\n smartlabelline: {\n /**#@+\n * @visprop\n */\n\n cssClass: 'smart-label-solid smart-label-line',\n highlightCssClass:'smart-label-solid smart-label-line',\n anchorX: 'middle',\n\n measure: 'length',\n\n /**\n * Orientation of the smartlabel relative to the line.\n * Available values are:\n * \n *
\n * Dependent on this value the label is positioned differently on the line.\n *\n * @type String\n * @name Smartlabel#orientation\n * @default 'parallel'\n */\n orientation: 'parallel',\n\n /**\n * Smartlabels of circles and lines are hidden automatically, if there is not enough space.\n * This value (between 0 and 1) controls, how much percent of the line length or circle diameter\n * the label is allowed to take place\n *\n * @type String\n * @name Smartlabel#visibleThreshold\n * @default \n *
\n */\n visibleThreshold: 0.7\n\n /**#@-*/\n },\n\n /* special options for smartlabel of point */\n smartlabelpoint: {\n /**#@+\n * @visprop\n */\n\n cssClass: 'smart-label-solid smart-label-point',\n highlightCssClass:'smart-label-solid smart-label-point',\n anchorX: 'middle',\n anchorY: 'top',\n\n measure: 'coords',\n /**\n * Display of point coordinates either as row vector or column vector.\n * Available values are 'row' or 'column'.\n * @type String\n * @name Smartlabel#dir\n * @default 'row'\n */\n dir: 'row'\n\n /**#@-*/\n },\n\n /* special options for smartlabel of polygon */\n smartlabelpolygon: {\n cssClass: 'smart-label-solid smart-label-polygon',\n highlightCssClass:'smart-label-solid smart-label-polygon',\n anchorX: 'middle',\n\n measure: 'area'\n },\n\n /* special options for step functions */\n stepfunction: {\n /**#@+\n * @visprop\n */\n\n /**#@-*/\n },\n\n /* special tangent options */\n tangent: {\n },\n\n /* special tangent options */\n tangentto: {\n /**#@+\n * @visprop\n */\n\n /**\n * Attributes for the polar line of the tangentto construction.\n *\n * @name polar\n * @memberOf TangentTo.prototype\n * @type JXG.Line\n */\n polar: {\n visible: false,\n strokeWidth: 1,\n dash: 3\n },\n\n /**\n * Attributes for the intersection point of the conic/circle with the polar line of the tangentto construction.\n *\n * @name point\n * @memberOf TangentTo.prototype\n * @type JXG.Point\n */\n point: {\n visible: false\n }\n\n /**#@-*/\n },\n\n /* special tape measure options */\n tapemeasure: {\n /**#@+\n * @visprop\n */\n\n strokeColor: '#000000',\n strokeWidth: 2,\n highlightStrokeColor: '#000000',\n\n /**\n * Show tape measure ticks.\n *\n * @type Boolean\n * @name Tapemeasure#withTicks\n * @default true\n */\n withTicks: true,\n\n /**\n * Show tape measure label.\n *\n * @type Boolean\n * @name Tapemeasure#withLabel\n * @default true\n */\n withLabel: true,\n\n /**\n * Text rotation in degrees.\n *\n * @name Tapemeasure#rotate\n * @type Number\n * @default 0\n */\n rotate: 0,\n\n /**\n * The precision of the tape measure value displayed in the optional text.\n * Replaced by the attribute digits\n *\n * @memberOf Tapemeasure.prototype\n * @name precision\n * @type Number\n * @deprecated\n * @see Tapemeasure#digits\n * @default 2\n */\n precision: 2,\n\n /**\n * The precision of the tape measure value displayed in the optional text.\n * @memberOf Tapemeasure.prototype\n * @name digits\n * @type Number\n * @default 2\n */\n digits: 2,\n\n /**\n * Attributes for first helper point defining the tape measure position.\n *\n * @type Point\n * @name Tapemeasure#point1\n */\n point1: {\n visible: true,\n strokeColor: '#000000',\n fillColor: '#ffffff',\n fillOpacity: 0.0,\n highlightFillOpacity: 0.1,\n size: 6,\n snapToPoints: true,\n attractorUnit: 'screen',\n attractorDistance: 20,\n showInfobox: false,\n withLabel: false,\n name: ''\n },\n\n /**\n * Attributes for second helper point defining the tape measure position.\n *\n * @type Point\n * @name Tapemeasure#point2\n */\n point2: {\n visible: true,\n strokeColor: '#000000',\n fillColor: '#ffffff',\n fillOpacity: 0.0,\n highlightFillOpacity: 0.1,\n size: 6,\n snapToPoints: true,\n attractorUnit: 'screen',\n attractorDistance: 20,\n showInfobox: false,\n withLabel: false,\n name: ''\n },\n\n /**\n * Attributes for the ticks of the tape measure.\n *\n * @type Ticks\n * @name Tapemeasure#ticks\n */\n ticks: {\n drawLabels: false,\n drawZero: true,\n insertTicks: true,\n ticksDistance: 0.1, // Ignored, since insertTicks=true\n minorHeight: 8,\n majorHeight: 16,\n minorTicks: 4,\n tickEndings: [0, 1],\n majorTickEndings: [0, 1],\n strokeOpacity: 1,\n strokeWidth: 1,\n strokeColor: '#000000',\n visible: 'inherit',\n label: {\n anchorY: 'top',\n anchorX: 'middle',\n offset: [0, -10]\n }\n },\n\n /**\n * Attributes for the tape measure label.\n *\n * @type Label\n * @name Tapemeasure#label\n */\n label: {\n position: 'top'\n }\n /**#@-*/\n },\n\n /* special text options */\n text: {\n /**#@+\n * @visprop\n */\n\n /**\n * The font size in pixels.\n *\n * @name fontSize\n * @memberOf Text.prototype\n * @default 12\n * @type Number\n * @see Text#fontUnit\n */\n fontSize: 12,\n\n /**\n * CSS unit for the font size of a text element. Usually, this will be the default value 'px' but\n * for responsive application, also 'vw', 'vh', vmax', 'vmin' or 'rem' might be useful.\n *\n * @name fontUnit\n * @memberOf Text.prototype\n * @default 'px'\n * @type String\n * @see Text#fontSize\n *\n * @example\n * var txt = board.create('text', [2, 2, \"hello\"], {fontSize: 8, fontUnit: 'vmin'});\n *\n * \n * \n *\n */\n fontUnit: 'px',\n\n /**\n * If the text content is solely a number and\n * this attribute is true (default) then the number is either formatted\n * according to the number of digits\n * given by the attribute 'digits' or converted into a fraction if 'toFraction'\n * is true.\n *
\n * {\n * enabled: 'inherit',\n * options: {\n * minimumFractionDigits: 0,\n * maximumFractionDigits: 2\n * }\n * }\n * @see JXG.Board#intl\n *\n * @example\n * var t = board.create('text', [1, 2, -Math.PI*100], {\n * formatNumber: true,\n * digits: 2,\n * intl: {\n * enabled: true,\n * options: {\n * style: 'unit',\n * unit: 'celsius'\n * }\n * }\n * });\n *\n * \n *\n *\n * @example\n * var t = board.create('text', [0.05, -0.2, ''], {\n * intl: {\n * enabled: true,\n * locale: 'it-IT',\n * options: {\n * style: 'unit',\n * unit: 'kilometer-per-hour',\n * unitDisplay: 'narrow',\n * maximumFractionDigits: 2\n * }\n * }\n * });\n *\n * // Set dynamic text consisting of text and number.\n * t.setText(function() {\n * var txt = 'Speed: ',\n * number = t.X();\n *\n * // Add formatted number to variable txt\n * // with fallback if locale is not supported.\n * if (t.useLocale()) {\n * txt += t.formatNumberLocale(number);\n * } else {\n * txt += JXG.toFixed(number, 2);\n * }\n * return txt;\n * });\n *\n * \n * \n *\n */\n intl: {\n enabled: 'inherit',\n options: {\n minimumFractionDigits: 0,\n maximumFractionDigits: 2\n }\n },\n\n /**\n * If set to true, the text is parsed and evaluated.\n * For labels parse==true results in converting names of the form k_a to subscripts.\n * If the text is given by string and parse==true, the string is parsed as\n * JessieCode expression.\n *\n * @name parse\n * @memberOf Text.prototype\n * @default true\n * @type Boolean\n */\n parse: true,\n\n /**\n * If set to true and caja's sanitizeHTML function can be found it\n * will be used to sanitize text output.\n *\n * @name useCaja\n * @memberOf Text.prototype\n * @default false\n * @type Boolean\n */\n useCaja: false,\n\n /**\n * If enabled, the text will be handled as label. Intended for internal use.\n *\n * @name isLabel\n * @memberOf Text.prototype\n * @default false\n * @type Boolean\n */\n isLabel: false,\n\n strokeColor: '#000000',\n highlightStrokeColor: '#000000',\n highlightStrokeOpacity: 0.666666,\n\n /**\n * Default CSS properties of the HTML text element.\n * \n * \n * \n * \n * \n *
\n * @example\n * If all texts should get its font-family from the default CSS class\n * before initializing the board\n * \n * JXG.Options.text.cssDefaultStyle = '';\n * JXG.Options.text.highlightCssDefaultStyle = '';\n *
\n * should be called.\n *\n * @name cssDefaultStyle\n * @memberOf Text.prototype\n * @default 'font-family: Arial, Helvetica, Geneva, sans-serif;'\n * @type String\n * @see Text#highlightCssDefaultStyle\n * @see Text#cssStyle\n * @see Text#highlightCssStyle\n */\n cssDefaultStyle: 'font-family: Arial, Helvetica, Geneva, sans-serif;',\n\n /**\n * Default CSS properties of the HTML text element in case of highlighting.\n * \n * JXG.Options.text.cssDefaultStyle = '';\n * JXG.Options.text.highlightCssDefaultStyle = '';\n *
\n * should be called.\n *\n * @name highlightCssDefaultStyle\n * @memberOf Text.prototype\n * @default 'font-family: Arial, Helvetica, Geneva, sans-serif;'\n * @type String\n * @see Text#cssDefaultStyle\n * @see Text#cssStyle\n * @see Text#highlightCssStyle\n */\n highlightCssDefaultStyle: 'font-family: Arial, Helvetica, Geneva, sans-serif;',\n\n /**\n * CSS properties of the HTML text element.\n * \n *\n *\n * @example\n * // Load MathJax:\n * // <script src=\"https://cdn.jsdelivr.net/npm/mathjax@4/tex-svg.js\"></script>\n *\n * // function and its derivative\n * var f1 = function(x) { return x * x * x; },\n * graph1 = board.create('functiongraph', [f1, -0.1, 1.1]),\n *\n * A = board.create('glider', [0.5, f1(0.5), graph1], {\n * name: 'f(x)',\n * color: 'black',\n * face:'x',\n * fixed: true,\n * size: 3,\n * label: {offset: [-30, 10], fontSize: 15}\n * }),\n * B = board.create('glider', [0.7, f1(0.7), graph1], {\n * name: 'f(x+Δx)',\n * size: 3,\n * label: {offset: [-60, 10], fontSize: 15}\n * }),\n *\n * secant_line = board.create('line', [A,B],{dash: 1, color: 'green'}),\n * a_h_segment = board.create('segment', [A, [\n * function(){ return B.X() > A.X() ? B.X() : A.X()},\n * function(){ return B.X() > A.X() ? A.Y() : B.Y()}\n * ]],{ name: 'Δx', dash: 1, color: 'black'}),\n *\n * b_v_segment = board.create('segment', [B, [\n * function(){ return B.X() > A.X() ? B.X() : A.X()},\n * function(){ return B.X() > A.X() ? A.Y() : B.Y()}\n * ]],{ name: 'Δy', dash: 1, color: 'black'}),\n *\n * ma = board.create('midpoint', [a_h_segment.point1, a_h_segment.point2], {visible: false});\n *\n * board.create('text', [0, 0, function() {return '\\\\[\\\\Delta_x='+(B.X()-A.X()).toFixed(4)+'\\\\]'}], {\n * anchor: ma, parse: false, useMathJax: true, fixed: true, color: 'green', anchorY: 'top'\n * });\n *\n * var mb = board.create('midpoint', [b_v_segment.point1, b_v_segment.point2], {visible: false});\n *\n * board.create('text', [0, 0, function() {return '\\\\[\\\\Delta_y='+(B.Y()-A.Y()).toFixed(4)+'\\\\]'}], {\n * anchor: mb, parse: false, useMathJax: true, fixed: true, color: 'green'\n * });\n *\n * var dval = board.create('text',[0.1, 0.8,\n * function(){\n * return '\\\\[\\\\frac{\\\\Delta_y}{\\\\Delta_x}=\\\\frac{' + ((B.Y()-A.Y()).toFixed(4)) + '}{' + ((B.X()-A.X()).toFixed(4)) +\n * '}=' + (((B.Y()-A.Y()).toFixed(4))/((B.X()-A.X()).toFixed(4))).toFixed(4) + '\\\\]';\n * }],{fontSize: 15, useMathJax: true});\n *\n * \n * \n * \n *\n * @example\n * var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 10, 11, -2], axis: true});\n * board.options.text.useMathjax = true;\n *\n * var a = board.create('slider',[[-0.7,1.5],[5,1.5],[0,0.5,1]], {\n * suffixlabel:'\\\\(t_1=\\\\)',\n * unitLabel: ' \\\\(\\\\text{ ms}\\\\)',\n * snapWidth:0.01}),\n *\n * func = board.create('functiongraph',[function(x){return (a.Value()*x*x)}], {strokeColor: \"red\"}),\n * text1 = board.create('text', [5, 1, function(){\n * return '\\\\(a(t)= { 1 \\\\over ' + a.Value().toFixed(3) + '}\\\\)';\n * }], {fontSize: 15, fixed:true, strokeColor:'red', anchorY: 'top', parse: false});\n *\n * \n * \n *\n */\n useMathJax: false,\n\n /**\n *\n * If true, KaTeX will be used to render the input string.\n * For this feature, katex.min.js and katex.min.css have to be included.\n *
\n * \n * \n * \n * \n */\n useKatex: false,\n\n /**\n * Object or function returning an object that contains macros for KaTeX.\n *\n * @name katexMacros\n * @memberOf Text.prototype\n * @default {}\n * @type Object\n *\n * @example\n * // to globally apply macros to all text elements use:\n * JXG.Options.text.katexMacros = {'\\\\jxg': 'JSXGraph is awesome'};\n *\n * const board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-2, 5, 8, -5], axis:true\n * });\n *\n * // This macro only get applied to the p ('text') element\n * var p = board.create('text', [1, 0, '\\\\jsg \\\\sR '], { katexMacros: {'\\\\sR':'\\\\mathbb{R}'} });\n */\n katexMacros: {},\n\n /**\n * Display number as integer + nominator / denominator. Needs also the setting formatNumber: true\n * Works together with MathJax, KaTex or as plain text.\n * @name toFraction\n * @memberOf Text.prototype\n * @type Boolean\n * @default false\n * @see Text#formatNumber\n *\n * @example\n * board.create('text', [2, 2, 2 / 7], { anchorY: 'top', fontSize: 24, toFraction: true, formatNumber: true, useMathjax: true });\n * board.create('text', [2, -2, 2 / 19], { toFraction: true, formatNumber: true, useMathjax: false });\n *\n * \n * \n *\n */\n toFraction: false,\n\n /**\n * Determines the rendering method of the text. Possible values\n * include 'html' and 'internal'.\n *\n * @name display\n * @memberOf Text.prototype\n * @default 'html'\n * @type String\n */\n display: 'html',\n\n /**\n * Anchor element {@link Point}, {@link Text} or {@link Image} of the text.\n * If it exists, the coordinates of the text are relative\n * to this anchor element. In this case, only numbers are possible coordinates,\n * functions are not supported.\n *\n * @name anchor\n * @memberOf Text.prototype\n * @default null\n * @type Object\n *\n * @example\n * var p = board.create('point', [0,1]);\n * board.create('text', [1, 0, 'message'], {anchor:p});\n *\n * \n * \n *\n */\n anchor: null,\n\n /**\n * The horizontal alignment of the text. Possible values include 'auto', 'left',\n * 'middle', and 'right'.\n *\n * @name anchorX\n * @memberOf Text.prototype\n * @default 'left'\n * @type String\n */\n anchorX: 'left',\n\n /**\n * The vertical alignment of the text. Possible values include 'auto, 'top', 'middle', and\n * 'bottom'.\n * For MathJax or KaTeX, 'top' is recommended.\n *\n * @name anchorY\n * @memberOf Text.prototype\n * @default 'middle'\n * @type String\n */\n anchorY: 'middle',\n\n /**\n * Apply CSS classes to the text in non-highlighted view. It is possible to supply one or more\n * CSS classes separated by blanks.\n *\n * @name cssClass\n * @memberOf Text.prototype\n * @type String\n * @default 'JXGtext'\n * @see Text#highlightCssClass\n * @see Image#cssClass\n * @see JXG.GeometryElement#cssClass\n */\n cssClass: 'JXGtext',\n\n /**\n * Apply CSS classes to the text in highlighted view. It is possible to supply one or more\n * CSS classes separated by blanks.\n *\n * @name highlightCssClass\n * @memberOf Text.prototype\n * @type String\n * @default 'JXGtext'\n * @see Text#cssClass\n * @see Image#highlightCssClass\n * @see JXG.GeometryElement#highlightCssClass\n */\n highlightCssClass: 'JXGtext',\n\n /**\n * Sensitive area for dragging the text.\n * Possible values are 'all', or something else.\n * If set to 'small', a sensitivity margin at the right and left border is taken.\n * This may be extended to left, right, ... in the future.\n *\n * @name Text#dragArea\n * @type String\n * @default 'all'\n */\n dragArea: 'all',\n\n withLabel: false,\n\n /**\n * Text rotation in degrees.\n * Works for non-zero values only in combination with display=='internal'.\n *\n * @name Text#rotate\n * @type Number\n * @default 0\n */\n rotate: 0,\n\n /**\n * @name Text#visible\n * @type Boolean\n * @default true\n */\n visible: true,\n\n /**\n * Defines together with {@link Text#snapSizeY} the grid the text snaps on to.\n * The text will only snap on integer multiples to snapSizeX in x and snapSizeY in y direction.\n * If this value is equal to or less than 0, it will use the grid displayed by the major ticks\n * of the default ticks of the default x axes of the board.\n *\n * @name snapSizeX\n * @memberOf Text.prototype\n *\n * @see Point#snapToGrid\n * @see Text#snapSizeY\n * @see JXG.Board#defaultAxes\n * @type Number\n * @default 1\n */\n snapSizeX: 1,\n\n /**\n * Defines together with {@link Text#snapSizeX} the grid the text snaps on to.\n * The text will only snap on integer multiples to snapSizeX in x and snapSizeY in y direction.\n * If this value is equal to or less than 0, it will use the grid displayed by the major ticks\n * of the default ticks of the default y axes of the board.\n *\n * @name snapSizeY\n * @memberOf Text.prototype\n *\n * @see Point#snapToGrid\n * @see Text#snapSizeX\n * @see JXG.Board#defaultAxes\n * @type Number\n * @default 1\n */\n snapSizeY: 1,\n\n /**\n * List of attractor elements. If the distance of the text is less than\n * attractorDistance the text is made to glider of this element.\n *\n * @name attractors\n * @memberOf Text.prototype\n * @type Array\n * @default empty\n */\n attractors: []\n\n /**#@-*/\n },\n\n /* special options for trace curves */\n tracecurve: {\n /**#@+\n * @visprop\n */\n strokeColor: '#000000',\n fillColor: 'none',\n\n /**\n * The number of evaluated data points.\n * @memberOf Tracecurve.prototype\n * @default 100\n * @name numberPoints\n * @type Number\n */\n numberPoints: 100\n\n /**#@-*/\n },\n\n /* special turtle options */\n turtle: {\n /**#@+\n * @visprop\n */\n\n strokeWidth: 1,\n fillColor: 'none',\n strokeColor: '#000000',\n\n /**\n * Attributes for the turtle arrow.\n *\n * @type Curve\n * @name Turtle#arrow\n */\n arrow: {\n strokeWidth: 2,\n withLabel: false,\n strokeColor: Color.palette.red,\n lastArrow: true\n }\n /**#@-*/\n },\n\n /* special vector field options */\n vectorfield: {\n /**#@+\n * @visprop\n */\n\n strokeWidth: 0.5,\n highlightStrokeWidth: 0.5,\n highlightStrokeColor: Color.palette.blue,\n highlightStrokeOpacity: 0.8,\n\n /**\n * Scaling factor of the vectors. This in contrast to slope fields, where this attribute sets the vector to the given length.\n * @name scale\n * @memberOf Vectorfield.prototype\n * @type {Number|Function}\n * @see Slopefield.scale\n * @default 1\n */\n scale: 1,\n\n /**\n * Customize arrow heads of vectors. Be careful! If enabled this will slow down the performance.\n * Fields are:\n * \n *
\n * @name arrowhead\n * @memberOf Vectorfield.prototype\n * @type {Object}\n * @default {enabled: true, size: 5, angle: Math.PI * 0.125}\n */\n arrowhead: {\n enabled: true,\n size: 5,\n angle: Math.PI * 0.125\n }\n\n /**#@-*/\n },\n\n /**\n * Abbreviations of attributes. Setting the shortcut means setting abbreviated properties\n * to the same value.\n * It is used in {@link JXG.GeometryElement#setAttribute} and in\n * the constructor {@link JXG.GeometryElement}.\n * Attention: In Options.js abbreviations are not allowed.\n * @type Object\n * @name JXG.Options#shortcuts\n *\n */\n shortcuts: {\n color: ['strokeColor', 'fillColor'],\n opacity: ['strokeOpacity', 'fillOpacity'],\n highlightColor: ['highlightStrokeColor', 'highlightFillColor'],\n highlightOpacity: ['highlightStrokeOpacity', 'highlightFillOpacity'],\n strokeWidth: ['strokeWidth', 'highlightStrokeWidth']\n }\n};\n\n /**\n * Holds all possible properties and the according validators for geometry elements.\n * A validator is either a function\n * which takes one parameter and returns true, if the value is valid for the property,\n * or it is false if no validator is required.\n */\n JXG.Validator = (function () {\n var i,\n validatePixel = function (v) {\n return (/^[0-9]+px$/).test(v);\n },\n validateDisplay = function (v) {\n return (v === 'html' || v === 'internal');\n },\n validateColor = function (v) {\n // for now this should do it...\n return Type.isString(v);\n },\n validatePointFace = function (v) {\n return Type.exists(JXG.normalizePointFace(v));\n },\n validateNumber = function (v) {\n return Type.isNumber(v, true, false);\n },\n validateInteger = function (v) {\n return (Math.abs(v - Math.round(v)) < Mat.eps);\n },\n validateNotNegativeInteger = function (v) {\n return validateInteger(v) && v >= 0;\n },\n validatePositiveInteger = function (v) {\n return validateInteger(v) && v > 0;\n },\n // validateScreenCoords = function (v) {\n // return v.length >= 2 && validateInteger(v[0]) && validateInteger(v[1]);\n // },\n validateRenderer = function (v) {\n return (v === 'vml' || v === 'svg' || v === 'canvas' || v === 'no');\n },\n validatePositive = function (v) {\n return v > 0;\n },\n validateNotNegative = function (v) {\n return v >= 0;\n },\n v = {},\n validators = {\n attractorDistance: validateNotNegative,\n color: validateColor,\n // defaultDistance: validateNumber,\n display: validateDisplay,\n doAdvancedPlot: false,\n draft: false,\n drawLabels: false,\n drawZero: false,\n face: validatePointFace,\n factor: validateNumber,\n fillColor: validateColor,\n fillOpacity: validateNumber,\n firstArrow: false,\n fontSize: validateInteger,\n dash: validateInteger,\n gridX: validateNumber,\n gridY: validateNumber,\n // POI: Do we have to add something here?\n hasGrid: false,\n highlightFillColor: validateColor,\n highlightFillOpacity: validateNumber,\n highlightStrokeColor: validateColor,\n highlightStrokeOpacity: validateNumber,\n insertTicks: false,\n //: validateScreenCoords,\n lastArrow: false,\n layer: validateNotNegativeInteger,\n majorHeight: validateInteger,\n minorHeight: validateInteger,\n minorTicks: validateNotNegative,\n minTicksDistance: validatePositiveInteger,\n numberPointsHigh: validatePositiveInteger,\n numberPointsLow: validatePositiveInteger,\n opacity: validateNumber,\n radius: validateNumber,\n RDPsmoothing: false,\n renderer: validateRenderer,\n right: validatePixel,\n showCopyright: false,\n showInfobox: false,\n showNavigation: false,\n size: validateNotNegative, //validateInteger,\n snapSizeX: validatePositive,\n snapSizeY: validatePositive,\n snapWidth: validateNumber,\n snapToGrid: false,\n snatchDistance: validateNotNegative,\n straightFirst: false,\n straightLast: false,\n stretch: false,\n strokeColor: validateColor,\n strokeOpacity: validateNumber,\n strokeWidth: validateNotNegative, //validateInteger,\n takeFirst: false,\n takeSizeFromFile: false,\n to10: false,\n toOrigin: false,\n translateTo10: false,\n translateToOrigin: false,\n useASCIIMathML: false,\n useDirection: false,\n useMathJax: false,\n withLabel: false,\n withTicks: false,\n zoom: false\n };\n\n // this seems like a redundant step but it makes sure that\n // all properties in the validator object have lower case names\n // and the validator object is easier to read.\n for (i in validators) {\n if (validators.hasOwnProperty(i)) {\n v[i.toLowerCase()] = validators[i];\n }\n }\n\n return v;\n }());\n\n /**\n * All point faces can be defined with more than one name, e.g. a cross faced point can be given\n * by face equal to 'cross' or equal to 'x'. This method maps all possible values to fixed ones to\n * simplify if- and switch-clauses regarding point faces. The translation table is as follows:\n * \n *
\n * @param {String} s A string which should determine a valid point face.\n * @returns {String} Returns a normalized string or undefined if the given string is not a valid\n * point face.\n */\n JXG.normalizePointFace = function (s) {\n var map = {\n cross: 'x',\n x: 'x',\n circle: 'o',\n o: 'o',\n square: '[]',\n '[]': '[]',\n plus: '+',\n '+': '+',\n divide: '|',\n '|': '|',\n minus: '-',\n '-': '-',\n diamond: '<>',\n '<>': '<>',\n diamond2: '<<>>',\n '<<>>': '<<>>',\n triangleup: '^',\n A: '^',\n a: '^',\n '^': '^',\n triangledown: 'v',\n v: 'v',\n triangleleft: '<',\n '<': '<',\n triangleright: '>',\n '>': '>'\n };\n\n return map[s];\n };\n\n /**\n * Apply the options stored in this object to all objects on the given board.\n * @param {JXG.Board} board The board to which objects the options will be applied.\n */\n JXG.useStandardOptions = function (board) {\n var el, t, p, copyProps,\n o = JXG.Options,\n boardHadGrid = board.hasGrid;\n\n board.options.grid.hasGrid = o.grid.hasGrid;\n board.options.grid.gridX = o.grid.gridX;\n board.options.grid.gridY = o.grid.gridY;\n // POI: Do we have to add something here?\n board.options.grid.gridColor = o.grid.gridColor;\n board.options.grid.gridOpacity = o.grid.gridOpacity;\n board.options.grid.gridDash = o.grid.gridDash;\n board.options.grid.snapToGrid = o.grid.snapToGrid;\n board.options.grid.snapSizeX = o.grid.SnapSizeX;\n board.options.grid.snapSizeY = o.grid.SnapSizeY;\n board.takeSizeFromFile = o.takeSizeFromFile;\n\n copyProps = function (p, o) {\n p.visProp.fillcolor = o.fillColor;\n p.visProp.highlightfillcolor = o.highlightFillColor;\n p.visProp.strokecolor = o.strokeColor;\n p.visProp.highlightstrokecolor = o.highlightStrokeColor;\n };\n\n for (el in board.objects) {\n if (board.objects.hasOwnProperty(el)) {\n p = board.objects[el];\n if (p.elementClass === Const.OBJECT_CLASS_POINT) {\n copyProps(p, o.point);\n } else if (p.elementClass === Const.OBJECT_CLASS_LINE) {\n copyProps(p, o.line);\n\n for (t = 0; t < p.ticks.length; t++) {\n p.ticks[t].majorTicks = o.line.ticks.majorTicks;\n p.ticks[t].minTicksDistance = o.line.ticks.minTicksDistance;\n p.ticks[t].visProp.minorheight = o.line.ticks.minorHeight;\n p.ticks[t].visProp.majorheight = o.line.ticks.majorHeight;\n }\n } else if (p.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n copyProps(p, o.circle);\n } else if (p.type === Const.OBJECT_TYPE_ANGLE) {\n copyProps(p, o.angle);\n } else if (p.type === Const.OBJECT_TYPE_ARC) {\n copyProps(p, o.arc);\n } else if (p.type === Const.OBJECT_TYPE_POLYGON) {\n copyProps(p, o.polygon);\n } else if (p.type === Const.OBJECT_TYPE_CONIC) {\n copyProps(p, o.conic);\n } else if (p.type === Const.OBJECT_TYPE_CURVE) {\n copyProps(p, o.curve);\n } else if (p.type === Const.OBJECT_TYPE_SECTOR) {\n p.arc.visProp.fillcolor = o.sector.fillColor;\n p.arc.visProp.highlightfillcolor = o.sector.highlightFillColor;\n p.arc.visProp.fillopacity = o.sector.fillOpacity;\n p.arc.visProp.highlightfillopacity = o.sector.highlightFillOpacity;\n }\n }\n }\n\n board.fullUpdate();\n if (boardHadGrid && !board.hasGrid) {\n board.removeGrids(board);\n } else if (!boardHadGrid && board.hasGrid) {\n board.create('grid', []);\n }\n };\n\n /**\n * Converts all color values to greyscale and calls useStandardOption to put them onto the board.\n * @param {JXG.Board} board The board to which objects the options will be applied.\n * @see JXG.useStandardOptions\n */\n JXG.useBlackWhiteOptions = function (board) {\n var o = JXG.Options;\n o.point.fillColor = Color.rgb2bw(o.point.fillColor);\n o.point.highlightFillColor = Color.rgb2bw(o.point.highlightFillColor);\n o.point.strokeColor = Color.rgb2bw(o.point.strokeColor);\n o.point.highlightStrokeColor = Color.rgb2bw(o.point.highlightStrokeColor);\n\n o.line.fillColor = Color.rgb2bw(o.line.fillColor);\n o.line.highlightFillColor = Color.rgb2bw(o.line.highlightFillColor);\n o.line.strokeColor = Color.rgb2bw(o.line.strokeColor);\n o.line.highlightStrokeColor = Color.rgb2bw(o.line.highlightStrokeColor);\n\n o.circle.fillColor = Color.rgb2bw(o.circle.fillColor);\n o.circle.highlightFillColor = Color.rgb2bw(o.circle.highlightFillColor);\n o.circle.strokeColor = Color.rgb2bw(o.circle.strokeColor);\n o.circle.highlightStrokeColor = Color.rgb2bw(o.circle.highlightStrokeColor);\n\n o.arc.fillColor = Color.rgb2bw(o.arc.fillColor);\n o.arc.highlightFillColor = Color.rgb2bw(o.arc.highlightFillColor);\n o.arc.strokeColor = Color.rgb2bw(o.arc.strokeColor);\n o.arc.highlightStrokeColor = Color.rgb2bw(o.arc.highlightStrokeColor);\n\n o.polygon.fillColor = Color.rgb2bw(o.polygon.fillColor);\n o.polygon.highlightFillColor = Color.rgb2bw(o.polygon.highlightFillColor);\n\n o.sector.fillColor = Color.rgb2bw(o.sector.fillColor);\n o.sector.highlightFillColor = Color.rgb2bw(o.sector.highlightFillColor);\n\n o.curve.strokeColor = Color.rgb2bw(o.curve.strokeColor);\n o.grid.gridColor = Color.rgb2bw(o.grid.gridColor);\n\n JXG.useStandardOptions(board);\n };\n\n// needs to be exported\nJXG.Options.normalizePointFace = JXG.normalizePointFace;\n\nexport default JXG.Options;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see Input Output cross x circle o square, [] [] plus + minus - divide | diamond <> triangleup ^, a, A triangledown v triangleleft < triangleright > \n *
\n * @return {Object} Returns result of computation as directed in cmd.\n */\n _genericParse: function (code, cmd, options) {\n var i, setTextBackup, ast, result,\n ccode = code.replace(/\\r\\n/g, '\\n').split('\\n'),\n cleaned = [];\n\n if (!Type.exists(options)) {\n options = {};\n }\n\n if (!options.dontstore) {\n this.code += code + '\\n';\n }\n\n if (Text) {\n setTextBackup = Text.prototype.setText;\n Text.prototype.setText = Text.prototype.setTextJessieCode;\n }\n\n try {\n for (i = 0; i < ccode.length; i++) {\n if (!!options.geonext) {\n ccode[i] = JXG.GeonextParser.geonext2JS(ccode[i], this.board);\n }\n cleaned.push(ccode[i]);\n }\n\n code = cleaned.join('\\n');\n ast = parser.parse(code);\n if (this.CA) {\n ast = this.CA.expandDerivatives(ast, null, ast);\n ast = this.CA.removeTrivialNodes(ast);\n }\n if (this.CAS) {\n // Search for expression of form `D(f, x)` and determine the\n // the derivative symbolically.\n ast = this.CAS.expandDerivatives(ast, null, ast);\n\n // options.method = options.method || \"strong\";\n // options.form = options.form || \"fractions\";\n // options.steps = options.steps || [];\n // options.iterations = options.iterations || 1000;\n // ast = this.CAS._simplify_aux(ast, options);\n }\n switch (cmd) {\n case 'parse':\n result = this.execute(ast);\n break;\n case 'manipulate':\n result = this.compile(ast);\n break;\n case 'simplify':\n if (Type.exists(this.CAS)) {\n options.method = options.method || \"strong\";\n options.form = options.form || \"fractions\";\n options.steps = options.steps || [];\n options.iterations = options.iterations || 1000;\n ast = this.CAS.simplify(ast, options);\n result = this.CAS.compile(ast);\n } else {\n result = this.compile(ast);\n }\n break;\n case 'format':\n result = this.compile(ast, false, options);\n break;\n case 'getAst':\n result = ast;\n break;\n default:\n result = false;\n }\n } catch (e) { // catch is mandatory in old IEs\n // console.log(e);\n // We throw the error again,\n // so the user can catch it.\n throw e;\n } finally {\n // make sure the original text method is back in place\n if (Text) {\n Text.prototype.setText = setTextBackup;\n }\n }\n\n return result;\n },\n\n /**\n * Parses JessieCode.\n * This consists of generating an AST with parser.parse, apply simplifying rules\n * from CA and executing the ast by calling this.execute(ast).\n *\n * @param {String} code JessieCode code to be parsed\n * @param {Boolean} [geonext=false] Geonext compatibility mode.\n * @param {Boolean} [dontstore=false] If false, the code string is stored in this.code.\n * @return {Object} Parse JessieCode code and execute it.\n */\n parse: function (code, geonext, dontstore) {\n return this._genericParse(code, 'parse', {geonext: geonext, dontstore: dontstore});\n },\n\n /**\n * Manipulate JessieCode.\n * This consists of generating an AST with parser.parse,\n * apply simplifying rules from CA\n * and compile the AST back to JessieCode.\n *\n * @param {String} code JessieCode code to be parsed\n * @param {Boolean} [geonext=false] Geonext compatibility mode.\n * @param {Boolean} [dontstore=false] If false, the code string is stored in this.code.\n * @return {String} Simplified JessieCode code\n */\n manipulate: function (code, geonext, dontstore) {\n return this._genericParse(code, 'manipulate', {geonext: geonext, dontstore: dontstore});\n },\n\n /**\n * Manipulate JessieCode.\n * This consists of generating an AST with parser.parse,\n * apply simplifying rules from CAS\n * and compile the AST back to JessieCode with minimal number of parentheses.\n *\n * @param {String} code JessieCode code to be parsed\n * @return {String} Simplified JessieCode code\n */\n simplify: function (code) {\n return this._genericParse(code, 'simplify');\n },\n\n /**\n * Format JessieCode.\n * This consists of generating an AST with parser.parse,\n * and compile the AST back to JessieCode with options.\n *\n * @param {String} code JessieCode code to be parsed.\n * @param {Object} options For possible options see param \"format\" in {@link JXG.JessieCode#compile}.\n * @return {String} Manipulated JessieCode string. This is no necessarily a parsable JessieCode code!\n */\n format: function (code, options) {\n return this._genericParse(code, 'format', options);\n },\n\n /**\n * Get abstract syntax tree (AST) from JessieCode code.\n * This consists of generating an AST with parser.parse.\n *\n * @param {String} code\n * @param {Boolean} [geonext=false] Geonext compatibility mode.\n * @param {Boolean} [dontstore=false] If false, the code string is stored in this.code.\n * @return {Node} AST\n */\n getAST: function (code, geonext, dontstore) {\n return this._genericParse(code, 'getAst', {geonext: geonext, dontstore: dontstore});\n },\n\n /**\n * Parses a JessieCode snippet, e.g. \"3+4\", and wraps it into a function, if desired.\n * @param {String} code A small snippet of JessieCode. Must not be an assignment.\n * @param {Boolean} [funwrap=true] If true, the code is wrapped in a function.\n * @param {String} [varname=''] Name of the parameter(s)\n * @param {Boolean} [geonext=false] Geonext compatibility mode.\n * @param {Boolean} [forceValueCall=true] Force evaluation of value method of sliders.\n */\n snippet: function (code, funwrap, varname, geonext, forceValueCall) {\n var c;\n\n funwrap = Type.def(funwrap, true);\n varname = Type.def(varname, '');\n geonext = Type.def(geonext, false);\n this.forceValueCall = Type.def(forceValueCall, true);\n\n c = (funwrap ? ' function (' + varname + ') { return ' : '') +\n code +\n (funwrap ? '; }' : '') + ';';\n\n return this.parse(c, geonext, true);\n },\n\n /**\n * Traverses through the given subtree and changes all values of nodes with the replaced flag set by\n * {@link JXG.JessieCode#replaceNames} to the name of the element (if not empty).\n * @param {Object} node\n */\n replaceIDs: function (node) {\n var i, v;\n\n if (node.replaced) {\n // These children exist, if node.replaced is set.\n v = this.board.objects[node.children[1][0].value];\n\n if (Type.exists(v) && v.name !== \"\") {\n node.type = 'node_var';\n node.value = v.name;\n\n // Maybe it's not necessary, but just to be sure that everything is cleaned up we better delete all\n // children and the replaced flag\n node.children.length = 0;\n delete node.replaced;\n }\n }\n\n if (Type.isArray(node)) {\n for (i = 0; i < node.length; i++) {\n node[i] = this.replaceIDs(node[i]);\n }\n }\n\n if (node.children) {\n // assignments are first evaluated on the right hand side\n for (i = node.children.length; i > 0; i--) {\n if (Type.exists(node.children[i - 1])) {\n node.children[i - 1] = this.replaceIDs(node.children[i - 1]);\n }\n\n }\n }\n\n return node;\n },\n\n /**\n * Traverses through the given subtree and changes all elements referenced by names through referencing them by ID.\n * An identifier is only replaced if it is not found in all scopes above the current scope and if it\n * has not been blacklisted within the codeblock determined by the given subtree.\n * @param {Object} node\n * @param {Boolean} [callValuePar=false] if true, uses $value() instead of $() in createReplacementNode\n */\n replaceNames: function (node, callValuePar) {\n var i, v,\n callValue = false;\n\n if (callValuePar !== undefined) {\n callValue = callValuePar;\n }\n\n v = node.value;\n\n // We are interested only in nodes of type node_var and node_op > op_lhs.\n // Currently, we are not checking if the id is a local variable. in this case, we're stuck anyway.\n\n if (node.type === 'node_op' && v === 'op_lhs' && node.children.length === 1) {\n this.isLHS = true;\n } else if (node.type === 'node_var') {\n if (this.isLHS) {\n this.letvar(v, true);\n } else if (!Type.exists(this.getvar(v, true)) && Type.exists(this.board.elementsByName[v])) {\n if (callValue && this.board.elementsByName[v].elType !== 'slider') {\n callValue = false;\n }\n node = this.createReplacementNode(node, callValue);\n }\n }\n\n if (Type.isArray(node)) {\n for (i = 0; i < node.length; i++) {\n node[i] = this.replaceNames(node[i], callValue);\n }\n }\n\n if (node.children) {\n // Replace slider reference by call of slider.Value()\n if (this.forceValueCall && // It must be enforced, see snippet.\n (\n // 1. case: sin(a), max(a, 0), ...\n (node.value === \"op_execfun\" &&\n // Not in cases V(a), $(a)\n node.children[0].value !== 'V' && node.children[0].value !== '$' &&\n // Function must be a math function. This ensures that a number is required as input.\n (Type.exists(Math[node.children[0].value]) || Type.exists(Mat[node.children[0].value])) &&\n // node.children[1].length === 1 &&\n node.children[1][0].type === 'node_var'\n ) ||\n // 2. case: slider is the whole expression: 'a'\n (node.value === \"op_return\" &&\n node.children.length === 1 &&\n node.children[0].type === 'node_var'\n )\n )\n ) {\n callValue = true;\n }\n\n // Assignments are first evaluated on the right hand side\n for (i = node.children.length; i > 0; i--) {\n if (Type.exists(node.children[i - 1])) {\n node.children[i - 1] = this.replaceNames(node.children[i - 1], callValue);\n }\n }\n }\n\n if (node.type === 'node_op' && node.value === 'op_lhs' && node.children.length === 1) {\n this.isLHS = false;\n }\n\n return node;\n },\n\n /**\n * Replaces node_var nodes with node_op>op_execfun nodes, calling the internal $() function with the id of the\n * element accessed by the node_var node.\n * @param {Object} node\n * @param {Boolean} [callValue=undefined] if true, uses $value() instead of $()\n * @returns {Object} op_execfun node\n */\n createReplacementNode: function (node, callValue) {\n var v = node.value,\n el = this.board.elementsByName[v];\n\n // If callValue: get handle to this node_var and call its Value method.\n // Otherwise return the object.\n node = this.createNode('node_op', 'op_execfun',\n this.createNode('node_var', ((callValue === true) ? '$value' : '$')),\n [this.createNode('node_str', el.id)]);\n\n node.replaced = true;\n\n return node;\n },\n\n /**\n * Search the parse tree below node for stationary dependencies, i.e. dependencies hard coded into\n * the function.\n * @param {Object} node\n * @param {Array} varnames List of variable names of the function\n * @param {Object} result An object where the referenced elements will be stored. Access key is their id.\n */\n collectDependencies: function (node, varnames, result) {\n var i, v, e, le;\n\n if (Type.isArray(node)) {\n le = node.length;\n for (i = 0; i < le; i++) {\n this.collectDependencies(node[i], varnames, result);\n }\n return;\n }\n\n v = node.value;\n\n if (node.type === 'node_var' &&\n varnames.indexOf(v) < 0 // v is not contained in the list of variables of that function\n ) {\n e = this.getvar(v);\n if (e && e.visProp && e.elType && e.elementClass && e.id\n // Sliders are the only elements which are given by names.\n // Wrong, a counter example is: circle(c, function() { return p1.Dist(p2); })\n // && e.elType === 'slider'\n ) {\n result[e.id] = e;\n }\n }\n\n // The $()-function-calls are special because their parameter is given as a string, not as a node_var.\n if (node.type === 'node_op' && node.value === 'op_execfun' &&\n node.children.length > 1 &&\n (node.children[0].value === '$' || node.children[0].value === '$value') &&\n node.children[1].length > 0) {\n\n e = node.children[1][0].value;\n result[e] = this.board.objects[e];\n }\n\n if (node.children) {\n for (i = node.children.length; i > 0; i--) {\n if (Type.exists(node.children[i - 1])) {\n this.collectDependencies(node.children[i - 1], varnames, result);\n }\n }\n }\n },\n\n resolveProperty: function (e, v, compile) {\n compile = Type.def(compile, false);\n\n // is it a geometry element or a board?\n if (e /*&& e.type && e.elementClass*/ && e.methodMap) {\n // yeah, it is. but what does the user want?\n if (Type.exists(e.subs) && Type.exists(e.subs[v])) {\n // a subelement it is, good sir.\n e = e.subs;\n } else if (Type.exists(e.methodMap[v])) {\n // the user wants to call a method\n v = e.methodMap[v];\n } else {\n // the user wants to change an attribute\n e = e.visProp;\n v = v.toLowerCase();\n }\n }\n\n if (Type.isFunction(e)) {\n this._error('Accessing function properties is not allowed.');\n }\n\n if (!Type.exists(e)) {\n this._error(e + ' is not an object');\n }\n\n if (!Type.exists(e[v])) {\n this._error('unknown property ' + v);\n }\n\n if (compile && typeof e[v] === 'function') {\n return function () { return e[v].apply(e, arguments); };\n }\n\n return e[v];\n },\n\n /**\n * Type inspection: check if the string vname appears as function name in the\n * AST node. Used in \"op_execfun\". This allows the JessieCode examples below.\n *\n * @private\n * @param {String} vname\n * @param {Object} node\n * @returns 'any' or 'function'\n * @see JXG.JessieCode#execute\n * @see JXG.JessieCode#getvar\n *\n * @example\n * var p = board.create('point', [2, 0], {name: 'X'});\n * var txt = 'X(X)';\n * console.log(board.jc.parse(txt));\n *\n * @example\n * var p = board.create('point', [2, 0], {name: 'X'});\n * var txt = 'f = function(el, X) { return X(el); }; f(X, X);';\n * console.log(board.jc.parse(txt));\n *\n * @example\n * var p = board.create('point', [2, 0], {name: 'point'});\n * var txt = 'B = point(1,3); X(point);';\n * console.log(board.jc.parse(txt));\n *\n * @example\n * var p = board.create('point', [2, 0], {name: 'A'});\n * var q = board.create('point', [-2, 0], {name: 'X'});\n * var txt = 'getCoord=function(p, f){ return f(p); }; getCoord(A, X);';\n * console.log(board.jc.parse(txt));\n */\n resolveType: function (vname, node) {\n var i, t,\n type = 'any'; // Possible values: 'function', 'any'\n\n if (Type.isArray(node)) {\n // node contains the parameters of a function call or function declaration\n for (i = 0; i < node.length; i++) {\n t = this.resolveType(vname, node[i]);\n if (t !== 'any') {\n type = t;\n return type;\n }\n }\n }\n\n if (node.type === 'node_op' && node.value === 'op_execfun' &&\n node.children[0].type === 'node_var' && node.children[0].value === vname) {\n return 'function';\n }\n\n if (node.type === 'node_op') {\n for (i = 0; i < node.children.length; i++) {\n if (node.children[0].type === 'node_var' && node.children[0].value === vname &&\n (node.value === 'op_add' || node.value === 'op_sub' || node.value === 'op_mul' ||\n node.value === 'op_div' || node.value === 'op_mod' || node.value === 'op_exp' ||\n node.value === 'op_neg')) {\n return 'any';\n }\n }\n\n for (i = 0; i < node.children.length; i++) {\n t = this.resolveType(vname, node.children[i]);\n if (t !== 'any') {\n type = t;\n return type;\n }\n }\n }\n\n return 'any';\n },\n\n /**\n * Resolves the lefthand side of an assignment operation\n * @param node\n * @returns {Object} An object with two properties. o which contains the object, and\n * a string what which contains the property name.\n */\n getLHS: function (node) {\n var res;\n\n if (node.type === 'node_var') {\n res = {\n o: this.scope.locals,\n what: node.value\n };\n } else if (node.type === 'node_op' && node.value === 'op_property') {\n res = {\n o: this.execute(node.children[0]),\n what: node.children[1]\n };\n } else if (node.type === 'node_op' && node.value === 'op_extvalue') {\n res = {\n o: this.execute(node.children[0]),\n what: this.execute(node.children[1])\n };\n } else {\n throw new Error('Syntax error: Invalid left-hand side of assignment.');\n }\n\n return res;\n },\n\n getLHSCompiler: function (node, js) {\n var res;\n\n if (node.type === 'node_var') {\n res = node.value;\n } else if (node.type === 'node_op' && node.value === 'op_property') {\n res = [\n this.compile(node.children[0], js),\n \"'\" + node.children[1] + \"'\"\n ];\n } else if (node.type === 'node_op' && node.value === 'op_extvalue') {\n res = [\n this.compile(node.children[0], js),\n (node.children[1].type === 'node_const') ? node.children[1].value : this.compile(node.children[1], js)\n ];\n } else {\n throw new Error('Syntax error: Invalid left-hand side of assignment.');\n }\n\n return res;\n },\n\n /**\n * Executes a parse subtree.\n * @param {Object} node\n * @returns {Number|String|Object|Boolean} Something\n * @private\n */\n execute: function (node) {\n var ret, v, i, e, l, undef, list, ilist,\n parents = [],\n // exec fun\n fun, attr, sc;\n\n ret = 0;\n\n if (!node) {\n return ret;\n }\n\n this.line = node.line;\n this.col = node.col;\n\n switch (node.type) {\n case 'node_op':\n switch (node.value) {\n case 'op_none':\n if (node.children[0]) {\n this.execute(node.children[0]);\n }\n if (node.children[1]) {\n ret = this.execute(node.children[1]);\n }\n break;\n case 'op_assign':\n v = this.getLHS(node.children[0]);\n this.lhs[this.scope.id] = v.what;\n\n if (v.o.type && v.o.elementClass && v.o.methodMap && v.what === 'label') {\n this._error('Left-hand side of assignment is read-only.');\n }\n\n ret = this.execute(node.children[1]);\n if (v.o !== this.scope.locals || (Type.isArray(v.o) && typeof v.what === 'number')) {\n // it is either an array component being set or a property of an object.\n this.setProp(v.o, v.what, ret);\n } else {\n // this is just a local variable inside JessieCode\n this.letvar(v.what, ret);\n }\n this.lhs[this.scope.id] = 0;\n break;\n case 'op_if':\n if (this.execute(node.children[0])) {\n ret = this.execute(node.children[1]);\n }\n break;\n case 'op_conditional':\n // fall through\n case 'op_if_else':\n if (this.execute(node.children[0])) {\n ret = this.execute(node.children[1]);\n } else {\n ret = this.execute(node.children[2]);\n }\n break;\n case 'op_while':\n while (this.execute(node.children[0])) {\n this.execute(node.children[1]);\n }\n break;\n case 'op_do':\n do {\n this.execute(node.children[0]);\n } while (this.execute(node.children[1]));\n break;\n case 'op_for':\n for (this.execute(node.children[0]); this.execute(node.children[1]); this.execute(node.children[2])) {\n this.execute(node.children[3]);\n }\n break;\n case 'op_proplst':\n if (node.children[0]) {\n this.execute(node.children[0]);\n }\n if (node.children[1]) {\n this.execute(node.children[1]);\n }\n break;\n case 'op_emptyobject':\n ret = {};\n break;\n case 'op_proplst_val':\n this.propstack.push({});\n this.propscope++;\n\n this.execute(node.children[0]);\n ret = this.propstack[this.propscope];\n\n this.propstack.pop();\n this.propscope--;\n break;\n case 'op_prop':\n // child 0: Identifier\n // child 1: Value\n this.propstack[this.propscope][node.children[0]] = this.execute(node.children[1]);\n break;\n case 'op_array':\n ret = [];\n l = node.children[0].length;\n\n for (i = 0; i < l; i++) {\n ret.push(this.execute(node.children[0][i]));\n }\n\n break;\n case 'op_extvalue':\n ret = this.execute(node.children[0]);\n i = this.execute(node.children[1]);\n\n if (typeof i === 'number' && Math.abs(Math.round(i) - i) < 1.e-12) {\n ret = ret[i];\n } else {\n ret = undef;\n }\n break;\n case 'op_return':\n if (this.scope === 0) {\n this._error('Unexpected return.');\n } else {\n return this.execute(node.children[0]);\n }\n break;\n case 'op_map':\n if (!node.children[1].isMath && node.children[1].type !== 'node_var') {\n this._error('execute: In a map only function calls and mathematical expressions are allowed.');\n }\n\n /** @ignore */\n fun = this.defineFunction(node);\n fun.isMap = true;\n\n ret = fun;\n break;\n case 'op_function':\n // parse the parameter list\n // after this, the parameters are in pstack\n\n /** @ignore */\n fun = this.defineFunction(node);\n fun.isMap = false;\n\n ret = fun;\n break;\n case 'op_execfun':\n // node.children:\n // [0]: Name of the function\n // [1]: Parameter list as a parse subtree\n // [2]: Properties, only used in case of a create function\n this.dpstack.push([]);\n this.pscope++;\n\n // parameter parsing is done below\n list = node.children[1];\n\n // parse the properties only if given\n if (Type.exists(node.children[2])) {\n if (node.children[3]) {\n ilist = node.children[2];\n attr = {};\n\n for (i = 0; i < ilist.length; i++) {\n attr = Type.deepCopy(attr, this.execute(ilist[i]), true);\n }\n } else {\n attr = this.execute(node.children[2]);\n }\n }\n\n // look up the variables name in the variable table\n node.children[0]._isFunctionName = true;\n fun = this.execute(node.children[0]);\n delete node.children[0]._isFunctionName;\n\n // determine the scope the function wants to run in\n if (Type.exists(fun) && Type.exists(fun.sc)) {\n sc = fun.sc;\n } else {\n sc = this;\n }\n\n if (!fun.creator && Type.exists(node.children[2])) {\n this._error('Unexpected value. Only element creators are allowed to have a value after the function call.');\n }\n\n // interpret ALL the parameters\n for (i = 0; i < list.length; i++) {\n if (Type.exists(fun.scope) && Type.exists(fun.scope.argtypes) && fun.scope.argtypes[i] === 'function') {\n // Type inspection\n list[i]._isFunctionName = true;\n parents[i] = this.execute(list[i]);\n delete list[i]._isFunctionName;\n } else {\n parents[i] = this.execute(list[i]);\n }\n //parents[i] = Type.evalSlider(this.execute(list[i]));\n this.dpstack[this.pscope].push({\n line: node.children[1][i].line,\n // SketchBin currently works only if the last column of the\n // parent position is taken. This is due to how I patched JS/CC\n // to count the lines and columns. So, ecol will do for now\n col: node.children[1][i].ecol\n });\n }\n\n // check for the function in the variable table\n if (typeof fun === 'function' && !fun.creator) {\n ret = fun.apply(sc, parents);\n } else if (typeof fun === 'function' && !!fun.creator) {\n e = this.line;\n\n // creator methods are the only ones that take properties, hence this special case\n try {\n ret = fun(parents, attr);\n ret.jcLineStart = e;\n ret.jcLineEnd = node.eline;\n\n for (i = e; i <= node.line; i++) {\n this.lineToElement[i] = ret;\n }\n\n ret.debugParents = this.dpstack[this.pscope];\n } catch (ex) {\n this._error(ex.toString());\n }\n } else {\n this._error('Function \\'' + fun + '\\' is undefined.');\n }\n\n // clear parameter stack\n this.dpstack.pop();\n this.pscope--;\n break;\n case 'op_property':\n e = this.execute(node.children[0]);\n v = node.children[1];\n\n ret = this.resolveProperty(e, v, false);\n\n // set the scope, in case this is a method the user wants to call\n if (Type.exists(ret) && ['number', 'string', 'boolean'].indexOf(typeof ret) < 0) {\n ret.sc = e;\n }\n\n break;\n case 'op_use':\n this._warn('Use of the \\'use\\' operator is deprecated.');\n this.use(node.children[0].toString());\n break;\n case 'op_delete':\n this._warn('Use of the \\'delete\\' operator is deprecated. Please use the remove() function.');\n v = this.getvar(node.children[0]);\n ret = this.del(v);\n break;\n case 'op_eq':\n // == is intentional\n /*jslint eqeq:true*/\n /* eslint-disable eqeqeq */\n ret = this.execute(node.children[0]) == this.execute(node.children[1]);\n /*jslint eqeq:false*/\n /* eslint-enable eqeqeq */\n break;\n case 'op_neq':\n // != is intentional\n /*jslint eqeq:true*/\n /* eslint-disable eqeqeq */\n ret = this.execute(node.children[0]) != this.execute(node.children[1]);\n /*jslint eqeq:true*/\n /* eslint-enable eqeqeq */\n break;\n case 'op_approx':\n ret = Math.abs(this.execute(node.children[0]) - this.execute(node.children[1])) < Mat.eps;\n break;\n case 'op_gt':\n ret = this.execute(node.children[0]) > this.execute(node.children[1]);\n break;\n case 'op_lt':\n ret = this.execute(node.children[0]) < this.execute(node.children[1]);\n break;\n case 'op_geq':\n ret = this.execute(node.children[0]) >= this.execute(node.children[1]);\n break;\n case 'op_leq':\n ret = this.execute(node.children[0]) <= this.execute(node.children[1]);\n break;\n case 'op_or':\n ret = this.execute(node.children[0]) || this.execute(node.children[1]);\n break;\n case 'op_and':\n ret = this.execute(node.children[0]) && this.execute(node.children[1]);\n break;\n case 'op_not':\n ret = !this.execute(node.children[0]);\n break;\n case 'op_add':\n ret = this.add(this.execute(node.children[0]), this.execute(node.children[1]));\n break;\n case 'op_sub':\n ret = this.sub(this.execute(node.children[0]), this.execute(node.children[1]));\n break;\n case 'op_div':\n ret = this.div(this.execute(node.children[0]), this.execute(node.children[1]));\n break;\n case 'op_mod':\n // use mathematical modulo, JavaScript implements the symmetric modulo.\n ret = this.mod(this.execute(node.children[0]), this.execute(node.children[1]), true);\n break;\n case 'op_mul':\n ret = this.mul(this.execute(node.children[0]), this.execute(node.children[1]));\n break;\n case 'op_exp':\n ret = this.pow(this.execute(node.children[0]), this.execute(node.children[1]));\n break;\n case 'op_neg':\n ret = this.neg(this.execute(node.children[0]));\n break;\n }\n break;\n\n case 'node_var':\n // node._isFunctionName is set in execute: at op_execfun.\n ret = this.getvar(node.value, false, node._isFunctionName);\n break;\n\n case 'node_const':\n if (node.value === null) {\n ret = null;\n } else {\n ret = Number(node.value);\n }\n break;\n\n case 'node_const_bool':\n ret = node.value;\n break;\n\n case 'node_str':\n //ret = node.value.replace(/\\\\'/, \"'\").replace(/\\\\\"/, '\"').replace(/\\\\\\\\/, '\\\\');\n /*jslint regexp:true*/\n ret = node.value.replace(/\\\\(.)/g, '$1'); // Remove backslash, important in JessieCode tags\n /*jslint regexp:false*/\n break;\n }\n\n return ret;\n },\n\n /**\n * Compiles a parse tree back to JessieCode.\n * @param {Object} ast\n * @param {Boolean} [js=false] Compile either to JavaScript or back to JessieCode (required for the UI).\n * @param {Object} [format] Options for formatting the output. Depending on some options, the function might return a not re-parsable string. This format options have only effect on JessieCode output.\n *
\n * @returns Something\n * @private\n */\n compile: function (ast, js, format) {\n var that = this;\n\n if (!Type.exists(js)) {\n js = false;\n }\n if (!Type.exists(format) || !Type.isObject(format)) {\n format = {};\n }\n format = Type.deepCopy({\n minParentheses: false,\n constToFixed: false,\n printable: false\n }, format);\n\n // node_const/node_var >> op_execfun >> op_neg >> op_exp >> op_mul/op_div >> op_add/op_sub >> op_map >> op_assign\n function prio(node) {\n switch (node.type) {\n case \"node_const\":\n case \"node_const_bool\":\n case \"node_str\":\n case \"node_var\":\n return 10;\n case \"node_op\":\n switch (node.value) {\n case \"op_none\":\n return 0;\n case \"op_assign\":\n return 1;\n case \"op_map\":\n case \"op_function\":\n case \"op_return\":\n return 2;\n case \"op_add\":\n case \"op_sub\":\n return 3;\n case \"op_mul\":\n case \"op_div\":\n case \"op_mod\":\n return 5;\n case \"op_neg\":\n return 4;\n case \"op_exp\":\n return 6;\n case \"op_array\":\n case \"op_execfun\":\n return 7;\n default:\n return 0;\n }\n default:\n return 0;\n }\n }\n\n function compile(node, prevOp, position = -1) {\n var e, i, c, list, scope, prioParent, prioChild,\n ret = '';\n\n if (!node) {\n return ret;\n }\n\n switch (node.type) {\n case 'node_op':\n switch (node.value) {\n case 'op_none':\n if (node.children[0]) {\n ret = compile(node.children[0], \"op_none\");\n }\n if (node.children[1]) {\n ret += compile(node.children[1], \"op_none\");\n }\n break;\n case 'op_block':\n ret = '{\\n' + compile(node.children[0], \"op_block\") + ' }\\n';\n break;\n case 'op_assign':\n if (js) {\n e = that.getLHSCompiler(node.children[0], js);\n if (Type.isArray(e)) {\n ret = '$jc$.setProp(' + e[0] + ', ' + e[1] + ', ' + compile(node.children[1], \"op_assign\") + ');\\n';\n } else {\n if (that.isLocalVariable(e) !== that.scope) {\n that.scope.locals[e] = true;\n }\n ret = '$jc$.scopes[' + that.scope.id + '].locals[\\'' + e + '\\'] = ' + compile(node.children[1], \"op_assign\") + ';\\n';\n }\n } else {\n e = compile(node.children[0], \"op_assign\");\n ret = e + ' = ' + compile(node.children[1], \"op_assign\") + ';\\n';\n }\n break;\n case 'op_if':\n ret = ' if (' + compile(node.children[0], \"op_if\") + ') ' + compile(node.children[1], \"op_if\");\n break;\n case 'op_if_else':\n ret = ' if (' + compile(node.children[0], \"op_if_else\") + ')' + compile(node.children[1], \"op_if_else\");\n ret += ' else ' + compile(node.children[2], \"op_if_else\");\n break;\n case 'op_conditional':\n ret = '((' + compile(node.children[0], \"op_conditional\") + ')?(' + compile(node.children[1], \"op_conditional\");\n ret += '):(' + compile(node.children[2], \"op_conditional\") + '))';\n break;\n case 'op_while':\n ret = ' while (' + compile(node.children[0], \"op_while\") + ') {\\n' + compile(node.children[1], \"op_while\") + '}\\n';\n break;\n case 'op_do':\n ret = ' do {\\n' + compile(node.children[0], \"op_do\") + '} while (' + compile(node.children[1], \"op_do\") + ');\\n';\n break;\n case 'op_for':\n //ret = ' for (' + compile(node.children[0]) + '; ' + compile(node.children[1]) + '; ' + compile(node.children[2]) + ') {\\n' + compile(node.children[3]) + '\\n}\\n';\n ret = ' for (' + compile(node.children[0], \"op_for\") + // Assignment ends with \";\"\n compile(node.children[1], \"op_for\") + '; ' + // Logical test comes without \";\"\n compile(node.children[2], \"op_for\").slice(0, -2) + // Counting comes with \";\" which has to be removed\n ') {\\n' + compile(node.children[3], \"op_for\") + '\\n}\\n';\n break;\n case 'op_proplst':\n if (node.children[0]) {\n ret = compile(node.children[0], \"op_proplst\") + ', ';\n }\n\n ret += compile(node.children[1], \"op_proplst\");\n break;\n case 'op_prop':\n // child 0: Identifier\n // child 1: Value\n ret = node.children[0] + ': ' + compile(node.children[1], \"op_prop\");\n break;\n case 'op_emptyobject':\n ret = js ? '{}' : '<< >>';\n break;\n case 'op_proplst_val':\n ret = compile(node.children[0], \"op_proplst_val\");\n break;\n case 'op_array':\n list = [];\n for (i = 0; i < node.children[0].length; i++) {\n list.push(compile(node.children[0][i], \"op_array\"));\n }\n ret = '[' + list.join(', ') + ']';\n break;\n case 'op_extvalue':\n ret = compile(node.children[0], \"op_extvalue\") + '[' + compile(node.children[1], \"op_extvalue\") + ']';\n break;\n case 'op_return':\n ret = ' return ' + compile(node.children[0], \"op_return\") + ';\\n';\n break;\n case 'op_map':\n if (!node.children[1].isMath && node.children[1].type !== 'node_var') {\n that._error('compile: In a map only function calls and mathematical expressions are allowed.');\n }\n\n list = node.children[0];\n if (js) {\n ret = ' $jc$.makeMap(function (' + list.join(', ') + ') { return ' + compile(node.children[1], \"op_map\") + '; })';\n } else {\n ret = 'map (' + list.join(', ') + ') -> ' + compile(node.children[1], \"op_map\");\n }\n\n break;\n case 'op_function':\n list = node.children[0];\n scope = that.pushScope(list);\n if (js) {\n ret = that.functionCodeJS(node);\n } else {\n ret = ' function (' + list.join(', ') + ') ' + compile(node.children[1], \"op_function\");\n }\n that.popScope();\n break;\n case 'op_execfunmath':\n console.log('op_execfunmath: TODO');\n ret = '-1';\n break;\n case 'op_execfun':\n // parse the properties only if given\n if (node.children[2]) {\n list = [];\n for (i = 0; i < node.children[2].length; i++) {\n list.push(compile(node.children[2][i], \"op_execfun\"));\n }\n\n if (js) {\n e = '$jc$.mergeAttributes(' + list.join(', ') + ')';\n } else {\n e = list.join(', ');\n }\n }\n node.children[0].withProps = !!node.children[2];\n list = [];\n for (i = 0; i < node.children[1].length; i++) {\n list.push(compile(node.children[1][i], \"op_execfun\"));\n }\n ret = compile(node.children[0], \"op_execfun\") + '(' + list.join(', ') + (node.children[2] && js ? ', ' + e : '') + ')' + ((node.children[2] && !js) ? ' ' + e : '');\n if (js) {\n // Inserting a newline here allows simultaneously\n // - procedural calls like Q.moveTo(...); and\n // - function calls in expressions like log(x) + 1;\n // Problem: procedural calls will not be ended by a semicolon.\n ret += '\\n';\n }\n\n // save us a function call when compiled to javascript\n if (js && node.children[0].value === '$') {\n ret = '$jc$.board.objects[' + compile(node.children[1][0], \"op_execfun\") + ']';\n }\n break;\n case 'op_property':\n if (js && node.children[1] !== 'X' && node.children[1] !== 'Y') {\n ret = '$jc$.resolveProperty(' + compile(node.children[0], \"op_property\") + ', \\'' + node.children[1] + '\\', true)';\n } else {\n ret = compile(node.children[0], \"op_property\") + '.' + node.children[1];\n }\n break;\n case 'op_use':\n that._warn('Use of the \\'use\\' operator is deprecated.');\n if (js) {\n ret = '$jc$.use(\\'';\n } else {\n ret = 'use(\\'';\n }\n\n ret += node.children[0].toString() + '\\');';\n break;\n case 'op_delete':\n that._warn('Use of the \\'delete\\' operator is deprecated. Please use the remove() function.');\n if (js) {\n ret = '$jc$.del(';\n } else {\n ret = 'remove(';\n }\n\n ret += compile(node.children[0], \"op_delete\") + ')';\n break;\n case 'op_eq':\n ret = '(' + compile(node.children[0], \"op_eq\") + ' === ' + compile(node.children[1], \"op_eq\") + ')';\n break;\n case 'op_neq':\n ret = '(' + compile(node.children[0], \"op_neq\") + ' !== ' + compile(node.children[1], \"op_neq\") + ')';\n break;\n case 'op_approx':\n ret = '(' + compile(node.children[0], \"op_approx\") + ' ~= ' + compile(node.children[1], \"op_approx\") + ')';\n break;\n case 'op_gt':\n if (js) {\n ret = '$jc$.gt(' + compile(node.children[0], \"op_gt\") + ', ' + compile(node.children[1], \"op_gt\") + ')';\n } else {\n ret = '(' + compile(node.children[0], \"op_gt\") + ' > ' + compile(node.children[1], \"op_gt\") + ')';\n }\n break;\n case 'op_lt':\n if (js) {\n ret = '$jc$.lt(' + compile(node.children[0], \"op_lt\") + ', ' + compile(node.children[1], \"op_lt\") + ')';\n } else {\n ret = '(' + compile(node.children[0], \"op_lt\") + ' < ' + compile(node.children[1], \"op_lt\") + ')';\n }\n break;\n case 'op_geq':\n if (js) {\n ret = '$jc$.geq(' + compile(node.children[0], \"op_geq\") + ', ' + compile(node.children[1], \"op_geq\") + ')';\n } else {\n ret = '(' + compile(node.children[0], \"op_geq\") + ' >= ' + compile(node.children[1], \"op_geq\") + ')';\n }\n break;\n case 'op_leq':\n if (js) {\n ret = '$jc$.leq(' + compile(node.children[0], \"op_leq\") + ', ' + compile(node.children[1], \"op_leq\") + ')';\n } else {\n ret = '(' + compile(node.children[0], \"op_leq\") + ' <= ' + compile(node.children[1], \"op_leq\") + ')';\n }\n break;\n case 'op_or':\n ret = '(' + compile(node.children[0], \"op_or\") + ' || ' + compile(node.children[1], \"op_or\") + ')';\n break;\n case 'op_and':\n ret = '(' + compile(node.children[0], \"op_and\") + ' && ' + compile(node.children[1], \"op_and\") + ')';\n break;\n case 'op_not':\n ret = '!(' + compile(node.children[0], \"op_not\") + ')';\n break;\n case \"op_add\":\n if (js) {\n ret = '$jc$.add(' + compile(node.children[0], \"op_add\") + ', ' + compile(node.children[1], \"op_add\") + ')';\n } else if (!format.minParentheses) {\n ret = '(' + compile(node.children[0], \"op_add\") + ' + ' + compile(node.children[1], \"op_add\") + ')';\n } else {\n prioParent = prio(node);\n\n e = compile(node.children[0], \"op_add\");\n prioChild = prio(node.children[0]);\n ret = (prioParent > prioChild) ? \"(\" + e + \")\" : e;\n\n ret += ' + ';\n\n e = compile(node.children[1], \"op_add\");\n prioChild = prio(node.children[1]);\n ret += (prioParent > prioChild) ? \"(\" + e + \")\" : e;\n }\n break;\n case 'op_sub':\n if (js) {\n ret = '$jc$.sub(' + compile(node.children[0], \"op_sub\") + ', ' + compile(node.children[1], \"op_sub\") + ')';\n } else if (!format.minParentheses) {\n ret = '(' + compile(node.children[0], \"op_sub\") + ' - ' + compile(node.children[1], \"op_sub\") + ')';\n } else {\n prioParent = prio(node);\n\n e = compile(node.children[0], \"op_sub\");\n prioChild = prio(node.children[0]);\n ret = (prioParent > prioChild) ? \"(\" + e + \")\" : e;\n\n ret += ' - ';\n\n e = compile(node.children[1], \"op_sub\");\n prioChild = prio(node.children[1]);\n ret += (prioParent >= prioChild) ? \"(\" + e + \")\" : e;\n }\n break;\n case 'op_div':\n if (js) {\n ret = '$jc$.div(' + compile(node.children[0], \"op_div\") + ', ' + compile(node.children[1], \"op_div\") + ')';\n } else if (!format.minParentheses) {\n ret = '(' + compile(node.children[0], \"op_div\") + ' / ' + compile(node.children[1], \"op_div\") + ')';\n } else {\n prioParent = prio(node);\n\n e = compile(node.children[0], \"op_div\");\n prioChild = prio(node.children[0]);\n ret = (prioParent > prioChild) ? \"(\" + e + \")\" : e;\n\n ret += ' / ';\n\n e = compile(node.children[1], \"op_div\");\n prioChild = prio(node.children[1]);\n ret += (prioParent >= prioChild) ? \"(\" + e + \")\" : e;\n }\n break;\n case 'op_mod':\n if (js) {\n ret = '$jc$.mod(' + compile(node.children[0], \"op_mod\") + ', ' + compile(node.children[1], \"op_mod\") + ', true)';\n } else if (!format.minParentheses) {\n ret = '(' + compile(node.children[0], \"op_mod\") + ' % ' + compile(node.children[1], \"op_mod\") + ')';\n } else {\n prioParent = prio(node);\n\n e = compile(node.children[0], \"op_mod\");\n prioChild = prio(node.children[0]);\n ret = (prioParent > prioChild) ? \"(\" + e + \")\" : e;\n\n ret += ' % ';\n\n e = compile(node.children[1], \"op_mod\");\n prioChild = prio(node.children[1]);\n ret += (prioParent >= prioChild) ? \"(\" + e + \")\" : e;\n }\n break;\n case 'op_mul':\n if (js) {\n ret = '$jc$.mul(' + compile(node.children[0], \"op_mul\") + ', ' + compile(node.children[1], \"op_mul\") + ')';\n } else if (!format.minParentheses) {\n ret = '(' + compile(node.children[0], \"op_mul\") + ' * ' + compile(node.children[1], \"op_mul\") + ')';\n } else {\n prioParent = prio(node);\n\n e = compile(node.children[0], \"op_mul\");\n prioChild = prio(node.children[0]);\n ret = (prioParent > prioChild) ? \"(\" + e + \")\" : e;\n\n ret += ' * ';\n\n e = compile(node.children[1], \"op_mul\");\n prioChild = prio(node.children[1]);\n ret += (prioParent > prioChild) ? \"(\" + e + \")\" : e;\n }\n break;\n case 'op_exp':\n if (js) {\n ret = '$jc$.pow(' + compile(node.children[0], \"op_exp\", 0) + ', ' + compile(node.children[1], \"op_exp\", 1) + ')';\n } else if (!format.minParentheses) {\n ret = '('\n + compile(node.children[0], \"op_exp\", 0)\n + '^' + compile(node.children[1], \"op_exp\", 1)\n + ')';\n } else {\n prioParent = prio(node);\n\n e = compile(node.children[0], \"op_exp\", 0);\n prioChild = prio(node.children[0]);\n ret = (prioParent >= prioChild)\n ? \"(\" + e + \")\"\n : e;\n\n ret += '^';\n\n e = compile(node.children[1], \"op_exp\", 1);\n prioChild = prio(node.children[1]);\n ret += (prioParent > prioChild && !(format.printable && e[0] === '{' && e[e.length - 1] === '}'))\n ? \"(\" + e + \")\"\n : e;\n }\n break;\n case 'op_neg':\n if (js) {\n ret = '$jc$.neg(' + compile(node.children[0], \"op_neg\") + ')';\n } else if (!format.minParentheses) {\n ret = '(-' + compile(node.children[0], \"op_neg\") + ')';\n } else {\n prioParent = prio(node);\n prioChild = prio(node.children[0]);\n e = compile(node.children[0], \"op_neg\");\n if (prioParent >= prioChild) {\n ret = '-(' + e + ')';\n } else {\n ret = '-' + e;\n }\n }\n break;\n }\n break;\n\n case 'node_var':\n if (js) {\n ret = that.getvarJS(node.value, false, node.withProps);\n } else {\n ret = node.value;\n }\n break;\n\n case 'node_const':\n if (js) {\n ret = node.value;\n break;\n }\n\n c = node.value;\n if (\n format.constToFixed !== false &&\n Type.isNumber(c) &&\n !(prevOp === \"op_exp\" && position === 1) // exponents will not be formatted\n ) {\n c = parseFloat(c);\n if (Type.isNumber(format.constToFixed)) {\n c = Type.toFixed(c, format.constToFixed);\n } else if (Type.isFunction(format.constToFixed)) {\n c = format.constToFixed(c);\n } else {\n c = node.value;\n }\n }\n if (format.minParentheses && parseFloat(c) < 0 && prevOp !== \"op_execfun\" && position !== 0) {\n ret = \"(\" + c + \")\";\n } else {\n ret = c;\n }\n break;\n\n case 'node_const_bool':\n ret = node.value;\n break;\n\n case 'node_str':\n ret = '\\'' + node.value + '\\'';\n break;\n }\n\n if (node.needsAngleBrackets) {\n if (js) {\n ret = '{\\n' + ret + ' }\\n';\n } else {\n ret = '<< ' + ret + ' >>\\n';\n }\n }\n\n if (format.printable && prevOp === \"op_exp\" && position === 1) {\n ret = '{' + ret + '}';\n }\n\n if (format.printable && Type.isString(ret)) {\n ret = ret.replaceAll('\\n', '');\n }\n\n return ret;\n }\n\n return compile(ast, \"\");\n },\n\n /**\n * This is used as the global getName() function.\n * @param {JXG.GeometryElement} obj\n * @param {Boolean} useId\n * @returns {String}\n */\n getName: function (obj, useId) {\n var name = '';\n\n if (Type.exists(obj) && Type.exists(obj.getName)) {\n name = obj.getName();\n if ((!Type.exists(name) || name === '') && useId) {\n name = obj.id;\n }\n } else if (useId) {\n name = obj.id;\n }\n\n return name;\n },\n\n /**\n * This is used as the global X() function.\n * @param {JXG.Point|JXG.Text} e\n * @returns {Number}\n */\n X: function (e) {\n return e.X();\n },\n\n /**\n * This is used as the global Y() function.\n * @param {JXG.Point|JXG.Text} e\n * @returns {Number}\n */\n Y: function (e) {\n return e.Y();\n },\n\n /**\n * This is used as the global V() function.\n * @param {Glider|Slider} e\n * @returns {Number}\n */\n V: function (e) {\n return e.Value();\n },\n\n /**\n * This is used as the global L() function.\n * @param {JXG.Line} e\n * @returns {Number}\n */\n L: function (e) {\n return e.L();\n },\n\n /**\n * This is used as the global area() function.\n * @param {JXG.Circle|JXG.Polygon} obj\n * @returns {Number}\n */\n area: function (obj) {\n if (!Type.exists(obj) || !Type.exists(obj.Area)) {\n this._error('Error: Can\\'t calculate area.');\n }\n\n return obj.Area();\n },\n\n /**\n * This is used as the global perimeter() function.\n * @param {JXG.Circle|JXG.Polygon} obj\n * @returns {Number}\n */\n perimeter: function (obj) {\n if (!Type.exists(obj) || !Type.exists(obj.Perimeter)) {\n this._error('Error: Can\\'t calculate perimeter.');\n }\n\n return obj.Perimeter();\n },\n\n /**\n * This is used as the global dist() function.\n * @param {JXG.Point} p1\n * @param {JXG.Point} p2\n * @returns {Number}\n */\n dist: function (p1, p2) {\n if (!Type.exists(p1) || !Type.exists(p1.Dist)) {\n this._error('Error: Can\\'t calculate distance.');\n }\n\n return p1.Dist(p2);\n },\n\n /**\n * This is used as the global radius() function.\n * @param {JXG.Circle|Sector} obj\n * @returns {Number}\n */\n radius: function (obj) {\n if (!Type.exists(obj) || !Type.exists(obj.Radius)) {\n this._error('Error: Can\\'t calculate radius.');\n }\n\n return obj.Radius();\n },\n\n /**\n * This is used as the global slope() function.\n * @param {JXG.Line} obj\n * @returns {Number}\n */\n slope: function (obj) {\n if (!Type.exists(obj) || !Type.exists(obj.Slope)) {\n this._error('Error: Can\\'t calculate slope.');\n }\n\n return obj.Slope();\n },\n\n /**\n * + operator implementation\n * @param {Number|Array|JXG.Point} a\n * @param {Number|Array|JXG.Point} b\n * @returns {Number|Array}\n */\n add: function (a, b) {\n var i, len, res;\n\n a = Type.evalSlider(a);\n b = Type.evalSlider(b);\n\n if (Interval.isInterval(a) || Interval.isInterval(b)) {\n res = Interval.add(a, b);\n } else if (Type.isArray(a) && Type.isArray(b)) {\n len = Math.min(a.length, b.length);\n res = [];\n\n for (i = 0; i < len; i++) {\n res[i] = a[i] + b[i];\n }\n } else if (Type.isNumber(a) && Type.isNumber(b)) {\n res = a + b;\n } else if (Type.isString(a) || Type.isString(b)) {\n res = a.toString() + b.toString();\n } else {\n this._error('Operation + not defined on operands ' + typeof a + ' and ' + typeof b);\n }\n\n return res;\n },\n\n /**\n * - operator implementation\n * @param {Number|Array|JXG.Point} a\n * @param {Number|Array|JXG.Point} b\n * @returns {Number|Array}\n */\n sub: function (a, b) {\n var i, len, res;\n\n a = Type.evalSlider(a);\n b = Type.evalSlider(b);\n\n if (Interval.isInterval(a) || Interval.isInterval(b)) {\n res = Interval.sub(a, b);\n } else if (Type.isArray(a) && Type.isArray(b)) {\n len = Math.min(a.length, b.length);\n res = [];\n\n for (i = 0; i < len; i++) {\n res[i] = a[i] - b[i];\n }\n } else if (Type.isNumber(a) && Type.isNumber(b)) {\n res = a - b;\n } else {\n this._error('Operation - not defined on operands ' + typeof a + ' and ' + typeof b);\n }\n\n return res;\n },\n\n /**\n * unary - operator implementation\n * @param {Number|Array|JXG.Point} a\n * @returns {Number|Array}\n */\n neg: function (a) {\n var i, len, res;\n\n a = Type.evalSlider(a);\n\n if (Interval.isInterval(a)) {\n res = Interval.negative(a);\n } else if (Type.isArray(a)) {\n len = a.length;\n res = [];\n\n for (i = 0; i < len; i++) {\n res[i] = -a[i];\n }\n } else if (Type.isNumber(a)) {\n res = -a;\n } else {\n this._error('Unary operation - not defined on operand ' + typeof a);\n }\n\n return res;\n },\n\n /**\n * Multiplication of vectors and numbers\n * @param {Number|Array} a\n * @param {Number|Array} b\n * @returns {Number|Array} (Inner) product of the given input values.\n */\n mul: function (a, b) {\n var i, len, res;\n\n a = Type.evalSlider(a);\n b = Type.evalSlider(b);\n\n if (Type.isArray(a) && Type.isNumber(b)) {\n // swap b and a\n i = a;\n a = b;\n b = a;\n }\n\n if (Interval.isInterval(a) || Interval.isInterval(b)) {\n res = Interval.mul(a, b);\n } else if (Type.isArray(a) && Type.isArray(b)) {\n len = Math.min(a.length, b.length);\n res = Mat.innerProduct(a, b, len);\n } else if (Type.isNumber(a) && Type.isArray(b)) {\n len = b.length;\n res = [];\n\n for (i = 0; i < len; i++) {\n res[i] = a * b[i];\n }\n } else if (Type.isNumber(a) && Type.isNumber(b)) {\n res = a * b;\n } else {\n this._error('Operation * not defined on operands ' + typeof a + ' and ' + typeof b);\n }\n\n return res;\n },\n\n /**\n * Implementation of the / operator.\n * @param {Number|Array} a\n * @param {Number} b\n * @returns {Number|Array}\n */\n div: function (a, b) {\n var i, len, res;\n\n a = Type.evalSlider(a);\n b = Type.evalSlider(b);\n\n if (Interval.isInterval(a) || Interval.isInterval(b)) {\n res = Interval.div(a, b);\n } else if (Type.isArray(a) && Type.isNumber(b)) {\n len = a.length;\n res = [];\n\n for (i = 0; i < len; i++) {\n res[i] = a[i] / b;\n }\n } else if (Type.isNumber(a) && Type.isNumber(b)) {\n res = a / b;\n } else {\n this._error('Operation * not defined on operands ' + typeof a + ' and ' + typeof b);\n }\n\n return res;\n },\n\n /**\n * Implementation of the % operator.\n * @param {Number|Array} a\n * @param {Number} b\n * @returns {Number|Array}\n */\n mod: function (a, b) {\n var i, len, res;\n\n a = Type.evalSlider(a);\n b = Type.evalSlider(b);\n\n if (Interval.isInterval(a) || Interval.isInterval(b)) {\n return Interval.fmod(a, b);\n } else if (Type.isArray(a) && Type.isNumber(b)) {\n len = a.length;\n res = [];\n\n for (i = 0; i < len; i++) {\n res[i] = Mat.mod(a[i], b, true);\n }\n } else if (Type.isNumber(a) && Type.isNumber(b)) {\n res = Mat.mod(a, b, true);\n } else {\n this._error('Operation * not defined on operands ' + typeof a + ' and ' + typeof b);\n }\n\n return res;\n },\n\n /**\n * Pow function wrapper to allow direct usage of sliders.\n * @param {Number|Slider} a\n * @param {Number|Slider} b\n * @returns {Number}\n */\n pow: function (a, b) {\n a = Type.evalSlider(a);\n b = Type.evalSlider(b);\n\n if (Interval.isInterval(a) || Interval.isInterval(b)) {\n return Interval.pow(a, b);\n }\n return Mat.pow(a, b);\n },\n\n lt: function (a, b) {\n if (Interval.isInterval(a) || Interval.isInterval(b)) {\n return Interval.lt(a, b);\n }\n return a < b;\n },\n leq: function (a, b) {\n if (Interval.isInterval(a) || Interval.isInterval(b)) {\n return Interval.leq(a, b);\n }\n return a <= b;\n },\n gt: function (a, b) {\n if (Interval.isInterval(a) || Interval.isInterval(b)) {\n return Interval.gt(a, b);\n }\n return a > b;\n },\n geq: function (a, b) {\n if (Interval.isInterval(a) || Interval.isInterval(b)) {\n return Interval.geq(a, b);\n }\n return a >= b;\n },\n\n randint: function (min, max, step) {\n if (!Type.exists(step)) {\n step = 1;\n }\n return Math.round(Math.random() * (max - min) / step) * step + min;\n },\n\n DDD: function (f) {\n console.log('Dummy derivative function. This should never appear!');\n },\n\n /**\n * Implementation of the ?: operator\n * @param {Boolean} cond Condition\n * @param {*} v1\n * @param {*} v2\n * @returns {*} Either v1 or v2.\n */\n ifthen: function (cond, v1, v2) {\n if (cond) {\n return v1;\n }\n\n return v2;\n },\n\n /**\n * Implementation of the delete() builtin function\n * @param {JXG.GeometryElement} element\n */\n del: function (element) {\n if (typeof element === 'object' && JXG.exists(element.type) && JXG.exists(element.elementClass)) {\n this.board.removeObject(element);\n }\n },\n\n /**\n * Implementation of the eval() builtin function. Calls JXG.evaluate().\n * @param {String|Number|Function} v\n */\n eval: function (v) {\n return JXG.evaluate(v);\n },\n\n /**\n * Implementation of the use() builtin function\n * @param {String} board\n */\n use: function (board) {\n var b, ref,\n found = false;\n\n if (typeof board === 'string') {\n // search all the boards for the one with the appropriate container div\n for (b in JXG.boards) {\n if (JXG.boards.hasOwnProperty(b) && JXG.boards[b].container === board) {\n ref = JXG.boards[b];\n found = true;\n break;\n }\n }\n } else {\n ref = board;\n found = true;\n }\n\n if (found) {\n this.board = ref;\n this.builtIn.$board = ref;\n this.builtIn.$board.src = '$jc$.board';\n } else {\n this._error('Board \\'' + board + '\\' not found!');\n }\n },\n\n /**\n * Find the first symbol to the given value from the given scope upwards.\n * @param v Value\n * @param {Number} [scope=-1] The scope, default is to start with current scope (-1).\n * @returns {Array} An array containing the symbol and the scope if a symbol could be found,\n * an empty array otherwise;\n */\n findSymbol: function (v, scope) {\n var i, s;\n\n scope = Type.def(scope, -1);\n\n if (scope === -1) {\n s = this.scope;\n } else {\n s = this.scopes[scope];\n }\n\n while (s !== null) {\n for (i in s.locals) {\n if (s.locals.hasOwnProperty(i) && s.locals[i] === v) {\n return [i, s];\n }\n }\n\n s = s.previous;\n }\n\n return [];\n },\n\n /**\n * Import modules into a JessieCode script.\n * @param {String} module\n */\n importModule: function (module) {\n return priv.modules[module.toLowerCase()];\n },\n\n /**\n * Defines built in methods and constants.\n * @returns {Object} BuiltIn control object\n */\n defineBuiltIn: function () {\n var that = this,\n builtIn = {\n PI: Math.PI,\n EULER: Math.E,\n D: that.DDD,\n X: that.X,\n Y: that.Y,\n V: that.V,\n Value: that.V,\n L: that.L,\n Length: that.L,\n\n acosh: Mat.acosh,\n acot: Mat.acot,\n asinh: Mat.asinh,\n binomial: Mat.binomial,\n cbrt: Mat.cbrt,\n cosh: Mat.cosh,\n cot: Mat.cot,\n deg: Geometry.trueAngle,\n A: that.area,\n area: that.area,\n Area: that.area,\n perimeter: that.perimeter,\n Perimeter: that.perimeter,\n dist: that.dist,\n Dist: that.dist,\n R: that.radius,\n radius: that.radius,\n Radius: that.radius,\n erf: Mat.erf,\n erfc: Mat.erfc,\n erfi: Mat.erfi,\n factorial: Mat.factorial,\n gcd: Mat.gcd,\n lb: Mat.log2,\n lcm: Mat.lcm,\n ld: Mat.log2,\n lg: Mat.log10,\n ln: Math.log,\n log: Mat.log,\n log10: Mat.log10,\n log2: Mat.log2,\n ndtr: Mat.ndtr,\n ndtri: Mat.ndtri,\n nthroot: Mat.nthroot,\n pow: Mat.pow,\n rad: Geometry.rad,\n ratpow: Mat.ratpow,\n trunc: Type.trunc,\n sinh: Mat.sinh,\n slope: that.slope,\n Slope: that.slope,\n\n randint: that.randint,\n\n IfThen: that.ifthen,\n 'import': that.importModule,\n 'eval': that.eval,\n 'use': that.use,\n 'remove': that.del,\n '$': that.getElementById,\n '$value': function(e) {return that.getElementById(e).Value(); },\n getName: that.getName,\n name: that.getName,\n '$board': that.board,\n '$log': that.log\n };\n\n // special scopes for factorial, deg, and rad\n builtIn.rad.sc = Geometry;\n builtIn.deg.sc = Geometry;\n builtIn.factorial.sc = Mat;\n\n // set the javascript equivalent for the builtIns\n // some of the anonymous functions should be replaced by global methods later on\n // EULER and PI don't get a source attribute - they will be lost anyways and apparently\n // some browser will throw an exception when a property is assigned to a primitive value.\n builtIn.X.src = '$jc$.X';\n builtIn.Y.src = '$jc$.Y';\n builtIn.V.src = '$jc$.V';\n builtIn.Value.src = '$jc$.V';\n builtIn.L.src = '$jc$.L';\n builtIn.Length.src = '$jc$.L';\n\n builtIn.acosh.src = 'JXG.Math.acosh';\n builtIn.acot.src = 'JXG.Math.acot';\n builtIn.asinh.src = 'JXG.Math.asinh';\n builtIn.binomial.src = 'JXG.Math.binomial';\n builtIn.cbrt.src = 'JXG.Math.cbrt';\n builtIn.cot.src = 'JXG.Math.cot';\n builtIn.cosh.src = 'JXG.Math.cosh';\n builtIn.deg.src = 'JXG.Math.Geometry.trueAngle';\n builtIn.erf.src = 'JXG.Math.erf';\n builtIn.erfc.src = 'JXG.Math.erfc';\n builtIn.erfi.src = 'JXG.Math.erfi';\n builtIn.A.src = '$jc$.area';\n builtIn.area.src = '$jc$.area';\n builtIn.Area.src = '$jc$.area';\n builtIn.perimeter.src = '$jc$.perimeter';\n builtIn.Perimeter.src = '$jc$.perimeter';\n builtIn.dist.src = '$jc$.dist';\n builtIn.Dist.src = '$jc$.dist';\n builtIn.R.src = '$jc$.radius';\n builtIn.radius.src = '$jc$.radius';\n builtIn.Radius.src = '$jc$.radius';\n builtIn.factorial.src = 'JXG.Math.factorial';\n builtIn.gcd.src = 'JXG.Math.gcd';\n builtIn.lb.src = 'JXG.Math.log2';\n builtIn.lcm.src = 'JXG.Math.lcm';\n builtIn.ld.src = 'JXG.Math.log2';\n builtIn.lg.src = 'JXG.Math.log10';\n builtIn.ln.src = 'Math.log';\n builtIn.log.src = 'JXG.Math.log';\n builtIn.log10.src = 'JXG.Math.log10';\n builtIn.log2.src = 'JXG.Math.log2';\n builtIn.ndtr.src = 'JXG.Math.ndtr';\n builtIn.ndtri.src = 'JXG.Math.ndtri';\n builtIn.nthroot.src = 'JXG.Math.nthroot';\n builtIn.pow.src = 'JXG.Math.pow';\n builtIn.rad.src = 'JXG.Math.Geometry.rad';\n builtIn.ratpow.src = 'JXG.Math.ratpow';\n builtIn.trunc.src = 'JXG.trunc';\n builtIn.sinh.src = 'JXG.Math.sinh';\n builtIn.slope.src = '$jc$.slope';\n builtIn.Slope.src = '$jc$.slope';\n\n builtIn.randint.src = '$jc$.randint';\n\n builtIn['import'].src = '$jc$.importModule';\n builtIn.eval.src = '$jc$.eval';\n builtIn.use.src = '$jc$.use';\n builtIn.remove.src = '$jc$.del';\n builtIn.IfThen.src = '$jc$.ifthen';\n // usually unused, see node_op > op_execfun\n builtIn.$.src = '(function (n) { return $jc$.board.select(n); 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$$[$0];\nbreak;\ncase 53: this.$ = AST.createNode(lc(_$[$0-1]), 'node_op', 'op_neg', $$[$0]); this.$.isMath = true;\nbreak;\ncase 54: this.$ = $$[$0];\nbreak;\ncase 55: this.$ = $$[$0];\nbreak;\ncase 56: this.$ = $$[$0];\nbreak;\ncase 57: this.$ = $$[$0]; this.$.isMath = false;\nbreak;\ncase 58: this.$ = $$[$0];\nbreak;\ncase 59: this.$ = AST.createNode(lc(_$[$0-2]), 'node_op', 'op_property', $$[$0-2], $$[$0]); this.$.isMath = true;\nbreak;\ncase 60: this.$ = AST.createNode(lc(_$[$0-3]), 'node_op', 'op_extvalue', $$[$0-3], $$[$0-1]); this.$.isMath = true;\nbreak;\ncase 61: this.$ = AST.createNode(lc(_$[$0]), 'node_var', $$[$0]);\nbreak;\ncase 62: this.$ = $$[$0];\nbreak;\ncase 63: this.$ = $$[$0]; this.$.isMath = false;\nbreak;\ncase 64: this.$ = $$[$0]; this.$.isMath = false;\nbreak;\ncase 65: this.$ = $$[$0-1];\nbreak;\ncase 66: this.$ = $$[$0]; this.$.isMath = false;\nbreak;\ncase 67: this.$ = $$[$0]; this.$.isMath = false;\nbreak;\ncase 68: this.$ = $$[$0]; this.$.isMath = false;\nbreak;\ncase 69: this.$ = $$[$0]; this.$.isMath = true;\nbreak;\ncase 70: this.$ = AST.createNode(lc(_$[$0]), 'node_const', null);\nbreak;\ncase 71: this.$ = AST.createNode(lc(_$[$0]), 'node_const_bool', true);\nbreak;\ncase 72: this.$ = AST.createNode(lc(_$[$0]), 'node_const_bool', false);\nbreak;\ncase 73: this.$ = AST.createNode(lc(_$[$0]), 'node_str', $$[$0].substring(1, $$[$0].length - 1));\nbreak;\ncase 74: this.$ = AST.createNode(lc(_$[$0]), 'node_const', parseFloat($$[$0]));\nbreak;\ncase 75: this.$ = AST.createNode(lc(_$[$0]), 'node_const', NaN);\nbreak;\ncase 76: this.$ = AST.createNode(lc(_$[$0]), 'node_const', Infinity);\nbreak;\ncase 77: this.$ = AST.createNode(lc(_$[$0-1]), 'node_op', 'op_array', []);\nbreak;\ncase 78: this.$ = AST.createNode(lc(_$[$0-2]), 'node_op', 'op_array', $$[$0-1]);\nbreak;\ncase 79: this.$ = AST.createNode(lc(_$[$0-1]), 'node_op', 'op_emptyobject', {}); this.$.needsAngleBrackets = true;\nbreak;\ncase 80: this.$ = AST.createNode(lc(_$[$0-2]), 'node_op', 'op_proplst_val', $$[$0-1]); this.$.needsAngleBrackets = true;\nbreak;\ncase 81: this.$ = $$[$0];\nbreak;\ncase 82: this.$ = AST.createNode(lc(_$[$0-2]), 'node_op', 'op_proplst', $$[$0-2], $$[$0]);\nbreak;\ncase 83: this.$ = AST.createNode(lc(_$[$0-2]), 'node_op', 'op_prop', $$[$0-2], $$[$0]);\nbreak;\ncase 84: this.$ = $$[$0];\nbreak;\ncase 85: this.$ = $$[$0];\nbreak;\ncase 86: this.$ = $$[$0];\nbreak;\ncase 87: this.$ = AST.createNode(lc(_$[$0-1]), 'node_op', 'op_execfun', $$[$0-1], $$[$0]); this.$.isMath = true;\nbreak;\ncase 88: this.$ = AST.createNode(lc(_$[$0-2]), 'node_op', 'op_execfun', $$[$0-2], $$[$0-1], $$[$0], true); this.$.isMath = false;\nbreak;\ncase 89: this.$ = AST.createNode(lc(_$[$0-1]), 'node_op', 'op_execfun', $$[$0-1], $$[$0]); this.$.isMath = true;\nbreak;\ncase 90: this.$ = AST.createNode(lc(_$[$0-3]), 'node_op', 'op_extvalue', $$[$0-3], $$[$0-1]); this.$.isMath = true;\nbreak;\ncase 91: this.$ = AST.createNode(lc(_$[$0-2]), 'node_op', 'op_property', $$[$0-2], $$[$0]); this.$.isMath = true;\nbreak;\ncase 92: this.$ = [];\nbreak;\ncase 93: this.$ = $$[$0-1];\nbreak;\ncase 94: this.$ = [$$[$0]];\nbreak;\ncase 95: this.$ = $$[$0-2].concat($$[$0]);\nbreak;\ncase 96: this.$ = AST.createNode(lc(_$[$0]), 'node_var', $$[$0]); this.$.isMath = true;\nbreak;\ncase 97: this.$ = $$[$0]; this.$.isMath = false;\nbreak;\ncase 98: this.$ = [$$[$0]];\nbreak;\ncase 99: this.$ = $$[$0-2].concat($$[$0]);\nbreak;\ncase 100: this.$ = AST.createNode(lc(_$[$0-3]), 'node_op', 'op_function', [], $$[$0]); this.$.isMath = false;\nbreak;\ncase 101: this.$ = AST.createNode(lc(_$[$0-4]), 'node_op', 'op_function', $$[$0-2], $$[$0]); this.$.isMath = false;\nbreak;\ncase 102: this.$ = AST.createNode(lc(_$[$0-4]), 'node_op', 'op_map', [], $$[$0]);\nbreak;\ncase 103: this.$ = AST.createNode(lc(_$[$0-5]), 'node_op', 'op_map', $$[$0-3], $$[$0]);\nbreak;\ncase 104: this.$ = [$$[$0]];\nbreak;\ncase 105: this.$ = $$[$0-2].concat($$[$0]);\nbreak;\n}\n},\ntable: 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[2,5],14:[2,5],15:[2,5],16:[2,5],17:[2,5],19:[2,5],20:[2,5],21:[2,5],23:[2,5],26:[2,5],27:[2,5],50:[2,5],51:[2,5],58:[2,5],65:[2,5],74:[2,5],75:[2,5],76:[2,5],77:[2,5],78:[2,5],79:[2,5],80:[2,5],82:[2,5],91:[2,5],93:[2,5]}],\ndefaultActions: {3:[2,1],97:[2,84],98:[2,85],99:[2,86]},\nparseError: function parseError (str, hash) {\n throw new Error(str);\n},\n/**\n * @class\n * @ignore\n */\nparse: function parse(input) {\n var self = this, stack = [0], vstack = [null], lstack = [], table = this.table, yytext = \"\", yylineno = 0, yyleng = 0, recovering = 0, TERROR = 2, EOF = 1;\n this.lexer.setInput(input);\n this.lexer.yy = this.yy;\n this.yy.lexer = this.lexer;\n this.yy.parser = this;\n if (typeof this.lexer.yylloc == \"undefined\")\n this.lexer.yylloc = {};\n var yyloc = this.lexer.yylloc;\n lstack.push(yyloc);\n var ranges = this.lexer.options && this.lexer.options.ranges;\n if (typeof this.yy.parseError === \"function\")\n this.parseError = this.yy.parseError;\n function popStack(n) {\n stack.length = stack.length - 2 * n;\n vstack.length = vstack.length - n;\n lstack.length = lstack.length - n;\n }\n function lex() {\n var token;\n token = self.lexer.lex() || 1;\n if (typeof token !== \"number\") {\n token = self.symbols_[token] || token;\n }\n return token;\n }\n var symbol, preErrorSymbol, state, action, a, r, yyval = {}, p, len, newState, expected;\n while (true) {\n state = stack[stack.length - 1];\n if (this.defaultActions[state]) {\n action = this.defaultActions[state];\n } else {\n if (symbol === null || typeof symbol == \"undefined\") {\n symbol = lex();\n }\n action = table[state] && table[state][symbol];\n }\n if (typeof action === \"undefined\" || !action.length || !action[0]) {\n var errStr = \"\";\n if (!recovering) {\n expected = [];\n for (p in table[state])\n if (this.terminals_[p] && p > 2) {\n expected.push(\"'\" + this.terminals_[p] + \"'\");\n }\n if (this.lexer.showPosition) {\n errStr = \"Parse error on line \" + (yylineno + 1) + \":\\n\" + this.lexer.showPosition() + \"\\nExpecting \" + expected.join(\", \") + \", got '\" + (this.terminals_[symbol] || symbol) + \"'\";\n } else {\n errStr = \"Parse error on line \" + (yylineno + 1) + \": Unexpected \" + (symbol == 1?\"end of input\":\"'\" + (this.terminals_[symbol] || symbol) + \"'\");\n }\n this.parseError(errStr, {text: this.lexer.match, token: this.terminals_[symbol] || symbol, line: this.lexer.yylineno, loc: yyloc, expected: expected});\n }\n }\n if (action[0] instanceof Array && action.length > 1) {\n throw new Error(\"Parse Error: multiple actions possible at state: \" + state + \", token: \" + symbol);\n }\n switch (action[0]) {\n case 1:\n stack.push(symbol);\n vstack.push(this.lexer.yytext);\n lstack.push(this.lexer.yylloc);\n stack.push(action[1]);\n symbol = null;\n if (!preErrorSymbol) {\n yyleng = this.lexer.yyleng;\n yytext = this.lexer.yytext;\n yylineno = this.lexer.yylineno;\n yyloc = this.lexer.yylloc;\n if (recovering > 0)\n recovering--;\n } else {\n symbol = preErrorSymbol;\n preErrorSymbol = null;\n }\n break;\n case 2:\n len = this.productions_[action[1]][1];\n yyval.$ = vstack[vstack.length - len];\n yyval._$ = {first_line: lstack[lstack.length - (len || 1)].first_line, last_line: lstack[lstack.length - 1].last_line, first_column: lstack[lstack.length - (len || 1)].first_column, last_column: lstack[lstack.length - 1].last_column};\n if (ranges) {\n yyval._$.range = [lstack[lstack.length - (len || 1)].range[0], lstack[lstack.length - 1].range[1]];\n }\n r = this.performAction.call(yyval, yytext, yyleng, yylineno, this.yy, action[1], vstack, lstack);\n if (typeof r !== \"undefined\") {\n return r;\n }\n if (len) {\n stack = stack.slice(0, -1 * len * 2);\n vstack = vstack.slice(0, -1 * len);\n lstack = lstack.slice(0, -1 * len);\n }\n stack.push(this.productions_[action[1]][0]);\n vstack.push(yyval.$);\n lstack.push(yyval._$);\n newState = table[stack[stack.length - 2]][stack[stack.length - 1]];\n stack.push(newState);\n break;\n case 3:\n return true;\n }\n }\n return true;\n}\n};\n\n\n var AST = {\n node: function (type, value, children) {\n return {\n type: type,\n value: value,\n children: children\n };\n },\n\n createNode: function (pos, type, value, children) {\n var i,\n n = this.node(type, value, []);\n\n for (i = 3; i < arguments.length; i++) {\n n.children.push(arguments[i]);\n }\n\n n.line = pos[0];\n n.col = pos[1];\n n.eline = pos[2];\n n.ecol = pos[3];\n\n return n;\n }\n };\n\n var lc = function (lc1) {\n return [lc1.first_line, lc1.first_column, lc1.last_line, lc1.last_column];\n };\n\n/* Jison generated lexer */\nvar lexer = (function(){\nvar lexer = ({EOF:1,\nparseError:function parseError(str, hash) {\n if (this.yy.parser) {\n this.yy.parser.parseError(str, hash);\n } else {\n throw new Error(str);\n }\n },\nsetInput:function (input) {\n this._input = input;\n this._more = this._less = this.done = false;\n this.yylineno = this.yyleng = 0;\n this.yytext = this.matched = this.match = '';\n this.conditionStack = ['INITIAL'];\n this.yylloc = {first_line:1,first_column:0,last_line:1,last_column:0};\n if (this.options.ranges) this.yylloc.range = [0,0];\n this.offset = 0;\n return this;\n },\ninput:function () {\n var ch = this._input[0];\n this.yytext += ch;\n this.yyleng++;\n this.offset++;\n this.match += ch;\n this.matched += ch;\n var lines = ch.match(/(?:\\r\\n?|\\n).*/g);\n if (lines) {\n this.yylineno++;\n this.yylloc.last_line++;\n } else {\n this.yylloc.last_column++;\n }\n if (this.options.ranges) this.yylloc.range[1]++;\n\n this._input = this._input.slice(1);\n return ch;\n },\nunput:function (ch) {\n var len = ch.length;\n var lines = ch.split(/(?:\\r\\n?|\\n)/g);\n\n this._input = ch + this._input;\n this.yytext = this.yytext.substr(0, this.yytext.length-len-1);\n //this.yyleng -= len;\n this.offset -= len;\n var oldLines = this.match.split(/(?:\\r\\n?|\\n)/g);\n this.match = this.match.substr(0, this.match.length-1);\n this.matched = this.matched.substr(0, this.matched.length-1);\n\n if (lines.length-1) this.yylineno -= lines.length-1;\n var r = this.yylloc.range;\n\n this.yylloc = {first_line: this.yylloc.first_line,\n last_line: this.yylineno+1,\n first_column: this.yylloc.first_column,\n last_column: lines ?\n (lines.length === oldLines.length ? this.yylloc.first_column : 0) + oldLines[oldLines.length - lines.length].length - lines[0].length:\n this.yylloc.first_column - len\n };\n\n if (this.options.ranges) {\n this.yylloc.range = [r[0], r[0] + this.yyleng - len];\n }\n return this;\n },\nmore:function () {\n this._more = true;\n return this;\n },\nless:function (n) {\n this.unput(this.match.slice(n));\n },\npastInput:function () {\n var past = this.matched.substr(0, this.matched.length - this.match.length);\n return (past.length > 20 ? '...':'') + past.substr(-20).replace(/\\n/g, \"\");\n },\nupcomingInput:function () {\n var next = this.match;\n if (next.length < 20) {\n next += this._input.substr(0, 20-next.length);\n }\n return (next.substr(0,20)+(next.length > 20 ? '...':'')).replace(/\\n/g, \"\");\n },\nshowPosition:function () {\n var pre = this.pastInput();\n var c = new Array(pre.length + 1).join(\"-\");\n return pre + this.upcomingInput() + \"\\n\" + c+\"^\";\n },\nnext:function () {\n if (this.done) {\n return this.EOF;\n }\n if (!this._input) this.done = true;\n\n var token,\n match,\n tempMatch,\n index,\n col,\n lines;\n if (!this._more) {\n this.yytext = '';\n this.match = '';\n }\n var rules = this._currentRules();\n for (var i=0;i < rules.length; i++) {\n tempMatch = this._input.match(this.rules[rules[i]]);\n if (tempMatch && (!match || tempMatch[0].length > match[0].length)) {\n match = tempMatch;\n index = i;\n if (!this.options.flex) break;\n }\n }\n if (match) {\n lines = match[0].match(/(?:\\r\\n?|\\n).*/g);\n if (lines) this.yylineno += lines.length;\n this.yylloc = {first_line: this.yylloc.last_line,\n last_line: this.yylineno+1,\n first_column: this.yylloc.last_column,\n last_column: lines ? lines[lines.length-1].length-lines[lines.length-1].match(/\\r?\\n?/)[0].length : this.yylloc.last_column + match[0].length};\n this.yytext += match[0];\n this.match += match[0];\n this.matches = match;\n this.yyleng = this.yytext.length;\n if (this.options.ranges) {\n this.yylloc.range = [this.offset, this.offset += this.yyleng];\n }\n this._more = false;\n this._input = this._input.slice(match[0].length);\n this.matched += match[0];\n token = this.performAction.call(this, this.yy, this, rules[index],this.conditionStack[this.conditionStack.length-1]);\n if (this.done && this._input) this.done = false;\n if (token) return token;\n else return;\n }\n if (this._input === \"\") {\n return this.EOF;\n } else {\n return this.parseError('Lexical error on line '+(this.yylineno+1)+'. Unrecognized text.\\n'+this.showPosition(),\n {text: \"\", token: null, line: this.yylineno});\n }\n },\nlex:function lex () {\n var r = this.next();\n if (typeof r !== 'undefined') {\n return r;\n } else {\n return this.lex();\n }\n },\nbegin:function begin (condition) {\n this.conditionStack.push(condition);\n },\npopState:function popState () {\n return this.conditionStack.pop();\n },\n_currentRules:function _currentRules () {\n return this.conditions[this.conditionStack[this.conditionStack.length-1]].rules;\n },\ntopState:function () {\n return this.conditionStack[this.conditionStack.length-2];\n },\npushState:function begin (condition) {\n this.begin(condition);\n }});\nlexer.options = {};\nlexer.performAction = function anonymous(yy,yy_,$avoiding_name_collisions,YY_START\n) {\n\nvar YYSTATE=YY_START\nswitch($avoiding_name_collisions) {\ncase 0:/* ignore */\nbreak;\ncase 1:return 78 /* New 123.1234e+-12 */\nbreak;\ncase 2:return 78 /* Old 123.1234 or .1234 */\nbreak;\ncase 3:return 78 /* Old 123 */\nbreak;\ncase 4: return 77;\nbreak;\ncase 5: return 77;\nbreak;\ncase 6:/* ignore comment */\nbreak;\ncase 7:/* ignore multiline comment */\nbreak;\ncase 8:return 7\nbreak;\ncase 9:return 12\nbreak;\ncase 10:return 14\nbreak;\ncase 11:return 17\nbreak;\ncase 12:return 15\nbreak;\ncase 13:return 91\nbreak;\ncase 14:return 93\nbreak;\ncase 15:return 19\nbreak;\ncase 16:return 23\nbreak;\ncase 17:return 21\nbreak;\ncase 18:return 75\nbreak;\ncase 19:return 76\nbreak;\ncase 20:return 74\nbreak;\ncase 21:return 80\nbreak;\ncase 22:return 94\nbreak;\ncase 23:return 94\nbreak;\ncase 24:return 82\nbreak;\ncase 25:return 83\nbreak;\ncase 26:return 26\nbreak;\ncase 27:return 27\nbreak;\ncase 28:return 16\nbreak;\ncase 29:return '#'\nbreak;\ncase 30:return 34\nbreak;\ncase 31:return 35\nbreak;\ncase 32:return 79\nbreak;\ncase 33:return 64\nbreak;\ncase 34:return 65\nbreak;\ncase 35:return 66\nbreak;\ncase 36:return 8\nbreak;\ncase 37:return 10\nbreak;\ncase 38:return 58\nbreak;\ncase 39:return 57\nbreak;\ncase 40:return 57\nbreak;\ncase 41:return 53\nbreak;\ncase 42:return 54\nbreak;\ncase 43:return 55\nbreak;\ncase 44:return 50\nbreak;\ncase 45:return 51\nbreak;\ncase 46:return 47\nbreak;\ncase 47:return 45\nbreak;\ncase 48:return 48\nbreak;\ncase 49:return 46\nbreak;\ncase 50:return 41\nbreak;\ncase 51:return 43\nbreak;\ncase 52:return 42\nbreak;\ncase 53:return 39\nbreak;\ncase 54:return 37\nbreak;\ncase 55:return 32\nbreak;\ncase 56:return 86\nbreak;\ncase 57:return 5\nbreak;\ncase 58:return 20\nbreak;\ncase 59:return 'INVALID'\nbreak;\n}\n};\nlexer.rules = [/^(?:\\s+)/,/^(?:[0-9]*\\.?[0-9]+([eE][-+]?[0-9]+))/,/^(?:[0-9]+\\.[0-9]*|[0-9]*\\.[0-9]+\\b)/,/^(?:[0-9]+)/,/^(?:\"(\\\\[\"]|[^\"])*\")/,/^(?:'(\\\\[']|[^'])*')/,/^(?:\\/\\/.*)/,/^(?:\\/\\*(.|\\n|\\r)*?\\*\\/)/,/^(?:if\\b)/,/^(?:else\\b)/,/^(?:while\\b)/,/^(?:do\\b)/,/^(?:for\\b)/,/^(?:function\\b)/,/^(?:map\\b)/,/^(?:use\\b)/,/^(?:return\\b)/,/^(?:delete\\b)/,/^(?:true\\b)/,/^(?:false\\b)/,/^(?:null\\b)/,/^(?:Infinity\\b)/,/^(?:->)/,/^(?:=>)/,/^(?:<<)/,/^(?:>>)/,/^(?:\\{)/,/^(?:\\})/,/^(?:;)/,/^(?:#)/,/^(?:\\?)/,/^(?::)/,/^(?:NaN\\b)/,/^(?:\\.)/,/^(?:\\[)/,/^(?:\\])/,/^(?:\\()/,/^(?:\\))/,/^(?:!)/,/^(?:\\^)/,/^(?:\\*\\*)/,/^(?:\\*)/,/^(?:\\/)/,/^(?:%)/,/^(?:\\+)/,/^(?:-)/,/^(?:<=)/,/^(?:<)/,/^(?:>=)/,/^(?:>)/,/^(?:==)/,/^(?:~=)/,/^(?:!=)/,/^(?:&&)/,/^(?:\\|\\|)/,/^(?:=)/,/^(?:,)/,/^(?:$)/,/^(?:[A-Za-z_\\$][A-Za-z0-9_]*)/,/^(?:.)/];\nlexer.conditions = {\"INITIAL\":{\"rules\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59],\"inclusive\":true}};\nreturn lexer;})()\nparser.lexer = lexer;\n/**\n * @class\n * @ignore\n */\nfunction Parser () { this.yy = {}; }Parser.prototype = parser;parser.Parser = Parser;\nreturn new Parser;\n})();\n// Work around an issue with browsers that don't support Object.getPrototypeOf()\nparser.yy.parseError = parser.parseError;\n\nexport default JXG.JessieCode;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Andreas Walter,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n *\n * As substitutes for standard colors, it contains the following aliases:\n *\n * \n *
\n *\n * See Bang Wong: \"Points of view: Color blindness\"\n * and\n * https://davidmathlogic.com/colorblind/.\n *\n * @name JXG.paletteWong\n * @type Object\n * @see JXG.palette\n * @example\n * var p = board.create('line', [[-1, 1], [2, -3]], {strokeColor: JXG.paletteWong.yellow});\n */\n paletteWong: {\n black: \"#000000\",\n orange: \"#E69F00\",\n skyblue: \"#56B4E9\",\n bluishgreen: \"#009E73\",\n yellow: \"#F0E442\",\n darkblue: \"#0072B2\",\n vermillion: \"#D55E00\",\n reddishpurple: \"#CC79A7\",\n\n blue: \"#0072B2\",\n red: \"#D55E00\", // vermillion\n green: \"#009E73\", // bluishgreen\n purple: \"#CC79A7\", // reddishpurple\n white: \"#ffffff\"\n }\n }\n);\n\n/**\n * Default color palette.\n * Contains at least color values for\n * \n *
\n *\n * @name JXG.palette\n * @type Object\n * @default JXG.paletteWong\n * @see JXG.paletteWong\n *\n * @example\n *\n * var p = board.create('line', [[-1, 1], [2, -3]], {strokeColor: JXG.palette.yellow});\n *\n */\nJXG.palette = JXG.paletteWong;\n\nexport default JXG;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Andreas Walter,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see @borrows JXG.EventEmitter#on as this.on
\n * @param {Object} o\n */\n eventify: function (o) {\n o.eventHandlers = {\n clicks: 0 // Needed to handle dblclicks\n };\n o.on = this.on;\n o.off = this.off;\n o.triggerEventHandlers = this.trigger;\n o.trigger = this.trigger;\n o.suspended = {};\n }\n};\n\nexport default JXG.EventEmitter;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n * In the last three cases a new point will be created.\n * @param {String} attrClass Main attribute class of newly created points, see {@link JXG#copyAttributes}\n * @param {Array} attrArray List of subtype attributes for the newly created points. The list of subtypes is mapped to the list of new points.\n * @returns {Array} List of newly created {@link JXG.Point} elements or false if not all returned elements are points.\n */\n providePoints: function (board, parents, attributes, attrClass, attrArray) {\n var i,\n j,\n len,\n lenAttr = 0,\n points = [],\n attr,\n val;\n\n if (!this.isArray(parents)) {\n parents = [parents];\n }\n len = parents.length;\n if (this.exists(attrArray)) {\n lenAttr = attrArray.length;\n }\n if (lenAttr === 0) {\n attr = this.copyAttributes(attributes, board.options, attrClass);\n }\n\n for (i = 0; i < len; ++i) {\n if (lenAttr > 0) {\n j = Math.min(i, lenAttr - 1);\n attr = this.copyAttributes(\n attributes,\n board.options,\n attrClass,\n attrArray[j].toLowerCase()\n );\n }\n if (this.isArray(parents[i]) && parents[i].length > 1) {\n points.push(board.create(\"point\", parents[i], attr));\n points[points.length - 1]._is_new = true;\n } else if (this.isFunction(parents[i])) {\n val = parents[i]();\n if (this.isArray(val) && val.length > 1) {\n points.push(board.create(\"point\", [parents[i]], attr));\n points[points.length - 1]._is_new = true;\n }\n } else {\n points.push(board.select(parents[i]));\n }\n\n if (!this.isPoint(points[i])) {\n return false;\n }\n }\n\n return points;\n },\n\n /**\n * Test if the parents array contains existing points. If instead parents contains coordinate arrays or\n * function returning coordinate arrays\n * free points with these coordinates are created.\n *\n * @param {JXG.View3D} view View3D object\n * @param {Array} parents Array containing parent elements for a new object. This array may contain\n * \n *
\n * In the last three cases a new 3D point will be created.\n * @param {String} attrClass Main attribute class of newly created 3D points, see {@link JXG#copyAttributes}\n * @param {Array} attrArray List of subtype attributes for the newly created 3D points. The list of subtypes is mapped to the list of new 3D points.\n * @returns {Array} List of newly created {@link JXG.Point3D} elements or false if not all returned elements are 3D points.\n */\n providePoints3D: function (view, parents, attributes, attrClass, attrArray) {\n var i,\n j,\n len,\n lenAttr = 0,\n points = [],\n attr,\n val;\n\n if (!this.isArray(parents)) {\n parents = [parents];\n }\n len = parents.length;\n if (this.exists(attrArray)) {\n lenAttr = attrArray.length;\n }\n if (lenAttr === 0) {\n attr = this.copyAttributes(attributes, view.board.options, attrClass);\n }\n\n for (i = 0; i < len; ++i) {\n if (lenAttr > 0) {\n j = Math.min(i, lenAttr - 1);\n attr = this.copyAttributes(\n attributes,\n view.board.options,\n attrClass,\n attrArray[j]\n );\n }\n\n if (this.isArray(parents[i]) && parents[i].length > 0 && parents[i].every((x)=>this.isArray(x) && this.isNumber(x[0]))) {\n // Testing for array-of-arrays-of-numbers, like [[1,2,3],[2,3,4]]\n for (j = 0; j < parents[i].length; j++) {\n points.push(view.create(\"point3d\", parents[i][j], attr));;\n points[points.length - 1]._is_new = true;\n }\n } else if (this.isArray(parents[i]) && parents[i].every((x)=> this.isNumber(x) || this.isFunction(x))) {\n // Single array [1,2,3]\n points.push(view.create(\"point3d\", parents[i], attr));\n points[points.length - 1]._is_new = true;\n\n } else if (this.isPoint3D(parents[i])) {\n points.push(parents[i]);\n } else if (this.isFunction(parents[i])) {\n val = parents[i]();\n if (this.isArray(val) && val.length > 1) {\n points.push(view.create(\"point3d\", [parents[i]], attr));\n points[points.length - 1]._is_new = true;\n }\n } else {\n points.push(view.select(parents[i]));\n }\n\n if (!this.isPoint3D(points[i])) {\n return false;\n }\n }\n\n return points;\n },\n\n /**\n * Generates a function which calls the function fn in the scope of owner.\n * @param {Function} fn Function to call.\n * @param {Object} owner Scope in which fn is executed.\n * @returns {Function} A function with the same signature as fn.\n */\n bind: function (fn, owner) {\n return function () {\n return fn.apply(owner, arguments);\n };\n },\n\n /**\n * If val is a function, it will be evaluated without giving any parameters, else the input value\n * is just returned.\n * @param val Could be anything. Preferably a number or a function. If it is an array, evaluate() recurses\n * into the elements.\n * @returns If val is a function, it is evaluated and the result is returned. Otherwise val is returned.\n */\n evaluate: function (val) {\n var i, le, arr;\n\n if (this.isFunction(val)) {\n return val();\n }\n if (this.isArray(val)) {\n le = val.length;\n arr = [];\n for (i = 0; i < le; i++) {\n arr.push(this.evaluate(val[i]));\n }\n return arr;\n }\n\n return val;\n },\n\n /**\n * Search an array for a given value.\n * @param {Array} array\n * @param value\n * @param {String} [sub] Use this property if the elements of the array are objects.\n * @returns {Number} The index of the first appearance of the given value, or\n * -1 if the value was not found.\n */\n indexOf: function (array, value, sub) {\n var i,\n s = this.exists(sub);\n\n if (Array.indexOf && !s) {\n return array.indexOf(value);\n }\n\n for (i = 0; i < array.length; i++) {\n if ((s && array[i][sub] === value) || (!s && array[i] === value)) {\n return i;\n }\n }\n\n return -1;\n },\n\n /**\n * Eliminates duplicate entries in an array consisting of numbers and strings.\n * @param {Array} a An array of numbers and/or strings.\n * @returns {Array} The array with duplicate entries eliminated.\n */\n eliminateDuplicates: function (a) {\n var i,\n len = a.length,\n result = [],\n obj = {};\n\n for (i = 0; i < len; i++) {\n obj[a[i]] = 0;\n }\n\n for (i in obj) {\n if (obj.hasOwnProperty(i)) {\n result.push(i);\n }\n }\n\n return result;\n },\n\n /**\n * Swaps to array elements.\n * @param {Array} arr\n * @param {Number} i\n * @param {Number} j\n * @returns {Array} Reference to the given array.\n */\n swap: function (arr, i, j) {\n var tmp;\n\n tmp = arr[i];\n arr[i] = arr[j];\n arr[j] = tmp;\n\n return arr;\n },\n\n /**\n * Generates a copy of an array and removes the duplicate entries.\n * The original array will be altered.\n * @param {Array} arr\n * @returns {Array}\n *\n * @see JXG.toUniqueArrayFloat\n */\n uniqueArray: function (arr) {\n var i,\n j,\n isArray,\n ret = [];\n\n if (arr.length === 0) {\n return [];\n }\n\n for (i = 0; i < arr.length; i++) {\n isArray = this.isArray(arr[i]);\n\n if (!this.exists(arr[i])) {\n arr[i] = \"\";\n continue;\n }\n for (j = i + 1; j < arr.length; j++) {\n if (isArray && JXG.cmpArrays(arr[i], arr[j])) {\n arr[i] = [];\n } else if (!isArray && arr[i] === arr[j]) {\n arr[i] = \"\";\n }\n }\n }\n\n j = 0;\n\n for (i = 0; i < arr.length; i++) {\n isArray = this.isArray(arr[i]);\n\n if (!isArray && arr[i] !== \"\") {\n ret[j] = arr[i];\n j++;\n } else if (isArray && arr[i].length !== 0) {\n ret[j] = arr[i].slice(0);\n j++;\n }\n }\n\n arr = ret;\n return ret;\n },\n\n /**\n * Generates a sorted copy of an array containing numbers and removes the duplicate entries up to a supplied precision eps.\n * An array element arr[i] will be removed if abs(arr[i] - arr[i-1]) is less than eps.\n *\n * The original array will stay unaltered.\n * @param {Array} arr\n * @returns {Array}\n *\n * @param {Array} arr Array of numbers\n * @param {Number} eps Precision\n * @returns {Array}\n *\n * @example\n * var arr = [2.3, 4, Math.PI, 2.300001, Math.PI+0.000000001];\n * console.log(JXG.toUniqueArrayFloat(arr, 0.00001));\n * // Output: Array(3) [ 2.3, 3.141592653589793, 4 ]\n *\n * @see JXG.uniqueArray\n */\n toUniqueArrayFloat: function (arr, eps) {\n var a,\n i, le;\n\n // if (false && Type.exists(arr.toSorted)) {\n // a = arr.toSorted(function(a, b) { return a - b; });\n // } else {\n // }\n // Backwards compatibility to avoid toSorted\n a = arr.slice();\n a.sort(function (a, b) { return a - b; });\n le = a.length;\n for (i = le - 1; i > 0; i--) {\n if (Math.abs(a[i] - a[i - 1]) < eps) {\n a.splice(i, 1);\n }\n }\n return a;\n },\n\n /**\n * Checks if an array contains an element equal to val but does not check the type!\n * @param {Array} arr\n * @param val\n * @returns {Boolean}\n */\n isInArray: function (arr, val) {\n return JXG.indexOf(arr, val) > -1;\n },\n\n /**\n * Converts an array of {@link JXG.Coords} objects into a coordinate matrix.\n * @param {Array} coords\n * @param {Boolean} split\n * @returns {Array}\n */\n coordsArrayToMatrix: function (coords, split) {\n var i,\n x = [],\n m = [];\n\n for (i = 0; i < coords.length; i++) {\n if (split) {\n x.push(coords[i].usrCoords[1]);\n m.push(coords[i].usrCoords[2]);\n } else {\n m.push([coords[i].usrCoords[1], coords[i].usrCoords[2]]);\n }\n }\n\n if (split) {\n m = [x, m];\n }\n\n return m;\n },\n\n /**\n * Compare two arrays.\n * @param {Array} a1\n * @param {Array} a2\n * @returns {Boolean} true, if the arrays coefficients are of same type and value.\n */\n cmpArrays: function (a1, a2) {\n var i;\n\n // trivial cases\n if (a1 === a2) {\n return true;\n }\n\n if (a1.length !== a2.length) {\n return false;\n }\n\n for (i = 0; i < a1.length; i++) {\n if (this.isArray(a1[i]) && this.isArray(a2[i])) {\n if (!this.cmpArrays(a1[i], a2[i])) {\n return false;\n }\n } else if (a1[i] !== a2[i]) {\n return false;\n }\n }\n\n return true;\n },\n\n /**\n * Removes an element from the given array\n * @param {Array} ar\n * @param el\n * @returns {Array}\n */\n removeElementFromArray: function (ar, el) {\n var i;\n\n for (i = 0; i < ar.length; i++) {\n if (ar[i] === el) {\n ar.splice(i, 1);\n return ar;\n }\n }\n\n return ar;\n },\n\n /**\n * Truncate a number n after p decimals.\n * @param {Number} n\n * @param {Number} p\n * @returns {Number}\n */\n trunc: function (n, p) {\n p = JXG.def(p, 0);\n\n return this.toFixed(n, p);\n },\n\n /**\n * Decimal adjustment of a number.\n * From https://developer.mozilla.org/de/docs/Web/JavaScript/Reference/Global_Objects/Math/round\n *\n * @param {String} type The type of adjustment.\n * @param {Number} value The number.\n * @param {Number} exp The exponent (the 10 logarithm of the adjustment base).\n * @returns {Number} The adjusted value.\n *\n * @private\n */\n _decimalAdjust: function (type, value, exp) {\n // If the exp is undefined or zero...\n if (exp === undefined || +exp === 0) {\n return Math[type](value);\n }\n\n value = +value;\n exp = +exp;\n // If the value is not a number or the exp is not an integer...\n if (isNaN(value) || !(typeof exp === \"number\" && exp % 1 === 0)) {\n return NaN;\n }\n\n // Shift\n value = value.toString().split('e');\n value = Math[type](+(value[0] + \"e\" + (value[1] ? +value[1] - exp : -exp)));\n\n // Shift back\n value = value.toString().split('e');\n return +(value[0] + \"e\" + (value[1] ? +value[1] + exp : exp));\n },\n\n /**\n * Round a number to given number of decimal digits.\n *\n * Example: JXG._toFixed(3.14159, -2) gives 3.14\n * @param {Number} value Number to be rounded\n * @param {Number} exp Number of decimal digits given as negative exponent\n * @return {Number} Rounded number.\n *\n * @private\n */\n _round10: function (value, exp) {\n return this._decimalAdjust(\"round\", value, exp);\n },\n\n /**\n * \"Floor\" a number to given number of decimal digits.\n *\n * Example: JXG._toFixed(3.14159, -2) gives 3.14\n * @param {Number} value Number to be floored\n * @param {Number} exp Number of decimal digits given as negative exponent\n * @return {Number} \"Floored\" number.\n *\n * @private\n */\n _floor10: function (value, exp) {\n return this._decimalAdjust(\"floor\", value, exp);\n },\n\n /**\n * \"Ceil\" a number to given number of decimal digits.\n *\n * Example: JXG._toFixed(3.14159, -2) gives 3.15\n * @param {Number} value Number to be ceiled\n * @param {Number} exp Number of decimal digits given as negative exponent\n * @return {Number} \"Ceiled\" number.\n *\n * @private\n */\n _ceil10: function (value, exp) {\n return this._decimalAdjust(\"ceil\", value, exp);\n },\n\n /**\n * Replacement of the default toFixed() method.\n * It does a correct rounding (independent of the browser) and\n * returns \"0.00\" for toFixed(-0.000001, 2) instead of \"-0.00\" which\n * is returned by JavaScript's toFixed()\n *\n * @memberOf JXG\n * @param {Number} num Number tp be rounded\n * @param {Number} digits Decimal digits\n * @return {String} Rounded number is returned as string\n */\n toFixed: function (num, digits) {\n return this._round10(num, -digits).toFixed(digits);\n },\n\n /**\n * Truncate a number val automatically.\n * @memberOf JXG\n * @param val\n * @returns {Number}\n */\n autoDigits: function (val) {\n var x = Math.abs(val),\n str;\n\n if (x >= 0.1) {\n str = this.toFixed(val, 2);\n } else if (x >= 0.01) {\n str = this.toFixed(val, 4);\n } else if (x >= 0.0001) {\n str = this.toFixed(val, 6);\n } else {\n str = val;\n }\n return str;\n },\n\n /**\n * Convert value v. If v has the form\n * \n *
\n * @param {String|Number} v\n * @param {Number} percentOfWhat\n * @param {Function|Number|*} convertPx\n * @returns {String|Number}\n */\n parseNumber: function(v, percentOfWhat, convertPx) {\n var str;\n\n if (this.isString(v) && v.indexOf('%') > -1) {\n str = v.replace(/\\s+%\\s+/, '');\n return parseFloat(str) * percentOfWhat * 0.01;\n }\n if (this.isString(v) && v.indexOf('fr') > -1) {\n str = v.replace(/\\s+fr\\s+/, '');\n return parseFloat(str) * percentOfWhat;\n }\n if (this.isString(v) && v.indexOf('px') > -1) {\n str = v.replace(/\\s+px\\s+/, '');\n str = parseFloat(str);\n if(this.isFunction(convertPx)) {\n return convertPx(str);\n } else if(this.isNumber(convertPx)) {\n return str * convertPx;\n } else {\n return str;\n }\n }\n // Number or String containing no unit\n return parseFloat(v);\n },\n\n /**\n * Parse a string for label positioning of the form 'left pos' or 'pos right'\n * and return e.g.\n * { side: 'left', pos: 'pos' }.\n * @param {String} str\n * @returns {Obj} { side, pos }\n */\n parsePosition: function(str) {\n var a, i,\n side = '',\n pos = '';\n\n str = str.trim();\n if (str !== '') {\n a = str.split(/[ ,]+/);\n for (i = 0; i < a.length; i++) {\n if (a[i] === 'left' || a[i] === 'right') {\n side = a[i];\n } else {\n pos = a[i];\n }\n }\n }\n\n return {\n side: side,\n pos: pos\n };\n },\n\n /**\n * Extracts the keys of a given object.\n * @param object The object the keys are to be extracted\n * @param onlyOwn If true, hasOwnProperty() is used to verify that only keys are collected\n * the object owns itself and not some other object in the prototype chain.\n * @returns {Array} All keys of the given object.\n */\n keys: function (object, onlyOwn) {\n var keys = [],\n property;\n\n // the caller decides if we use hasOwnProperty\n /*jslint forin:true*/\n for (property in object) {\n if (onlyOwn) {\n if (object.hasOwnProperty(property)) {\n keys.push(property);\n }\n } else {\n keys.push(property);\n }\n }\n /*jslint forin:false*/\n\n return keys;\n },\n\n /**\n * This outputs an object with a base class reference to the given object. This is useful if\n * you need a copy of an e.g. attributes object and want to overwrite some of the attributes\n * without changing the original object.\n * @param {Object} obj Object to be embedded.\n * @returns {Object} An object with a base class reference to obj.\n */\n clone: function (obj) {\n var cObj = {};\n\n cObj.prototype = obj;\n\n return cObj;\n },\n\n /**\n * Embeds an existing object into another one just like {@link #clone} and copies the contents of the second object\n * to the new one. Warning: The copied properties of obj2 are just flat copies.\n * @param {Object} obj Object to be copied.\n * @param {Object} obj2 Object with data that is to be copied to the new one as well.\n * @returns {Object} Copy of given object including some new/overwritten data from obj2.\n */\n cloneAndCopy: function (obj, obj2) {\n var r,\n cObj = function () {\n return undefined;\n };\n\n cObj.prototype = obj;\n\n // no hasOwnProperty on purpose\n /*jslint forin:true*/\n /*jshint forin:true*/\n\n for (r in obj2) {\n cObj[r] = obj2[r];\n }\n\n /*jslint forin:false*/\n /*jshint forin:false*/\n\n return cObj;\n },\n\n /**\n * Recursively merges obj2 into obj1 in-place. Contrary to {@link JXG#deepCopy} this won't create a new object\n * but instead will overwrite obj1.\n * \n */\n merge: function (obj1, obj2) {\n var i, j, o, oo;\n\n for (i in obj2) {\n if (obj2.hasOwnProperty(i)) {\n o = obj2[i];\n if (this.isArray(o)) {\n if (!obj1[i]) {\n obj1[i] = [];\n }\n\n for (j = 0; j < o.length; j++) {\n oo = obj2[i][j];\n if (typeof obj2[i][j] === 'object') {\n obj1[i][j] = this.merge(obj1[i][j], oo);\n } else {\n obj1[i][j] = obj2[i][j];\n }\n }\n } else if (typeof o === 'object') {\n if (!obj1[i]) {\n obj1[i] = {};\n }\n\n obj1[i] = this.merge(obj1[i], o);\n } else {\n if (typeof obj1 === 'boolean') {\n // This is necessary in the following scenario:\n // lastArrow == false\n // and call of\n // setAttribute({lastArrow: {type: 7}})\n obj1 = {};\n }\n obj1[i] = o;\n }\n }\n }\n\n return obj1;\n },\n\n /**\n * Creates a deep copy of an existing object, i.e. arrays or sub-objects are copied component resp.\n * element-wise instead of just copying the reference. If a second object is supplied, the two objects\n * are merged into one object. The properties of the second object have priority.\n * @param {Object} obj This object will be copied.\n * @param {Object} obj2 This object will merged into the newly created object\n * @param {Boolean} [toLower=false] If true the keys are convert to lower case. This is needed for visProp, see JXG#copyAttributes\n * @returns {Object} copy of obj or merge of obj and obj2.\n */\n deepCopy: function (obj, obj2, toLower) {\n var c, i, prop, i2;\n\n toLower = toLower || false;\n if (typeof obj !== 'object' || obj === null) {\n return obj;\n }\n\n // Missing hasOwnProperty is on purpose in this function\n if (this.isArray(obj)) {\n c = [];\n for (i = 0; i < obj.length; i++) {\n prop = obj[i];\n // Attention: typeof null === 'object'\n if (prop !== null && typeof prop === 'object') {\n // We certainly do not want to recurse into a JSXGraph object.\n // This would for sure result in an infinite recursion.\n // As alternative we copy the id of the object.\n if (this.exists(prop.board)) {\n c[i] = prop.id;\n } else {\n c[i] = this.deepCopy(prop, {}, toLower);\n }\n } else {\n c[i] = prop;\n }\n }\n } else {\n c = {};\n for (i in obj) {\n if (obj.hasOwnProperty(i)) {\n i2 = toLower ? i.toLowerCase() : i;\n prop = obj[i];\n if (prop !== null && typeof prop === 'object') {\n if (this.exists(prop.board)) {\n c[i2] = prop.id;\n } else {\n c[i2] = this.deepCopy(prop, {}, toLower);\n }\n } else {\n c[i2] = prop;\n }\n }\n }\n\n for (i in obj2) {\n if (obj2.hasOwnProperty(i)) {\n i2 = toLower ? i.toLowerCase() : i;\n\n prop = obj2[i];\n if (prop !== null && typeof prop === 'object') {\n if (this.isArray(prop) || !this.exists(c[i2])) {\n c[i2] = this.deepCopy(prop, {}, toLower);\n } else {\n c[i2] = this.deepCopy(c[i2], prop, toLower);\n }\n } else {\n c[i2] = prop;\n }\n }\n }\n }\n\n return c;\n },\n\n /**\n * In-place (deep) merging of attributes. Allows attributes like `{shadow: {enabled: true...}}`\n * \n * \n *\n *\n * @see JXG.Math.Extrapolate.iteration\n * @memberof JXG.Math.Extrapolate\n */\n limit: function (x0, h0, f) {\n return this.iteration_levin(x0, h0, f, 0);\n //return this.iteration(x0, h0, f, 'wynnEps', 1);\n\n // var algs = ['wynnEps', 'levin'], //, 'wynnEps', 'levin', 'aitken', 'brezinski'],\n // le = algs.length,\n // i, t, res;\n // for (i = 0; i < le; i++) {\n // for (t = 0; t < 1; t++) {\n // if (algs[i] === 'levin') {\n // res = this.iteration_levin(x0, h0, f, t);\n // } else {\n // res = this.iteration(x0, h0, f, algs[i], t);\n // }\n // if (res[2] > 0.6) {\n // return res;\n // }\n // console.log(algs[i], t, res)\n // }\n // }\n // return [f(x0 + Math.sign(h0) * Math.sqrt(Mat.eps)), 'direct', 0];\n }\n};\n\nexport default Mat.Extrapolate;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n * which define the axis-aligned bounding box (AABB) of that item. Additionally,\n * more properties can be given.\n *\n * @param {Array} items to be inserted\n * @returns {Object} reference to the box quadtree\n */\n insert: function(items) {\n var i, le,\n l, t, r, b,\n it,\n nw_it = [],\n ne_it = [],\n sw_it = [],\n se_it = [],\n in_nw, in_ne, in_sw, in_se;\n\n\n if (this.bbox === null) {\n // Use bounding box of the supplied items\n le = items.length;\n l = b = Infinity;\n r = t = -Infinity;\n for (i = 0; i < items.length; i++) {\n it = items[i];\n l = (it.xlb < l) ? it.xlb : l;\n t = (it.yub > t) ? it.yub : t;\n r = (it.xub > r) ? it.xub : r;\n b = (it.ylb < b) ? it.ylb : b;\n }\n this.cx = (l + r) * 0.5;\n this.cy = (t + b) * 0.5;\n this.bbox = [l, t, r, b];\n } else {\n l = this.bbox[0];\n t = this.bbox[1];\n r = this.bbox[2];\n b = this.bbox[3];\n }\n\n if (this.depth === 0 || this.items.length + items.length < this.capacity) {\n // if (items.length + items.length < this.capacity) {\n // console.log(\"Capacity sufficient, D=\", this.depth, this.items.length, items.length);\n // }\n // if (depth === 0) {console.log(\"Max depth reached\", items.length, this.capacity); }\n\n this.items = this.items.concat(items);\n return this;\n }\n\n le = items.length;\n for (i = 0; i < le; i++) {\n it = items[i];\n in_nw = it.xlb <= this.cx && it.yub > this.cy;\n in_sw = it.xlb <= this.cx && it.ylb <= this.cy;\n in_ne = it.xub > this.cx && it.yub > this.cy;\n in_se = it.xub > this.cx && it.ylb <= this.cy;\n\n // If it overlaps all 4 quadrants then insert it at the current\n // depth, otherwise append it to a list to be inserted under every\n // quadrant that it overlaps.\n if (in_nw && in_ne && in_se && in_sw) {\n this.items.push(it);\n } else {\n if (in_nw) { nw_it.push(it); }\n if (in_sw) { sw_it.push(it); }\n if (in_ne) { ne_it.push(it); }\n if (in_se) { se_it.push(it); }\n }\n }\n\n // Create the sub-quadrants, recursively.\n this.subdivide(nw_it, sw_it, ne_it, se_it, l, t, r, b);\n\n return this;\n },\n\n /**\n * Insert an item into the box quadtree, where an item is an object\n * containing at least the properties\n *\n * \n *
\n * which define the axis-aligned bounding box (AABB) of that item. Additionally,\n * more properties can be given.\n *\n * @param {Object} it Item to be inserted\n * @returns {Object} reference to the box quadtree\n */\n insertItem: function(it) {\n var l, t, r, b,\n nw_it = [],\n ne_it = [],\n sw_it = [],\n se_it = [],\n in_nw, in_ne, in_sw, in_se;\n\n\n if (this.bbox === null) {\n // Use bounding box of the supplied items\n l = b = Infinity;\n r = t = -Infinity;\n\n l = (it.xlb < l) ? it.xlb : l;\n t = (it.yub > t) ? it.yub : t;\n r = (it.xub > r) ? it.xub : r;\n b = (it.ylb < b) ? it.ylb : b;\n\n this.cx = (l + r) * 0.5;\n this.cy = (t + b) * 0.5;\n this.bbox = [l, t, r, b];\n } else {\n l = this.bbox[0];\n t = this.bbox[1];\n r = this.bbox[2];\n b = this.bbox[3];\n }\n\n if (this.depth === 0 || this.items.length + 1 < this.capacity) {\n this.items.push(it);\n return this;\n }\n\n in_nw = it.xlb <= this.cx && it.yub > this.cy;\n in_sw = it.xlb <= this.cx && it.ylb <= this.cy;\n in_ne = it.xub > this.cx && it.yub > this.cy;\n in_se = it.xub > this.cx && it.ylb <= this.cy;\n\n // If it overlaps all 4 quadrants then insert it at the current\n // depth, otherwise append it to a list to be inserted under every\n // quadrant that it overlaps.\n if (in_nw && in_ne && in_se && in_sw) {\n this.items.push(it);\n } else {\n if (in_nw) { nw_it.push(it); }\n if (in_sw) { sw_it.push(it); }\n if (in_ne) { ne_it.push(it); }\n if (in_se) { se_it.push(it); }\n }\n\n // Create the sub-quadrants, recursively.\n this.subdivide(nw_it, sw_it, ne_it, se_it, l, t, r, b);\n\n return this;\n },\n\n /**\n * Create the sub-quadrants if necessary, recursively\n * @param {Array} nw_it list of items for northWest subtree\n * @param {Array} sw_it list of items for southWest subtree\n * @param {Array} ne_it list of items for northEast subtree\n * @param {Array} se_it list of items for southEast subtree\n * @param {Number} l bounding box left\n * @param {Number} t bounding box top\n * @param {Number} r bounding box right\n * @param {Number} b bounding box bottom\n * @returns {Object} reference to the box quadtree\n * @private\n */\n subdivide: function(nw_it, sw_it, ne_it, se_it, l, t, r, b) {\n if (nw_it.length > 0) {\n if (this.northWest === null) {\n this.northWest = new JXG.Math.BoxQuadtree(this.depth, this.capacity, [l, t, this.cx, this.cy]);\n }\n this.northWest.insert(nw_it);\n }\n if (sw_it.length > 0) {\n if (this.southWest === null) {\n this.southWest = new JXG.Math.BoxQuadtree(this.depth, this.capacity, [l, this.cy, this.cx, b]);\n }\n this.southWest.insert(sw_it);\n }\n if (ne_it.length > 0) {\n if (this.northEast === null) {\n this.northEast = new JXG.Math.BoxQuadtree(this.depth, this.capacity, [this.cx, t, r, this.cy]);\n }\n this.northEast.insert(ne_it);\n }\n if (se_it.length > 0) {\n if (this.southEast === null) {\n this.southEast = new JXG.Math.BoxQuadtree(this.depth, this.capacity, [this.cx, this.cy, r, b]);\n }\n this.southEast.insert(se_it);\n }\n\n return this;\n },\n\n /**\n * Find all entries of the box quadtree which have an overlap\n * with the given rectangle (AABB). Items may appear multiple times.\n *\n * @param {Array} box AABB of the form [l, t, r, b]\n * @returns {Array} list of items overlapping with box\n */\n find: function(box) {\n var overlaps = function(item) {\n return box[2] >= item.xlb && box[0] <= item.xub &&\n box[3] <= item.yub && box[1] >= item.ylb;\n },\n hits = [],\n i, le;\n\n le = this.items.length;\n for (i = 0; i < le; i++) {\n if (overlaps(this.items[i])) {\n hits.push(this.items[i]);\n }\n }\n\n if (this.northWest !== null && box[0] <= this.cx & box[1] >= this.cy) {\n Type.concat(hits, this.northWest.find(box));\n }\n if (this.southWest !== null && box[0] <= this.cx & box[3] <= this.cy) {\n Type.concat(hits, this.southWest.find(box));\n }\n if (this.northEast !== null && box[2] >= this.cx & box[1] >= this.cy) {\n Type.concat(hits, this.northEast.find(box));\n }\n if (this.southEast !== null && box[2] >= this.cx & box[3] <= this.cy) {\n Type.concat(hits, this.southEast.find(box));\n }\n\n return hits;\n },\n\n /**\n * Analyze the box quadtree.\n *\n * @returns {Object} data about the box quadtree\n */\n analyzeTree: function() {\n var stats = {\n number_items: this.items.length,\n depth: 1\n }, tmp;\n\n if (this.northWest !== null) {\n tmp = this.northWest.analyzeTree();\n stats.number_items += tmp.number_items;\n stats.depth = Math.max(stats.depth, 1 + tmp.depth);\n }\n if (this.southWest !== null) {\n tmp = this.southWest.analyzeTree();\n stats.number_items += tmp.number_items;\n stats.depth = Math.max(stats.depth, 1 + tmp.depth);\n }\n if (this.northEast !== null) {\n tmp = this.northEast.analyzeTree();\n stats.number_items += tmp.number_items;\n stats.depth = Math.max(stats.depth, 1 + tmp.depth);\n }\n if (this.southEast !== null) {\n tmp = this.southEast.analyzeTree();\n stats.number_items += tmp.number_items;\n stats.depth = Math.max(stats.depth, 1 + tmp.depth);\n }\n\n return stats;\n },\n\n /**\n * Generate data to plot the box quadtree as curve using updateDataArray.\n *\n * @returns {Array} containing arrays dataX and dataY\n *\n * @example\n *\n * // qdt contains a BoxQuadtree\n *\n * var qdtcurve = board.create('curve', [[], []], { strokeWidth: 1, strokeColor: '#0000ff', strokeOpacity: 0.3 });\n * qdtcurve.updateDataArray = function () {\n * var ret = qdt.plot();\n *\n * this.dataX = ret[0];\n * this.dataY = ret[1];\n * console.log(qdt.analyzeTree());\n * };\n * board.update();\n */\n plot: function () {\n var dataX = [],\n dataY = [],\n ret;\n\n dataX.push(this.bbox[0]); dataY.push(this.bbox[3]);\n dataX.push(this.bbox[2]); dataY.push(this.bbox[3]);\n dataX.push(this.bbox[2]); dataY.push(this.bbox[1]);\n dataX.push(this.bbox[0]); dataY.push(this.bbox[1]);\n dataX.push(this.bbox[0]); dataY.push(this.bbox[3]);\n dataX.push(NaN); dataY.push(NaN);\n\n if (this.northWest !== null) {\n ret = this.northWest.plot();\n Type.concat(dataX, ret[0]);\n Type.concat(dataY, ret[1]);\n }\n\n if (this.northEast !== null) {\n ret = this.northEast.plot();\n Type.concat(dataX, ret[0]);\n Type.concat(dataY, ret[1]);\n }\n\n if (this.southEast !== null) {\n ret = this.southEast.plot();\n Type.concat(dataX, ret[0]);\n Type.concat(dataY, ret[1]);\n }\n\n if (this.southWest !== null) {\n ret = this.southWest.plot();\n Type.concat(dataX, ret[0]);\n Type.concat(dataY, ret[1]);\n }\n\n return [dataX, dataY];\n }\n }\n);\n\nexport default Mat.BoxQuadtree;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Reinhard Oldenburg,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * {\n * resolution_out: 5, // Horizontal resolution: distance between vertical lines to search for components\n * resolution_in: 5, // Vertical resolution to search for components\n * max_steps: 1024, // Max number of points in one call of tracing\n * alpha_0: 0.05, // Angle between two successive tangents: smoothness of curve\n *\n * tol_u0: Mat.eps, // Tolerance to find starting points for tracing.\n * tol_newton: 1.0e-7, // Tolerance for Newton steps.\n * tol_cusp: 0.05, // Tolerance for cusp / bifurcation detection\n * tol_progress: 0.0001, // If two points are closer than this value, we bail out\n * qdt_box: 0.2, // half of box size to search in qdt\n * kappa_0: 0.2, // Inverse of planned number of Newton steps\n * delta_0: 0.05, // Distance of predictor point to curve\n *\n * h_initial: 0.1, // Initial stepwidth\n * h_critical: 0.001, // If h is below this threshold we bail out\n * h_max: 1, // Maximal value of h (user units)\n * loop_dist: 0.09, // Allowed distance (multiplied by actual stepwidth) to detect loop\n * loop_dir: 0.99, // Should be > 0.95\n * loop_detection: true, // Use Gosper's loop detector\n * unitX: 10, // unitX of board\n * unitY: 10 // unitX of board\n * };\n * \n * @param {function} f function from R2 to R\n * @param {function} [dfx] Optional partial derivative of f with regard to x\n * @param {function} [dfy] Optional partial derivative of f with regard to y\n *\n * @constructor\n * @example\n * var f = (x, y) => x**3 - 2 * x * y + y**3;\n * var c = board.create('curve', [[], []], {\n * strokeWidth: 3,\n * strokeColor: JXG.palette.red\n * });\n *\n * c.updateDataArray = function () {\n * var bbox = this.board.getBoundingBox(),\n * ip, cfg,\n * ret = [],\n * mgn = 1;\n *\n * bbox[0] -= mgn;\n * bbox[1] += mgn;\n * bbox[2] += mgn;\n * bbox[3] -= mgn;\n *\n * cfg = {\n * resolution_out: 5,\n * resolution_in: 5,\n * unitX: this.board.unitX,\n * unitY: this.board.unitX\n * };\n *\n * this.dataX = [];\n * this.dataY = [];\n * ip = new JXG.Math.ImplicitPlot(bbox, cfg, f, null, null);\n * ret = ip.plot();\n * this.dataX = ret[0];\n * this.dataY = ret[1];\n * };\n * board.update();\n * \n * \n *\n */\nMat.ImplicitPlot = function (bbox, config, f, dfx, dfy) {\n\n // Default values\n var cfg_default = {\n resolution_out: 5, // Distance between vertical lines to search for components\n resolution_in: 5, // Distance between vertical lines to search for components\n max_steps: 1024, // Max number of points in one call of tracing\n alpha_0: 0.05, // Angle between two successive tangents: smoothness of curve\n\n tol_u0: Mat.eps, // Tolerance to find starting points for tracing.\n tol_newton: 1.0e-7, // Tolerance for Newton steps.\n tol_cusp: 0.05, // Tolerance for cusp / bifurcation detection\n tol_progress: 0.0001, // If two points are closer than this value, we bail out\n qdt_box: 0.2, // half of box size to search in qdt\n kappa_0: 0.2, // Inverse of planned number of Newton steps\n delta_0: 0.05, // Distance of predictor point to curve\n\n h_initial: 0.1, // Initial step width\n h_critical: 0.001, // If h is below this threshold we bail out\n h_max: 1, // Maximum value of h (user units)\n loop_dist: 0.09, // Allowed distance (multiplied by actual step width) to detect loop\n loop_dir: 0.99, // Should be > 0.95\n loop_detection: true, // Use Gosper's loop detector\n unitX: 10, // unitX of board\n unitY: 10 // unitX of board\n };\n\n this.config = Type.merge(cfg_default, config);\n\n this.f = f;\n\n this.dfx = null;\n this.dfy = null;\n\n if (Type.isFunction(dfx)) {\n this.dfx = dfx;\n } else {\n this.dfx = function (x, y) {\n var h = Mat.eps * Mat.eps;\n return (this.f(x + h, y) - this.f(x - h, y)) * 0.5 / h;\n };\n }\n\n if (Type.isFunction(dfy)) {\n this.dfy = dfy;\n } else {\n this.dfy = function (x, y) {\n var h = Mat.eps * Mat.eps;\n return (this.f(x, y + h) - this.f(x, y - h)) * 0.5 / h;\n };\n }\n\n this.bbox = bbox;\n this.qdt = new Quadtree(20, 5, bbox);\n\n this.components = [];\n};\n\nType.extend(\n Mat.ImplicitPlot.prototype,\n /** @lends JXG.Math.ImplicitPlot.prototype */ {\n\n /**\n * Implicit plotting method.\n *\n * @returns {Array} consisting of [dataX, dataY, number_of_components]\n */\n plot: function () {\n var // components = [],\n doVerticalSearch = true,\n doHorizontalSearch = true,\n x, y,\n mi_x, ma_x, mi_y, ma_y,\n dataX = [],\n dataY = [],\n ret = [],\n num_components = 0,\n max_level = 8,\n\n delta,\n that = this,\n\n fmi_x = function (t) {\n return that.f(x, t);\n },\n fma_x = function (t) {\n return -that.f(x, t);\n },\n fmi_y = function (t) {\n return that.f(t, y);\n },\n fma_y = function (t) {\n return -that.f(t, y);\n };\n\n // Vertical lines or circular search:\n mi_x = Math.min(this.bbox[0], this.bbox[2]) - Mat.eps;\n ma_x = Math.max(this.bbox[0], this.bbox[2]);\n mi_y = Math.min(this.bbox[1], this.bbox[3]) + Mat.eps;\n ma_y = Math.max(this.bbox[1], this.bbox[3]);\n\n if (doVerticalSearch) {\n delta = this.config.resolution_out / this.config.unitX;\n delta *= (1 + Mat.eps);\n // console.log(\"Outer delta x\", delta)\n\n for (x = mi_x; x < ma_x; x += delta) {\n ret = this.searchLine(\n fmi_x, fma_x, x,\n [mi_y, ma_y], 'vertical',\n num_components, dataX, dataY, max_level);\n\n if (ret !== false) {\n dataX = ret[0];\n dataY = ret[1];\n num_components = ret[2];\n }\n\n }\n }\n if (doHorizontalSearch) {\n delta = this.config.resolution_out / this.config.unitY;\n delta *= (1 + Mat.eps);\n // console.log(\"Outer delta y\", delta)\n\n for (y = mi_y; y < ma_y; y += delta) {\n ret = this.searchLine(\n fmi_y, fma_y, y,\n [mi_x, ma_x], 'horizontal',\n num_components, dataX, dataY, max_level);\n\n if (ret !== false) {\n dataX = ret[0];\n dataY = ret[1];\n num_components = ret[2];\n }\n }\n }\n\n return [dataX, dataY, num_components];\n },\n\n /**\n * Recursively search a horizontal or vertical line for points on the\n * fulfilling the given equation.\n *\n * @param {Function} fmi Minimization function\n * @param {Function} fma Maximization function\n * @param {Number} fix Value of the fixed variable\n * @param {Array} interval Search interval of the free variable\n * @param {String} dir 'vertical' or 'horizontal'\n * @param {Number} num_components Number of components before search\n * @param {Array} dataX x-coordinates of points so far\n * @param {Array} dataY y-coordinates of points so far\n * @param {Number} level Recursion level\n * @returns {Array} consisting of [dataX, dataY, number_of_components]-\n * @private\n */\n searchLine: function (fmi, fma, fix, interval, dir,\n num_components, dataX, dataY, level) {\n var t_mi, t_ma, t,\n ft,\n mi, ma, tmp, m,\n is_in,\n u0, i, le,\n ret,\n offset,\n delta,\n eps = this.config.tol_u0,\n DEBUG = false,\n b = interval[0],\n e = interval[1];\n\n t_mi = Numerics.fminbr(fmi, [b, e]);\n mi = fmi(t_mi);\n t_ma = Numerics.fminbr(fma, [b, e]);\n ma = fmi(t_ma);\n\n if (mi < eps && ma > -eps) {\n tmp = t_mi;\n t_mi = Math.min(tmp, t_ma);\n t_ma = Math.max(tmp, t_ma);\n\n t = Numerics.fzero(fmi, [t_mi, t_ma]);\n // t = Numerics.chandrupatla(fmi, [t_mi, t_ma]);\n\n ft = fmi(t);\n if (Math.abs(ft) > Math.max((ma - mi) * Mat.eps, 0.001)) {\n //console.log(\"searchLine:\", dir, fix, t, \"no root \" + ft);\n return false;\n // throw new Error(\"searchLine: no root \" + ft);\n }\n if (dir === 'vertical') {\n u0 = [1, fix, t];\n delta = this.config.resolution_in / this.config.unitY;\n // console.log(\"Inner delta x\", delta)\n } else {\n u0 = [1, t, fix];\n delta = this.config.resolution_in / this.config.unitX;\n // console.log(\"Inner delta y\", delta)\n }\n delta *= (1 + Mat.eps);\n\n is_in = this.curveContainsPoint(u0, dataX, dataY,\n delta * 2, // Allowed dist from segment\n this.config.qdt_box // 0.5 of box size to search in qdt\n );\n\n if (is_in) {\n if (DEBUG) {\n console.log(\"Found in quadtree\", u0, \"level:\", level);\n }\n } else {\n if (DEBUG) {\n console.log(\"Not in quadtree\", u0, dataX.length);\n }\n ret = this.traceComponent(u0, 1);\n if (ret[0].length > 0) {\n // Add jump in curve\n if (num_components > 0) {\n dataX.push(NaN);\n dataY.push(NaN);\n }\n\n offset = dataX.length;\n le = ret[0].length;\n for (i = 1; i < le; i++) {\n this.qdt.insertItem({\n xlb: Math.min(ret[0][i - 1], ret[0][i]),\n xub: Math.max(ret[0][i - 1], ret[0][i]),\n ylb: Math.min(ret[1][i - 1], ret[1][i]),\n yub: Math.max(ret[1][i - 1], ret[1][i]),\n idx1: offset + i - 1,\n idx2: offset + i,\n comp: num_components\n });\n }\n\n num_components++;\n Type.concat(dataX, ret[0]);\n Type.concat(dataY, ret[1]);\n }\n }\n\n m = t - delta * 0.01;\n if (m - b > delta && level > 0) {\n ret = this.searchLine(\n fmi, fma, fix, [b, m], dir,\n num_components, dataX, dataY, level - 1);\n if (ret !== false) {\n dataX = ret[0];\n dataY = ret[1];\n num_components = ret[2];\n }\n }\n m = t + delta * 0.01;\n if (e - m > delta && level > 0) {\n ret = this.searchLine(\n fmi, fma, fix, [m, e], dir,\n num_components, dataX, dataY, level - 1);\n if (ret !== false) {\n dataX = ret[0];\n dataY = ret[1];\n num_components = ret[2];\n }\n }\n\n return [dataX, dataY, num_components];\n }\n\n return false;\n },\n\n /**\n * Test if the data points contain a given coordinate, i.e. if the\n * given coordinate is close enough to the polygonal chain\n * through the data points.\n *\n * @param {Array} p Homogenous coordinates [1, x, y] of the coordinate point\n * @param {Array} dataX x-coordinates of points so far\n * @param {Array} dataY y-coordinates of points so far\n * @param {Number} tol Maximal distance of p from the polygonal chain through the data points\n * @param {Number} eps Helper tolerance used for the quadtree\n * @returns Boolean\n */\n curveContainsPoint: function (p, dataX, dataY, tol, eps) {\n var i, le, hits, d,\n x = p[1],\n y = p[2];\n\n hits = this.qdt.find([x - eps, y + eps, x + eps, y - eps]);\n\n le = hits.length;\n for (i = 0; i < le; i++) {\n d = Geometry.distPointSegment(\n p,\n [1, dataX[hits[i].idx1], dataY[hits[i].idx1]],\n [1, dataX[hits[i].idx2], dataY[hits[i].idx2]]\n );\n if (d < tol) {\n return true;\n }\n }\n return false;\n },\n\n /**\n * Starting at an initial point the curve is traced with a Euler-Newton method.\n * After tracing in one direction the algorithm stops if the component is a closed loop.\n * Otherwise, the curved is traced in the opposite direction, starting from\n * the same initial point. Finally, the two components are glued together.\n *\n * @param {Array} u0 Initial point in homogenous coordinates [1, x, y].\n * @returns Array [dataX, dataY] containing a new component.\n * @private\n */\n traceComponent: function (u0) {\n var dataX = [],\n dataY = [],\n arr = [];\n\n // Trace in first direction\n // console.log(\"---- Start tracing forward ---------\")\n arr = this.tracing(u0, 1);\n\n if (arr.length === 0) {\n // console.log(\"Could not start tracing due to singularity\")\n } else {\n // console.log(\"Trace from\", [arr[0][0], arr[1][0]], \"to\", [arr[0][arr[0].length - 1], arr[1][arr[1].length - 1]],\n // \"num points:\", arr[0].length);\n dataX = arr[0];\n dataY = arr[1];\n }\n\n // Trace in the other direction\n if (!arr[2]) {\n // No loop in the first tracing step,\n // now explore the other direction.\n\n // console.log(\"---- Start tracing backward ---------\")\n arr = this.tracing(u0, -1);\n\n if (arr.length === 0) {\n // console.log(\"Could not start backward tracing due to singularity\")\n } else {\n // console.log(\"Trace backwards from\", [arr[0][0], arr[1][0]], \"to\",\n // [arr[0][arr[0].length - 1], arr[1][arr[1].length - 1]], \"num points:\", arr[0].length);\n dataX = arr[0].reverse().concat(dataX.slice(1));\n dataY = arr[1].reverse().concat(dataY.slice(1));\n }\n }\n\n if (dataX.length > 0 && dataX.length < 6) {\n // Solitary point\n dataX.push(dataX[dataX.length - 1]);\n dataY.push(dataY[dataY.length - 1]);\n }\n\n return [dataX, dataY];\n },\n\n /**\n * Starting at a point u0, this routine traces the curve f(u)=0 until\n * a loop is detected, a critical point is reached, the curve leaves the bounding box,\n * or the maximum number of points is reached.\n * \n * \n *
\n *\n * @param {JXG.Circle|JXG.Curve|JXG.Polygon} subject First closed path, usually called 'subject'.\n * Maybe curve, arc, sector, circle, polygon, array of points, array of JXG.Coords,\n * array of coordinate pairs.\n * @param {JXG.Circle|JXG.Curve|JXG.Polygon} clip Second closed path, usually called 'clip'.\n * Maybe curve, arc, sector, circle, polygon, array of points, array of JXG.Coords,\n * array of coordinate pairs.\n * @param {String} clip_type Determines the type of boolean operation on the two paths.\n * Possible values are 'intersection', 'union', or 'difference'.\n * @param {JXG.Board} board JSXGraph board object. It is needed to convert between\n * user coordinates and screen coordinates.\n * @return {Array} Array consisting of two arrays containing the x-coordinates and the y-coordinates of\n * the resulting path.\n *\n * @see JXG.Math.Clip.intersection\n * @see JXG.Math.Clip.union\n * @see JXG.Math.Clip.difference\n *\n * @example\n * var curve1 = board.create('curve', [\n * [-3, 3, 0, -3],\n * [3, 3, 0, 3]\n * ],\n * {strokeColor: 'black'});\n *\n * var curve2 = board.create('curve', [\n * [-4, 4, 0, -4],\n * [2, 2, 4, 2]\n * ],\n * {strokeColor: 'blue'});\n *\n * var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.6});\n * clip_path.updateDataArray = function() {\n * var a = JXG.Math.Clip.greinerHormann(curve2, curve1, 'intersection', this.board);\n *\n * this.dataX = a[0];\n * this.dataY = a[1];\n * };\n *\n * board.update();\n *\n * \n *\n * @example\n * var curve1 = board.create('curve', [\n * [-3, 3, 0, -3],\n * [3, 3, 0, 3]\n * ],\n * {strokeColor: 'black', fillColor: 'none', fillOpacity: 0.8});\n *\n * var curve2 = board.create('polygon', [[3, 4], [-4, 0], [-4, 4]],\n * {strokeColor: 'blue', fillColor: 'none'});\n *\n * var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.6});\n * clip_path.updateDataArray = function() {\n * var a = JXG.Math.Clip.greinerHormann(curve1, curve2, 'union', this.board);\n * this.dataX = a[0];\n * this.dataY = a[1];\n * };\n *\n * board.update();\n *\n * \n * \n *\n * @example\n * var curve1 = board.create('curve', [\n * [-4, 4, 0, -4],\n * [4, 4, -2, 4]\n * ],\n * {strokeColor: 'black', fillColor: 'none', fillOpacity: 0.8});\n *\n * var curve2 = board.create('circle', [[0, 0], [0, -2]],\n * {strokeColor: 'blue', strokeWidth: 1, fillColor: 'red', fixed: true, fillOpacity: 0.3,\n * center: {visible: true, size: 5}, point2: {size: 5}});\n *\n * var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.6});\n * clip_path.updateDataArray = function() {\n * var a = JXG.Math.Clip.greinerHormann(curve1, curve2, 'difference', this.board);\n *\n * this.dataX = a[0];\n * this.dataY = a[1];\n * };\n *\n * board.update();\n *\n * \n * \n *\n * @example\n * var clip_path = board.create('curve', [[], []], {strokeWidth: 1, fillColor: 'yellow', fillOpacity: 0.6});\n * clip_path.updateDataArray = function() {\n * var bbox = this.board.getBoundingBox(),\n * canvas, triangle;\n *\n * canvas = [[bbox[0], bbox[1]], // ul\n * [bbox[0], bbox[3]], // ll\n * [bbox[2], bbox[3]], // lr\n * [bbox[2], bbox[1]], // ur\n * [bbox[0], bbox[1]]] // ul\n * triangle = [[-1,1], [1,1], [0,-1], [-1,1]];\n *\n * var a = JXG.Math.Clip.greinerHormann(canvas, triangle, 'difference', this.board);\n * this.dataX = a[0];\n * this.dataY = a[1];\n * };\n *\n * \n * \n *\n */\n greinerHormann: function (subject, clip, clip_type, board) {\n //},\n // subject_first_point_type, clip_first_point_type) {\n\n var len,\n S = [],\n C = [],\n S_intersect = [],\n // C_intersect = [],\n S_starters,\n C_starters,\n res = [],\n DEBUG = false;\n\n if (DEBUG) {\n console.log(\"\\n------------ GREINER-HORMANN --------------\");\n }\n // Collect all subject points into subject array S\n S = this._getPath(subject, board);\n len = S.length;\n if (\n len > 0 &&\n Geometry.distance(S[0].coords.usrCoords, S[len - 1].coords.usrCoords, 3) < Mat.eps\n ) {\n S.pop();\n }\n\n // Collect all points into clip array C\n C = this._getPath(clip, board);\n len = C.length;\n if (\n len > 0 &&\n Geometry.distance(C[0].coords.usrCoords, C[len - 1].coords.usrCoords, 3) <\n Mat.eps * Mat.eps\n ) {\n C.pop();\n }\n\n // Handle cases where at least one of the paths is empty\n if (this.isEmptyCase(S, C, clip_type)) {\n return [[], []];\n }\n\n // Add pointers for doubly linked lists\n S_starters = this.makeDoublyLinkedList(S);\n C_starters = this.makeDoublyLinkedList(C);\n\n if (DEBUG) {\n this._print_array(S);\n console.log(\"Components:\", S_starters);\n this._print_array(C);\n console.log(\"Components:\", C_starters);\n }\n\n res = this.findIntersections(S, C, board);\n S_intersect = res[0];\n\n this._handleFullyDegenerateCase(S, C, board);\n\n // Phase 2: mark intersection points as entry or exit points\n this.markEntryExit(S, C, S_starters);\n\n // if (S[0].coords.distance(Const.COORDS_BY_USER, C[0].coords) === 0) {\n // // Randomly disturb the first point of the second path\n // // if both paths start at the same point.\n // C[0].usrCoords[1] *= 1 + Math.random() * 0.0001 - 0.00005;\n // C[0].usrCoords[2] *= 1 + Math.random() * 0.0001 - 0.00005;\n // }\n this.markEntryExit(C, S, C_starters);\n\n // Handle cases without intersections\n if (this._countCrossingIntersections(S_intersect) === 0) {\n return this.handleEmptyIntersection(S, C, clip_type);\n }\n\n // Phase 3: tracing\n return this.tracing(S, S_intersect, clip_type);\n },\n\n /**\n * Union of two closed paths. The paths could be JSXGraph elements circle, curve, or polygon.\n * Computed by the Greiner-Hormann algorithm.\n *\n * @param {JXG.Circle|JXG.Curve|JXG.Polygon} subject First closed path.\n * @param {JXG.Circle|JXG.Curve|JXG.Polygon} clip Second closed path.\n * @param {JXG.Board} board JSXGraph board object. It is needed to convert between\n * user coordinates and screen coordinates.\n * @return {Array} Array consisting of two arrays containing the x-coordinates and the y-coordinates of\n * the resulting path.\n *\n * @see JXG.Math.Clip.greinerHormann\n * @see JXG.Math.Clip.intersection\n * @see JXG.Math.Clip.difference\n *\n * @example\n * var curve1 = board.create('curve', [\n * [-3, 3, 0, -3],\n * [3, 3, 0, 3]\n * ],\n * {strokeColor: 'black'});\n *\n * var curve2 = board.create('polygon', [[3, 4], [-4, 0], [-4, 4]],\n * {strokeColor: 'blue', fillColor: 'none'});\n *\n * var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.3});\n * clip_path.updateDataArray = function() {\n * var a = JXG.Math.Clip.union(curve1, curve2, this.board);\n * this.dataX = a[0];\n * this.dataY = a[1];\n * };\n *\n * board.update();\n *\n * \n * \n *\n */\n union: function (path1, path2, board) {\n return this.greinerHormann(path1, path2, \"union\", board);\n },\n\n /**\n * Intersection of two closed paths. The paths could be JSXGraph elements circle, curve, or polygon.\n * Computed by the Greiner-Hormann algorithm.\n *\n * @param {JXG.Circle|JXG.Curve|JXG.Polygon} subject First closed path.\n * @param {JXG.Circle|JXG.Curve|JXG.Polygon} clip Second closed path.\n * @param {JXG.Board} board JSXGraph board object. It is needed to convert between\n * user coordinates and screen coordinates.\n * @return {Array} Array consisting of two arrays containing the x-coordinates and the y-coordinates of\n * the resulting path.\n *\n * @see JXG.Math.Clip.greinerHormann\n * @see JXG.Math.Clip.union\n * @see JXG.Math.Clip.difference\n *\n * @example\n * var p = [];\n * p.push(board.create('point', [0, -5]));\n * p.push(board.create('point', [-5, 0]));\n * p.push(board.create('point', [-3, 3]));\n *\n * var curve1 = board.create('ellipse', p,\n * {strokeColor: 'black'});\n *\n * var curve2 = board.create('curve', [function(phi){return 4 * Math.cos(2*phi); },\n * [0, 0],\n * 0, 2 * Math.PI],\n * {curveType:'polar', strokeColor: 'blue', strokewidth:1});\n *\n * var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.3});\n * clip_path.updateDataArray = function() {\n * var a = JXG.Math.Clip.intersection(curve2, curve1, this.board);\n *\n * this.dataX = a[0];\n * this.dataY = a[1];\n * };\n *\n * board.update();\n *\n * \n * \n *\n *\n */\n intersection: function (path1, path2, board) {\n return this.greinerHormann(path1, path2, \"intersection\", board);\n },\n\n /**\n * Difference of two closed paths, i.e. path1 minus path2.\n * The paths could be JSXGraph elements circle, curve, or polygon.\n * Computed by the Greiner-Hormann algorithm.\n *\n * @param {JXG.Circle|JXG.Curve|JXG.Polygon} subject First closed path.\n * @param {JXG.Circle|JXG.Curve|JXG.Polygon} clip Second closed path.\n * @param {JXG.Board} board JSXGraph board object. It is needed to convert between\n * user coordinates and screen coordinates.\n * @return {Array} Array consisting of two arrays containing the x-coordinates and the y-coordinates of\n * the resulting path.\n *\n * @see JXG.Math.Clip.greinerHormann\n * @see JXG.Math.Clip.intersection\n * @see JXG.Math.Clip.union\n *\n * @example\n * var curve1 = board.create('polygon', [[-4, 4], [4, 4], [0, -1]],\n * {strokeColor: 'blue', fillColor: 'none'});\n *\n * var curve2 = board.create('curve', [\n * [-1, 1, 0, -1],\n * [1, 1, 3, 1]\n * ],\n * {strokeColor: 'black', fillColor: 'none', fillOpacity: 0.8});\n *\n * var clip_path = board.create('curve', [[], []], {strokeWidth: 3, fillColor: 'yellow', fillOpacity: 0.3});\n * clip_path.updateDataArray = function() {\n * var a = JXG.Math.Clip.difference(curve1, curve2, this.board);\n * this.dataX = a[0];\n * this.dataY = a[1];\n * };\n *\n * board.update();\n *\n * \n * \n *\n */\n difference: function (path1, path2, board) {\n return this.greinerHormann(path1, path2, \"difference\", board);\n }\n};\n\n// JXG.extend(Mat.Clip, /** @lends JXG.Math.Clip */ {});\n\nexport default Mat.Clip;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * var z1 = new JXG.Complex(1, 0);\n * var z2 = new JXG.Complex(0, 1);\n * z = JXG.C.add(z1, z1);
\n * z1 and z2 here remain unmodified. With the object oriented approach above this\n * section the code would look like:\n * \n * var z1 = new JXG.Complex(1, 0);\n * var z2 = new JXG.Complex(0, 1);\n * var z = new JXG.Complex(z1);\n * z.add(z2);
\n * @see JXG.Complex\n */\nJXG.C = {};\n\n/**\n * Add two (complex) numbers z1 and z2 and return the result as a (complex) number.\n * @param {JXG.Complex|Number} z1 Summand\n * @param {JXG.Complex|Number} z2 Summand\n * @returns {JXG.Complex} A complex number equal to the sum of the given parameters.\n */\nJXG.C.add = function (z1, z2) {\n var z = new JXG.Complex(z1);\n z.add(z2);\n return z;\n};\n\n/**\n * Subtract two (complex) numbers z1 and z2 and return the result as a (complex) number.\n * @param {JXG.Complex|Number} z1 Minuend\n * @param {JXG.Complex|Number} z2 Subtrahend\n * @returns {JXG.Complex} A complex number equal to the difference of the given parameters.\n */\nJXG.C.sub = function (z1, z2) {\n var z = new JXG.Complex(z1);\n z.sub(z2);\n return z;\n};\n\n/**\n * Multiply two (complex) numbers z1 and z2 and return the result as a (complex) number.\n * @param {JXG.Complex|Number} z1 Factor\n * @param {JXG.Complex|Number} z2 Factor\n * @returns {JXG.Complex} A complex number equal to the product of the given parameters.\n */\nJXG.C.mult = function (z1, z2) {\n var z = new JXG.Complex(z1);\n z.mult(z2);\n return z;\n};\n\n/**\n * Divide two (complex) numbers z1 and z2 and return the result as a (complex) number.\n * @param {JXG.Complex|Number} z1 Dividend\n * @param {JXG.Complex|Number} z2 Divisor\n * @returns {JXG.Complex} A complex number equal to the quotient of the given parameters.\n */\nJXG.C.div = function (z1, z2) {\n var z = new JXG.Complex(z1);\n z.div(z2);\n return z;\n};\n\n/**\n * Conjugate a complex number and return the result.\n * @param {JXG.Complex|Number} z1 Complex number\n * @returns {JXG.Complex} A complex number equal to the conjugate of the given parameter.\n */\nJXG.C.conj = function (z1) {\n var z = new JXG.Complex(z1);\n z.conj();\n return z;\n};\n\n/**\n * Absolute value of a complex number.\n * @param {JXG.Complex|Number} z1 Complex number\n * @returns {Number} real number equal to the absolute value of the given parameter.\n */\nJXG.C.abs = function (z1) {\n var z = new JXG.Complex(z1);\n // z.conj();\n // z.mult(z1);\n // return Math.sqrt(z.real);\n return z.abs();\n};\n\n/**\n * Angle of a complex number (in radians).\n * @param {JXG.Complex|Number} z1 Complex number\n * @returns {Number} real number equal to the angle value of the given parameter.\n */\nJXG.C.angle = function (z1) {\n var z = new JXG.Complex(z1);\n return z.angle();\n};\n\n/**\n * Create copy of complex number.\n *\n * @param {JXG.Complex|Number} z\n * @returns {JXG.Complex}\n */\nJXG.C.copy = function(z) {\n return new JXG.Complex(z);\n};\n\nJXG.Complex.C = JXG.C;\n\nexport default JXG.Complex;\n","/*\n Copyright 2005-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *\n */\n triangulation: function (el, rg_u, rg_v, stepsU, stepsV) {\n var i, j, le,\n up,\n ru, rv, du, dv,\n vertices = [],\n faces = [];\n\n if (stepsV === undefined || stepsV === 0) {\n // Approximate equilateral triangles\n ru = JXG.evaluate(rg_u);\n rv = JXG.evaluate(rg_v);\n du = (ru[1] - ru[0]) / stepsU;\n dv = du * Math.sqrt(3) / 2;\n stepsV = Math.round(Math.abs(rv[1] - rv[0]) / dv);\n }\n for (j = 0; j <= stepsV; j++) {\n up = (j % 2 === 0) ? stepsU : stepsU + 1;\n for (i = 0; i <= up; i++) {\n // Generate vertices\n vertices.push(\n (function (ii, jj, up) {\n var s = ii;\n if (jj % 2 === 1) {\n s = (ii === up) ? (ii - 1) : ((ii > 0) ? (ii - 0.5) : s);\n }\n\n return function () {\n var ru = JXG.evaluate(rg_u),\n rv = JXG.evaluate(rg_v),\n u = ru[0] + s * (ru[1] - ru[0]) / stepsU,\n v = rv[0] + jj * (rv[1] - rv[0]) / stepsV,\n val = el.F(u, v);\n // return [u, v, val];\n return (val.length === 4) ? val.slice(1) : val;\n };\n })(i, j, up)\n );\n\n // Generate faces\n if (j > 0) {\n le = vertices.length - 1;\n if (j % 2 === 1) {\n if (i > 0) {\n faces.push([le - 1, le, le - 2 - stepsU]);\n if (i < up) {\n faces.push([le, le - 1 - stepsU, le - 2 - stepsU]);\n } else {\n faces.push([le - 1, le, le - 2 - stepsU]);\n }\n }\n } else {\n if (i > 0) {\n faces.push([le, le - 2 - stepsU, le - 1]);\n }\n faces.push([le, le - 1 - stepsU, le - 2 - stepsU]);\n }\n }\n }\n }\n return [vertices, faces];\n },\n\n /**\n * Rectangulate (partition it into rectangles) a given two dimensional domain.\n * The number of rectangles the original rectangle is divided into depends on the parameters stepsU and stepsV.\n * Input are the ranges of u and v, as well as stepsU and stepsV which are static.\n * @name rectangulation\n * @param {JXG.ParametricSurface3D|JXG.Plane3D} el element which is displayed using a polyhedron3d.\n * From this element its function F is used.\n * @param {Array} rg_u Begin and end of first direction (numbers or functions)\n * @param {Array} rg_v Begin and end of second direction (numbers or functions)\n * @param {Number} stepsU Immutable\n * @param {Number} stepsV Immutable\n * @returns [coords,faces]\n * @memberof JXG.Math.Tiling\n *\n * @example\n * var rg = board.create('slider', [[-7, -7], [3, -7], [1, 4, 5]], { name: 'rg' });\n *\n * var box = [-5, 5];\n * var view = board.create('view3d',\n * [[-5, -3], [8, 8],\n * [box, box, box]],\n * {\n * projection: 'central',\n * // axesPosition: 'center',\n * xPlaneRear: { visible: false },\n * yPlaneRear: { visible: false },\n * zPlaneRear: { visible: false }\n * });\n *\n * var range = [() => -rg.Value(), () => rg.Value()],\n * stepsU = 15,\n * stepsV = 5,\n * F = (x, y) => [x, y, 3 * Math.sin(Math.sqrt(x ** 2 + y ** 2))];\n *\n * view.setView(0, Math.PI / 2); // Set view from above\n *\n * var el = { F: F }; // Fake surface3d element\n *\n * var surface = JXG.Math.Tiling.rectangulation(el, range, range, stepsU, stepsV);\n * var pol = view.create('polyhedron3d', surface, {\n * shader: {\n * enabled: true,\n * light: {\n * dir: 0\n * }\n * },\n * fillColorArray: ['white'],\n * fillOpacity: 0.9,\n * strokeWidth: 0.2\n * });\n *\n * \n * \n *\n */\n rectangulation: function (el, rg_u, rg_v, stepsU, stepsV) {\n var vertices = [],\n faces = [],\n i, j, le;\n\n for (j = 0; j <= stepsV; j++) {\n for (i = 0; i <= stepsU; i++) {\n vertices.push(\n (function (ii, jj) {\n return function () {\n var ru = JXG.evaluate(rg_u),\n rv = JXG.evaluate(rg_v),\n u = ru[0] + ii * (ru[1] - ru[0]) / stepsU,\n v = rv[0] + jj * (rv[1] - rv[0]) / stepsV,\n val = el.F(u, v);\n return (val.length === 4) ? val.slice(1) : val;\n };\n })(i, j)\n );\n if (i > 0 && j > 0) {\n le = vertices.length - 1;\n faces.push(\n // [le - 1 - stepsU - 1, le - 1 - stepsU, le, le - 1]\n [le - 1, le, le - 1 - stepsU, le - 1 - stepsU - 1]\n );\n }\n }\n }\n return [vertices, faces];\n }\n\n // triangulation_old: function (p1, p2, p3, p4, stepsU, stepsV) {\n // // Vectors used for checking if the given coordinates create a rectangle\n // var vec1 = [p2[0] - p1[0], p2[1] - p1[1]],\n // vec2 = [p3[0] - p2[0], p3[1] - p2[1]],\n // vec3 = [p4[0] - p3[0], p4[1] - p3[1]],\n // vec4 = [p1[0] - p4[0], p1[1] - p4[1]],\n\n // coords = [],\n // faces = [],\n // width, height,\n // wSide, hSide,\n // triangleWidth, triangleHeight,\n // s1, s2,\n // i, j,\n // numRows,\n // widthX, widthY, heightX, heightY,\n // oddPoints,\n // evenPoints;\n\n // // Check if the given coordinates create a rectangle, otherwise an exception is thrown\n // if (\n // vec1[0] * vec4[0] + vec1[1] * vec4[1] !== 0 ||\n // vec2[0] * vec1[0] + vec2[1] * vec1[1] !== 0 ||\n // vec3[0] * vec2[0] + vec3[1] * vec2[1] !== 0 ||\n // vec4[0] * vec3[0] + vec4[1] * vec3[1] !== 0\n // ) {\n // throw new Error(\" the board created is not rectangle \");\n // }\n\n // // Set initial values for wSide, hSide\n // wSide = [0, 0];\n // hSide = [0, 0];\n\n // // Check for longer side of rectangle:\n // // longer side is appointed height, shorter side is appointed width\n // s1 = Math.sqrt((p2[0] - p1[0]) * (p2[0] - p1[0]) + (p2[1] - p1[1]) * (p2[1] - p1[1]));\n // s2 = Math.sqrt((p3[0] - p2[0]) * (p3[0] - p2[0]) + (p3[1] - p2[1]) * (p3[1] - p2[1]));\n // if (s1 <= s2) {\n // width = s1;\n // height = s2;\n // // Determine start and end points of the width-side and height-side\n // wSide = [p1, p2];\n // hSide = [p2, p3];\n // } else {\n // width = s2;\n // height = s1;\n // // Determine start and end points of the width-side and height-side\n // wSide = [p2, p3];\n // hSide = [p1, p2];\n // }\n // // Calculate height and width of the triangles and number of rows\n // triangleWidth = width / stepsU;\n\n // if (stepsV === undefined || stepsV === 0) {\n // // Equilateral triangles, depending on parameter \"stepsU\"\n // triangleHeight = (triangleWidth * Math.sqrt(3)) / 2;\n // numRows = Math.round(height / triangleHeight);\n // } else {\n // // Two parameters stepsU, stepsV\n // numRows = stepsV;\n // triangleHeight = height / numRows;\n // }\n\n // // Calculate values of \"shifting vectors\"\n // widthX = (wSide[1][0] - wSide[0][0]) / stepsU;\n // widthY = (wSide[1][1] - wSide[0][1]) / stepsU;\n // heightX = (hSide[1][0] - hSide[0][0]) / numRows;\n // heightY = (hSide[1][1] - hSide[0][1]) / numRows;\n\n // oddPoints = [];\n // evenPoints = [];\n\n // // Push coordinates of the base point (p1)\n // coords.push([p1[0], p1[1]]);\n // evenPoints.push(coords.length - 1);\n\n // // Calculate point coordinates of layer 0 and store indices in evenPoints\n // for (i = 1; i <= stepsU; i++) {\n // coords.push([p1[0] + i * widthX, p1[1] + i * widthY]); // Points first line\n // evenPoints.push(coords.length - 1);\n // }\n\n // for (i = 1; i <= numRows; i++) {\n // if (i % 2 === 0) {\n // // Points and faces of layers with an even index\n\n // evenPoints = [];\n // // Calculate first point coordinates within the layer\n // coords.push([\n // p1[0] + i * heightX,\n // p1[1] + i * heightY\n // ]);\n // // evenPoints stores index of the first point of the layer\n // evenPoints.push(coords.length - 1);\n // // Calculate all other point coordinates within the layer\n // for (j = 1; j <= stepsU; j++) {\n // coords.push([\n // coords[evenPoints[0]][0] + j * widthX,\n // coords[evenPoints[0]][1] + j * widthY\n // ]);\n // //evenPoints stores index of the most recently calculated point of the layer\n // evenPoints.push(coords.length - 1);\n // }\n // // Connect the faces of the row by grouping indices of points\n // faces.push([evenPoints[0], oddPoints[0], oddPoints[1]]);\n // for (j = 1; j <= stepsU; j++) {\n // faces.push([evenPoints[j - 1], oddPoints[j], evenPoints[j]]);\n // faces.push([evenPoints[j], oddPoints[j], oddPoints[j + 1]]);\n // }\n // } else {\n // // Points and faces of layers with an odd index\n\n // oddPoints = [];\n // // Calculate first point coordinates within the layer\n // coords.push([\n // p1[0] + i * heightX,\n // p1[1] + i * heightY\n // ]);\n // // oddPoints stores index of the first point of the layer\n // oddPoints.push(coords.length - 1);\n // // Calculate all other point coordinates within the layer except for the last point\n // for (j = 1; j <= stepsU; j++) {\n // coords.push([\n // coords[oddPoints[0]][0] + j * widthX - widthX / 2,\n // coords[oddPoints[0]][1] + j * widthY - widthY / 2\n // ]);\n // // oddPoints stores index of the most recently calculated point of the layer\n // oddPoints.push(coords.length - 1);\n // }\n // // Calculate last point coordinates within the layer\n // coords.push([\n // coords[oddPoints[0]][0] + stepsU * widthX,\n // coords[oddPoints[0]][1] + stepsU * widthY\n // ]);\n // // oddPoints stores index of last point within the layer\n // oddPoints.push(coords.length - 1);\n // // Connect the faces of the row by grouping indices of points\n // faces.push([oddPoints[0], evenPoints[0], oddPoints[1]]);\n // for (j = 1; j <= stepsU; j++) {\n // faces.push([oddPoints[j], evenPoints[j - 1], evenPoints[j]]);\n // faces.push([oddPoints[j], evenPoints[j], oddPoints[j + 1]]);\n // }\n // }\n // }\n\n // return [coords, faces];\n // },\n\n // rectangulation_old: function (p1, p2, p3, p4, stepsU, stepsV) {\n // // Vectors used for checking if the given coordinates create a rectangle\n // var vec1 = [p2[0] - p1[0], p2[1] - p1[1]],\n // vec2 = [p3[0] - p2[0], p3[1] - p2[1]],\n // vec3 = [p4[0] - p3[0], p4[1] - p3[1]],\n // vec4 = [p1[0] - p4[0], p1[1] - p4[1]],\n\n // coords = [],\n // faces = [],\n // wSide, hSide,\n // s1, s2,\n // i, j,\n // widthX, widthY,\n // heightX, heightY,\n // startPointLayer;\n\n // // Check if the given coordinates create a rectangle, otherwise an exception is thrown\n // if (\n // vec1[0] * vec4[0] + vec1[1] * vec4[1] !== 0 ||\n // vec2[0] * vec1[0] + vec2[1] * vec1[1] !== 0 ||\n // vec3[0] * vec2[0] + vec3[1] * vec2[1] !== 0 ||\n // vec4[0] * vec3[0] + vec4[1] * vec3[1] !== 0\n // ) {\n // throw new Error(\"rectangulation_old: area is not rectangle \");\n // // console.log(\"rectangulation_old: area is not rectangle \");\n // }\n\n // // Set initial values for wSide, hSide\n // wSide = [0, 0];\n // hSide = [0, 0];\n\n // // Check for longer side of rectangle:\n // // longer side is appointed height, shorter side is appointed width\n // // s1 = Math.sqrt((p2[0] - p1[0]) * (p2[0] - p1[0]) + (p2[1] - p1[1]) * (p2[1] - p1[1]));\n // // s2 = Math.sqrt((p3[0] - p2[0]) * (p3[0] - p2[0]) + (p3[1] - p2[1]) * (p3[1] - p2[1]));\n // s1 = Mat.hypot(vec1[0], vec1[1]);\n // s2 = Mat.hypot(vec2[0], vec2[1]);\n\n // if (s1 <= s2) {\n // // Determine start and end points of the width-side and height-side\n // wSide = [p1, p2];\n // hSide = [p2, p3];\n // } else {\n // // Determine start and end points of the width-side and height-side\n // wSide = [p2, p3];\n // hSide = [p1, p2];\n // }\n\n // // Calculate values of \"shifting vectors\"\n // widthX = (wSide[1][0] - wSide[0][0]) / stepsV;\n // widthY = (wSide[1][1] - wSide[0][1]) / stepsV;\n // heightX = (hSide[1][0] - hSide[0][0]) / stepsU;\n // heightY = (hSide[1][1] - hSide[0][1]) / stepsU;\n\n // // Initialize startPointLayer that stores coordinates of the first point of the current layer\n // startPointLayer = [];\n\n // // Push coordinates of base point (p1)\n // coords.push([p1[0], p1[1]]);\n // startPointLayer = coords[0];\n\n // // Calculate point coordinates of layer 0\n // for (j = 1; j <= stepsV; j++) {\n // coords.push([startPointLayer[0] + j * widthX, startPointLayer[1] + j * widthY]);\n // }\n\n // for (i = 1; i <= stepsU; i++) {\n // startPointLayer = [];\n\n // // Calculate point coordinates of first point of layer\n // coords.push([\n // p1[0] + i * heightX,\n // p1[1] + i * heightY\n // ]);\n // startPointLayer = coords[coords.length - 1];\n\n // // Calculating remaining point coordinates of layer\n // for (j = 1; j <= stepsV; j++) {\n // coords.push([\n // startPointLayer[0] + j * widthX,\n // startPointLayer[1] + j * widthY\n // ]);\n // }\n\n // // Connect rectangles by grouping indices of points\n // for (\n // j = coords.length - stepsV - 1;\n // j < coords.length - 1;\n // j++\n // ) {\n // faces.push([j, j - stepsV - 1, j - stepsV, j + 1]);\n // }\n // }\n\n // return [coords, faces];\n // },\n\n // /**\n // * This function creates an array of dynamic 3-dimensional points\n // * based on an array of pairs of two coordinates.\n // * It uses a mathematical function to assign a third coordinate (the z-coordinate)\n // * to each pair of two coordinates.\n // * The 3-dimensional points are not stored directly.\n // * Instead the array stores JavaScript functions that utilize the mentioned mathematical function\n // * to return an array of three coordinates.\n // * This allows the recognition and proper visualization of changes to the underlying\n // * mathematical function.\n // * @name mapMeshTo3D\n // * @param {Array} surface\n // * @param {Parametricsurface3d} el\n // * @returns {Array} dynamicPoints array of [x, y, z] coordinates\n // *\n // * @private\n // * @memberof JXG.Math.Tiling\n // */\n // mapMeshTo3D: function (surface, el) {\n // var dynamicPoints = [], i;\n\n // for (i = 0; i < surface[0].length; i++) {\n // dynamicPoints.push(\n // (function (u, v) {\n // return function(x, y) { return el.F(u, v); };\n // })(surface[0][i][0], surface[0][i][1])\n // ); // Capture values explicitly\n // // dynamicPoints.push(\n // // (function (u, v) {\n // // return function(x, y) { return el.F(Type.evaluate(u), Type.evaluate(v)); };\n // // })(surface[0][i][0], surface[0][i][1])\n // // ); // Capture values explicitly\n // }\n\n // return dynamicPoints;\n // }\n};\n\nexport default Mat.Tiling;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n *
\n * This means, the numbering is 1-based.\n * Solid lines are set with dash:0.\n * If the object's attribute \"dashScale:true\" the dash pattern is multiplied by\n * strokeWidth / 2.\n *\n * @type Array\n * @default [[2, 2], [5, 5], [10, 10], [20, 20], [20, 10, 10, 10], [20, 5, 10, 5], [0, 5]]\n * @see JXG.GeometryElement#dash\n * @see JXG.GeometryElement#dashScale\n */\n this.dashArray = [\n [2, 2],\n [5, 5],\n [10, 10],\n [20, 20],\n [20, 10, 10, 10],\n [20, 5, 10, 5],\n [0, 5]\n ];\n};\n\nJXG.extend(\n JXG.AbstractRenderer.prototype,\n /** @lends JXG.AbstractRenderer.prototype */ {\n\n /* ********* Private methods *********** */\n\n /**\n * Update visual properties, but only if {@link JXG.AbstractRenderer#enhancedRendering} or enhanced is set to true.\n * @param {JXG.GeometryElement} el The element to update\n * @param {Object} [not={}] Select properties you don't want to be updated: {fill: true, dash: true} updates\n * everything except for fill and dash. Possible values are stroke, fill, dash, shadow, gradient.\n * @param {Boolean} [enhanced=false] If true, {@link JXG.AbstractRenderer#enhancedRendering} is assumed to be true.\n * @private\n */\n _updateVisual: function (el, not, enhanced) {\n if (enhanced || this.enhancedRendering) {\n not = not || {};\n\n this.setObjectTransition(el);\n\n // Set clip-path\n // The clip-path of the label is handled in updateText()\n this.setClipPath(el, !!el.evalVisProp('clip'));\n\n if (!el.evalVisProp('draft')) {\n if (!not.stroke) {\n if (el.highlighted) {\n this.setObjectStrokeColor(\n el,\n el.evalVisProp('highlightstrokecolor'),\n el.evalVisProp('highlightstrokeopacity')\n );\n this.setObjectStrokeWidth(el, el.evalVisProp('highlightstrokewidth'));\n } else {\n this.setObjectStrokeColor(\n el,\n el.evalVisProp('strokecolor'),\n el.evalVisProp('strokeopacity')\n );\n this.setObjectStrokeWidth(el, el.evalVisProp('strokewidth'));\n }\n }\n\n if (!not.fill) {\n if (el.highlighted) {\n this.setObjectFillColor(\n el,\n el.evalVisProp('highlightfillcolor'),\n el.evalVisProp('highlightfillopacity')\n );\n } else {\n this.setObjectFillColor(\n el,\n el.evalVisProp('fillcolor'),\n el.evalVisProp('fillopacity')\n );\n }\n }\n\n if (!not.dash) {\n this.setDashStyle(el, el.visProp);\n }\n\n if (!not.shadow) {\n this.setShadow(el);\n }\n\n // if (!not.gradient) {\n // // this.setGradient(el);\n // this.setShadow(el);\n // }\n\n if (!not.tabindex) {\n this.setTabindex(el);\n }\n } else {\n this.setDraft(el);\n }\n\n if (el.highlighted) {\n this.setCssClass(el, el.evalVisProp('highlightcssclass'));\n } else {\n this.setCssClass(el, el.evalVisProp('cssclass'));\n }\n\n if (el.evalVisProp('aria.enabled')) {\n this.setARIA(el);\n }\n }\n },\n\n /**\n * Get information if element is highlighted.\n * @param {JXG.GeometryElement} el The element which is tested for being highlighted.\n * @returns {String} 'highlight' if highlighted, otherwise the ampty string '' is returned.\n * @private\n */\n _getHighlighted: function (el) {\n var isTrace = false,\n hl;\n\n if (!Type.exists(el.board) || !Type.exists(el.board.highlightedObjects)) {\n // This case handles trace elements.\n // To make them work, we simply neglect highlighting.\n isTrace = true;\n }\n\n if (!isTrace && Type.exists(el.board.highlightedObjects[el.id])) {\n hl = 'highlight';\n } else {\n hl = \"\";\n }\n return hl;\n },\n\n /* ********* Point related stuff *********** */\n\n /**\n * Draws a point on the {@link JXG.Board}.\n * @param {JXG.Point} el Reference to a {@link JXG.Point} object that has to be drawn.\n * @see Point\n * @see JXG.Point\n * @see JXG.AbstractRenderer#updatePoint\n * @see JXG.AbstractRenderer#changePointStyle\n */\n drawPoint: function (el) {\n var prim,\n // Sometimes el is not a real point and lacks the methods of a JXG.Point instance,\n // in these cases to not use el directly.\n face = Options.normalizePointFace(el.evalVisProp('face'));\n\n // Determine how the point looks like\n if (face === 'o') {\n prim = 'ellipse';\n } else if (face === \"[]\") {\n prim = 'rect';\n } else {\n // cross/x, diamond/<>, triangleup/A/^, triangledown/v, triangleleft/<,\n // triangleright/>, plus/+, |, -\n prim = 'path';\n }\n\n el.rendNode = this.appendChildPrim(\n this.createPrim(prim, el.id),\n el.evalVisProp('layer')\n );\n this.appendNodesToElement(el, prim);\n\n // Adjust visual properties\n this._updateVisual(el, { dash: true, shadow: true }, true);\n\n // By now we only created the xml nodes and set some styles, in updatePoint\n // the attributes are filled with data.\n this.updatePoint(el);\n },\n\n /**\n * Updates visual appearance of the renderer element assigned to the given {@link JXG.Point}.\n * @param {JXG.Point} el Reference to a {@link JXG.Point} object, that has to be updated.\n * @see Point\n * @see JXG.Point\n * @see JXG.AbstractRenderer#drawPoint\n * @see JXG.AbstractRenderer#changePointStyle\n */\n updatePoint: function (el) {\n var size = el.evalVisProp('size'),\n // sometimes el is not a real point and lacks the methods of a JXG.Point instance,\n // in these cases to not use el directly.\n face = Options.normalizePointFace(el.evalVisProp('face')),\n unit = el.evalVisProp('sizeunit'),\n zoom = el.evalVisProp('zoom'),\n s1;\n\n if (!isNaN(el.coords.scrCoords[2] + el.coords.scrCoords[1])) {\n if (unit === 'user') {\n size *= Math.sqrt(Math.abs(el.board.unitX * el.board.unitY));\n }\n size *= !el.board || !zoom ? 1.0 : Math.sqrt(el.board.zoomX * el.board.zoomY);\n s1 = size === 0 ? 0 : size + 1;\n\n if (face === 'o') {\n // circle\n this.updateEllipsePrim(\n el.rendNode,\n el.coords.scrCoords[1],\n el.coords.scrCoords[2],\n s1,\n s1\n );\n } else if (face === \"[]\") {\n // rectangle\n this.updateRectPrim(\n el.rendNode,\n el.coords.scrCoords[1] - size,\n el.coords.scrCoords[2] - size,\n size * 2,\n size * 2\n );\n } else {\n // x, +, <>, <<>>, ^, v, <, >\n this.updatePathPrim(\n el.rendNode,\n this.updatePathStringPoint(el, size, face),\n el.board\n );\n }\n this._updateVisual(el, { dash: false, shadow: false });\n this.setShadow(el);\n }\n },\n\n /**\n * Changes the style of a {@link JXG.Point}. This is required because the point styles differ in what\n * elements have to be drawn, e.g. if the point is marked by a \"x\" or a \"+\" two lines are drawn, if\n * it's marked by spot a circle is drawn. This method removes the old renderer element(s) and creates\n * the new one(s).\n * @param {JXG.Point} el Reference to a {@link JXG.Point} object, that's style is changed.\n * @see Point\n * @see JXG.Point\n * @see JXG.AbstractRenderer#updatePoint\n * @see JXG.AbstractRenderer#drawPoint\n */\n changePointStyle: function (el) {\n var node = this.getElementById(el.id);\n\n // remove the existing point rendering node\n if (Type.exists(node)) {\n this.remove(node);\n }\n\n // and make a new one\n this.drawPoint(el);\n Type.clearVisPropOld(el);\n\n if (!el.visPropCalc.visible) {\n this.display(el, false);\n }\n\n if (el.evalVisProp('draft')) {\n this.setDraft(el);\n }\n },\n\n /* ********* Line related stuff *********** */\n\n /**\n * Draws a line on the {@link JXG.Board}.\n * @param {JXG.Line} el Reference to a line object, that has to be drawn.\n * @see Line\n * @see JXG.Line\n * @see JXG.AbstractRenderer#updateLine\n */\n drawLine: function (el) {\n el.rendNode = this.appendChildPrim(\n this.createPrim(\"line\", el.id),\n el.evalVisProp('layer')\n );\n this.appendNodesToElement(el, 'lines');\n this.updateLine(el);\n },\n\n /**\n * Updates visual appearance of the renderer element assigned to the given {@link JXG.Line}.\n * @param {JXG.Line} el Reference to the {@link JXG.Line} object that has to be updated.\n * @see Line\n * @see JXG.Line\n * @see JXG.AbstractRenderer#drawLine\n */\n updateLine: function (el) {\n this._updateVisual(el);\n this.updatePathWithArrowHeads(el); // Calls the renderer primitive\n this.setLineCap(el);\n },\n\n /* ********* Curve related stuff *********** */\n\n /**\n * Draws a {@link JXG.Curve} on the {@link JXG.Board}.\n * @param {JXG.Curve} el Reference to a graph object, that has to be plotted.\n * @see Curve\n * @see JXG.Curve\n * @see JXG.AbstractRenderer#updateCurve\n */\n drawCurve: function (el) {\n el.rendNode = this.appendChildPrim(\n this.createPrim(\"path\", el.id),\n el.evalVisProp('layer')\n );\n this.appendNodesToElement(el, 'path');\n this.updateCurve(el);\n },\n\n /**\n * Updates visual appearance of the renderer element assigned to the given {@link JXG.Curve}.\n * @param {JXG.Curve} el Reference to a {@link JXG.Curve} object, that has to be updated.\n * @see Curve\n * @see JXG.Curve\n * @see JXG.AbstractRenderer#drawCurve\n */\n updateCurve: function (el) {\n this._updateVisual(el);\n this.updatePathWithArrowHeads(el); // Calls the renderer primitive\n this.setLineCap(el);\n },\n\n /* ********* Arrow heads and related stuff *********** */\n\n /**\n * Handles arrow heads of a line or curve element and calls the renderer primitive.\n *\n * @param {JXG.GeometryElement} el Reference to a line or curve object that has to be drawn.\n * @param {Boolean} doHighlight\n *\n * @private\n * @see Line\n * @see JXG.Line\n * @see Curve\n * @see JXG.Curve\n * @see JXG.AbstractRenderer#updateLine\n * @see JXG.AbstractRenderer#updateCurve\n * @see JXG.AbstractRenderer#makeArrows\n * @see JXG.AbstractRenderer#getArrowHeadData\n */\n updatePathWithArrowHeads: function (el, doHighlight) {\n var hl = doHighlight ? 'highlight' : '',\n w,\n arrowData;\n\n if (doHighlight && el.evalVisProp('highlightstrokewidth')) {\n w = Math.max(\n el.evalVisProp('highlightstrokewidth'),\n el.evalVisProp('strokewidth')\n );\n } else {\n w = el.evalVisProp('strokewidth');\n }\n\n // Get information if there are arrow heads and how large they are.\n arrowData = this.getArrowHeadData(el, w, hl);\n\n // Create the SVG nodes if necessary\n this.makeArrows(el, arrowData);\n\n // Draw the paths with arrow heads\n if (el.elementClass === Const.OBJECT_CLASS_LINE) {\n this.updateLineWithEndings(el, arrowData);\n } else if (el.elementClass === Const.OBJECT_CLASS_CURVE) {\n this.updatePath(el);\n }\n\n this.setArrowSize(el, arrowData);\n },\n\n /**\n * This method determines some data about the line endings of this element.\n * If there are arrow heads, the offset is determined so that no parts of the line stroke\n * lap over the arrow head.\n * \n *
\n * @param {Boolean} async Call ajax asynchonously.\n * @param {function} callback A function that is run when the board is ready.\n */\n parseFileContent: function (url, board, format, async, encoding, callback) {\n if (Type.isString(url) || FileReader === undefined) {\n this.handleRemoteFile(url, board, format, async, encoding, callback);\n } else {\n this.handleLocalFile(url, board, format, async, encoding, callback);\n }\n },\n\n /**\n * Parses a given string according to the file format given in format.\n * @param {String} str Contents of the file.\n * @param {JXG.Board} board The board the construction in the file should be loaded in.\n * @param {String} format Possible values are \n *
\n * @param {function} callback\n */\n parseString: function (str, board, format, callback) {\n var Reader, read;\n\n format = format.toLowerCase();\n Reader = JXG.readers[format];\n\n if (Type.exists(Reader)) {\n read = new Reader(board, str);\n read.read();\n } else if (format === 'jessiecode') {\n } else {\n throw new Error(\"JSXGraph: There is no reader available for '\" + format + \"'.\");\n }\n\n if (Type.isFunction(callback)) {\n callback(board);\n }\n }\n};\n\n// The following code is vbscript. This is a workaround to enable binary data downloads via AJAX in\n// Microsoft Internet Explorer.\n\n/*jslint evil:true, es5:true, white:true*/\n/*jshint multistr:true*/\nif (\n !Env.isMetroApp() &&\n Env.isBrowser &&\n typeof navigator === \"object\" &&\n /msie/i.test(navigator.userAgent) &&\n !/opera/i.test(navigator.userAgent) &&\n document &&\n document.write\n) {\n document.write(\n '\\n'\n );\n}\n\nexport default JXG.FileReader;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n * @type Number\n */\n this.mode = this.BOARD_MODE_NONE;\n\n /**\n * The update quality of the board. In most cases this is set to {@link JXG.Board#BOARD_QUALITY_HIGH}.\n * If {@link JXG.Board#mode} equals {@link JXG.Board#BOARD_MODE_DRAG} this is set to\n * {@link JXG.Board#BOARD_QUALITY_LOW} to speed up the update process by e.g. reducing the number of\n * evaluation points when plotting functions. Possible values are\n * \n *
\n * @type Number\n * @see JXG.Board#mode\n */\n this.updateQuality = this.BOARD_QUALITY_HIGH;\n\n /**\n * If true updates are skipped.\n * @type Boolean\n */\n this.isSuspendedRedraw = false;\n\n this.calculateSnapSizes();\n\n /**\n * The distance from the mouse to the dragged object in x direction when the user clicked the mouse button.\n * @type Number\n * @see JXG.Board#drag_dy\n */\n this.drag_dx = 0;\n\n /**\n * The distance from the mouse to the dragged object in y direction when the user clicked the mouse button.\n * @type Number\n * @see JXG.Board#drag_dx\n */\n this.drag_dy = 0;\n\n /**\n * The last position where a drag event has been fired.\n * @type Array\n * @see JXG.Board#moveObject\n */\n this.drag_position = [0, 0];\n\n /**\n * References to the object that is dragged with the mouse on the board.\n * @type JXG.GeometryElement\n * @see JXG.Board#touches\n */\n this.mouse = {};\n\n /**\n * Keeps track on touched elements, like {@link JXG.Board#mouse} does for mouse events.\n * @type Array\n * @see JXG.Board#mouse\n */\n this.touches = [];\n\n /**\n * A string containing the XML text of the construction.\n * This is set in {@link JXG.FileReader.parseString}.\n * Only useful if a construction is read from a GEONExT-, Intergeo-, Geogebra-, or Cinderella-File.\n * @type String\n */\n this.xmlString = '';\n\n /**\n * Cached result of getCoordsTopLeftCorner for touch/mouseMove-Events to save some DOM operations.\n * @type Array\n */\n this.cPos = [];\n\n /**\n * Contains the last time (epoch, msec) since the last touchMove event which was not thrown away or since\n * touchStart because Android's Webkit browser fires too much of them.\n * @type Number\n */\n this.touchMoveLast = 0;\n\n /**\n * Contains the pointerId of the last touchMove event which was not thrown away or since\n * touchStart because Android's Webkit browser fires too much of them.\n * @type Number\n */\n this.touchMoveLastId = Infinity;\n\n /**\n * Contains the last time (epoch, msec) since the last getCoordsTopLeftCorner call which was not thrown away.\n * @type Number\n */\n this.positionAccessLast = 0;\n\n /**\n * Collects all elements that triggered a mouse down event.\n * @type Array\n */\n this.downObjects = [];\n this.clickObjects = {};\n\n /**\n * Collects all elements that have keyboard focus. Should be either one or no element.\n * Elements are stored with their id.\n * @type Array\n */\n this.focusObjects = [];\n\n if (this.attr.showcopyright || this.attr.showlogo) {\n this.renderer.displayLogo(Const.licenseLogo, parseInt(this.options.text.fontSize, 10), this);\n }\n\n if (this.attr.showcopyright) {\n this.renderer.displayCopyright(Const.licenseText, parseInt(this.options.text.fontSize, 10));\n }\n\n /**\n * Full updates are needed after zoom and axis translates. This saves some time during an update.\n * @default false\n * @type Boolean\n */\n this.needsFullUpdate = false;\n\n /**\n * If reducedUpdate is set to true then only the dragged element and few (e.g. 2) following\n * elements are updated during mouse move. On mouse up the whole construction is\n * updated. This enables us to be fast even on very slow devices.\n * @type Boolean\n * @default false\n */\n this.reducedUpdate = false;\n\n /**\n * The current color blindness deficiency is stored in this property. If color blindness is not emulated\n * at the moment, it's value is 'none'.\n */\n this.currentCBDef = 'none';\n\n /**\n * If GEONExT constructions are displayed, then this property should be set to true.\n * At the moment there should be no difference. But this may change.\n * This is set in {@link JXG.GeonextReader.readGeonext}.\n * @type Boolean\n * @default false\n * @see JXG.GeonextReader.readGeonext\n */\n this.geonextCompatibilityMode = false;\n\n if (this.options.text.useASCIIMathML && translateASCIIMath) {\n init();\n } else {\n this.options.text.useASCIIMathML = false;\n }\n\n /**\n * A flag which tells if the board registers mouse events.\n * @type Boolean\n * @default false\n */\n this.hasMouseHandlers = false;\n\n /**\n * A flag which tells if the board registers touch events.\n * @type Boolean\n * @default false\n */\n this.hasTouchHandlers = false;\n\n /**\n * A flag which stores if the board registered pointer events.\n * @type Boolean\n * @default false\n */\n this.hasPointerHandlers = false;\n\n /**\n * A flag which stores if the board registered zoom events, i.e. mouse wheel scroll events.\n * @type Boolean\n * @default false\n */\n this.hasWheelHandlers = false;\n\n /**\n * A flag which tells if the board the JXG.Board#mouseUpListener is currently registered.\n * @type Boolean\n * @default false\n */\n this.hasMouseUp = false;\n\n /**\n * A flag which tells if the board the JXG.Board#touchEndListener is currently registered.\n * @type Boolean\n * @default false\n */\n this.hasTouchEnd = false;\n\n /**\n * A flag which tells us if the board has a pointerUp event registered at the moment.\n * @type Boolean\n * @default false\n */\n this.hasPointerUp = false;\n\n /**\n * Array containing the events related to resizing that have event listeners.\n * @type Array\n * @default []\n */\n this.resizeHandlers = [];\n\n /**\n * Offset for large coords elements like images\n * @type Array\n * @private\n * @default [0, 0]\n */\n this._drag_offset = [0, 0];\n\n /**\n * Stores the input device used in the last down or move event.\n * @type String\n * @private\n * @default 'mouse'\n */\n this._inputDevice = 'mouse';\n\n /**\n * Keeps a list of pointer devices which are currently touching the screen.\n * @type Array\n * @private\n */\n this._board_touches = [];\n\n /**\n * A flag which tells us if the board is in the selecting mode\n * @type Boolean\n * @default false\n */\n this.selectingMode = false;\n\n /**\n * A flag which tells us if the user is selecting\n * @type Boolean\n * @default false\n */\n this.isSelecting = false;\n\n /**\n * A flag which tells us if the user is scrolling the viewport\n * @type Boolean\n * @private\n * @default false\n * @see JXG.Board#scrollListener\n */\n this._isScrolling = false;\n\n /**\n * A flag which tells us if a resize is in process\n * @type Boolean\n * @private\n * @default false\n * @see JXG.Board#resizeListener\n */\n this._isResizing = false;\n\n /**\n * A flag which tells us if the update is triggered by a change of the\n * 3D view. In that case we only have to update the projection of\n * the 3D elements and can avoid a full board update.\n *\n * @type Boolean\n * @private\n * @default false\n */\n this._change3DView = false;\n\n /**\n * A bounding box for the selection\n * @type Array\n * @default [ [0,0], [0,0] ]\n */\n this.selectingBox = [[0, 0], [0, 0]];\n\n /**\n * Array to log user activity.\n * Entries are objects of the form '{type, id, start, end}' notifying\n * the start time as well as the last time of a single event of type 'type'\n * on a JSXGraph element of id 'id'.\n * \n *\n * @type Array\n * @see SketchCurve\n * @see JXG.Board#sketch\n */\n this.sketches = [null, null];\n\n /**\n * Alias for the first sketchcurve, i.e. for board.sketches[0].\n * @type {JXG.Curve}\n * @see JXG.Board#sketches\n */\n this.sketch = null; //this.sketches[0];\n\n /**\n * Array of length two of Boolean flags indicating if a pointer device (finger, mouse, pen) is\n * adding points to board.sketches[i] (i=0,1). i=1 is only used for multi-touch with fingers.\n * \n *
\n *\n * @name Board#getPointLoc\n * @param {Array} position Array of requested position [x, y] or [w, x, y].\n * @param {Array|Number} [margin] Optional margin for the inner of the board: [top, right, bottom, left]. A single number m is interpreted as [m, m, m, m].\n * @returns {Array} [u,v] with the following meanings:\n * \n * v u > | -1 | 0 | 1 |\n * ------------------------------------------\n * 1 | [-1,1] | [0,1] | [1,1] |\n * ------------------------------------------\n * 0 | [-1,0] | Board | [1,0] |\n * ------------------------------------------\n * -1 | [-1,-1] | [0,-1] | [1,-1] |\n *
\n * Positions inside the board (minus margin) return the value [0,0].\n *\n * @example\n * var point1, point2, point3, point4, margin,\n * p1Location, p2Location, p3Location, p4Location,\n * helppoint1, helppoint2, helppoint3, helppoint4;\n *\n * // margin to make the boundingBox virtually smaller\n * margin = [2,2,2,2];\n *\n * // Points which are seen on screen\n * point1 = board.create('point', [0,0]);\n * point2 = board.create('point', [0,7]);\n * point3 = board.create('point', [7,7]);\n * point4 = board.create('point', [-7,-5]);\n *\n * p1Location = board.getPointLoc(point1.coords.usrCoords, margin);\n * p2Location = board.getPointLoc(point2.coords.usrCoords, margin);\n * p3Location = board.getPointLoc(point3.coords.usrCoords, margin);\n * p4Location = board.getPointLoc(point4.coords.usrCoords, margin);\n *\n * // Text seen on screen\n * board.create('text', [1,-1, \"getPointLoc(A): \" + \"[\" + p1Location + \"]\"])\n * board.create('text', [1,-2, \"getPointLoc(B): \" + \"[\" + p2Location + \"]\"])\n * board.create('text', [1,-3, \"getPointLoc(C): \" + \"[\" + p3Location + \"]\"])\n * board.create('text', [1,-4, \"getPointLoc(D): \" + \"[\" + p4Location + \"]\"])\n *\n *\n * // Helping points that are used to create the helping lines\n * helppoint1 = board.create('point', [(function (){\n * var bbx = board.getBoundingBox();\n * return [bbx[2] - 2, bbx[1] -2];\n * })], {\n * visible: false,\n * })\n *\n * helppoint2 = board.create('point', [(function (){\n * var bbx = board.getBoundingBox();\n * return [bbx[0] + 2, bbx[1] -2];\n * })], {\n * visible: false,\n * })\n *\n * helppoint3 = board.create('point', [(function (){\n * var bbx = board.getBoundingBox();\n * return [bbx[0]+ 2, bbx[3] + 2];\n * })],{\n * visible: false,\n * })\n *\n * helppoint4 = board.create('point', [(function (){\n * var bbx = board.getBoundingBox();\n * return [bbx[2] -2, bbx[3] + 2];\n * })], {\n * visible: false,\n * })\n *\n * // Helping lines to visualize the 9 sectors and the margin\n * board.create('line', [helppoint1, helppoint2]);\n * board.create('line', [helppoint2, helppoint3]);\n * board.create('line', [helppoint3, helppoint4]);\n * board.create('line', [helppoint4, helppoint1]);\n *\n * \n *\n */\n getPointLoc: function (position, margin) {\n var bbox, pos, res, marg;\n\n bbox = this.getBoundingBox();\n pos = position;\n if (pos.length === 2) {\n pos.unshift(undefined);\n }\n res = [0, 0];\n marg = margin || 0;\n if (Type.isNumber(marg)) {\n marg = [marg, marg, marg, marg];\n }\n\n if (pos[1] > (bbox[2] - marg[1])) {\n res[0] = 1;\n }\n if (pos[1] < (bbox[0] + marg[3])) {\n res[0] = -1;\n }\n\n if (pos[2] > (bbox[1] - marg[0])) {\n res[1] = 1;\n }\n if (pos[2] < (bbox[3] + marg[2])) {\n res[1] = -1;\n }\n\n return res;\n },\n\n /**\n * This function calculates where the origin is located (@link Board#getPointLoc).\n * Optional a margin to the inner of the board is respected.
\n *\n * @name Board#getLocationOrigin\n * @param {Array|Number} [margin] Optional margin for the inner of the board: [top, right, bottom, left]. A single number m is interpreted as [m, m, m, m].\n * @returns {Array} [u,v] which shows where the origin is located (@link Board#getPointLoc).\n */\n getLocationOrigin: function (margin) {\n return this.getPointLoc([0, 0], margin);\n },\n\n /**\n * Get the position of the pointing device in screen coordinates, relative to the upper left corner\n * of the host tag.\n * @param {Event} e Event object given by the browser.\n * @param {Number} [i] Only use in case of touch events. This determines which finger to use and should not be set\n * for mouseevents.\n * @returns {Array} Contains the mouse coordinates in screen coordinates, ready for {@link JXG.Coords}\n */\n getMousePosition: function (e, i) {\n var cPos = this.getCoordsTopLeftCorner(),\n absPos,\n v;\n\n // Position of cursor using clientX/Y\n absPos = Env.getPosition(e, i, this.document);\n\n // Old:\n // This seems to be obsolete anyhow:\n // \"In case there has been no down event before.\"\n // if (!Type.exists(this.cssTransMat)) {\n // this.updateCSSTransforms();\n // }\n // New:\n // We have to update the CSS transform matrix all the time,\n // since libraries like ZIMJS do not notify JSXGraph about a change.\n // In particular, sending a resize event event to JSXGraph\n // would be necessary.\n this.updateCSSTransforms();\n\n // Position relative to the top left corner\n v = [1, absPos[0] - cPos[0], absPos[1] - cPos[1]];\n v = Mat.matVecMult(this.cssTransMat, v);\n v[1] /= v[0];\n v[2] /= v[0];\n return [v[1], v[2]];\n\n // Method without CSS transformation\n /*\n return [absPos[0] - cPos[0], absPos[1] - cPos[1]];\n */\n },\n\n /**\n * Initiate moving the origin. This is used in mouseDown and touchStart listeners.\n * @param {Number} x Current mouse/touch coordinates\n * @param {Number} y Current mouse/touch coordinates\n */\n initMoveOrigin: function (x, y) {\n this.drag_dx = x - this.origin.scrCoords[1];\n this.drag_dy = y - this.origin.scrCoords[2];\n\n this.mode = this.BOARD_MODE_MOVE_ORIGIN;\n this._change3DView = false;\n this.updateQuality = this.BOARD_QUALITY_LOW;\n },\n\n /**\n * Collects all elements below the current mouse pointer and fulfilling the following constraints:\n * \n *
\n * @param {Number} x Current mouse/touch coordinates\n * @param {Number} y current mouse/touch coordinates\n * @param {Object} evt An event object\n * @param {String} type What type of event? 'touch', 'mouse' or 'pen'.\n * @returns {Array} A list of geometric elements.\n */\n initMoveObject: function (x, y, evt, type) {\n var pEl,\n el,\n collect = [],\n offset = [],\n haspoint,\n len = this.objectsList.length,\n dragEl = { visProp: { layer: -10000 } };\n\n // Store status of key presses for 3D movement\n this._shiftKey = evt.shiftKey;\n this._ctrlKey = evt.ctrlKey;\n\n //for (el in this.objects) {\n for (el = 0; el < len; el++) {\n pEl = this.objectsList[el];\n haspoint = pEl.hasPoint && pEl.hasPoint(x, y);\n\n if (pEl.visPropCalc.visible && haspoint) {\n pEl.triggerEventHandlers([type + 'down', 'down'], [evt]);\n this.downObjects.push(pEl);\n }\n\n if (haspoint &&\n pEl.isDraggable &&\n pEl.visPropCalc.visible &&\n ((this.geonextCompatibilityMode &&\n (Type.isPoint(pEl) || pEl.elementClass === Const.OBJECT_CLASS_TEXT)) ||\n !this.geonextCompatibilityMode) &&\n !pEl.evalVisProp('fixed')\n /*(!pEl.visProp.frozen) &&*/\n ) {\n // Elements in the highest layer get priority.\n if (\n pEl.visProp.layer > dragEl.visProp.layer ||\n (pEl.visProp.layer === dragEl.visProp.layer &&\n pEl.lastDragTime.getTime() >= dragEl.lastDragTime.getTime())\n ) {\n // If an element and its label have the focus\n // simultaneously, the element is taken.\n // This only works if we assume that every browser runs\n // through this.objects in the right order, i.e. an element A\n // added before element B turns up here before B does.\n if (\n !this.attr.ignorelabels ||\n !Type.exists(dragEl.label) ||\n pEl !== dragEl.label\n ) {\n dragEl = pEl;\n collect.push(dragEl);\n\n // Store offset for large coords elements.\n if (Type.exists(dragEl.coords)) {\n if (dragEl.elementClass === Const.OBJECT_CLASS_POINT ||\n dragEl.relativeCoords // Relative texts like labels\n ) {\n offset.push(Statistics.subtract(dragEl.coords.scrCoords.slice(1), [x, y]));\n } else {\n // Images and texts\n offset.push(Statistics.subtract(dragEl.actualCoords.scrCoords.slice(1), [x, y]));\n }\n } else {\n offset.push([0, 0]);\n }\n\n // We can't drop out of this loop because of the event handling system\n //if (this.attr.takefirst) {\n // return collect;\n //}\n }\n }\n }\n }\n\n if (this.attr.drag.enabled && collect.length > 0) {\n this.mode = this.BOARD_MODE_DRAG;\n }\n\n // A one-element array is returned.\n if (this.attr.takefirst) {\n collect.length = 1;\n this._drag_offset = offset[0];\n } else {\n collect = collect.slice(-1);\n this._drag_offset = offset[offset.length - 1];\n }\n\n if (!this._drag_offset) {\n this._drag_offset = [0, 0];\n }\n\n // Move drag element to the top of the layer\n if (this.renderer.type === 'svg' && Type.exists(collect[0]) &&\n collect.length === 1 && Type.exists(collect[0].rendNode)\n ) {\n // Move object to top\n if (collect[0].evalVisProp('dragtotopoflayer')) {\n collect[0].rendNode.parentNode.appendChild(collect[0].rendNode);\n }\n // Move object's label to top\n if (collect[0].hasLabel &&\n collect[0].label.evalVisProp('display') === 'html' &&\n collect[0].label.evalVisProp('dragtotopoflayer')\n ) {\n collect[0].label.rendNode.parentNode.appendChild(collect[0].label.rendNode);\n }\n }\n\n // // Init rotation angle and scale factor for two finger movements\n // this.previousRotation = 0.0;\n // this.previousScale = 1.0;\n\n if (collect.length >= 1) {\n collect[0].highlight(true);\n this.triggerEventHandlers(['mousehit', 'hit'], [evt, collect[0]]);\n }\n\n return collect;\n },\n\n /**\n * Moves an object.\n * @param {Number} x Coordinate\n * @param {Number} y Coordinate\n * @param {Object} o The touch object that is dragged: {JXG.Board#mouse} or {JXG.Board#touches}.\n * @param {Object} evt The event object.\n * @param {String} type Mouse or touch event?\n */\n moveObject: function (x, y, o, evt, type) {\n var newPos = new Coords(\n Const.COORDS_BY_SCREEN,\n this.getScrCoordsOfMouse(x, y),\n this\n ),\n drag,\n dragScrCoords,\n newDragScrCoords;\n\n if (!(o && o.obj)) {\n return;\n }\n drag = o.obj;\n\n // Avoid updates for very small movements of coordsElements, see below\n if (drag.coords) {\n dragScrCoords = drag.coords.scrCoords.slice();\n }\n\n this.addLogEntry('drag', drag, newPos.usrCoords.slice(1));\n\n // Store the position and add the correctionvector from the mouse\n // position to the object's coords.\n this.drag_position = [newPos.scrCoords[1], newPos.scrCoords[2]];\n this.drag_position = Statistics.add(this.drag_position, this._drag_offset);\n\n // Store status of key presses for 3D movement\n this._shiftKey = evt.shiftKey;\n this._ctrlKey = evt.ctrlKey;\n\n //\n // We have to distinguish between CoordsElements and other elements like lines.\n // The latter need the difference between two move events.\n if (Type.exists(drag.coords)) {\n drag.setPositionDirectly(Const.COORDS_BY_SCREEN, this.drag_position, [x, y]);\n } else {\n this.displayInfobox(false);\n // Hide infobox in case the user has touched an intersection point\n // and drags the underlying line now.\n\n if (!isNaN(o.targets[0].Xprev + o.targets[0].Yprev)) {\n drag.setPositionDirectly(\n Const.COORDS_BY_SCREEN,\n [newPos.scrCoords[1], newPos.scrCoords[2]],\n [o.targets[0].Xprev, o.targets[0].Yprev]\n );\n }\n // Remember the actual position for the next move event. Then we are able to\n // compute the difference vector.\n o.targets[0].Xprev = newPos.scrCoords[1];\n o.targets[0].Yprev = newPos.scrCoords[2];\n }\n // This may be necessary for some gliders and labels\n if (Type.exists(drag.coords)) {\n drag.prepareUpdate().update(false).updateRenderer();\n this.updateInfobox(drag);\n drag.prepareUpdate().update(true).updateRenderer();\n }\n\n if (drag.coords) {\n newDragScrCoords = drag.coords.scrCoords;\n }\n // No updates for very small movements of coordsElements\n if (\n !drag.coords ||\n dragScrCoords[1] !== newDragScrCoords[1] ||\n dragScrCoords[2] !== newDragScrCoords[2]\n ) {\n drag.triggerEventHandlers([type + 'drag', 'drag'], [evt]);\n // Update all elements of the board\n this.update(drag);\n }\n drag.highlight(true);\n this.triggerEventHandlers(['mousehit', 'hit'], [evt, drag]);\n\n drag.lastDragTime = new Date();\n },\n\n /**\n * Moves elements in multitouch mode.\n * @param {Array} p1 x,y coordinates of first touch\n * @param {Array} p2 x,y coordinates of second touch\n * @param {Object} o The touch object that is dragged: {JXG.Board#touches}.\n * @param {Object} evt The event object that lead to this movement.\n */\n twoFingerMove: function (o, id, evt) {\n var drag;\n\n if (Type.exists(o) && Type.exists(o.obj)) {\n drag = o.obj;\n } else {\n return;\n }\n\n if (\n drag.elementClass === Const.OBJECT_CLASS_LINE ||\n drag.type === Const.OBJECT_TYPE_POLYGON\n ) {\n this.twoFingerTouchObject(o.targets, drag, id);\n } else if (drag.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n this.twoFingerTouchCircle(o.targets, drag, id);\n }\n\n if (evt) {\n drag.triggerEventHandlers(['touchdrag', 'drag'], [evt]);\n }\n },\n\n /**\n * Compute the transformation matrix to move an element according to the\n * previous and actual positions of finger 1 and finger 2.\n * See also https://math.stackexchange.com/questions/4010538/solve-for-2d-translation-rotation-and-scale-given-two-touch-point-movements\n *\n * @param {Object} finger1 Actual and previous position of finger 1\n * @param {Object} finger1 Actual and previous position of finger 1\n * @param {Boolean} scalable Flag if element may be scaled\n * @param {Boolean} rotatable Flag if element may be rotated\n * @returns {Array}\n */\n getTwoFingerTransform(finger1, finger2, scalable, rotatable) {\n var crd,\n x1, y1, x2, y2,\n dx, dy,\n xx1, yy1, xx2, yy2,\n dxx, dyy,\n C, S, LL, tx, ty, lbda;\n\n crd = new Coords(Const.COORDS_BY_SCREEN, [finger1.Xprev, finger1.Yprev], this).usrCoords;\n x1 = crd[1];\n y1 = crd[2];\n crd = new Coords(Const.COORDS_BY_SCREEN, [finger2.Xprev, finger2.Yprev], this).usrCoords;\n x2 = crd[1];\n y2 = crd[2];\n\n crd = new Coords(Const.COORDS_BY_SCREEN, [finger1.X, finger1.Y], this).usrCoords;\n xx1 = crd[1];\n yy1 = crd[2];\n crd = new Coords(Const.COORDS_BY_SCREEN, [finger2.X, finger2.Y], this).usrCoords;\n xx2 = crd[1];\n yy2 = crd[2];\n\n dx = x2 - x1;\n dy = y2 - y1;\n dxx = xx2 - xx1;\n dyy = yy2 - yy1;\n\n LL = dx * dx + dy * dy;\n C = (dxx * dx + dyy * dy) / LL;\n S = (dyy * dx - dxx * dy) / LL;\n if (!scalable) {\n lbda = Mat.hypot(C, S);\n C /= lbda;\n S /= lbda;\n }\n if (!rotatable) {\n S = 0;\n }\n tx = 0.5 * (xx1 + xx2 - C * (x1 + x2) + S * (y1 + y2));\n ty = 0.5 * (yy1 + yy2 - S * (x1 + x2) - C * (y1 + y2));\n\n return [1, 0, 0,\n tx, C, -S,\n ty, S, C];\n },\n\n /**\n * Moves, rotates and scales a line or polygon with two fingers.\n * \n *\n */\n this.infobox = this.create('text', [0, 0, '0,0'], attr);\n // this.infobox.needsUpdateSize = false; // That is not true, but it speeds drawing up.\n this.infobox.dump = false;\n\n this.displayInfobox(false);\n return this;\n },\n\n /**\n * Updates and displays a little info box to show coordinates of current selected points.\n * @param {JXG.GeometryElement} el A GeometryElement\n * @returns {JXG.Board} Reference to the board\n * @see JXG.Board#displayInfobox\n * @see JXG.Board#showInfobox\n * @see Point#showInfobox\n *\n */\n updateInfobox: function (el) {\n var x, y, xc, yc,\n vpinfoboxdigits,\n distX, distY,\n vpsi = el.evalVisProp('showinfobox');\n\n if ((!Type.evaluate(this.attr.showinfobox) && vpsi === 'inherit') || !vpsi) {\n return this;\n }\n\n if (Type.isPoint(el)) {\n xc = el.coords.usrCoords[1];\n yc = el.coords.usrCoords[2];\n distX = this.infobox.evalVisProp('distancex');\n distY = this.infobox.evalVisProp('distancey');\n\n this.infobox.setCoords(\n xc + distX / this.unitX,\n yc + distY / this.unitY\n );\n\n vpinfoboxdigits = el.evalVisProp('infoboxdigits');\n if (typeof el.infoboxText !== 'string') {\n if (vpinfoboxdigits === 'auto') {\n if (this.infobox.useLocale()) {\n x = this.infobox.formatNumberLocale(xc);\n y = this.infobox.formatNumberLocale(yc);\n } else {\n x = Type.autoDigits(xc);\n y = Type.autoDigits(yc);\n }\n } else if (Type.isNumber(vpinfoboxdigits)) {\n if (this.infobox.useLocale()) {\n x = this.infobox.formatNumberLocale(xc, vpinfoboxdigits);\n y = this.infobox.formatNumberLocale(yc, vpinfoboxdigits);\n } else {\n x = Type.toFixed(xc, vpinfoboxdigits);\n y = Type.toFixed(yc, vpinfoboxdigits);\n }\n\n } else {\n x = xc;\n y = yc;\n }\n\n this.highlightInfobox(x, y, el);\n } else {\n this.highlightCustomInfobox(el.infoboxText, el);\n }\n\n this.displayInfobox(true);\n }\n return this;\n },\n\n /**\n * Set infobox visible / invisible.\n *\n * It uses its property hiddenByParent to memorize its status.\n * In this way, many DOM access can be avoided.\n *\n * @param {Boolean} val true for visible, false for invisible\n * @returns {JXG.Board} Reference to the board.\n * @see JXG.Board#updateInfobox\n *\n */\n displayInfobox: function (val) {\n if (!val && this.focusObjects.length > 0 &&\n this.select(this.focusObjects[0]).elementClass === Const.OBJECT_CLASS_POINT) {\n // If an element has focus we do not hide its infobox\n return this;\n }\n if (this.infobox.hiddenByParent === val) {\n this.infobox.hiddenByParent = !val;\n this.infobox.prepareUpdate().updateVisibility(val).updateRenderer();\n }\n return this;\n },\n\n // Alias for displayInfobox to be backwards compatible.\n // The method showInfobox clashes with the board attribute showInfobox\n showInfobox: function (val) {\n return this.displayInfobox(val);\n },\n\n /**\n * Changes the text of the info box to show the given coordinates.\n * @param {Number} x\n * @param {Number} y\n * @param {JXG.GeometryElement} [el] The element the mouse is pointing at\n * @returns {JXG.Board} Reference to the board.\n */\n highlightInfobox: function (x, y, el) {\n this.highlightCustomInfobox('(' + x + ', ' + y + ')', el);\n return this;\n },\n\n /**\n * Changes the text of the info box to what is provided via text.\n * @param {String} text\n * @param {JXG.GeometryElement} [el]\n * @returns {JXG.Board} Reference to the board.\n */\n highlightCustomInfobox: function (text, el) {\n this.infobox.setText(text);\n return this;\n },\n\n /**\n * Remove highlighting of all elements.\n * @returns {JXG.Board} Reference to the board.\n */\n dehighlightAll: function () {\n var el,\n pEl,\n stillHighlighted = {},\n needsDeHighlight = false;\n\n for (el in this.highlightedObjects) {\n if (this.highlightedObjects.hasOwnProperty(el)) {\n\n pEl = this.highlightedObjects[el];\n if (this.focusObjects.indexOf(el) < 0) { // Element does not have focus\n if (this.hasMouseHandlers || this.hasPointerHandlers) {\n pEl.noHighlight();\n }\n needsDeHighlight = true;\n } else {\n stillHighlighted[el] = pEl;\n }\n // In highlightedObjects should only be objects which fulfill all these conditions\n // And in case of complex elements, like a turtle based fractal, it should be faster to\n // just de-highlight the element instead of checking hasPoint...\n // if ((!Type.exists(pEl.hasPoint)) || !pEl.hasPoint(x, y) || !pEl.visPropCalc.visible)\n }\n }\n\n this.highlightedObjects = stillHighlighted;\n\n // We do not need to redraw during dehighlighting in CanvasRenderer\n // because we are redrawing anyhow\n // -- We do need to redraw during dehighlighting. Otherwise objects won't be dehighlighted until\n // another object is highlighted.\n if (this.renderer.type === 'canvas' && needsDeHighlight) {\n this.prepareUpdate();\n this.renderer.suspendRedraw(this);\n this.updateRenderer();\n this.renderer.unsuspendRedraw();\n }\n\n return this;\n },\n\n /**\n * Returns the input parameters in an array. This method looks pointless and it really is, but it had a purpose\n * once.\n * @private\n * @param {Number} x X coordinate in screen coordinates\n * @param {Number} y Y coordinate in screen coordinates\n * @returns {Array} Coordinates [x, y] of the mouse in screen coordinates.\n * @see JXG.Board#getUsrCoordsOfMouse\n */\n getScrCoordsOfMouse: function (x, y) {\n return [x, y];\n },\n\n /**\n * This method calculates the user coords of the current mouse coordinates.\n * @param {Event} evt Event object containing the mouse coordinates.\n * @returns {Array} Coordinates [x, y] of the mouse in user coordinates.\n * @example\n * board.on('up', function (evt) {\n * var a = board.getUsrCoordsOfMouse(evt),\n * x = a[0],\n * y = a[1],\n * somePoint = board.create('point', [x,y], {name:'SomePoint',size:4});\n * // Shorter version:\n * //somePoint = board.create('point', a, {name:'SomePoint',size:4});\n * });\n *\n * \n * \n *\n * @see JXG.Board#getScrCoordsOfMouse\n * @see JXG.Board#getAllUnderMouse\n */\n getUsrCoordsOfMouse: function (evt) {\n var cPos = this.getCoordsTopLeftCorner(),\n absPos = Env.getPosition(evt, null, this.document),\n x = absPos[0] - cPos[0],\n y = absPos[1] - cPos[1],\n newCoords = new Coords(Const.COORDS_BY_SCREEN, [x, y], this);\n\n return newCoords.usrCoords.slice(1);\n },\n\n /**\n * Collects all elements under current mouse position plus current user coordinates of mouse cursor.\n * @param {Event} evt Event object containing the mouse coordinates.\n * @returns {Array} Array of elements at the current mouse position plus current user coordinates of mouse.\n * @see JXG.Board#getUsrCoordsOfMouse\n * @see JXG.Board#getAllObjectsUnderMouse\n */\n getAllUnderMouse: function (evt) {\n var elList = this.getAllObjectsUnderMouse(evt);\n elList.push(this.getUsrCoordsOfMouse(evt));\n\n return elList;\n },\n\n /**\n * Collects all elements under current mouse position.\n * @param {Event} evt Event object containing the mouse coordinates.\n * @returns {Array} Array of elements at the current mouse position.\n * @see JXG.Board#getAllUnderMouse\n */\n getAllObjectsUnderMouse: function (evt) {\n var cPos = this.getCoordsTopLeftCorner(),\n absPos = Env.getPosition(evt, null, this.document),\n dx = absPos[0] - cPos[0],\n dy = absPos[1] - cPos[1],\n elList = [],\n el,\n pEl,\n len = this.objectsList.length;\n\n for (el = 0; el < len; el++) {\n pEl = this.objectsList[el];\n if (pEl.visPropCalc.visible && pEl.hasPoint && pEl.hasPoint(dx, dy)) {\n elList[elList.length] = pEl;\n }\n }\n\n return elList;\n },\n\n /**\n * Update the coords object of all elements which possess this\n * property. This is necessary after changing the viewport.\n * @returns {JXG.Board} Reference to this board.\n **/\n updateCoords: function () {\n var el, ob,\n len = this.objectsList.length;\n\n for (ob = 0; ob < len; ob++) {\n el = this.objectsList[ob];\n\n if (Type.exists(el.coords)) {\n if (el.evalVisProp('frozen') === true) {\n if (el.is3D) {\n el.element2D.coords.screen2usr();\n } else {\n el.coords.screen2usr();\n }\n } else {\n if (el.is3D) {\n el.element2D.coords.usr2screen();\n } else {\n el.coords.usr2screen();\n if (Type.exists(el.actualCoords)) {\n el.actualCoords.usr2screen();\n }\n }\n }\n }\n }\n return this;\n },\n\n /**\n * Moves the origin and initializes an update of all elements.\n * @param {Number} x\n * @param {Number} y\n * @param {Boolean} [diff=false]\n * @returns {JXG.Board} Reference to this board.\n */\n moveOrigin: function (x, y, diff) {\n var ox, oy, ul, lr;\n if (Type.exists(x) && Type.exists(y)) {\n ox = this.origin.scrCoords[1];\n oy = this.origin.scrCoords[2];\n\n this.origin.scrCoords[1] = x;\n this.origin.scrCoords[2] = y;\n\n if (diff) {\n this.origin.scrCoords[1] -= this.drag_dx;\n this.origin.scrCoords[2] -= this.drag_dy;\n }\n\n ul = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this).usrCoords;\n lr = new Coords(\n Const.COORDS_BY_SCREEN,\n [this.canvasWidth, this.canvasHeight],\n this\n ).usrCoords;\n if (\n ul[1] < this.maxboundingbox[0] - Mat.eps ||\n ul[2] > this.maxboundingbox[1] + Mat.eps ||\n lr[1] > this.maxboundingbox[2] + Mat.eps ||\n lr[2] < this.maxboundingbox[3] - Mat.eps\n ) {\n this.origin.scrCoords[1] = ox;\n this.origin.scrCoords[2] = oy;\n }\n }\n\n this.updateCoords().clearTraces().fullUpdate();\n this.triggerEventHandlers(['boundingbox']);\n\n return this;\n },\n\n /**\n * Add conditional updates to the elements.\n * @param {String} str String containing conditional update in geonext syntax\n */\n addConditions: function (str) {\n var term,\n m,\n left,\n right,\n name,\n el,\n property,\n functions = [],\n // plaintext = 'var el, x, y, c, rgbo;\\n',\n i = str.indexOf(''),\n j = str.indexOf('<' + '/data>'),\n xyFun = function (board, el, f, what) {\n return function () {\n var e, t;\n\n e = board.select(el.id);\n t = e.coords.usrCoords[what];\n\n if (what === 2) {\n e.setPositionDirectly(Const.COORDS_BY_USER, [f(), t]);\n } else {\n e.setPositionDirectly(Const.COORDS_BY_USER, [t, f()]);\n }\n e.prepareUpdate().update();\n };\n },\n visFun = function (board, el, f) {\n return function () {\n var e, v;\n\n e = board.select(el.id);\n v = f();\n\n e.setAttribute({ visible: v });\n };\n },\n colFun = function (board, el, f, what) {\n return function () {\n var e, v;\n\n e = board.select(el.id);\n v = f();\n\n if (what === 'strokewidth') {\n e.visProp.strokewidth = v;\n } else {\n v = Color.rgba2rgbo(v);\n e.visProp[what + 'color'] = v[0];\n e.visProp[what + 'opacity'] = v[1];\n }\n };\n },\n posFun = function (board, el, f) {\n return function () {\n var e = board.select(el.id);\n\n e.position = f();\n };\n },\n styleFun = function (board, el, f) {\n return function () {\n var e = board.select(el.id);\n\n e.setStyle(f());\n };\n };\n\n if (i < 0) {\n return;\n }\n\n while (i >= 0) {\n term = str.slice(i + 6, j); // throw away \n m = term.indexOf('=');\n left = term.slice(0, m);\n right = term.slice(m + 1);\n m = left.indexOf('.'); // Resulting variable names must not contain dots, e.g. ' Steuern akt.'\n name = left.slice(0, m); //.replace(/\\s+$/,''); // do NOT cut out name (with whitespace)\n el = this.elementsByName[Type.unescapeHTML(name)];\n\n property = left\n .slice(m + 1)\n .replace(/\\s+/g, '')\n .toLowerCase(); // remove whitespace in property\n right = Type.createFunction(right, this, '', true);\n\n // Debug\n if (!Type.exists(this.elementsByName[name])) {\n JXG.debug('debug conditions: |' + name + '| undefined');\n } else {\n // plaintext += 'el = this.objects[\\'' + el.id + '\\'];\\n';\n\n switch (property) {\n case 'x':\n functions.push(xyFun(this, el, right, 2));\n break;\n case 'y':\n functions.push(xyFun(this, el, right, 1));\n break;\n case 'visible':\n functions.push(visFun(this, el, right));\n break;\n case 'position':\n functions.push(posFun(this, el, right));\n break;\n case 'stroke':\n functions.push(colFun(this, el, right, 'stroke'));\n break;\n case 'style':\n functions.push(styleFun(this, el, right));\n break;\n case 'strokewidth':\n functions.push(colFun(this, el, right, 'strokewidth'));\n break;\n case 'fill':\n functions.push(colFun(this, el, right, 'fill'));\n break;\n case 'label':\n break;\n default:\n JXG.debug(\n 'property \"' +\n property +\n '\" in conditions not yet implemented:' +\n right\n );\n break;\n }\n }\n str = str.slice(j + 7); // cut off ''\n i = str.indexOf('');\n j = str.indexOf('<' + '/data>');\n }\n\n this.updateConditions = function () {\n var i;\n\n for (i = 0; i < functions.length; i++) {\n functions[i]();\n }\n\n this.prepareUpdate().updateElements();\n return true;\n };\n this.updateConditions();\n },\n\n /**\n * Computes the commands in the conditions-section of the gxt file.\n * It is evaluated after an update, before the unsuspendRedraw.\n * The function is generated in\n * @see JXG.Board#addConditions\n * @private\n */\n updateConditions: function () {\n return false;\n },\n\n /**\n * Calculates adequate snap sizes.\n * @returns {JXG.Board} Reference to the board.\n */\n calculateSnapSizes: function () {\n var p1, p2,\n bbox = this.getBoundingBox(),\n gridStep = Type.evaluate(this.options.grid.majorStep),\n gridX = Type.evaluate(this.options.grid.gridX),\n gridY = Type.evaluate(this.options.grid.gridY),\n x, y;\n\n if (!Type.isArray(gridStep)) {\n gridStep = [gridStep, gridStep];\n }\n if (gridStep.length < 2) {\n gridStep = [gridStep[0], gridStep[0]];\n }\n if (Type.exists(gridX)) {\n gridStep[0] = gridX;\n }\n if (Type.exists(gridY)) {\n gridStep[1] = gridY;\n }\n\n if (gridStep[0] === 'auto') {\n gridStep[0] = 1;\n } else {\n gridStep[0] = Type.parseNumber(gridStep[0], Math.abs(bbox[1] - bbox[3]), 1 / this.unitX);\n }\n if (gridStep[1] === 'auto') {\n gridStep[1] = 1;\n } else {\n gridStep[1] = Type.parseNumber(gridStep[1], Math.abs(bbox[0] - bbox[2]), 1 / this.unitY);\n }\n\n p1 = new Coords(Const.COORDS_BY_USER, [0, 0], this);\n p2 = new Coords(\n Const.COORDS_BY_USER,\n [gridStep[0], gridStep[1]],\n this\n );\n x = p1.scrCoords[1] - p2.scrCoords[1];\n y = p1.scrCoords[2] - p2.scrCoords[2];\n\n this.options.grid.snapSizeX = gridStep[0];\n while (Math.abs(x) > 25) {\n this.options.grid.snapSizeX *= 2;\n x /= 2;\n }\n\n this.options.grid.snapSizeY = gridStep[1];\n while (Math.abs(y) > 25) {\n this.options.grid.snapSizeY *= 2;\n y /= 2;\n }\n\n return this;\n },\n\n /**\n * Apply update on all objects with the new zoom-factors. Clears all traces.\n * @returns {JXG.Board} Reference to the board.\n */\n applyZoom: function () {\n this.updateCoords().calculateSnapSizes().clearTraces().fullUpdate();\n\n return this;\n },\n\n /**\n * Zooms into the board by the factors board.attr.zoom.factorX and board.attr.zoom.factorY and applies the zoom.\n * The zoom operation is centered at x, y.\n * @param {Number} [x]\n * @param {Number} [y]\n * @returns {JXG.Board} Reference to the board\n */\n zoomIn: function (x, y) {\n var bb = this.getBoundingBox(),\n zX = Type.evaluate(this.attr.zoom.factorx),\n zY = Type.evaluate(this.attr.zoom.factory),\n dX = (bb[2] - bb[0]) * (1.0 - 1.0 / zX),\n dY = (bb[1] - bb[3]) * (1.0 - 1.0 / zY),\n lr = 0.5,\n tr = 0.5,\n ma = Type.evaluate(this.attr.zoom.max),\n mi = Type.evaluate(this.attr.zoom.eps) || Type.evaluate(this.attr.zoom.min) || 0.001; // this.attr.zoom.eps is deprecated\n\n if (\n (this.zoomX > ma && zX > 1.0) ||\n (this.zoomY > ma && zY > 1.0) ||\n (this.zoomX < mi && zX < 1.0) || // zoomIn is used for all zooms on touch devices\n (this.zoomY < mi && zY < 1.0)\n ) {\n return this;\n }\n\n if (Type.isNumber(x) && Type.isNumber(y)) {\n lr = (x - bb[0]) / (bb[2] - bb[0]);\n tr = (bb[1] - y) / (bb[1] - bb[3]);\n }\n\n this.setBoundingBox(\n [\n bb[0] + dX * lr,\n bb[1] - dY * tr,\n bb[2] - dX * (1 - lr),\n bb[3] + dY * (1 - tr)\n ],\n this.keepaspectratio,\n 'update'\n );\n return this.applyZoom();\n },\n\n /**\n * Zooms out of the board by the factors board.attr.zoom.factorX and board.attr.zoom.factorY and applies the zoom.\n * The zoom operation is centered at x, y.\n *\n * @param {Number} [x]\n * @param {Number} [y]\n * @returns {JXG.Board} Reference to the board\n */\n zoomOut: function (x, y) {\n var bb = this.getBoundingBox(),\n zX = Type.evaluate(this.attr.zoom.factorx),\n zY = Type.evaluate(this.attr.zoom.factory),\n dX = (bb[2] - bb[0]) * (1.0 - zX),\n dY = (bb[1] - bb[3]) * (1.0 - zY),\n lr = 0.5,\n tr = 0.5,\n mi = Type.evaluate(this.attr.zoom.eps) || Type.evaluate(this.attr.zoom.min) || 0.001; // this.attr.zoom.eps is deprecated\n\n if (this.zoomX < mi || this.zoomY < mi) {\n return this;\n }\n\n if (Type.isNumber(x) && Type.isNumber(y)) {\n lr = (x - bb[0]) / (bb[2] - bb[0]);\n tr = (bb[1] - y) / (bb[1] - bb[3]);\n }\n\n this.setBoundingBox(\n [\n bb[0] + dX * lr,\n bb[1] - dY * tr,\n bb[2] - dX * (1 - lr),\n bb[3] + dY * (1 - tr)\n ],\n this.keepaspectratio,\n 'update'\n );\n\n return this.applyZoom();\n },\n\n /**\n * Reset the zoom level to the original zoom level from initBoard();\n * Additionally, if the board as been initialized with a boundingBox (which is the default),\n * restore the viewport to the original viewport during initialization. Otherwise,\n * (i.e. if the board as been initialized with unitX/Y and originX/Y),\n * just set the zoom level to 100%.\n *\n * @returns {JXG.Board} Reference to the board\n */\n zoom100: function () {\n var bb, dX, dY;\n\n if (Type.exists(this.attr.boundingbox)) {\n this.setBoundingBox(this.attr.boundingbox, this.keepaspectratio, 'reset');\n } else {\n // Board has been set up with unitX/Y and originX/Y\n bb = this.getBoundingBox();\n dX = (bb[2] - bb[0]) * (1.0 - this.zoomX) * 0.5;\n dY = (bb[1] - bb[3]) * (1.0 - this.zoomY) * 0.5;\n this.setBoundingBox(\n [bb[0] + dX, bb[1] - dY, bb[2] - dX, bb[3] + dY],\n this.keepaspectratio,\n 'reset'\n );\n }\n return this.applyZoom();\n },\n\n /**\n * Zooms the board so every visible point is shown. Keeps aspect ratio.\n * @returns {JXG.Board} Reference to the board\n */\n zoomAllPoints: function () {\n var el,\n border,\n borderX,\n borderY,\n pEl,\n minX = 0,\n maxX = 0,\n minY = 0,\n maxY = 0,\n len = this.objectsList.length;\n\n for (el = 0; el < len; el++) {\n pEl = this.objectsList[el];\n\n if (Type.isPoint(pEl) && pEl.visPropCalc.visible) {\n if (pEl.coords.usrCoords[1] < minX) {\n minX = pEl.coords.usrCoords[1];\n } else if (pEl.coords.usrCoords[1] > maxX) {\n maxX = pEl.coords.usrCoords[1];\n }\n if (pEl.coords.usrCoords[2] > maxY) {\n maxY = pEl.coords.usrCoords[2];\n } else if (pEl.coords.usrCoords[2] < minY) {\n minY = pEl.coords.usrCoords[2];\n }\n }\n }\n\n border = 50;\n borderX = border / this.unitX;\n borderY = border / this.unitY;\n\n this.setBoundingBox(\n [minX - borderX, maxY + borderY, maxX + borderX, minY - borderY],\n this.keepaspectratio,\n 'update'\n );\n\n return this.applyZoom();\n },\n\n /**\n * Reset the bounding box and the zoom level to 100% such that a given set of elements is\n * within the board's viewport.\n * @param {Array} elements A set of elements given by id, reference, or name.\n * @returns {JXG.Board} Reference to the board.\n */\n zoomElements: function (elements) {\n var i, e,\n box,\n newBBox = [Infinity, -Infinity, -Infinity, Infinity],\n cx, cy,\n dx, dy,\n d;\n\n if (!Type.isArray(elements) || elements.length === 0) {\n return this;\n }\n\n for (i = 0; i < elements.length; i++) {\n e = this.select(elements[i]);\n\n box = e.bounds();\n if (Type.isArray(box)) {\n if (box[0] < newBBox[0]) {\n newBBox[0] = box[0];\n }\n if (box[1] > newBBox[1]) {\n newBBox[1] = box[1];\n }\n if (box[2] > newBBox[2]) {\n newBBox[2] = box[2];\n }\n if (box[3] < newBBox[3]) {\n newBBox[3] = box[3];\n }\n }\n }\n\n if (Type.isArray(newBBox)) {\n cx = 0.5 * (newBBox[0] + newBBox[2]);\n cy = 0.5 * (newBBox[1] + newBBox[3]);\n dx = 1.5 * (newBBox[2] - newBBox[0]) * 0.5;\n dy = 1.5 * (newBBox[1] - newBBox[3]) * 0.5;\n d = Math.max(dx, dy);\n this.setBoundingBox(\n [cx - d, cy + d, cx + d, cy - d],\n this.keepaspectratio,\n 'update'\n );\n }\n\n return this;\n },\n\n /**\n * Sets the zoom level to fX resp fY.\n * @param {Number} fX\n * @param {Number} fY\n * @returns {JXG.Board} Reference to the board.\n */\n setZoom: function (fX, fY) {\n var oX = this.attr.zoom.factorx,\n oY = this.attr.zoom.factory;\n\n this.attr.zoom.factorx = fX / this.zoomX;\n this.attr.zoom.factory = fY / this.zoomY;\n\n this.zoomIn();\n\n this.attr.zoom.factorx = oX;\n this.attr.zoom.factory = oY;\n\n return this;\n },\n\n /**\n * Inner, recursive method of removeObject.\n *\n * @param {JXG.GeometryElement|Array} object The object to remove or array of objects to be removed.\n * The element(s) is/are given by name, id or a reference.\n * @param {Boolean} [saveMethod=false] If saveMethod=true, the algorithm runs through all elements\n * and tests if the element to be deleted is a child element. If this is the case, it will be\n * removed from the list of child elements. If saveMethod=false (default), the element\n * is removed from the lists of child elements of all its ancestors.\n * The latter should be much faster.\n * @returns {JXG.Board} Reference to the board\n * @private\n */\n _removeObj: function (object, saveMethod) {\n var el, o, i;\n\n if (Type.isArray(object)) {\n for (i = 0; i < object.length; i++) {\n this._removeObj(object[i], saveMethod);\n }\n\n return this;\n }\n\n object = this.select(object);\n\n // If the object which is about to be removed is unknown or a string, do nothing.\n // it is a string if a string was given and could not be resolved to an element.\n if (!Type.exists(object) || Type.isString(object)) {\n return this;\n }\n\n try {\n // remove all children.\n for (el in object.childElements) {\n if (object.childElements.hasOwnProperty(el)) {\n object.childElements[el].board._removeObj(object.childElements[el]);\n }\n }\n\n // Remove all children in elements like turtle\n for (el in object.objects) {\n if (object.objects.hasOwnProperty(el)) {\n object.objects[el].board._removeObj(object.objects[el]);\n }\n }\n\n // Remove the element from the childElement list and the descendant list of all elements.\n if (saveMethod) {\n // Running through all objects has quadratic complexity if many objects are deleted.\n for (el in this.objects) {\n if (this.objects.hasOwnProperty(el)) {\n if (\n Type.exists(this.objects[el].childElements) &&\n Type.exists(\n this.objects[el].childElements.hasOwnProperty(object.id)\n )\n ) {\n delete this.objects[el].childElements[object.id];\n delete this.objects[el].descendants[object.id];\n }\n }\n }\n } else if (Type.exists(object.ancestors)) {\n // Running through the ancestors should be much more efficient.\n for (el in object.ancestors) {\n if (object.ancestors.hasOwnProperty(el)) {\n if (\n Type.exists(object.ancestors[el].childElements) &&\n Type.exists(\n object.ancestors[el].childElements.hasOwnProperty(object.id)\n )\n ) {\n delete object.ancestors[el].childElements[object.id];\n delete object.ancestors[el].descendants[object.id];\n }\n }\n }\n }\n\n // remove the object itself from our control structures\n if (object._pos > -1) {\n this.objectsList.splice(object._pos, 1);\n // Quadratic complexity for reindexing the positions:\n for (i = object._pos; i < this.objectsList.length; i++) {\n o = this.objectsList[i];\n if (o._pos > -1) {\n o._pos--;\n }\n }\n } else if (object.type !== Const.OBJECT_TYPE_TURTLE) {\n JXG.debug(\n 'Board.removeObject: object ' + object.id + ' not found in list.'\n );\n }\n\n delete this.objects[object.id];\n delete this.elementsByName[object.name];\n\n if (object.visProp && object.evalVisProp('trace')) {\n object.clearTrace();\n }\n\n // the object deletion itself is handled by the object.\n if (Type.exists(object.remove)) {\n object.remove();\n }\n } catch (e) {\n JXG.debug(object.id + ': Could not be removed: ' + e);\n }\n\n return this;\n },\n\n /**\n * Removes object from board and from the renderer object.\n * \n * \n *
\n * @param {JXG.GeometryElement|Array} object The object to remove or array of objects to be removed.\n * The element(s) is/are given by name, id or a reference.\n * @param {Boolean} saveMethod If true, the algorithm runs through all elements\n * and tests if the element to be deleted is a child element. If yes, it will be\n * removed from the list of child elements. If false (default), the element\n * is removed from the lists of child elements of all its ancestors.\n * This should be much faster.\n * @returns {JXG.Board} Reference to the board\n */\n removeObject: function (object, saveMethod) {\n var i;\n\n this.renderer.suspendRedraw(this);\n if (Type.isArray(object)) {\n for (i = 0; i < object.length; i++) {\n this._removeObj(object[i], saveMethod);\n }\n } else {\n this._removeObj(object, saveMethod);\n }\n this.renderer.unsuspendRedraw();\n\n this.update();\n return this;\n },\n\n /**\n * Removes the ancestors of an object an the object itself from board and renderer.\n * @param {JXG.GeometryElement} object The object to remove.\n * @returns {JXG.Board} Reference to the board\n */\n removeAncestors: function (object) {\n var anc;\n\n for (anc in object.ancestors) {\n if (object.ancestors.hasOwnProperty(anc)) {\n this.removeAncestors(object.ancestors[anc]);\n }\n }\n\n this.removeObject(object);\n\n return this;\n },\n\n /**\n * Initialize some objects which are contained in every GEONExT construction by default,\n * but are not contained in the gxt files.\n * @returns {JXG.Board} Reference to the board\n */\n initGeonextBoard: function () {\n var p1, p2, p3;\n\n p1 = this.create('point', [0, 0], {\n id: this.id + 'g00e0',\n name: 'Ursprung',\n withLabel: false,\n visible: false,\n fixed: true\n });\n\n p2 = this.create('point', [1, 0], {\n id: this.id + 'gX0e0',\n name: 'Punkt_1_0',\n withLabel: false,\n visible: false,\n fixed: true\n });\n\n p3 = this.create('point', [0, 1], {\n id: this.id + 'gY0e0',\n name: 'Punkt_0_1',\n withLabel: false,\n visible: false,\n fixed: true\n });\n\n this.create('line', [p1, p2], {\n id: this.id + 'gXLe0',\n name: 'X-Achse',\n withLabel: false,\n visible: false\n });\n\n this.create('line', [p1, p3], {\n id: this.id + 'gYLe0',\n name: 'Y-Achse',\n withLabel: false,\n visible: false\n });\n\n return this;\n },\n\n /**\n * Change the height and width of the board's container.\n * After doing so, {@link JXG.JSXGraph.setBoundingBox} is called using\n * the actual size of the bounding box and the actual value of keepaspectratio.\n * If setBoundingbox() should not be called automatically,\n * call resizeContainer with dontSetBoundingBox == true.\n * @param {Number} canvasWidth New width of the container.\n * @param {Number} canvasHeight New height of the container.\n * @param {Boolean} [dontset=false] If true do not set the CSS width and height of the DOM element.\n * @param {Boolean} [dontSetBoundingBox=false] If true do not call setBoundingBox(), but keep view centered around original visible center.\n * @returns {JXG.Board} Reference to the board\n */\n resizeContainer: function (canvasWidth, canvasHeight, dontset, dontSetBoundingBox) {\n var box,\n oldWidth, oldHeight,\n oX, oY;\n\n oldWidth = this.canvasWidth;\n oldHeight = this.canvasHeight;\n\n if (!dontSetBoundingBox) {\n box = this.getBoundingBox(); // This is the actual bounding box.\n }\n\n // this.canvasWidth = Math.max(parseFloat(canvasWidth), Mat.eps);\n // this.canvasHeight = Math.max(parseFloat(canvasHeight), Mat.eps);\n this.canvasWidth = parseFloat(canvasWidth);\n this.canvasHeight = parseFloat(canvasHeight);\n\n if (!dontset) {\n this.containerObj.style.width = this.canvasWidth + 'px';\n this.containerObj.style.height = this.canvasHeight + 'px';\n }\n this.renderer.resize(this.canvasWidth, this.canvasHeight);\n\n if (!dontSetBoundingBox) {\n this.setBoundingBox(box, this.keepaspectratio, 'keep');\n } else {\n oX = (this.canvasWidth - oldWidth) * 0.5;\n oY = (this.canvasHeight - oldHeight) * 0.5;\n\n this.moveOrigin(\n this.origin.scrCoords[1] + oX,\n this.origin.scrCoords[2] + oY\n );\n }\n\n return this;\n },\n\n /**\n * Lists the dependencies graph in a new HTML-window.\n * @returns {JXG.Board} Reference to the board\n */\n showDependencies: function () {\n var el, t, c, f, i;\n\n t = '' + Type.escapeHTML(this.xmlString) + '<' + '/pre>');\n f.document.close();\n return this;\n },\n\n /**\n * Sets for all objects the needsUpdate flag to 'true'.\n * @param{JXG.GeometryElement} [drag=undefined] Optional element that is dragged.\n * @returns {JXG.Board} Reference to the board\n */\n prepareUpdate: function (drag) {\n var el, i,\n pEl,\n len = this.objectsList.length;\n\n /*\n if (this.attr.updatetype === 'hierarchical') {\n return this;\n }\n */\n\n for (el = 0; el < len; el++) {\n pEl = this.objectsList[el];\n if (this._change3DView ||\n (Type.exists(drag) && drag.elType === 'view3d_slider')\n ) {\n // The 3D view has changed. No elements are recomputed,\n // only 3D elements are projected to the new view.\n pEl.needsUpdate =\n pEl.visProp.element3d ||\n pEl.elType === 'view3d' ||\n pEl.elType === 'view3d_slider' ||\n this.needsFullUpdate;\n\n // Special case sphere3d in central projection:\n // We have to update the defining points of the ellipse\n if (pEl.visProp.element3d &&\n pEl.visProp.element3d.type === Const.OBJECT_TYPE_SPHERE3D\n ) {\n for (i = 0; i < pEl.parents.length; i++) {\n this.objects[pEl.parents[i]].needsUpdate = true;\n }\n }\n } else {\n pEl.needsUpdate = pEl.needsRegularUpdate || this.needsFullUpdate;\n }\n }\n\n for (el in this.groups) {\n if (this.groups.hasOwnProperty(el)) {\n pEl = this.groups[el];\n pEl.needsUpdate = pEl.needsRegularUpdate || this.needsFullUpdate;\n }\n }\n\n return this;\n },\n\n /**\n * Runs through all elements and calls their update() method.\n * @param {JXG.GeometryElement} drag Element that caused the update.\n * @returns {JXG.Board} Reference to the board\n */\n updateElements: function (drag) {\n var el, pEl;\n //var childId, i = 0;\n\n drag = this.select(drag);\n\n /*\n if (Type.exists(drag)) {\n for (el = 0; el < this.objectsList.length; el++) {\n pEl = this.objectsList[el];\n if (pEl.id === drag.id) {\n i = el;\n break;\n }\n }\n }\n */\n for (el = 0; el < this.objectsList.length; el++) {\n pEl = this.objectsList[el];\n if (this.needsFullUpdate && pEl.elementClass === Const.OBJECT_CLASS_TEXT) {\n pEl.updateSize();\n }\n\n // For updates of an element we distinguish if the dragged element is updated or\n // other elements are updated.\n // The difference lies in the treatment of gliders and points based on transformations.\n pEl.update(!Type.exists(drag) || pEl.id !== drag.id).updateVisibility();\n }\n\n // update groups last\n for (el in this.groups) {\n if (this.groups.hasOwnProperty(el)) {\n this.groups[el].update(drag);\n }\n }\n\n return this;\n },\n\n /**\n * Runs through all elements and calls their update() method.\n * @returns {JXG.Board} Reference to the board\n */\n updateRenderer: function () {\n var el,\n len = this.objectsList.length,\n autoPositionLabelList = [],\n currentIndex, randomIndex;\n\n if (!this.renderer) {\n return;\n }\n\n /*\n objs = this.objectsList.slice(0);\n objs.sort(function (a, b) {\n if (a.visProp.layer < b.visProp.layer) {\n return -1;\n } else if (a.visProp.layer === b.visProp.layer) {\n return b.lastDragTime.getTime() - a.lastDragTime.getTime();\n } else {\n return 1;\n }\n });\n */\n\n if (this.renderer.type === 'canvas') {\n this.updateRendererCanvas();\n } else {\n for (el = 0; el < len; el++) {\n if (this.objectsList[el].visProp.islabel && this.objectsList[el].visProp.autoposition) {\n autoPositionLabelList.push(el);\n } else {\n this.objectsList[el].updateRenderer();\n }\n }\n\n currentIndex = autoPositionLabelList.length;\n\n // Randomize the order of the labels\n while (currentIndex !== 0) {\n randomIndex = Math.floor(Math.random() * currentIndex);\n currentIndex--;\n [autoPositionLabelList[currentIndex], autoPositionLabelList[randomIndex]] = [autoPositionLabelList[randomIndex], autoPositionLabelList[currentIndex]];\n }\n\n for (el = 0; el < autoPositionLabelList.length; el++) {\n this.objectsList[autoPositionLabelList[el]].updateRenderer();\n }\n /*\n for (el = autoPositionLabelList.length - 1; el >= 0; el--) {\n this.objectsList[autoPositionLabelList[el]].updateRenderer();\n }\n */\n }\n return this;\n },\n\n /**\n * Runs through all elements and calls their update() method.\n * This is a special version for the CanvasRenderer.\n * Here, we have to do our own layer handling.\n * @returns {JXG.Board} Reference to the board\n */\n updateRendererCanvas: function () {\n var el, pEl,\n olen = this.objectsList.length,\n // i, minim, lay,\n // layers = this.options.layer,\n // len = this.options.layer.numlayers,\n // last = Number.NEGATIVE_INFINITY.toExponential,\n depth_order_layers = [],\n objects_sorted,\n\n /**\n * Function to sort elements for depth ordering in canvas renderer.\n * Only relevant for elements having a zIndex.\n * Sort the elements for the canvas rendering according to\n * their layer, _pos, depthOrder (with this priority).\n * @param {JXG.GeometryObject} a\n * @param {JXG.GeometryObject} b\n * @returns Number\n * @private\n */\n _compareDepth = function(a, b) {\n if (a.visProp.layer !== b.visProp.layer) {\n // For elements in different layers, the element in the\n // higher layer is in front.\n return a.visProp.layer - b.visProp.layer;\n }\n\n // From here on, both objects are in the same layer.\n\n if (depth_order_layers.indexOf(a.visProp.layer) === -1) {\n // The layer is not depth ordered.\n return a._pos - b._pos;\n }\n\n // From here on, both objects are in the same layer\n // and the layer is depth ordered.\n\n // The objects are in the same layer and the layer is depth ordered\n // But neither element is the 2D element of a 3D element.\n if (!a.visProp.element3d && !b.visProp.element3d) {\n return a._pos - b._pos;\n }\n\n if (a.visProp.element3d && !b.visProp.element3d) {\n return -1;\n }\n\n if (!a.visProp.element3d && b.visProp.element3d) {\n return 1;\n }\n\n // Finqally, both elements are 2D elements of a 3D element.\n return a.visProp.element3d.zIndex - b.visProp.element3d.zIndex;\n };\n\n // Only one view3d element is supported. Get the depth order layers and\n // update the zIndices of the 3D elements.\n for (el = 0; el < olen; el++) {\n pEl = this.objectsList[el];\n if (pEl.elType === 'view3d' &&\n pEl.evalVisProp('depthorder.enabled')\n ) {\n depth_order_layers = pEl.evalVisProp('depthorder.layers');\n pEl.updateRenderer();\n break;\n }\n }\n\n // objects_sorted = this.objectsList.toSorted(_compareDepth);\n\n // 3D elements are not rendered, but their subelements element2D\n objects_sorted = this.objectsList.filter(function(e) { return !e.is3D; }).toSorted(_compareDepth);\n olen = objects_sorted.length;\n for (el = 0; el < olen; el++) {\n if (\n objects_sorted[el].visPropCalc.visible &&\n objects_sorted[el].type !== Const.OBJECT_TYPE_FACE3D // For these, updateRenderer is triggered in polyhedron3d.updateRenderer\n ) {\n objects_sorted[el].prepareUpdate().updateRenderer();\n }\n }\n\n return this;\n },\n\n /**\n * Please use {@link JXG.Board.on} instead.\n * @param {Function} hook A function to be called by the board after an update occurred.\n * @param {String} [m='update'] When the hook is to be called. Possible values are mouseup, mousedown and update.\n * @param {Object} [context=board] Determines the execution context the hook is called. This parameter is optional, default is the\n * board object the hook is attached to.\n * @returns {Number} Id of the hook, required to remove the hook from the board.\n * @deprecated\n */\n addHook: function (hook, m, context) {\n JXG.deprecated('Board.addHook()', 'Board.on()');\n m = Type.def(m, 'update');\n\n context = Type.def(context, this);\n\n this.hooks.push([m, hook]);\n this.on(m, hook, context);\n\n return this.hooks.length - 1;\n },\n\n /**\n * Alias of {@link JXG.Board.on}.\n */\n addEvent: JXG.shortcut(JXG.Board.prototype, 'on'),\n\n /**\n * Please use {@link JXG.Board.off} instead.\n * @param {Number|function} id The number you got when you added the hook or a reference to the event handler.\n * @returns {JXG.Board} Reference to the board\n * @deprecated\n */\n removeHook: function (id) {\n JXG.deprecated('Board.removeHook()', 'Board.off()');\n if (this.hooks[id]) {\n this.off(this.hooks[id][0], this.hooks[id][1]);\n this.hooks[id] = null;\n }\n\n return this;\n },\n\n /**\n * Alias of {@link JXG.Board.off}.\n */\n removeEvent: JXG.shortcut(JXG.Board.prototype, 'off'),\n\n /**\n * Runs through all hooked functions and calls them.\n * @returns {JXG.Board} Reference to the board\n * @deprecated\n */\n updateHooks: function (m) {\n var arg = Array.prototype.slice.call(arguments, 0);\n\n JXG.deprecated('Board.updateHooks()', 'Board.triggerEventHandlers()');\n\n arg[0] = Type.def(arg[0], 'update');\n this.triggerEventHandlers([arg[0]], arguments);\n\n return this;\n },\n\n /**\n * Adds a dependent board to this board.\n * @param {JXG.Board} board A reference to board which will be updated after an update of this board occurred.\n * @returns {JXG.Board} Reference to the board\n */\n addChild: function (board) {\n if (Type.exists(board) && Type.exists(board.containerObj)) {\n this.dependentBoards.push(board);\n this.update();\n }\n return this;\n },\n\n /**\n * Deletes a board from the list of dependent boards.\n * @param {JXG.Board} board Reference to the board which will be removed.\n * @returns {JXG.Board} Reference to the board\n */\n removeChild: function (board) {\n var i;\n\n for (i = this.dependentBoards.length - 1; i >= 0; i--) {\n if (this.dependentBoards[i] === board) {\n this.dependentBoards.splice(i, 1);\n }\n }\n return this;\n },\n\n /**\n * Runs through most elements and calls their update() method and update the conditions.\n * @param {JXG.GeometryElement} [drag] Element that caused the update.\n * @returns {JXG.Board} Reference to the board\n */\n update: function (drag) {\n var i, len, b, insert, storeActiveEl;\n\n if (this.inUpdate || this.isSuspendedUpdate) {\n return this;\n }\n this.inUpdate = true;\n\n if (\n this.attr.minimizereflow === 'all' &&\n this.containerObj &&\n this.renderer.type !== 'vml'\n ) {\n storeActiveEl = this.document.activeElement; // Store focus element\n insert = this.renderer.removeToInsertLater(this.containerObj);\n }\n\n if (this.attr.minimizereflow === 'svg' && this.renderer.type === 'svg') {\n storeActiveEl = this.document.activeElement;\n insert = this.renderer.removeToInsertLater(this.renderer.svgRoot);\n }\n\n this.prepareUpdate(drag).updateElements(drag).updateConditions();\n\n this.renderer.suspendRedraw(this);\n this.updateRenderer();\n this.renderer.unsuspendRedraw();\n this.triggerEventHandlers(['update'], []);\n\n if (insert) {\n insert();\n storeActiveEl.focus(); // Restore focus element\n }\n\n // To resolve dependencies between boards\n // for (var board in JXG.boards) {\n len = this.dependentBoards.length;\n for (i = 0; i < len; i++) {\n b = this.dependentBoards[i];\n if (Type.exists(b) && b !== this) {\n b.updateQuality = this.updateQuality;\n b.prepareUpdate().updateElements().updateConditions();\n b.renderer.suspendRedraw(this);\n b.updateRenderer();\n b.renderer.unsuspendRedraw();\n b.triggerEventHandlers(['update'], []);\n }\n }\n\n this.inUpdate = false;\n return this;\n },\n\n /**\n * Runs through all elements and calls their update() method and update the conditions.\n * This is necessary after zooming and changing the bounding box.\n * @returns {JXG.Board} Reference to the board\n */\n fullUpdate: function () {\n this.needsFullUpdate = true;\n this.update();\n this.needsFullUpdate = false;\n return this;\n },\n\n /**\n * Adds a grid to the board according to the settings given in board.options.\n * @returns {JXG.Board} Reference to the board.\n */\n addGrid: function () {\n this.create('grid', []);\n\n return this;\n },\n\n /**\n * Removes all grids assigned to this board. Warning: This method also removes all objects depending on one or\n * more of the grids.\n * @returns {JXG.Board} Reference to the board object.\n */\n removeGrids: function () {\n var i;\n\n for (i = 0; i < this.grids.length; i++) {\n this.removeObject(this.grids[i]);\n }\n\n this.grids.length = 0;\n this.update(); // required for canvas renderer\n\n return this;\n },\n\n /**\n * Creates a new geometric element of type elementType.\n * @param {String} elementType Type of the element to be constructed given as a string e.g. 'point' or 'circle'.\n * @param {Array} parents Array of parent elements needed to construct the element e.g. coordinates for a point or two\n * points to construct a line. This highly depends on the elementType that is constructed. See the corresponding JXG.create*\n * methods for a list of possible parameters.\n * @param {Object} [attributes] An object containing the attributes to be set. This also depends on the elementType.\n * Common attributes are name, visible, strokeColor.\n * @returns {Object} Reference to the created element. This is usually a GeometryElement, but can be an array containing\n * two or more elements.\n */\n create: function (elementType, parents, attributes) {\n var el, i;\n\n elementType = elementType.toLowerCase();\n\n if (!Type.exists(parents)) {\n parents = [];\n }\n\n if (!Type.exists(attributes)) {\n attributes = {};\n }\n\n for (i = 0; i < parents.length; i++) {\n if (\n Type.isString(parents[i]) &&\n !(elementType === 'text' && i === 2) &&\n !(elementType === 'solidofrevolution3d' && i === 2) &&\n !(elementType === 'text3d' && (i === 2 || i === 4)) &&\n !(\n (elementType === 'input' ||\n elementType === 'checkbox' ||\n elementType === 'button') &&\n (i === 2 || i === 3)\n ) &&\n !(elementType === 'curve' /*&& i > 0*/) && // Allow curve plots with jessiecode, parents[0] is the\n // variable name\n !(elementType === 'functiongraph') && // Prevent problems with function terms like 'x', 'y'\n !(elementType === 'implicitcurve')\n ) {\n if (i > 0 && parents[0].elType === 'view3d') {\n // 3D elements are based on 3D elements, only\n parents[i] = parents[0].select(parents[i]);\n } else {\n parents[i] = this.select(parents[i]);\n }\n }\n }\n\n if (Type.isFunction(JXG.elements[elementType])) {\n el = JXG.elements[elementType](this, parents, attributes);\n } else {\n throw new Error('JSXGraph: create: Unknown element type given: ' + elementType);\n }\n\n if (!Type.exists(el)) {\n JXG.debug('JSXGraph: create: failure creating ' + elementType);\n return el;\n }\n\n if (el.prepareUpdate && el.update && el.updateRenderer) {\n el.fullUpdate();\n }\n return el;\n },\n\n /**\n * Deprecated name for {@link JXG.Board.create}.\n * @deprecated\n */\n createElement: function () {\n JXG.deprecated('Board.createElement()', 'Board.create()');\n return this.create.apply(this, arguments);\n },\n\n /**\n * Delete the elements drawn as part of a trace of an element.\n * @returns {JXG.Board} Reference to the board\n */\n clearTraces: function () {\n var el;\n\n for (el = 0; el < this.objectsList.length; el++) {\n this.objectsList[el].clearTrace();\n }\n\n this.numTraces = 0;\n return this;\n },\n\n /**\n * Stop updates of the board.\n * @returns {JXG.Board} Reference to the board\n */\n suspendUpdate: function () {\n if (!this.inUpdate) {\n this.isSuspendedUpdate = true;\n }\n return this;\n },\n\n /**\n * Enable updates of the board.\n * @returns {JXG.Board} Reference to the board\n */\n unsuspendUpdate: function () {\n if (this.isSuspendedUpdate) {\n this.isSuspendedUpdate = false;\n this.fullUpdate();\n }\n return this;\n },\n\n /**\n * Set the bounding box of the board.\n * @param {Array} bbox New bounding box [x1,y1,x2,y2]\n * @param {Boolean} [keepaspectratio=false] If set to true, the aspect ratio will be 1:1, but\n * the resulting viewport may be larger.\n * @param {String} [setZoom='reset'] Reset, keep or update the zoom level of the board. 'reset'\n * sets {@link JXG.Board#zoomX} and {@link JXG.Board#zoomY} to the start values (or 1.0).\n * 'update' adapts these values accoring to the new bounding box and 'keep' does nothing.\n * @returns {JXG.Board} Reference to the board\n */\n setBoundingBox: function (bbox, keepaspectratio, setZoom) {\n var h, w, ux, uy,\n offX = 0,\n offY = 0,\n zoom_ratio = 1,\n ratio, dx, dy, prev_w, prev_h,\n dim = Env.getDimensions(this.containerObj, this.document);\n\n if (!Type.isArray(bbox)) {\n return this;\n }\n\n if (\n bbox[0] < this.maxboundingbox[0] - Mat.eps ||\n bbox[1] > this.maxboundingbox[1] + Mat.eps ||\n bbox[2] > this.maxboundingbox[2] + Mat.eps ||\n bbox[3] < this.maxboundingbox[3] - Mat.eps\n ) {\n return this;\n }\n\n if (!Type.exists(setZoom)) {\n setZoom = 'reset';\n }\n\n ux = this.unitX;\n uy = this.unitY;\n this.canvasWidth = parseFloat(dim.width); // parseInt(dim.width, 10);\n this.canvasHeight = parseFloat(dim.height); // parseInt(dim.height, 10);\n w = this.canvasWidth;\n h = this.canvasHeight;\n if (keepaspectratio) {\n if (this.keepaspectratio) {\n ratio = ux / uy; // Keep this ratio if keepaspectratio was true\n if (isNaN(ratio)) {\n ratio = 1.0;\n }\n } else {\n ratio = 1.0;\n }\n if (setZoom === 'keep') {\n zoom_ratio = this.zoomX / this.zoomY;\n }\n dx = bbox[2] - bbox[0];\n dy = bbox[1] - bbox[3];\n prev_w = ux * dx;\n prev_h = uy * dy;\n if (w >= h) {\n if (prev_w >= prev_h) {\n this.unitY = h / dy;\n this.unitX = this.unitY * ratio;\n } else {\n // Switch dominating interval\n this.unitY = h / Math.abs(dx) * Mat.sign(dy) / zoom_ratio;\n this.unitX = this.unitY * ratio;\n }\n } else {\n if (prev_h > prev_w) {\n this.unitX = w / dx;\n this.unitY = this.unitX / ratio;\n } else {\n // Switch dominating interval\n this.unitX = w / Math.abs(dy) * Mat.sign(dx) * zoom_ratio;\n this.unitY = this.unitX / ratio;\n }\n }\n // Add the additional units in equal portions left and right\n offX = (w / this.unitX - dx) * 0.5;\n // Add the additional units in equal portions above and below\n offY = (h / this.unitY - dy) * 0.5;\n this.keepaspectratio = true;\n } else {\n this.unitX = w / (bbox[2] - bbox[0]);\n this.unitY = h / (bbox[1] - bbox[3]);\n this.keepaspectratio = false;\n }\n\n this.moveOrigin(-this.unitX * (bbox[0] - offX), this.unitY * (bbox[1] + offY));\n\n if (setZoom === 'update') {\n this.zoomX *= this.unitX / ux;\n this.zoomY *= this.unitY / uy;\n } else if (setZoom === 'reset') {\n this.zoomX = Type.exists(this.attr.zoomx) ? this.attr.zoomx : 1.0;\n this.zoomY = Type.exists(this.attr.zoomy) ? this.attr.zoomy : 1.0;\n }\n\n return this;\n },\n\n /**\n * Get the bounding box of the board.\n * @returns {Array} bounding box [x1,y1,x2,y2] upper left corner, lower right corner\n */\n getBoundingBox: function () {\n var ul = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this).usrCoords,\n lr = new Coords(\n Const.COORDS_BY_SCREEN,\n [this.canvasWidth, this.canvasHeight],\n this\n ).usrCoords;\n return [ul[1], ul[2], lr[1], lr[2]];\n },\n\n /**\n * Sets the value of attribute key to value.\n * @param {String} key The attribute's name.\n * @param value The new value\n * @private\n */\n _set: function (key, value) {\n key = key.toLocaleLowerCase();\n\n if (\n value !== null &&\n Type.isObject(value) &&\n !Type.exists(value.id) &&\n !Type.exists(value.name)\n ) {\n // value is of type {prop: val, prop: val,...}\n // Convert these attributes to lowercase, too\n // this.attr[key] = {};\n // for (el in value) {\n // if (value.hasOwnProperty(el)) {\n // this.attr[key][el.toLocaleLowerCase()] = value[el];\n // }\n // }\n Type.mergeAttr(this.attr[key], value);\n } else {\n this.attr[key] = value;\n }\n },\n\n /**\n * Sets an arbitrary number of attributes. This method has one or more\n * parameters of the following types:\n * \n *
\n * Some board attributes are immutable, like e.g. the renderer type.\n *\n * @param {Object} attributes An object with attributes\n * @param {Boolean} [force=false] if true the attributes are set regardless of the previous setting was identical.\n * @returns {JXG.Board} Reference to the board\n *\n * @example\n * const board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-5, 5, 5, -5],\n * keepAspectRatio: false,\n * axis:true,\n * showFullscreen: true,\n * showScreenshot: true,\n * showCopyright: false\n * });\n *\n * board.setAttribute({\n * animationDelay: 10,\n * boundingbox: [-10, 5, 10, -5],\n * defaultAxes: {\n * x: { strokeColor: 'blue', ticks: { strokeColor: 'blue'}}\n * },\n * description: 'test',\n * fullscreen: {\n * scale: 0.5\n * },\n * intl: {\n * enabled: true,\n * locale: 'de-DE'\n * }\n * });\n *\n * board.setAttribute({\n * selection: {\n * enabled: true,\n * fillColor: 'blue'\n * },\n * showInfobox: false,\n * zoomX: 0.5,\n * zoomY: 2,\n * fullscreen: { symbol: 'x' },\n * screenshot: { symbol: 'y' },\n * showCopyright: true,\n * showFullscreen: false,\n * showScreenshot: false,\n * showZoom: false,\n * showNavigation: false\n * });\n * board.setAttribute('showCopyright:false');\n *\n * var p = board.create('point', [1, 1], {size: 10,\n * label: {\n * fontSize: 24,\n * highlightStrokeOpacity: 0.1,\n * offset: [5, 0]\n * }\n * });\n *\n *\n * \n *\n *\n */\n setAttribute: function (attr, force) {\n var i, arg, pair,\n key, value, oldvalue,// j, le,\n node, lst, e,\n attributes = {};\n\n // Normalize the user input\n for (i = 0; i < arguments.length; i++) {\n arg = arguments[i];\n if (Type.isString(arg)) {\n // pairRaw is string of the form 'key:value'\n pair = arg.split(\":\");\n attributes[Type.trim(pair[0])] = Type.trim(pair[1]);\n } else if (!Type.isArray(arg)) {\n // pairRaw consists of objects of the form {key1:value1,key2:value2,...}\n JXG.extend(attributes, arg);\n } else {\n // pairRaw consists of array [key,value]\n attributes[arg[0]] = arg[1];\n }\n }\n\n for (i in attributes) {\n if (attributes.hasOwnProperty(i)) {\n key = i.replace(/\\s+/g, \"\").toLowerCase();\n value = attributes[i];\n }\n value = (value.toLowerCase && value.toLowerCase() === 'false')\n ? false\n : value;\n oldvalue = this.attr[key];\n if (!force && oldvalue === value) {\n continue;\n }\n switch (key) {\n case 'axis':\n if (Type.exists(this.defaultAxes)) {\n this.defaultAxes.x.setAttribute({ visible: value });\n this.defaultAxes.y.setAttribute({ visible: value });\n this.attr[key] = value;\n } else {\n if (value === true) {\n // create the default axis\n this.defaultAxes = {};\n this.defaultAxes.x = this.create(\"axis\", [[0, 0], [1, 0]]);\n this.defaultAxes.y = this.create(\"axis\", [[0, 0], [0, 1]]);\n this.attr[key] = true;\n }\n }\n break;\n case 'cssstyle':\n lst = Type.css2js(value);\n node = this.containerObj;\n // node = this.renderer.svgRoot;\n for (e in lst) if (lst.hasOwnProperty(e)) {\n pair = lst[e];\n node.style[pair.key] = pair.val;\n }\n\n this._set(key, value);\n break;\n case 'boundingbox':\n this.setBoundingBox(value, this.keepaspectratio);\n this._set(key, value);\n break;\n case 'defaultaxes':\n if (Type.exists(this.defaultAxes.x) && Type.exists(value.x)) {\n this.defaultAxes.x.setAttribute(value.x);\n }\n if (Type.exists(this.defaultAxes.y) && Type.exists(value.y)) {\n this.defaultAxes.y.setAttribute(value.y);\n }\n break;\n case 'title':\n this.document.getElementById(this.container + '_ARIAlabel')\n .innerText = value;\n this._set(key, value);\n break;\n case 'keepaspectratio':\n this._set(key, value);\n this.setBoundingBox(this.getBoundingBox(), value, 'keep');\n break;\n\n // /* eslint-disable no-fallthrough */\n case 'document':\n case 'maxboundingbox':\n this[key] = value;\n this._set(key, value);\n break;\n\n case 'zoomx':\n case 'zoomy':\n this[key] = value;\n this._set(key, value);\n this.setZoom(this.attr.zoomx, this.attr.zoomy);\n break;\n\n case 'registerevents':\n case 'renderer':\n // immutable, i.e. ignored\n break;\n\n case 'fullscreen':\n case 'screenshot':\n node = this.containerObj.ownerDocument.getElementById(\n this.container + '_navigation_' + key);\n if (node && Type.exists(value.symbol)) {\n node.innerText = Type.evaluate(value.symbol);\n }\n this._set(key, value);\n break;\n\n case 'selection':\n value.visible = false;\n value.withLines = false;\n value.vertices = { visible: false };\n this._set(key, value);\n break;\n\n case 'showcopyright':\n if (this.renderer.type === 'svg') {\n node = this.containerObj.ownerDocument.getElementById(\n this.renderer.uniqName('licenseText')\n );\n if (node) {\n node.style.display = ((Type.evaluate(value)) ? 'inline' : 'none');\n } else if (Type.evaluate(value)) {\n this.renderer.displayCopyright(Const.licenseText, parseInt(this.options.text.fontSize, 10));\n }\n }\n this._set(key, value);\n break;\n\n case 'showlogo':\n if (this.renderer.type === 'svg') {\n node = this.containerObj.ownerDocument.getElementById(\n this.renderer.uniqName('licenseLogo')\n );\n if (node) {\n node.style.display = ((Type.evaluate(value)) ? 'inline' : 'none');\n } else if (Type.evaluate(value)) {\n this.renderer.displayLogo(Const.licenseLogo, parseInt(this.options.text.fontSize, 10));\n }\n }\n this._set(key, value);\n break;\n\n default:\n if (Type.exists(this.attr[key])) {\n this._set(key, value);\n }\n break;\n // /* eslint-enable no-fallthrough */\n }\n }\n\n // Redraw navbar to handle the remaining show* attributes\n node = this.containerObj.ownerDocument.getElementById(this.container + \"_navigationbar\");\n if (Type.exists(node)) {\n node.remove();\n this.renderer.drawNavigationBar(this, this.attr.navbar);\n }\n\n this.triggerEventHandlers([\"attribute\"], [attributes, this]);\n this.fullUpdate();\n\n return this;\n },\n\n /**\n * Adds an animation. Animations are controlled by the boards, so the boards need to be aware of the\n * animated elements. This function tells the board about new elements to animate.\n * @param {JXG.GeometryElement} element The element which is to be animated.\n * @returns {JXG.Board} Reference to the board\n */\n addAnimation: function (element) {\n var that = this;\n\n this.animationObjects[element.id] = element;\n\n if (!this.animationIntervalCode) {\n this.animationIntervalCode = window.setInterval(function () {\n that.animate();\n }, element.board.attr.animationdelay);\n }\n\n return this;\n },\n\n /**\n * Cancels all running animations.\n * @returns {JXG.Board} Reference to the board\n */\n stopAllAnimation: function () {\n var el;\n\n for (el in this.animationObjects) {\n if (\n this.animationObjects.hasOwnProperty(el) &&\n Type.exists(this.animationObjects[el])\n ) {\n this.animationObjects[el] = null;\n delete this.animationObjects[el];\n }\n }\n\n window.clearInterval(this.animationIntervalCode);\n delete this.animationIntervalCode;\n\n return this;\n },\n\n /**\n * General purpose animation function. This currently only supports moving points from one place to another. This\n * is faster than managing the animation per point, especially if there is more than one animated point at the same time.\n * @returns {JXG.Board} Reference to the board\n */\n animate: function () {\n var props,\n el,\n o,\n newCoords,\n r,\n p,\n c,\n cbtmp,\n count = 0,\n obj = null;\n\n for (el in this.animationObjects) {\n if (\n this.animationObjects.hasOwnProperty(el) &&\n Type.exists(this.animationObjects[el])\n ) {\n count += 1;\n o = this.animationObjects[el];\n\n if (o.animationPath) {\n if (Type.isFunction(o.animationPath)) {\n newCoords = o.animationPath(\n new Date().getTime() - o.animationStart\n );\n } else {\n newCoords = o.animationPath.pop();\n }\n\n if (\n !Type.exists(newCoords) ||\n (!Type.isArray(newCoords) && isNaN(newCoords))\n ) {\n delete o.animationPath;\n } else {\n o.setPositionDirectly(Const.COORDS_BY_USER, newCoords);\n o.fullUpdate();\n obj = o;\n }\n }\n if (o.animationData) {\n c = 0;\n\n for (r in o.animationData) {\n if (o.animationData.hasOwnProperty(r)) {\n p = o.animationData[r].pop();\n\n if (!Type.exists(p)) {\n delete o.animationData[p];\n } else {\n c += 1;\n props = {};\n props[r] = p;\n o.setAttribute(props);\n }\n }\n }\n\n if (c === 0) {\n delete o.animationData;\n }\n }\n\n if (!Type.exists(o.animationData) && !Type.exists(o.animationPath)) {\n this.animationObjects[el] = null;\n delete this.animationObjects[el];\n\n if (Type.exists(o.animationCallback)) {\n cbtmp = o.animationCallback;\n o.animationCallback = null;\n cbtmp();\n }\n }\n }\n }\n\n if (count === 0) {\n window.clearInterval(this.animationIntervalCode);\n delete this.animationIntervalCode;\n } else {\n this.update(obj);\n }\n\n return this;\n },\n\n /**\n * Migrate the dependency properties of the point src\n * to the point dest and delete the point src.\n * For example, a circle around the point src\n * receives the new center dest. The old center src\n * will be deleted.\n * @param {JXG.Point} src Original point which will be deleted\n * @param {JXG.Point} dest New point with the dependencies of src.\n * @param {Boolean} copyName Flag which decides if the name of the src element is copied to the\n * dest element.\n * @returns {JXG.Board} Reference to the board\n */\n migratePoint: function (src, dest, copyName) {\n var child,\n childId,\n prop,\n found,\n i,\n srcLabelId,\n srcHasLabel = false;\n\n src = this.select(src);\n dest = this.select(dest);\n\n if (Type.exists(src.label)) {\n srcLabelId = src.label.id;\n srcHasLabel = true;\n this.removeObject(src.label);\n }\n\n for (childId in src.childElements) {\n if (src.childElements.hasOwnProperty(childId)) {\n child = src.childElements[childId];\n found = false;\n\n for (prop in child) {\n if (child.hasOwnProperty(prop)) {\n if (child[prop] === src) {\n child[prop] = dest;\n found = true;\n }\n }\n }\n\n if (found) {\n delete src.childElements[childId];\n }\n\n for (i = 0; i < child.parents.length; i++) {\n if (child.parents[i] === src.id) {\n child.parents[i] = dest.id;\n }\n }\n\n dest.addChild(child);\n }\n }\n\n // The destination object should receive the name\n // and the label of the originating (src) object\n if (copyName) {\n if (srcHasLabel) {\n delete dest.childElements[srcLabelId];\n delete dest.descendants[srcLabelId];\n }\n\n if (dest.label) {\n this.removeObject(dest.label);\n }\n\n delete this.elementsByName[dest.name];\n dest.name = src.name;\n if (srcHasLabel) {\n dest.createLabel();\n }\n }\n\n this.removeObject(src);\n\n if (Type.exists(dest.name) && dest.name !== '') {\n this.elementsByName[dest.name] = dest;\n }\n\n this.fullUpdate();\n\n return this;\n },\n\n /**\n * Initializes color blindness simulation.\n * @param {String} deficiency Describes the color blindness deficiency which is simulated. Accepted values are 'protanopia', 'deuteranopia', and 'tritanopia'.\n * @returns {JXG.Board} Reference to the board\n */\n emulateColorblindness: function (deficiency) {\n var e, o;\n\n if (!Type.exists(deficiency)) {\n deficiency = 'none';\n }\n\n if (this.currentCBDef === deficiency) {\n return this;\n }\n\n for (e in this.objects) {\n if (this.objects.hasOwnProperty(e)) {\n o = this.objects[e];\n\n if (deficiency !== 'none') {\n if (this.currentCBDef === 'none') {\n // this could be accomplished by JXG.extend, too. But do not use\n // JXG.deepCopy as this could result in an infinite loop because in\n // visProp there could be geometry elements which contain the board which\n // contains all objects which contain board etc.\n o.visPropOriginal = {\n strokecolor: o.visProp.strokecolor,\n fillcolor: o.visProp.fillcolor,\n highlightstrokecolor: o.visProp.highlightstrokecolor,\n highlightfillcolor: o.visProp.highlightfillcolor\n };\n }\n o.setAttribute({\n strokecolor: Color.rgb2cb(\n o.eval(o.visPropOriginal.strokecolor),\n deficiency\n ),\n fillcolor: Color.rgb2cb(\n o.eval(o.visPropOriginal.fillcolor),\n deficiency\n ),\n highlightstrokecolor: Color.rgb2cb(\n o.eval(o.visPropOriginal.highlightstrokecolor),\n deficiency\n ),\n highlightfillcolor: Color.rgb2cb(\n o.eval(o.visPropOriginal.highlightfillcolor),\n deficiency\n )\n });\n } else if (Type.exists(o.visPropOriginal)) {\n JXG.extend(o.visProp, o.visPropOriginal);\n }\n }\n }\n this.currentCBDef = deficiency;\n this.update();\n\n return this;\n },\n\n /**\n * Select a single or multiple elements at once.\n * @param {String|Object|function} str The name, id or a reference to a JSXGraph element on this board. An object will\n * be used as a filter to return multiple elements at once filtered by the properties of the object.\n * @param {Boolean} onlyByIdOrName If true (default:false) elements are only filtered by their id, name or groupId.\n * The advanced filters consisting of objects or functions are ignored.\n * @returns {JXG.GeometryElement|JXG.Composition}\n * @example\n * // select the element with name A\n * board.select('A');\n *\n * // select all elements with strokecolor set to 'red' (but not '#ff0000')\n * board.select({\n * strokeColor: 'red'\n * });\n *\n * // select all points on or below the x axis and make them black.\n * board.select({\n * elementClass: JXG.OBJECT_CLASS_POINT,\n * Y: function (v) {\n * return v <= 0;\n * }\n * }).setAttribute({color: 'black'});\n *\n * // select all elements\n * board.select(function (el) {\n * return true;\n * });\n */\n select: function (str, onlyByIdOrName) {\n var flist,\n olist,\n i,\n l,\n s = str;\n\n if (s === null) {\n return s;\n }\n\n // It's a string, most likely an id or a name.\n if (Type.isString(s) && s !== '') {\n // Search by ID\n if (Type.exists(this.objects[s])) {\n s = this.objects[s];\n // Search by name\n } else if (Type.exists(this.elementsByName[s])) {\n s = this.elementsByName[s];\n // Search by group ID\n } else if (Type.exists(this.groups[s])) {\n s = this.groups[s];\n }\n\n // It's a function or an object, but not an element\n } else if (\n !onlyByIdOrName &&\n (Type.isFunction(s) || (Type.isObject(s) && !Type.isFunction(s.setAttribute)))\n ) {\n flist = Type.filterElements(this.objectsList, s);\n\n olist = {};\n l = flist.length;\n for (i = 0; i < l; i++) {\n olist[flist[i].id] = flist[i];\n }\n s = new Composition(olist);\n\n // It's an element which has been deleted (and still hangs around, e.g. in an attractor list\n } else if (\n Type.isObject(s) &&\n Type.exists(s.id) &&\n !Type.exists(this.objects[s.id])\n ) {\n s = null;\n }\n\n return s;\n },\n\n /**\n * Checks if the given point is inside the boundingbox.\n * @param {Number|JXG.Coords} x User coordinate or {@link JXG.Coords} object.\n * @param {Number} [y] User coordinate. May be omitted in case x is a {@link JXG.Coords} object.\n * @returns {Boolean}\n */\n hasPoint: function (x, y) {\n var px = x,\n py = y,\n bbox = this.getBoundingBox();\n\n if (Type.exists(x) && Type.isArray(x.usrCoords)) {\n px = x.usrCoords[1];\n py = x.usrCoords[2];\n }\n\n return !!(\n Type.isNumber(px) &&\n Type.isNumber(py) &&\n bbox[0] < px &&\n px < bbox[2] &&\n bbox[1] > py &&\n py > bbox[3]\n );\n },\n\n /**\n * Update CSS transformations of type scaling. It is used to correct the mouse position\n * in {@link JXG.Board.getMousePosition}.\n * The inverse transformation matrix is updated on each mouseDown and touchStart event.\n *\n * It is up to the user to call this method after an update of the CSS transformation\n * in the DOM.\n */\n updateCSSTransforms: function () {\n var obj = this.containerObj,\n o = obj,\n o2 = obj;\n\n this.cssTransMat = Env.getCSSTransformMatrix(o);\n\n // Newer variant of walking up the tree.\n // We walk up all parent nodes and collect possible CSS transforms.\n // Works also for ShadowDOM\n if (Type.exists(o.getRootNode)) {\n o = o.parentNode === o.getRootNode() ? o.parentNode.host : o.parentNode;\n while (o) {\n this.cssTransMat = Mat.matMatMult(Env.getCSSTransformMatrix(o), this.cssTransMat);\n o = o.parentNode === o.getRootNode() ? o.parentNode.host : o.parentNode;\n }\n this.cssTransMat = Mat.inverse(this.cssTransMat);\n } else {\n /*\n * This is necessary for IE11\n */\n o = o.offsetParent;\n while (o) {\n this.cssTransMat = Mat.matMatMult(Env.getCSSTransformMatrix(o), this.cssTransMat);\n\n o2 = o2.parentNode;\n while (o2 !== o) {\n this.cssTransMat = Mat.matMatMult(Env.getCSSTransformMatrix(o), this.cssTransMat);\n o2 = o2.parentNode;\n }\n o = o.offsetParent;\n }\n this.cssTransMat = Mat.inverse(this.cssTransMat);\n }\n return this;\n },\n\n /**\n * Start selection mode. This function can either be triggered from outside or by\n * a down event together with correct key pressing. The default keys are\n * shift+ctrl. But this can be changed in the options.\n *\n * Starting from out side can be realized for example with a button like this:\n * \n * \n * \t<button onclick='board.startSelectionMode()'>Start</button>\n *
\n * @example\n * //\n * // Set a new bounding box from the selection rectangle\n * //\n * var board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingBox:[-3,2,3,-2],\n * keepAspectRatio: false,\n * axis:true,\n * selection: {\n * enabled: true,\n * needShift: false,\n * needCtrl: true,\n * withLines: false,\n * vertices: {\n * visible: false\n * },\n * fillColor: '#ffff00',\n * }\n * });\n *\n * var f = function f(x) { return Math.cos(x); },\n * curve = board.create('functiongraph', [f]);\n *\n * board.on('stopselecting', function(){\n * var box = board.stopSelectionMode(),\n *\n * // bbox has the coordinates of the selection rectangle.\n * // Attention: box[i].usrCoords have the form [1, x, y], i.e.\n * // are homogeneous coordinates.\n * bbox = box[0].usrCoords.slice(1).concat(box[1].usrCoords.slice(1));\n *\n * // Set a new bounding box\n * board.setBoundingBox(bbox, false);\n * });\n *\n *\n * \n *\n */\n startSelectionMode: function () {\n this.selectingMode = true;\n this.selectionPolygon.setAttribute({ visible: true });\n this.selectingBox = [\n [0, 0],\n [0, 0]\n ];\n this._setSelectionPolygonFromBox();\n this.selectionPolygon.fullUpdate();\n },\n\n /**\n * Finalize the selection: disable selection mode and return the coordinates\n * of the selection rectangle.\n * @returns {Array} Coordinates of the selection rectangle. The array\n * contains two {@link JXG.Coords} objects. One the upper left corner and\n * the second for the lower right corner.\n */\n stopSelectionMode: function () {\n this.selectingMode = false;\n this.selectionPolygon.setAttribute({ visible: false });\n return [\n this.selectionPolygon.vertices[0].coords,\n this.selectionPolygon.vertices[2].coords\n ];\n },\n\n /**\n * Start the selection of a region.\n * @private\n * @param {Array} pos Screen coordiates of the upper left corner of the\n * selection rectangle.\n */\n _startSelecting: function (pos) {\n this.isSelecting = true;\n this.selectingBox = [\n [pos[0], pos[1]],\n [pos[0], pos[1]]\n ];\n this._setSelectionPolygonFromBox();\n },\n\n /**\n * Update the selection rectangle during a move event.\n * @private\n * @param {Array} pos Screen coordiates of the move event\n */\n _moveSelecting: function (pos) {\n if (this.isSelecting) {\n this.selectingBox[1] = [pos[0], pos[1]];\n this._setSelectionPolygonFromBox();\n this.selectionPolygon.fullUpdate();\n }\n },\n\n /**\n * Update the selection rectangle during an up event. Stop selection.\n * @private\n * @param {Object} evt Event object\n */\n _stopSelecting: function (evt) {\n var pos = this.getMousePosition(evt);\n\n this.isSelecting = false;\n this.selectingBox[1] = [pos[0], pos[1]];\n this._setSelectionPolygonFromBox();\n },\n\n /**\n * Update the Selection rectangle.\n * @private\n */\n _setSelectionPolygonFromBox: function () {\n var A = this.selectingBox[0],\n B = this.selectingBox[1];\n\n this.selectionPolygon.vertices[0].setPositionDirectly(JXG.COORDS_BY_SCREEN, [\n A[0],\n A[1]\n ]);\n this.selectionPolygon.vertices[1].setPositionDirectly(JXG.COORDS_BY_SCREEN, [\n A[0],\n B[1]\n ]);\n this.selectionPolygon.vertices[2].setPositionDirectly(JXG.COORDS_BY_SCREEN, [\n B[0],\n B[1]\n ]);\n this.selectionPolygon.vertices[3].setPositionDirectly(JXG.COORDS_BY_SCREEN, [\n B[0],\n A[1]\n ]);\n },\n\n /**\n * Test if a down event should start a selection. Test if the\n * required keys are pressed. If yes, {@link JXG.Board.startSelectionMode} is called.\n * @param {Object} evt Event object\n */\n _testForSelection: function (evt) {\n if (this._isRequiredKeyPressed(evt, 'selection')) {\n if (!Type.exists(this.selectionPolygon)) {\n this._createSelectionPolygon(this.attr);\n }\n this.startSelectionMode();\n }\n },\n\n /**\n * Create the internal selection polygon, which will be available as board.selectionPolygon.\n * @private\n * @param {Object} attr board attributes, e.g. the subobject board.attr.\n * @returns {Object} pointer to the board to enable chaining.\n */\n _createSelectionPolygon: function (attr) {\n var selectionattr;\n\n if (!Type.exists(this.selectionPolygon)) {\n selectionattr = Type.copyAttributes(attr, Options, 'board', 'selection');\n if (selectionattr.enabled === true) {\n this.selectionPolygon = this.create(\n 'polygon',\n [\n [0, 0],\n [0, 0],\n [0, 0],\n [0, 0]\n ],\n selectionattr\n );\n }\n }\n\n return this;\n },\n\n /**\n * Reset the sketchcurves in board.sketches[] to length 0 and add the position\n * of the event as first point of the sketch curve. Called at down events.\n * \n * \n */\n __evt__hit: function (e, el, target) { },\n\n /**\n * @event\n * @description Whenever an element is highlighted this event is fired.\n * @name JXG.Board#mousehit\n * @see JXG.Board#hit\n * @param {Event} e The browser's event object.\n * @param {JXG.GeometryElement} el The hit element.\n * @param target\n */\n __evt__mousehit: function (e, el, target) { },\n\n /**\n * @event\n * @description This board is updated.\n * @name JXG.Board#update\n */\n __evt__update: function () { },\n\n /**\n * @event\n * @description The bounding box of the board has changed.\n * @name JXG.Board#boundingbox\n */\n __evt__boundingbox: function () { },\n\n /**\n * @event\n * @description Select a region is started during a down event or by calling\n * {@link JXG.Board.startSelectionMode}\n * @name JXG.Board#startselecting\n */\n __evt__startselecting: function () { },\n\n /**\n * @event\n * @description Select a region is started during a down event\n * from a device sending mouse events or by calling\n * {@link JXG.Board.startSelectionMode}.\n * @name JXG.Board#mousestartselecting\n */\n __evt__mousestartselecting: function () { },\n\n /**\n * @event\n * @description Select a region is started during a down event\n * from a device sending pointer events or by calling\n * {@link JXG.Board.startSelectionMode}.\n * @name JXG.Board#pointerstartselecting\n */\n __evt__pointerstartselecting: function () { },\n\n /**\n * @event\n * @description Select a region is started during a down event\n * from a device sending touch events or by calling\n * {@link JXG.Board.startSelectionMode}.\n * @name JXG.Board#touchstartselecting\n */\n __evt__touchstartselecting: function () { },\n\n /**\n * @event\n * @description Selection of a region is stopped during an up event.\n * @name JXG.Board#stopselecting\n */\n __evt__stopselecting: function () { },\n\n /**\n * @event\n * @description Selection of a region is stopped during an up event\n * from a device sending mouse events.\n * @name JXG.Board#mousestopselecting\n */\n __evt__mousestopselecting: function () { },\n\n /**\n * @event\n * @description Selection of a region is stopped during an up event\n * from a device sending pointer events.\n * @name JXG.Board#pointerstopselecting\n */\n __evt__pointerstopselecting: function () { },\n\n /**\n * @event\n * @description Selection of a region is stopped during an up event\n * from a device sending touch events.\n * @name JXG.Board#touchstopselecting\n */\n __evt__touchstopselecting: function () { },\n\n /**\n * @event\n * @description A move event while selecting of a region is active.\n * @name JXG.Board#moveselecting\n */\n __evt__moveselecting: function () { },\n\n /**\n * @event\n * @description A move event while selecting of a region is active\n * from a device sending mouse events.\n * @name JXG.Board#mousemoveselecting\n */\n __evt__mousemoveselecting: function () { },\n\n /**\n * @event\n * @description Select a region is started during a down event\n * from a device sending mouse events.\n * @name JXG.Board#pointermoveselecting\n */\n __evt__pointermoveselecting: function () { },\n\n /**\n * @event\n * @description Select a region is started during a down event\n * from a device sending touch events.\n * @name JXG.Board#touchmoveselecting\n */\n __evt__touchmoveselecting: function () { },\n\n /**\n * @ignore\n */\n __evt: function () { },\n\n //endregion\n\n /**\n * Expand the JSXGraph construction to fullscreen.\n * In order to preserve the proportions of the JSXGraph element,\n * a wrapper div is created which is set to fullscreen.\n * This function is called when fullscreen mode is triggered\n * and when it is closed.\n * \n * \n * \n * \n *\n * @example\n * <div id='outer' style='max-width: 500px; margin: 0 auto;'>\n * <div id='jxgbox' class='jxgbox' style='height: 0; padding-bottom: 100%'></div>\n * </div>\n * <button onClick='board.toFullscreen('outer')'>Fullscreen</button>\n *\n * <script language='Javascript' type='text/javascript'>\n * var board = JXG.JSXGraph.initBoard('jxgbox', {\n * axis:true,\n * boundingbox:[-5,5,5,-5],\n * fullscreen: { id: 'outer' },\n * showFullscreen: true\n * });\n * var p = board.create('point', [-2, 3], {});\n * </script>\n *\n * \n *\n *\n */\n toFullscreen: function (id) {\n var wrap_id,\n wrap_node,\n inner_node,\n dim,\n doc = this.document,\n fullscreenElement;\n\n id = id || this.container;\n this._fullscreen_inner_id = id;\n inner_node = doc.getElementById(id);\n wrap_id = 'fullscreenwrap_' + id;\n\n if (!Type.exists(inner_node._cssFullscreenStore)) {\n // Store the actual, absolute size of the div\n // This is used in scaleJSXGraphDiv\n dim = this.containerObj.getBoundingClientRect();\n inner_node._cssFullscreenStore = {\n w: dim.width,\n h: dim.height\n };\n }\n\n // Wrap a div around the JSXGraph div.\n // It is removed when fullscreen mode is closed.\n if (doc.getElementById(wrap_id)) {\n wrap_node = doc.getElementById(wrap_id);\n } else {\n wrap_node = document.createElement('div');\n wrap_node.classList.add('JXG_wrap_private');\n wrap_node.setAttribute('id', wrap_id);\n inner_node.parentNode.insertBefore(wrap_node, inner_node);\n wrap_node.appendChild(inner_node);\n }\n\n // Trigger fullscreen mode\n wrap_node.requestFullscreen =\n wrap_node.requestFullscreen ||\n wrap_node.webkitRequestFullscreen ||\n wrap_node.mozRequestFullScreen ||\n wrap_node.msRequestFullscreen;\n\n if (doc.fullscreenElement !== undefined) {\n fullscreenElement = doc.fullscreenElement;\n } else if (doc.webkitFullscreenElement !== undefined) {\n fullscreenElement = doc.webkitFullscreenElement;\n } else {\n fullscreenElement = doc.msFullscreenElement;\n }\n\n if (fullscreenElement === null) {\n // Start fullscreen mode\n if (wrap_node.requestFullscreen) {\n wrap_node.requestFullscreen();\n this.startFullscreenResizeObserver(wrap_node);\n }\n } else {\n this.stopFullscreenResizeObserver(wrap_node);\n if (Type.exists(document.exitFullscreen)) {\n document.exitFullscreen();\n } else if (Type.exists(document.webkitExitFullscreen)) {\n document.webkitExitFullscreen();\n }\n }\n\n return this;\n },\n\n /**\n * If fullscreen mode is toggled, the possible CSS transformations\n * which are applied to the JSXGraph canvas have to be reread.\n * Otherwise the position of upper left corner is wrongly interpreted.\n *\n * @param {Object} evt fullscreen event object (unused)\n */\n fullscreenListener: function (evt) {\n var inner_id,\n inner_node,\n fullscreenElement,\n doc = this.document;\n\n inner_id = this._fullscreen_inner_id;\n if (!Type.exists(inner_id)) {\n return;\n }\n\n if (doc.fullscreenElement !== undefined) {\n fullscreenElement = doc.fullscreenElement;\n } else if (doc.webkitFullscreenElement !== undefined) {\n fullscreenElement = doc.webkitFullscreenElement;\n } else {\n fullscreenElement = doc.msFullscreenElement;\n }\n\n inner_node = doc.getElementById(inner_id);\n // If full screen mode is started we have to remove CSS margin around the JSXGraph div.\n // Otherwise, the positioning of the fullscreen div will be false.\n // When leaving the fullscreen mode, the margin is put back in.\n if (fullscreenElement) {\n // Just entered fullscreen mode\n\n // Store the original data.\n // Further, the CSS margin has to be removed when in fullscreen mode,\n // and must be restored later.\n //\n // Obsolete:\n // It is used in AbstractRenderer.updateText to restore the scaling matrix\n // which is removed by MathJax.\n inner_node._cssFullscreenStore.id = fullscreenElement.id;\n inner_node._cssFullscreenStore.isFullscreen = true;\n inner_node._cssFullscreenStore.margin = inner_node.style.margin;\n inner_node._cssFullscreenStore.width = inner_node.style.width;\n inner_node._cssFullscreenStore.height = inner_node.style.height;\n inner_node._cssFullscreenStore.transform = inner_node.style.transform;\n // Be sure to replace relative width / height units by absolute units\n inner_node.style.width = inner_node._cssFullscreenStore.w + 'px';\n inner_node.style.height = inner_node._cssFullscreenStore.h + 'px';\n inner_node.style.margin = '';\n\n // Do the shifting and scaling via CSS properties\n // We do this after fullscreen mode has been established to get the correct size\n // of the JSXGraph div.\n Env.scaleJSXGraphDiv(fullscreenElement.id, inner_id, doc,\n Type.evaluate(this.attr.fullscreen.scale));\n\n // Clear this.doc.fullscreenElement, because Safari doesn't to it and\n // when leaving full screen mode it is still set.\n fullscreenElement = null;\n } else if (Type.exists(inner_node._cssFullscreenStore)) {\n // Just left the fullscreen mode\n\n inner_node._cssFullscreenStore.isFullscreen = false;\n inner_node.style.margin = inner_node._cssFullscreenStore.margin;\n inner_node.style.width = inner_node._cssFullscreenStore.width;\n inner_node.style.height = inner_node._cssFullscreenStore.height;\n inner_node.style.transform = inner_node._cssFullscreenStore.transform;\n inner_node._cssFullscreenStore = null;\n\n // Remove the wrapper div\n inner_node.parentElement.replaceWith(inner_node);\n }\n\n this.updateCSSTransforms();\n },\n\n /**\n * Start resize observer to handle\n * orientation changes in fullscreen mode.\n *\n * @param {Object} node DOM object which is in fullscreen mode. It is the wrapper element\n * around the JSXGraph div.\n * @returns {JXG.Board} Reference to the board\n * @private\n * @see JXG.Board#toFullscreen\n *\n */\n startFullscreenResizeObserver: function(node) {\n var that = this;\n\n if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {\n return this;\n }\n\n this.resizeObserver = new ResizeObserver(function (entries) {\n var inner_id,\n fullscreenElement,\n doc = that.document;\n\n if (!that._isResizing) {\n that._isResizing = true;\n window.setTimeout(function () {\n try {\n inner_id = that._fullscreen_inner_id;\n if (doc.fullscreenElement !== undefined) {\n fullscreenElement = doc.fullscreenElement;\n } else if (doc.webkitFullscreenElement !== undefined) {\n fullscreenElement = doc.webkitFullscreenElement;\n } else {\n fullscreenElement = doc.msFullscreenElement;\n }\n if (fullscreenElement !== null) {\n Env.scaleJSXGraphDiv(fullscreenElement.id, inner_id, doc,\n Type.evaluate(that.attr.fullscreen.scale));\n }\n } catch (err) {\n that.stopFullscreenResizeObserver(node);\n } finally {\n that._isResizing = false;\n }\n }, that.attr.resize.throttle);\n }\n });\n this.resizeObserver.observe(node);\n return this;\n },\n\n /**\n * Remove resize observer to handle orientation changes in fullscreen mode.\n * @param {Object} node DOM object which is in fullscreen mode. It is the wrapper element\n * around the JSXGraph div.\n * @returns {JXG.Board} Reference to the board\n * @private\n * @see JXG.Board#toFullscreen\n */\n stopFullscreenResizeObserver: function(node) {\n if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {\n return this;\n }\n\n if (Type.exists(this.resizeObserver)) {\n this.resizeObserver.unobserve(node);\n }\n return this;\n },\n\n /**\n * Add user activity to the array 'board.userLog'.\n *\n * @param {String} type Event type, e.g. 'drag'\n * @param {Object} obj JSXGraph element object\n *\n * @see JXG.Board#userLog\n * @return {JXG.Board} Reference to the board\n */\n addLogEntry: function (type, obj, pos) {\n var t, id,\n last = this.userLog.length - 1;\n\n if (Type.exists(obj.elementClass)) {\n id = obj.id;\n }\n if (Type.evaluate(this.attr.logging.enabled)) {\n t = (new Date()).getTime();\n if (last >= 0 &&\n this.userLog[last].type === type &&\n this.userLog[last].id === id &&\n // Distinguish consecutive drag events of\n // the same element\n t - this.userLog[last].end < 500) {\n\n this.userLog[last].end = t;\n this.userLog[last].endpos = pos;\n } else {\n this.userLog.push({\n type: type,\n id: id,\n start: t,\n startpos: pos,\n end: t,\n endpos: pos,\n bbox: this.getBoundingBox(),\n canvas: [this.canvasWidth, this.canvasHeight],\n zoom: [this.zoomX, this.zoomY]\n });\n }\n }\n return this;\n },\n\n /**\n * Function to animate a curve rolling on another curve.\n * @param {Curve} c1 JSXGraph curve building the floor where c2 rolls\n * @param {Curve} c2 JSXGraph curve which rolls on c1.\n * @param {number} start_c1 The parameter t such that c1(t) touches c2. This is the start position of the\n * rolling process\n * @param {Number} stepsize Increase in t in each step for the curve c1\n * @param {Number} direction\n * @param {Number} time Delay time for setInterval()\n * @param {Array} pointlist Array of points which are rolled in each step. This list should contain\n * all points which define c2 and gliders on c2.\n *\n * @example\n *\n * // Line which will be the floor to roll upon.\n * var line = board.create('curve', [function (t) { return t;}, function (t){ return 1;}], {strokeWidth:6});\n * // Center of the rolling circle\n * var C = board.create('point',[0,2],{name:'C'});\n * // Starting point of the rolling circle\n * var P = board.create('point',[0,1],{name:'P', trace:true});\n * // Circle defined as a curve. The circle 'starts' at P, i.e. circle(0) = P\n * var circle = board.create('curve',[\n * function (t){var d = P.Dist(C),\n * beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);\n * t += beta;\n * return C.X()+d*Math.cos(t);\n * },\n * function (t){var d = P.Dist(C),\n * beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);\n * t += beta;\n * return C.Y()+d*Math.sin(t);\n * },\n * 0,2*Math.PI],\n * {strokeWidth:6, strokeColor:'green'});\n *\n * // Point on circle\n * var B = board.create('glider',[0,2,circle],{name:'B', color:'blue',trace:false});\n * var roll = board.createRoulette(line, circle, 0, Math.PI/20, 1, 100, [C,P,B]);\n * roll.start() // Start the rolling, to be stopped by roll.stop()\n *\n * \n * \n */\n createRoulette: function (c1, c2, start_c1, stepsize, direction, time, pointlist) {\n var brd = this,\n Roulette = function () {\n var alpha = 0,\n Tx = 0,\n Ty = 0,\n t1 = start_c1,\n t2 = Numerics.root(\n function (t) {\n var c1x = c1.X(t1),\n c1y = c1.Y(t1),\n c2x = c2.X(t),\n c2y = c2.Y(t);\n\n return (c1x - c2x) * (c1x - c2x) + (c1y - c2y) * (c1y - c2y);\n },\n [0, Math.PI * 2]\n ),\n t1_new = 0.0,\n t2_new = 0.0,\n c1dist,\n rotation = brd.create(\n 'transform',\n [\n function () {\n return alpha;\n }\n ],\n { type: 'rotate' }\n ),\n rotationLocal = brd.create(\n 'transform',\n [\n function () {\n return alpha;\n },\n function () {\n return c1.X(t1);\n },\n function () {\n return c1.Y(t1);\n }\n ],\n { type: 'rotate' }\n ),\n translate = brd.create(\n 'transform',\n [\n function () {\n return Tx;\n },\n function () {\n return Ty;\n }\n ],\n { type: 'translate' }\n ),\n // arc length via Simpson's rule.\n arclen = function (c, a, b) {\n var cpxa = Numerics.D(c.X)(a),\n cpya = Numerics.D(c.Y)(a),\n cpxb = Numerics.D(c.X)(b),\n cpyb = Numerics.D(c.Y)(b),\n cpxab = Numerics.D(c.X)((a + b) * 0.5),\n cpyab = Numerics.D(c.Y)((a + b) * 0.5),\n fa = Mat.hypot(cpxa, cpya),\n fb = Mat.hypot(cpxb, cpyb),\n fab = Mat.hypot(cpxab, cpyab);\n\n return ((fa + 4 * fab + fb) * (b - a)) / 6;\n },\n exactDist = function (t) {\n return c1dist - arclen(c2, t2, t);\n },\n beta = Math.PI / 18,\n beta9 = beta * 9,\n interval = null;\n\n this.rolling = function () {\n var h, g, hp, gp, z;\n\n t1_new = t1 + direction * stepsize;\n\n // arc length between c1(t1) and c1(t1_new)\n c1dist = arclen(c1, t1, t1_new);\n\n // find t2_new such that arc length between c2(t2) and c1(t2_new) equals c1dist.\n t2_new = Numerics.root(exactDist, t2);\n\n // c1(t) as complex number\n h = new Complex(c1.X(t1_new), c1.Y(t1_new));\n\n // c2(t) as complex number\n g = new Complex(c2.X(t2_new), c2.Y(t2_new));\n\n hp = new Complex(Numerics.D(c1.X)(t1_new), Numerics.D(c1.Y)(t1_new));\n gp = new Complex(Numerics.D(c2.X)(t2_new), Numerics.D(c2.Y)(t2_new));\n\n // z is angle between the tangents of c1 at t1_new, and c2 at t2_new\n z = Complex.C.div(hp, gp);\n\n alpha = Math.atan2(z.imaginary, z.real);\n // Normalizing the quotient\n z.div(Complex.C.abs(z));\n z.mult(g);\n Tx = h.real - z.real;\n\n // T = h(t1_new)-g(t2_new)*h'(t1_new)/g'(t2_new);\n Ty = h.imaginary - z.imaginary;\n\n // -(10-90) degrees: make corners roll smoothly\n if (alpha < -beta && alpha > -beta9) {\n alpha = -beta;\n rotationLocal.applyOnce(pointlist);\n } else if (alpha > beta && alpha < beta9) {\n alpha = beta;\n rotationLocal.applyOnce(pointlist);\n } else {\n rotation.applyOnce(pointlist);\n translate.applyOnce(pointlist);\n t1 = t1_new;\n t2 = t2_new;\n }\n brd.update();\n };\n\n this.start = function () {\n if (time > 0) {\n interval = window.setInterval(this.rolling, time);\n }\n return this;\n };\n\n this.stop = function () {\n window.clearInterval(interval);\n return this;\n };\n return this;\n };\n return new Roulette();\n }\n }\n);\n\nexport default JXG.Board;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n * \n *\n */\n dumpToDataURI: function (ignoreTexts) {\n var svgRoot = this.svgRoot,\n btoa = window.btoa || Base64.encode,\n svg, i, len, str,\n values = [];\n\n // Move all HTML tags (beside the SVG root) of the container\n // to the foreignObject element inside of the svgRoot node\n // Problem:\n // input values are not copied. This can be verified by looking at an innerHTML output\n // of an input element. Therefore, we do it \"by hand\".\n if (this.container.hasChildNodes() && Type.exists(this.foreignObjLayer)) {\n if (!ignoreTexts) {\n this.foreignObjLayer.setAttribute(\"display\", 'inline');\n }\n while (svgRoot.nextSibling) {\n // Copy all value attributes\n Type.concat(values, this._getValuesOfDOMElements(svgRoot.nextSibling));\n this.foreignObjLayer.appendChild(svgRoot.nextSibling);\n }\n }\n\n // Dump all image tags\n this._getImgDataURL(svgRoot);\n\n // Convert the SVG graphic into a string containing SVG code\n svgRoot.setAttribute(\"xmlns\", \"http://www.w3.org/2000/svg\");\n svg = new XMLSerializer().serializeToString(svgRoot);\n\n if (ignoreTexts !== true) {\n // Handle SVG texts\n // Insert all value attributes back into the svg string\n len = values.length;\n for (i = 0; i < len; i++) {\n svg = svg.replace(\n 'id=\"' + values[i][0] + '\"',\n 'id=\"' + values[i][0] + '\" value=\"' + values[i][1] + '\"'\n );\n }\n }\n\n // if (false) {\n // // Debug: use example svg image\n // svg = '';\n // }\n\n // In IE we have to remove the namespace again.\n // Since 2024 we have to check if the namespace attribute appears twice in one tag, because\n // there might by a svg inside of the svg, e.g. the screenshot icon.\n if (this.isIE &&\n (svg.match(/xmlns=\"http:\\/\\/www.w3.org\\/2000\\/svg\"\\s+xmlns=\"http:\\/\\/www.w3.org\\/2000\\/svg\"/g) || []).length > 1\n ) {\n svg = svg.replace(/xmlns=\"http:\\/\\/www.w3.org\\/2000\\/svg\"\\s+xmlns=\"http:\\/\\/www.w3.org\\/2000\\/svg\"/g, \"\");\n }\n\n // Safari fails if the svg string contains a \" \"\n // Obsolete with Safari 12+\n svg = svg.replace(/ /g, \" \");\n // Replacing "s might be necessary for older Safari versions\n // svg = svg.replace(/url\\("(.*)"\\)/g, \"url($1)\"); // Bug: does not replace matching "s\n // svg = svg.replace(/"/g, \"\");\n\n // Move all HTML tags back from\n // the foreignObject element to the container\n if (Type.exists(this.foreignObjLayer) && this.foreignObjLayer.hasChildNodes()) {\n // Restore all HTML elements\n while (this.foreignObjLayer.firstChild) {\n this.container.appendChild(this.foreignObjLayer.firstChild);\n }\n this.foreignObjLayer.setAttribute(\"display\", 'none');\n }\n\n // Parameter for btoa(): Replace utf-16 chars by their numerical entity\n // In particular, this is necessary for the coyright sign\n // From https://stackoverflow.com/questions/23223718/failed-to-execute-btoa-on-window-the-string-to-be-encoded-contains-characte/26603875#26603875\n\n // str = btoa(svg.replace(/[\\u00A0-\\u2666]/g, function(c) { return '&#' + c.charCodeAt(0) + ';'; })); // Fails for MathJax-SVG\n str = btoa(unescape(encodeURIComponent(svg))); // unescape is deprecated and can handle utf-16 chars only partially\n return \"data:image/svg+xml;base64,\" + str;\n },\n\n /**\n * Convert the SVG construction into an HTML canvas image.\n * This works for all SVG supporting browsers. Implemented as Promise.\n * \n *
\n *\n * @param {JXG.Board} board Link to the board.\n * @param {String} imgId Optional id of an img object. If given and different from the empty string,\n * the screenshot is copied to this img object. The width and height will be set to the values of the\n * JSXGraph container.\n * @param {Boolean} ignoreTexts If set to true, the foreignObject is taken out of the\n * SVGRoot and texts are not displayed. This is mandatory for Safari. Default: false\n * @return {Object} the svg renderer object\n */\n screenshot: function (board, imgId, ignoreTexts) {\n var node,\n doc = this.container.ownerDocument,\n parent = this.container.parentNode,\n // cPos,\n // cssTxt,\n canvas, id, img,\n button, buttonText,\n w, h,\n bas = board.attr.screenshot,\n navbar, navbarDisplay, insert,\n newImg = false,\n _copyCanvasToImg,\n isDebug = false;\n\n if (this.type === 'no') {\n return this;\n }\n\n w = bas.scale * this.container.getBoundingClientRect().width;\n h = bas.scale * this.container.getBoundingClientRect().height;\n\n if (imgId === undefined || imgId === \"\") {\n newImg = true;\n img = new Image(); //doc.createElement('img');\n img.style.width = w + 'px';\n img.style.height = h + 'px';\n } else {\n newImg = false;\n img = doc.getElementById(imgId);\n }\n // img.crossOrigin = 'anonymous';\n\n // Create div which contains canvas element and close button\n if (newImg) {\n node = doc.createElement('div');\n node.style.cssText = bas.css;\n node.style.width = w + 'px';\n node.style.height = h + 'px';\n node.style.zIndex = this.container.style.zIndex + 120;\n\n // Try to position the div exactly over the JSXGraph board\n node.style.position = 'absolute';\n node.style.top = this.container.offsetTop + 'px';\n node.style.left = this.container.offsetLeft + 'px';\n }\n\n if (!isDebug) {\n // Create canvas element and add it to the DOM\n // It will be removed after the image has been stored.\n canvas = doc.createElement('canvas');\n id = Math.random().toString(36).slice(2, 7);\n canvas.setAttribute(\"id\", id);\n canvas.setAttribute(\"width\", w);\n canvas.setAttribute(\"height\", h);\n canvas.style.width = w + 'px';\n canvas.style.height = w + 'px';\n canvas.style.display = 'none';\n parent.appendChild(canvas);\n } else {\n // Debug: use canvas element 'jxgbox_canvas' from jsxdev/dump.html\n id = \"jxgbox_canvas\";\n canvas = doc.getElementById(id);\n }\n\n if (newImg) {\n // Create close button\n button = doc.createElement('span');\n buttonText = doc.createTextNode(\"\\u2716\");\n button.style.cssText = bas.cssButton;\n button.appendChild(buttonText);\n button.onclick = function () {\n node.parentNode.removeChild(node);\n };\n\n // Add all nodes\n node.appendChild(img);\n node.appendChild(button);\n parent.insertBefore(node, this.container.nextSibling);\n }\n\n // Hide navigation bar in board\n navbar = doc.getElementById(this.uniqName('navigationbar'));\n if (Type.exists(navbar)) {\n navbarDisplay = navbar.style.display;\n navbar.style.display = 'none';\n insert = this.removeToInsertLater(navbar);\n }\n\n _copyCanvasToImg = function () {\n // Show image in img tag\n img.src = canvas.toDataURL(\"image/png\");\n\n // Remove canvas node\n if (!isDebug) {\n parent.removeChild(canvas);\n }\n };\n\n // Create screenshot in image element\n if (\"Promise\" in window) {\n this.dumpToCanvas(id, w, h, ignoreTexts).then(_copyCanvasToImg);\n } else {\n // IE\n this.dumpToCanvas(id, w, h, ignoreTexts);\n window.setTimeout(_copyCanvasToImg, 200);\n }\n\n // Reinsert navigation bar in board\n if (Type.exists(navbar)) {\n navbar.style.display = navbarDisplay;\n insert();\n }\n\n return this;\n }\n }\n);\n\nexport default JXG.SVGRenderer;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see
\\n\");\n }\n },\n\n /* ******************************** *\n * This renderer does not need to\n * override draw/update* methods\n * since it provides draw/update*Prim\n * methods.\n * ******************************** */\n\n /* **************************\n * Lines\n * **************************/\n\n // documented in AbstractRenderer\n updateTicks: function (ticks) {\n var i,\n len,\n c,\n x,\n y,\n r = this.resolution,\n tickArr = [];\n\n len = ticks.ticks.length;\n for (i = 0; i < len; i++) {\n c = ticks.ticks[i];\n x = c[0];\n y = c[1];\n\n if (Type.isNumber(x[0]) && Type.isNumber(x[1])) {\n tickArr.push(\n \" m \" +\n Math.round(r * x[0]) +\n \", \" +\n Math.round(r * y[0]) +\n \" l \" +\n Math.round(r * x[1]) +\n \", \" +\n Math.round(r * y[1]) +\n \" \"\n );\n }\n }\n\n if (!Type.exists(ticks.rendNode)) {\n ticks.rendNode = this.createPrim(\"path\", ticks.id);\n this.appendChildPrim(ticks.rendNode, ticks.evalVisProp('layer'));\n }\n\n this._setAttr(ticks.rendNode, \"stroked\", 'true');\n this._setAttr(\n ticks.rendNode,\n \"strokecolor\",\n ticks.evalVisProp('strokecolor'),\n 1\n );\n this._setAttr(\n ticks.rendNode,\n \"strokeweight\",\n ticks.evalVisProp('strokewidth')\n );\n this._setAttr(\n ticks.rendNodeStroke,\n \"opacity\",\n ticks.evalVisProp('strokeopacity') * 100 + \"%\"\n );\n this.updatePathPrim(ticks.rendNode, tickArr, ticks.board);\n },\n\n /* **************************\n * Text related stuff\n * **************************/\n\n // Already documented in JXG.AbstractRenderer\n displayCopyright: function (str, fontsize) {\n var node, t;\n\n node = this.createNode('textbox');\n node.style.position = 'absolute';\n this._setAttr(node, \"id\", this.container.id + \"_\" + 'licenseText');\n\n node.style.left = 20;\n node.style.top = 2;\n node.style.fontSize = fontsize;\n node.style.color = \"#356AA0\";\n node.style.fontFamily = \"Arial,Helvetica,sans-serif\";\n this._setAttr(node, \"opacity\", \"30%\");\n node.style.filter =\n \"progid:DXImageTransform.Microsoft.Matrix(M11='1.0', sizingMethod='auto expand', enabled = false) progid:DXImageTransform.Microsoft.Alpha(opacity = 30, enabled = true)\";\n\n t = this.container.ownerDocument.createTextNode(str);\n node.appendChild(t);\n this.appendChildPrim(node, 0);\n },\n\n // documented in AbstractRenderer\n drawInternalText: function (el) {\n var node;\n node = this.createNode('textbox');\n node.style.position = 'absolute';\n el.rendNodeText = this.container.ownerDocument.createTextNode(\"\");\n node.appendChild(el.rendNodeText);\n this.appendChildPrim(node, 9);\n node.style.filter =\n \"progid:DXImageTransform.Microsoft.Matrix(M11='1.0', sizingMethod='auto expand', enabled = false) progid:DXImageTransform.Microsoft.Alpha(opacity = 100, enabled = false)\";\n\n return node;\n },\n\n // documented in AbstractRenderer\n updateInternalText: function (el) {\n var v,\n content = el.plaintext,\n m = this.joinTransforms(el, el.transformations),\n offset = [0, 0],\n maxX,\n maxY,\n minX,\n minY,\n i,\n node = el.rendNode,\n p = [],\n ev_ax = el.getAnchorX(),\n ev_ay = el.getAnchorY();\n\n if (!isNaN(el.coords.scrCoords[1] + el.coords.scrCoords[2])) {\n // Horizontal\n if (ev_ax === 'right') {\n offset[0] = 1;\n } else if (ev_ax === 'middle') {\n offset[0] = 0.5;\n } // default (ev_ax === 'left') offset[0] = 0;\n\n // Vertical\n if (ev_ay === 'bottom') {\n offset[1] = 1;\n } else if (ev_ay === 'middle') {\n offset[1] = 0.5;\n } // default (ev_ay === 'top') offset[1] = 0;\n\n // Compute maxX, maxY, minX, minY\n p[0] = Mat.matVecMult(m, [\n 1,\n el.coords.scrCoords[1] - offset[0] * el.size[0],\n el.coords.scrCoords[2] + (1 - offset[1]) * el.size[1] + this.vOffsetText\n ]);\n p[0][1] /= p[0][0];\n p[0][2] /= p[0][0];\n p[1] = Mat.matVecMult(m, [\n 1,\n el.coords.scrCoords[1] + (1 - offset[0]) * el.size[0],\n el.coords.scrCoords[2] + (1 - offset[1]) * el.size[1] + this.vOffsetText\n ]);\n p[1][1] /= p[1][0];\n p[1][2] /= p[1][0];\n p[2] = Mat.matVecMult(m, [\n 1,\n el.coords.scrCoords[1] + (1 - offset[0]) * el.size[0],\n el.coords.scrCoords[2] - offset[1] * el.size[1] + this.vOffsetText\n ]);\n p[2][1] /= p[2][0];\n p[2][2] /= p[2][0];\n p[3] = Mat.matVecMult(m, [\n 1,\n el.coords.scrCoords[1] - offset[0] * el.size[0],\n el.coords.scrCoords[2] - offset[1] * el.size[1] + this.vOffsetText\n ]);\n p[3][1] /= p[3][0];\n p[3][2] /= p[3][0];\n maxX = p[0][1];\n minX = p[0][1];\n maxY = p[0][2];\n minY = p[0][2];\n\n for (i = 1; i < 4; i++) {\n maxX = Math.max(maxX, p[i][1]);\n minX = Math.min(minX, p[i][1]);\n maxY = Math.max(maxY, p[i][2]);\n minY = Math.min(minY, p[i][2]);\n }\n\n // Horizontal\n v =\n offset[0] === 1\n ? Math.floor(el.board.canvasWidth - maxX)\n : Math.floor(minX);\n if (el.visPropOld.left !== ev_ax + v) {\n if (offset[0] === 1) {\n el.rendNode.style.right = v + 'px';\n el.rendNode.style.left = 'auto';\n } else {\n el.rendNode.style.left = v + 'px';\n el.rendNode.style.right = 'auto';\n }\n el.visPropOld.left = ev_ax + v;\n }\n\n // Vertical\n v =\n offset[1] === 1\n ? Math.floor(el.board.canvasHeight - maxY)\n : Math.floor(minY);\n if (el.visPropOld.top !== ev_ay + v) {\n if (offset[1] === 1) {\n el.rendNode.style.bottom = v + 'px';\n el.rendNode.style.top = 'auto';\n } else {\n el.rendNode.style.top = v + 'px';\n el.rendNode.style.bottom = 'auto';\n }\n el.visPropOld.top = ev_ay + v;\n }\n }\n\n if (el.htmlStr !== content) {\n el.rendNodeText.data = content;\n el.htmlStr = content;\n }\n\n //this.transformRect(el, el.transformations);\n node.filters.item(0).M11 = m[1][1];\n node.filters.item(0).M12 = m[1][2];\n node.filters.item(0).M21 = m[2][1];\n node.filters.item(0).M22 = m[2][2];\n node.filters.item(0).enabled = true;\n },\n\n /* **************************\n * Image related stuff\n * **************************/\n\n // Already documented in JXG.AbstractRenderer\n drawImage: function (el) {\n // IE 8: Bilder ueber data URIs werden bis 32kB unterstuetzt.\n var node;\n\n node = this.container.ownerDocument.createElement('img');\n node.style.position = 'absolute';\n this._setAttr(node, \"id\", this.container.id + \"_\" + el.id);\n\n this.container.appendChild(node);\n this.appendChildPrim(node, el.evalVisProp('layer'));\n\n // Adding the rotation filter. This is always filter item 0:\n // node.filters.item(0), see transformRect\n // Also add the alpha filter. This is always filter item 1\n // node.filters.item(1), see setObjectFillColor and setObjectSTrokeColor\n //node.style.filter = node.style['-ms-filter'] = \"progid:DXImageTransform.Microsoft.Matrix(M11='1.0', sizingMethod='auto expand')\";\n node.style.filter =\n \"progid:DXImageTransform.Microsoft.Matrix(M11='1.0', sizingMethod='auto expand') progid:DXImageTransform.Microsoft.Alpha(opacity = 100, enabled = false)\";\n el.rendNode = node;\n this.updateImage(el);\n },\n\n // Already documented in JXG.AbstractRenderer\n transformRect: function (el, t) {\n var m,\n maxX,\n maxY,\n minX,\n minY,\n i,\n node = el.rendNode,\n p = [],\n len = t.length;\n\n if (len > 0) {\n /*\n nt = el.rendNode.style.filter.toString();\n if (!nt.match(/DXImageTransform/)) {\n node.style.filter = \"progid:DXImageTransform.Microsoft.Matrix(M11='1.0', sizingMethod='auto expand') \" + nt;\n }\n */\n\n m = this.joinTransforms(el, t);\n p[0] = Mat.matVecMult(m, el.coords.scrCoords);\n p[0][1] /= p[0][0];\n p[0][2] /= p[0][0];\n p[1] = Mat.matVecMult(m, [\n 1,\n el.coords.scrCoords[1] + el.size[0],\n el.coords.scrCoords[2]\n ]);\n p[1][1] /= p[1][0];\n p[1][2] /= p[1][0];\n p[2] = Mat.matVecMult(m, [\n 1,\n el.coords.scrCoords[1] + el.size[0],\n el.coords.scrCoords[2] - el.size[1]\n ]);\n p[2][1] /= p[2][0];\n p[2][2] /= p[2][0];\n p[3] = Mat.matVecMult(m, [\n 1,\n el.coords.scrCoords[1],\n el.coords.scrCoords[2] - el.size[1]\n ]);\n p[3][1] /= p[3][0];\n p[3][2] /= p[3][0];\n maxX = p[0][1];\n minX = p[0][1];\n maxY = p[0][2];\n minY = p[0][2];\n\n for (i = 1; i < 4; i++) {\n maxX = Math.max(maxX, p[i][1]);\n minX = Math.min(minX, p[i][1]);\n maxY = Math.max(maxY, p[i][2]);\n minY = Math.min(minY, p[i][2]);\n }\n node.style.left = Math.floor(minX) + 'px';\n node.style.top = Math.floor(minY) + 'px';\n\n node.filters.item(0).M11 = m[1][1];\n node.filters.item(0).M12 = m[1][2];\n node.filters.item(0).M21 = m[2][1];\n node.filters.item(0).M22 = m[2][2];\n node.filters.item(0).enabled = true;\n }\n },\n\n // Already documented in JXG.AbstractRenderer\n updateImageURL: function (el) {\n var url = el.eval(el.url);\n\n this._setAttr(el.rendNode, \"src\", url);\n },\n\n /* **************************\n * Render primitive objects\n * **************************/\n\n // Already documented in JXG.AbstractRenderer\n appendChildPrim: function (node, level) {\n // For trace nodes\n if (!Type.exists(level)) {\n level = 0;\n }\n\n node.style.zIndex = level;\n this.container.appendChild(node);\n\n return node;\n },\n\n // Already documented in JXG.AbstractRenderer\n appendNodesToElement: function (el, type) {\n if (type === \"shape\" || type === \"path\" || type === 'polygon') {\n el.rendNodePath = this.getElementById(el.id + \"_path\");\n }\n el.rendNodeFill = this.getElementById(el.id + \"_fill\");\n el.rendNodeStroke = this.getElementById(el.id + \"_stroke\");\n el.rendNodeShadow = this.getElementById(el.id + \"_shadow\");\n el.rendNode = this.getElementById(el.id);\n },\n\n // Already documented in JXG.AbstractRenderer\n createPrim: function (type, id) {\n var node,\n pathNode,\n fillNode = this.createNode('fill'),\n strokeNode = this.createNode('stroke'),\n shadowNode = this.createNode('shadow');\n\n this._setAttr(fillNode, \"id\", this.container.id + \"_\" + id + \"_fill\");\n this._setAttr(strokeNode, \"id\", this.container.id + \"_\" + id + \"_stroke\");\n this._setAttr(shadowNode, \"id\", this.container.id + \"_\" + id + \"_shadow\");\n\n if (type === \"circle\" || type === 'ellipse') {\n node = this.createNode('oval');\n node.appendChild(fillNode);\n node.appendChild(strokeNode);\n node.appendChild(shadowNode);\n } else if (\n type === \"polygon\" ||\n type === \"path\" ||\n type === \"shape\" ||\n type === \"line\"\n ) {\n node = this.createNode('shape');\n node.appendChild(fillNode);\n node.appendChild(strokeNode);\n node.appendChild(shadowNode);\n pathNode = this.createNode('path');\n this._setAttr(pathNode, \"id\", this.container.id + \"_\" + id + \"_path\");\n node.appendChild(pathNode);\n } else {\n node = this.createNode(type);\n node.appendChild(fillNode);\n node.appendChild(strokeNode);\n node.appendChild(shadowNode);\n }\n\n node.style.position = 'absolute';\n node.style.left = '0px';\n node.style.top = '0px';\n this._setAttr(node, \"id\", this.container.id + \"_\" + id);\n\n return node;\n },\n\n // Already documented in JXG.AbstractRenderer\n remove: function (node) {\n if (Type.exists(node)) {\n node.removeNode(true);\n }\n },\n\n // Already documented in JXG.AbstractRenderer\n makeArrows: function (el) {\n var nodeStroke,\n ev_fa = el.evalVisProp('firstarrow'),\n ev_la = el.evalVisProp('lastarrow');\n\n if (el.visPropOld.firstarrow === ev_fa && el.visPropOld.lastarrow === ev_la) {\n return;\n }\n\n if (ev_fa) {\n nodeStroke = el.rendNodeStroke;\n this._setAttr(nodeStroke, \"startarrow\", 'block');\n this._setAttr(nodeStroke, \"startarrowlength\", 'long');\n } else {\n nodeStroke = el.rendNodeStroke;\n if (Type.exists(nodeStroke)) {\n this._setAttr(nodeStroke, \"startarrow\", 'none');\n }\n }\n\n if (ev_la) {\n nodeStroke = el.rendNodeStroke;\n this._setAttr(nodeStroke, \"id\", this.container.id + \"_\" + el.id + 'stroke');\n this._setAttr(nodeStroke, \"endarrow\", 'block');\n this._setAttr(nodeStroke, \"endarrowlength\", 'long');\n } else {\n nodeStroke = el.rendNodeStroke;\n if (Type.exists(nodeStroke)) {\n this._setAttr(nodeStroke, \"endarrow\", 'none');\n }\n }\n el.visPropOld.firstarrow = ev_fa;\n el.visPropOld.lastarrow = ev_la;\n },\n\n // Already documented in JXG.AbstractRenderer\n updateEllipsePrim: function (node, x, y, rx, ry) {\n node.style.left = Math.floor(x - rx) + 'px';\n node.style.top = Math.floor(y - ry) + 'px';\n node.style.width = Math.floor(Math.abs(rx) * 2) + 'px';\n node.style.height = Math.floor(Math.abs(ry) * 2) + 'px';\n },\n\n // Already documented in JXG.AbstractRenderer\n updateLinePrim: function (node, p1x, p1y, p2x, p2y, board) {\n var s,\n r = this.resolution;\n\n if (!isNaN(p1x + p1y + p2x + p2y)) {\n s = [\n \"m \",\n Math.floor(r * p1x),\n \", \",\n Math.floor(r * p1y),\n \" l \",\n Math.floor(r * p2x),\n \", \",\n Math.floor(r * p2y)\n ];\n this.updatePathPrim(node, s, board);\n }\n },\n\n // Already documented in JXG.AbstractRenderer\n updatePathPrim: function (node, pointString, board) {\n var x = board.canvasWidth,\n y = board.canvasHeight;\n if (pointString.length <= 0) {\n pointString = [\"m 0,0\"];\n }\n node.style.width = x;\n node.style.height = y;\n this._setAttr(\n node,\n \"coordsize\",\n [Math.floor(this.resolution * x), Math.floor(this.resolution * y)].join(\",\")\n );\n this._setAttr(node, \"path\", pointString.join(\"\"));\n },\n\n // Already documented in JXG.AbstractRenderer\n updatePathStringPoint: function (el, size, type) {\n var s = [],\n mround = Math.round,\n scr = el.coords.scrCoords,\n sqrt32 = size * Math.sqrt(3) * 0.5,\n s05 = size * 0.5,\n r = this.resolution;\n\n if (type === 'x') {\n s.push(\n [\n \" m \",\n mround(r * (scr[1] - size)),\n \", \",\n mround(r * (scr[2] - size)),\n \" l \",\n mround(r * (scr[1] + size)),\n \", \",\n mround(r * (scr[2] + size)),\n \" m \",\n mround(r * (scr[1] + size)),\n \", \",\n mround(r * (scr[2] - size)),\n \" l \",\n mround(r * (scr[1] - size)),\n \", \",\n mround(r * (scr[2] + size))\n ].join(\"\")\n );\n } else if (type === \"+\") {\n s.push(\n [\n \" m \",\n mround(r * (scr[1] - size)),\n \", \",\n mround(r * scr[2]),\n \" l \",\n mround(r * (scr[1] + size)),\n \", \",\n mround(r * scr[2]),\n \" m \",\n mround(r * scr[1]),\n \", \",\n mround(r * (scr[2] - size)),\n \" l \",\n mround(r * scr[1]),\n \", \",\n mround(r * (scr[2] + size))\n ].join(\"\")\n );\n } else if (type === \"<>\" || type === \"<<>>\") {\n if (type === \"<<>>\") {\n size *= 1.41;\n }\n s.push(\n [\n \" m \",\n mround(r * (scr[1] - size)),\n \", \",\n mround(r * scr[2]),\n \" l \",\n mround(r * scr[1]),\n \", \",\n mround(r * (scr[2] + size)),\n \" l \",\n mround(r * (scr[1] + size)),\n \", \",\n mround(r * scr[2]),\n \" l \",\n mround(r * scr[1]),\n \", \",\n mround(r * (scr[2] - size)),\n \" x e \"\n ].join(\"\")\n );\n } else if (type === \"^\") {\n s.push(\n [\n \" m \",\n mround(r * scr[1]),\n \", \",\n mround(r * (scr[2] - size)),\n \" l \",\n mround(r * (scr[1] - sqrt32)),\n \", \",\n mround(r * (scr[2] + s05)),\n \" l \",\n mround(r * (scr[1] + sqrt32)),\n \", \",\n mround(r * (scr[2] + s05)),\n \" x e \"\n ].join(\"\")\n );\n } else if (type === 'v') {\n s.push(\n [\n \" m \",\n mround(r * scr[1]),\n \", \",\n mround(r * (scr[2] + size)),\n \" l \",\n mround(r * (scr[1] - sqrt32)),\n \", \",\n mround(r * (scr[2] - s05)),\n \" l \",\n mround(r * (scr[1] + sqrt32)),\n \", \",\n mround(r * (scr[2] - s05)),\n \" x e \"\n ].join(\"\")\n );\n } else if (type === \">\") {\n s.push(\n [\n \" m \",\n mround(r * (scr[1] + size)),\n \", \",\n mround(r * scr[2]),\n \" l \",\n mround(r * (scr[1] - s05)),\n \", \",\n mround(r * (scr[2] - sqrt32)),\n \" l \",\n mround(r * (scr[1] - s05)),\n \", \",\n mround(r * (scr[2] + sqrt32)),\n \" l \",\n mround(r * (scr[1] + size)),\n \", \",\n mround(r * scr[2])\n ].join(\"\")\n );\n } else if (type === \"<\") {\n s.push(\n [\n \" m \",\n mround(r * (scr[1] - size)),\n \", \",\n mround(r * scr[2]),\n \" l \",\n mround(r * (scr[1] + s05)),\n \", \",\n mround(r * (scr[2] - sqrt32)),\n \" l \",\n mround(r * (scr[1] + s05)),\n \", \",\n mround(r * (scr[2] + sqrt32)),\n \" x e \"\n ].join(\"\")\n );\n }\n\n return s;\n },\n\n // Already documented in JXG.AbstractRenderer\n updatePathStringPrim: function (el) {\n var i,\n scr,\n pStr = [],\n r = this.resolution,\n mround = Math.round,\n symbm = \" m \",\n symbl = \" l \",\n symbc = \" c \",\n nextSymb = symbm,\n len = Math.min(el.numberPoints, 8192); // otherwise IE 7 crashes in hilbert.html\n\n if (el.numberPoints <= 0) {\n return \"\";\n }\n len = Math.min(len, el.points.length);\n\n if (el.bezierDegree === 1) {\n for (i = 0; i < len; i++) {\n scr = el.points[i].scrCoords;\n if (isNaN(scr[1]) || isNaN(scr[2])) {\n // PenUp\n nextSymb = symbm;\n } else {\n // IE has problems with values being too far away.\n if (scr[1] > 20000.0) {\n scr[1] = 20000.0;\n } else if (scr[1] < -20000.0) {\n scr[1] = -20000.0;\n }\n\n if (scr[2] > 20000.0) {\n scr[2] = 20000.0;\n } else if (scr[2] < -20000.0) {\n scr[2] = -20000.0;\n }\n\n pStr.push(\n [nextSymb, mround(r * scr[1]), \", \", mround(r * scr[2])].join(\"\")\n );\n nextSymb = symbl;\n }\n }\n } else if (el.bezierDegree === 3) {\n i = 0;\n while (i < len) {\n scr = el.points[i].scrCoords;\n if (isNaN(scr[1]) || isNaN(scr[2])) {\n // PenUp\n nextSymb = symbm;\n } else {\n pStr.push(\n [nextSymb, mround(r * scr[1]), \", \", mround(r * scr[2])].join(\"\")\n );\n if (nextSymb === symbc) {\n i += 1;\n scr = el.points[i].scrCoords;\n pStr.push(\n [\" \", mround(r * scr[1]), \", \", mround(r * scr[2])].join(\"\")\n );\n i += 1;\n scr = el.points[i].scrCoords;\n pStr.push(\n [\" \", mround(r * scr[1]), \", \", mround(r * scr[2])].join(\"\")\n );\n }\n nextSymb = symbc;\n }\n i += 1;\n }\n }\n pStr.push(\" e\");\n return pStr;\n },\n\n // Already documented in JXG.AbstractRenderer\n updatePathStringBezierPrim: function (el) {\n var i,\n j,\n k,\n scr,\n lx,\n ly,\n pStr = [],\n f = el.evalVisProp('strokewidth'),\n r = this.resolution,\n mround = Math.round,\n symbm = \" m \",\n symbl = \" c \",\n nextSymb = symbm,\n isNoPlot = el.evalVisProp('curvetype') !== \"plot\",\n len = Math.min(el.numberPoints, 8192); // otherwise IE 7 crashes in hilbert.html\n\n if (el.numberPoints <= 0) {\n return \"\";\n }\n if (isNoPlot && el.board.options.curve.RDPsmoothing) {\n el.points = Numerics.RamerDouglasPeucker(el.points, 1.0);\n }\n len = Math.min(len, el.points.length);\n\n for (j = 1; j < 3; j++) {\n nextSymb = symbm;\n for (i = 0; i < len; i++) {\n scr = el.points[i].scrCoords;\n if (isNaN(scr[1]) || isNaN(scr[2])) {\n // PenUp\n nextSymb = symbm;\n } else {\n // IE has problems with values being too far away.\n if (scr[1] > 20000.0) {\n scr[1] = 20000.0;\n } else if (scr[1] < -20000.0) {\n scr[1] = -20000.0;\n }\n\n if (scr[2] > 20000.0) {\n scr[2] = 20000.0;\n } else if (scr[2] < -20000.0) {\n scr[2] = -20000.0;\n }\n\n if (nextSymb === symbm) {\n pStr.push(\n [nextSymb, mround(r * scr[1]), \" \", mround(r * scr[2])].join(\"\")\n );\n } else {\n k = 2 * j;\n pStr.push(\n [\n nextSymb,\n mround(\n r *\n (lx +\n (scr[1] - lx) * 0.333 +\n f * (k * Math.random() - j))\n ),\n \" \",\n mround(\n r *\n (ly +\n (scr[2] - ly) * 0.333 +\n f * (k * Math.random() - j))\n ),\n \" \",\n mround(\n r *\n (lx +\n (scr[1] - lx) * 0.666 +\n f * (k * Math.random() - j))\n ),\n \" \",\n mround(\n r *\n (ly +\n (scr[2] - ly) * 0.666 +\n f * (k * Math.random() - j))\n ),\n \" \",\n mround(r * scr[1]),\n \" \",\n mround(r * scr[2])\n ].join(\"\")\n );\n }\n nextSymb = symbl;\n lx = scr[1];\n ly = scr[2];\n }\n }\n }\n pStr.push(\" e\");\n return pStr;\n },\n\n // Already documented in JXG.AbstractRenderer\n updatePolygonPrim: function (node, el) {\n var i,\n len = el.vertices.length,\n r = this.resolution,\n scr,\n pStr = [];\n\n this._setAttr(node, \"stroked\", 'false');\n scr = el.vertices[0].coords.scrCoords;\n\n if (isNaN(scr[1] + scr[2])) {\n return;\n }\n\n pStr.push(\n [\"m \", Math.floor(r * scr[1]), \",\", Math.floor(r * scr[2]), \" l \"].join(\"\")\n );\n\n for (i = 1; i < len - 1; i++) {\n if (el.vertices[i].isReal) {\n scr = el.vertices[i].coords.scrCoords;\n\n if (isNaN(scr[1] + scr[2])) {\n return;\n }\n\n pStr.push(Math.floor(r * scr[1]) + \",\" + Math.floor(r * scr[2]));\n } else {\n this.updatePathPrim(node, \"\", el.board);\n return;\n }\n if (i < len - 2) {\n pStr.push(\", \");\n }\n }\n pStr.push(\" x e\");\n this.updatePathPrim(node, pStr, el.board);\n },\n\n // Already documented in JXG.AbstractRenderer\n updateRectPrim: function (node, x, y, w, h) {\n node.style.left = Math.floor(x) + 'px';\n node.style.top = Math.floor(y) + 'px';\n\n if (w >= 0) {\n node.style.width = w + 'px';\n }\n\n if (h >= 0) {\n node.style.height = h + 'px';\n }\n },\n\n /* **************************\n * Set Attributes\n * **************************/\n\n // Already documented in JXG.AbstractRenderer\n setPropertyPrim: function (node, key, val) {\n var keyVml = \"\",\n v;\n\n switch (key) {\n case \"stroke\":\n keyVml = 'strokecolor';\n break;\n case \"stroke-width\":\n keyVml = 'strokeweight';\n break;\n case \"stroke-dasharray\":\n keyVml = 'dashstyle';\n break;\n }\n\n if (keyVml !== \"\") {\n v = val;\n this._setAttr(node, keyVml, v);\n }\n },\n\n // Already documented in JXG.AbstractRenderer\n display: function (el, val) {\n if (el && el.rendNode) {\n el.visPropOld.visible = val;\n if (val) {\n el.rendNode.style.visibility = 'inherit';\n } else {\n el.rendNode.style.visibility = 'hidden';\n }\n }\n },\n\n // Already documented in JXG.AbstractRenderer\n show: function (el) {\n JXG.deprecated(\"Board.renderer.show()\", \"Board.renderer.display()\");\n\n if (el && el.rendNode) {\n el.rendNode.style.visibility = 'inherit';\n }\n },\n\n // Already documented in JXG.AbstractRenderer\n hide: function (el) {\n JXG.deprecated(\"Board.renderer.hide()\", \"Board.renderer.display()\");\n\n if (el && el.rendNode) {\n el.rendNode.style.visibility = 'hidden';\n }\n },\n\n // Already documented in JXG.AbstractRenderer\n setDashStyle: function (el, visProp) {\n var node;\n if (visProp.dash >= 0) {\n node = el.rendNodeStroke;\n this._setAttr(node, \"dashstyle\", this.dashArray[visProp.dash]);\n }\n },\n\n // Already documented in JXG.AbstractRenderer\n setGradient: function (el) {\n var nodeFill = el.rendNodeFill,\n ev_g = el.evalVisProp('gradient');\n\n if (ev_g === 'linear') {\n this._setAttr(nodeFill, \"type\", 'gradient');\n this._setAttr(\n nodeFill,\n \"color2\",\n el.evalVisProp('gradientsecondcolor')\n );\n this._setAttr(\n nodeFill,\n \"opacity2\",\n el.evalVisProp('gradientsecondopacity')\n );\n this._setAttr(nodeFill, \"angle\", el.evalVisProp('gradientangle'));\n } else if (ev_g === 'radial') {\n this._setAttr(nodeFill, \"type\", 'gradientradial');\n this._setAttr(\n nodeFill,\n \"color2\",\n el.evalVisProp('gradientsecondcolor')\n );\n this._setAttr(\n nodeFill,\n \"opacity2\",\n el.evalVisProp('gradientsecondopacity')\n );\n this._setAttr(\n nodeFill,\n \"focusposition\",\n el.evalVisProp('gradientpositionx') * 100 +\n \"%,\" +\n el.evalVisProp('gradientpositiony') * 100 +\n \"%\"\n );\n this._setAttr(nodeFill, \"focussize\", \"0,0\");\n } else {\n this._setAttr(nodeFill, \"type\", 'solid');\n }\n },\n\n // Already documented in JXG.AbstractRenderer\n setObjectFillColor: function (el, color, opacity) {\n var rgba = color,\n c,\n rgbo,\n o = opacity,\n oo,\n node = el.rendNode;\n\n o = o > 0 ? o : 0;\n\n if (el.visPropOld.fillcolor === rgba && el.visPropOld.fillopacity === o) {\n return;\n }\n\n if (Type.exists(rgba) && rgba !== false) {\n // RGB, not RGBA\n if (rgba.length !== 9) {\n c = rgba;\n oo = o;\n // True RGBA, not RGB\n } else {\n rgbo = Color.rgba2rgbo(rgba);\n c = rgbo[0];\n oo = o * rgbo[1];\n }\n if (c === \"none\" || c === false) {\n this._setAttr(el.rendNode, \"filled\", 'false');\n } else {\n this._setAttr(el.rendNode, \"filled\", 'true');\n this._setAttr(el.rendNode, \"fillcolor\", c);\n\n if (Type.exists(oo) && el.rendNodeFill) {\n this._setAttr(el.rendNodeFill, \"opacity\", oo * 100 + \"%\");\n }\n }\n if (el.type === Const.OBJECT_TYPE_IMAGE) {\n /*\n t = el.rendNode.style.filter.toString();\n if (t.match(/alpha/)) {\n el.rendNode.style.filter = t.replace(/alpha\\(opacity *= *[0-9\\.]+\\)/, 'alpha(opacity = ' + (oo * 100) + ')');\n } else {\n el.rendNode.style.filter += ' alpha(opacity = ' + (oo * 100) + ')';\n }\n */\n if (node.filters.length > 1) {\n // Why am I sometimes seeing node.filters.length==0 here when I move the pointer around near [0,0]?\n // Setting axes:true shows text labels!\n node.filters.item(1).opacity = Math.round(oo * 100); // Why does setObjectFillColor not use Math.round?\n node.filters.item(1).enabled = true;\n }\n }\n }\n el.visPropOld.fillcolor = rgba;\n el.visPropOld.fillopacity = o;\n },\n\n // Already documented in JXG.AbstractRenderer\n setObjectStrokeColor: function (el, color, opacity) {\n var rgba = color,\n c,\n rgbo,\n o = opacity,\n oo,\n node = el.rendNode,\n nodeStroke;\n\n o = o > 0 ? o : 0;\n\n if (el.visPropOld.strokecolor === rgba && el.visPropOld.strokeopacity === o) {\n return;\n }\n\n // this looks like it could be merged with parts of VMLRenderer.setObjectFillColor\n\n if (Type.exists(rgba) && rgba !== false) {\n // RGB, not RGBA\n if (rgba.length !== 9) {\n c = rgba;\n oo = o;\n // True RGBA, not RGB\n } else {\n rgbo = color.rgba2rgbo(rgba);\n c = rgbo[0];\n oo = o * rgbo[1];\n }\n if (el.elementClass === Const.OBJECT_CLASS_TEXT) {\n //node.style.filter = ' alpha(opacity = ' + oo + ')';\n /*\n t = node.style.filter.toString();\n if (t.match(/alpha/)) {\n node.style.filter =\n t.replace(/alpha\\(opacity *= *[0-9\\.]+\\)/, 'alpha(opacity = ' + oo + ')');\n } else {\n node.style.filter += ' alpha(opacity = ' + oo + ')';\n }\n */\n if (node.filters.length > 1) {\n // Why am I sometimes seeing node.filters.length==0 here when I move the pointer around near [0,0]?\n // Setting axes:true shows text labels!\n node.filters.item(1).opacity = Math.round(oo * 100);\n node.filters.item(1).enabled = true;\n }\n\n node.style.color = c;\n } else {\n if (c !== false) {\n this._setAttr(node, \"stroked\", 'true');\n this._setAttr(node, \"strokecolor\", c);\n }\n\n nodeStroke = el.rendNodeStroke;\n if (Type.exists(oo) && el.type !== Const.OBJECT_TYPE_IMAGE) {\n this._setAttr(nodeStroke, \"opacity\", oo * 100 + \"%\");\n }\n }\n }\n el.visPropOld.strokecolor = rgba;\n el.visPropOld.strokeopacity = o;\n },\n\n // Already documented in JXG.AbstractRenderer\n setObjectStrokeWidth: function (el, width) {\n var w = Type.evaluate(width),\n node;\n\n if (isNaN(w) || el.visPropOld.strokewidth === w) {\n return;\n }\n\n node = el.rendNode;\n this.setPropertyPrim(node, \"stroked\", 'true');\n\n if (Type.exists(w)) {\n this.setPropertyPrim(node, \"stroke-width\", w);\n if (w === 0 && Type.exists(el.rendNodeStroke)) {\n this._setAttr(node, \"stroked\", 'false');\n }\n }\n\n el.visPropOld.strokewidth = w;\n },\n\n // Already documented in JXG.AbstractRenderer\n setShadow: function (el) {\n var nodeShadow = el.rendNodeShadow,\n ev_s = el.evalVisProp('shadow');\n\n if (!nodeShadow || el.visPropOld.shadow === ev_s) {\n return;\n }\n\n if (ev_s) {\n this._setAttr(nodeShadow, \"On\", 'True');\n this._setAttr(nodeShadow, \"Offset\", \"3pt,3pt\");\n this._setAttr(nodeShadow, \"Opacity\", \"60%\");\n this._setAttr(nodeShadow, \"Color\", \"#aaaaaa\");\n } else {\n this._setAttr(nodeShadow, \"On\", 'False');\n }\n\n el.visPropOld.shadow = ev_s;\n },\n\n /* **************************\n * renderer control\n * **************************/\n\n // Already documented in JXG.AbstractRenderer\n suspendRedraw: function () {\n this.container.style.display = 'none';\n },\n\n // Already documented in JXG.AbstractRenderer\n unsuspendRedraw: function () {\n this.container.style.display = \"\";\n }\n }\n);\n\nexport default JXG.VMLRenderer;\n","/**\n * Generate a random uuid.\n * Written by https://www.broofa.com (robert@broofa.com)\n *\n * Copyright (c) 2010 Robert Kieffer\n * Dual licensed under the MIT and GPL licenses.\n * @returns {String}\n * @example\n * var uuid = JXG.Util.genUUID();\n * > uuid = '92329D39-6F5C-4520-ABFC-AAB64544E172'\n */\n\n/*global JXG: true, define: true*/\n/*jslint nomen: true, plusplus: true, bitwise: true*/\n\nimport JXG from \"../jxg.js\";\n\n// constants\nvar uuidCharsStr = \"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz\",\n uuidChars = uuidCharsStr.split(\"\");\n\n/**\n * General utility routines\n * @namespace\n */\nJXG.Util = JXG.Util || {};\n\nJXG.Util.genUUID = function (prefix) {\n var r,\n i,\n uuid = [],\n rnd = 0;\n\n prefix = prefix || \"\";\n\n if (prefix !== \"\" && prefix.slice(prefix.length - 1) !== \"-\") {\n prefix = prefix + \"-\";\n }\n\n for (i = 0; i < 36; i++) {\n if (i === 8 || i === 13 || i === 18 || i === 23) {\n uuid[i] = \"-\";\n } else if (i === 14) {\n uuid[i] = '4';\n } else {\n if (rnd <= 0x02) {\n rnd = (0x2000000 + Math.random() * 0x1000000) | 0;\n }\n\n r = rnd & 0xf;\n rnd = rnd >> 4;\n uuid[i] = uuidChars[i === 19 ? (r & 0x3) | 0x8 : r];\n }\n }\n\n return prefix + uuid.join(\"\");\n};\n\nexport default JXG.Util;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *\n *\n * @example\n * const board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-10, 10, 10, -10],\n * axis: true,\n * showCopyright: true,\n * showFullscreen: true,\n * showScreenshot: false,\n * showClearTraces: false,\n * showInfobox: false,\n * showNavigation: true,\n * grid: false,\n * defaultAxes: {\n * x: {\n * withLabel: true,\n * label: {\n * position: '95% left',\n * offset: [-10, 10]\n * },\n * lastArrow: {\n * type: 4,\n * size: 10\n * }\n * },\n * y: {\n * withLabel: true,\n * label: {\n * position: '0.90fr right',\n * offset: [6, -6]\n * },\n * lastArrow: {\n * type: 4,\n * size: 10\n * }\n * }\n * }\n * });\n *\n * \n * \n * @example\n * const board = JXG.JSXGraph.initBoard('jxgbox', {\n * boundingbox: [-5, 5, 5, -5],\n * intl: {\n * enabled: false,\n * locale: 'en-EN'\n * },\n * keepaspectratio: true,\n * axis: true,\n * defaultAxes: {\n * x: {\n * ticks: {\n * intl: {\n * enabled: true,\n * options: {\n * style: 'unit',\n * unit: 'kilometer-per-hour',\n * unitDisplay: 'narrow'\n * }\n * }\n * }\n * },\n * y: {\n * ticks: {\n * }\n * }\n * },\n * infobox: {\n * fontSize: 20,\n * intl: {\n * enabled: true,\n * options: {\n * minimumFractionDigits: 4,\n * maximumFractionDigits: 5\n * }\n * }\n * }\n * });\n *\n * \n * \n *\n *\n */\n // *\n // * @param {Array} [attributes.boundingbox=[-5, 5, 5, -5]] An array containing four numbers describing the left, top, right and bottom boundary of the board in user coordinates\n // * @param {Boolean} [attributes.keepaspectratio=false] If true, the bounding box is adjusted to the same aspect ratio as the aspect ratio of the div containing the board.\n // * @param {Boolean} [attributes.showCopyright=false] Show the copyright string in the top left corner.\n // * @param {Boolean} [attributes.showNavigation=false] Show the navigation buttons in the bottom right corner.\n // * @param {Object} [attributes.zoom] Allow the user to zoom with the mouse wheel or the two-fingers-zoom gesture.\n // * @param {Object} [attributes.pan] Allow the user to pan with shift+drag mouse or two-fingers-pan gesture.\n // * @param {Object} [attributes.drag] Allow the user to drag objects with a pointer device.\n // * @param {Object} [attributes.keyboard] Allow the user to drag objects with arrow keys on keyboard.\n // * @param {Boolean} [attributes.axis=false] If set to true, show the axis. Can also be set to an object that is given to both axes as an attribute object.\n // * @param {Boolean|Object} [attributes.grid] If set to true, shows the grid. Can also be set to an object that is given to the grid as its attribute object.\n // * @param {Boolean} [attributes.registerEvents=true] Register mouse / touch events.\n initBoard: function (box, attributes) {\n var originX, originY, unitX, unitY, w, h,\n offX = 0, offY = 0,\n renderer, dimensions, bbox,\n attr, axattr, axattr_x, axattr_y,\n options,\n theme = {},\n board;\n\n attributes = attributes || {}; // User supplied attributes\n // Merge a possible theme\n if (attributes.theme !== 'default' && Type.exists(JXG.themes[attributes.theme])) {\n theme = JXG.themes[attributes.theme];\n }\n options = Type.deepCopy(Options, theme, true); // Copy global options\n attr = this._setAttributes(attributes, options); // Merge user supplied attributes into global options\n\n dimensions = Env.getDimensions(box, attr.document);\n\n if (attr.unitx || attr.unity) {\n originX = Type.def(attr.originx, 150);\n originY = Type.def(attr.originy, 150);\n unitX = Type.def(attr.unitx, 50);\n unitY = Type.def(attr.unity, 50);\n } else {\n bbox = attr.boundingbox;\n if (bbox[0] < attr.maxboundingbox[0]) {\n bbox[0] = attr.maxboundingbox[0];\n }\n if (bbox[1] > attr.maxboundingbox[1]) {\n bbox[1] = attr.maxboundingbox[1];\n }\n if (bbox[2] > attr.maxboundingbox[2]) {\n bbox[2] = attr.maxboundingbox[2];\n }\n if (bbox[3] < attr.maxboundingbox[3]) {\n bbox[3] = attr.maxboundingbox[3];\n }\n\n // Size of HTML div.\n // If zero, the size is set to a small value to avoid\n // division by zero.\n // w = Math.max(parseInt(dimensions.width, 10), Mat.eps);\n // h = Math.max(parseInt(dimensions.height, 10), Mat.eps);\n w = parseInt(dimensions.width, 10);\n h = parseInt(dimensions.height, 10);\n\n if (Type.exists(bbox) && attr.keepaspectratio) {\n /*\n * If the boundingbox attribute is given and the ratio of height and width of the\n * sides defined by the bounding box and the ratio of the dimensions of the div tag\n * which contains the board do not coincide, then the smaller side is chosen.\n */\n unitX = w / (bbox[2] - bbox[0]);\n unitY = h / (bbox[1] - bbox[3]);\n\n if (Math.abs(unitX) < Math.abs(unitY)) {\n unitY = (Math.abs(unitX) * unitY) / Math.abs(unitY);\n // Add the additional units in equal portions above and below\n offY = (h / unitY - (bbox[1] - bbox[3])) * 0.5;\n } else {\n unitX = (Math.abs(unitY) * unitX) / Math.abs(unitX);\n // Add the additional units in equal portions left and right\n offX = (w / unitX - (bbox[2] - bbox[0])) * 0.5;\n }\n } else {\n unitX = w / (bbox[2] - bbox[0]);\n unitY = h / (bbox[1] - bbox[3]);\n }\n originX = -unitX * (bbox[0] - offX);\n originY = unitY * (bbox[1] + offY);\n }\n\n renderer = this.initRenderer(box, dimensions, attr.document, attr.renderer);\n this._setARIA(box, attr);\n\n // Create the board.\n // board.options will contain the user supplied board attributes\n board = new Board(\n box,\n renderer,\n attr.id,\n [originX, originY],\n /*attr.zoomfactor * */ attr.zoomx,\n /*attr.zoomfactor * */ attr.zoomy,\n unitX,\n unitY,\n dimensions.width,\n dimensions.height,\n attr\n );\n\n board.keepaspectratio = attr.keepaspectratio;\n\n this._fillBoard(board, attr, dimensions);\n\n // Create elements like axes, grid, navigation, ...\n board.suspendUpdate();\n attr = board.attr;\n if (attr.axis) {\n axattr = typeof attr.axis === \"object\" ? attr.axis : {};\n\n // The defaultAxes attributes are overwritten by user supplied axis object.\n axattr_x = Type.deepCopy(options.board.defaultaxes.x, axattr);\n axattr_y = Type.deepCopy(options.board.defaultaxes.y, axattr);\n\n // The user supplied defaultAxes attributes are merged in.\n if (attr.defaultaxes.x) {\n axattr_x = Type.deepCopy(axattr_x, attr.defaultaxes.x);\n }\n if (attr.defaultaxes.y) {\n axattr_y = Type.deepCopy(axattr_y, attr.defaultaxes.y);\n }\n\n board.defaultAxes = {};\n board.defaultAxes.x = board.create(\"axis\", [[0, 0], [1, 0]], axattr_x);\n board.defaultAxes.y = board.create(\"axis\", [[0, 0], [0, 1]], axattr_y);\n }\n if (attr.grid) {\n board.create(\"grid\", [], typeof attr.grid === \"object\" ? attr.grid : {});\n }\n\n board.sketches = [\n board.create('sketchcurve', [], board.attr.sketches[0]),\n board.create('sketchcurve', [], board.attr.sketches[1])\n ];\n board.sketches[0].dump = false;\n board.sketches[1].dump = false;\n board.sketch = board.sketches[0];\n\n board.unsuspendUpdate();\n\n // Set CSS styles of JSXGraph div\n board.setAttribute({cssStyle: attr.cssstyle}, true);\n\n return board;\n },\n\n /**\n * Load a board from a file containing a construction made with either GEONExT,\n * Intergeo, Geogebra, or Cinderella.\n * @param {String|Object} box id of or reference to the HTML element in which the board is painted.\n * @param {String} file base64 encoded string.\n * @param {String} format containing the file format: 'Geonext' or 'Intergeo'.\n * @param {Object} attributes Attributes for the board and 'encoding'.\n * Compressed files need encoding 'iso-8859-1'. Otherwise it probably is 'utf-8'.\n * @param {Function} callback\n * @returns {JXG.Board} Reference to the created board.\n * @see JXG.FileReader\n * @see JXG.GeonextReader\n * @see JXG.GeogebraReader\n * @see JXG.IntergeoReader\n * @see JXG.CinderellaReader\n *\n * @example\n * // Uncompressed file\n * var board = JXG.JSXGraph.loadBoardFromFile('jxgbox', 'filename', 'geonext',\n * {encoding: 'utf-8'},\n * function (board) { console.log(\"Done loading\"); }\n * );\n * // Compressed file\n * var board = JXG.JSXGraph.loadBoardFromFile('jxgbox', 'filename', 'geonext',\n * {encoding: 'iso-8859-1'},\n * function (board) { console.log(\"Done loading\"); }\n * );\n *\n * @example\n * // From \n * var file = document.getElementById('localfile').files[0];\n * JXG.JSXGraph.loadBoardFromFile('jxgbox', file, 'geonext',\n * {encoding: 'utf-8'},\n * function (board) { console.log(\"Done loading\"); }\n * );\n */\n loadBoardFromFile: function (box, file, format, attributes, callback) {\n var attr, renderer, board, dimensions, encoding;\n\n attributes = attributes || {};\n attr = this._setAttributes(attributes);\n\n dimensions = Env.getDimensions(box, attr.document);\n renderer = this.initRenderer(box, dimensions, attr.document, attr.renderer);\n this._setARIA(box, attr);\n\n /* User default parameters, in parse* the values in the gxt files are submitted to board */\n board = new Board(\n box,\n renderer,\n \"\",\n [150, 150],\n 1,\n 1,\n 50,\n 50,\n dimensions.width,\n dimensions.height,\n attr\n );\n this._fillBoard(board, attr, dimensions);\n encoding = attr.encoding || \"iso-8859-1\";\n FileReader.parseFileContent(file, board, format, true, encoding, callback);\n\n return board;\n },\n\n /**\n * Load a board from a base64 encoded string containing a construction made with either GEONExT,\n * Intergeo, Geogebra, or Cinderella.\n * @param {String|Object} box id of or reference to the HTML element in which the board is painted.\n * @param {String} string base64 encoded string.\n * @param {String} format containing the file format: 'Geonext', 'Intergeo', 'Geogebra'.\n * @param {Object} attributes Attributes for the board and 'encoding'.\n * Compressed files need encoding 'iso-8859-1'. Otherwise it probably is 'utf-8'.\n * @param {Function} callback\n * @returns {JXG.Board} Reference to the created board.\n * @see JXG.FileReader\n * @see JXG.GeonextReader\n * @see JXG.GeogebraReader\n * @see JXG.IntergeoReader\n * @see JXG.CinderellaReader\n */\n loadBoardFromString: function (box, string, format, attributes, callback) {\n var attr, renderer, board, dimensions;\n\n attributes = attributes || {};\n attr = this._setAttributes(attributes);\n\n dimensions = Env.getDimensions(box, attr.document);\n renderer = this.initRenderer(box, dimensions, attr.document, attr.renderer);\n this._setARIA(box, attr);\n\n /* User default parameters, in parse* the values in the gxt files are submitted to board */\n board = new Board(\n box,\n renderer,\n \"\",\n [150, 150],\n 1.0,\n 1.0,\n 50,\n 50,\n dimensions.width,\n dimensions.height,\n attr\n );\n this._fillBoard(board, attr, dimensions);\n FileReader.parseString(string, board, format, true, callback);\n\n return board;\n },\n\n /**\n * Delete a board and all its contents.\n * @param {JXG.Board|String} board id of or reference to the DOM element in which the board is drawn.\n *\n */\n freeBoard: function (board) {\n var el;\n\n if (typeof board === 'string') {\n board = JXG.boards[board];\n }\n\n this._removeARIANodes(board);\n board.removeEventHandlers();\n board.suspendUpdate();\n\n // Remove all objects from the board.\n for (el in board.objects) {\n if (board.objects.hasOwnProperty(el)) {\n board.objects[el].remove();\n }\n }\n\n // Remove all the other things, left on the board, XHTML save\n while (board.containerObj.firstChild) {\n board.containerObj.removeChild(board.containerObj.firstChild);\n }\n\n // Tell the browser the objects aren't needed anymore\n for (el in board.objects) {\n if (board.objects.hasOwnProperty(el)) {\n delete board.objects[el];\n }\n }\n\n // Free the renderer and the algebra object\n delete board.renderer;\n\n // clear the creator cache\n board.jc.creator.clearCache();\n delete board.jc;\n\n // Finally remove the board itself from the boards array\n delete JXG.boards[board.id];\n },\n\n /**\n * @deprecated Use JXG#registerElement\n * @param element\n * @param creator\n */\n registerElement: function (element, creator) {\n JXG.deprecated(\"JXG.JSXGraph.registerElement()\", \"JXG.registerElement()\");\n JXG.registerElement(element, creator);\n }\n};\n\n// JessieScript/JessieCode startup:\n// Search for script tags of type text/jessiecode and execute them.\nif (Env.isBrowser && typeof window === 'object' && typeof document === 'object') {\n Env.addEvent(window, 'load',\n function () {\n var type, i, j, div, id,\n board, txt, width, height, maxWidth, aspectRatio,\n cssClasses, bbox, axis, grid, code, src, request,\n postpone = false,\n\n scripts = document.getElementsByTagName('script'),\n init = function (code, type, bbox) {\n var board = JXG.JSXGraph.initBoard(id, {\n boundingbox: bbox,\n keepaspectratio: true,\n grid: grid,\n axis: axis,\n showReload: true\n });\n\n if (type.toLowerCase().indexOf('script') > -1) {\n board.construct(code);\n } else {\n try {\n board.jc.parse(code);\n } catch (e2) {\n JXG.debug(e2);\n }\n }\n\n return board;\n },\n makeReload = function (board, code, type, bbox) {\n return function () {\n var newBoard;\n\n JXG.JSXGraph.freeBoard(board);\n newBoard = init(code, type, bbox);\n newBoard.reload = makeReload(newBoard, code, type, bbox);\n };\n };\n\n for (i = 0; i < scripts.length; i++) {\n type = scripts[i].getAttribute(\"type\", false);\n\n if (\n Type.exists(type) &&\n (type.toLowerCase() === \"text/jessiescript\" ||\n type.toLowerCase() === \"jessiescript\" ||\n type.toLowerCase() === \"text/jessiecode\" ||\n type.toLowerCase() === 'jessiecode')\n ) {\n cssClasses = scripts[i].getAttribute(\"class\", false) || \"\";\n width = scripts[i].getAttribute(\"width\", false) || \"\";\n height = scripts[i].getAttribute(\"height\", false) || \"\";\n maxWidth = scripts[i].getAttribute(\"maxwidth\", false) || \"100%\";\n aspectRatio = scripts[i].getAttribute(\"aspectratio\", false) || \"1/1\";\n bbox = scripts[i].getAttribute(\"boundingbox\", false) || \"-5, 5, 5, -5\";\n id = scripts[i].getAttribute(\"container\", false);\n src = scripts[i].getAttribute(\"src\", false);\n\n bbox = bbox.split(\",\");\n if (bbox.length !== 4) {\n bbox = [-5, 5, 5, -5];\n } else {\n for (j = 0; j < bbox.length; j++) {\n bbox[j] = parseFloat(bbox[j]);\n }\n }\n axis = Type.str2Bool(scripts[i].getAttribute(\"axis\", false) || 'false');\n grid = Type.str2Bool(scripts[i].getAttribute(\"grid\", false) || 'false');\n\n if (!Type.exists(id)) {\n id = \"jessiescript_autgen_jxg_\" + i;\n div = document.createElement('div');\n div.setAttribute(\"id\", id);\n\n txt = width !== \"\" ? \"width:\" + width + \";\" : \"\";\n txt += height !== \"\" ? \"height:\" + height + \";\" : \"\";\n txt += maxWidth !== \"\" ? \"max-width:\" + maxWidth + \";\" : \"\";\n txt += aspectRatio !== \"\" ? \"aspect-ratio:\" + aspectRatio + \";\" : \"\";\n\n div.setAttribute(\"style\", txt);\n div.setAttribute(\"class\", \"jxgbox \" + cssClasses);\n try {\n document.body.insertBefore(div, scripts[i]);\n } catch (e) {\n // there's probably jquery involved...\n if (Type.exists(jQuery) && typeof jQuery === 'object') {\n jQuery(div).insertBefore(scripts[i]);\n }\n }\n } else {\n div = document.getElementById(id);\n }\n\n code = \"\";\n\n if (Type.exists(src)) {\n postpone = true;\n request = new XMLHttpRequest();\n request.open(\"GET\", src);\n request.overrideMimeType(\"text/plain; charset=x-user-defined\");\n /* jshint ignore:start */\n request.addEventListener(\"load\", function () {\n if (this.status < 400) {\n code = this.responseText + \"\\n\" + code;\n board = init(code, type, bbox);\n board.reload = makeReload(board, code, type, bbox);\n } else {\n throw new Error(\n \"\\nJSXGraph: failed to load file\",\n src,\n \":\",\n this.responseText\n );\n }\n });\n request.addEventListener(\"error\", function (e) {\n throw new Error(\"\\nJSXGraph: failed to load file\", src, \":\", e);\n });\n /* jshint ignore:end */\n request.send();\n } else {\n postpone = false;\n }\n\n if (document.getElementById(id)) {\n code = scripts[i].innerHTML;\n code = code.replace(//g, \"\");\n scripts[i].innerHTML = code;\n\n if (!postpone) {\n // Do no wait for data from \"src\" attribute\n board = init(code, type, bbox);\n board.reload = makeReload(board, code, type, bbox);\n }\n } else {\n JXG.debug(\n \"JSXGraph: Apparently the div injection failed. Can't create a board, sorry.\"\n );\n }\n }\n }\n },\n window\n );\n}\n\nexport default JXG.JSXGraph;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
' +\n * 'point on seg: ' + point.isOn(seg) + '
' +\n * 'point on circ = ' + point.isOn(circ) + '
' +\n * 'point on point = ' + point.isOn(po) + '
' +\n * 'point on curve = ' + point.isOn(curve) + '
' +\n * 'point on polygon = ' + point.isOn(pol) + '
';\n * }]);\n *\n * \n *\n */\n isOn: function (el, tol) {\n var arr, crds;\n\n tol = tol || Mat.eps;\n\n if (Type.isPoint(el)) {\n return this.Dist(el) < tol;\n } else if (el.elementClass === Const.OBJECT_CLASS_LINE) {\n if (el.elType === \"segment\" && !this.evalVisProp('alwaysintersect')) {\n arr = JXG.Math.Geometry.projectCoordsToSegment(\n this.coords.usrCoords,\n el.point1.coords.usrCoords,\n el.point2.coords.usrCoords\n );\n if (\n arr[1] >= 0 &&\n arr[1] <= 1 &&\n Geometry.distPointLine(this.coords.usrCoords, el.stdform) < tol\n ) {\n return true;\n } else {\n return false;\n }\n } else {\n return Geometry.distPointLine(this.coords.usrCoords, el.stdform) < tol;\n }\n } else if (el.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n if (el.evalVisProp('hasinnerpoints')) {\n return this.Dist(el.center) < el.Radius() + tol;\n }\n return Math.abs(this.Dist(el.center) - el.Radius()) < tol;\n } else if (el.elementClass === Const.OBJECT_CLASS_CURVE) {\n crds = Geometry.projectPointToCurve(this, el, this.board)[0];\n return Geometry.distance(this.coords.usrCoords, crds.usrCoords, 3) < tol;\n } else if (el.type === Const.OBJECT_TYPE_POLYGON) {\n if (el.evalVisProp('hasinnerpoints')) {\n if (\n el.pnpoly(\n this.coords.usrCoords[1],\n this.coords.usrCoords[2],\n JXG.COORDS_BY_USER\n )\n ) {\n return true;\n }\n }\n arr = Geometry.projectCoordsToPolygon(this.coords.usrCoords, el);\n return Geometry.distance(this.coords.usrCoords, arr, 3) < tol;\n } else if (el.type === Const.OBJECT_TYPE_TURTLE) {\n crds = Geometry.projectPointToTurtle(this, el, this.board);\n return Geometry.distance(this.coords.usrCoords, crds.usrCoords, 3) < tol;\n }\n\n // TODO: Arc, Sector\n return false;\n },\n\n // Already documented in GeometryElement\n cloneToBackground: function () {\n var copy = Type.getCloneObject(this);\n\n this.board.renderer.drawPoint(copy);\n this.traces[copy.id] = copy.rendNode;\n\n return this;\n }\n }\n);\n\n/**\n * @class Construct a free or a fixed point. A free point is created if the given parent elements are all numbers\n * and the property fixed is not set or set to false. If one or more parent elements is not a number but a string containing a GEONExT\n * constraint or a function the point will be considered as constrained). That means that the user won't be able to change the point's\n * position directly.\n * @see Glider for a non-free point that is attached to another geometric element.\n * @pseudo\n * @name Point\n * @augments JXG.Point\n * @constructor\n * @type JXG.Point\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Number,string,function_Number,string,function_Number,string,function} z_,x,y Parent elements can be two or three elements of type number, a string containing a GEONExT\n * constraint, or a function which takes no parameter and returns a number. Every parent element determines one coordinate. If a coordinate is\n * given by a number, the number determines the initial position of a free point. If given by a string or a function that coordinate will be constrained\n * that means the user won't be able to change the point's position directly by mouse because it will be calculated automatically depending on the string\n * or the function's return value. If two parent elements are given the coordinates will be interpreted as 2D affine Euclidean coordinates, if three such\n * parent elements are given they will be interpreted as homogeneous coordinates.\n * @param {JXG.Point_JXG.Transformation_Array} Point,Transformation A point can also be created providing a transformation or an array of transformations.\n * The resulting point is a clone of the base point transformed by the given Transformation. {@see JXG.Transformation}.\n *\n * @example\n * // Create a free point using affine Euclidean coordinates\n * var p1 = board.create('point', [3.5, 2.0]);\n * \n * \n * @example\n * // Create a constrained point using anonymous function\n * var p2 = board.create('point', [3.5, function () { return p1.X(); }]);\n * \n * \n * @example\n * // Create a point using transformations\n * var trans = board.create('transform', [2, 0.5], {type:'scale'});\n * var p3 = board.create('point', [p2, trans]);\n * \n * \n */\nJXG.createPoint = function (board, parents, attributes) {\n var el, attr;\n\n attr = Type.copyAttributes(attributes, board.options, 'point');\n el = CoordsElement.create(JXG.Point, board, parents, attr);\n if (!el) {\n throw new Error(\n \"JSXGraph: Can't create point with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [x,y], [z,x,y], [element,transformation]\"\n );\n }\n\n return el;\n};\n\n/**\n * @class A glider is a point bound to a line, circle or curve or even another point.\n * @pseudo\n * @description A glider is a point which lives on another geometric element like a line, circle, curve, turtle.\n * @name Glider\n * @augments JXG.Point\n * @constructor\n * @type JXG.Point\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Number_Number_Number_JXG.GeometryElement} z_,x_,y_,GlideObject Parent elements can be two or three elements of type number and the object the glider lives on.\n * The coordinates are completely optional. If not given the origin is used. If you provide two numbers for coordinates they will be interpreted as affine Euclidean\n * coordinates, otherwise they will be interpreted as homogeneous coordinates. In any case the point will be projected on the glide object.\n * @example\n * // Create a glider with user defined coordinates. If the coordinates are not on\n * // the circle (like in this case) the point will be projected onto the circle.\n * var p1 = board.create('point', [2.0, 2.0]);\n * var c1 = board.create('circle', [p1, 2.0]);\n * var p2 = board.create('glider', [2.0, 1.5, c1]);\n * \n * \n * @example\n * // Create a glider with default coordinates (1,0,0). Same premises as above.\n * var p1 = board.create('point', [2.0, 2.0]);\n * var c1 = board.create('circle', [p1, 2.0]);\n * var p2 = board.create('glider', [c1]);\n * \n * \n *@example\n * //animate example 2\n * var p1 = board.create('point', [2.0, 2.0]);\n * var c1 = board.create('circle', [p1, 2.0]);\n * var p2 = board.create('glider', [c1]);\n * var button1 = board.create('button', [1, 7, 'start animation',function(){p2.startAnimation(1,4)}]);\n * var button2 = board.create('button', [1, 5, 'stop animation',function(){p2.stopAnimation()}]);\n * \n * \n */\nJXG.createGlider = function (board, parents, attributes) {\n var el,\n coords,\n attr = Type.copyAttributes(attributes, board.options, 'glider');\n\n if (parents.length === 1) {\n coords = [0, 0];\n } else {\n coords = parents.slice(0, 2);\n }\n el = board.create(\"point\", coords, attr);\n\n // eltype is set in here\n el.makeGlider(parents[parents.length - 1]);\n\n return el;\n};\n\n/**\n * @class A point intersecting two 1-dimensional elements.\n * It is one point of the set consisting of the intersection points of the two elements.\n * The following element types can be (mutually) intersected: line, circle,\n * curve, polygon, polygonal chain.\n *\n * @pseudo\n * @name Intersection\n * @augments JXG.Point\n * @constructor\n * @type JXG.Point\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Line,JXG.Circle_JXG.Line,JXG.Circle_Number|Function} el1,el2,i The result will be a intersection point on el1 and el2. i determines the\n * intersection point if two points are available: \n *
\n * @example\n * // Create an intersection point of circle and line\n * var p1 = board.create('point', [4.0, 4.0]);\n * var c1 = board.create('circle', [p1, 2.0]);\n *\n * var p2 = board.create('point', [1.0, 1.0]);\n * var p3 = board.create('point', [5.0, 3.0]);\n * var l1 = board.create('line', [p2, p3]);\n *\n * var i = board.create('intersection', [c1, l1, 0]);\n * \n * \n */\nJXG.createIntersectionPoint = function (board, parents, attributes) {\n var el, el1, el2, func,\n i, j,\n attr = Type.copyAttributes(attributes, board.options, 'intersection');\n\n // make sure we definitely have the indices\n parents.push(0, 0);\n\n el1 = board.select(parents[0]);\n el2 = board.select(parents[1]);\n\n i = parents[2] || 0;\n j = parents[3] || 0;\n\n el = board.create(\"point\", [0, 0, 0], attr);\n\n // el.visProp.alwaysintersect is evaluated as late as in the returned function\n func = Geometry.intersectionFunction(board, el1, el2, i, j, el.visProp.alwaysintersect);\n el.addConstraint([func]);\n\n try {\n el1.addChild(el);\n el2.addChild(el);\n } catch (e) {\n throw new Error(\n \"JSXGraph: Can't create 'intersection' with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\"\n );\n }\n\n el.type = Const.OBJECT_TYPE_INTERSECTION;\n el.elType = 'intersection';\n el.setParents([el1.id, el2.id]);\n\n /**\n * Array of length 2 containing the numbers i and j.\n * The intersection point is i-th intersection point.\n * j is unused.\n * @type Array\n * @name intersectionNumbers\n * @memberOf Intersection\n * @private\n */\n el.intersectionNumbers = [i, j];\n el.getParents = function () {\n return this.parents.concat(this.intersectionNumbers);\n };\n\n el.generatePolynomial = function () {\n var poly1 = el1.generatePolynomial(el),\n poly2 = el2.generatePolynomial(el);\n\n if (poly1.length === 0 || poly2.length === 0) {\n return [];\n }\n\n return [poly1[0], poly2[0]];\n };\n\n return el;\n};\n\n/**\n * @class Given a set of intersection points, this is another ('other') intersection point,\n * @pseudo\n * @description If two elements of type curve, circle or line intersect in more than one point, with this element it is possible\n * to construct the \"other\" intersection. This is a an intersection which is different from a supplied point or different from any\n * point in an array of supplied points. This might be helpful in situtations where one intersection point is already part of the construction\n * or in situtation where the order of the intersection points changes while interacting with the construction.\n *\n * @name OtherIntersection\n * @augments JXG.Point\n * @constructor\n * @type JXG.Point\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Line,JXG.Circle_JXG.Line,JXG.Circle_JXG.Point,Array} el1,el2,p Two elements which are intersected and a point or an array of points\n * which have to be different from the new intersection point.\n *\n * @example\n * // Create an intersection point of circle and line\n * var p1 = board.create('point', [2.0, 2.0]);\n * var c1 = board.create('circle', [p1, 2.0]);\n *\n * var p2 = board.create('point', [2.0, 2.0]);\n * var p3 = board.create('point', [2.0, 2.0]);\n * var l1 = board.create('line', [p2, p3]);\n *\n * var p1 = board.create('intersection', [c1, l1, 0]);\n * var p2 = board.create('otherintersection', [c1, l1, p1]);\n * \n * \n *\n * @example\n * // circle / circle\n * var c1 = board.create('circle', [[0, 0], 3]);\n * var c2 = board.create('circle', [[2, 2], 3]);\n *\n * var p1 = board.create('intersection', [c1, c2, 0]);\n * var p2 = board.create('otherintersection', [c1, c2, p1]);\n *\n * \n * \n *\n * @example\n * // curve / line\n * var curve = board.create('implicitcurve', ['-(y**2) + x**3 - 2 * x + 1'], { strokeWidth: 2 });\n * var A = board.create('glider', [-1.5, 1, curve]);\n * var B = board.create('glider', [0.5, 0.5, curve]);\n * var line = board.create('line', [A, B], { color: 'black', strokeWidth: 1 });\n * var C = board.create('otherintersection', [curve, line, [A, B]], {precision: 0.01});\n * var D = board.create('point', [() => C.X(), () => -C.Y()], { name: '-C = A + B' });\n *\n * \n * \n *\n * @example\n * // curve / curve\n * var c1 = board.create('functiongraph', ['x**2 - 3'], { strokeWidth: 2 });\n * var A = board.create('point', [0, 2]);\n * var c2 = board.create('functiongraph', [(x) => -(x**2) + 2 * A.X() * x + A.Y() - A.X()**2], { strokeWidth: 2 });\n * var p1 = board.create('intersection', [c1, c2]);\n * var p2 = board.create('otherintersection', [c1, c2, [p1]]);\n *\n * \n * \n *\n */\nJXG.createOtherIntersectionPoint = function (board, parents, attributes) {\n var el, el1, el2, i,\n others, func, input,\n isGood = true,\n attr = Type.copyAttributes(attributes, board.options, 'otherintersection');\n\n if (parents.length !== 3) {\n isGood = false;\n } else {\n el1 = board.select(parents[0]);\n el2 = board.select(parents[1]);\n if (Type.isArray(parents[2])) {\n others = parents[2];\n } else {\n others = [parents[2]];\n }\n\n for (i = 0; i < others.length; i++) {\n others[i] = board.select(others[i]);\n if (!Type.isPoint(others[i])) {\n isGood = false;\n break;\n }\n }\n if (isGood) {\n input = [el1, el2];\n // Sort parent elements in order: curve, circle, line\n input.sort(function (a, b) { return b.elementClass - a.elementClass; });\n\n // Two lines are forbidden:\n if ([Const.OBJECT_CLASS_CIRCLE, Const.OBJECT_CLASS_CURVE].indexOf(input[0].elementClass) < 0) {\n isGood = false;\n } else if ([Const.OBJECT_CLASS_CIRCLE, Const.OBJECT_CLASS_CURVE, Const.OBJECT_CLASS_LINE].indexOf(input[1].elementClass) < 0) {\n isGood = false;\n }\n }\n }\n\n if (!isGood) {\n throw new Error(\n \"JSXGraph: Can't create 'other intersection point' with parent types '\" +\n typeof parents[0] + \"', '\" + typeof parents[1] + \"'and '\" + typeof parents[2] + \"'.\" +\n \"\\nPossible parent types: [circle|curve|line,circle|curve|line, point], not two lines\"\n );\n }\n\n el = board.create('point', [0, 0, 0], attr);\n // el.visProp.alwaysintersect is evaluated as late as in the returned function\n func = Geometry.otherIntersectionFunction(input, others, el.visProp.alwaysintersect, el.visProp.precision);\n el.addConstraint([func]);\n\n el.type = Const.OBJECT_TYPE_INTERSECTION;\n el.elType = 'otherintersection';\n el.setParents([el1.id, el2.id]);\n el.addParents(others);\n\n el1.addChild(el);\n el2.addChild(el);\n\n if (el1.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n // circle, circle|line\n el.generatePolynomial = function () {\n var poly1 = el1.generatePolynomial(el),\n poly2 = el2.generatePolynomial(el);\n\n if (poly1.length === 0 || poly2.length === 0) {\n return [];\n }\n\n return [poly1[0], poly2[0]];\n };\n }\n\n return el;\n};\n\n/**\n * @class This element is used to provide a constructor for the pole point of a line with respect to a conic or a circle.\n * @pseudo\n * @description The pole point is the unique reciprocal relationship of a line with respect to a conic.\n * The lines tangent to the intersections of a conic and a line intersect at the pole point of that line with respect to that conic.\n * A line tangent to a conic has the pole point of that line with respect to that conic as the tangent point.\n * See {@link https://en.wikipedia.org/wiki/Pole_and_polar} for more information on pole and polar.\n * @name PolePoint\n * @augments JXG.Point\n * @constructor\n * @type JXG.Point\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Conic,JXG.Circle_JXG.Point} el1,el2 or\n * @param {JXG.Point_JXG.Conic,JXG.Circle} el1,el2 The result will be the pole point of the line with respect to the conic or the circle.\n * @example\n * // Create the pole point of a line with respect to a conic\n * var p1 = board.create('point', [-1, 2]);\n * var p2 = board.create('point', [ 1, 4]);\n * var p3 = board.create('point', [-1,-2]);\n * var p4 = board.create('point', [ 0, 0]);\n * var p5 = board.create('point', [ 4,-2]);\n * var c1 = board.create('conic',[p1,p2,p3,p4,p5]);\n * var p6 = board.create('point', [-1, 4]);\n * var p7 = board.create('point', [2, -2]);\n * var l1 = board.create('line', [p6, p7]);\n * var p8 = board.create('polepoint', [c1, l1]);\n * \n * \n * @example\n * // Create the pole point of a line with respect to a circle\n * var p1 = board.create('point', [1, 1]);\n * var p2 = board.create('point', [2, 3]);\n * var c1 = board.create('circle',[p1,p2]);\n * var p3 = board.create('point', [-1, 4]);\n * var p4 = board.create('point', [4, -1]);\n * var l1 = board.create('line', [p3, p4]);\n * var p5 = board.create('polepoint', [c1, l1]);\n * \n * \n */\nJXG.createPolePoint = function (board, parents, attributes) {\n var el,\n el1,\n el2,\n firstParentIsConic,\n secondParentIsConic,\n firstParentIsLine,\n secondParentIsLine;\n\n if (parents.length > 1) {\n firstParentIsConic =\n parents[0].type === Const.OBJECT_TYPE_CONIC ||\n parents[0].elementClass === Const.OBJECT_CLASS_CIRCLE;\n secondParentIsConic =\n parents[1].type === Const.OBJECT_TYPE_CONIC ||\n parents[1].elementClass === Const.OBJECT_CLASS_CIRCLE;\n\n firstParentIsLine = parents[0].elementClass === Const.OBJECT_CLASS_LINE;\n secondParentIsLine = parents[1].elementClass === Const.OBJECT_CLASS_LINE;\n }\n\n /* if (parents.length !== 2 || !((\n parents[0].type === Const.OBJECT_TYPE_CONIC ||\n parents[0].elementClass === Const.OBJECT_CLASS_CIRCLE) &&\n parents[1].elementClass === Const.OBJECT_CLASS_LINE ||\n parents[0].elementClass === Const.OBJECT_CLASS_LINE && (\n parents[1].type === Const.OBJECT_TYPE_CONIC ||\n parents[1].elementClass === Const.OBJECT_CLASS_CIRCLE))) {*/\n if (\n parents.length !== 2 ||\n !(\n (firstParentIsConic && secondParentIsLine) ||\n (firstParentIsLine && secondParentIsConic)\n )\n ) {\n // Failure\n throw new Error(\n \"JSXGraph: Can't create 'pole point' with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent type: [conic|circle,line], [line,conic|circle]\"\n );\n }\n\n if (secondParentIsLine) {\n el1 = board.select(parents[0]);\n el2 = board.select(parents[1]);\n } else {\n el1 = board.select(parents[1]);\n el2 = board.select(parents[0]);\n }\n\n el = board.create(\n \"point\",\n [\n function () {\n var q = el1.quadraticform,\n s = el2.stdform.slice(0, 3);\n\n return [\n JXG.Math.Numerics.det([s, q[1], q[2]]),\n JXG.Math.Numerics.det([q[0], s, q[2]]),\n JXG.Math.Numerics.det([q[0], q[1], s])\n ];\n }\n ],\n attributes\n );\n\n el.elType = 'polepoint';\n el.setParents([el1.id, el2.id]);\n\n el1.addChild(el);\n el2.addChild(el);\n\n return el;\n};\n\nJXG.registerElement(\"point\", JXG.createPoint);\nJXG.registerElement(\"glider\", JXG.createGlider);\nJXG.registerElement(\"intersection\", JXG.createIntersectionPoint);\nJXG.registerElement(\"otherintersection\", JXG.createOtherIntersectionPoint);\nJXG.registerElement(\"polepoint\", JXG.createPolePoint);\n\nexport default JXG.Point;\n// export default {\n// Point: JXG.Point,\n// createPoint: JXG.createPoint,\n// createGlider: JXG.createGlider,\n// createIntersection: JXG.createIntersectionPoint,\n// createOtherIntersection: JXG.createOtherIntersectionPoint,\n// createPolePoint: JXG.createPolePoint\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n * @returns {Number}\n */\n getAngle: function (unit) {\n var val,\n rad = Math.atan2(-this.stdform[1], this.stdform[2]);\n\n if (Type.isString(unit) && unit !== '') {\n unit = unit.toLocaleLowerCase();\n } else {\n return rad;\n }\n\n if (unit === '' || unit.indexOf('rad') === 0) {\n val = rad;\n } else if (unit.indexOf('deg') === 0) {\n val = rad * 180 / Math.PI;\n } else if (unit.indexOf('sem') === 0) {\n val = rad / Math.PI;\n } else if (unit.indexOf('cir') === 0) {\n val = rad * 0.5 / Math.PI;\n }\n\n return val;\n },\n\n /**\n * Returns the direction vector of the line. This is an array of length two\n * containing the direction vector as [x, y]. It is defined as\n * \n * @example\n * // Create a line using three coordinates\n * var l1 = board.create('line', [1.0, -2.0, 3.0]);\n * \n * \n * @example\n * // Create a line (l2) as reflection of another line (l1)\n * // reflection line\n * var li = board.create('line', [1,1,1], {strokeColor: '#aaaaaa'});\n * var reflect = board.create('transform', [li], {type: 'reflect'});\n *\n * var l1 = board.create('line', [1,-5,1]);\n * var l2 = board.create('line', [l1, reflect]);\n *\n * \n * \n *\n * @example\n * var t = board.create('transform', [2, 1.5], {type: 'scale'});\n * var l1 = board.create('line', [1, -5, 1]);\n * var l2 = board.create('line', [l1, t]);\n *\n * \n * \n *\n * @example\n * //create line between two points\n * var p1 = board.create('point', [0,0]);\n * var p2 = board.create('point', [2,2]);\n * var l1 = board.create('line', [p1,p2], {straightFirst:false, straightLast:false});\n * \n * \n */\nJXG.createLine = function (board, parents, attributes) {\n var ps, el, p1, p2, i, attr,\n c = [],\n doTransform = false,\n constrained = false,\n isDraggable;\n\n if (parents.length === 2) {\n // The line is defined by two points or coordinates of two points.\n // In the latter case, the points are created.\n attr = Type.copyAttributes(attributes, board.options, 'line', 'point1');\n if (Type.isArray(parents[0]) && parents[0].length > 1) {\n p1 = board.create(\"point\", parents[0], attr);\n } else if (Type.isString(parents[0]) || Type.isPoint(parents[0])) {\n p1 = board.select(parents[0]);\n } else if (Type.isFunction(parents[0]) && Type.isPoint(parents[0]())) {\n p1 = parents[0]();\n constrained = true;\n } else if (\n Type.isFunction(parents[0]) &&\n parents[0]().length &&\n parents[0]().length >= 2\n ) {\n p1 = JXG.createPoint(board, parents[0](), attr);\n constrained = true;\n } else if (Type.isObject(parents[0]) && Type.isTransformationOrArray(parents[1])) {\n doTransform = true;\n p1 = board.create(\"point\", [parents[0].point1, parents[1]], attr);\n } else {\n throw new Error(\n \"JSXGraph: Can't create line with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]\"\n );\n }\n\n // point 2 given by coordinates\n attr = Type.copyAttributes(attributes, board.options, \"line\", 'point2');\n if (doTransform) {\n p2 = board.create(\"point\", [parents[0].point2, parents[1]], attr);\n } else if (Type.isArray(parents[1]) && parents[1].length > 1) {\n p2 = board.create(\"point\", parents[1], attr);\n } else if (Type.isString(parents[1]) || Type.isPoint(parents[1])) {\n p2 = board.select(parents[1]);\n } else if (Type.isFunction(parents[1]) && Type.isPoint(parents[1]())) {\n p2 = parents[1]();\n constrained = true;\n } else if (\n Type.isFunction(parents[1]) &&\n parents[1]().length &&\n parents[1]().length >= 2\n ) {\n p2 = JXG.createPoint(board, parents[1](), attr);\n constrained = true;\n } else {\n throw new Error(\n \"JSXGraph: Can't create line with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'line');\n el = new JXG.Line(board, p1, p2, attr);\n\n if (constrained) {\n el.constrained = true;\n el.funp1 = parents[0];\n el.funp2 = parents[1];\n } else if (!doTransform) {\n el.isDraggable = true;\n }\n\n //if (!el.constrained) {\n el.setParents([p1.id, p2.id]);\n //}\n\n } else if (parents.length === 3) {\n // Free line:\n // Line is defined by three homogeneous coordinates.\n // Also in this case points are created.\n isDraggable = true;\n for (i = 0; i < 3; i++) {\n if (Type.isNumber(parents[i])) {\n // createFunction will just wrap a function around our constant number\n // that does nothing else but to return that number.\n c[i] = Type.createFunction(parents[i]);\n } else if (Type.isFunction(parents[i])) {\n c[i] = parents[i];\n isDraggable = false;\n } else {\n throw new Error(\n \"JSXGraph: Can't create line with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]\"\n );\n }\n }\n\n // point 1 is the midpoint between (0, c, -b) and point 2. => point1 is finite.\n attr = Type.copyAttributes(attributes, board.options, \"line\", 'point1');\n if (isDraggable) {\n p1 = board.create(\"point\", [\n c[2]() * c[2]() + c[1]() * c[1](),\n c[2]() - c[1]() * c[0]() + c[2](),\n -c[1]() - c[2]() * c[0]() - c[1]()\n ], attr);\n } else {\n p1 = board.create(\"point\", [\n function () {\n return (c[2]() * c[2]() + c[1]() * c[1]()) * 0.5;\n },\n function () {\n return (c[2]() - c[1]() * c[0]() + c[2]()) * 0.5;\n },\n function () {\n return (-c[1]() - c[2]() * c[0]() - c[1]()) * 0.5;\n }\n ], attr);\n }\n\n // point 2: (b^2+c^2,-ba+c,-ca-b)\n attr = Type.copyAttributes(attributes, board.options, \"line\", 'point2');\n if (isDraggable) {\n p2 = board.create(\"point\", [\n c[2]() * c[2]() + c[1]() * c[1](),\n -c[1]() * c[0]() + c[2](),\n -c[2]() * c[0]() - c[1]()\n ], attr);\n } else {\n p2 = board.create(\"point\", [\n function () {\n return c[2]() * c[2]() + c[1]() * c[1]();\n },\n function () {\n return -c[1]() * c[0]() + c[2]();\n },\n function () {\n return -c[2]() * c[0]() - c[1]();\n }\n ], attr);\n }\n\n // If the line will have a glider and board.suspendUpdate() has been called, we\n // need to compute the initial position of the two points p1 and p2.\n p1.prepareUpdate().update();\n p2.prepareUpdate().update();\n attr = Type.copyAttributes(attributes, board.options, 'line');\n el = new JXG.Line(board, p1, p2, attr);\n // Not yet working, because the points are not draggable.\n el.isDraggable = isDraggable;\n el.setParents([p1, p2]);\n\n } else if (\n // The parent array contains a function which returns two points.\n parents.length === 1 &&\n Type.isFunction(parents[0]) &&\n parents[0]().length === 2 &&\n Type.isPoint(parents[0]()[0]) &&\n Type.isPoint(parents[0]()[1])\n ) {\n ps = parents[0]();\n attr = Type.copyAttributes(attributes, board.options, 'line');\n el = new JXG.Line(board, ps[0], ps[1], attr);\n el.constrained = true;\n el.funps = parents[0];\n el.setParents(ps);\n } else if (\n parents.length === 1 &&\n Type.isFunction(parents[0]) &&\n parents[0]().length === 3 &&\n Type.isNumber(parents[0]()[0]) &&\n Type.isNumber(parents[0]()[1]) &&\n Type.isNumber(parents[0]()[2])\n ) {\n ps = parents[0];\n\n attr = Type.copyAttributes(attributes, board.options, \"line\", 'point1');\n p1 = board.create(\"point\", [\n function () {\n var c = ps();\n\n return [\n (c[2] * c[2] + c[1] * c[1]) * 0.5,\n (c[2] - c[1] * c[0] + c[2]) * 0.5,\n (-c[1] - c[2] * c[0] - c[1]) * 0.5\n ];\n }\n ], attr);\n\n attr = Type.copyAttributes(attributes, board.options, \"line\", 'point2');\n p2 = board.create(\"point\", [\n function () {\n var c = ps();\n\n return [\n c[2] * c[2] + c[1] * c[1],\n -c[1] * c[0] + c[2],\n -c[2] * c[0] - c[1]\n ];\n }\n ], attr);\n\n attr = Type.copyAttributes(attributes, board.options, 'line');\n el = new JXG.Line(board, p1, p2, attr);\n\n el.constrained = true;\n el.funps = parents[0];\n el.setParents([p1, p2]);\n } else {\n throw new Error(\n \"JSXGraph: Can't create line with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]\"\n );\n }\n\n return el;\n};\n\nJXG.registerElement(\"line\", JXG.createLine);\n\n/**\n * @class A (line) segment defined by two points.\n * It's strictly spoken just a wrapper for element {@link Line} with {@link Line#straightFirst}\n * and {@link Line#straightLast} properties set to false. If there is a third variable then the\n * segment has a fixed length (which may be a function, too) determined by the absolute value of\n * that number.\n * @pseudo\n * @name Segment\n * @augments JXG.Line\n * @constructor\n * @type JXG.Line\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point,array_JXG.Point,array} point1,point2 Parent elements can be two elements either of type {@link JXG.Point}\n * or array of numbers describing the\n * coordinates of a point. In the latter case the point will be constructed automatically as a fixed invisible point.\n * @param {number,function} [length] The points are adapted - if possible - such that their distance\n * is equal to the absolute value of this number.\n * @see Line\n * @example\n * // Create a segment providing two points.\n * var p1 = board.create('point', [4.5, 2.0]);\n * var p2 = board.create('point', [1.0, 1.0]);\n * var l1 = board.create('segment', [p1, p2]);\n * \n * \n *\n * @example\n * // Create a segment providing two points.\n * var p1 = board.create('point', [4.0, 1.0]);\n * var p2 = board.create('point', [1.0, 1.0]);\n * // AB\n * var l1 = board.create('segment', [p1, p2]);\n * var p3 = board.create('point', [4.0, 2.0]);\n * var p4 = board.create('point', [1.0, 2.0]);\n * // CD\n * var l2 = board.create('segment', [p3, p4, 3]); // Fixed length\n * var p5 = board.create('point', [4.0, 3.0]);\n * var p6 = board.create('point', [1.0, 4.0]);\n * // EF\n * var l3 = board.create('segment', [p5, p6, function(){ return l1.L();} ]); // Fixed, but dependent length\n * \n * \n *\n */\nJXG.createSegment = function (board, parents, attributes) {\n var el, attr;\n\n attributes.straightFirst = false;\n attributes.straightLast = false;\n attr = Type.copyAttributes(attributes, board.options, 'segment');\n\n el = board.create(\"line\", parents.slice(0, 2), attr);\n\n if (parents.length === 3) {\n try {\n el.hasFixedLength = true;\n el.fixedLengthOldCoords = [];\n el.fixedLengthOldCoords[0] = new Coords(\n Const.COORDS_BY_USER,\n el.point1.coords.usrCoords.slice(1, 3),\n board\n );\n el.fixedLengthOldCoords[1] = new Coords(\n Const.COORDS_BY_USER,\n el.point2.coords.usrCoords.slice(1, 3),\n board\n );\n\n el.setFixedLength(parents[2]);\n } catch (err) {\n throw new Error(\n \"JSXGraph: Can't create segment with third parent type '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible third parent types: number or function\"\n );\n }\n // if (Type.isNumber(parents[2])) {\n // el.fixedLength = function () {\n // return parents[2];\n // };\n // } else if (Type.isFunction(parents[2])) {\n // el.fixedLength = Type.createFunction(parents[2], this.board);\n // } else {\n // throw new Error(\n // \"JSXGraph: Can't create segment with third parent type '\" +\n // typeof parents[2] +\n // \"'.\" +\n // \"\\nPossible third parent types: number or function\"\n // );\n // }\n\n el.getParents = function () {\n return this.parents.concat(this.fixedLength());\n };\n\n }\n\n el.elType = 'segment';\n\n return el;\n};\n\nJXG.registerElement(\"segment\", JXG.createSegment);\n\n/**\n * @class A segment with an arrow head.\n * This element is just a wrapper for element\n * {@link Line} with {@link Line#straightFirst}\n * and {@link Line#straightLast} properties set to false and {@link Line#lastArrow} set to true.\n * @pseudo\n * @name Arrow\n * @augments JXG.Line\n * @constructor\n * @type JXG.Line\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point,array_JXG.Point,array} point1,point2 Parent elements can be two elements either of type {@link JXG.Point} or array of numbers describing the\n * coordinates of a point. In the latter case the point will be constructed automatically as a fixed invisible point.\n * @param {Number_Number_Number} a,b,c A line can also be created providing three numbers. The line is then described by the set of solutions\n * of the equation a*x+b*y+c*z = 0.\n * @see Line\n * @example\n * // Create an arrow providing two points.\n * var p1 = board.create('point', [4.5, 2.0]);\n * var p2 = board.create('point', [1.0, 1.0]);\n * var l1 = board.create('arrow', [p1, p2]);\n * \n * \n */\nJXG.createArrow = function (board, parents, attributes) {\n var el, attr;\n\n attributes.straightFirst = false;\n attributes.straightLast = false;\n attr = Type.copyAttributes(attributes, board.options, 'arrow');\n el = board.create(\"line\", parents, attr);\n //el.setArrow(false, true);\n el.type = Const.OBJECT_TYPE_VECTOR;\n el.elType = 'arrow';\n\n return el;\n};\n\nJXG.registerElement(\"arrow\", JXG.createArrow);\n\n/**\n * @class Axis is a line with optional ticks and labels.\n * It's strictly spoken just a wrapper for element {@link Line} with {@link Line#straightFirst}\n * and {@link Line#straightLast} properties set to true. Additionally {@link Line#lastArrow} is set to true and default {@link Ticks} will be created.\n * @pseudo\n * @name Axis\n * @augments JXG.Line\n * @constructor\n * @type JXG.Line\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point,array_JXG.Point,array} point1,point2 Parent elements can be two elements either of type {@link JXG.Point} or array of numbers describing the\n * coordinates of a point. In the latter case, the point will be constructed automatically as a fixed invisible point.\n * @param {Number_Number_Number} a,b,c A line can also be created providing three numbers. The line is then described by the set of solutions\n * of the equation a*x+b*y+c*z = 0.\n * @example\n * // Create an axis providing two coords pairs.\n * var l1 = board.create('axis', [[0.0, 1.0], [1.0, 1.3]]);\n * \n * \n * @example\n * // Create ticks labels as fractions\n * board.create('axis', [[0,1], [1,1]], {\n * ticks: {\n * label: {\n * toFraction: true,\n * useMathjax: false,\n * anchorX: 'middle',\n * offset: [0, -10]\n * }\n * }\n * });\n *\n *\n * \n * \n * \n *\n */\nJXG.createAxis = function (board, parents, attributes) {\n var axis, attr,\n ancestor, ticksDist;\n\n // Create line\n attr = Type.copyAttributes(attributes, board.options, 'axis');\n try {\n axis = board.create(\"line\", parents, attr);\n } catch (err) {\n throw new Error(\n \"JSXGraph: Can't create axis with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,point], [[x1,y1],[x2,y2]]\"\n );\n }\n\n axis.type = Const.OBJECT_TYPE_AXIS;\n axis.isDraggable = false;\n axis.point1.isDraggable = false;\n axis.point2.isDraggable = false;\n\n // Save usrCoords of points\n axis._point1UsrCoordsOrg = axis.point1.coords.usrCoords.slice();\n axis._point2UsrCoordsOrg = axis.point2.coords.usrCoords.slice();\n\n for (ancestor in axis.ancestors) {\n if (axis.ancestors.hasOwnProperty(ancestor)) {\n axis.ancestors[ancestor].type = Const.OBJECT_TYPE_AXISPOINT;\n }\n }\n\n // Create ticks\n // attrTicks = attr.ticks;\n if (Type.exists(attr.ticks.ticksdistance)) {\n ticksDist = attr.ticks.ticksdistance;\n } else if (Type.isArray(attr.ticks.ticks)) {\n ticksDist = attr.ticks.ticks;\n } else {\n ticksDist = 1.0;\n }\n\n /**\n * The ticks attached to the axis.\n * @memberOf Axis.prototype\n * @name defaultTicks\n * @type JXG.Ticks\n */\n axis.defaultTicks = board.create(\"ticks\", [axis, ticksDist], attr.ticks);\n axis.defaultTicks.dump = false;\n axis.elType = 'axis';\n axis.subs = {\n ticks: axis.defaultTicks\n };\n axis.inherits.push(axis.defaultTicks);\n\n axis.update = function () {\n var bbox,\n position, i,\n direction, horizontal, vertical,\n ticksAutoPos, ticksAutoPosThres, dist,\n anchor, left, right,\n distUsr,\n newPosP1, newPosP2,\n locationOrg,\n visLabel, anchr, off;\n\n if (!this.needsUpdate) {\n return this;\n }\n\n bbox = this.board.getBoundingBox();\n position = this.evalVisProp('position');\n direction = this.Direction();\n horizontal = this.isHorizontal();\n vertical = this.isVertical();\n ticksAutoPos = this.evalVisProp('ticksautopos');\n ticksAutoPosThres = this.evalVisProp('ticksautoposthreshold');\n\n if (horizontal) {\n ticksAutoPosThres = Type.parseNumber(ticksAutoPosThres, Math.abs(bbox[1] - bbox[3]), 1 / this.board.unitX) * this.board.unitX;\n } else if (vertical) {\n ticksAutoPosThres = Type.parseNumber(ticksAutoPosThres, Math.abs(bbox[1] - bbox[3]), 1 / this.board.unitY) * this.board.unitY;\n } else {\n ticksAutoPosThres = Type.parseNumber(ticksAutoPosThres, 1, 1);\n }\n\n anchor = this.evalVisProp('anchor');\n left = anchor.indexOf('left') > -1;\n right = anchor.indexOf('right') > -1;\n\n distUsr = this.evalVisProp('anchordist');\n if (horizontal) {\n distUsr = Type.parseNumber(distUsr, Math.abs(bbox[1] - bbox[3]), 1 / this.board.unitX);\n } else if (vertical) {\n distUsr = Type.parseNumber(distUsr, Math.abs(bbox[0] - bbox[2]), 1 / this.board.unitY);\n } else {\n distUsr = 0;\n }\n\n locationOrg = this.board.getPointLoc(this._point1UsrCoordsOrg, distUsr);\n\n // Set position of axis\n newPosP1 = this.point1.coords.usrCoords.slice();\n newPosP2 = this.point2.coords.usrCoords.slice();\n\n if (position === 'static' || (!vertical && !horizontal)) {\n // Do nothing\n\n } else if (position === 'fixed') {\n if (horizontal) { // direction[1] === 0\n if ((direction[0] > 0 && right) || (direction[0] < 0 && left)) {\n newPosP1[2] = bbox[3] + distUsr;\n newPosP2[2] = bbox[3] + distUsr;\n } else if ((direction[0] > 0 && left) || (direction[0] < 0 && right)) {\n newPosP1[2] = bbox[1] - distUsr;\n newPosP2[2] = bbox[1] - distUsr;\n\n } else {\n newPosP1 = this._point1UsrCoordsOrg.slice();\n newPosP2 = this._point2UsrCoordsOrg.slice();\n }\n }\n if (vertical) { // direction[0] === 0\n if ((direction[1] > 0 && left) || (direction[1] < 0 && right)) {\n newPosP1[1] = bbox[0] + distUsr;\n newPosP2[1] = bbox[0] + distUsr;\n\n } else if ((direction[1] > 0 && right) || (direction[1] < 0 && left)) {\n newPosP1[1] = bbox[2] - distUsr;\n newPosP2[1] = bbox[2] - distUsr;\n\n } else {\n newPosP1 = this._point1UsrCoordsOrg.slice();\n newPosP2 = this._point2UsrCoordsOrg.slice();\n }\n }\n\n } else if (position === 'sticky') {\n if (horizontal) { // direction[1] === 0\n if (locationOrg[1] < 0 && ((direction[0] > 0 && right) || (direction[0] < 0 && left))) {\n newPosP1[2] = bbox[3] + distUsr;\n newPosP2[2] = bbox[3] + distUsr;\n\n } else if (locationOrg[1] > 0 && ((direction[0] > 0 && left) || (direction[0] < 0 && right))) {\n newPosP1[2] = bbox[1] - distUsr;\n newPosP2[2] = bbox[1] - distUsr;\n\n } else {\n newPosP1 = this._point1UsrCoordsOrg.slice();\n newPosP2 = this._point2UsrCoordsOrg.slice();\n }\n }\n if (vertical) { // direction[0] === 0\n if (locationOrg[0] < 0 && ((direction[1] > 0 && left) || (direction[1] < 0 && right))) {\n newPosP1[1] = bbox[0] + distUsr;\n newPosP2[1] = bbox[0] + distUsr;\n\n } else if (locationOrg[0] > 0 && ((direction[1] > 0 && right) || (direction[1] < 0 && left))) {\n newPosP1[1] = bbox[2] - distUsr;\n newPosP2[1] = bbox[2] - distUsr;\n\n } else {\n newPosP1 = this._point1UsrCoordsOrg.slice();\n newPosP2 = this._point2UsrCoordsOrg.slice();\n }\n }\n }\n\n this.point1.setPositionDirectly(JXG.COORDS_BY_USER, newPosP1);\n this.point2.setPositionDirectly(JXG.COORDS_BY_USER, newPosP2);\n\n // Set position of tick labels\n if (Type.exists(this.defaultTicks)) {\n visLabel = this.defaultTicks.visProp.label;\n if (ticksAutoPos && (horizontal || vertical)) {\n\n if (!Type.exists(visLabel._anchorx_org)) {\n visLabel._anchorx_org = Type.def(visLabel.anchorx, this.board.options.text.anchorX);\n }\n if (!Type.exists(visLabel._anchory_org)) {\n visLabel._anchory_org = Type.def(visLabel.anchory, this.board.options.text.anchorY);\n }\n if (!Type.exists(visLabel._offset_org)) {\n visLabel._offset_org = visLabel.offset.slice();\n }\n\n off = visLabel.offset;\n if (horizontal) {\n dist = axis.point1.coords.scrCoords[2] - (this.board.canvasHeight * 0.5);\n\n anchr = visLabel.anchory;\n\n // The last position of the labels is stored in visLabel._side\n if (dist < 0 && Math.abs(dist) > ticksAutoPosThres) {\n // Put labels on top of the line\n if (visLabel._side === 'bottom') {\n // Switch position\n if (visLabel.anchory === 'top') {\n anchr = 'bottom';\n }\n off[1] *= -1;\n visLabel._side = 'top';\n }\n\n } else if (dist > 0 && Math.abs(dist) > ticksAutoPosThres) {\n // Put labels below the line\n if (visLabel._side === 'top') {\n // Switch position\n if (visLabel.anchory === 'bottom') {\n anchr = 'top';\n }\n off[1] *= -1;\n visLabel._side = 'bottom';\n }\n\n } else {\n // Put to original position\n anchr = visLabel._anchory_org;\n off = visLabel._offset_org.slice();\n\n if (anchr === 'top') {\n visLabel._side = 'bottom';\n } else if (anchr === 'bottom') {\n visLabel._side = 'top';\n } else if (off[1] < 0) {\n visLabel._side = 'bottom';\n } else {\n visLabel._side = 'top';\n }\n }\n\n for (i = 0; i < axis.defaultTicks.labels.length; i++) {\n this.defaultTicks.labels[i].visProp.anchory = anchr;\n }\n visLabel.anchory = anchr;\n\n } else if (vertical) {\n dist = axis.point1.coords.scrCoords[1] - (this.board.canvasWidth * 0.5);\n\n if (dist < 0 && Math.abs(dist) > ticksAutoPosThres) {\n // Put labels to the left of the line\n if (visLabel._side === 'right') {\n // Switch position\n if (visLabel.anchorx === 'left') {\n anchr = 'right';\n }\n off[0] *= -1;\n visLabel._side = 'left';\n }\n\n } else if (dist > 0 && Math.abs(dist) > ticksAutoPosThres) {\n // Put labels to the right of the line\n if (visLabel._side === 'left') {\n // Switch position\n if (visLabel.anchorx === 'right') {\n anchr = 'left';\n }\n off[0] *= -1;\n visLabel._side = 'right';\n }\n\n } else {\n // Put to original position\n anchr = visLabel._anchorx_org;\n off = visLabel._offset_org.slice();\n\n if (anchr === 'left') {\n visLabel._side = 'right';\n } else if (anchr === 'right') {\n visLabel._side = 'left';\n } else if (off[0] < 0) {\n visLabel._side = 'left';\n } else {\n visLabel._side = 'right';\n }\n }\n\n for (i = 0; i < axis.defaultTicks.labels.length; i++) {\n this.defaultTicks.labels[i].visProp.anchorx = anchr;\n }\n visLabel.anchorx = anchr;\n }\n visLabel.offset = off;\n\n } else {\n delete visLabel._anchorx_org;\n delete visLabel._anchory_org;\n delete visLabel._offset_org;\n }\n this.defaultTicks.needsUpdate = true;\n }\n\n JXG.Line.prototype.update.call(this);\n\n return this;\n };\n\n return axis;\n};\n\nJXG.registerElement(\"axis\", JXG.createAxis);\n\n/**\n * @class The tangent line at a point on a line, circle, conic, turtle, or curve.\n * A tangent line is always constructed\n * by a point on a line, circle, or curve and describes the tangent in the point on that line, circle, or curve.\n * \n * \n */\nJXG.createTangent = function (board, parents, attributes) {\n var p, c, j, el, tangent, attr,\n getCurveTangentDir,\n res, isTransformed,\n slides = [];\n\n if (parents.length === 1) {\n // One argument: glider on line, circle or curve\n p = parents[0];\n c = p.slideObject;\n\n } else if (parents.length === 2) {\n // Two arguments: (point,line|curve|circle|conic) or (line|curve|circle|conic,point).\n // In fact, for circles and conics it is the polar\n if (Type.isPoint(parents[0])) {\n p = parents[0];\n c = parents[1];\n } else if (Type.isPoint(parents[1])) {\n c = parents[0];\n p = parents[1];\n } else {\n throw new Error(\n \"JSXGraph: Can't create tangent with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [glider|point], [point,line|curve|circle|conic]\"\n );\n }\n } else {\n throw new Error(\n \"JSXGraph: Can't create tangent with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [glider|point], [point,line|curve|circle|conic]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'tangent');\n if (c.elementClass === Const.OBJECT_CLASS_LINE) {\n tangent = board.create(\"line\", [c.point1, c.point2], attr);\n tangent.glider = p;\n } else if (\n c.elementClass === Const.OBJECT_CLASS_CURVE &&\n c.type !== Const.OBJECT_TYPE_CONIC\n ) {\n res = c.getTransformationSource();\n isTransformed = res[0];\n if (isTransformed) {\n // Curve is result of a transformation\n // We recursively collect all curves from which\n // the curve is transformed.\n slides.push(c);\n while (res[0] && Type.exists(res[1]._transformationSource)) {\n slides.push(res[1]);\n res = res[1].getTransformationSource();\n }\n }\n\n if (c.evalVisProp('curvetype') !== \"plot\" || isTransformed) {\n // Functiongraph or parametric curve or\n // transformed curve thereof.\n tangent = board.create(\n \"line\",\n [\n function () {\n var g = c.X,\n f = c.Y,\n df, dg,\n li, i, c_org, invMat, po,\n t;\n\n if (p.type === Const.OBJECT_TYPE_GLIDER) {\n t = p.position;\n } else if (c.evalVisProp('curvetype') === 'functiongraph') {\n t = p.X();\n } else {\n t = Geometry.projectPointToCurve(p, c, board)[1];\n }\n\n // po are the coordinates of the point\n // on the \"original\" curve. That is the curve or\n // the original curve which is transformed (maybe multiple times)\n // to this curve.\n // t is the position of the point on the \"original\" curve\n po = p.Coords(true);\n if (isTransformed) {\n c_org = slides[slides.length - 1]._transformationSource;\n g = c_org.X;\n f = c_org.Y;\n for (i = 0; i < slides.length; i++) {\n slides[i].updateTransformMatrix();\n invMat = Mat.inverse(slides[i].transformMat);\n po = Mat.matVecMult(invMat, po);\n }\n\n if (p.type !== Const.OBJECT_TYPE_GLIDER) {\n po[1] /= po[0];\n po[2] /= po[0];\n po[0] /= po[0];\n t = Geometry.projectCoordsToCurve(po[1], po[2], 0, c_org, board)[1];\n }\n }\n\n // li are the coordinates of the line on the \"original\" curve\n df = Numerics.D(f)(t);\n dg = Numerics.D(g)(t);\n li = [\n -po[1] * df + po[2] * dg,\n po[0] * df,\n -po[0] * dg\n ];\n\n if (isTransformed) {\n // Transform the line to the transformed curve\n for (i = slides.length - 1; i >= 0; i--) {\n invMat = Mat.transpose(Mat.inverse(slides[i].transformMat));\n li = Mat.matVecMult(invMat, li);\n }\n }\n\n return li;\n }\n ],\n attr\n );\n\n p.addChild(tangent);\n // this is required for the geogebra reader to display a slope\n tangent.glider = p;\n } else {\n // curveType 'plot': discrete data\n /**\n * @ignore\n *\n * In case of bezierDegree == 1:\n * Find two points p1, p2 enclosing the glider.\n * Then the equation of the line segment is: 0 = y*(x1-x2) + x*(y2-y1) + y1*x2-x1*y2,\n * which is the cross product of p1 and p2.\n *\n * In case of bezierDegree === 3:\n * The slope dy / dx of the tangent is determined. Then the\n * tangent is computed as cross product between\n * the glider p and [1, p.X() + dx, p.Y() + dy]\n *\n */\n getCurveTangentDir = function (position, c, num) {\n var i = Math.floor(position),\n p1, p2, t, A, B, C, D, dx, dy, d,\n points, le;\n\n if (c.bezierDegree === 1) {\n if (i === c.numberPoints - 1) {\n i--;\n }\n } else if (c.bezierDegree === 3) {\n // i is start of the Bezier segment\n // t is the position in the Bezier segment\n if (c.elType === 'sector') {\n points = c.points.slice(3, c.numberPoints - 3);\n le = points.length;\n } else {\n points = c.points;\n le = points.length;\n }\n i = Math.floor((position * (le - 1)) / 3) * 3;\n t = (position * (le - 1) - i) / 3;\n if (i >= le - 1) {\n i = le - 4;\n t = 1;\n }\n } else {\n return 0;\n }\n\n if (i < 0) {\n return 1;\n }\n\n // The curve points are transformed (if there is a transformation)\n // c.X(i) is not transformed.\n if (c.bezierDegree === 1) {\n p1 = c.points[i].usrCoords;\n p2 = c.points[i + 1].usrCoords;\n } else {\n A = points[i].usrCoords;\n B = points[i + 1].usrCoords;\n C = points[i + 2].usrCoords;\n D = points[i + 3].usrCoords;\n dx = (1 - t) * (1 - t) * (B[1] - A[1]) +\n 2 * (1 - t) * t * (C[1] - B[1]) +\n t * t * (D[1] - C[1]);\n dy = (1 - t) * (1 - t) * (B[2] - A[2]) +\n 2 * (1 - t) * t * (C[2] - B[2]) +\n t * t * (D[2] - C[2]);\n d = Mat.hypot(dx, dy);\n dx /= d;\n dy /= d;\n p1 = p.coords.usrCoords;\n p2 = [1, p1[1] + dx, p1[2] + dy];\n }\n\n switch (num) {\n case 0:\n return p1[2] * p2[1] - p1[1] * p2[2];\n case 1:\n return p2[2] - p1[2];\n case 2:\n return p1[1] - p2[1];\n default:\n return [\n p1[2] * p2[1] - p1[1] * p2[2],\n p2[2] - p1[2],\n p1[1] - p2[1]\n ];\n }\n };\n\n tangent = board.create(\n \"line\",\n [\n function () {\n var t;\n\n if (p.type === Const.OBJECT_TYPE_GLIDER) {\n t = p.position;\n } else {\n t = Geometry.projectPointToCurve(p, c, board)[1];\n }\n\n return getCurveTangentDir(t, c);\n }\n ],\n attr\n );\n\n p.addChild(tangent);\n // this is required for the geogebra reader to display a slope\n tangent.glider = p;\n }\n } else if (c.type === Const.OBJECT_TYPE_TURTLE) {\n tangent = board.create(\n \"line\",\n [\n function () {\n var i, t;\n if (p.type === Const.OBJECT_TYPE_GLIDER) {\n t = p.position;\n } else {\n t = Geometry.projectPointToTurtle(p, c, board)[1];\n }\n\n i = Math.floor(t);\n\n // run through all curves of this turtle\n for (j = 0; j < c.objects.length; j++) {\n el = c.objects[j];\n\n if (el.type === Const.OBJECT_TYPE_CURVE) {\n if (i < el.numberPoints) {\n break;\n }\n\n i -= el.numberPoints;\n }\n }\n\n if (i === el.numberPoints - 1) {\n i--;\n }\n\n if (i < 0) {\n return [1, 0, 0];\n }\n\n return [\n el.Y(i) * el.X(i + 1) - el.X(i) * el.Y(i + 1),\n el.Y(i + 1) - el.Y(i),\n el.X(i) - el.X(i + 1)\n ];\n }\n ],\n attr\n );\n p.addChild(tangent);\n\n // this is required for the geogebra reader to display a slope\n tangent.glider = p;\n } else if (\n c.elementClass === Const.OBJECT_CLASS_CIRCLE ||\n c.type === Const.OBJECT_TYPE_CONIC\n ) {\n // If p is not on c, the tangent is the polar.\n // This construction should work on conics, too. p has to lie on c.\n tangent = board.create(\n \"line\",\n [\n function () {\n return Mat.matVecMult(c.quadraticform, p.coords.usrCoords);\n }\n ],\n attr\n );\n\n p.addChild(tangent);\n // this is required for the geogebra reader to display a slope\n tangent.glider = p;\n }\n\n if (!Type.exists(tangent)) {\n throw new Error(\"JSXGraph: Couldn't create tangent with the given parents.\");\n }\n\n tangent.elType = 'tangent';\n tangent.type = Const.OBJECT_TYPE_TANGENT;\n tangent.setParents(parents);\n\n return tangent;\n};\n\n/**\n * @class A normal is the line perpendicular to a line or to a tangent of a circle or curve.\n * @pseudo\n * @description A normal is a line through a given point on an element of type line, circle, curve, or turtle and orthogonal to that object.\n * @constructor\n * @name Normal\n * @type JXG.Line\n * @augments JXG.Line\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Line,JXG.Circle,JXG.Curve,JXG.Turtle_JXG.Point} o,p The constructed line contains p which lies on the object and is orthogonal\n * to the tangent to the object in the given point.\n * @param {Glider} p Works like above, however the object is given by {@link JXG.CoordsElement#slideObject}.\n * @example\n * // Create a normal to a circle.\n * var p1 = board.create('point', [2.0, 2.0]);\n * var p2 = board.create('point', [3.0, 2.0]);\n * var c1 = board.create('circle', [p1, p2]);\n *\n * var norm1 = board.create('normal', [c1, p2]);\n * \n * \n */\nJXG.createNormal = function (board, parents, attributes) {\n var p, c, l, i, attr, pp, attrp,\n getCurveNormalDir,\n res, isTransformed,\n slides = [];\n\n for (i = 0; i < parents.length; ++i) {\n parents[i] = board.select(parents[i]);\n }\n // One arguments: glider on line, circle or curve\n if (parents.length === 1) {\n p = parents[0];\n c = p.slideObject;\n // Two arguments: (point,line), (point,circle), (line,point) or (circle,point)\n } else if (parents.length === 2) {\n if (Type.isPointType(board, parents[0])) {\n p = Type.providePoints(board, [parents[0]], attributes, 'point')[0];\n c = parents[1];\n } else if (Type.isPointType(board, parents[1])) {\n c = parents[0];\n p = Type.providePoints(board, [parents[1]], attributes, 'point')[0];\n } else {\n throw new Error(\n \"JSXGraph: Can't create normal with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,line], [point,circle], [glider]\"\n );\n }\n } else {\n throw new Error(\n \"JSXGraph: Can't create normal with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,line], [point,circle], [glider]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'normal');\n if (c.elementClass === Const.OBJECT_CLASS_LINE) {\n // Private point\n attrp = Type.copyAttributes(attributes, board.options, \"normal\", 'point');\n pp = board.create(\n \"point\",\n [\n function () {\n var p = Mat.crossProduct([1, 0, 0], c.stdform);\n return [p[0], -p[2], p[1]];\n }\n ],\n attrp\n );\n pp.isDraggable = true;\n\n l = board.create(\"line\", [p, pp], attr);\n\n /**\n * A helper point used to create a normal to a {@link JXG.Line} object. For normals to circles or curves this\n * element is undefined.\n * @type JXG.Point\n * @name point\n * @memberOf Normal.prototype\n */\n l.point = pp;\n l.subs = {\n point: pp\n };\n l.inherits.push(pp);\n } else if (c.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n l = board.create(\"line\", [c.midpoint, p], attr);\n } else if (c.elementClass === Const.OBJECT_CLASS_CURVE) {\n res = c.getTransformationSource();\n isTransformed = res[0];\n if (isTransformed) {\n // Curve is result of a transformation\n // We recursively collect all curves from which\n // the curve is transformed.\n slides.push(c);\n while (res[0] && Type.exists(res[1]._transformationSource)) {\n slides.push(res[1]);\n res = res[1].getTransformationSource();\n }\n }\n\n if (c.evalVisProp('curvetype') !== \"plot\" || isTransformed) {\n // Functiongraph or parametric curve or\n // transformed curve thereof.\n l = board.create(\n \"line\",\n [\n function () {\n var g = c.X,\n f = c.Y,\n df, dg,\n li, i, c_org, invMat, po,\n t;\n\n if (p.type === Const.OBJECT_TYPE_GLIDER) {\n t = p.position;\n } else if (c.evalVisProp('curvetype') === 'functiongraph') {\n t = p.X();\n } else {\n t = Geometry.projectPointToCurve(p, c, board)[1];\n }\n\n // po are the coordinates of the point\n // on the \"original\" curve. That is the curve or\n // the original curve which is transformed (maybe multiple times)\n // to this curve.\n // t is the position of the point on the \"original\" curve\n po = p.Coords(true);\n if (isTransformed) {\n c_org = slides[slides.length - 1]._transformationSource;\n g = c_org.X;\n f = c_org.Y;\n for (i = 0; i < slides.length; i++) {\n slides[i].updateTransformMatrix();\n invMat = Mat.inverse(slides[i].transformMat);\n po = Mat.matVecMult(invMat, po);\n }\n\n if (p.type !== Const.OBJECT_TYPE_GLIDER) {\n po[1] /= po[0];\n po[2] /= po[0];\n po[0] /= po[0];\n t = Geometry.projectCoordsToCurve(po[1], po[2], 0, c_org, board)[1];\n }\n }\n\n df = Numerics.D(f)(t);\n dg = Numerics.D(g)(t);\n li = [\n -po[1] * dg - po[2] * df,\n po[0] * dg,\n po[0] * df\n ];\n\n if (isTransformed) {\n // Transform the line to the transformed curve\n for (i = slides.length - 1; i >= 0; i--) {\n invMat = Mat.transpose(Mat.inverse(slides[i].transformMat));\n li = Mat.matVecMult(invMat, li);\n }\n }\n\n return li;\n }\n ],\n attr\n );\n } else {\n // curveType 'plot': discrete data\n getCurveNormalDir = function (position, c, num) {\n var i = Math.floor(position),\n lbda,\n p1, p2, t, A, B, C, D, dx, dy, d,\n li, p_org, pp,\n points, le;\n\n if (c.bezierDegree === 1) {\n if (i === c.numberPoints - 1) {\n i--;\n }\n t = position;\n } else if (c.bezierDegree === 3) {\n // i is start of the Bezier segment\n // t is the position in the Bezier segment\n if (c.elType === 'sector') {\n points = c.points.slice(3, c.numberPoints - 3);\n le = points.length;\n } else {\n points = c.points;\n le = points.length;\n }\n i = Math.floor((position * (le - 1)) / 3) * 3;\n t = (position * (le - 1) - i) / 3;\n if (i >= le - 1) {\n i = le - 4;\n t = 1;\n }\n } else {\n return 0;\n }\n\n if (i < 0) {\n return 1;\n }\n\n lbda = t - i;\n if (c.bezierDegree === 1) {\n p1 = c.points[i].usrCoords;\n p2 = c.points[i + 1].usrCoords;\n p_org = [\n p1[0] + lbda * (p2[0] - p1[0]),\n p1[1] + lbda * (p2[1] - p1[1]),\n p1[2] + lbda * (p2[2] - p1[2])\n ];\n li = Mat.crossProduct(p1, p2);\n pp = Mat.crossProduct([1, 0, 0], li);\n pp = [pp[0], -pp[2], pp[1]];\n li = Mat.crossProduct(p_org, pp);\n\n } else {\n A = points[i].usrCoords;\n B = points[i + 1].usrCoords;\n C = points[i + 2].usrCoords;\n D = points[i + 3].usrCoords;\n dx =\n (1 - t) * (1 - t) * (B[1] - A[1]) +\n 2 * (1 - t) * t * (C[1] - B[1]) +\n t * t * (D[1] - C[1]);\n dy =\n (1 - t) * (1 - t) * (B[2] - A[2]) +\n 2 * (1 - t) * t * (C[2] - B[2]) +\n t * t * (D[2] - C[2]);\n d = Mat.hypot(dx, dy);\n dx /= d;\n dy /= d;\n p1 = p.coords.usrCoords;\n p2 = [1, p1[1] - dy, p1[2] + dx];\n\n li = [\n p1[2] * p2[1] - p1[1] * p2[2],\n p2[2] - p1[2],\n p1[1] - p2[1]\n ];\n }\n\n switch (num) {\n case 0:\n return li[0];\n case 1:\n return li[1];\n case 2:\n return li[2];\n default:\n return li;\n }\n };\n\n l = board.create(\n \"line\",\n [\n function () {\n var t;\n\n if (p.type === Const.OBJECT_TYPE_GLIDER) {\n t = p.position;\n } else {\n t = Geometry.projectPointToCurve(p, c, board)[1];\n }\n\n return getCurveNormalDir(t, c);\n }\n ],\n attr\n );\n p.addChild(l);\n l.glider = p;\n }\n } else if (c.type === Const.OBJECT_TYPE_TURTLE) {\n l = board.create(\n \"line\",\n [\n function () {\n var el,\n j,\n i = Math.floor(p.position),\n lbda = p.position - i;\n\n // run through all curves of this turtle\n for (j = 0; j < c.objects.length; j++) {\n el = c.objects[j];\n\n if (el.type === Const.OBJECT_TYPE_CURVE) {\n if (i < el.numberPoints) {\n break;\n }\n\n i -= el.numberPoints;\n }\n }\n\n if (i === el.numberPoints - 1) {\n i -= 1;\n lbda = 1;\n }\n\n if (i < 0) {\n return 1;\n }\n\n return (\n (el.Y(i) + lbda * (el.Y(i + 1) - el.Y(i))) * (el.Y(i) - el.Y(i + 1)) -\n (el.X(i) + lbda * (el.X(i + 1) - el.X(i))) * (el.X(i + 1) - el.X(i))\n );\n },\n function () {\n var el,\n j,\n i = Math.floor(p.position);\n\n // run through all curves of this turtle\n for (j = 0; j < c.objects.length; j++) {\n el = c.objects[j];\n if (el.type === Const.OBJECT_TYPE_CURVE) {\n if (i < el.numberPoints) {\n break;\n }\n\n i -= el.numberPoints;\n }\n }\n\n if (i === el.numberPoints - 1) {\n i -= 1;\n }\n\n if (i < 0) {\n return 0;\n }\n\n return el.X(i + 1) - el.X(i);\n },\n function () {\n var el,\n j,\n i = Math.floor(p.position);\n\n // run through all curves of this turtle\n for (j = 0; j < c.objects.length; j++) {\n el = c.objects[j];\n if (el.type === Const.OBJECT_TYPE_CURVE) {\n if (i < el.numberPoints) {\n break;\n }\n\n i -= el.numberPoints;\n }\n }\n\n if (i === el.numberPoints - 1) {\n i -= 1;\n }\n\n if (i < 0) {\n return 0;\n }\n\n return el.Y(i + 1) - el.Y(i);\n }\n ],\n attr\n );\n } else {\n throw new Error(\n \"JSXGraph: Can't create normal with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,line], [point,circle], [glider]\"\n );\n }\n\n l.elType = 'normal';\n l.setParents(parents);\n\n if (Type.exists(p._is_new)) {\n l.addChild(p);\n delete p._is_new;\n } else {\n p.addChild(l);\n }\n c.addChild(l);\n\n return l;\n};\n\n/**\n * @class The radical axis is the line connecting the two interstion points of two circles with distinct centers.\n * The angular bisector of the polar lines of the circle centers with respect to the other circle is always the radical axis.\n * The radical axis passes through the intersection points when the circles intersect.\n * When a circle about the midpoint of circle centers, passing through the circle centers, intersects the circles, the polar lines pass through those intersection points.\n * @pseudo\n * @name RadicalAxis\n * @augments JXG.Line\n * @constructor\n * @type JXG.Line\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Circle} circle one of the two respective circles.\n * @param {JXG.Circle} circle the other of the two respective circles.\n * @example\n * // Create the radical axis line with respect to two circles\n * var board = JXG.JSXGraph.initBoard('7b7233a0-f363-47dd-9df5-5018d0d17a98', {boundingbox: [-1, 9, 9, -1], axis: true, showcopyright: false, shownavigation: false});\n * var p1 = board.create('point', [2, 3]);\n * var p2 = board.create('point', [1, 4]);\n * var c1 = board.create('circle', [p1, p2]);\n * var p3 = board.create('point', [6, 5]);\n * var p4 = board.create('point', [8, 6]);\n * var c2 = board.create('circle', [p3, p4]);\n * var r1 = board.create('radicalaxis', [c1, c2]);\n * \n * \n */\nJXG.createRadicalAxis = function (board, parents, attributes) {\n var el, el1, el2;\n\n if (\n parents.length !== 2 ||\n parents[0].elementClass !== Const.OBJECT_CLASS_CIRCLE ||\n parents[1].elementClass !== Const.OBJECT_CLASS_CIRCLE\n ) {\n // Failure\n throw new Error(\n \"JSXGraph: Can't create 'radical axis' with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent type: [circle,circle]\"\n );\n }\n\n el1 = board.select(parents[0]);\n el2 = board.select(parents[1]);\n\n el = board.create(\n \"line\",\n [\n function () {\n var a = el1.stdform,\n b = el2.stdform;\n\n return Mat.matVecMult(Mat.transpose([a.slice(0, 3), b.slice(0, 3)]), [\n b[3],\n -a[3]\n ]);\n }\n ],\n attributes\n );\n\n el.elType = 'radicalaxis';\n el.setParents([el1.id, el2.id]);\n\n el1.addChild(el);\n el2.addChild(el);\n\n return el;\n};\n\n/**\n * @class The polar line of a point with respect to a conic or a circle.\n * @pseudo\n * @description The polar line is the unique reciprocal relationship of a point with respect to a conic.\n * The lines through the intersections of a conic and the polar line of a point\n * with respect to that conic and through that point are tangent to the conic.\n * A point on a conic has the polar line of that point with respect to that\n * conic as the tangent line to that conic at that point.\n * See {@link https://en.wikipedia.org/wiki/Pole_and_polar} for more information on pole and polar.\n * @name PolarLine\n * @augments JXG.Line\n * @constructor\n * @type JXG.Line\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Conic,JXG.Circle_JXG.Point} el1,el2 or\n * @param {JXG.Point_JXG.Conic,JXG.Circle} el1,el2 The result will be the polar line of the point with respect to the conic or the circle.\n * @example\n * // Create the polar line of a point with respect to a conic\n * var p1 = board.create('point', [-1, 2]);\n * var p2 = board.create('point', [ 1, 4]);\n * var p3 = board.create('point', [-1,-2]);\n * var p4 = board.create('point', [ 0, 0]);\n * var p5 = board.create('point', [ 4,-2]);\n * var c1 = board.create('conic',[p1,p2,p3,p4,p5]);\n * var p6 = board.create('point', [-1, 1]);\n * var l1 = board.create('polarline', [c1, p6]);\n * \n * \n * @example\n * // Create the polar line of a point with respect to a circle.\n * var p1 = board.create('point', [ 1, 1]);\n * var p2 = board.create('point', [ 2, 3]);\n * var c1 = board.create('circle',[p1,p2]);\n * var p3 = board.create('point', [ 6, 6]);\n * var l1 = board.create('polarline', [c1, p3]);\n * \n * \n */\nJXG.createPolarLine = function (board, parents, attributes) {\n var el,\n el1,\n el2,\n firstParentIsConic,\n secondParentIsConic,\n firstParentIsPoint,\n secondParentIsPoint;\n\n if (parents.length > 1) {\n firstParentIsConic =\n parents[0].type === Const.OBJECT_TYPE_CONIC ||\n parents[0].elementClass === Const.OBJECT_CLASS_CIRCLE;\n secondParentIsConic =\n parents[1].type === Const.OBJECT_TYPE_CONIC ||\n parents[1].elementClass === Const.OBJECT_CLASS_CIRCLE;\n\n firstParentIsPoint = Type.isPoint(parents[0]);\n secondParentIsPoint = Type.isPoint(parents[1]);\n }\n\n if (\n parents.length !== 2 ||\n !(\n (firstParentIsConic && secondParentIsPoint) ||\n (firstParentIsPoint && secondParentIsConic)\n )\n ) {\n // Failure\n throw new Error(\n \"JSXGraph: Can't create 'polar line' with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent type: [conic|circle,point], [point,conic|circle]\"\n );\n }\n\n if (secondParentIsPoint) {\n el1 = board.select(parents[0]);\n el2 = board.select(parents[1]);\n } else {\n el1 = board.select(parents[1]);\n el2 = board.select(parents[0]);\n }\n\n // Polar lines have been already provided in the tangent element.\n el = board.create(\"tangent\", [el1, el2], attributes);\n\n el.elType = 'polarline';\n return el;\n};\n\n/**\n *\n * @class One of the two tangent lines to a conic or a circle through an external point.\n * @pseudo\n * @description Construct the tangent line through a point to a conic or a circle. There will be either two, one or no\n * such tangent, depending if the point is outside of the conic, on the conic, or inside of the conic.\n * Similar to the intersection of a line with a circle, the specific tangent can be chosen with a third (optional) parameter\n * number.\n * \n * \n *\n * @example\n * var p = board.create('point', [0, 6]);\n * var ell = board.create('ellipse', [[-5, 1], [-2, -1], [-3, 2]]);\n * var t0 = board.create('tangentto', [ell, p, 0]);\n * var t1 = board.create('tangentto', [ell, p, 1]);\n *\n * \n * \n *\n */\nJXG.createTangentTo = function (board, parents, attributes) {\n var el, attr,\n conic, pointFrom, num,\n intersect, polar;\n\n conic = board.select(parents[0]);\n pointFrom = Type.providePoints(board, parents[1], attributes, 'point')[0];\n num = Type.def(parents[2], 0);\n\n if (\n (conic.type !== Const.OBJECT_TYPE_CIRCLE && conic.type !== Const.OBJECT_TYPE_CONIC) ||\n (pointFrom.elementClass !== Const.OBJECT_CLASS_POINT)\n ) {\n throw new Error(\n \"JSXGraph: Can't create tangentto with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [circle|conic,point,number]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'tangentto');\n // A direct analytic geometry approach would be in\n // Richter-Gebert: Perspectives on projective geometry, 11.3\n polar = board.create('polar', [conic, pointFrom], attr.polar);\n intersect = board.create('intersection', [polar, conic, num], attr.point);\n\n el = board.create('tangent', [conic, intersect], attr);\n\n /**\n * The intersection point of the conic/circle with the polar line of the tangentto construction.\n * @memberOf TangentTo.prototype\n * @name point\n * @type JXG.Point\n */\n el.point = intersect;\n\n /**\n * The polar line of the tangentto construction.\n * @memberOf TangentTo.prototype\n * @name polar\n * @type JXG.Line\n */\n el.polar = polar;\n\n el.elType = 'tangentto';\n\n return el;\n};\n\n/**\n * Register the element type tangent at JSXGraph\n * @private\n */\nJXG.registerElement(\"tangent\", JXG.createTangent);\nJXG.registerElement(\"normal\", JXG.createNormal);\nJXG.registerElement('tangentto', JXG.createTangentTo);\nJXG.registerElement(\"polar\", JXG.createTangent);\nJXG.registerElement(\"radicalaxis\", JXG.createRadicalAxis);\nJXG.registerElement(\"polarline\", JXG.createPolarLine);\n\nexport default JXG.Line;\n// export default {\n// Line: JXG.Line,\n// createLine: JXG.createLine,\n// createTangent: JXG.createTangent,\n// createPolar: JXG.createTangent,\n// createSegment: JXG.createSegment,\n// createAxis: JXG.createAxis,\n// createArrow: JXG.createArrow,\n// createRadicalAxis: JXG.createRadicalAxis,\n// createPolarLine: JXG.createPolarLine\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n *\n * @example\n *\n * // Create some free points. e.g. A, B, C, D\n * // Create a group\n * // If the points define a polygon and the polygon has the attribute hasInnerPoints:true,\n * // the polygon can be dragged around.\n *\n * var p, col, pol, g;\n * col = 'blue';\n * p = [];\n * p.push(board.create('point',[-2, -1 ], {size: 5, strokeColor:col, fillColor:col}));\n * p.push(board.create('point',[2, -1 ], {size: 5, strokeColor:col, fillColor:col}));\n * p.push(board.create('point',[2, 1 ], {size: 5, strokeColor:col, fillColor:col}));\n * p.push(board.create('point',[-2, 1], {size: 5, strokeColor:col, fillColor:col}));\n *\n * pol = board.create('polygon', p, {hasInnerPoints: true});\n * g = board.create('group', p);\n *\n * \n * \n *\n * @example\n *\n * // Allow rotations:\n * // Define a center of rotation and declare points of the group as \"rotation points\".\n *\n * var p, col, pol, g;\n * col = 'blue';\n * p = [];\n * p.push(board.create('point',[-2, -1 ], {size: 5, strokeColor:col, fillColor:col}));\n * p.push(board.create('point',[2, -1 ], {size: 5, strokeColor:'red', fillColor:'red'}));\n * p.push(board.create('point',[2, 1 ], {size: 5, strokeColor:'red', fillColor:'red'}));\n * p.push(board.create('point',[-2, 1], {size: 5, strokeColor:col, fillColor:col}));\n *\n * pol = board.create('polygon', p, {hasInnerPoints: true});\n * g = board.create('group', p);\n * g.setRotationCenter(p[0]);\n * g.setRotationPoints([p[1], p[2]]);\n *\n * \n * \n *\n * @example\n *\n * // Allow rotations:\n * // As rotation center, arbitrary points, coordinate arrays,\n * // or functions returning coordinate arrays can be given.\n * // Another possibility is to use the predefined string 'centroid'.\n *\n * // The methods to define the rotation points can be chained.\n *\n * var p, col, pol, g;\n * col = 'blue';\n * p = [];\n * p.push(board.create('point',[-2, -1 ], {size: 5, strokeColor:col, fillColor:col}));\n * p.push(board.create('point',[2, -1 ], {size: 5, strokeColor:'red', fillColor:'red'}));\n * p.push(board.create('point',[2, 1 ], {size: 5, strokeColor:'red', fillColor:'red'}));\n * p.push(board.create('point',[-2, 1], {size: 5, strokeColor:col, fillColor:col}));\n *\n * pol = board.create('polygon', p, {hasInnerPoints: true});\n * g = board.create('group', p).setRotationCenter('centroid').setRotationPoints([p[1], p[2]]);\n *\n * \n * \n *\n * @example\n *\n * // Allow scaling:\n * // As for rotation one can declare points of the group to trigger a scaling operation.\n * // For this, one has to define a scaleCenter, in analogy to rotations.\n *\n * // Here, the yellow point enables scaling, the red point a rotation.\n *\n * var p, col, pol, g;\n * col = 'blue';\n * p = [];\n * p.push(board.create('point',[-2, -1 ], {size: 5, strokeColor:col, fillColor:col}));\n * p.push(board.create('point',[2, -1 ], {size: 5, strokeColor:'yellow', fillColor:'yellow'}));\n * p.push(board.create('point',[2, 1 ], {size: 5, strokeColor:'red', fillColor:'red'}));\n * p.push(board.create('point',[-2, 1], {size: 5, strokeColor:col, fillColor:col}));\n *\n * pol = board.create('polygon', p, {hasInnerPoints: true});\n * g = board.create('group', p).setRotationCenter('centroid').setRotationPoints([p[2]]);\n * g.setScaleCenter(p[0]).setScalePoints(p[1]);\n *\n * \n * \n *\n * @example\n *\n * // Allow Translations:\n * // By default, every point of a group triggers a translation.\n * // There may be situations, when this is not wanted.\n *\n * // In this example, E triggers nothing, but itself is rotation center\n * // and is translated, if other points are moved around.\n *\n * var p, q, col, pol, g;\n * col = 'blue';\n * p = [];\n * p.push(board.create('point',[-2, -1 ], {size: 5, strokeColor:col, fillColor:col}));\n * p.push(board.create('point',[2, -1 ], {size: 5, strokeColor:'yellow', fillColor:'yellow'}));\n * p.push(board.create('point',[2, 1 ], {size: 5, strokeColor:'red', fillColor:'red'}));\n * p.push(board.create('point',[-2, 1], {size: 5, strokeColor:col, fillColor:col}));\n * q = board.create('point',[0, 0], {size: 5, strokeColor:col, fillColor:col});\n *\n * pol = board.create('polygon', p, {hasInnerPoints: true});\n * g = board.create('group', p.concat(q)).setRotationCenter('centroid').setRotationPoints([p[2]]);\n * g.setScaleCenter(p[0]).setScalePoints(p[1]);\n * g.removeTranslationPoint(q);\n *\n * \n * \n *\n * @example\n *\n * // Add an image and use the group tools to manipulate it\n * let urlImg = \"https://jsxgraph.org/distrib/images/uccellino.jpg\";\n * let lowleft = [-2, -1]\n *\n * let col = 'blue';\n * let p = [];\n * p.push(board.create('point', lowleft, { size: 5, strokeColor: col, fillColor: col }));\n * p.push(board.create('point', [2, -1], { size: 5, strokeColor: 'yellow', fillColor: 'yellow', name: 'scale' }));\n * p.push(board.create('point', [2, 1], { size: 5, strokeColor: 'red', fillColor: 'red', name: 'rotate' }));\n * p.push(board.create('point', [-2, 1], { size: 5, strokeColor: col, fillColor: col, name: 'translate' }));\n *\n * let im = board.create('image', [urlImg, lowleft, [2, 2]]);\n * let pol = board.create('polygon', p, { hasInnerPoints: true });\n *\n * let g = board.create('group', p.concat(im))\n * // g.addPoint(im) // image, but adds as a point\n *\n * g.setRotationCenter(lowleft)\n * g.setRotationPoints([p[2]]);\n *\n * g.setScaleCenter(p[0]).setScalePoints(p[1]);\n *\n * \n * \n */\nJXG.createGroup = function (board, parents, attributes) {\n var attr = Type.copyAttributes(attributes, board.options, 'group'),\n g = new JXG.Group(board, attr.id, attr.name, parents, attr);\n\n g.elType = 'group';\n g.setParents(parents);\n\n return g;\n};\n\nJXG.registerElement(\"group\", JXG.createGroup);\n\nexport default JXG.Group;\n// export default {\n// Group: JXG.Group,\n// createGroup: JXG.createGroup\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see
\n * The parameters p1, p2 and radius must be set according to this method parameter.\n * @param {JXG.Point} par1 center of the circle.\n * @param {JXG.Point|JXG.Line|JXG.Circle} par2 Can be\n *
\n * @param {Object} attributes\n * @see JXG.Board#generateName\n */\nJXG.Circle = function (board, method, par1, par2, attributes) {\n // Call the constructor of GeometryElement\n this.constructor(board, attributes, Const.OBJECT_TYPE_CIRCLE, Const.OBJECT_CLASS_CIRCLE);\n\n /**\n * Stores the given method.\n * Can be\n *
\n * @type String\n * @see JXG.Circle#center\n * @see JXG.Circle#point2\n * @see JXG.Circle#radius\n * @see JXG.Circle#line\n * @see JXG.Circle#circle\n */\n this.method = method;\n\n // this is kept so existing code won't ne broken\n this.midpoint = this.board.select(par1);\n\n /**\n * The circles center. Do not set this parameter directly as it will break JSXGraph's update system.\n * @type JXG.Point\n */\n this.center = this.board.select(par1);\n\n /** Point on the circle only set if method equals 'twoPoints'. Do not set this parameter directly as it will break JSXGraph's update system.\n * @type JXG.Point\n * @see JXG.Circle#method\n */\n this.point2 = null;\n\n /** Radius of the circle\n * only set if method equals 'pointRadius'\n * @type Number\n * @default 0\n * @see JXG.Circle#method\n */\n this.radius = 0;\n\n /** Line defining the radius of the circle given by the distance from the startpoint and the endpoint of the line\n * only set if method equals 'pointLine'. Do not set this parameter directly as it will break JSXGraph's update system.\n * @type JXG.Line\n * @default null\n * @see JXG.Circle#method\n */\n this.line = null;\n\n /** Circle defining the radius of the circle given by the radius of the other circle\n * only set if method equals 'pointLine'. Do not set this parameter directly as it will break JSXGraph's update system.\n * @type JXG.Circle\n * @default null\n * @see JXG.Circle#method\n */\n this.circle = null;\n\n this.points = [];\n\n if (method === 'twoPoints') {\n this.point2 = board.select(par2);\n this.radius = this.Radius();\n } else if (method === 'pointRadius') {\n this.gxtterm = par2;\n // Converts JessieCode syntax into JavaScript syntax and generally ensures that the radius is a function\n this.updateRadius = Type.createFunction(par2, this.board);\n // First evaluation of the radius function\n this.updateRadius();\n this.addParentsFromJCFunctions([this.updateRadius]);\n } else if (method === 'pointLine') {\n // dann ist p2 die Id eines Objekts vom Typ Line!\n this.line = board.select(par2);\n this.radius = this.line.point1.coords.distance(\n Const.COORDS_BY_USER,\n this.line.point2.coords\n );\n } else if (method === 'pointCircle') {\n // dann ist p2 die Id eines Objekts vom Typ Circle!\n this.circle = board.select(par2);\n this.radius = this.circle.Radius();\n }\n\n // create Label\n this.id = this.board.setId(this, 'C');\n this.board.renderer.drawEllipse(this);\n this.board.finalizeAdding(this);\n\n this.createGradient();\n this.elType = 'circle';\n this.createLabel();\n\n if (Type.exists(this.center._is_new)) {\n this.addChild(this.center);\n delete this.center._is_new;\n } else {\n this.center.addChild(this);\n }\n\n if (method === 'pointRadius') {\n this.notifyParents(par2);\n } else if (method === 'pointLine') {\n this.line.addChild(this);\n } else if (method === 'pointCircle') {\n this.circle.addChild(this);\n } else if (method === 'twoPoints') {\n if (Type.exists(this.point2._is_new)) {\n this.addChild(this.point2);\n delete this.point2._is_new;\n } else {\n this.point2.addChild(this);\n }\n }\n};\n\nJXG.Circle.prototype = new GeometryElement();\n\nType.copyMethodMap(JXG.Circle, {\n setRadius: \"setRadius\",\n getRadius: \"getRadius\",\n Area: \"Area\",\n area: \"Area\",\n Perimeter: \"Perimeter\",\n Circumference: \"Perimeter\",\n radius: \"Radius\",\n Radius: \"Radius\",\n Diameter: \"Diameter\",\n center: \"center\",\n line: \"line\",\n point2: \"point2\"\n});\n\nJXG.extend(\n JXG.Circle.prototype,\n /** @lends JXG.Circle.prototype */ {\n /**\n * Checks whether (x,y) is near the circle line or inside of the ellipse\n * (in case JXG.Options.conic#hasInnerPoints is true).\n * @param {Number} x Coordinate in x direction, screen coordinates.\n * @param {Number} y Coordinate in y direction, screen coordinates.\n * @returns {Boolean} True if (x,y) is near the circle, False otherwise.\n * @private\n */\n hasPoint: function (x, y) {\n var prec, type,\n mp = this.center.coords.usrCoords,\n p = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),\n r = this.Radius(),\n dx, dy, dist;\n\n if (Type.isObject(this.evalVisProp('precision'))) {\n type = this.board._inputDevice;\n prec = this.evalVisProp('precision.' + type);\n } else {\n // 'inherit'\n prec = this.board.options.precision.hasPoint;\n }\n dx = mp[1] - p.usrCoords[1];\n dy = mp[2] - p.usrCoords[2];\n dist = Mat.hypot(dx, dy);\n\n // We have to use usrCoords, since Radius is available in usrCoords only.\n prec += this.evalVisProp('strokewidth') * 0.5;\n prec /= Math.sqrt(Math.abs(this.board.unitX * this.board.unitY));\n\n if (this.evalVisProp('hasinnerpoints')) {\n return dist < r + prec;\n }\n\n return Math.abs(dist - r) < prec;\n },\n\n // /**\n // * Used to generate a polynomial for a point p that lies on this circle.\n // * @param {JXG.Point} p The point for which the polynomial is generated.\n // * @returns {Array} An array containing the generated polynomial.\n // * @private\n // */\n generatePolynomial: function (p) {\n /*\n * We have four methods to construct a circle:\n * (a) Two points\n * (b) center and radius\n * (c) center and radius given by length of a segment\n * (d) center and radius given by another circle\n *\n * In case (b) we have to distinguish two cases:\n * (i) radius is given as a number\n * (ii) radius is given as a function\n * In the latter case there's no guarantee the radius depends on other geometry elements\n * in a polynomial way so this case has to be omitted.\n *\n * Another tricky case is case (d):\n * The radius depends on another circle so we have to cycle through the ancestors of each circle\n * until we reach one that's radius does not depend on another circles radius.\n *\n *\n * All cases (a) to (d) vary only in calculation of the radius. So the basic formulae for\n * a glider G (g1,g2) on a circle with center M (m1,m2) and radius r is just:\n *\n * (g1-m1)^2 + (g2-m2)^2 - r^2 = 0\n *\n * So the easiest case is (b) with a fixed radius given as a number. The other two cases (a)\n * and (c) are quite the same: Euclidean distance between two points A (a1,a2) and B (b1,b2),\n * squared:\n *\n * r^2 = (a1-b1)^2 + (a2-b2)^2\n *\n * For case (d) we have to cycle recursively through all defining circles and finally return the\n * formulae for calculating r^2. For that we use JXG.Circle.symbolic.generateRadiusSquared().\n */\n var m1 = this.center.symbolic.x,\n m2 = this.center.symbolic.y,\n g1 = p.symbolic.x,\n g2 = p.symbolic.y,\n rsq = this.generateRadiusSquared();\n\n /* No radius can be calculated (Case b.ii) */\n if (rsq === \"\") {\n return [];\n }\n\n return [\n \"((\" + g1 + \")-(\" + m1 + \"))^2 + ((\" + g2 + \")-(\" + m2 + \"))^2 - (\" + rsq + \")\"\n ];\n },\n\n /**\n * Generate symbolic radius calculation for loci determination with Groebner-Basis algorithm.\n * @returns {String} String containing symbolic calculation of the circle's radius or an empty string\n * if the radius can't be expressed in a polynomial equation.\n * @private\n */\n generateRadiusSquared: function () {\n /*\n * Four cases:\n *\n * (a) Two points\n * (b) center and radius\n * (c) center and radius given by length of a segment\n * (d) center and radius given by another circle\n */\n var m1,\n m2,\n p1,\n p2,\n q1,\n q2,\n rsq = \"\";\n\n if (this.method === 'twoPoints') {\n m1 = this.center.symbolic.x;\n m2 = this.center.symbolic.y;\n p1 = this.point2.symbolic.x;\n p2 = this.point2.symbolic.y;\n\n rsq = \"((\" + p1 + \")-(\" + m1 + \"))^2 + ((\" + p2 + \")-(\" + m2 + \"))^2\";\n } else if (this.method === 'pointRadius') {\n if (Type.isNumber(this.radius)) {\n rsq = (this.radius * this.radius).toString();\n }\n } else if (this.method === 'pointLine') {\n p1 = this.line.point1.symbolic.x;\n p2 = this.line.point1.symbolic.y;\n\n q1 = this.line.point2.symbolic.x;\n q2 = this.line.point2.symbolic.y;\n\n rsq = \"((\" + p1 + \")-(\" + q1 + \"))^2 + ((\" + p2 + \")-(\" + q2 + \"))^2\";\n } else if (this.method === 'pointCircle') {\n rsq = this.circle.Radius();\n }\n\n return rsq;\n },\n\n /**\n * Uses the boards renderer to update the circle.\n */\n update: function () {\n var x, y, z, r, c, i;\n\n if (this.needsUpdate) {\n if (this.evalVisProp('trace')) {\n this.cloneToBackground(true);\n }\n\n if (this.method === 'pointLine') {\n this.radius = this.line.point1.coords.distance(\n Const.COORDS_BY_USER,\n this.line.point2.coords\n );\n } else if (this.method === 'pointCircle') {\n this.radius = this.circle.Radius();\n } else if (this.method === 'pointRadius') {\n this.radius = this.updateRadius();\n }\n this.radius = Math.abs(this.radius);\n\n this.updateStdform();\n this.updateQuadraticform();\n\n // Approximate the circle by 4 Bezier segments\n // This will be used for intersections of type curve / circle.\n // See https://spencermortensen.com/articles/bezier-circle/\n z = this.center.coords.usrCoords[0];\n x = this.center.coords.usrCoords[1] / z;\n y = this.center.coords.usrCoords[2] / z;\n z /= z;\n r = this.Radius();\n c = 0.551915024494;\n\n this.numberPoints = 13;\n this.dataX = [\n x + r, x + r, x + r * c, x, x - r * c, x - r, x - r, x - r, x - r * c, x, x + r * c, x + r, x + r\n ];\n this.dataY = [\n y, y + r * c, y + r, y + r, y + r, y + r * c, y, y - r * c, y - r, y - r, y - r, y - r * c, y\n ];\n this.bezierDegree = 3;\n for (i = 0; i < this.numberPoints; i++) {\n this.points[i] = new Coords(\n Const.COORDS_BY_USER,\n [this.dataX[i], this.dataY[i]],\n this.board\n );\n }\n }\n\n return this;\n },\n\n /**\n * Updates this circle's {@link JXG.Circle#quadraticform}.\n * @private\n */\n updateQuadraticform: function () {\n var m = this.center,\n mX = m.X(),\n mY = m.Y(),\n r = this.Radius();\n\n this.quadraticform = [\n [mX * mX + mY * mY - r * r, -mX, -mY],\n [-mX, 1, 0],\n [-mY, 0, 1]\n ];\n },\n\n /**\n * Updates the stdform derived from the position of the center and the circle's radius.\n * @private\n */\n updateStdform: function () {\n this.stdform[3] = 0.5;\n this.stdform[4] = this.Radius();\n this.stdform[1] = -this.center.coords.usrCoords[1];\n this.stdform[2] = -this.center.coords.usrCoords[2];\n if (!isFinite(this.stdform[4])) {\n this.stdform[0] = Type.exists(this.point2)\n ? -(\n this.stdform[1] * this.point2.coords.usrCoords[1] +\n this.stdform[2] * this.point2.coords.usrCoords[2]\n )\n : 0;\n }\n this.normalize();\n },\n\n /**\n * Uses the boards renderer to update the circle.\n * @private\n */\n updateRenderer: function () {\n // var wasReal;\n\n if (!this.needsUpdate) {\n return this;\n }\n\n if (this.visPropCalc.visible) {\n // wasReal = this.isReal;\n this.isReal =\n !isNaN(\n this.center.coords.usrCoords[1] +\n this.center.coords.usrCoords[2] +\n this.Radius()\n ) && this.center.isReal;\n\n if (\n //wasReal &&\n !this.isReal\n ) {\n this.updateVisibility(false);\n }\n }\n\n // Update the position\n if (this.visPropCalc.visible) {\n this.board.renderer.updateEllipse(this);\n }\n\n // Update the label if visible.\n if (\n this.hasLabel &&\n this.visPropCalc.visible &&\n this.label &&\n this.label.visPropCalc.visible &&\n this.isReal\n ) {\n this.label.update();\n this.board.renderer.updateText(this.label);\n }\n\n // Update rendNode display\n this.setDisplayRendNode();\n // if (this.visPropCalc.visible !== this.visPropOld.visible) {\n // this.board.renderer.display(this, this.visPropCalc.visible);\n // this.visPropOld.visible = this.visPropCalc.visible;\n //\n // if (this.hasLabel) {\n // this.board.renderer.display(this.label, this.label.visPropCalc.visible);\n // }\n // }\n\n this.needsUpdate = false;\n return this;\n },\n\n /**\n * Finds dependencies in a given term and resolves them by adding the elements referenced in this\n * string to the circle's list of ancestors.\n * @param {String} contentStr\n * @private\n */\n notifyParents: function (contentStr) {\n if (Type.isString(contentStr)) {\n GeonextParser.findDependencies(this, contentStr, this.board);\n }\n },\n\n /**\n * Set a new radius, then update the board.\n * @param {String|Number|function} r A string, function or number describing the new radius.\n * @returns {JXG.Circle} Reference to this circle\n */\n setRadius: function (r) {\n this.updateRadius = Type.createFunction(r, this.board);\n this.addParentsFromJCFunctions([this.updateRadius]);\n this.board.update();\n\n return this;\n },\n\n /**\n * Calculates the radius of the circle.\n * @param {String|Number|function} [value] Set new radius\n * @returns {Number} The radius of the circle\n */\n Radius: function (value) {\n if (Type.exists(value)) {\n this.setRadius(value);\n return this.Radius();\n }\n\n if (this.method === 'twoPoints') {\n if (\n Type.cmpArrays(this.point2.coords.usrCoords, [0, 0, 0]) ||\n Type.cmpArrays(this.center.coords.usrCoords, [0, 0, 0])\n ) {\n return NaN;\n }\n\n return this.center.Dist(this.point2);\n }\n\n if (this.method === \"pointLine\" || this.method === 'pointCircle') {\n return this.radius;\n }\n\n if (this.method === 'pointRadius') {\n return (this.evalVisProp('nonnegativeonly')) ?\n Math.max(0.0, this.updateRadius()) :\n Math.abs(this.updateRadius());\n }\n\n return NaN;\n },\n\n /**\n * Calculates the diameter of the circle.\n * @returns {Number} The Diameter of the circle\n */\n Diameter: function () {\n return 2 * this.Radius();\n },\n\n /**\n * Use {@link JXG.Circle#Radius}.\n * @deprecated\n */\n getRadius: function () {\n JXG.deprecated(\"Circle.getRadius()\", \"Circle.Radius()\");\n return this.Radius();\n },\n\n // documented in geometry element\n getTextAnchor: function () {\n return this.center.coords;\n },\n\n // documented in geometry element\n getLabelAnchor: function () {\n var x, y, pos,\n xy, lbda, sgn,\n dist = 1.5,\n r = this.Radius(),\n c = this.center.coords.usrCoords,\n SQRTH = 7.071067811865e-1; // sqrt(2)/2\n\n if (!Type.exists(this.label)) {\n return new Coords(Const.COORDS_BY_SCREEN, [NaN, NaN], this.board);\n }\n\n pos = this.label.evalVisProp('position');\n if (!Type.isString(pos)) {\n return new Coords(Const.COORDS_BY_SCREEN, [NaN, NaN], this.board);\n }\n\n if (pos.indexOf('right') < 0 && pos.indexOf('left') < 0) {\n switch (this.evalVisProp('label.position')) {\n case \"lft\":\n x = c[1] - r;\n y = c[2];\n break;\n case \"llft\":\n x = c[1] - SQRTH * r;\n y = c[2] - SQRTH * r;\n break;\n case \"rt\":\n x = c[1] + r;\n y = c[2];\n break;\n case \"lrt\":\n x = c[1] + SQRTH * r;\n y = c[2] - SQRTH * r;\n break;\n case \"urt\":\n x = c[1] + SQRTH * r;\n y = c[2] + SQRTH * r;\n break;\n case \"top\":\n x = c[1];\n y = c[2] + r;\n break;\n case \"bot\":\n x = c[1];\n y = c[2] - r;\n break;\n default:\n // includes case 'ulft'\n x = c[1] - SQRTH * r;\n y = c[2] + SQRTH * r;\n break;\n }\n } else {\n // New positioning\n c = this.center.coords.scrCoords;\n\n xy = Type.parsePosition(pos);\n lbda = Type.parseNumber(xy.pos, 2 * Math.PI, 1);\n if (xy.pos.indexOf('fr') < 0 &&\n xy.pos.indexOf('%') < 0) {\n if (xy.pos.indexOf('px') >= 0) {\n // 'px' or numbers are not supported\n lbda = 0;\n } else {\n // Pure numbers are interpreted as degrees\n lbda *= Math.PI / 180;\n }\n }\n\n // Position left or right\n sgn = 1;\n if (xy.side === 'left') {\n sgn = -1;\n }\n\n if (Type.exists(this.label)) {\n dist = sgn * 0.5 * this.label.evalVisProp('distance');\n }\n\n x = c[1] + (r * this.board.unitX + this.label.size[0] * dist) * Math.cos(lbda);\n y = c[2] - (r * this.board.unitY + this.label.size[1] * dist) * Math.sin(lbda);\n\n return new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board);\n }\n\n return new Coords(Const.COORDS_BY_USER, [x, y], this.board);\n },\n\n // documented in geometry element\n cloneToBackground: function () {\n var er,\n r = this.Radius(),\n copy = Type.getCloneObject(this);\n\n copy.center = {\n coords: this.center.coords\n };\n copy.Radius = function () {\n return r;\n };\n copy.getRadius = function () {\n return r;\n };\n\n er = this.board.renderer.enhancedRendering;\n this.board.renderer.enhancedRendering = true;\n this.board.renderer.drawEllipse(copy);\n this.board.renderer.enhancedRendering = er;\n this.traces[copy.id] = copy.rendNode;\n\n return this;\n },\n\n /**\n * Add transformations to this circle.\n * @param {JXG.Transformation|Array} transform Either one {@link JXG.Transformation} or an array of {@link JXG.Transformation}s.\n * @returns {JXG.Circle} Reference to this circle object.\n */\n addTransform: function (transform) {\n var i,\n list = Type.isArray(transform) ? transform : [transform],\n len = list.length;\n\n for (i = 0; i < len; i++) {\n this.center.transformations.push(list[i]);\n\n if (this.method === 'twoPoints') {\n this.point2.transformations.push(list[i]);\n }\n }\n\n return this;\n },\n\n removeTransform: function (transform) {\n var i,\n list = Type.isArray(transform) ? transform : [transform],\n len = list.length;\n\n for (i = 0; i < len; i++) {\n Type.removeElementFromArray(this.center.transformations, list[i]);\n\n if (this.method === 'twoPoints') {\n Type.removeElementFromArray(this.point2.transformations, list[i]);\n }\n }\n\n return this;\n },\n\n clearTransforms: function () {\n this.center.transformations = [];\n\n if (this.method === 'twoPoints') {\n this.point2.transformations = [];\n }\n\n return this;\n },\n\n // see element.js\n snapToGrid: function () {\n var forceIt = this.evalVisProp('snaptogrid');\n\n this.center.handleSnapToGrid(forceIt, true);\n if (this.method === 'twoPoints') {\n this.point2.handleSnapToGrid(forceIt, true);\n }\n\n return this;\n },\n\n // see element.js\n snapToPoints: function () {\n var forceIt = this.evalVisProp('snaptopoints');\n\n this.center.handleSnapToPoints(forceIt);\n if (this.method === 'twoPoints') {\n this.point2.handleSnapToPoints(forceIt);\n }\n\n return this;\n },\n\n /**\n * Treats the circle as parametric curve and calculates its X coordinate.\n * @param {Number} t Number between 0 and 1.\n * @returns {Number} X(t)= radius*cos(t)+centerX.\n */\n X: function (t) {\n return this.Radius() * Math.cos(t * 2 * Math.PI) + this.center.coords.usrCoords[1];\n },\n\n /**\n * Treats the circle as parametric curve and calculates its Y coordinate.\n * @param {Number} t Number between 0 and 1.\n * @returns {Number} X(t)= radius*sin(t)+centerY.\n */\n Y: function (t) {\n return this.Radius() * Math.sin(t * 2 * Math.PI) + this.center.coords.usrCoords[2];\n },\n\n /**\n * Treat the circle as parametric curve and calculates its Z coordinate.\n * @param {Number} t ignored\n * @returns {Number} 1.0\n */\n Z: function (t) {\n return 1.0;\n },\n\n /**\n * Returns 0.\n * @private\n */\n minX: function () {\n return 0.0;\n },\n\n /**\n * Returns 1.\n * @private\n */\n maxX: function () {\n return 1.0;\n },\n\n /**\n * Circle area\n * @returns {Number} area of the circle.\n */\n Area: function () {\n var r = this.Radius();\n\n return r * r * Math.PI;\n },\n\n /**\n * Perimeter (circumference) of circle.\n * @returns {Number} Perimeter of circle in user units.\n */\n Perimeter: function () {\n return 2 * this.Radius() * Math.PI;\n },\n\n /**\n * Get bounding box of the circle.\n * @returns {Array} [x1, y1, x2, y2]\n */\n bounds: function () {\n var uc = this.center.coords.usrCoords,\n r = this.Radius();\n\n return [uc[1] - r, uc[2] + r, uc[1] + r, uc[2] - r];\n },\n\n /**\n * Get data to construct this element. Data consists of the parent elements\n * and static data like radius.\n * @returns {Array} data necessary to construct this element\n */\n getParents: function () {\n if (this.parents.length === 1) {\n // i.e. this.method === 'pointRadius'\n return this.parents.concat(this.radius);\n }\n return this.parents;\n }\n }\n);\n\n/**\n * @class A circle can be defined by various combinations of points and numbers.\n * @pseudo\n * @description A circle consists of all points with a given distance from one point. This point is called center, the distance is called radius.\n * A circle can be constructed by providing a center and a point on the circle or a center and a radius (given as a number, function,\n * line, or circle). If the radius is a negative value, its absolute values is taken.\n * @name Circle\n * @augments JXG.Circle\n * @constructor\n * @type JXG.Circle\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_number,JXG.Point,JXG.Line,JXG.Circle} center,radius The center must be given as a {@link JXG.Point},\n * see {@link JXG.providePoints}, but the radius can be given\n * as a number (which will create a circle with a fixed radius),\n * another {@link JXG.Point}, a {@link JXG.Line} (the distance of start and end point of the\n * line will determine the radius), or another {@link JXG.Circle}.\n * \n * @example\n * // Create a circle providing two points\n * var p1 = board.create('point', [2.0, 2.0]),\n * c1 = board.create('circle', [p1, 3]);\n *\n * // Create another circle using the above circle\n * var c2 = board.create('circle', [function() { return [p1.X(), p1.Y() + 1];}, function() { return c1.Radius(); }]);\n * \n * \n * @example\n * var li = board.create('line', [1,1,1], {strokeColor: '#aaaaaa'});\n * var reflect = board.create('transform', [li], {type: 'reflect'});\n *\n * var c1 = board.create('circle', [[-2,-2], [-2, -1]], {center: {visible:true}});\n * var c2 = board.create('circle', [c1, reflect]);\n * * \n * \n *\n * @example\n * var t = board.create('transform', [2, 1.5], {type: 'scale'});\n * var c1 = board.create('circle', [[1.3, 1.3], [0, 1.3]], {strokeColor: 'black', center: {visible:true}});\n * var c2 = board.create('circle', [c1, t], {strokeColor: 'black'});\n *\n * \n * \n *\n */\nJXG.createCircle = function (board, parents, attributes) {\n var el,\n p,\n i,\n attr,\n obj,\n isDraggable = true,\n point_style = [\"center\", \"point2\"];\n\n p = [];\n obj = board.select(parents[0]);\n if (\n Type.isObject(obj) &&\n obj.elementClass === Const.OBJECT_CLASS_CIRCLE &&\n Type.isTransformationOrArray(parents[1])\n ) {\n attr = Type.copyAttributes(attributes, board.options, 'circle');\n // if (!Type.exists(attr.type) || attr.type.toLowerCase() !== 'euclidean') {\n // // Create a circle element from a circle and a Euclidean transformation\n // el = JXG.createCircle(board, [obj.center, function() { return obj.Radius(); }], attr);\n // } else {\n // Create a conic element from a circle and a projective transformation\n el = JXG.createEllipse(\n board,\n [\n obj.center,\n obj.center,\n function () {\n return 2 * obj.Radius();\n }\n ],\n attr\n );\n // }\n el.addTransform(parents[1]);\n return el;\n }\n // Circle defined by points\n for (i = 0; i < parents.length; i++) {\n if (Type.isPointType(board, parents[i])) {\n if (parents.length < 3) {\n p.push(\n Type.providePoints(board, [parents[i]], attributes, \"circle\", [point_style[i]])[0]\n );\n } else {\n p.push(\n Type.providePoints(board, [parents[i]], attributes, 'point')[0]\n );\n }\n if (p[p.length - 1] === false) {\n throw new Error(\n \"JSXGraph: Can't create circle from this type. Please provide a point type.\"\n );\n }\n } else {\n p.push(parents[i]);\n }\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'circle');\n\n if (p.length === 2 && Type.isPoint(p[0]) && Type.isPoint(p[1])) {\n // Point/Point\n el = new JXG.Circle(board, \"twoPoints\", p[0], p[1], attr);\n } else if (\n (Type.isNumber(p[0]) || Type.isFunction(p[0]) || Type.isString(p[0])) &&\n Type.isPoint(p[1])\n ) {\n // Number/Point\n el = new JXG.Circle(board, \"pointRadius\", p[1], p[0], attr);\n } else if (\n (Type.isNumber(p[1]) || Type.isFunction(p[1]) || Type.isString(p[1])) &&\n Type.isPoint(p[0])\n ) {\n // Point/Number\n el = new JXG.Circle(board, \"pointRadius\", p[0], p[1], attr);\n } else if (p[0].elementClass === Const.OBJECT_CLASS_CIRCLE && Type.isPoint(p[1])) {\n // Circle/Point\n el = new JXG.Circle(board, \"pointCircle\", p[1], p[0], attr);\n } else if (p[1].elementClass === Const.OBJECT_CLASS_CIRCLE && Type.isPoint(p[0])) {\n // Point/Circle\n el = new JXG.Circle(board, \"pointCircle\", p[0], p[1], attr);\n } else if (p[0].elementClass === Const.OBJECT_CLASS_LINE && Type.isPoint(p[1])) {\n // Line/Point\n el = new JXG.Circle(board, \"pointLine\", p[1], p[0], attr);\n } else if (p[1].elementClass === Const.OBJECT_CLASS_LINE && Type.isPoint(p[0])) {\n // Point/Line\n el = new JXG.Circle(board, \"pointLine\", p[0], p[1], attr);\n } else if (\n parents.length === 3 &&\n Type.isPoint(p[0]) &&\n Type.isPoint(p[1]) &&\n Type.isPoint(p[2])\n ) {\n // Circle through three points\n // Check if circumcircle element is available\n if (JXG.elements.circumcircle) {\n el = JXG.elements.circumcircle(board, p, attr);\n } else {\n throw new Error(\n \"JSXGraph: Can't create circle with three points. Please include the circumcircle element (element/composition).\"\n );\n }\n } else {\n throw new Error(\n \"JSXGraph: Can't create circle with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,point], [point,number], [point,function], [point,circle], [point,point,point], [circle,transformation]\"\n );\n }\n\n el.isDraggable = isDraggable;\n el.setParents(p);\n el.elType = 'circle';\n for (i = 0; i < p.length; i++) {\n if (Type.isPoint(p[i])) {\n el.inherits.push(p[i]);\n }\n }\n return el;\n};\n\nJXG.registerElement(\"circle\", JXG.createCircle);\n\nexport default JXG.Circle;\n// export default {\n// Circle: JXG.Circle,\n// createCircle: JXG.createCircle\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n * @example\n * // Create an elliptical arc\n * var p1 = board.create('point', [-1, 2]);\n * var p2 = board.create('point', [ 1, 2]);\n * var p3 = board.create('point', [0, 3]);\n *\n * var ell = board.create('ellipse', [\n * p1, p2, p3, 0, Math.PI], {\n * lastArrow: {type: 7}\n * });\n *\n * \n * \n *\n *\n */\nJXG.createEllipse = function (board, parents, attributes) {\n var polarForm,\n curve,\n M,\n C,\n majorAxis,\n i,\n hasPointOrg,\n // focus 1 and focus 2\n F = [],\n attr_foci = Type.copyAttributes(attributes, board.options, \"conic\", 'foci'),\n attr_center = Type.copyAttributes(attributes, board.options, \"conic\", 'center'),\n attr_curve = Type.copyAttributes(attributes, board.options, 'conic');\n\n // The foci and the third point are either points or coordinate arrays.\n for (i = 0; i < 2; i++) {\n // focus i given by coordinates\n if (parents[i].length > 1) {\n F[i] = board.create(\"point\", parents[i], attr_foci);\n // focus i given by point\n } else if (Type.isPoint(parents[i])) {\n F[i] = board.select(parents[i]);\n // given by function\n } else if (Type.isFunction(parents[i]) && Type.isPoint(parents[i]())) {\n F[i] = parents[i]();\n // focus i given by point name\n } else if (Type.isString(parents[i])) {\n F[i] = board.select(parents[i]);\n } else {\n throw new Error(\n \"JSXGraph: Can't create Ellipse with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point], [point,point,number|function]\"\n );\n }\n }\n\n // length of major axis\n if (Type.isNumber(parents[2])) {\n majorAxis = Type.createFunction(parents[2], board);\n } else if (Type.isFunction(parents[2]) && Type.isNumber(parents[2]())) {\n majorAxis = parents[2];\n } else {\n // point on ellipse\n if (Type.isPoint(parents[2])) {\n C = board.select(parents[2]);\n // point on ellipse given by coordinates\n } else if (parents[2].length > 1) {\n C = board.create(\"point\", parents[2], attr_foci);\n // given by function\n } else if (Type.isFunction(parents[2]) && Type.isPoint(parents[2]())) {\n C = parents[2]();\n // focus i given by point name\n } else if (Type.isString(parents[2])) {\n C = board.select(parents[2]);\n } else {\n throw new Error(\n \"JSXGraph: Can't create Ellipse with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point], [point,point,number|function]\"\n );\n }\n /** @ignore */\n majorAxis = function () {\n return C.Dist(F[0]) + C.Dist(F[1]);\n };\n }\n\n // to\n if (!Type.exists(parents[4])) {\n parents[4] = 2 * Math.PI;\n }\n\n // from\n if (!Type.exists(parents[3])) {\n parents[3] = 0.0;\n }\n\n M = board.create(\n \"point\",\n [\n function () {\n return (F[0].X() + F[1].X()) * 0.5;\n },\n function () {\n return (F[0].Y() + F[1].Y()) * 0.5;\n }\n ],\n attr_center\n );\n\n /**\n * @class\n * @ignore\n */\n curve = board.create(\n \"curve\",\n [\n function (x) {\n return 0;\n },\n function (x) {\n return 0;\n },\n parents[3],\n parents[4]\n ],\n attr_curve\n );\n\n curve.majorAxis = majorAxis;\n\n // Store the original hasPoint method. It will be called inside of the new hasPoint method.\n hasPointOrg = curve.hasPoint;\n\n /** @ignore */\n polarForm = function (phi, suspendUpdate) {\n var r, rr, ax, ay, bx, by, axbx, ayby, f;\n\n if (!suspendUpdate) {\n r = majorAxis();\n rr = r * r;\n ax = F[0].X();\n ay = F[0].Y();\n bx = F[1].X();\n by = F[1].Y();\n axbx = ax - bx;\n ayby = ay - by;\n f = (rr - ax * ax - ay * ay + bx * bx + by * by) / (2 * r);\n\n curve.quadraticform = [\n [f * f - bx * bx - by * by, (f * axbx) / r + bx, (f * ayby) / r + by],\n [(f * axbx) / r + bx, (axbx * axbx) / rr - 1, (axbx * ayby) / rr],\n [(f * ayby) / r + by, (axbx * ayby) / rr, (ayby * ayby) / rr - 1]\n ];\n }\n };\n\n /** @ignore */\n curve.X = function (phi, suspendUpdate) {\n var r = majorAxis(),\n c = F[1].Dist(F[0]),\n b = (0.5 * (c * c - r * r)) / (c * Math.cos(phi) - r),\n beta = Math.atan2(F[1].Y() - F[0].Y(), F[1].X() - F[0].X());\n\n if (!suspendUpdate) {\n polarForm(phi, suspendUpdate);\n }\n\n return F[0].X() + Math.cos(beta + phi) * b;\n };\n\n /** @ignore */\n curve.Y = function (phi, suspendUpdate) {\n var r = majorAxis(),\n c = F[1].Dist(F[0]),\n b = (0.5 * (c * c - r * r)) / (c * Math.cos(phi) - r),\n beta = Math.atan2(F[1].Y() - F[0].Y(), F[1].X() - F[0].X());\n\n return F[0].Y() + Math.sin(beta + phi) * b;\n };\n\n curve.midpoint = curve.center = M;\n curve.type = Const.OBJECT_TYPE_CONIC;\n curve.subs = {\n center: curve.center\n };\n curve.inherits.push(curve.center, F[0], F[1]);\n if (Type.isPoint(C)) {\n curve.inherits.push(C);\n }\n\n /**\n * Checks whether (x,y) is near the ellipse line or inside of the ellipse\n * (in case JXG.Options.conic#hasInnerPoints is true).\n * @param {Number} x Coordinate in x direction, screen coordinates.\n * @param {Number} y Coordinate in y direction, screen coordinates.\n * @returns {Boolean} True if (x,y) is near the ellipse, False otherwise.\n * @private\n * @ignore\n */\n curve.hasPoint = function (x, y) {\n var ac, bc, r, p, dist;\n\n if (this.evalVisProp('hasinnerpoints')) {\n ac = F[0].coords;\n bc = F[1].coords;\n r = this.majorAxis();\n p = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board);\n dist = p.distance(Const.COORDS_BY_USER, ac) + p.distance(Const.COORDS_BY_USER, bc);\n\n return dist <= r;\n }\n\n return hasPointOrg.apply(this, arguments);\n };\n\n M.addChild(curve);\n for (i = 0; i < 2; i++) {\n if (Type.isPoint(F[i])) {\n F[i].addChild(curve);\n }\n }\n if (Type.isPoint(C)) {\n C.addChild(curve);\n }\n curve.setParents(parents);\n\n return curve;\n};\n\n/**\n * @class A hyperbola is a special conic section given by two points (the foci) and a third point on the hyperbola or\n * the length of the major axis.\n * @pseudo\n * @name Hyperbola\n * @augments Conic\n * @constructor\n * @type JXG.Curve\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point,array_JXG.Point,array_JXG.Point,array} point1,point2,point3 Parent elements can be three elements either of type {@link JXG.Point} or array of\n * numbers describing the coordinates of a point. In the latter case the point will be constructed automatically as a fixed invisible point.\n * @param {JXG.Point,array_JXG.Point,array_number,function} point1,point2,number Parent elements can be two elements either of type {@link JXG.Point} or array of\n * numbers describing the coordinates of a point. The third parameter is a number/function which defines the length of the major axis\n * @param {Number} start (Optional) parameter of the curve start, default: -π.\n * @param {Number} end (Optional) parameter for the curve end, default: π.\n * @example\n * // Create an Hyperbola by three points\n * var A = board.create('point', [-1,4]);\n * var B = board.create('point', [-1,-4]);\n * var C = board.create('point', [1,1]);\n * var el = board.create('hyperbola',[A,B,C]);\n * \n * \n */\nJXG.createHyperbola = function (board, parents, attributes) {\n var polarForm,\n curve,\n M,\n C,\n majorAxis,\n i,\n // focus 1 and focus 2\n F = [],\n attr_foci = Type.copyAttributes(attributes, board.options, \"conic\", 'foci'),\n attr_center = Type.copyAttributes(attributes, board.options, \"conic\", 'center'),\n attr_curve = Type.copyAttributes(attributes, board.options, 'conic');\n\n // The foci and the third point are either points or coordinate arrays.\n for (i = 0; i < 2; i++) {\n // focus i given by coordinates\n if (parents[i].length > 1) {\n F[i] = board.create(\"point\", parents[i], attr_foci);\n // focus i given by point\n } else if (Type.isPoint(parents[i])) {\n F[i] = board.select(parents[i]);\n // given by function\n } else if (Type.isFunction(parents[i]) && Type.isPoint(parents[i]())) {\n F[i] = parents[i]();\n // focus i given by point name\n } else if (Type.isString(parents[i])) {\n F[i] = board.select(parents[i]);\n } else {\n throw new Error(\n \"JSXGraph: Can't create Hyperbola with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point], [point,point,number|function]\"\n );\n }\n }\n\n // length of major axis\n if (Type.isNumber(parents[2])) {\n majorAxis = Type.createFunction(parents[2], board);\n } else if (Type.isFunction(parents[2]) && Type.isNumber(parents[2]())) {\n majorAxis = parents[2];\n } else {\n // point on ellipse\n if (Type.isPoint(parents[2])) {\n C = board.select(parents[2]);\n // point on ellipse given by coordinates\n } else if (parents[2].length > 1) {\n C = board.create(\"point\", parents[2], attr_foci);\n // given by function\n } else if (Type.isFunction(parents[2]) && Type.isPoint(parents[2]())) {\n C = parents[2]();\n // focus i given by point name\n } else if (Type.isString(parents[2])) {\n C = board.select(parents[2]);\n } else {\n throw new Error(\n \"JSXGraph: Can't create Hyperbola with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point], [point,point,number|function]\"\n );\n }\n /** @ignore */\n majorAxis = function () {\n return C.Dist(F[0]) - C.Dist(F[1]);\n };\n }\n\n // to\n if (!Type.exists(parents[4])) {\n parents[4] = 1.0001 * Math.PI;\n }\n\n // from\n if (!Type.exists(parents[3])) {\n parents[3] = -1.0001 * Math.PI;\n }\n\n M = board.create(\n \"point\",\n [\n function () {\n return (F[0].X() + F[1].X()) * 0.5;\n },\n function () {\n return (F[0].Y() + F[1].Y()) * 0.5;\n }\n ],\n attr_center\n );\n\n /**\n * @class\n * @ignore\n */\n curve = board.create(\n \"curve\",\n [\n function (x) {\n return 0;\n },\n function (x) {\n return 0;\n },\n parents[3],\n parents[4]\n ],\n attr_curve\n );\n\n curve.majorAxis = majorAxis;\n\n // Hyperbola is defined by (a*sec(t),b*tan(t)) and sec(t) = 1/cos(t)\n /** @ignore */\n polarForm = function (phi, suspendUpdate) {\n var r, rr, ax, ay, bx, by, axbx, ayby, f;\n\n if (!suspendUpdate) {\n r = majorAxis();\n rr = r * r;\n ax = F[0].X();\n ay = F[0].Y();\n bx = F[1].X();\n by = F[1].Y();\n axbx = ax - bx;\n ayby = ay - by;\n f = (rr - ax * ax - ay * ay + bx * bx + by * by) / (2 * r);\n\n curve.quadraticform = [\n [f * f - bx * bx - by * by, (f * axbx) / r + bx, (f * ayby) / r + by],\n [(f * axbx) / r + bx, (axbx * axbx) / rr - 1, (axbx * ayby) / rr],\n [(f * ayby) / r + by, (axbx * ayby) / rr, (ayby * ayby) / rr - 1]\n ];\n }\n };\n\n /** @ignore */\n curve.X = function (phi, suspendUpdate) {\n var r = majorAxis(),\n c = F[1].Dist(F[0]),\n b = (0.5 * (c * c - r * r)) / (c * Math.cos(phi) + r),\n beta = Math.atan2(F[1].Y() - F[0].Y(), F[1].X() - F[0].X());\n\n if (!suspendUpdate) {\n polarForm(phi, suspendUpdate);\n }\n\n return F[0].X() + Math.cos(beta + phi) * b;\n };\n\n /** @ignore */\n curve.Y = function (phi, suspendUpdate) {\n var r = majorAxis(),\n c = F[1].Dist(F[0]),\n b = (0.5 * (c * c - r * r)) / (c * Math.cos(phi) + r),\n beta = Math.atan2(F[1].Y() - F[0].Y(), F[1].X() - F[0].X());\n\n return F[0].Y() + Math.sin(beta + phi) * b;\n };\n\n curve.midpoint = curve.center = M;\n curve.subs = {\n center: curve.center\n };\n curve.inherits.push(curve.center, F[0], F[1]);\n if (Type.isPoint(C)) {\n curve.inherits.push(C);\n }\n curve.type = Const.OBJECT_TYPE_CONIC;\n\n M.addChild(curve);\n for (i = 0; i < 2; i++) {\n if (Type.isPoint(F[i])) {\n F[i].addChild(curve);\n }\n }\n if (Type.isPoint(C)) {\n C.addChild(curve);\n }\n curve.setParents(parents);\n\n return curve;\n};\n\n/**\n * @class A parabola is a special conic section given by one point (the focus) and a line (the directrix).\n * @pseudo\n * @name Parabola\n * @augments Conic\n * @constructor\n * @type Object\n * @description JXG.Curve\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point,array_JXG.Line} point,line Parent elements are a point and a line or a pair of coordinates.\n * Optional parameters three and four are numbers which define the curve length (e.g. start/end). Default values are -pi and pi.\n * @example\n * // Create a parabola by a point C and a line l.\n * var A = board.create('point', [-1,4]);\n * var B = board.create('point', [-1,-4]);\n * var l = board.create('line', [A,B]);\n * var C = board.create('point', [1,1]);\n * var el = board.create('parabola',[C,l]);\n * \n * \n *\n * @example\n * var par = board.create('parabola',[[3.25, 0], [[0.25, 1],[0.25, 0]]]);\n *\n * \n * \n *\n */\nJXG.createParabola = function (board, parents, attributes) {\n var polarForm,\n curve,\n M,\n // focus\n F1 = parents[0],\n // directrix\n l = parents[1],\n attr_foci = Type.copyAttributes(attributes, board.options, \"conic\", 'foci'),\n attr_center = Type.copyAttributes(attributes, board.options, \"conic\", 'center'),\n attr_curve = Type.copyAttributes(attributes, board.options, 'conic'),\n attr_line;\n\n // focus 1 given by coordinates\n if (parents[0].length > 1) {\n F1 = board.create(\"point\", parents[0], attr_foci);\n // focus 1 given by point\n } else if (Type.isPoint(parents[0])) {\n F1 = board.select(parents[0]);\n // given by function\n } else if (Type.isFunction(parents[0]) && Type.isPoint(parents[0]())) {\n F1 = parents[0]();\n // focus 1 given by point name\n } else if (Type.isString(parents[0])) {\n F1 = board.select(parents[0]);\n } else {\n throw new Error(\n \"JSXGraph: Can't create Parabola with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,line]\"\n );\n }\n\n // Create line if given as array of two points.\n if (Type.isArray(l) && l.length === 2) {\n attr_line = Type.copyAttributes(attributes, board.options, \"conic\", 'line');\n l = board.create(\"line\", l, attr_line);\n }\n\n // to\n if (!Type.exists(parents[3])) {\n parents[3] = 2 * Math.PI;\n }\n\n // from\n if (!Type.exists(parents[2])) {\n parents[2] = 0;\n }\n\n M = board.create(\n \"point\",\n [\n function () {\n /*\n var v = [0, l.stdform[1], l.stdform[2]];\n v = Mat.crossProduct(v, F1.coords.usrCoords);\n return Geometry.meetLineLine(v, l.stdform, 0, board).usrCoords;\n */\n return Geometry.projectPointToLine(F1, l, board).usrCoords;\n }\n ],\n attr_center\n );\n\n /**\n * @class\n * @ignore\n */\n curve = board.create(\n \"curve\",\n [\n function (x) {\n return 0;\n },\n function (x) {\n return 0;\n },\n parents[2],\n parents[3]\n ],\n attr_curve\n );\n\n curve.midpoint = curve.center = M;\n curve.subs = {\n center: curve.center\n };\n curve.inherits.push(curve.center);\n\n /** @ignore */\n polarForm = function (t, suspendUpdate) {\n var a, b, c, ab, px, py;\n\n if (!suspendUpdate) {\n a = l.stdform[1];\n b = l.stdform[2];\n c = l.stdform[0];\n ab = a * a + b * b;\n px = F1.X();\n py = F1.Y();\n\n curve.quadraticform = [\n [c * c - ab * (px * px + py * py), c * a + ab * px, c * b + ab * py],\n [c * a + ab * px, -b * b, a * b],\n [c * b + ab * py, a * b, -a * a]\n ];\n }\n };\n\n /** @ignore */\n curve.X = function (phi, suspendUpdate) {\n var a,\n det,\n beta = l.getAngle(),\n d = Geometry.distPointLine(F1.coords.usrCoords, l.stdform),\n A = l.point1.coords.usrCoords,\n B = l.point2.coords.usrCoords,\n M = F1.coords.usrCoords;\n\n // Handle the case if one of the two defining points of the line is an ideal point\n if (A[0] === 0) {\n A = [1, B[1] + l.stdform[2], B[2] - l.stdform[1]];\n } else if (B[0] === 0) {\n B = [1, A[1] + l.stdform[2], A[2] - l.stdform[1]];\n }\n det = (B[1] - A[1]) * (M[2] - A[2]) - (B[2] - A[2]) * (M[1] - A[1]) >= 0 ? 1 : -1;\n a = (det * d) / (1 - Math.sin(phi));\n\n if (!suspendUpdate) {\n polarForm(phi, suspendUpdate);\n }\n\n return F1.X() + Math.cos(phi + beta) * a;\n };\n\n /** @ignore */\n curve.Y = function (phi, suspendUpdate) {\n var a,\n det,\n beta = l.getAngle(),\n d = Geometry.distPointLine(F1.coords.usrCoords, l.stdform),\n A = l.point1.coords.usrCoords,\n B = l.point2.coords.usrCoords,\n M = F1.coords.usrCoords;\n\n // Handle the case if one of the two defining points of the line is an ideal point\n if (A[0] === 0) {\n A = [1, B[1] + l.stdform[2], B[2] - l.stdform[1]];\n } else if (B[0] === 0) {\n B = [1, A[1] + l.stdform[2], A[2] - l.stdform[1]];\n }\n det = (B[1] - A[1]) * (M[2] - A[2]) - (B[2] - A[2]) * (M[1] - A[1]) >= 0 ? 1 : -1;\n a = (det * d) / (1 - Math.sin(phi));\n\n return F1.Y() + Math.sin(phi + beta) * a;\n };\n\n curve.type = Const.OBJECT_TYPE_CONIC;\n M.addChild(curve);\n\n if (Type.isPoint(F1)) {\n F1.addChild(curve);\n curve.inherits.push(F1);\n }\n\n l.addChild(curve);\n curve.setParents(parents);\n\n return curve;\n};\n\n/**\n *\n * @class Create a generic conic section either by five points or the coefficients of the general conic's equation.\n * If the conic section is defined by the coefficients of the equation\n * \n * \n * board.create('conic', [A, C, F, B/2, D/2, E/2]);\n * \n * @pseudo\n * @name Conic\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Conic\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point,Array_JXG.Point,Array_JXG.Point,Array_JXG.Point,Array_JXG.Point,Array} a,b,c,d,e Parent elements are five points.\n * @param {Number_Number_Number_Number_Number_Number} a_00,a_11,a_22,a_01,a_02,a_12 6 numbers, i.e. A, C, F, B/2, D/2, E/2\n * @example\n * // Create a conic section through the points A, B, C, D, and E.\n * var A = board.create('point', [1,5]);\n * var B = board.create('point', [1,2]);\n * var C = board.create('point', [2,0]);\n * var D = board.create('point', [0,0]);\n * var E = board.create('point', [-1,5]);\n * var conic = board.create('conic',[A,B,C,D,E]);\n * \n *\n * @example\n * // Parameters: A, C, F, B/2, D/2, E/2\n * var conic = board.create('conic', [1, 2, -4, 0, 0, 0]);\n *\n * \n * \n *\n */\nJXG.createConic = function (board, parents, attributes) {\n var polarForm,\n curve,\n fitConic,\n degconic,\n sym,\n eigen,\n a,\n b,\n c,\n c1,\n c2,\n i,\n definingMat,\n givenByPoints,\n rotationMatrix = [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1]\n ],\n M = [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1]\n ],\n points = [],\n p = [],\n attr_point = Type.copyAttributes(attributes, board.options, \"conic\", 'point'),\n attr_center = Type.copyAttributes(attributes, board.options, \"conic\", 'center'),\n attr_curve = Type.copyAttributes(attributes, board.options, 'conic');\n\n if (parents.length === 5) {\n givenByPoints = true;\n } else if (parents.length === 6) {\n givenByPoints = false;\n } else {\n throw new Error(\n \"JSXGraph: Can't create generic Conic with \" + parents.length + \" parameters.\"\n );\n }\n\n if (givenByPoints) {\n for (i = 0; i < 5; i++) {\n // point i given by coordinates\n if (parents[i].length > 1) {\n points[i] = board.create(\"point\", parents[i], attr_point);\n // point i given by point\n } else if (Type.isPoint(parents[i])) {\n points[i] = board.select(parents[i]);\n // given by function\n } else if (Type.isFunction(parents[i]) && Type.isPoint(parents[i]())) {\n points[i] = parents[i]();\n // point i given by point name\n } else if (Type.isString(parents[i])) {\n points[i] = board.select(parents[i]);\n } else {\n throw new Error(\n \"JSXGraph: Can't create Conic section with parent types '\" +\n typeof parents[i] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point,point,point], [a00,a11,a22,a01,a02,a12]\"\n );\n }\n }\n } else {\n /* Usual notation (x,y,z):\n * [[A0,A3,A4],\n * [A3,A1,A5],\n * [A4,A5,A2]].\n * Our notation (z,x,y):\n * [[A2, A4, A5],\n * [A4, A0, A3],\n * [A5, A3, A1]]\n */\n definingMat = [\n [0, 0, 0],\n [0, 0, 0],\n [0, 0, 0]\n ];\n definingMat[0][0] = Type.isFunction(parents[2])\n ? function () {\n return parents[2]();\n }\n : function () {\n return parents[2];\n };\n definingMat[0][1] = Type.isFunction(parents[4])\n ? function () {\n return parents[4]();\n }\n : function () {\n return parents[4];\n };\n definingMat[0][2] = Type.isFunction(parents[5])\n ? function () {\n return parents[5]();\n }\n : function () {\n return parents[5];\n };\n definingMat[1][1] = Type.isFunction(parents[0])\n ? function () {\n return parents[0]();\n }\n : function () {\n return parents[0];\n };\n definingMat[1][2] = Type.isFunction(parents[3])\n ? function () {\n return parents[3]();\n }\n : function () {\n return parents[3];\n };\n definingMat[2][2] = Type.isFunction(parents[1])\n ? function () {\n return parents[1]();\n }\n : function () {\n return parents[1];\n };\n }\n\n // sym(A) = A + A^t . Manipulates A in place.\n sym = function (A) {\n var i, j;\n for (i = 0; i < 3; i++) {\n for (j = i; j < 3; j++) {\n A[i][j] += A[j][i];\n }\n }\n for (i = 0; i < 3; i++) {\n for (j = 0; j < i; j++) {\n A[i][j] = A[j][i];\n }\n }\n return A;\n };\n\n // degconic(v,w) = sym(v*w^t)\n degconic = function (v, w) {\n var i,\n j,\n mat = [\n [0, 0, 0],\n [0, 0, 0],\n [0, 0, 0]\n ];\n\n for (i = 0; i < 3; i++) {\n for (j = 0; j < 3; j++) {\n mat[i][j] = v[i] * w[j];\n }\n }\n\n return sym(mat);\n };\n\n // (p^t*B*p)*A-(p^t*A*p)*B\n fitConic = function (A, B, p) {\n var i,\n j,\n pBp,\n pAp,\n Mv,\n mat = [\n [0, 0, 0],\n [0, 0, 0],\n [0, 0, 0]\n ];\n\n Mv = Mat.matVecMult(B, p);\n pBp = Mat.innerProduct(p, Mv);\n Mv = Mat.matVecMult(A, p);\n pAp = Mat.innerProduct(p, Mv);\n\n for (i = 0; i < 3; i++) {\n for (j = 0; j < 3; j++) {\n mat[i][j] = pBp * A[i][j] - pAp * B[i][j];\n }\n }\n return mat;\n };\n\n // Here, the defining functions for the curve are just dummy functions.\n // In polarForm there is a reference to curve.quadraticform.\n /**\n * @class\n * @ignore\n */\n curve = board.create(\n \"curve\",\n [\n function (x) {\n return 0;\n },\n function (x) {\n return 0;\n },\n 0,\n 2 * Math.PI\n ],\n attr_curve\n );\n\n /** @ignore */\n polarForm = function (phi, suspendUpdate) {\n var i, j, v; // len,;\n\n if (!suspendUpdate) {\n if (givenByPoints) {\n // Copy the point coordinate vectors\n for (i = 0; i < 5; i++) {\n p[i] = points[i].coords.usrCoords;\n }\n\n // Compute the quadratic form\n c1 = degconic(Mat.crossProduct(p[0], p[1]), Mat.crossProduct(p[2], p[3]));\n c2 = degconic(Mat.crossProduct(p[0], p[2]), Mat.crossProduct(p[1], p[3]));\n M = fitConic(c1, c2, p[4]);\n } else {\n for (i = 0; i < 3; i++) {\n for (j = i; j < 3; j++) {\n M[i][j] = definingMat[i][j]();\n if (j > i) {\n M[j][i] = M[i][j];\n }\n }\n }\n }\n\n // Here is the reference back to the curve.\n curve.quadraticform = M;\n\n // Compute Eigenvalues and Eigenvectors\n eigen = Numerics.Jacobi(M);\n\n // Scale the Eigenvalues such that the first Eigenvalue is positive\n if (eigen[0][0][0] < 0) {\n eigen[0][0][0] *= -1;\n eigen[0][1][1] *= -1;\n eigen[0][2][2] *= -1;\n }\n\n // Normalize the Eigenvectors\n // for (i = 0; i < 3; i++) {\n // // len = Mat.hypot(eigen[1][0][i], eigen[1][1][i], eigen[1][2][i])\n // for (j = 0; j < 3; j++) {\n // len += eigen[1][j][i] * eigen[1][j][i];\n // }\n // len = Math.sqrt(len);\n // /*for (j = 0; j < 3; j++) {\n // //eigen[1][j][i] /= len;\n // }*/\n // }\n rotationMatrix = eigen[1];\n c = Math.sqrt(Math.abs(eigen[0][0][0]));\n a = Math.sqrt(Math.abs(eigen[0][1][1]));\n b = Math.sqrt(Math.abs(eigen[0][2][2]));\n }\n\n // The degenerate cases with eigen[0][i][i]==0 are not handled correct yet.\n if (eigen[0][1][1] <= 0.0 && eigen[0][2][2] <= 0.0) {\n v = Mat.matVecMult(rotationMatrix, [1 / c, Math.cos(phi) / a, Math.sin(phi) / b]);\n } else if (eigen[0][1][1] <= 0.0 && eigen[0][2][2] > 0.0) {\n v = Mat.matVecMult(rotationMatrix, [Math.cos(phi) / c, 1 / a, Math.sin(phi) / b]);\n } else if (eigen[0][2][2] < 0.0) {\n v = Mat.matVecMult(rotationMatrix, [Math.sin(phi) / c, Math.cos(phi) / a, 1 / b]);\n }\n\n if (Type.exists(v)) {\n // Normalize\n v[1] /= v[0];\n v[2] /= v[0];\n v[0] = 1.0;\n } else {\n v = [1, NaN, NaN];\n }\n\n return v;\n };\n\n /** @ignore */\n curve.X = function (phi, suspendUpdate) {\n return polarForm(phi, suspendUpdate)[1];\n };\n\n /** @ignore */\n curve.Y = function (phi, suspendUpdate) {\n return polarForm(phi, suspendUpdate)[2];\n };\n\n // Center coordinates see https://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections\n curve.midpoint = board.create(\n \"point\",\n [\n function () {\n var m = curve.quadraticform;\n\n return [\n m[1][1] * m[2][2] - m[1][2] * m[1][2],\n m[1][2] * m[0][2] - m[2][2] * m[0][1],\n m[0][1] * m[1][2] - m[1][1] * m[0][2]\n ];\n }\n ],\n attr_center\n );\n\n curve.type = Const.OBJECT_TYPE_CONIC;\n curve.center = curve.midpoint;\n curve.subs = {\n center: curve.center\n };\n curve.inherits.push(curve.center);\n curve.inherits = curve.inherits.concat(points);\n\n if (givenByPoints) {\n for (i = 0; i < 5; i++) {\n if (Type.isPoint(points[i])) {\n points[i].addChild(curve);\n }\n }\n curve.setParents(parents);\n }\n curve.addChild(curve.center);\n\n return curve;\n};\n\nJXG.registerElement(\"ellipse\", JXG.createEllipse);\nJXG.registerElement(\"hyperbola\", JXG.createHyperbola);\nJXG.registerElement(\"parabola\", JXG.createParabola);\nJXG.registerElement(\"conic\", JXG.createConic);\n\n// export default {\n// createEllipse: JXG.createEllipse,\n// createHyperbola: JXG.createHyperbola,\n// createParabola: JXG.createParabola,\n// createConic: JXG.createConic\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n */\n pnpoly: function (x_in, y_in, coord_type) {\n return Geometry.pnpoly(x_in, y_in, this.vertices, coord_type, this.board);\n },\n\n /**\n * Checks whether (x,y) is near the polygon.\n * @param {Number} x Coordinate in x direction, screen coordinates.\n * @param {Number} y Coordinate in y direction, screen coordinates.\n * @returns {Boolean} Returns true, if (x,y) is inside or at the boundary the polygon, otherwise false.\n */\n hasPoint: function (x, y) {\n var i, len;\n\n if (this.evalVisProp('hasinnerpoints')) {\n // All points of the polygon trigger hasPoint: inner and boundary points\n if (this.pnpoly(x, y)) {\n return true;\n }\n }\n\n // Only boundary points trigger hasPoint\n // We additionally test the boundary also in case hasInnerPoints.\n // Since even if the above test has failed, the strokewidth may be large and (x, y) may\n // be inside of hasPoint() of a vertices.\n len = this.borders.length;\n for (i = 0; i < len; i++) {\n if (this.borders[i].hasPoint(x, y)) {\n return true;\n }\n }\n\n return false;\n },\n\n /**\n * Uses the boards renderer to update the polygon.\n */\n updateRenderer: function () {\n var i, len;\n\n if (!this.needsUpdate) {\n return this;\n }\n\n if (this.visPropCalc.visible) {\n len = this.vertices.length - ((this.elType === 'polygonalchain') ? 0 : 1);\n this.isReal = true;\n for (i = 0; i < len; ++i) {\n if (!this.vertices[i].isReal) {\n this.isReal = false;\n break;\n }\n }\n\n if (!this.isReal) {\n this.updateVisibility(false);\n\n for (i in this.childElements) {\n if (this.childElements.hasOwnProperty(i)) {\n // All child elements are hidden.\n // This may be weakened to all borders and only vertices with with visible:'inherit'\n this.childElements[i].setDisplayRendNode(false);\n }\n }\n }\n }\n\n if (this.visPropCalc.visible) {\n this.board.renderer.updatePolygon(this);\n }\n\n /* Update the label if visible. */\n if (this.hasLabel &&\n this.visPropCalc.visible &&\n this.label &&\n this.label.visPropCalc.visible &&\n this.isReal\n ) {\n this.label.update();\n this.board.renderer.updateText(this.label);\n }\n\n // Update rendNode display\n this.setDisplayRendNode();\n\n this.needsUpdate = false;\n return this;\n },\n\n /**\n * return TextAnchor\n */\n getTextAnchor: function () {\n var a, b, x, y, i;\n\n if (this.vertices.length === 0) {\n return new Coords(Const.COORDS_BY_USER, [1, 0, 0], this.board);\n }\n\n a = this.vertices[0].X();\n b = this.vertices[0].Y();\n x = a;\n y = b;\n for (i = 0; i < this.vertices.length; i++) {\n if (this.vertices[i].X() < a) {\n a = this.vertices[i].X();\n }\n\n if (this.vertices[i].X() > x) {\n x = this.vertices[i].X();\n }\n\n if (this.vertices[i].Y() > b) {\n b = this.vertices[i].Y();\n }\n\n if (this.vertices[i].Y() < y) {\n y = this.vertices[i].Y();\n }\n }\n\n return new Coords(Const.COORDS_BY_USER, [(a + x) * 0.5, (b + y) * 0.5], this.board);\n },\n\n getLabelAnchor: JXG.shortcut(JXG.Polygon.prototype, 'getTextAnchor'),\n\n // documented in geometry element\n cloneToBackground: function () {\n var er,\n copy = Type.getCloneObject(this);\n\n copy.vertices = this.vertices;\n er = this.board.renderer.enhancedRendering;\n this.board.renderer.enhancedRendering = true;\n this.board.renderer.drawPolygon(copy);\n this.board.renderer.enhancedRendering = er;\n this.traces[copy.id] = copy.rendNode;\n\n return this;\n },\n\n /**\n * Hide the polygon including its border lines. It will still exist but not visible on the board.\n * @param {Boolean} [borderless=false] If set to true, the polygon is treated as a polygon without\n * borders, i.e. the borders will not be hidden.\n */\n hideElement: function (borderless) {\n var i;\n\n JXG.deprecated(\"Element.hideElement()\", \"Element.setDisplayRendNode()\");\n\n this.visPropCalc.visible = false;\n this.board.renderer.display(this, false);\n\n if (!borderless) {\n for (i = 0; i < this.borders.length; i++) {\n this.borders[i].hideElement();\n }\n }\n\n if (this.hasLabel && Type.exists(this.label)) {\n this.label.hiddenByParent = true;\n if (this.label.visPropCalc.visible) {\n this.label.hideElement();\n }\n }\n },\n\n /**\n * Make the element visible.\n * @param {Boolean} [borderless=false] If set to true, the polygon is treated as a polygon without\n * borders, i.e. the borders will not be shown.\n */\n showElement: function (borderless) {\n var i;\n\n JXG.deprecated(\"Element.showElement()\", \"Element.setDisplayRendNode()\");\n\n this.visPropCalc.visible = true;\n this.board.renderer.display(this, true);\n\n if (!borderless) {\n for (i = 0; i < this.borders.length; i++) {\n this.borders[i].showElement().updateRenderer();\n }\n }\n\n if (Type.exists(this.label) && this.hasLabel && this.label.hiddenByParent) {\n this.label.hiddenByParent = false;\n if (!this.label.visPropCalc.visible) {\n this.label.showElement().updateRenderer();\n }\n }\n return this;\n },\n\n /**\n * Area of (not self-intersecting) polygon\n * @returns {Number} Area of (not self-intersecting) polygon\n */\n Area: function () {\n return Math.abs(Geometry.signedPolygon(this.vertices, true));\n },\n\n /**\n * Perimeter of polygon. For a polygonal chain, this method returns its length.\n *\n * @returns {Number} Perimeter of polygon in user units.\n * @see JXG.Polygon#L\n *\n * @example\n * var p = [[0.0, 2.0], [2.0, 1.0], [4.0, 6.0], [1.0, 3.0]];\n *\n * var pol = board.create('polygon', p, {hasInnerPoints: true});\n * var t = board.create('text', [5, 5, function() { return pol.Perimeter(); }]);\n * \n * \n *\n */\n Perimeter: function () {\n var i,\n len = this.vertices.length,\n val = 0.0;\n\n for (i = 1; i < len; ++i) {\n val += this.vertices[i].Dist(this.vertices[i - 1]);\n }\n\n return val;\n },\n\n /**\n * Alias for Perimeter. For polygons, the perimeter is returned. For polygonal chains the length is returned.\n *\n * @returns Number\n * @see JXG.Polygon#Perimeter\n */\n L: function() {\n return this.Perimeter();\n },\n\n /**\n * Bounding box of a polygon. The bounding box is an array of four numbers: the first two numbers\n * determine the upper left corner, the last two numbers determine the lower right corner of the bounding box.\n *\n * The width and height of a polygon can then determined like this:\n * @example\n * var box = polygon.boundingBox();\n * var width = box[2] - box[0];\n * var height = box[1] - box[3];\n *\n * @returns {Array} Array containing four numbers: [minX, maxY, maxX, minY]\n */\n boundingBox: function () {\n var box = [0, 0, 0, 0],\n i,\n v,\n le = this.vertices.length - 1;\n\n if (le === 0) {\n return box;\n }\n box[0] = this.vertices[0].X();\n box[2] = box[0];\n box[1] = this.vertices[0].Y();\n box[3] = box[1];\n\n for (i = 1; i < le; ++i) {\n v = this.vertices[i].X();\n if (v < box[0]) {\n box[0] = v;\n } else if (v > box[2]) {\n box[2] = v;\n }\n\n v = this.vertices[i].Y();\n if (v > box[1]) {\n box[1] = v;\n } else if (v < box[3]) {\n box[3] = v;\n }\n }\n\n return box;\n },\n\n // Already documented in GeometryElement\n bounds: function () {\n return this.boundingBox();\n },\n\n /**\n * This method removes the SVG or VML nodes of the lines and the filled area from the renderer, to remove\n * the object completely you should use {@link JXG.Board#removeObject}.\n *\n * @private\n */\n remove: function () {\n var i;\n\n for (i = 0; i < this.borders.length; i++) {\n this.board.removeObject(this.borders[i]);\n }\n\n GeometryElement.prototype.remove.call(this);\n },\n\n /**\n * Finds the index to a given point reference.\n * @param {JXG.Point} p Reference to an element of type {@link JXG.Point}\n * @returns {Number} Index of the point or -1.\n */\n findPoint: function (p) {\n var i;\n\n if (!Type.isPoint(p)) {\n return -1;\n }\n\n for (i = 0; i < this.vertices.length; i++) {\n if (this.vertices[i].id === p.id) {\n return i;\n }\n }\n\n return -1;\n },\n\n /**\n * Add more points to the polygon. The new points will be inserted at the end.\n * The attributes of new border segments are set to the same values\n * as those used when the polygon was created.\n * If new vertices are supplied by coordinates, the default attributes of polygon\n * vertices are taken as their attributes. Therefore, the visual attributes of\n * new vertices and borders may have to be adapted afterwards.\n * @param {JXG.Point} p Arbitrary number of points or coordinate arrays\n * @returns {JXG.Polygon} Reference to the polygon\n * @example\n * var pg = board.create('polygon', [[1,2], [3,4], [-3,1]], {hasInnerPoints: true});\n * var newPoint = board.create('point', [-1, -1]);\n * var newPoint2 = board.create('point', [-1, -2]);\n * pg.addPoints(newPoint, newPoint2, [1, -2]);\n *\n * \n * \n *\n */\n addPoints: function (p) {\n var idx,\n args = Array.prototype.slice.call(arguments);\n\n if (this.elType === 'polygonalchain') {\n idx = this.vertices.length - 1;\n } else {\n idx = this.vertices.length - 2;\n }\n return this.insertPoints.apply(this, [idx].concat(args));\n },\n\n /**\n * Insert points to the vertex list of the polygon after index idx.\n * The attributes of new border segments are set to the same values\n * as those used when the polygon was created.\n * If new vertices are supplied by coordinates, the default attributes of polygon\n * vertices are taken as their attributes. Therefore, the visual attributes of\n * new vertices and borders may have to be adapted afterwards.\n *\n * @param {Number} idx The position after which the new vertices are inserted.\n * Setting idx to -1 inserts the new points at the front, i.e. at position 0.\n * @param {JXG.Point} p Arbitrary number of points or coordinate arrays to insert.\n * @returns {JXG.Polygon} Reference to the polygon object\n *\n * @example\n * var pg = board.create('polygon', [[1,2], [3,4], [-3,1]], {hasInnerPoints: true});\n * var newPoint = board.create('point', [-1, -1]);\n * pg.insertPoints(0, newPoint, newPoint, [1, -2]);\n *\n * \n * \n *\n */\n insertPoints: function (idx, p) {\n var i, le, last, start, q;\n\n if (arguments.length === 0) {\n return this;\n }\n\n last = this.vertices.length - 1;\n if (this.elType === 'polygon') {\n last--;\n }\n\n // Wrong insertion index, get out of here\n if (idx < -1 || idx > last) {\n return this;\n }\n\n le = arguments.length - 1;\n for (i = 1; i < le + 1; i++) {\n q = Type.providePoints(this.board, [arguments[i]], {}, \"polygon\", [\n \"vertices\"\n ])[0];\n if (q._is_new) {\n // Add the point as child of the polygon, but not of the borders.\n this.addChild(q);\n delete q._is_new;\n }\n this.vertices.splice(idx + i, 0, q);\n }\n\n if (this.withLines) {\n start = idx + 1;\n if (this.elType === 'polygon') {\n if (idx < 0) {\n // Add point(s) in the front\n this.vertices[this.vertices.length - 1] = this.vertices[0];\n this.borders[this.borders.length - 1].point2 =\n this.vertices[this.vertices.length - 1];\n } else {\n // Insert point(s) (middle or end)\n this.borders[idx].point2 = this.vertices[start];\n }\n } else {\n // Add point(s) in the front: do nothing\n // Else:\n if (idx >= 0) {\n if (idx < this.borders.length) {\n // Insert point(s) in the middle\n this.borders[idx].point2 = this.vertices[start];\n } else {\n // Add point at the end\n start = idx;\n }\n }\n }\n for (i = start; i < start + le; i++) {\n this.borders.splice(\n i,\n 0,\n this.board.create(\n \"segment\",\n [this.vertices[i], this.vertices[i + 1]],\n this.attr_line\n )\n );\n }\n }\n this.inherits = [];\n this.inherits.push(this.vertices, this.borders);\n this.board.update();\n\n return this;\n },\n\n /**\n * Removes given set of vertices from the polygon\n * @param {JXG.Point} p Arbitrary number of vertices as {@link JXG.Point} elements or index numbers\n * @returns {JXG.Polygon} Reference to the polygon\n */\n removePoints: function (p) {\n var i, j, idx,\n firstPoint,\n nvertices = [],\n nborders = [],\n nidx = [],\n partition = [];\n\n // Partition:\n // in order to keep the borders which could be recycled, we have to partition\n // the set of removed points. I.e. if the points 1, 2, 5, 6, 7, 10 are removed,\n // the partitions are\n // 1-2, 5-7, 10-10\n // this gives us the borders, that can be removed and the borders we have to create.\n\n // In case of polygon: remove the last vertex from the list of vertices since\n // it is identical to the first\n if (this.elType === 'polygon') {\n firstPoint = this.vertices.pop();\n }\n\n // Collect all valid parameters as indices in nidx\n for (i = 0; i < arguments.length; i++) {\n idx = arguments[i];\n if (Type.isPoint(idx)) {\n idx = this.findPoint(idx);\n }\n if (\n Type.isNumber(idx) &&\n idx > -1 &&\n idx < this.vertices.length &&\n Type.indexOf(nidx, idx) === -1\n ) {\n nidx.push(idx);\n }\n }\n\n if (nidx.length === 0) {\n // Wrong index, get out of here\n if (this.elType === 'polygon') {\n this.vertices.push(firstPoint);\n }\n return this;\n }\n\n // Remove the polygon from each removed point's children\n for (i = 0; i < nidx.length; i++) {\n this.vertices[nidx[i]].removeChild(this);\n }\n\n // Sort the elements to be eliminated\n nidx = nidx.sort();\n nvertices = this.vertices.slice();\n nborders = this.borders.slice();\n\n // Initialize the partition with an array containing the last point to be removed\n if (this.withLines) {\n partition.push([nidx[nidx.length - 1]]);\n }\n\n // Run through all existing vertices and copy all remaining ones to nvertices,\n // compute the partition\n for (i = nidx.length - 1; i > -1; i--) {\n nvertices[nidx[i]] = -1;\n\n // Find gaps between the list of points to be removed.\n // In this case a new partition is added.\n if (this.withLines && nidx.length > 1 && nidx[i] - 1 > nidx[i - 1]) {\n partition[partition.length - 1][1] = nidx[i];\n partition.push([nidx[i - 1]]);\n }\n }\n\n // Finalize the partition computation\n if (this.withLines) {\n partition[partition.length - 1][1] = nidx[0];\n }\n\n // Update vertices\n this.vertices = [];\n for (i = 0; i < nvertices.length; i++) {\n if (Type.isPoint(nvertices[i])) {\n this.vertices.push(nvertices[i]);\n }\n }\n\n // Close the polygon again\n if (\n this.elType === \"polygon\" &&\n this.vertices.length > 1 &&\n this.vertices[this.vertices.length - 1].id !== this.vertices[0].id\n ) {\n this.vertices.push(this.vertices[0]);\n }\n\n // Delete obsolete and create missing borders\n if (this.withLines) {\n for (i = 0; i < partition.length; i++) {\n for (j = partition[i][1] - 1; j < partition[i][0] + 1; j++) {\n // special cases\n if (j < 0) {\n if (this.elType === 'polygon') {\n // First vertex is removed, so the last border has to be removed, too\n this.board.removeObject(this.borders[nborders.length - 1]);\n nborders[nborders.length - 1] = -1;\n }\n } else if (j < nborders.length) {\n this.board.removeObject(this.borders[j]);\n nborders[j] = -1;\n }\n }\n\n // Only create the new segment if it's not the closing border.\n // The closing border is getting a special treatment at the end.\n if (partition[i][1] !== 0 && partition[i][0] !== nvertices.length - 1) {\n // nborders[partition[i][0] - 1] = this.board.create('segment', [\n // nvertices[Math.max(partition[i][1] - 1, 0)],\n // nvertices[Math.min(partition[i][0] + 1, this.vertices.length - 1)]\n // ], this.attr_line);\n nborders[partition[i][0] - 1] = this.board.create(\n \"segment\",\n [nvertices[partition[i][1] - 1], nvertices[partition[i][0] + 1]],\n this.attr_line\n );\n }\n }\n\n this.borders = [];\n for (i = 0; i < nborders.length; i++) {\n if (nborders[i] !== -1) {\n this.borders.push(nborders[i]);\n }\n }\n\n // if the first and/or the last vertex is removed, the closing border is created at the end.\n if (\n this.elType === \"polygon\" &&\n this.vertices.length > 2 && // Avoid trivial case of polygon with 1 vertex\n (partition[0][1] === this.vertices.length - 1 ||\n partition[partition.length - 1][1] === 0)\n ) {\n this.borders.push(\n this.board.create(\n \"segment\",\n [this.vertices[this.vertices.length - 2], this.vertices[0]],\n this.attr_line\n )\n );\n }\n }\n this.inherits = [];\n this.inherits.push(this.vertices, this.borders);\n\n this.board.update();\n\n return this;\n },\n\n // documented in element.js\n getParents: function () {\n this.setParents(this.vertices);\n return this.parents;\n },\n\n getAttributes: function () {\n var attr = GeometryElement.prototype.getAttributes.call(this),\n i;\n\n if (this.withLines) {\n attr.lines = attr.lines || {};\n attr.lines.ids = [];\n attr.lines.colors = [];\n\n for (i = 0; i < this.borders.length; i++) {\n attr.lines.ids.push(this.borders[i].id);\n attr.lines.colors.push(this.borders[i].visProp.strokecolor);\n }\n }\n\n return attr;\n },\n\n snapToGrid: function () {\n var i, force;\n\n if (this.evalVisProp('snaptogrid')) {\n force = true;\n } else {\n force = false;\n }\n\n for (i = 0; i < this.vertices.length; i++) {\n this.vertices[i].handleSnapToGrid(force, true);\n }\n },\n\n /**\n * Moves the polygon by the difference of two coordinates.\n * @param {Number} method The type of coordinates used here. Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.\n * @param {Array} coords coordinates in screen/user units\n * @param {Array} oldcoords previous coordinates in screen/user units\n * @returns {JXG.Polygon} this element\n */\n setPositionDirectly: function (method, coords, oldcoords) {\n var dc,\n t,\n i,\n len,\n c = new Coords(method, coords, this.board),\n oldc = new Coords(method, oldcoords, this.board);\n\n len = this.vertices.length - 1;\n for (i = 0; i < len; i++) {\n if (!this.vertices[i].draggable()) {\n return this;\n }\n }\n\n dc = Statistics.subtract(c.usrCoords, oldc.usrCoords);\n t = this.board.create(\"transform\", dc.slice(1), { type: \"translate\" });\n t.applyOnce(this.vertices.slice(0, -1));\n\n return this;\n },\n\n /**\n * Algorithm by Sutherland and Hodgman to compute the intersection of two convex polygons.\n * The polygon itself is the clipping polygon, it expects as parameter a polygon to be clipped.\n * See wikipedia entry.\n * Called by {@link JXG.Polygon#intersect}.\n *\n * @private\n *\n * @param {JXG.Polygon} polygon Polygon which will be clipped.\n *\n * @returns {Array} of (normalized homogeneous user) coordinates (i.e. [z, x, y], where z==1 in most cases,\n * representing the vertices of the intersection polygon.\n *\n */\n sutherlandHodgman: function (polygon) {\n // First the two polygons are sorted counter clockwise\n var clip = JXG.Math.Geometry.sortVertices(this.vertices), // \"this\" is the clipping polygon\n subject = JXG.Math.Geometry.sortVertices(polygon.vertices), // \"polygon\" is the subject polygon\n lenClip = clip.length - 1,\n lenSubject = subject.length - 1,\n lenIn,\n outputList = [],\n inputList,\n i,\n j,\n S,\n E,\n cross,\n // Determines if the point c3 is right of the line through c1 and c2.\n // Since the polygons are sorted counter clockwise, \"right of\" and therefore >= is needed here\n isInside = function (c1, c2, c3) {\n return (\n (c2[1] - c1[1]) * (c3[2] - c1[2]) - (c2[2] - c1[2]) * (c3[1] - c1[1]) >=\n 0\n );\n };\n\n for (i = 0; i < lenSubject; i++) {\n outputList.push(subject[i]);\n }\n\n for (i = 0; i < lenClip; i++) {\n inputList = outputList.slice(0);\n lenIn = inputList.length;\n outputList = [];\n\n S = inputList[lenIn - 1];\n\n for (j = 0; j < lenIn; j++) {\n E = inputList[j];\n if (isInside(clip[i], clip[i + 1], E)) {\n if (!isInside(clip[i], clip[i + 1], S)) {\n cross = JXG.Math.Geometry.meetSegmentSegment(\n S,\n E,\n clip[i],\n clip[i + 1]\n );\n cross[0][1] /= cross[0][0];\n cross[0][2] /= cross[0][0];\n cross[0][0] = 1;\n outputList.push(cross[0]);\n }\n outputList.push(E);\n } else if (isInside(clip[i], clip[i + 1], S)) {\n cross = JXG.Math.Geometry.meetSegmentSegment(\n S,\n E,\n clip[i],\n clip[i + 1]\n );\n cross[0][1] /= cross[0][0];\n cross[0][2] /= cross[0][0];\n cross[0][0] = 1;\n outputList.push(cross[0]);\n }\n S = E;\n }\n }\n\n return outputList;\n },\n\n /**\n * Generic method for the intersection of this polygon with another polygon.\n * The parent object is the clipping polygon, it expects as parameter a polygon to be clipped.\n * Both polygons have to be convex.\n * Calls the algorithm by Sutherland, Hodgman, {@link JXG.Polygon#sutherlandHodgman}.\n * \n * \n *\n * @example\n * // Dynamic intersection of two polygons pol1 and pol2\n * var pol1 = board.create('polygon', [[-2, 3], [-4, -3], [2, 0], [4, 4]], {\n * name:'pol1', withLabel: true,\n * fillColor: 'yellow'\n * });\n * var pol2 = board.create('polygon', [[-2, -3], [-4, 1], [0, 4], [5, 1]], {\n * name:'pol2', withLabel: true\n * });\n *\n * // Dynamic version:\n * // the intersection polygon does adapt to changes of pol1 or pol2.\n * // For this a curve element is used.\n * var curve = board.create('curve', [[],[]], {fillColor: 'blue', fillOpacity: 0.4});\n * curve.updateDataArray = function() {\n * var mat = JXG.Math.transpose(pol1.intersect(pol2));\n *\n * if (mat.length == 3) {\n * this.dataX = mat[1];\n * this.dataY = mat[2];\n * } else {\n * this.dataX = [];\n * this.dataY = [];\n * }\n * };\n * board.update();\n * \n * \n *\n */\n intersect: function (polygon) {\n return this.sutherlandHodgman(polygon);\n }\n }\n);\n\n/**\n * @class A polygon is a plane figure made up of line segments (the borders) connected\n * to form a closed polygonal chain.\n * It is determined by\n * \n *
\n * Each two consecutive points of the list define a line.\n * @pseudo\n * @constructor\n * @name Polygon\n * @type JXG.Polygon\n * @augments JXG.Polygon\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Array} vertices The polygon's vertices. If the first and the last vertex don't match the first one will be\n * added to the array by the creator. Here, two points match if they have the same 'id' attribute.\n *\n * Additionally, a polygon can be created by providing a polygon and a transformation (or an array of transformations).\n * The result is a polygon which is the transformation of the supplied polygon.\n *\n * @example\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n * var p3 = board.create('point', [4.0, 6.0]);\n * var p4 = board.create('point', [1.0, 4.0]);\n *\n * var pol = board.create('polygon', [p1, p2, p3, p4]);\n * \n * \n *\n * @example\n * var p = [[0.0, 2.0], [2.0, 1.0], [4.0, 6.0], [1.0, 3.0]];\n *\n * var pol = board.create('polygon', p, {hasInnerPoints: true});\n * \n * \n *\n * @example\n * var f1 = function() { return [0.0, 2.0]; },\n * f2 = function() { return [2.0, 1.0]; },\n * f3 = function() { return [4.0, 6.0]; },\n * f4 = function() { return [1.0, 4.0]; },\n * cc1 = board.create('polygon', [f1, f2, f3, f4]);\n * board.update();\n *\n * \n * \n *\n * @example\n * var t = board.create('transform', [2, 1.5], {type: 'scale'});\n * var a = board.create('point', [-3,-2], {name: 'a'});\n * var b = board.create('point', [-1,-4], {name: 'b'});\n * var c = board.create('point', [-2,-0.5], {name: 'c'});\n * var pol1 = board.create('polygon', [a,b,c], {vertices: {withLabel: false}});\n * var pol2 = board.create('polygon', [pol1, t], {vertices: {withLabel: true}});\n *\n * \n * \n *\n */\nJXG.createPolygon = function (board, parents, attributes) {\n var el, i, le, obj,\n points = [],\n attr,\n attr_points,\n is_transform = false;\n\n attr = Type.copyAttributes(attributes, board.options, 'polygon');\n obj = board.select(parents[0]);\n if (obj === null) {\n // This is necessary if the original polygon is defined in another board.\n obj = parents[0];\n }\n if (\n Type.isObject(obj) &&\n obj.type === Const.OBJECT_TYPE_POLYGON &&\n Type.isTransformationOrArray(parents[1])\n ) {\n is_transform = true;\n le = obj.vertices.length - 1;\n attr_points = Type.copyAttributes(attributes, board.options, \"polygon\", 'vertices');\n for (i = 0; i < le; i++) {\n if (attr_points.withlabel) {\n attr_points.name =\n obj.vertices[i].name === \"\" ? \"\" : obj.vertices[i].name + \"'\";\n }\n points.push(board.create(\"point\", [obj.vertices[i], parents[1]], attr_points));\n }\n } else {\n points = Type.providePoints(board, parents, attributes, \"polygon\", [\"vertices\"]);\n if (points === false) {\n throw new Error(\n \"JSXGraph: Can't create polygon / polygonalchain with parent types other than 'point' and 'coordinate arrays' or a function returning an array of coordinates. Alternatively, a polygon and a transformation can be supplied\"\n );\n }\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'polygon');\n el = new JXG.Polygon(board, points, attr);\n el.isDraggable = true;\n\n // Put the points to their position\n if (is_transform) {\n el.prepareUpdate().update().updateVisibility().updateRenderer();\n le = obj.vertices.length - 1;\n for (i = 0; i < le; i++) {\n points[i].prepareUpdate().update().updateVisibility().updateRenderer();\n }\n }\n\n return el;\n};\n\n/**\n * @class A regular polygon is a polygon that is\n * direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length).\n * It needs two points which define the base line and the number of vertices.\n * @pseudo\n * @description Constructs a regular polygon. It needs two points which define the base line and the number of vertices, or a set of points.\n * @constructor\n * @name RegularPolygon\n * @type Polygon\n * @augments Polygon\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_Number} p1,p2,n The constructed regular polygon has n vertices and the base line defined by p1 and p2.\n * @example\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n *\n * var pol = board.create('regularpolygon', [p1, p2, 5]);\n * \n * \n * @example\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [4.0,4.0]);\n * var p3 = board.create('point', [2.0,0.0]);\n *\n * var pol = board.create('regularpolygon', [p1, p2, p3]);\n * \n * \n *\n * @example\n * // Line of reflection\n * var li = board.create('line', [1,1,1], {strokeColor: '#aaaaaa'});\n * var reflect = board.create('transform', [li], {type: 'reflect'});\n * var pol1 = board.create('polygon', [[-3,-2], [-1,-4], [-2,-0.5]]);\n * var pol2 = board.create('polygon', [pol1, reflect]);\n *\n * \n * \n *\n */\nJXG.createRegularPolygon = function (board, parents, attributes) {\n var el, i, n,\n p = [],\n rot, len,\n pointsExist,\n attr;\n\n len = parents.length;\n n = parents[len - 1];\n\n if (Type.isNumber(n) && (parents.length !== 3 || n < 3)) {\n throw new Error(\n \"JSXGraph: A regular polygon needs two point types and a number > 2 as input.\"\n );\n }\n\n if (Type.isNumber(board.select(n))) {\n // Regular polygon given by 2 points and a number\n len--;\n pointsExist = false;\n } else {\n // Regular polygon given by n points\n n = len;\n pointsExist = true;\n }\n\n p = Type.providePoints(board, parents.slice(0, len), attributes, \"regularpolygon\", [\n \"vertices\"\n ]);\n if (p === false) {\n throw new Error(\n \"JSXGraph: Can't create regular polygon with parent types other than 'point' and 'coordinate arrays' or a function returning an array of coordinates\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, \"regularpolygon\", 'vertices');\n for (i = 2; i < n; i++) {\n rot = board.create(\"transform\", [Math.PI * (2 - (n - 2) / n), p[i - 1]], {\n type: \"rotate\"\n });\n if (pointsExist) {\n p[i].addTransform(p[i - 2], rot);\n p[i].fullUpdate();\n } else {\n if (Type.isArray(attr.ids) && attr.ids.length >= n - 2) {\n attr.id = attr.ids[i - 2];\n }\n p[i] = board.create(\"point\", [p[i - 2], rot], attr);\n p[i].type = Const.OBJECT_TYPE_CAS;\n\n // The next two lines of code are needed to make regular polygons draggable\n // The new helper points are set to be draggable.\n p[i].isDraggable = true;\n p[i].visProp.fixed = false;\n }\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'regularpolygon');\n el = board.create(\"polygon\", p, attr);\n el.elType = 'regularpolygon';\n\n return el;\n};\n\n/**\n * @class A polygonal chain is a connected series of line segments (borders).\n * It is determined by\n * \n *
\n * Each two consecutive points of the list define a line.\n * In JSXGraph, a polygonal chain is simply realized as polygon without the last - closing - point.\n * This may lead to unexpected results. Polygonal chains can be distinguished from polygons by the attribute 'elType' which\n * is 'polygonalchain' for the first and 'polygon' for the latter.\n * @pseudo\n * @constructor\n * @name PolygonalChain\n * @type Polygon\n * @augments JXG.Polygon\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Array} vertices The polygon's vertices.\n *\n * Additionally, a polygonal chain can be created by providing a polygonal chain and a transformation (or an array of transformations).\n * The result is a polygonal chain which is the transformation of the supplied polygonal chain.\n *\n * @example\n * var attr = {\n * snapToGrid: true\n * },\n * p = [];\n *\n * \tp.push(board.create('point', [-4, 0], attr));\n * \tp.push(board.create('point', [-1, -3], attr));\n * \tp.push(board.create('point', [0, 2], attr));\n * \tp.push(board.create('point', [2, 1], attr));\n * \tp.push(board.create('point', [4, -2], attr));\n *\n * var chain = board.create('polygonalchain', p, {borders: {strokeWidth: 3}});\n *\n * \n * \n *\n */\nJXG.createPolygonalChain = function (board, parents, attributes) {\n var attr, el;\n\n attr = Type.copyAttributes(attributes, board.options, 'polygonalchain');\n el = board.create(\"polygon\", parents, attr);\n el.elType = 'polygonalchain';\n\n // A polygonal chain is not necessarily closed.\n el.vertices.pop();\n board.removeObject(el.borders[el.borders.length - 1]);\n el.borders.pop();\n\n return el;\n};\n\n/**\n * @class A quadrilateral polygon with parallel opposite sides.\n * @pseudo\n * @description Constructs a parallelogram. As input, three points or coordinate arrays are expected.\n * @constructor\n * @name Parallelogram\n * @type Polygon\n * @augments Polygon\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point,Array_JXG.Point,Array_JXG.Point,Array} p1,p2,p3 The parallelogram is a polygon through\n * the points [p1, p2, pp, p3], where pp is a parallelpoint, available as sub-object parallelogram.parallelPoint.\n *\n * @example\n * var p1 = board.create('point', [-3, -4]);\n * var p2 = board.create('point', [3, -1]);\n * var p3 = board.create('point', [-2, 0]);\n * var par = board.create('parallelogram', [p1, p2, p3], {\n * hasInnerPoints: true,\n * parallelpoint: {\n * size: 6,\n * face: '<<>>'\n * }\n * });\n *\n * \n * \n *\n *\n */\nJXG.createParallelogram = function (board, parents, attributes) {\n var el, pp,\n points = [],\n attr,\n attr_pp;\n\n points = Type.providePoints(board, parents, attributes, \"polygon\", [\"vertices\"]);\n if (points === false || points.length < 3) {\n throw new Error(\n \"JSXGraph: Can't create parallelogram with parent types other than 'point' and 'coordinate arrays' or a function returning an array of coordinates.\"\n );\n }\n\n attr_pp = Type.copyAttributes(attributes, board.options, \"parallelogram\", 'parallelpoint');\n pp = board.create('parallelpoint', points, attr_pp);\n attr = Type.copyAttributes(attributes, board.options, 'parallelogram');\n el = board.create('polygon', [points[0], points[1], pp, points[2]], attr);\n\n el.elType = 'parallelogram';\n\n /**\n * Parallel point which makes the quadrilateral a parallelogram. Can also be accessed with\n * parallelogram.vertices[2].\n * @name Parallelogram#parallelPoint\n * @type {JXG.Point}\n */\n el.parallelPoint = pp;\n\n el.isDraggable = true;\n pp.isDraggable = true;\n pp.visProp.fixed = false;\n\n return el;\n};\n\nJXG.registerElement(\"polygon\", JXG.createPolygon);\nJXG.registerElement(\"regularpolygon\", JXG.createRegularPolygon);\nJXG.registerElement(\"polygonalchain\", JXG.createPolygonalChain);\nJXG.registerElement(\"parallelogram\", JXG.createParallelogram);\n\nexport default JXG.Polygon;\n// export default {\n// Polygon: JXG.Polygon,\n// createPolygon: JXG.createPolygon,\n// createRegularPolygon: JXG.createRegularPolygon\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n * @example\n * // This is an example which overwrites updateDataArray and produces\n * // a Bezier curve of degree three.\n * var A = board.create('point', [-3,3]);\n * var B = board.create('point', [3,-2]);\n * var line = board.create('segment', [A,B]);\n *\n * var height = 0.5; // height of the curly brace\n *\n * // Curly brace\n * var crl = board.create('curve', [[0],[0]], {strokeWidth:1, strokeColor:'black'});\n * crl.bezierDegree = 3;\n * crl.updateDataArray = function() {\n * var d = [B.X()-A.X(), B.Y()-A.Y()],\n * dl = Math.sqrt(d[0]*d[0]+d[1]*d[1]),\n * mid = [(A.X()+B.X())*0.5, (A.Y()+B.Y())*0.5];\n *\n * d[0] *= height/dl;\n * d[1] *= height/dl;\n *\n * this.dataX = [ A.X(), A.X()-d[1], mid[0], mid[0]-d[1], mid[0], B.X()-d[1], B.X() ];\n * this.dataY = [ A.Y(), A.Y()+d[0], mid[1], mid[1]+d[0], mid[1], B.Y()+d[0], B.Y() ];\n * };\n *\n * // Text\n * var txt = board.create('text', [\n * function() {\n * var d = [B.X()-A.X(), B.Y()-A.Y()],\n * dl = Math.sqrt(d[0]*d[0]+d[1]*d[1]),\n * mid = (A.X()+B.X())*0.5;\n *\n * d[1] *= height/dl;\n * return mid-d[1]+0.1;\n * },\n * function() {\n * var d = [B.X()-A.X(), B.Y()-A.Y()],\n * dl = Math.sqrt(d[0]*d[0]+d[1]*d[1]),\n * mid = (A.Y()+B.Y())*0.5;\n *\n * d[0] *= height/dl;\n * return mid+d[0]+0.1;\n * },\n * function() { return \"length=\" + JXG.toFixed(B.Dist(A), 2); }\n * ]);\n *\n *\n * board.update(); // This update is necessary to call updateDataArray the first time.\n *\n * \n * \n *\n *\n */\n updateDataArray: function () {\n // this used to return this, but we shouldn't rely on the user to implement it.\n },\n\n /**\n * Computes the curve path\n * @see JXG.Curve#update\n * @returns {JXG.Curve} Reference to the curve object.\n */\n updateCurve: function () {\n var i, len, mi, ma,\n x, y,\n bb, eps,\n version = this.visProp.plotversion,\n //t1, t2, l1,\n suspendUpdate = false;\n\n this.updateTransformMatrix();\n this.updateDataArray();\n mi = this.minX();\n ma = this.maxX();\n\n if (Type.exists(this.dataX)) {\n // Discrete data points, i.e. x-coordinates are given in an array\n this.numberPoints = this.dataX.length;\n len = this.numberPoints;\n\n // It is possible, that the array length has increased.\n this.allocatePoints();\n\n for (i = 0; i < len; i++) {\n x = i;\n\n // y-coordinates are in an array\n if (Type.exists(this.dataY)) {\n y = i;\n // The last parameter prevents rounding in usr2screen().\n this.points[i].setCoordinates(\n Const.COORDS_BY_USER,\n [this.dataX[i], this.dataY[i]],\n false\n );\n } else {\n // discrete x data, continuous y data\n y = this.X(x);\n // The last parameter prevents rounding in usr2screen().\n this.points[i].setCoordinates(\n Const.COORDS_BY_USER,\n [this.dataX[i], this.Y(y, suspendUpdate)],\n false\n );\n }\n this.points[i]._t = i;\n\n // this.updateTransform(this.points[i]);\n suspendUpdate = true;\n }\n\n } else {\n // Continuous x-data, i.e. given as a function\n if (this.evalVisProp('doadvancedplot')) {\n // console.time('plot');\n\n if (version === 1 || this.evalVisProp('doadvancedplotold')) {\n Plot.updateParametricCurveOld(this, mi, ma);\n } else if (version === 2) {\n Plot.updateParametricCurve_v2(this, mi, ma);\n } else if (version === 3) {\n Plot.updateParametricCurve_v3(this, mi, ma);\n } else if (version === 4) {\n Plot.updateParametricCurve_v4(this, mi, ma);\n } else {\n Plot.updateParametricCurve_v2(this, mi, ma);\n }\n // console.timeEnd('plot');\n } else {\n if (this.board.updateQuality === this.board.BOARD_QUALITY_HIGH) {\n this.numberPoints = this.evalVisProp('numberpointshigh');\n } else {\n this.numberPoints = this.evalVisProp('numberpointslow');\n }\n\n // It is possible, that the array length has increased.\n this.allocatePoints();\n Plot.updateParametricCurveNaive(this, mi, ma, this.numberPoints);\n }\n len = this.numberPoints;\n\n if (\n this.evalVisProp('useqdt') &&\n this.board.updateQuality === this.board.BOARD_QUALITY_HIGH\n ) {\n this.qdt = new QDT(this.board.getBoundingBox());\n for (i = 0; i < this.points.length; i++) {\n this.qdt.insert(this.points[i]);\n\n if (i > 0) {\n this.points[i].prev = this.points[i - 1];\n }\n\n if (i < len - 1) {\n this.points[i].next = this.points[i + 1];\n }\n }\n }\n }\n\n if (\n this.bezierDegree === 1 &&\n // this.evalVisProp('curvetype') !== \"plot\" &&\n this.evalVisProp('rdpsmoothing')\n ) {\n // console.time('rdp');\n // RDP in screen coords:\n // this.points = Numerics.RamerDouglasPeucker(this.points, 0.2);\n\n // RDP in user coords:\n // Use a default size of 800 x 800 pixel and\n // maximum distance of 0.2 pixel:\n // Determine the geometric mean M of the horizontal and vertical box size in user coords, i.e.\n // 1 u = 1000 / M px => 1 px = M / 1000 u => eps := 0.2 * M / 800\n bb = this.board.getBoundingBox();\n eps = this.evalVisProp('rdpthreshold') * Math.sqrt((bb[2] - bb[0]) * (bb[1] - bb[3])) * 0.00125;\n this.points = Numerics.RamerDouglasPeucker(this.points, eps, true);\n\n this.numberPoints = this.points.length;\n // console.timeEnd('rdp');\n // console.log(this.numberPoints);\n }\n\n len = this.numberPoints;\n for (i = 0; i < len; i++) {\n this.updateTransform(this.points[i]);\n }\n\n return this;\n },\n\n updateTransformMatrix: function () {\n var t,\n i,\n len = this.transformations.length;\n\n this.transformMat = [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1]\n ];\n\n for (i = 0; i < len; i++) {\n t = this.transformations[i];\n t.update();\n this.transformMat = Mat.matMatMult(t.matrix, this.transformMat);\n }\n\n return this;\n },\n\n /**\n * Applies the transformations of the curve to the given point p.\n * Before using it, {@link JXG.Curve#updateTransformMatrix} has to be called.\n * @param {JXG.Point} p\n * @returns {JXG.Point} The given point.\n */\n updateTransform: function (p) {\n var c,\n len = this.transformations.length;\n\n if (len > 0) {\n c = Mat.matVecMult(this.transformMat, p.usrCoords);\n p.setCoordinates(Const.COORDS_BY_USER, c, false, true);\n }\n\n return p;\n },\n\n /**\n * Add transformations to this curve.\n * @param {JXG.Transformation|Array} transform Either one {@link JXG.Transformation} or an array of {@link JXG.Transformation}s.\n * @returns {JXG.Curve} Reference to the curve object.\n */\n addTransform: function (transform) {\n var i,\n list = Type.isArray(transform) ? transform : [transform],\n len = list.length;\n\n for (i = 0; i < len; i++) {\n this.transformations.push(list[i]);\n }\n\n return this;\n },\n\n removeTransform: function (transform) {\n var i,\n list = Type.isArray(transform) ? transform : [transform],\n len = list.length;\n\n for (i = 0; i < len; i++) {\n Type.removeElementFromArray(this.transformations, list[i]);\n }\n\n return this;\n },\n\n clearTransforms: function () {\n this.transformations = [];\n\n return this;\n },\n\n /**\n * Generate the method curve.X() in case curve.dataX is an array\n * and generate the method curve.Y() in case curve.dataY is an array.\n * @private\n * @param {String} which Either 'X' or 'Y'\n * @returns {function}\n **/\n interpolationFunctionFromArray: function (which) {\n var data = \"data\" + which,\n that = this;\n\n return function (t, suspendedUpdate) {\n var i,\n j,\n t0,\n t1,\n arr = that[data],\n len = arr.length,\n last,\n f = [];\n\n if (isNaN(t)) {\n return NaN;\n }\n\n if (t < 0) {\n if (Type.isFunction(arr[0])) {\n return arr[0]();\n }\n\n return arr[0];\n }\n\n if (that.bezierDegree === 3) {\n last = (len - 1) / 3;\n\n if (t >= last) {\n if (Type.isFunction(arr[arr.length - 1])) {\n return arr[arr.length - 1]();\n }\n\n return arr[arr.length - 1];\n }\n\n i = Math.floor(t) * 3;\n t0 = t % 1;\n t1 = 1 - t0;\n\n for (j = 0; j < 4; j++) {\n if (Type.isFunction(arr[i + j])) {\n f[j] = arr[i + j]();\n } else {\n f[j] = arr[i + j];\n }\n }\n\n return (\n t1 * t1 * (t1 * f[0] + 3 * t0 * f[1]) +\n (3 * t1 * f[2] + t0 * f[3]) * t0 * t0\n );\n }\n\n if (t > len - 2) {\n i = len - 2;\n } else {\n i = parseInt(Math.floor(t), 10);\n }\n\n if (i === t) {\n if (Type.isFunction(arr[i])) {\n return arr[i]();\n }\n return arr[i];\n }\n\n for (j = 0; j < 2; j++) {\n if (Type.isFunction(arr[i + j])) {\n f[j] = arr[i + j]();\n } else {\n f[j] = arr[i + j];\n }\n }\n return f[0] + (f[1] - f[0]) * (t - i);\n };\n },\n\n /**\n * Converts the JavaScript/JessieCode/GEONExT syntax of the defining function term into JavaScript.\n * New methods X() and Y() for the Curve object are generated, further\n * new methods for minX() and maxX().\n * If mi or ma are not supplied, default functions are set.\n *\n * @param {String} varname Name of the parameter in xterm and yterm, e.g. 'x' or 't'\n * @param {String|Number|Function|Array} xterm Term for the x coordinate. Can also be an array consisting of discrete values.\n * @param {String|Number|Function|Array} yterm Term for the y coordinate. Can also be an array consisting of discrete values.\n * @param {String|Number|Function} [mi] Lower bound on the parameter\n * @param {String|Number|Function} [ma] Upper bound on the parameter\n * @see JXG.GeonextParser.geonext2JS\n */\n generateTerm: function (varname, xterm, yterm, mi, ma) {\n var fx, fy, mat, i;\n\n // Generate the methods X() and Y()\n if (Type.isArray(xterm)) {\n // Discrete data\n this.dataX = xterm;\n\n this.numberPoints = this.dataX.length;\n this.X = this.interpolationFunctionFromArray.apply(this, [\"X\"]);\n this.visProp.curvetype = 'plot';\n this.isDraggable = true;\n } else {\n // Continuous data\n this.X = Type.createFunction(xterm, this.board, varname);\n if (Type.isString(xterm)) {\n this.visProp.curvetype = 'functiongraph';\n } else if (Type.isFunction(xterm) || Type.isNumber(xterm)) {\n this.visProp.curvetype = 'parameter';\n }\n\n this.isDraggable = true;\n }\n\n if (Type.isArray(yterm)) {\n this.dataY = yterm;\n this.Y = this.interpolationFunctionFromArray.apply(this, [\"Y\"]);\n } else if (!Type.exists(yterm)) {\n // Discrete data as an array of coordinate pairs,\n // i.e. transposed input\n mat = Mat.transpose(xterm);\n // Ignore first cooordinate if given as [z, x, y]\n i = (mat.length > 2) ? 1 : 0;\n this.dataX = mat[i];\n this.dataY = mat[i + 1];\n this.numberPoints = this.dataX.length;\n this.Y = this.interpolationFunctionFromArray.apply(this, [\"Y\"]);\n } else {\n this.Y = Type.createFunction(yterm, this.board, varname);\n }\n\n /**\n * Polar form\n * Input data is function xterm() and offset coordinates yterm\n */\n if (Type.isFunction(xterm) && Type.isArray(yterm)) {\n // Xoffset, Yoffset\n fx = Type.createFunction(yterm[0], this.board, \"\");\n fy = Type.createFunction(yterm[1], this.board, \"\");\n\n this.X = function (phi) {\n return xterm(phi) * Math.cos(phi) + fx();\n };\n this.X.deps = fx.deps;\n\n this.Y = function (phi) {\n return xterm(phi) * Math.sin(phi) + fy();\n };\n this.Y.deps = fy.deps;\n\n this.visProp.curvetype = 'polar';\n }\n\n // Set the upper and lower bounds for the parameter of the curve.\n // If not defined, reset the bounds to the default values\n // given in Curve.prototype.minX, Curve.prototype.maxX\n if (Type.exists(mi)) {\n this.minX = Type.createFunction(mi, this.board, \"\");\n } else {\n delete this.minX;\n }\n if (Type.exists(ma)) {\n this.maxX = Type.createFunction(ma, this.board, \"\");\n } else {\n delete this.maxX;\n }\n\n this.addParentsFromJCFunctions([this.X, this.Y, this.minX, this.maxX]);\n },\n\n /**\n * Finds dependencies in a given term and notifies the parents by adding the\n * dependent object to the found objects child elements.\n * @param {String} contentStr String containing dependencies for the given object.\n */\n notifyParents: function (contentStr) {\n var fstr,\n dep,\n isJessieCode = false,\n obj;\n\n // Read dependencies found by the JessieCode parser\n obj = { xterm: 1, yterm: 1 };\n for (fstr in obj) {\n if (\n obj.hasOwnProperty(fstr) &&\n this.hasOwnProperty(fstr) &&\n this[fstr].origin\n ) {\n isJessieCode = true;\n for (dep in this[fstr].origin.deps) {\n if (this[fstr].origin.deps.hasOwnProperty(dep)) {\n this[fstr].origin.deps[dep].addChild(this);\n }\n }\n }\n }\n\n if (!isJessieCode) {\n GeonextParser.findDependencies(this, contentStr, this.board);\n }\n },\n\n /**\n * Position a curve label according to the attributes \"position\" and distance.\n * This function is also used for angle, arc and sector.\n *\n * @param {String} pos\n * @param {Number} distance\n * @returns {JXG.Coords}\n */\n getLabelPosition: function(pos, distance) {\n var x, y, xy,\n c, d, e,\n c_t, c_te, c_ma, c_mi,\n lbda,\n mi, ma, ar,\n t, dx, dy,\n dist = 1.5;\n\n // Shrink domain if necessary\n mi = this.minX();\n ma = this.maxX();\n ar = Numerics.findDomain(this.X, [mi, ma], null, false);\n ar = Numerics.findDomain(this.Y, ar, null, false);\n mi = Math.max(ar[0], ar[0]); // ???\n ma = Math.min(ar[1], ar[1]); // ???\n\n xy = Type.parsePosition(pos);\n lbda = Type.parseNumber(xy.pos, ma - mi, 1);\n\n if (xy.pos.indexOf('fr') < 0 && xy.pos.indexOf('%') < 0) {\n // The unit has to be 'fr' or '%'. 'px' or plain numbers are not supported\n lbda = 0;\n }\n\n t = mi + lbda;\n\n // x = this.X(t);\n // y = this.Y(t);\n c_t = this.Ft(t); // Include transformations\n x = c_t[1];\n y = c_t[2];\n // If x or y are NaN, the label is set to the line\n // between the first and last point.\n if (isNaN(x + y)) {\n lbda /= (ma - mi);\n t = mi + lbda;\n\n // x = this.X(mi) + lbda * (this.X(ma) - this.X(mi));\n // y = this.Y(mi) + lbda * (this.Y(ma) - this.Y(mi));\n c_mi = this.Ft(mi);\n c_ma = this.Ft(ma);\n x = c_mi[1] + lbda * (c_ma[1] - c_mi[1]);\n y = c_mi[2] + lbda * (c_ma[2] - c_mi[2]);\n }\n c = (new Coords(Const.COORDS_BY_USER, [x, y], this.board)).scrCoords;\n\n e = Mat.eps;\n if (t < mi + e) {\n // dx = (this.X(t + e) - this.X(t)) / e;\n // dy = (this.Y(t + e) - this.Y(t)) / e;\n c_te = this.Ft(t + e);\n dx = (c_te[1] - c_t[1]) / e;\n dy = (c_te[2] - c_t[2]) / e;\n } else if (t > ma - e) {\n // dx = (this.X(t) - this.X(t - e)) / e;\n // dy = (this.Y(t) - this.Y(t - e)) / e;\n c_te = this.Ft(t - e);\n dx = (c_t[1] - c_te[1]) / e;\n dy = (c_t[2] - c_te[2]) / e;\n } else {\n // dx = 0.5 * (this.X(t + e) - this.X(t - e)) / e;\n // dy = 0.5 * (this.Y(t + e) - this.Y(t - e)) / e;\n c_te = this.Ft(t + e);\n c_t = this.Ft(t - e);\n dx = 0.5 * (c_te[1] - c_t[1]) / e;\n dy = 0.5 * (c_te[2] - c_t[2]) / e;\n }\n dx = isNaN(dx) ? 1. : dx;\n dy = isNaN(dy) ? 1. : dy;\n d = Mat.hypot(dx, dy);\n\n if (xy.side === 'left') {\n dy *= -1;\n } else {\n dx *= -1;\n }\n\n // Position left or right\n\n if (Type.exists(this.label)) {\n dist = 0.5 * distance / d;\n }\n\n x = c[1] + dy * this.label.size[0] * dist;\n y = c[2] - dx * this.label.size[1] * dist;\n\n return new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board);\n },\n\n // documented in geometryElement\n getLabelAnchor: function () {\n var x, y, pos,\n // xy, lbda, e,\n // t, dx, dy, d,\n // dist = 1.5,\n c,\n lo = 0.1,\n up = 0.9,\n ax = lo * this.board.canvasWidth,\n ay = lo * this.board.canvasHeight,\n bx = up * this.board.canvasWidth,\n by = up * this.board.canvasHeight;\n\n if (!Type.exists(this.label)) {\n return new Coords(Const.COORDS_BY_SCREEN, [NaN, NaN], this.board);\n }\n pos = this.label.evalVisProp('position');\n if (!Type.isString(pos)) {\n return new Coords(Const.COORDS_BY_SCREEN, [NaN, NaN], this.board);\n }\n\n if (pos.indexOf('right') < 0 && pos.indexOf('left') < 0) {\n // Old system\n switch (this.evalVisProp('label.position')) {\n case \"ulft\":\n x = ax;\n y = ay;\n break;\n case \"llft\":\n x = ax;\n y = by;\n break;\n case \"rt\":\n x = bx;\n y = 0.5 * by;\n break;\n case \"lrt\":\n x = bx;\n y = by;\n break;\n case \"urt\":\n x = bx;\n y = ay;\n break;\n case \"top\":\n x = 0.5 * bx;\n y = ay;\n break;\n case \"bot\":\n x = 0.5 * bx;\n y = by;\n break;\n default:\n // includes case 'lft'\n x = ax;\n y = 0.5 * by;\n }\n } else {\n // New positioning, e.g. \"25% left\"\n return this.getLabelPosition(pos, this.label.evalVisProp('distance'));\n }\n c = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board, false);\n return Geometry.projectCoordsToCurve(\n c.usrCoords[1], c.usrCoords[2], 0, this, this.board\n )[0];\n },\n\n // documented in geometry element\n cloneToBackground: function () {\n var er,\n copy = Type.getCloneObject(this);\n\n copy.points = this.points.slice(0);\n copy.bezierDegree = this.bezierDegree;\n copy.numberPoints = this.numberPoints;\n\n er = this.board.renderer.enhancedRendering;\n this.board.renderer.enhancedRendering = true;\n this.board.renderer.drawCurve(copy);\n this.board.renderer.enhancedRendering = er;\n this.traces[copy.id] = copy.rendNode;\n\n return this;\n },\n\n // Already documented in GeometryElement\n bounds: function () {\n var minX = Infinity,\n maxX = -Infinity,\n minY = Infinity,\n maxY = -Infinity,\n l = this.points.length,\n i,\n bezier,\n up;\n\n if (this.bezierDegree === 3) {\n // Add methods X(), Y()\n for (i = 0; i < l; i++) {\n this.points[i].X = Type.bind(function () {\n return this.usrCoords[1];\n }, this.points[i]);\n this.points[i].Y = Type.bind(function () {\n return this.usrCoords[2];\n }, this.points[i]);\n }\n bezier = Numerics.bezier(this.points);\n up = bezier[3]();\n minX = Numerics.fminbr(\n function (t) {\n return bezier[0](t);\n },\n [0, up]\n );\n maxX = Numerics.fminbr(\n function (t) {\n return -bezier[0](t);\n },\n [0, up]\n );\n minY = Numerics.fminbr(\n function (t) {\n return bezier[1](t);\n },\n [0, up]\n );\n maxY = Numerics.fminbr(\n function (t) {\n return -bezier[1](t);\n },\n [0, up]\n );\n\n minX = bezier[0](minX);\n maxX = bezier[0](maxX);\n minY = bezier[1](minY);\n maxY = bezier[1](maxY);\n return [minX, maxY, maxX, minY];\n }\n\n // Linear segments\n for (i = 0; i < l; i++) {\n if (minX > this.points[i].usrCoords[1]) {\n minX = this.points[i].usrCoords[1];\n }\n\n if (maxX < this.points[i].usrCoords[1]) {\n maxX = this.points[i].usrCoords[1];\n }\n\n if (minY > this.points[i].usrCoords[2]) {\n minY = this.points[i].usrCoords[2];\n }\n\n if (maxY < this.points[i].usrCoords[2]) {\n maxY = this.points[i].usrCoords[2];\n }\n }\n\n return [minX, maxY, maxX, minY];\n },\n\n // documented in element.js\n getParents: function () {\n var p = [this.xterm, this.yterm, this.minX(), this.maxX()];\n\n if (this.parents.length !== 0) {\n p = this.parents;\n }\n\n return p;\n },\n\n /**\n * Shift the curve by the vector 'where'.\n *\n * @param {Array} where Array containing the x and y coordinate of the target location.\n * @returns {JXG.Curve} Reference to itself.\n */\n moveTo: function (where) {\n // TODO add animation\n var delta = [],\n p;\n if (this.points.length > 0 && !this.evalVisProp('fixed')) {\n p = this.points[0];\n if (where.length === 3) {\n delta = [\n where[0] - p.usrCoords[0],\n where[1] - p.usrCoords[1],\n where[2] - p.usrCoords[2]\n ];\n } else {\n delta = [where[0] - p.usrCoords[1], where[1] - p.usrCoords[2]];\n }\n this.setPosition(Const.COORDS_BY_USER, delta);\n return this.board.update(this);\n }\n return this;\n },\n\n /**\n * If the curve is the result of a transformation applied\n * to a continuous curve, the glider projection has to be done\n * on the original curve. Otherwise there will be problems\n * when changing between high and low precision plotting,\n * since there number of points changes.\n *\n * @private\n * @returns {Array} [Boolean, curve]: Array contining 'true' if curve is result of a transformation,\n * and the source curve of the transformation.\n */\n getTransformationSource: function () {\n var isTransformed, curve_org;\n if (Type.exists(this._transformationSource)) {\n curve_org = this._transformationSource;\n if (\n curve_org.elementClass === Const.OBJECT_CLASS_CURVE //&&\n //curve_org.evalVisProp('curvetype') !== 'plot'\n ) {\n isTransformed = true;\n }\n }\n return [isTransformed, curve_org];\n },\n\n /**\n * Return the points of the curve as array of length-three-arrays [z, x, y], i.e.\n * return an array of homogeneous coordinates.\n * The returned coordinates are in user coordinates. Finite homogeneous coordinates have the first value set to 1,\n * i.e. it can be ignored.\n * \n *
\n * @pseudo\n * @name Curve\n * @augments JXG.Curve\n * @constructor\n * @type Object\n * @description JXG.Curve\n\n * @param {function,number_function,number_function,number_function,number} x,y,a_,b_ Parent elements for Parametric Curves.\n * \n * @example\n * // Data plots\n * // Connect a set of points given by coordinates with dashed line segments.\n * // The x- and y-coordinates of the points are given in two separate\n * // arrays.\n * var x = [0,1,2,3,4,5,6,7,8,9];\n * var y = [9.2,1.3,7.2,-1.2,4.0,5.3,0.2,6.5,1.1,0.0];\n * var graph = board.create('curve', [x,y], {dash:2});\n * \n * \n * @example\n * // Polar plot\n * // Create a curve with the equation r(phi)= a*(1+phi), i.e.\n * // a cardioid.\n * var a = board.create('slider',[[0,2],[2,2],[0,1,2]]);\n * var graph = board.create('curve',\n * [function(phi){ return a.Value()*(1-Math.cos(phi));},\n * [1,0],\n * 0, 2*Math.PI],\n * {curveType: 'polar'}\n * );\n * \n * \n *\n * @example\n * // Draggable Bezier curve\n * var col, p, c;\n * col = 'blue';\n * p = [];\n * p.push(board.create('point',[-2, -1 ], {size: 5, strokeColor:col, fillColor:col}));\n * p.push(board.create('point',[1, 2.5 ], {size: 5, strokeColor:col, fillColor:col}));\n * p.push(board.create('point',[-1, -2.5 ], {size: 5, strokeColor:col, fillColor:col}));\n * p.push(board.create('point',[2, -2], {size: 5, strokeColor:col, fillColor:col}));\n *\n * c = board.create('curve', JXG.Math.Numerics.bezier(p),\n * {strokeColor:'red', name:\"curve\", strokeWidth:5, fixed: false}); // Draggable curve\n * c.addParents(p);\n * \n * \n *\n * @example\n * // The curve cu2 is the reflection of cu1 against line li\n * var li = board.create('line', [1,1,1], {strokeColor: '#aaaaaa'});\n * var reflect = board.create('transform', [li], {type: 'reflect'});\n * var cu1 = board.create('curve', [[-1, -1, -0.5, -1, -1, -0.5], [-3, -2, -2, -2, -2.5, -2.5]]);\n * var cu2 = board.create('curve', [cu1, reflect], {strokeColor: 'red'});\n *\n * \n * \n */\nJXG.createCurve = function (board, parents, attributes) {\n var obj,\n cu,\n attr = Type.copyAttributes(attributes, board.options, 'curve');\n\n obj = board.select(parents[0], true);\n if (\n Type.isTransformationOrArray(parents[1]) &&\n Type.isObject(obj) &&\n (obj.type === Const.OBJECT_TYPE_CURVE ||\n obj.type === Const.OBJECT_TYPE_ANGLE ||\n obj.type === Const.OBJECT_TYPE_ARC ||\n obj.type === Const.OBJECT_TYPE_CONIC ||\n obj.type === Const.OBJECT_TYPE_SECTOR)\n ) {\n if (obj.type === Const.OBJECT_TYPE_SECTOR) {\n attr = Type.copyAttributes(attributes, board.options, 'sector');\n } else if (obj.type === Const.OBJECT_TYPE_ARC) {\n attr = Type.copyAttributes(attributes, board.options, 'arc');\n } else if (obj.type === Const.OBJECT_TYPE_ANGLE) {\n if (!Type.exists(attributes.withLabel)) {\n attributes.withLabel = false;\n }\n attr = Type.copyAttributes(attributes, board.options, 'angle');\n } else {\n attr = Type.copyAttributes(attributes, board.options, 'curve');\n }\n attr = Type.copyAttributes(attr, board.options, 'curve');\n\n cu = new JXG.Curve(board, [\"x\", [], []], attr);\n /**\n * @class\n * @ignore\n */\n cu.updateDataArray = function () {\n var i,\n le = obj.numberPoints;\n this.bezierDegree = obj.bezierDegree;\n this.dataX = [];\n this.dataY = [];\n for (i = 0; i < le; i++) {\n this.dataX.push(obj.points[i].usrCoords[1]);\n this.dataY.push(obj.points[i].usrCoords[2]);\n }\n return this;\n };\n cu.addTransform(parents[1]);\n obj.addChild(cu);\n cu.setParents([obj]);\n cu._transformationSource = obj;\n\n return cu;\n }\n attr = Type.copyAttributes(attributes, board.options, 'curve');\n return new JXG.Curve(board, [\"x\"].concat(parents), attr);\n};\n\nJXG.registerElement(\"curve\", JXG.createCurve);\n\n/**\n * @class A functiongraph visualizes a map x → f(x).\n * The graph is displayed for x in the interval [a,b] and is a {@link Curve} element.\n * @pseudo\n * @name Functiongraph\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n * @param {function_number,function_number,function} f,a_,b_ Parent elements are a function term f(x) describing the function graph.\n * \n * \n * @example\n * // Create a function graph for f(x) = 0.5*x*x-2*x with variable interval\n * var s = board.create('slider',[[0,4],[3,4],[-2,4,5]]);\n * var graph = board.create('functiongraph',\n * [function(x){ return 0.5*x*x-2*x;},\n * -2,\n * function(){return s.Value();}]\n * );\n * \n * \n */\nJXG.createFunctiongraph = function (board, parents, attributes) {\n var attr,\n par = [\"x\", \"x\"].concat(parents); // variable name and identity function for x-coordinate\n // par = [\"x\", function(x) { return x; }].concat(parents);\n\n attr = Type.copyAttributes(attributes, board.options, 'functiongraph');\n attr = Type.copyAttributes(attr, board.options, 'curve');\n attr.curvetype = 'functiongraph';\n return new JXG.Curve(board, par, attr);\n};\n\nJXG.registerElement(\"functiongraph\", JXG.createFunctiongraph);\nJXG.registerElement(\"plot\", JXG.createFunctiongraph);\n\n/**\n * @class The (natural) cubic spline curves (function graph) interpolating a set of points.\n * Create a dynamic spline interpolated curve given by sample points p_1 to p_n.\n * @pseudo\n * @name Spline\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n * @param {JXG.Board} board Reference to the board the spline is drawn on.\n * @param {Array} parents Array of points the spline interpolates. This can be\n * \n *
\n * All individual entries of coordinates arrays may be numbers or functions returning numbers.\n * @param {Object} attributes Define color, width, ... of the spline\n * @returns {JXG.Curve} Returns reference to an object of type JXG.Curve.\n * @see JXG.Curve\n * @example\n *\n * var p = [];\n * p[0] = board.create('point', [-2,2], {size: 4, face: 'o'});\n * p[1] = board.create('point', [0,-1], {size: 4, face: 'o'});\n * p[2] = board.create('point', [2,0], {size: 4, face: 'o'});\n * p[3] = board.create('point', [4,1], {size: 4, face: 'o'});\n *\n * var c = board.create('spline', p, {strokeWidth:3});\n * \n * \n *\n */\nJXG.createSpline = function (board, parents, attributes) {\n var el, funcs, ret;\n\n funcs = function () {\n var D,\n x = [],\n y = [];\n\n return [\n function (t, suspended) {\n // Function term\n var i, j, c;\n\n if (!suspended) {\n x = [];\n y = [];\n\n // given as [x[], y[]]\n if (\n parents.length === 2 &&\n Type.isArray(parents[0]) &&\n Type.isArray(parents[1]) &&\n parents[0].length === parents[1].length\n ) {\n for (i = 0; i < parents[0].length; i++) {\n if (Type.isFunction(parents[0][i])) {\n x.push(parents[0][i]());\n } else {\n x.push(parents[0][i]);\n }\n\n if (Type.isFunction(parents[1][i])) {\n y.push(parents[1][i]());\n } else {\n y.push(parents[1][i]);\n }\n }\n } else {\n for (i = 0; i < parents.length; i++) {\n if (Type.isPoint(parents[i])) {\n x.push(parents[i].X());\n y.push(parents[i].Y());\n // given as [[x1,y1], [x2, y2], ...]\n } else if (Type.isArray(parents[i]) && parents[i].length === 2) {\n for (j = 0; j < parents.length; j++) {\n if (Type.isFunction(parents[j][0])) {\n x.push(parents[j][0]());\n } else {\n x.push(parents[j][0]);\n }\n\n if (Type.isFunction(parents[j][1])) {\n y.push(parents[j][1]());\n } else {\n y.push(parents[j][1]);\n }\n }\n } else if (\n Type.isFunction(parents[i]) &&\n parents[i]().length === 2\n ) {\n c = parents[i]();\n x.push(c[0]);\n y.push(c[1]);\n }\n }\n }\n\n // The array D has only to be calculated when the position of one or more sample points\n // changes. Otherwise D is always the same for all points on the spline.\n D = Numerics.splineDef(x, y);\n }\n\n return Numerics.splineEval(t, x, y, D);\n },\n // minX()\n function () {\n return x[0];\n },\n //maxX()\n function () {\n return x[x.length - 1];\n }\n ];\n };\n\n attributes = Type.copyAttributes(attributes, board.options, 'curve');\n attributes.curvetype = 'functiongraph';\n ret = funcs();\n el = new JXG.Curve(board, [\"x\", \"x\", ret[0], ret[1], ret[2]], attributes);\n el.setParents(parents);\n el.elType = 'spline';\n\n return el;\n};\n\n/**\n * Register the element type spline at JSXGraph\n * @private\n */\nJXG.registerElement(\"spline\", JXG.createSpline);\n\n/**\n * @class Cardinal spline curve through a given data set.\n * Create a dynamic cardinal spline interpolated curve given by sample points p_1 to p_n.\n * @pseudo\n * @name Cardinalspline\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n * @param {Array} points Points array defining the cardinal spline. This can be\n * \n *
\n * All individual entries of coordinates arrays may be numbers or functions returning numbers.\n * @param {function,Number} tau Tension parameter\n * @param {String} [type='uniform'] Type of the cardinal spline, may be 'uniform' (default) or 'centripetal'\n * @see JXG.Curve\n * @example\n * //Create a cardinal spline out of an array of JXG points with adjustable tension\n *\n * //Create array of points\n * var p = [];\n * p.push(board.create('point',[0,0]));\n * p.push(board.create('point',[1,4]));\n * p.push(board.create('point',[4,5]));\n * p.push(board.create('point',[2,3]));\n * p.push(board.create('point',[3,0]));\n *\n * // tension\n * var tau = board.create('slider', [[-4,-5],[2,-5],[0.001,0.5,1]], {name:'tau'});\n * var c = board.create('cardinalspline', [p, function(){ return tau.Value();}], {strokeWidth:3});\n *\n * \n * \n *\n */\nJXG.createCardinalSpline = function (board, parents, attributes) {\n var el,\n getPointLike,\n points,\n tau,\n type,\n p,\n q,\n i,\n le,\n splineArr,\n errStr = \"\\nPossible parent types: [points:array, tau:number|function, type:string]\";\n\n if (!Type.exists(parents[0]) || !Type.isArray(parents[0])) {\n throw new Error(\n \"JSXGraph: JXG.createCardinalSpline: argument 1 'points' has to be array of points or coordinate pairs\" +\n errStr\n );\n }\n if (\n !Type.exists(parents[1]) ||\n (!Type.isNumber(parents[1]) && !Type.isFunction(parents[1]))\n ) {\n throw new Error(\n \"JSXGraph: JXG.createCardinalSpline: argument 2 'tau' has to be number between [0,1] or function'\" +\n errStr\n );\n }\n if (!Type.exists(parents[2]) || !Type.isString(parents[2])) {\n type = 'uniform';\n // throw new Error(\n // \"JSXGraph: JXG.createCardinalSpline: argument 3 'type' has to be string 'uniform' or 'centripetal'\" +\n // errStr\n // );\n } else {\n type = parents[2];\n }\n\n attributes = Type.copyAttributes(attributes, board.options, 'curve');\n attributes = Type.copyAttributes(attributes, board.options, 'cardinalspline');\n attributes.curvetype = 'parameter';\n\n p = parents[0];\n q = [];\n\n // Given as [x[], y[]]\n if (\n !attributes.isarrayofcoordinates &&\n p.length === 2 &&\n Type.isArray(p[0]) &&\n Type.isArray(p[1]) &&\n p[0].length === p[1].length\n ) {\n for (i = 0; i < p[0].length; i++) {\n q[i] = [];\n if (Type.isFunction(p[0][i])) {\n q[i].push(p[0][i]());\n } else {\n q[i].push(p[0][i]);\n }\n\n if (Type.isFunction(p[1][i])) {\n q[i].push(p[1][i]());\n } else {\n q[i].push(p[1][i]);\n }\n }\n } else {\n // given as [[x0, y0], [x1, y1], point, ...]\n for (i = 0; i < p.length; i++) {\n if (Type.isString(p[i])) {\n q.push(board.select(p[i]));\n } else if (Type.isPoint(p[i])) {\n q.push(p[i]);\n // given as [[x0,y0], [x1, y2], ...]\n } else if (Type.isArray(p[i]) && p[i].length === 2) {\n q[i] = [];\n if (Type.isFunction(p[i][0])) {\n q[i].push(p[i][0]());\n } else {\n q[i].push(p[i][0]);\n }\n\n if (Type.isFunction(p[i][1])) {\n q[i].push(p[i][1]());\n } else {\n q[i].push(p[i][1]);\n }\n } else if (Type.isFunction(p[i]) && p[i]().length === 2) {\n q.push(parents[i]());\n }\n }\n }\n\n if (attributes.createpoints === true) {\n points = Type.providePoints(board, q, attributes, \"cardinalspline\", [\"points\"]);\n } else {\n points = [];\n\n /**\n * @ignore\n */\n getPointLike = function (ii) {\n return {\n X: function () {\n return q[ii][0];\n },\n Y: function () {\n return q[ii][1];\n },\n Dist: function (p) {\n var dx = this.X() - p.X(),\n dy = this.Y() - p.Y();\n\n return Mat.hypot(dx, dy);\n }\n };\n };\n\n for (i = 0; i < q.length; i++) {\n if (Type.isPoint(q[i])) {\n points.push(q[i]);\n } else {\n points.push(getPointLike(i));\n }\n }\n }\n\n tau = parents[1];\n // type = parents[2];\n\n splineArr = [\"x\"].concat(Numerics.CardinalSpline(points, tau, type));\n\n el = new JXG.Curve(board, splineArr, attributes);\n le = points.length;\n el.setParents(points);\n for (i = 0; i < le; i++) {\n p = points[i];\n if (Type.isPoint(p)) {\n if (Type.exists(p._is_new)) {\n el.addChild(p);\n delete p._is_new;\n } else {\n p.addChild(el);\n }\n }\n }\n el.elType = 'cardinalspline';\n\n return el;\n};\n\n/**\n * Register the element type cardinalspline at JSXGraph\n * @private\n */\nJXG.registerElement(\"cardinalspline\", JXG.createCardinalSpline);\n\n/**\n * @class Interpolate data points by the spline curve from Metapost (by Donald Knuth and John Hobby).\n * Create a dynamic metapost spline interpolated curve given by sample points p_1 to p_n.\n * @pseudo\n * @name Metapostspline\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n * @param {JXG.Board} board Reference to the board the metapost spline is drawn on.\n * @param {Array} parents Array with two entries.\n * \n *
\n * All individual entries of coordinates arrays may be numbers or functions returning numbers.\n * \n *\n */\nJXG.createMetapostSpline = function (board, parents, attributes) {\n var el,\n getPointLike,\n points,\n controls,\n p,\n q,\n i,\n le,\n errStr = \"\\nPossible parent types: [points:array, controls:object\";\n\n if (!Type.exists(parents[0]) || !Type.isArray(parents[0])) {\n throw new Error(\n \"JSXGraph: JXG.createMetapostSpline: argument 1 'points' has to be array of points or coordinate pairs\" +\n errStr\n );\n }\n if (!Type.exists(parents[1]) || !Type.isObject(parents[1])) {\n throw new Error(\n \"JSXGraph: JXG.createMetapostSpline: argument 2 'controls' has to be a JavaScript object'\" +\n errStr\n );\n }\n\n attributes = Type.copyAttributes(attributes, board.options, 'curve');\n attributes = Type.copyAttributes(attributes, board.options, 'metapostspline');\n attributes.curvetype = 'parameter';\n\n p = parents[0];\n q = [];\n\n // given as [x[], y[]]\n if (\n !attributes.isarrayofcoordinates &&\n p.length === 2 &&\n Type.isArray(p[0]) &&\n Type.isArray(p[1]) &&\n p[0].length === p[1].length\n ) {\n for (i = 0; i < p[0].length; i++) {\n q[i] = [];\n if (Type.isFunction(p[0][i])) {\n q[i].push(p[0][i]());\n } else {\n q[i].push(p[0][i]);\n }\n\n if (Type.isFunction(p[1][i])) {\n q[i].push(p[1][i]());\n } else {\n q[i].push(p[1][i]);\n }\n }\n } else {\n // given as [[x0, y0], [x1, y1], point, ...]\n for (i = 0; i < p.length; i++) {\n if (Type.isString(p[i])) {\n q.push(board.select(p[i]));\n } else if (Type.isPoint(p[i])) {\n q.push(p[i]);\n // given as [[x0,y0], [x1, y2], ...]\n } else if (Type.isArray(p[i]) && p[i].length === 2) {\n q[i] = [];\n if (Type.isFunction(p[i][0])) {\n q[i].push(p[i][0]());\n } else {\n q[i].push(p[i][0]);\n }\n\n if (Type.isFunction(p[i][1])) {\n q[i].push(p[i][1]());\n } else {\n q[i].push(p[i][1]);\n }\n } else if (Type.isFunction(p[i]) && p[i]().length === 2) {\n q.push(parents[i]());\n }\n }\n }\n\n if (attributes.createpoints === true) {\n points = Type.providePoints(board, q, attributes, 'metapostspline', ['points']);\n } else {\n points = [];\n\n /**\n * @ignore\n */\n getPointLike = function (ii) {\n return {\n X: function () {\n return q[ii][0];\n },\n Y: function () {\n return q[ii][1];\n }\n };\n };\n\n for (i = 0; i < q.length; i++) {\n if (Type.isPoint(q[i])) {\n points.push(q[i]);\n } else {\n points.push(getPointLike);\n }\n }\n }\n\n controls = parents[1];\n\n el = new JXG.Curve(board, [\"t\", [], [], 0, p.length - 1], attributes);\n /**\n * @class\n * @ignore\n */\n el.updateDataArray = function () {\n var res,\n i,\n len = points.length,\n p = [];\n\n for (i = 0; i < len; i++) {\n p.push([points[i].X(), points[i].Y()]);\n }\n\n res = Metapost.curve(p, controls);\n this.dataX = res[0];\n this.dataY = res[1];\n };\n el.bezierDegree = 3;\n\n le = points.length;\n el.setParents(points);\n for (i = 0; i < le; i++) {\n if (Type.isPoint(points[i])) {\n points[i].addChild(el);\n }\n }\n el.elType = 'metapostspline';\n\n return el;\n};\n\nJXG.registerElement(\"metapostspline\", JXG.createMetapostSpline);\n\n/**\n * @class Visualize the Riemann sum which is an approximation of an integral by a finite sum.\n * It is realized as a special curve.\n * The returned element has the method Value() which returns the sum of the areas of the bars.\n * \n * \n *\n * @example\n * // Riemann sum between two functions\n * var s = board.create('slider',[[0,4],[3,4],[0,4,10]],{snapWidth:1});\n * var g = function(x) { return 0.5*x*x-2*x; };\n * var f = function(x) { return -x*(x-4); };\n * var r = board.create('riemannsum',\n * [[g,f], function(){return s.Value();}, 'lower', 0, 4],\n * {fillOpacity:0.4}\n * );\n * var f = board.create('functiongraph',[f, -2, 5]);\n * var g = board.create('functiongraph',[g, -2, 5]);\n * var t = board.create('text',[-2,-2, function(){ return 'Sum=' + JXG.toFixed(r.Value(), 4); }]);\n * \n * \n */\nJXG.createRiemannsum = function (board, parents, attributes) {\n var n, type, f, par, c, attr;\n\n attr = Type.copyAttributes(attributes, board.options, 'riemannsum');\n attr.curvetype = 'plot';\n\n f = parents[0];\n n = Type.createFunction(parents[1], board, \"\");\n\n if (!Type.exists(n)) {\n throw new Error(\n \"JSXGraph: JXG.createRiemannsum: argument '2' n has to be number or function.\" +\n \"\\nPossible parent types: [function,n:number|function,type,start:number|function,end:number|function]\"\n );\n }\n\n if (typeof parents[2] === 'string') {\n parents[2] = '\\'' + parents[2] + '\\'';\n }\n\n type = Type.createFunction(parents[2], board, \"\");\n if (!Type.exists(type)) {\n throw new Error(\n \"JSXGraph: JXG.createRiemannsum: argument 3 'type' has to be string or function.\" +\n \"\\nPossible parent types: [function,n:number|function,type,start:number|function,end:number|function]\"\n );\n }\n\n par = [[0], [0]].concat(parents.slice(3));\n\n c = board.create(\"curve\", par, attr);\n\n c.sum = 0.0;\n /**\n * Returns the value of the Riemann sum, i.e. the sum of the (signed) areas of the rectangles.\n * @name Value\n * @memberOf Riemannsum.prototype\n * @function\n * @returns {Number} value of Riemann sum.\n */\n c.Value = function () {\n return this.sum;\n };\n\n /**\n * @class\n * @ignore\n */\n c.updateDataArray = function () {\n var u = Numerics.riemann(f, n(), type(), this.minX(), this.maxX());\n this.dataX = u[0];\n this.dataY = u[1];\n\n // Update \"Riemann sum\"\n this.sum = u[2];\n };\n\n c.addParentsFromJCFunctions([n, type]);\n\n return c;\n};\n\nJXG.registerElement(\"riemannsum\", JXG.createRiemannsum);\n\n/**\n * @class A trace curve is simple locus curve showing the orbit of a point that depends on a glider point.\n * @pseudo\n * @name Tracecurve\n * @augments JXG.Curve\n * @constructor\n * @type Object\n * @descript JXG.Curve\n * @param {Point} Parent elements of Tracecurve are a\n * glider point and a point whose locus is traced.\n * @param {point}\n * @see JXG.Curve\n * @example\n * // Create trace curve.\n * var c1 = board.create('circle',[[0, 0], [2, 0]]),\n * p1 = board.create('point',[-3, 1]),\n * g1 = board.create('glider',[2, 1, c1]),\n * s1 = board.create('segment',[g1, p1]),\n * p2 = board.create('midpoint',[s1]),\n * curve = board.create('tracecurve', [g1, p2]);\n *\n * \n * \n */\nJXG.createTracecurve = function (board, parents, attributes) {\n var c, glider, tracepoint, attr;\n\n if (parents.length !== 2) {\n throw new Error(\n \"JSXGraph: Can't create trace curve with given parent'\" +\n \"\\nPossible parent types: [glider, point]\"\n );\n }\n\n glider = board.select(parents[0]);\n tracepoint = board.select(parents[1]);\n\n if (glider.type !== Const.OBJECT_TYPE_GLIDER || !Type.isPoint(tracepoint)) {\n throw new Error(\n \"JSXGraph: Can't create trace curve with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [glider, point]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'tracecurve');\n attr.curvetype = 'plot';\n c = board.create(\"curve\", [[0], [0]], attr);\n\n /**\n * @class\n * @ignore\n */\n c.updateDataArray = function () {\n var i, step, t, el, pEl, x, y, from,\n savetrace,\n le = this.visProp.numberpoints,\n savePos = glider.position,\n slideObj = glider.slideObject,\n mi = slideObj.minX(),\n ma = slideObj.maxX();\n\n // set step width\n step = (ma - mi) / le;\n this.dataX = [];\n this.dataY = [];\n\n /*\n * For gliders on circles and lines a closed curve is computed.\n * For gliders on curves the curve is not closed.\n */\n if (slideObj.elementClass !== Const.OBJECT_CLASS_CURVE) {\n le++;\n }\n\n // Loop over all steps\n for (i = 0; i < le; i++) {\n t = mi + i * step;\n x = slideObj.X(t) / slideObj.Z(t);\n y = slideObj.Y(t) / slideObj.Z(t);\n\n // Position the glider\n glider.setPositionDirectly(Const.COORDS_BY_USER, [x, y]);\n from = false;\n\n // Update all elements from the glider up to the trace element\n for (el in this.board.objects) {\n if (this.board.objects.hasOwnProperty(el)) {\n pEl = this.board.objects[el];\n\n if (pEl === glider) {\n from = true;\n }\n\n if (from && pEl.needsRegularUpdate) {\n // Save the trace mode of the element\n savetrace = pEl.visProp.trace;\n pEl.visProp.trace = false;\n pEl.needsUpdate = true;\n pEl.update(true);\n\n // Restore the trace mode\n pEl.visProp.trace = savetrace;\n if (pEl === tracepoint) {\n break;\n }\n }\n }\n }\n\n // Store the position of the trace point\n this.dataX[i] = tracepoint.X();\n this.dataY[i] = tracepoint.Y();\n }\n\n // Restore the original position of the glider\n glider.position = savePos;\n from = false;\n\n // Update all elements from the glider to the trace point\n for (el in this.board.objects) {\n if (this.board.objects.hasOwnProperty(el)) {\n pEl = this.board.objects[el];\n if (pEl === glider) {\n from = true;\n }\n\n if (from && pEl.needsRegularUpdate) {\n savetrace = pEl.visProp.trace;\n pEl.visProp.trace = false;\n pEl.needsUpdate = true;\n pEl.update(true);\n pEl.visProp.trace = savetrace;\n\n if (pEl === tracepoint) {\n break;\n }\n }\n }\n }\n };\n\n return c;\n};\n\nJXG.registerElement(\"tracecurve\", JXG.createTracecurve);\n\n/**\n * @class A step function is a function graph that is piecewise constant.\n *\n * In case the data points should be updated after creation time,\n * they can be accessed by curve.xterm and curve.yterm.\n * @pseudo\n * @name Stepfunction\n * @augments JXG.Curve\n * @constructor\n * @type Curve\n * @description JXG.Curve\n * @param {Array|Function} Parent1 elements of Stepfunction are two arrays containing the coordinates.\n * @param {Array|Function} Parent2\n * @see JXG.Curve\n * @example\n * // Create step function.\n var curve = board.create('stepfunction', [[0,1,2,3,4,5], [1,3,0,2,2,1]]);\n\n * \n * \n */\nJXG.createStepfunction = function (board, parents, attributes) {\n var c, attr;\n if (parents.length !== 2) {\n throw new Error(\n \"JSXGraph: Can't create step function with given parent'\" +\n \"\\nPossible parent types: [array, array|function]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'stepfunction');\n c = board.create(\"curve\", parents, attr);\n /**\n * @class\n * @ignore\n */\n c.updateDataArray = function () {\n var i,\n j = 0,\n len = this.xterm.length;\n\n this.dataX = [];\n this.dataY = [];\n\n if (len === 0) {\n return;\n }\n\n this.dataX[j] = this.xterm[0];\n this.dataY[j] = this.yterm[0];\n ++j;\n\n for (i = 1; i < len; ++i) {\n this.dataX[j] = this.xterm[i];\n this.dataY[j] = this.dataY[j - 1];\n ++j;\n this.dataX[j] = this.xterm[i];\n this.dataY[j] = this.yterm[i];\n ++j;\n }\n };\n\n return c;\n};\n\nJXG.registerElement(\"stepfunction\", JXG.createStepfunction);\n\n/**\n * @class A curve visualizing the function graph of the (numerical) derivative of a given curve.\n *\n * @pseudo\n * @name Derivative\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n * @param {JXG.Curve} Parent Curve for which the derivative is generated.\n * @see JXG.Curve\n * @example\n * var cu = board.create('cardinalspline', [[[-3,0], [-1,2], [0,1], [2,0], [3,1]], 0.5, 'centripetal'], {createPoints: false});\n * var d = board.create('derivative', [cu], {dash: 2});\n *\n * \n * \n *\n */\nJXG.createDerivative = function (board, parents, attributes) {\n var c, curve, dx, dy, attr;\n\n if (parents.length !== 1 && parents[0].class !== Const.OBJECT_CLASS_CURVE) {\n throw new Error(\n \"JSXGraph: Can't create derivative curve with given parent'\" +\n \"\\nPossible parent types: [curve]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'curve');\n\n curve = parents[0];\n dx = Numerics.D(curve.X);\n dy = Numerics.D(curve.Y);\n\n c = board.create(\n \"curve\",\n [\n function (t) {\n return curve.X(t);\n },\n function (t) {\n return dy(t) / dx(t);\n },\n curve.minX(),\n curve.maxX()\n ],\n attr\n );\n\n c.setParents(curve);\n\n return c;\n};\n\nJXG.registerElement(\"derivative\", JXG.createDerivative);\n\n/**\n * @class The path forming the intersection of two closed path elements.\n * The elements may be of type curve, circle, polygon, inequality.\n * If one element is a curve, it has to be closed.\n * The resulting element is of type curve.\n * @pseudo\n * @name CurveIntersection\n * @param {JXG.Curve|JXG.Polygon|JXG.Circle} curve1 First element which is intersected\n * @param {JXG.Curve|JXG.Polygon|JXG.Circle} curve2 Second element which is intersected\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n *\n * @example\n * var f = board.create('functiongraph', ['cos(x)']);\n * var ineq = board.create('inequality', [f], {inverse: true, fillOpacity: 0.1});\n * var circ = board.create('circle', [[0,0], 4]);\n * var clip = board.create('curveintersection', [ineq, circ], {fillColor: 'yellow', fillOpacity: 0.6});\n *\n * \n * \n *\n */\nJXG.createCurveIntersection = function (board, parents, attributes) {\n var c;\n\n if (parents.length !== 2) {\n throw new Error(\n \"JSXGraph: Can't create curve intersection with given parent'\" +\n \"\\nPossible parent types: [array, array|function]\"\n );\n }\n\n c = board.create(\"curve\", [[], []], attributes);\n /**\n * @class\n * @ignore\n */\n c.updateDataArray = function () {\n var a = Clip.intersection(parents[0], parents[1], this.board);\n this.dataX = a[0];\n this.dataY = a[1];\n };\n return c;\n};\n\n/**\n * @class The path forming the union of two closed path elements.\n * The elements may be of type curve, circle, polygon, inequality.\n * If one element is a curve, it has to be closed.\n * The resulting element is of type curve.\n * @pseudo\n * @name CurveUnion\n * @param {JXG.Curve|JXG.Polygon|JXG.Circle} curve1 First element defining the union\n * @param {JXG.Curve|JXG.Polygon|JXG.Circle} curve2 Second element defining the union\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n *\n * @example\n * var f = board.create('functiongraph', ['cos(x)']);\n * var ineq = board.create('inequality', [f], {inverse: true, fillOpacity: 0.1});\n * var circ = board.create('circle', [[0,0], 4]);\n * var clip = board.create('curveunion', [ineq, circ], {fillColor: 'yellow', fillOpacity: 0.6});\n *\n * \n * \n *\n */\nJXG.createCurveUnion = function (board, parents, attributes) {\n var c;\n\n if (parents.length !== 2) {\n throw new Error(\n \"JSXGraph: Can't create curve union with given parent'\" +\n \"\\nPossible parent types: [array, array|function]\"\n );\n }\n\n c = board.create(\"curve\", [[], []], attributes);\n /**\n * @class\n * @ignore\n */\n c.updateDataArray = function () {\n var a = Clip.union(parents[0], parents[1], this.board);\n this.dataX = a[0];\n this.dataY = a[1];\n };\n return c;\n};\n\n/**\n * @class The path forming the difference of two closed path elements.\n * The elements may be of type curve, circle, polygon, inequality.\n * If one element is a curve, it has to be closed.\n * The resulting element is of type curve.\n * @pseudo\n * @name CurveDifference\n * @param {JXG.Curve|JXG.Polygon|JXG.Circle} curve1 First element from which the second element is \"subtracted\"\n * @param {JXG.Curve|JXG.Polygon|JXG.Circle} curve2 Second element which is subtracted from the first element\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n *\n * @example\n * var f = board.create('functiongraph', ['cos(x)']);\n * var ineq = board.create('inequality', [f], {inverse: true, fillOpacity: 0.1});\n * var circ = board.create('circle', [[0,0], 4]);\n * var clip = board.create('curvedifference', [ineq, circ], {fillColor: 'yellow', fillOpacity: 0.6});\n *\n * \n * \n *\n */\nJXG.createCurveDifference = function (board, parents, attributes) {\n var c;\n\n if (parents.length !== 2) {\n throw new Error(\n \"JSXGraph: Can't create curve difference with given parent'\" +\n \"\\nPossible parent types: [array, array|function]\"\n );\n }\n\n c = board.create(\"curve\", [[], []], attributes);\n /**\n * @class\n * @ignore\n */\n c.updateDataArray = function () {\n var a = Clip.difference(parents[0], parents[1], this.board);\n this.dataX = a[0];\n this.dataY = a[1];\n };\n return c;\n};\n\nJXG.registerElement(\"curvedifference\", JXG.createCurveDifference);\nJXG.registerElement(\"curveintersection\", JXG.createCurveIntersection);\nJXG.registerElement(\"curveunion\", JXG.createCurveUnion);\n\n// /**\n// * @class Concat of two path elements, in general neither is a closed path. The parent elements have to be curves, too.\n// * The resulting element is of type curve. The curve points are simply concatenated.\n// * @pseudo\n// * @name CurveConcat\n// * @param {JXG.Curve} curve1 First curve element.\n// * @param {JXG.Curve} curve2 Second curve element.\n// * @augments JXG.Curve\n// * @constructor\n// * @type JXG.Curve\n// */\n// JXG.createCurveConcat = function (board, parents, attributes) {\n// var c;\n\n// if (parents.length !== 2) {\n// throw new Error(\n// \"JSXGraph: Can't create curve difference with given parent'\" +\n// \"\\nPossible parent types: [array, array|function]\"\n// );\n// }\n\n// c = board.create(\"curve\", [[], []], attributes);\n// /**\n// * @class\n// * @ignore\n// */\n// c.updateCurve = function () {\n// this.points = parents[0].points.concat(\n// [new JXG.Coords(Const.COORDS_BY_USER, [NaN, NaN], this.board)]\n// ).concat(parents[1].points);\n// this.numberPoints = this.points.length;\n// return this;\n// };\n\n// return c;\n// };\n\n// JXG.registerElement(\"curveconcat\", JXG.createCurveConcat);\n\n/**\n * @class Vertical or horizontal boxplot or also called box-and-whisker plot to present numerical data through their quartiles.\n * The direction of the boxplot is controlled by the attribute \"dir\". Internally, a boxplot is realized with a single JSXGraph curve.\n * \n * \n *\n * @example\n * // With outliers\n * var Q = [ -1, 2, 3, 3.5, 5, [-4, -6] ];\n * var b = board.create('boxplot', [Q, 3, 4], {dir: 'horizontal', width: 2, smallWidth: 0.25, color:'red'});\n *\n * \n * \n *\n * @example\n * var data = [57, 57, 57, 58, 63, 66, 66, 67, 67, 68, 69, 70, 70, 70, 70, 72, 73, 75, 75, 76, 76, 78, 79, 81];\n * var Q = JXG.Math.Statistics.boxplot(data);\n * var b = board.create('boxplot', [Q, 0, 3]);\n *\n * \n * \n *\n * @example\n * var mi = board.create('glider', [0, -1, board.defaultAxes.y]);\n * var ma = board.create('glider', [0, 5, board.defaultAxes.y]);\n * var Q = [function() { return mi.Y(); }, 2, 3, 3.5, function() { return ma.Y(); }];\n *\n * var b = board.create('boxplot', [Q, 0, 2]);\n *\n * \n * \n *\n */\nJXG.createBoxPlot = function (board, parents, attributes) {\n var box, i, len,\n attr = Type.copyAttributes(attributes, board.options, 'boxplot');\n\n if (parents.length !== 3) {\n throw new Error(\n \"JSXGraph: Can't create boxplot with given parent'\" +\n \"\\nPossible parent types: [array, number|function, number|function] containing quantiles, axis, width\"\n );\n }\n if (parents[0].length < 5) {\n throw new Error(\n \"JSXGraph: Can't create boxplot with given parent[0]'\" +\n \"\\nparent[0] has to contain at least 5 quantiles.\"\n );\n }\n box = board.create(\"curve\", [[], []], attr);\n\n len = parents[0].length; // Quantiles\n box.Q = [];\n for (i = 0; i < len; i++) {\n box.Q[i] = Type.createFunction(parents[0][i], board);\n }\n box.x = Type.createFunction(parents[1], board);\n box.w = Type.createFunction(parents[2], board);\n\n /**\n * @class\n * @ignore\n */\n box.updateDataArray = function () {\n var v1, v2, l1, l2, r1, r2, w2, dir, x,\n i, le, q5, y, sx, sy, sx2, sy2, t, f;\n\n w2 = this.evalVisProp('smallwidth');\n dir = this.evalVisProp('dir');\n x = this.x();\n l1 = x - this.w() * 0.5;\n l2 = x - this.w() * 0.5 * w2;\n r1 = x + this.w() * 0.5;\n r2 = x + this.w() * 0.5 * w2;\n v1 = [x, l2, r2, x, x, l1, l1, r1, r1, x, NaN, l1, r1, NaN, x, x, l2, r2, x];\n v2 = [\n this.Q[0](),\n this.Q[0](),\n this.Q[0](),\n this.Q[0](),\n this.Q[1](),\n this.Q[1](),\n this.Q[3](),\n this.Q[3](),\n this.Q[1](),\n this.Q[1](),\n NaN,\n this.Q[2](),\n this.Q[2](),\n NaN,\n this.Q[3](),\n this.Q[4](),\n this.Q[4](),\n this.Q[4](),\n this.Q[4]()\n ];\n\n // Outliers\n if (this.Q.length > 5 && Type.isArray(this.Q[5]())) {\n v1.push(NaN);\n v2.push(NaN);\n\n f = this.evalVisProp('outlier.face');\n\n if (dir === 'vertical') {\n sx = this.evalVisProp('outlier.size') / this.board.unitX;\n sy = this.evalVisProp('outlier.size') / this.board.unitY;\n } else {\n sy = this.evalVisProp('outlier.size') / this.board.unitX;\n sx = this.evalVisProp('outlier.size') / this.board.unitY;\n }\n sx2 = sx * Math.sqrt(2);\n sy2 = sy * Math.sqrt(2);\n\n q5 = this.Q[5]();\n le = q5.length;\n for (i = 0; i < le; i++) {\n y = q5[i];\n switch (f) {\n case 'x':\n case 'cross':\n v1.push(x - sx, x + sx, NaN, x - sx, x + sx, NaN);\n v2.push(y + sy, y - sy, NaN, y - sy, y + sy, NaN);\n break;\n case '[]':\n case 'square':\n v1.push(x - sx, x + sx, x + sx, x - sx, x - sx, NaN);\n v2.push(y + sy, y + sy, y - sy, y - sy, y + sy, NaN);\n break;\n case '<>':\n case 'diamond':\n v1.push(x, x + sx, x, x - sx, x, NaN);\n v2.push(y + sy, y, y - sy, y, y + sy, NaN);\n break;\n case '<<>>':\n case 'diamond2':\n v1.push(x, x + sx2, x, x - sx2, x, NaN);\n v2.push(y + sy2, y, y - sy2, y, y + sy2, NaN);\n break;\n case '+':\n case 'plus':\n v1.push(x - sx, x + sx, NaN, x, x, NaN);\n v2.push(y, y, NaN, y - sy, y + sy, NaN);\n break;\n case '-':\n case 'minus':\n v1.push(x - sx, x + sx, NaN);\n v2.push(y, y, NaN);\n break;\n case '|':\n case 'divide':\n v1.push(x, x, NaN);\n v2.push(y - sy, y + sy, NaN);\n break;\n default:\n case 'o':\n case 'circle':\n for (t = 0; t <= 2 * Math.PI; t += (2 * Math.PI) / 17) {\n v1.push(x - sx * Math.sin(t));\n v2.push(y - sy * Math.cos(t));\n }\n v1.push(NaN);\n v2.push(NaN);\n }\n }\n }\n\n if (dir === 'vertical') {\n this.dataX = v1;\n this.dataY = v2;\n } else {\n this.dataX = v2;\n this.dataY = v1;\n }\n };\n\n box.addParentsFromJCFunctions([box.Q, box.x, box.w]);\n\n return box;\n};\n\nJXG.registerElement(\"boxplot\", JXG.createBoxPlot);\n\n/**\n * @class An implicit curve is a plane curve defined by an implicit equation\n * relating two coordinate variables, commonly x and y.\n * For example, the unit circle is defined by the implicit equation\n * x2 + y2 = 1.\n * In general, every implicit curve is defined by an equation of the form\n * f(x, y) = 0\n * for some function f of two variables. (Wikipedia)\n * \n * \n *\n * @example\n * var a, c, f;\n * a = board.create('slider', [[-3, 6], [3, 6], [-3, 1, 3]], {\n * name: 'a', stepWidth: 0.1\n * });\n * f = (x, y) => x ** 2 - 2 * x * y - 2 * x + (a.Value() + 1) * y ** 2 + (4 * a.Value() + 2) * y + 4 * a.Value() - 3;\n * c = board.create('implicitcurve', [f], {\n * strokeWidth: 3,\n * strokeColor: JXG.palette.red,\n * strokeOpacity: 0.8,\n * resolution_outer: 20,\n * resolution_inner: 20\n * });\n *\n * \n * \n *\n * @example\n * var c = board.create('implicitcurve', ['abs(x * y) - 3'], {\n * strokeWidth: 3,\n * strokeColor: JXG.palette.red,\n * strokeOpacity: 0.8\n * });\n *\n * \n * \n *\n * @example\n * var niveauline = [];\n * niveauline = [0.5, 1, 1.5, 2];\n * for (let i = 0; i < niveauline.length; i++) {\n * board.create(\"implicitcurve\", [\n * (x, y) => x ** .5 * y ** .5 - niveauline[i],\n [0.25, 3], [0.5, 4] // Domain\n * ], {\n * strokeWidth: 2,\n * strokeColor: JXG.palette.red,\n * strokeOpacity: (1 + i) / niveauline.length,\n * needsRegularUpdate: false\n * });\n * }\n *\n * \n * \n *\n */\nJXG.createImplicitCurve = function (board, parents, attributes) {\n var c, attr;\n\n if ([1, 3, 5].indexOf(parents.length) < 0) {\n throw new Error(\n \"JSXGraph: Can't create curve implicitCurve with given parent'\" +\n \"\\nPossible parent types: [f], [f, rangex, rangey], [f, dfx, dfy] or [f, dfx, dfy, rangex, rangey]\" +\n \"\\nwith functions f, dfx, dfy and arrays of length 2 rangex, rangey.\"\n );\n }\n\n // if (parents.length === 3) {\n // if (!Type.isArray(parents[1]) && !Type.isArray(parents[2])) {\n // throw new Error(\n // \"JSXGraph: Can't create curve implicitCurve with given parent'\" +\n // \"\\nPossible parent types: [f], [f, rangex, rangey], [f, dfx, dfy] or [f, dfx, dfy, rangex, rangey]\" +\n // \"\\nwith functions f, dfx, dfy and arrays of length 2 rangex, rangey.\"\n // );\n // }\n // }\n // if (parents.length === 5) {\n // if (!Type.isArray(parents[3]) && !Type.isArray(parents[4])) {\n // throw new Error(\n // \"JSXGraph: Can't create curve implicitCurve with given parent'\" +\n // \"\\nPossible parent types: [f], [f, rangex, rangey], [f, dfx, dfy] or [f, dfx, dfy, rangex, rangey]\" +\n // \"\\nwith functions f, dfx, dfy and arrays of length 2 rangex, rangey.\"\n // );\n // }\n // }\n\n attr = Type.copyAttributes(attributes, board.options, 'implicitcurve');\n c = board.create(\"curve\", [[], []], attr);\n\n /**\n * Function of two variables for the left side of the equation f(x,y)=0.\n *\n * @name f\n * @memberOf ImplicitCurve.prototype\n * @function\n * @returns {Number}\n */\n c.f = Type.createFunction(parents[0], board, 'x, y');\n\n /**\n * Partial derivative in the first variable of\n * the left side of the equation f(x,y)=0.\n * If null, then numerical derivative is used.\n *\n * @name dfx\n * @memberOf ImplicitCurve.prototype\n * @function\n * @returns {Number}\n */\n if (parents.length === 5 || Type.isString(parents[1]) || Type.isFunction(parents[1])) {\n c.dfx = Type.createFunction(parents[1], board, 'x, y');\n } else {\n c.dfx = null;\n }\n\n /**\n * Partial derivative in the second variable of\n * the left side of the equation f(x,y)=0.\n * If null, then numerical derivative is used.\n *\n * @name dfy\n * @memberOf ImplicitCurve.prototype\n * @function\n * @returns {Number}\n */\n if (parents.length === 5 || Type.isString(parents[2]) || Type.isFunction(parents[2])) {\n c.dfy = Type.createFunction(parents[2], board, 'x, y');\n } else {\n c.dfy = null;\n }\n\n /**\n * Defines a domain for searching f(x,y)=0. Default is null, meaning\n * the bounding box of the board is used.\n * Using domain, visProp.margin is ignored.\n * @name domain\n * @memberOf ImplicitCurve.prototype\n * @param {Array} of length 4 defining the domain used to compute the implict curve.\n * Syntax: [x_min, y_max, x_max, y_min]\n */\n // c.domain = board.getBoundingBox();\n c.domain = null;\n if (parents.length === 5) {\n c.domain = [parents[3], parents[4]];\n // [Math.min(parents[3][0], parents[3][1]), Math.max(parents[3][0], parents[3][1])],\n // [Math.min(parents[4][0], parents[4][1]), Math.max(parents[4][0], parents[4][1])]\n // ];\n } else if (parents.length === 3) {\n c.domain = [parents[1], parents[2]];\n // [Math.min(parents[1][0], parents[1][1]), Math.max(parents[1][0], parents[1][1])],\n // [Math.min(parents[2][0], parents[2][1]), Math.max(parents[2][0], parents[2][1])]\n // ];\n }\n\n /**\n * @class\n * @ignore\n */\n c.updateDataArray = function () {\n var bbox, rx, ry,\n ip, cfg,\n ret = [],\n mgn;\n\n if (this.domain === null) {\n mgn = this.evalVisProp('margin');\n bbox = this.board.getBoundingBox();\n bbox[0] -= mgn;\n bbox[1] += mgn;\n bbox[2] += mgn;\n bbox[3] -= mgn;\n } else {\n rx = Type.evaluate(this.domain[0]);\n ry = Type.evaluate(this.domain[1]);\n bbox = [\n Math.min(rx[0], rx[1]),\n Math.max(ry[0], ry[1]),\n Math.max(rx[0], rx[1]),\n Math.min(ry[0], ry[1])\n // rx[0], ry[1], rx[1], ry[0]\n ];\n }\n\n cfg = {\n resolution_out: Math.max(0.01, this.evalVisProp('resolution_outer')),\n resolution_in: Math.max(0.01, this.evalVisProp('resolution_inner')),\n max_steps: this.evalVisProp('max_steps'),\n alpha_0: this.evalVisProp('alpha_0'),\n tol_u0: this.evalVisProp('tol_u0'),\n tol_newton: this.evalVisProp('tol_newton'),\n tol_cusp: this.evalVisProp('tol_cusp'),\n tol_progress: this.evalVisProp('tol_progress'),\n qdt_box: this.evalVisProp('qdt_box'),\n kappa_0: this.evalVisProp('kappa_0'),\n delta_0: this.evalVisProp('delta_0'),\n h_initial: this.evalVisProp('h_initial'),\n h_critical: this.evalVisProp('h_critical'),\n h_max: this.evalVisProp('h_max'),\n loop_dist: this.evalVisProp('loop_dist'),\n loop_dir: this.evalVisProp('loop_dir'),\n loop_detection: this.evalVisProp('loop_detection'),\n unitX: this.board.unitX,\n unitY: this.board.unitY\n };\n this.dataX = [];\n this.dataY = [];\n\n // console.time(\"implicit plot\");\n ip = new ImplicitPlot(bbox, cfg, this.f, this.dfx, this.dfy);\n this.qdt = ip.qdt;\n\n ret = ip.plot();\n // console.timeEnd(\"implicit plot\");\n\n this.dataX = ret[0];\n this.dataY = ret[1];\n };\n\n c.elType = 'implicitcurve';\n\n return c;\n};\n\nJXG.registerElement(\"implicitcurve\", JXG.createImplicitCurve);\n\n/**\n * @class Sketch a curve by dragging the pointer device on the board.\n * If enabled:true, it is always done even if the curve is invisible.\n * A JSXGraph borad contains a length two array board.sketches\n * with two sketchcurves.\n *\n * @pseudo\n * @name SketchCurve\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n * @see JXG.Board#sketches\n * @see JXG.Board#sketch\n * @private\n */\nJXG.createSketchCurve = function (board, parents, attributes) {\n var c, attr;\n\n attr = Type.copyAttributes(attributes, board.options, 'sketchcurve');\n c = board.create(\"curve\", [[], []], attr);\n\n c.elType = 'sketchcurve';\n\n return c;\n};\n\nJXG.registerElement(\"sketchcurve\", JXG.createSketchCurve);\n\nexport default JXG.Curve;\n\n// export default {\n// Curve: JXG.Curve,\n// createCardinalSpline: JXG.createCardinalSpline,\n// createCurve: JXG.createCurve,\n// createCurveDifference: JXG.createCurveDifference,\n// createCurveIntersection: JXG.createCurveIntersection,\n// createCurveUnion: JXG.createCurveUnion,\n// createDerivative: JXG.createDerivative,\n// createFunctiongraph: JXG.createFunctiongraph,\n// createMetapostSpline: JXG.createMetapostSpline,\n// createPlot: JXG.createFunctiongraph,\n// createSpline: JXG.createSpline,\n// createRiemannsum: JXG.createRiemannsum,\n// createStepfunction: JXG.createStepfunction,\n// createTracecurve: JXG.createTracecurve\n// };\n\n// const Curve = JXG.Curve;\n// export { Curve as default, Curve};\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n * @example\n * var t = board.create('transform', [2, 1.5], {type: 'scale'});\n * var a1 = board.create('arc', [[1, 1], [0, 1], [1, 0]], {strokeColor: 'red'});\n * var a2 = board.create('curve', [a1, t], {strokeColor: 'red'});\n *\n * \n * \n *\n */\nJXG.createArc = function (board, parents, attributes) {\n var el, attr, points;\n\n // attributes.radiusPoint = {visible: false};\n points = Type.providePoints(board, parents, attributes, \"arc\", [\n \"center\",\n \"radiuspoint\",\n \"anglepoint\"\n ]);\n if (points === false || points.length < 3) {\n throw new Error(\n \"JSXGraph: Can't create Arc with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point], [arc, transformation]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'arc');\n el = board.create(\"curve\", [[0], [0], 0, 4], attr);\n\n el.elType = 'arc';\n el.setParents(points);\n\n /**\n * documented in JXG.GeometryElement\n * @ignore\n */\n el.type = Const.OBJECT_TYPE_ARC;\n\n /**\n * Center of the arc.\n * @memberOf Arc.prototype\n * @name center\n * @type JXG.Point\n */\n el.center = points[0];\n\n /**\n * Point defining the arc's radius.\n * @memberOf Arc.prototype\n * @name radiuspoint\n * @type JXG.Point\n */\n el.radiuspoint = points[1];\n el.point2 = el.radiuspoint;\n\n /**\n * The point defining the arc's angle.\n * @memberOf Arc.prototype\n * @name anglepoint\n * @type JXG.Point\n */\n el.anglepoint = points[2];\n el.point3 = el.anglepoint;\n\n // Add arc as child to defining points\n // or vice versa if the points are provided as coordinates\n if (Type.exists(el.center._is_new)) {\n el.addChild(el.center);\n delete el.center._is_new;\n } else {\n el.center.addChild(el);\n }\n if (Type.exists(el.radiuspoint._is_new)) {\n el.addChild(el.radiuspoint);\n delete el.radiuspoint._is_new;\n } else {\n el.radiuspoint.addChild(el);\n }\n if (Type.exists(el.anglepoint._is_new)) {\n el.addChild(el.anglepoint);\n delete el.anglepoint._is_new;\n } else {\n el.anglepoint.addChild(el);\n }\n\n // This attribute is necessary for circumCircleArcs\n el.useDirection = attr.usedirection; // This makes the attribute immutable\n\n // documented in JXG.Curve\n /**\n * @class\n * @ignore\n */\n el.updateDataArray = function () {\n var ar, phi, det,\n p0c, p1c, p2c,\n sgn = 1,\n A = this.radiuspoint,\n B = this.center,\n C = this.anglepoint,\n a, b, c,\n vp_s = this.evalVisProp('selection'),\n vp_o = this.evalVisProp('orientation');\n\n phi = Geometry.rad(A, B, C);\n if ((vp_s === 'minor' && phi > Math.PI) || (vp_s === 'major' && phi < Math.PI) || (vp_s === 'auto' && vp_o === 'clockwise')) {\n sgn = -1;\n }\n\n // This is true for circumCircleArcs. In that case there is\n // a fourth parent element: [center, point1, point3, point2]\n if (this.useDirection) {\n p0c = points[1].coords.usrCoords;\n p1c = points[3].coords.usrCoords;\n p2c = points[2].coords.usrCoords;\n det = (p0c[1] - p2c[1]) * (p0c[2] - p1c[2]) - (p0c[2] - p2c[2]) * (p0c[1] - p1c[1]);\n\n if (det < 0) {\n this.radiuspoint = points[1];\n this.anglepoint = points[2];\n } else {\n this.radiuspoint = points[2];\n this.anglepoint = points[1];\n }\n }\n\n a = A.coords.usrCoords;\n b = B.coords.usrCoords;\n c = C.coords.usrCoords;\n\n ar = Geometry.bezierArc(a, b, c, false, sgn);\n\n this.dataX = ar[0];\n this.dataY = ar[1];\n\n this.bezierDegree = 3;\n\n this.updateStdform();\n this.updateQuadraticform();\n };\n\n /**\n * Determines the arc's current radius. I.e. the distance between {@link Arc#center} and {@link Arc#radiuspoint}.\n * @memberOf Arc.prototype\n * @name Radius\n * @function\n * @returns {Number} The arc's radius\n */\n el.Radius = function () {\n return this.radiuspoint.Dist(this.center);\n };\n\n /**\n * @deprecated Use {@link Arc#Radius}\n * @memberOf Arc.prototype\n * @name getRadius\n * @function\n * @returns {Number}\n */\n el.getRadius = function () {\n JXG.deprecated(\"Arc.getRadius()\", \"Arc.Radius()\");\n return this.Radius();\n };\n\n /**\n * Returns the length of the arc or the value of the angle spanned by the arc.\n * @memberOf Arc.prototype\n * @name Value\n * @function\n * @param {String} [unit='length'] Unit of the returned values. Possible units are\n * \n *
\n * It is sufficient to supply the first three characters of the unit, e.g. 'len'.\n * @param {Number} [rad=undefined] Value of angle which can be used instead of the generic one.\n * @returns {Number} The arc length or the angle value in various units.\n */\n el.Value = function (unit, rad) {\n var val;\n\n if (rad === undefined) {\n rad = Geometry.rad(this.radiuspoint, this.center, this.anglepoint);\n\n if (this.evalVisProp('orientation') === 'clockwise') {\n rad = 2 * Math.PI - rad;\n }\n }\n\n unit = unit || 'length';\n unit = unit.toLocaleLowerCase();\n if (unit === '' || unit.indexOf('len') === 0) {\n val = rad * this.Radius();\n } else if (unit.indexOf('rad') === 0) {\n val = rad;\n } else if (unit.indexOf('deg') === 0) {\n val = rad * 180 / Math.PI;\n } else if (unit.indexOf('sem') === 0) {\n val = rad / Math.PI;\n } else if (unit.indexOf('cir') === 0) {\n val = rad * 0.5 / Math.PI;\n }\n\n return val;\n };\n\n /**\n * Arc length.\n * @memberOf Arc.prototype\n * @name L\n * @returns {Number} Length of the arc.\n * @see Arc#Value\n */\n el.L = function() {\n return this.Value('length');\n };\n\n // documented in geometry element\n el.hasPoint = function (x, y) {\n var dist,\n checkPoint,\n has,\n invMat,\n c,\n prec,\n type,\n r = this.Radius();\n\n if (this.evalVisProp('hasinnerpoints')) {\n return this.hasPointSector(x, y);\n }\n\n if (Type.isObject(this.evalVisProp('precision'))) {\n type = this.board._inputDevice;\n prec = this.evalVisProp('precision.' + type);\n } else {\n // 'inherit'\n prec = this.board.options.precision.hasPoint;\n }\n prec /= Math.min(Math.abs(this.board.unitX), Math.abs(this.board.unitY));\n checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board);\n\n if (this.transformations.length > 0) {\n // Transform the mouse/touch coordinates\n // back to the original position of the curve.\n this.updateTransformMatrix();\n invMat = Mat.inverse(this.transformMat);\n c = Mat.matVecMult(invMat, checkPoint.usrCoords);\n checkPoint = new Coords(Const.COORDS_BY_USER, c, this.board);\n }\n\n dist = this.center.coords.distance(Const.COORDS_BY_USER, checkPoint);\n has = Math.abs(dist - r) < prec;\n\n /**\n * At that point we know that the user has touched the circle line.\n * Now, we have to check, if the user has hit the arc path.\n */\n if (has) {\n has = Geometry.coordsOnArc(this, checkPoint);\n }\n return has;\n };\n\n /**\n * Checks whether (x,y) is within the sector defined by the arc.\n * @memberOf Arc.prototype\n * @name hasPointSector\n * @function\n * @param {Number} x Coordinate in x direction, screen coordinates.\n * @param {Number} y Coordinate in y direction, screen coordinates.\n * @returns {Boolean} True if (x,y) is within the sector defined by the arc, False otherwise.\n */\n el.hasPointSector = function (x, y) {\n var checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),\n r = this.Radius(),\n dist = this.center.coords.distance(Const.COORDS_BY_USER, checkPoint),\n has = dist < r;\n\n if (has) {\n has = Geometry.coordsOnArc(this, checkPoint);\n }\n return has;\n };\n\n // documented in geometry element\n el.getTextAnchor = function () {\n return this.center.coords;\n };\n\n // documented in geometry element\n /**\n * @class\n * @ignore\n */\n el.getLabelAnchor = function () {\n var coords,\n vec, vecx, vecy,\n len,\n pos = this.label.evalVisProp('position'),\n angle = Geometry.rad(this.radiuspoint, this.center, this.anglepoint),\n dx = 10 / this.board.unitX,\n dy = 10 / this.board.unitY,\n p2c = this.point2.coords.usrCoords,\n pmc = this.center.coords.usrCoords,\n bxminusax = p2c[1] - pmc[1],\n byminusay = p2c[2] - pmc[2],\n vp_s = this.evalVisProp('selection'),\n vp_o = this.evalVisProp('orientation'),\n l_vp = this.label ? this.label.visProp : this.visProp.label;\n\n // If this is uncommented, the angle label can not be dragged\n //if (Type.exists(this.label)) {\n // this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);\n //}\n\n if (\n !Type.isString(pos) ||\n (pos.indexOf('right') < 0 && pos.indexOf('left') < 0)\n ) {\n\n if ((vp_s === 'minor' && angle > Math.PI) || (vp_s === 'major' && angle < Math.PI) || (vp_s === 'auto' && vp_o === 'clockwise')) {\n angle = -(2 * Math.PI - angle);\n }\n\n coords = new Coords(\n Const.COORDS_BY_USER,\n [\n pmc[1] + Math.cos(angle * 0.5) * bxminusax - Math.sin(angle * 0.5) * byminusay,\n pmc[2] + Math.sin(angle * 0.5) * bxminusax + Math.cos(angle * 0.5) * byminusay\n ],\n this.board\n );\n\n vecx = coords.usrCoords[1] - pmc[1];\n vecy = coords.usrCoords[2] - pmc[2];\n\n len = Mat.hypot(vecx, vecy);\n vecx = (vecx * (len + dx)) / len;\n vecy = (vecy * (len + dy)) / len;\n vec = [pmc[1] + vecx, pmc[2] + vecy];\n\n l_vp.position = Geometry.calcLabelQuadrant(Geometry.rad([1, 0], [0, 0], vec));\n\n return new Coords(Const.COORDS_BY_USER, vec, this.board);\n } else {\n return this.getLabelPosition(pos, this.label.evalVisProp('distance'));\n }\n\n };\n\n // documentation in jxg.circle\n el.updateQuadraticform = Circle.prototype.updateQuadraticform;\n\n // documentation in jxg.circle\n el.updateStdform = Circle.prototype.updateStdform;\n\n el.prepareUpdate().update();\n\n Type.extendInstanceMethodMap(el, {\n getRadius: \"getRadius\",\n radius: \"Radius\",\n Radius: \"Radius\",\n center: \"center\",\n radiuspoint: \"radiuspoint\",\n anglepoint: \"anglepoint\",\n Value: \"Value\",\n L: \"L\"\n });\n\n return el;\n};\n\nJXG.registerElement(\"arc\", JXG.createArc);\n\n/**\n * @class A semicircle is a special arc defined by two points. The arc hits both points.\n * @pseudo\n * @name Semicircle\n * @augments Arc\n * @constructor\n * @type Arc\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point} p1,p2 The result will be a composition of an arc drawn clockwise from p1 and\n * p2 and the midpoint of p1 and p2.\n * @example\n * // Create an arc out of three free points\n * var p1 = board.create('point', [4.5, 2.0]);\n * var p2 = board.create('point', [1.0, 0.5]);\n *\n * var a = board.create('semicircle', [p1, p2]);\n * \n * \n */\nJXG.createSemicircle = function (board, parents, attributes) {\n var el, mp, attr, points;\n\n // we need 2 points\n points = Type.providePoints(board, parents, attributes, 'point');\n if (points === false || points.length !== 2) {\n throw new Error(\n \"JSXGraph: Can't create Semicircle with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,point]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, \"semicircle\", 'center');\n mp = board.create(\"midpoint\", points, attr);\n mp.dump = false;\n\n attr = Type.copyAttributes(attributes, board.options, 'semicircle');\n el = board.create(\"arc\", [mp, points[1], points[0]], attr);\n el.elType = 'semicircle';\n el.setParents([points[0].id, points[1].id]);\n el.subs = {\n midpoint: mp\n };\n el.inherits.push(mp);\n\n /**\n * The midpoint of the two defining points.\n * @memberOf Semicircle.prototype\n * @name midpoint\n * @type Midpoint\n */\n el.midpoint = el.center = mp;\n\n return el;\n};\n\nJXG.registerElement(\"semicircle\", JXG.createSemicircle);\n\n/**\n * @class A partial circum circle through three points.\n * @pseudo\n * @name CircumcircleArc\n * @augments Arc\n * @constructor\n * @type Arc\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The result will be a composition of an arc of the circumcircle of\n * p1, p2, and p3 and the midpoint of the circumcircle of the three points. The arc is drawn\n * counter-clockwise from p1 over p2 to p3.\n * @example\n * // Create a circum circle arc out of three free points\n * var p1 = board.create('point', [2.0, 2.0]);\n * var p2 = board.create('point', [1.0, 0.5]);\n * var p3 = board.create('point', [3.5, 1.0]);\n *\n * var a = board.create('circumcirclearc', [p1, p2, p3]);\n * \n * \n */\nJXG.createCircumcircleArc = function (board, parents, attributes) {\n var el, mp, attr, points;\n\n // We need three points\n points = Type.providePoints(board, parents, attributes, 'point');\n if (points === false || points.length !== 3) {\n throw new Error(\n \"JSXGraph: create Circumcircle Arc with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, \"circumcirclearc\", 'center');\n mp = board.create(\"circumcenter\", points, attr);\n mp.dump = false;\n\n attr = Type.copyAttributes(attributes, board.options, 'circumcirclearc');\n attr.usedirection = true;\n el = board.create(\"arc\", [mp, points[0], points[2], points[1]], attr);\n\n el.elType = 'circumcirclearc';\n el.setParents([points[0].id, points[1].id, points[2].id]);\n el.subs = {\n center: mp\n };\n el.inherits.push(mp);\n\n /**\n * The midpoint of the circumcircle of the three points defining the circumcircle arc.\n * @memberOf CircumcircleArc.prototype\n * @name center\n * @type Circumcenter\n */\n el.center = mp;\n\n return el;\n};\n\nJXG.registerElement(\"circumcirclearc\", JXG.createCircumcircleArc);\n\n/**\n * @class A minor arc given by three points is that part of the circumference of a circle having\n * measure at most 180 degrees (pi radians). It is defined by a center, one point that\n * defines the radius, and a third point that defines the angle of the arc.\n * @pseudo\n * @name MinorArc\n * @augments Curve\n * @constructor\n * @type JXG.Curve\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor arc is an arc of a circle around p1 having measure less than or equal to\n * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.\n * @example\n * // Create an arc out of three free points\n * var p1 = board.create('point', [2.0, 2.0]);\n * var p2 = board.create('point', [1.0, 0.5]);\n * var p3 = board.create('point', [3.5, 1.0]);\n *\n * var a = board.create('arc', [p1, p2, p3]);\n * \n * \n */\n\nJXG.createMinorArc = function (board, parents, attributes) {\n attributes.selection = 'minor';\n return JXG.createArc(board, parents, attributes);\n};\n\nJXG.registerElement(\"minorarc\", JXG.createMinorArc);\n\n/**\n * @class A major arc given by three points is that part of the circumference of a circle having\n * measure at least 180 degrees (pi radians). It is defined by a center, one point that\n * defines the radius, and a third point that defines the angle of the arc.\n * @pseudo\n * @name MajorArc\n * @augments Curve\n * @constructor\n * @type JXG.Curve\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Major arc is an arc of a circle around p1 having measure greater than or equal to\n * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.\n * @example\n * // Create an arc out of three free points\n * var p1 = board.create('point', [2.0, 2.0]);\n * var p2 = board.create('point', [1.0, 0.5]);\n * var p3 = board.create('point', [3.5, 1.0]);\n *\n * var a = board.create('majorarc', [p1, p2, p3]);\n * \n * \n */\nJXG.createMajorArc = function (board, parents, attributes) {\n attributes.selection = 'major';\n return JXG.createArc(board, parents, attributes);\n};\n\nJXG.registerElement(\"majorarc\", JXG.createMajorArc);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n * @pseudo\n * @name Sector\n * @augments JXG.Curve\n * @constructor\n * @type JXG.Curve\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n *\n * First possibility of input parameters are:\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 A sector is defined by three points: The sector's center p1,\n * a second point p2 defining the radius and a third point p3 defining the angle of the sector. The\n * Sector is always drawn counter clockwise from p2 to p3.\n * \n *\n * @example\n * // Create a sector out of two lines, two directions and a radius\n * var p1 = board.create('point', [-1, 4]),\n * p2 = board.create('point', [4, 1]),\n * q1 = board.create('point', [-2, -3]),\n * q2 = board.create('point', [4,3]),\n *\n * li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),\n * li2 = board.create('line', [q1,q2], {lastArrow:true}),\n *\n * sec1 = board.create('sector', [li1, li2, [5.5, 0], [4, 3], 3]),\n * sec2 = board.create('sector', [li1, li2, 1, -1, 4]);\n *\n * \n * \n *\n * @example\n * var t = board.create('transform', [2, 1.5], {type: 'scale'});\n * var s1 = board.create('sector', [[-3.5,-3], [-3.5, -2], [-3.5,-4]], {\n * anglePoint: {visible:true}, center: {visible: true}, radiusPoint: {visible: true},\n * fillColor: 'yellow', strokeColor: 'black'});\n * var s2 = board.create('curve', [s1, t], {fillColor: 'yellow', strokeColor: 'black'});\n *\n * \n * \n *\n * @example\n * var A = board.create('point', [3, -2]),\n * B = board.create('point', [-2, -2]),\n * C = board.create('point', [0, 4]);\n *\n * var angle = board.create('sector', [B, A, C], {\n * strokeWidth: 0,\n * arc: {\n * \tvisible: true,\n * \tstrokeWidth: 3,\n * lastArrow: {size: 4},\n * firstArrow: {size: 4}\n * }\n * });\n * //angle.arc.setAttribute({firstArrow: false});\n * angle.arc.setAttribute({lastArrow: false});\n *\n * \n * \n *\n *\n */\nJXG.createSector = function (board, parents, attributes) {\n var el,\n attr,\n i,\n eps = 1.0e-14,\n type = \"invalid\",\n s, v,\n attrPoints = [\"center\", \"radiusPoint\", \"anglePoint\"],\n points;\n\n // Three points?\n if (\n parents[0].elementClass === Const.OBJECT_CLASS_LINE &&\n parents[1].elementClass === Const.OBJECT_CLASS_LINE &&\n (Type.isArray(parents[2]) || Type.isNumber(parents[2])) &&\n (Type.isArray(parents[3]) || Type.isNumber(parents[3])) &&\n (Type.isNumber(parents[4]) || Type.isFunction(parents[4]) || Type.isString(parents[4]))\n ) {\n type = '2lines';\n } else {\n points = Type.providePoints(board, parents, attributes, \"sector\", attrPoints);\n if (points === false) {\n throw new Error(\n \"JSXGraph: Can't create Sector with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\"\n );\n }\n type = '3points';\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'sector');\n // The curve length is 6: 0-1: leg 1, 1-5: arc, 5-6: leg 2\n el = board.create(\"curve\", [[0], [0], 0, 6], attr);\n el.type = Const.OBJECT_TYPE_SECTOR;\n el.elType = 'sector';\n\n /**\n * Sets radius if the attribute `radius` has value 'auto'.\n * Sets a radius between 20 and 50 points, depending on the distance\n * between the center and the radius point.\n * This function is used in {@link Angle}.\n *\n * @name autoRadius\n * @memberof Sector.prototype\n * @function\n * @returns {Number} returns a radius value in user coordinates.\n * @private\n */\n el.autoRadius = function () {\n var r1 = 20 / el.board.unitX, // 20px\n r2 = Infinity,\n r3 = 50 / el.board.unitX; // 50px\n\n if (Type.isPoint(el.center)) {\n // This does not work for 2-lines sectors / angles\n r2 = el.center.Dist(el.point2) * 0.3333;\n }\n\n return Math.max(r1, Math.min(r2, r3));\n };\n\n if (type === '2lines') {\n /**\n * @ignore\n */\n el.Radius = function () {\n var r = Type.evaluate(parents[4]);\n if (r === 'auto') {\n return this.autoRadius();\n }\n return r;\n };\n\n el.line1 = board.select(parents[0]);\n el.line2 = board.select(parents[1]);\n\n el.line1.addChild(el);\n el.line2.addChild(el);\n el.setParents(parents);\n\n el.point1 = { visProp: {} };\n el.point2 = { visProp: {} };\n el.point3 = { visProp: {} };\n\n // Intersection point, just used locally for direction1 and direction2\n s = Geometry.meetLineLine(el.line1.stdform, el.line2.stdform, 0, board);\n if (Geometry.distance(s.usrCoords, [0, 0, 0], 3) < eps) {\n // Parallel lines\n if (\n el.line1.point1.Dist(el.line2.point1) < eps ||\n el.line1.point1.Dist(el.line2.point2) < eps\n ) {\n s = el.line1.point1.coords;\n } else if (\n el.line1.point2.Dist(el.line2.point1) < eps ||\n el.line1.point2.Dist(el.line2.point1) < eps\n ) {\n s = el.line1.point2.coords;\n } else {\n console.log(\n \"JSXGraph warning: Can't create Sector from parallel lines with no common defining point.\"\n );\n }\n }\n\n if (Type.isArray(parents[2])) {\n /* project p1 to l1 */\n if (parents[2].length === 2) {\n parents[2] = [1].concat(parents[2]);\n }\n /*\n v = [0, el.line1.stdform[1], el.line1.stdform[2]];\n v = Mat.crossProduct(v, parents[2]);\n v = Geometry.meetLineLine(v, el.line1.stdform, 0, board);\n */\n v = Geometry.projectPointToLine(\n { coords: { usrCoords: parents[2] } },\n el.line1,\n board\n );\n v = Statistics.subtract(v.usrCoords, s.usrCoords);\n el.direction1 =\n Mat.innerProduct(v, [0, el.line1.stdform[2], -el.line1.stdform[1]], 3) >= 0\n ? +1\n : -1;\n } else {\n el.direction1 = parents[2] >= 0 ? 1 : -1;\n }\n\n if (Type.isArray(parents[3])) {\n /* project p2 to l2 */\n if (parents[3].length === 2) {\n parents[3] = [1].concat(parents[3]);\n }\n /*\n v = [0, el.line2.stdform[1], el.line2.stdform[2]];\n v = Mat.crossProduct(v, parents[3]);\n v = Geometry.meetLineLine(v, el.line2.stdform, 0, board);\n */\n v = Geometry.projectPointToLine(\n { coords: { usrCoords: parents[3] } },\n el.line2,\n board\n );\n v = Statistics.subtract(v.usrCoords, s.usrCoords);\n el.direction2 =\n Mat.innerProduct(v, [0, el.line2.stdform[2], -el.line2.stdform[1]], 3) >= 0\n ? +1\n : -1;\n } else {\n el.direction2 = parents[3] >= 0 ? 1 : -1;\n }\n\n /**\n * @class\n * @ignore\n */\n el.updateDataArray = function () {\n var r,\n l1, l2,\n eps = 1.0e-14,\n A = [0, 0, 0],\n B = [0, 0, 0],\n C = [0, 0, 0],\n ar;\n\n l1 = this.line1;\n l2 = this.line2;\n\n // Intersection point of the lines\n B = Mat.crossProduct(l1.stdform, l2.stdform);\n if (Geometry.distance(B, [0, 0, 0], 3) < eps) {\n // Parallel lines\n if (\n l1.point1.Dist(l2.point1) < eps ||\n l1.point1.Dist(l2.point2) < eps\n ) {\n B = l1.point1.coords.usrCoords;\n } else if (\n l1.point2.Dist(l2.point1) < eps ||\n l1.point2.Dist(l2.point1) < eps\n ) {\n B = l1.point2.coords.usrCoords;\n } else {\n }\n }\n\n if (Math.abs(B[0]) > eps) {\n B[1] /= B[0];\n B[2] /= B[0];\n B[0] /= B[0];\n }\n // First point\n r = this.direction1 * this.Radius();\n A = Statistics.add(B, [0, r * l1.stdform[2], -r * l1.stdform[1]]);\n\n // Second point\n r = this.direction2 * this.Radius();\n C = Statistics.add(B, [0, r * l2.stdform[2], -r * l2.stdform[1]]);\n\n this.point2.coords = new Coords(Const.COORDS_BY_USER, A, el.board);\n this.point1.coords = new Coords(Const.COORDS_BY_USER, B, el.board);\n this.point3.coords = new Coords(Const.COORDS_BY_USER, C, el.board);\n\n if (\n Math.abs(A[0]) < Mat.eps ||\n Math.abs(B[0]) < Mat.eps ||\n Math.abs(C[0]) < Mat.eps\n ) {\n this.dataX = [NaN];\n this.dataY = [NaN];\n return;\n }\n\n ar = Geometry.bezierArc(A, B, C, true, 1);\n\n this.dataX = ar[0];\n this.dataY = ar[1];\n\n this.bezierDegree = 3;\n };\n\n // Arc does not work yet, since point1, point2 and point3 are\n // virtual points.\n //\n // attr = Type.copyAttributes(attributes, board.options, 'arc');\n // attr = Type.copyAttributes(attr, board.options, \"sector\", 'arc');\n // attr.withlabel = false;\n // attr.name += \"_arc\";\n // // el.arc = board.create(\"arc\", [el.point1, el.point2, el.point3], attr);\n // // The arc's radius is always the radius of sector.\n // // This is important for angles.\n // el.updateDataArray();\n // el.arc = board.create(\"arc\", [\n // function() {\n // return el.point1.coords.usrCoords;\n // }, // Center\n // function() {\n // var d = el.point2.coords.distance(Const.COORDS_BY_USER, el.point1.coords);\n // if (d === 0) {\n // return [el.point1.coords.usrCoords[1], el.point1.coords.usrCoords[2]];\n // }\n // return [\n // el.point1.coords.usrCoords[1] + el.Radius() * (el.point2.coords.usrCoords[1] - el.point1.coords.usrCoords[1]) / d,\n // el.point1.coords.usrCoords[2] + el.Radius() * (el.point2.coords.usrCoords[2] - el.point1.coords.usrCoords[2]) / d\n // ];\n // },\n // function() {\n // return el.point3.coords.usrCoords;\n // }, // Center\n // ], attr);\n // el.addChild(el.arc);\n\n Type.extendInstanceMethodMap(el, {\n arc: \"arc\",\n center: \"center\",\n line1: \"line1\",\n line2: \"line2\"\n });\n\n // end '2lines'\n } else if (type === '3points') {\n /**\n * Midpoint of the sector.\n * @memberOf Sector.prototype\n * @name point1\n * @type JXG.Point\n */\n el.point1 = points[0];\n\n /**\n * This point together with {@link Sector#point1} defines the radius.\n * @memberOf Sector.prototype\n * @name point2\n * @type JXG.Point\n */\n el.point2 = points[1];\n\n /**\n * Defines the sector's angle.\n * @memberOf Sector.prototype\n * @name point3\n * @type JXG.Point\n */\n el.point3 = points[2];\n\n /* Add arc as child to defining points */\n for (i = 0; i < 3; i++) {\n if (Type.exists(points[i]._is_new)) {\n el.addChild(points[i]);\n delete points[i]._is_new;\n } else {\n points[i].addChild(el);\n }\n }\n\n // useDirection is necessary for circumCircleSectors\n el.useDirection = attributes.usedirection; // this makes the attribute immutable\n el.setParents(points);\n\n /**\n * Defines the sectors orientation in case of circumCircleSectors.\n * @memberOf Sector.prototype\n * @name point4\n * @type JXG.Point\n */\n if (Type.exists(points[3])) {\n el.point4 = points[3];\n el.point4.addChild(el);\n }\n\n /**\n * @class\n * @ignore\n */\n el.updateDataArray = function () {\n var ar, det,\n p0c, p1c, p2c,\n A = this.point2,\n B = this.point1,\n C = this.point3,\n a, b, c,\n phi,\n sgn = 1,\n vp_s = this.evalVisProp('selection'),\n vp_o = this.evalVisProp('orientation');\n\n if (!A.isReal || !B.isReal || !C.isReal) {\n this.dataX = [NaN];\n this.dataY = [NaN];\n return;\n }\n\n phi = Geometry.rad(A, B, C);\n if (\n (vp_o === 'counterclockwise' &&\n ((vp_s === 'minor' && phi > Math.PI) ||\n (vp_s === 'major' && phi < Math.PI))\n ) ||\n (vp_o === 'clockwise' &&\n ((vp_s === 'auto') ||\n (vp_s === 'minor' && phi > Math.PI) ||\n (vp_s === 'major' && phi < Math.PI))\n )\n ) {\n sgn = -1;\n }\n // if ((vp_s === 'minor' && phi > Math.PI) ||\n // (vp_s === 'major' && phi < Math.PI) ||\n // (vp_s === 'auto' && vp_o === 'clockwise')) {\n // sgn = -1;\n // }\n\n // This is true for circumCircleSectors. In that case there is\n // a fourth parent element: [midpoint, point1, point3, point2]\n if (this.useDirection && Type.exists(this.point4)) {\n p0c = this.point2.coords.usrCoords;\n p1c = this.point4.coords.usrCoords;\n p2c = this.point3.coords.usrCoords;\n det =\n (p0c[1] - p2c[1]) * (p0c[2] - p1c[2]) -\n (p0c[2] - p2c[2]) * (p0c[1] - p1c[1]);\n\n if (det >= 0.0) {\n C = this.point2;\n A = this.point3;\n }\n }\n\n a = A.coords.usrCoords;\n b = B.coords.usrCoords;\n c = C.coords.usrCoords;\n\n ar = Geometry.bezierArc(a, b, c, true, sgn);\n\n this.dataX = ar[0];\n this.dataY = ar[1];\n this.bezierDegree = 3;\n };\n\n /**\n * Returns the radius of the sector.\n * @memberOf Sector.prototype\n * @name Radius\n * @function\n * @returns {Number} The distance between {@link Sector#point1} and {@link Sector#point2}.\n */\n el.Radius = function () {\n return this.point2.Dist(this.point1);\n };\n\n Type.extendInstanceMethodMap(el, {\n arc: \"arc\",\n center: \"center\",\n radiuspoint: \"radiuspoint\",\n anglepoint: \"anglepoint\"\n });\n\n } // end '3points'\n\n el.center = el.point1;\n el.radiuspoint = el.point2;\n el.anglepoint = el.point3;\n\n attr = Type.copyAttributes(attributes, board.options, 'arc');\n attr = Type.copyAttributes(attr, board.options, \"sector\", 'arc');\n attr.withlabel = false;\n\n // Minor or major arc:\n attr.selection = el.visProp.selection;\n attr.name += \"_arc\";\n\n if (type === '2lines') {\n el.updateDataArray();\n el.arc = board.create(\"arc\", [\n function() {\n return el.point1.coords.usrCoords;\n }, // Center\n function() {\n var d = el.point2.coords.distance(Const.COORDS_BY_USER, el.point1.coords);\n if (d === 0) {\n return [el.point1.coords.usrCoords[1], el.point1.coords.usrCoords[2]];\n }\n return [\n el.point1.coords.usrCoords[1] + el.Radius() * (el.point2.coords.usrCoords[1] - el.point1.coords.usrCoords[1]) / d,\n el.point1.coords.usrCoords[2] + el.Radius() * (el.point2.coords.usrCoords[2] - el.point1.coords.usrCoords[2]) / d\n ];\n },\n function() {\n return el.point3.coords.usrCoords;\n } // Center\n ], attr);\n } else {\n // The arc's radius is always the radius of sector.\n // This is important for angles.\n el.arc = board.create(\"arc\", [\n el.point1, // Center\n function() {\n var d = el.point2.Dist(el.point1),\n A, B;\n\n A = el.point1;\n B = el.point2;\n if (d === 0) {\n return [A.X(), A.Y()];\n }\n\n return [\n A.X() + el.Radius() * (B.X() - A.X()) / d,\n A.Y() + el.Radius() * (B.Y() - A.Y()) / d\n ];\n },\n el.point3\n ], attr);\n }\n el.addChild(el.arc);\n el.inherits.push(el.arc);\n\n // Default hasPoint method. Documented in geometry element\n el.hasPointCurve = function (x, y) {\n var angle,\n alpha,\n beta,\n prec,\n type,\n checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),\n r = this.Radius(),\n dist = this.center.coords.distance(Const.COORDS_BY_USER, checkPoint),\n has,\n vp_s = this.evalVisProp('selection'),\n vp_o = this.evalVisProp('orientation');\n\n if (Type.isObject(this.evalVisProp('precision'))) {\n type = this.board._inputDevice;\n prec = this.evalVisProp('precision.' + type);\n } else {\n // 'inherit'\n prec = this.board.options.precision.hasPoint;\n }\n prec /= Math.min(Math.abs(this.board.unitX), Math.abs(this.board.unitY));\n has = Math.abs(dist - r) < prec;\n\n if (has) {\n angle = Geometry.rad(this.point2, this.center, checkPoint.usrCoords.slice(1));\n alpha = 0;\n beta = Geometry.rad(this.point2, this.center, this.point3);\n\n if (vp_o === 'clockwise') {\n angle = 2 * Math.PI - angle;\n beta = 2 * Math.PI - beta;\n }\n\n if ((vp_s === 'minor' && beta > Math.PI) || (vp_s === 'major' && beta < Math.PI)) {\n alpha = beta;\n beta = 2 * Math.PI;\n }\n\n if (angle < alpha || angle > beta) {\n has = false;\n }\n }\n\n return has;\n };\n\n /**\n * Checks whether (x,y) is within the area defined by the sector.\n * @memberOf Sector.prototype\n * @name hasPointSector\n * @function\n * @param {Number} x Coordinate in x direction, screen coordinates.\n * @param {Number} y Coordinate in y direction, screen coordinates.\n * @returns {Boolean} True if (x,y) is within the sector defined by the arc, False otherwise.\n */\n el.hasPointSector = function (x, y) {\n var angle,\n checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),\n r = this.Radius(),\n dist = this.point1.coords.distance(Const.COORDS_BY_USER, checkPoint),\n alpha,\n beta,\n has = dist < r,\n vp_s = this.evalVisProp('selection'),\n vp_o = this.evalVisProp('orientation');\n\n if (has) {\n angle = Geometry.rad(this.radiuspoint, this.center, checkPoint.usrCoords.slice(1));\n alpha = 0.0;\n beta = Geometry.rad(this.radiuspoint, this.center, this.anglepoint);\n\n if (vp_o === 'clockwise') {\n angle = 2 * Math.PI - angle;\n beta = 2 * Math.PI - beta;\n }\n\n if ((vp_s === 'minor' && beta > Math.PI) || (vp_s === 'major' && beta < Math.PI)) {\n alpha = beta;\n beta = 2 * Math.PI;\n }\n\n //if (angle > Geometry.rad(this.point2, this.point1, this.point3)) {\n if (angle < alpha || angle > beta) {\n has = false;\n }\n }\n return has;\n };\n\n el.hasPoint = function (x, y) {\n if (\n this.evalVisProp('highlightonsector') ||\n this.evalVisProp('hasinnerpoints')\n ) {\n return this.hasPointSector(x, y);\n }\n\n return this.hasPointCurve(x, y);\n };\n\n // documented in GeometryElement\n el.getTextAnchor = function () {\n return this.point1.coords;\n };\n\n // documented in GeometryElement\n // this method is very similar to arc.getLabelAnchor()\n // there are some additions in the arc version though, mainly concerning\n // 'major' and 'minor' arcs. Maybe these methods can be merged.\n /**\n * @class\n * @ignore\n */\n el.getLabelAnchor = function () {\n var coords,\n vec, vecx, vecy,\n len,\n pos = this.label.evalVisProp('position'),\n angle = Geometry.rad(this.point2, this.point1, this.point3),\n dx = 13 / this.board.unitX,\n dy = 13 / this.board.unitY,\n p2c = this.point2.coords.usrCoords,\n pmc = this.point1.coords.usrCoords,\n bxminusax = p2c[1] - pmc[1],\n byminusay = p2c[2] - pmc[2],\n vp_s = this.evalVisProp('selection'),\n vp_o = this.evalVisProp('orientation'),\n l_vp = this.label ? this.label.visProp : this.visProp.label;\n\n // If this is uncommented, the angle label can not be dragged\n //if (Type.exists(this.label)) {\n // this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);\n //}\n\n if (\n !Type.isString(pos) ||\n (pos.indexOf('right') < 0 && pos.indexOf('left') < 0)\n ) {\n\n if ((vp_s === 'minor' && angle > Math.PI) || (vp_s === 'major' && angle < Math.PI) || (vp_s === 'auto' && vp_o === 'clockwise')) {\n angle = -(2 * Math.PI - angle);\n }\n\n coords = new Coords(\n Const.COORDS_BY_USER,\n [\n pmc[1] + Math.cos(angle * 0.5) * bxminusax - Math.sin(angle * 0.5) * byminusay,\n pmc[2] + Math.sin(angle * 0.5) * bxminusax + Math.cos(angle * 0.5) * byminusay\n ],\n this.board\n );\n\n vecx = coords.usrCoords[1] - pmc[1];\n vecy = coords.usrCoords[2] - pmc[2];\n\n len = Mat.hypot(vecx, vecy);\n vecx = (vecx * (len + dx)) / len;\n vecy = (vecy * (len + dy)) / len;\n vec = [pmc[1] + vecx, pmc[2] + vecy];\n\n l_vp.position = Geometry.calcLabelQuadrant(Geometry.rad([1, 0], [0, 0], vec));\n\n return new Coords(Const.COORDS_BY_USER, vec, this.board);\n } else {\n return this.getLabelPosition(pos, this.label.evalVisProp('distance'));\n }\n };\n\n /**\n * Overwrite the Radius method of the sector.\n * Used in {@link GeometryElement#setAttribute}.\n * @memberOf Sector.prototype\n * @name setRadius\n * @param {Number|Function} value New radius.\n * @function\n */\n el.setRadius = function (val) {\n var res,\n e = Type.evaluate(val);\n\n if (val === 'auto' || e === 'auto') {\n res = 'auto';\n } else if (Type.isNumber(val)) {\n res = 'number';\n } else if (Type.isFunction(val) && !Type.isString(e)) {\n res = 'function';\n } else {\n res = 'undefined';\n }\n if (res !== 'undefined') {\n this.visProp.radius = val;\n }\n\n /**\n * @ignore\n */\n el.Radius = function () {\n var r = Type.evaluate(val);\n if (r === 'auto') {\n return this.autoRadius();\n }\n return r;\n };\n };\n\n /**\n * @deprecated\n * @ignore\n */\n el.getRadius = function () {\n JXG.deprecated(\"Sector.getRadius()\", \"Sector.Radius()\");\n return this.Radius();\n };\n\n /**\n * Length of the sector's arc or the angle in various units, see {@link Arc#Value}.\n * @memberOf Sector.prototype\n * @name Value\n * @function\n * @param {String} unit\n * @returns {Number} The arc length or the angle value in various units.\n * @see Arc#Value\n */\n el.Value = function(unit) {\n return this.arc.Value(unit);\n };\n\n /**\n * Arc length.\n * @memberOf Sector.prototype\n * @name L\n * @returns {Number} Length of the sector's arc.\n * @function\n * @see Arc#L\n */\n el.L = function() {\n return this.arc.L();\n };\n\n /**\n * Area of the sector.\n * @memberOf Sector.prototype\n * @name Area\n * @function\n * @returns {Number} The area of the sector.\n */\n el.Area = function () {\n var r = this.Radius();\n\n return 0.5 * r * r * this.Value('radians');\n };\n\n /**\n * Sector perimeter, i.e. arc length plus 2 * radius.\n * @memberOf Sector.prototype\n * @name Perimeter\n * @function\n * @returns {Number} Perimeter of sector.\n */\n el.Perimeter = function () {\n return this.L() + 2 * this.Radius();\n };\n\n if (type === '3points') {\n /**\n * Moves the sector by the difference of two coordinates.\n * @memberOf Sector.prototype\n * @name setPositionDirectly\n * @function\n * @param {Number} method The type of coordinates used here. Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.\n * @param {Array} coords coordinates in screen/user units\n * @param {Array} oldcoords previous coordinates in screen/user units\n * @returns {JXG.Curve} this element\n * @private\n */\n el.setPositionDirectly = function (method, coords, oldcoords) {\n var dc, t,\n c = new Coords(method, coords, this.board),\n oldc = new Coords(method, oldcoords, this.board);\n\n if (!el.point1.draggable() || !el.point2.draggable() || !el.point3.draggable()) {\n return this;\n }\n\n dc = Statistics.subtract(c.usrCoords, oldc.usrCoords);\n t = this.board.create(\"transform\", dc.slice(1), { type: \"translate\" });\n t.applyOnce([el.point1, el.point2, el.point3]);\n\n return this;\n };\n }\n\n Type.extendInstanceMethodMap(el, {\n radius: \"Radius\",\n Radius: \"Radius\",\n getRadius: \"Radius\",\n setRadius: \"setRadius\",\n Value: \"Value\",\n L: \"L\",\n Area: \"Area\",\n Perimeter: \"Perimeter\"\n });\n\n return el;\n};\n\nJXG.registerElement(\"sector\", JXG.createSector);\n\n/**\n * @class A sector whose arc is a circum circle arc through three points.\n * A circumcircle sector is different from a {@link Sector} mostly in the way the parent elements are interpreted.\n * At first, the circum center is determined from the three given points.\n * Then the sector is drawn from p1 through\n * p2 to p3.\n * @pseudo\n * @name CircumcircleSector\n * @augments Sector\n * @constructor\n * @type Sector\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 A circumcircle sector is defined by the circumcircle which is determined\n * by these three given points. The circumcircle sector is always drawn from p1 through p2 to p3.\n * @example\n * // Create an arc out of three free points\n * var p1 = board.create('point', [1.5, 5.0]),\n * p2 = board.create('point', [1.0, 0.5]),\n * p3 = board.create('point', [5.0, 3.0]),\n *\n * a = board.create('circumcirclesector', [p1, p2, p3]);\n * \n * \n */\nJXG.createCircumcircleSector = function (board, parents, attributes) {\n var el, mp, attr, points;\n\n points = Type.providePoints(board, parents, attributes, 'point');\n if (points === false) {\n throw new Error(\n \"JSXGraph: Can't create circumcircle sector with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\"\n );\n }\n\n mp = board.create(\"circumcenter\", points.slice(0, 3), attr);\n mp.dump = false;\n\n attr = Type.copyAttributes(attributes, board.options, 'circumcirclesector');\n el = board.create(\"sector\", [mp, points[0], points[2], points[1]], attr);\n\n el.elType = 'circumcirclesector';\n el.setParents(points);\n\n /**\n * Center of the circumcirclesector\n * @memberOf CircumcircleSector.prototype\n * @name center\n * @type Circumcenter\n */\n el.center = mp;\n el.subs = {\n center: mp\n };\n\n return el;\n};\n\nJXG.registerElement(\"circumcirclesector\", JXG.createCircumcircleSector);\n\n/**\n * @class A minor sector is a sector of a circle having measure at most\n * 180 degrees (pi radians). It is defined by a center, one point that\n * defines the radius, and a third point that defines the angle of the sector.\n * @pseudo\n * @name MinorSector\n * @augments Curve\n * @constructor\n * @type JXG.Curve\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor sector is a sector of a circle around p1 having measure less than or equal to\n * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.\n * @example\n * // Create sector out of three free points\n * var p1 = board.create('point', [2.0, 2.0]);\n * var p2 = board.create('point', [1.0, 0.5]);\n * var p3 = board.create('point', [3.5, 1.0]);\n *\n * var a = board.create('minorsector', [p1, p2, p3]);\n * \n * \n *\n * @example\n * var A = board.create('point', [3, -2]),\n * B = board.create('point', [-2, -2]),\n * C = board.create('point', [0, 4]);\n *\n * var angle = board.create('minorsector', [B, A, C], {\n * strokeWidth: 0,\n * arc: {\n * \tvisible: true,\n * \tstrokeWidth: 3,\n * lastArrow: {size: 4},\n * firstArrow: {size: 4}\n * }\n * });\n * //angle.arc.setAttribute({firstArrow: false});\n * angle.arc.setAttribute({lastArrow: false});\n *\n *\n * \n * \n *\n */\nJXG.createMinorSector = function (board, parents, attributes) {\n attributes.selection = 'minor';\n return JXG.createSector(board, parents, attributes);\n};\n\nJXG.registerElement(\"minorsector\", JXG.createMinorSector);\n\n/**\n * @class A major sector is a sector of a circle having measure at least\n * 180 degrees (pi radians). It is defined by a center, one point that\n * defines the radius, and a third point that defines the angle of the sector.\n * @pseudo\n * @name MajorSector\n * @augments Curve\n * @constructor\n * @type JXG.Curve\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Major sector is a sector of a circle around p1 having measure greater than or equal to\n * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.\n * @example\n * // Create an arc out of three free points\n * var p1 = board.create('point', [2.0, 2.0]);\n * var p2 = board.create('point', [1.0, 0.5]);\n * var p3 = board.create('point', [3.5, 1.0]);\n *\n * var a = board.create('majorsector', [p1, p2, p3]);\n * \n * \n */\nJXG.createMajorSector = function (board, parents, attributes) {\n attributes.selection = 'major';\n return JXG.createSector(board, parents, attributes);\n};\n\nJXG.registerElement(\"majorsector\", JXG.createMajorSector);\n\n/**\n * @class Angle sector defined by three points or two lines.\n * Visually it is just a {@link Sector}\n * element with a radius not defined by the parent elements but by an attribute radius. As opposed to the sector,\n * an angle has two angle points and no radius point.\n * Sector is displayed if type==\"sector\".\n * If type==\"square\", instead of a sector a parallelogram is displayed.\n * In case of type==\"auto\", a square is displayed if the angle is near orthogonal. The precision\n * to decide if an angle is orthogonal is determined by the attribute\n * {@link Angle#orthoSensitivity}.\n * \n * \n *\n * @example\n * // Create an angle out of two lines and two directions\n * var p1 = board.create('point', [-1, 4]),\n * p2 = board.create('point', [4, 1]),\n * q1 = board.create('point', [-2, -3]),\n * q2 = board.create('point', [4,3]),\n *\n * li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),\n * li2 = board.create('line', [q1,q2], {lastArrow:true}),\n *\n * a1 = board.create('angle', [li1, li2, [5.5, 0], [4, 3]], { radius:1 }),\n * a2 = board.create('angle', [li1, li2, 1, -1], { radius:2 });\n *\n *\n * \n * \n *\n *\n * @example\n * // Display the angle value instead of the name\n * var p1 = board.create('point', [0,2]);\n * var p2 = board.create('point', [0,0]);\n * var p3 = board.create('point', [-2,0.2]);\n *\n * var a = board.create('angle', [p1, p2, p3], {\n * \t radius: 1,\n * name: function() {\n * \treturn JXG.Math.Geometry.trueAngle(p1, p2, p3).toFixed(1) + '°';\n * }});\n *\n * \n * \n *\n *\n * @example\n * // Apply a transformation to an angle.\n * var t = board.create('transform', [2, 1.5], {type: 'scale'});\n * var an1 = board.create('angle', [[-4,3.9], [-3, 4], [-3, 3]]);\n * var an2 = board.create('curve', [an1, t]);\n *\n * \n * \n *\n */\nJXG.createAngle = function (board, parents, attributes) {\n var el,\n radius, attr, attrsub,\n i, points,\n type = 'invalid';\n\n // Two lines or three points?\n if (\n parents[0].elementClass === Const.OBJECT_CLASS_LINE &&\n parents[1].elementClass === Const.OBJECT_CLASS_LINE &&\n (Type.isArray(parents[2]) || Type.isNumber(parents[2])) &&\n (Type.isArray(parents[3]) || Type.isNumber(parents[3]))\n ) {\n type = '2lines';\n } else {\n attr = {\n name: ''\n };\n points = Type.providePoints(board, parents, attr, 'point');\n if (points === false) {\n throw new Error(\n \"JSXGraph: Can't create angle with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\"\n );\n }\n type = '3points';\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'angle');\n\n // If empty, create a new name\n if (!Type.exists(attr.name) /*|| attr.name === \"\"*/) {\n attr.name = board.generateName({ type: Const.OBJECT_TYPE_ANGLE });\n }\n\n if (Type.exists(attr.radius)) {\n radius = attr.radius;\n } else {\n radius = 0;\n }\n\n board.suspendUpdate(); // Necessary for immediate availability of radius.\n if (type === '2lines') {\n // Angle defined by two lines\n parents.push(radius);\n el = board.create(\"sector\", parents, attr);\n /**\n * @class\n * @ignore\n */\n el.updateDataArraySector = el.updateDataArray;\n\n // TODO\n /**\n * @class\n * @ignore\n */\n el.setAngle = function (val) {};\n /**\n * @class\n * @ignore\n */\n el.free = function (val) {};\n } else {\n // Angle defined by three points\n el = board.create(\"sector\", [points[1], points[0], points[2]], attr);\n el.arc.visProp.priv = true;\n\n /**\n * The point defining the radius of the angle element.\n * Alias for {@link Sector#radiuspoint}.\n * @type JXG.Point\n * @name point\n * @memberOf Angle.prototype\n *\n */\n el.point = el.point2 = el.radiuspoint = points[0];\n\n /**\n * Helper point for angles of type 'square'.\n * @type JXG.Point\n * @name pointsquare\n * @memberOf Angle.prototype\n */\n el.pointsquare = el.point3 = el.anglepoint = points[2];\n\n /**\n * @ignore\n */\n el.Radius = function () {\n // Set the angle radius, also @see @link Sector#autoRadius\n var r = Type.evaluate(radius);\n if (r === 'auto') {\n return el.autoRadius();\n }\n return r;\n };\n\n /**\n * @class\n * @ignore\n */\n el.updateDataArraySector = function () {\n var A = this.point2,\n B = this.point1,\n C = this.point3,\n r = this.Radius(),\n d = B.Dist(A),\n a, b, c,\n ar,\n phi,\n sgn = 1,\n vp_s = this.evalVisProp('selection'),\n vp_o = this.evalVisProp('orientation');\n\n phi = Geometry.rad(A, B, C);\n if ((vp_s === 'minor' && phi > Math.PI) || (vp_s === 'major' && phi < Math.PI) || (vp_s === 'auto' && vp_o === 'clockwise')) {\n sgn = -1;\n }\n\n a = A.coords.usrCoords;\n b = B.coords.usrCoords;\n c = C.coords.usrCoords;\n\n a = [1, b[1] + ((a[1] - b[1]) * r) / d, b[2] + ((a[2] - b[2]) * r) / d];\n c = [1, b[1] + ((c[1] - b[1]) * r) / d, b[2] + ((c[2] - b[2]) * r) / d];\n\n ar = Geometry.bezierArc(a, b, c, true, sgn);\n\n this.dataX = ar[0];\n this.dataY = ar[1];\n this.bezierDegree = 3;\n };\n\n /**\n * Set an angle to a prescribed value given in radians.\n * This is only possible if the third point of the angle, i.e.\n * the anglepoint is a free point.\n * Removing the constraint again is done by calling \"angle.free()\".\n *\n * Changing the angle requires to call the method \"free()\":\n *\n * \n * \n * angle.setAngle(Math.PI / 6);\n * // ...\n * angle.free().setAngle(Math.PI / 4);\n *
\n *\n * @name setAngle\n * @memberof Angle.prototype\n * @function\n * @param {Number|Function} val Number or Function which returns the size of the angle in Radians\n * @returns {Object} Pointer to the angle element..\n * @see Angle#free\n *\n * @example\n * var p1, p2, p3, c, a, s;\n *\n * p1 = board.create('point',[0,0]);\n * p2 = board.create('point',[5,0]);\n * p3 = board.create('point',[0,5]);\n *\n * c1 = board.create('circle',[p1, p2]);\n *\n * a = board.create('angle',[p2, p1, p3], {radius:3});\n *\n * a.setAngle(function() {\n * return Math.PI / 3;\n * });\n * board.update();\n *\n * \n *\n * @example\n * var p1, p2, p3, c, a, s;\n *\n * p1 = board.create('point',[0,0]);\n * p2 = board.create('point',[5,0]);\n * p3 = board.create('point',[0,5]);\n *\n * c1 = board.create('circle',[p1, p2]);\n *\n * a = board.create('angle',[p2, p1, p3], {radius:3});\n * s = board.create('slider',[[-2,1], [2,1], [0, Math.PI*0.5, 2*Math.PI]]);\n *\n * a.setAngle(function() {\n * return s.Value();\n * });\n * board.update();\n *\n * \n * \n *\n */\n el.setAngle = function (val) {\n var t1, t2,\n phi, phiInv,\n p = this.anglepoint,\n q = this.radiuspoint;\n\n if (p.draggable()) {\n\n if (this.evalVisProp('orientation') === 'clockwise') {\n /**\n * @ignore\n */\n phi = function() {\n return Math.PI * 2 - Type.evaluate(val);\n };\n } else {\n /**\n * @ignore\n */\n phi = function() {\n return Type.evaluate(val);\n };\n }\n\n t1 = this.board.create(\"transform\", [phi, this.center], {\n type: \"rotate\"\n });\n p.addTransform(q, t1);\n // Immediately apply the transformation.\n // This prevents that jumping elements can be watched.\n t1.update();\n p.moveTo(Mat.matVecMult(t1.matrix, q.coords.usrCoords));\n\n phiInv = function () {\n return Math.PI * 2 - phi();\n };\n t2 = this.board.create(\"transform\", [phiInv, this.center], {\n type: \"rotate\"\n });\n p.coords.on(\"update\", function () {\n t2.update();\n // q.moveTo(Mat.matVecMult(t2.matrix, p.coords.usrCoords));\n q.setPositionDirectly(Const.COORDS_BY_USER, Mat.matVecMult(t2.matrix, p.coords.usrCoords));\n });\n\n p.setParents(q);\n\n this.hasFixedAngle = true;\n }\n return this;\n };\n\n /**\n * Frees an angle from a prescribed value. This is only relevant if the angle size has been set by\n * \"setAngle()\" previously. The anglepoint is set to a free point.\n * @name free\n * @function\n * @memberof Angle.prototype\n * @returns {Object} Pointer to the angle element..\n * @see Angle#setAngle\n */\n el.free = function () {\n var p = this.anglepoint;\n\n if (p.transformations.length > 0) {\n p.transformations.pop();\n p.isDraggable = true;\n p.parents = [];\n\n p.coords.off('update');\n }\n\n this.hasFixedAngle = false;\n\n return this;\n };\n\n el.setParents(points); // Important: This overwrites the parents order in underlying sector\n } // end '3points'\n\n // GEONExT compatible labels.\n if (Type.exists(el.visProp.text)) {\n el.label.setText(el.evalVisProp('text'));\n }\n\n el.elType = 'angle';\n el.type = Const.OBJECT_TYPE_ANGLE;\n el.subs = {};\n\n /**\n * @class\n * @ignore\n */\n el.updateDataArraySquare = function () {\n var A, B, C,\n d1, d2, v, l1, l2,\n r = this.Radius();\n\n if (type === '2lines') {\n // This is necessary to update this.point1, this.point2, this.point3.\n this.updateDataArraySector();\n }\n\n A = this.point2;\n B = this.point1;\n C = this.point3;\n\n A = A.coords.usrCoords;\n B = B.coords.usrCoords;\n C = C.coords.usrCoords;\n\n d1 = Geometry.distance(A, B, 3);\n d2 = Geometry.distance(C, B, 3);\n\n // In case of type=='2lines' this is redundant, because r == d1 == d2\n A = [1, B[1] + ((A[1] - B[1]) * r) / d1, B[2] + ((A[2] - B[2]) * r) / d1];\n C = [1, B[1] + ((C[1] - B[1]) * r) / d2, B[2] + ((C[2] - B[2]) * r) / d2];\n\n v = Mat.crossProduct(C, B);\n l1 = [-A[1] * v[1] - A[2] * v[2], A[0] * v[1], A[0] * v[2]];\n v = Mat.crossProduct(A, B);\n l2 = [-C[1] * v[1] - C[2] * v[2], C[0] * v[1], C[0] * v[2]];\n\n v = Mat.crossProduct(l1, l2);\n v[1] /= v[0];\n v[2] /= v[0];\n\n this.dataX = [B[1], A[1], v[1], C[1], B[1]];\n this.dataY = [B[2], A[2], v[2], C[2], B[2]];\n\n this.bezierDegree = 1;\n };\n\n /**\n * @class\n * @ignore\n */\n el.updateDataArrayNone = function () {\n this.dataX = [NaN];\n this.dataY = [NaN];\n this.bezierDegree = 1;\n };\n\n /**\n * @class\n * @ignore\n */\n el.updateDataArray = function () {\n var type = this.evalVisProp('type'),\n deg = Geometry.trueAngle(this.point2, this.point1, this.point3),\n vp_s = this.evalVisProp('selection'),\n vp_o = this.evalVisProp('orientation');\n\n if ((vp_s === 'minor' && deg > 180.0) || (vp_s === 'major' && deg < 180.0) || (vp_s === 'auto' && vp_o === 'clockwise')) {\n deg = 360.0 - deg;\n }\n\n if (Math.abs(deg - 90.0) < this.evalVisProp('orthosensitivity') + Mat.eps) {\n type = this.evalVisProp('orthotype');\n }\n\n if (type === 'none') {\n this.updateDataArrayNone();\n this.maxX = function() { return 0; };\n } else if (type === 'square') {\n this.updateDataArraySquare();\n this.maxX = function() { return 4; };\n } else if (type === 'sector') {\n this.updateDataArraySector();\n this.maxX = function() { return 6; };\n } else if (type === 'sectordot') {\n this.updateDataArraySector();\n this.maxX = function() { return 6; };\n if (!this.dot.visProp.visible) {\n this.dot.setAttribute({ visible: true });\n }\n }\n\n if (!this.visProp.visible || (type !== \"sectordot\" && this.dot.visProp.visible)) {\n this.dot.setAttribute({ visible: false });\n }\n };\n\n attrsub = Type.copyAttributes(attributes, board.options, \"angle\", 'dot');\n /**\n * Indicates a right angle. Invisible by default, use dot.visible: true to show.\n * Though this dot indicates a right angle, it can be visible even if the angle is not a right\n * one.\n * @type JXG.Point\n * @name dot\n * @memberOf Angle.prototype\n */\n el.dot = board.create(\n \"point\",\n [\n function () {\n var A, B, r, d, a2, co, si, mat, vp_s, vp_o;\n\n if (Type.exists(el.dot) && !el.dot.visProp.visible) {\n return [0, 0];\n }\n\n A = el.point2.coords.usrCoords;\n B = el.point1.coords.usrCoords;\n r = el.Radius();\n d = Geometry.distance(A, B, 3);\n a2 = Geometry.rad(el.point2, el.point1, el.point3);\n\n vp_s = el.evalVisProp('selection');\n vp_o = el.evalVisProp('orientation');\n if ((vp_s === 'minor' && a2 > Math.PI) || (vp_s === 'major' && a2 < Math.PI) || (vp_s === 'auto' && vp_o === 'clockwise')) {\n a2 = -(2 * Math.PI - a2);\n }\n a2 *= 0.5;\n\n co = Math.cos(a2);\n si = Math.sin(a2);\n\n A = [1, B[1] + ((A[1] - B[1]) * r) / d, B[2] + ((A[2] - B[2]) * r) / d];\n\n mat = [\n [1, 0, 0],\n [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],\n [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5, co * 0.5]\n ];\n return Mat.matVecMult(mat, A);\n }\n ],\n attrsub\n );\n\n el.dot.dump = false;\n el.subs.dot = el.dot;\n\n if (type === '2lines') {\n for (i = 0; i < 2; i++) {\n board.select(parents[i]).addChild(el.dot);\n }\n } else {\n for (i = 0; i < 3; i++) {\n board.select(points[i]).addChild(el.dot);\n }\n }\n board.unsuspendUpdate();\n\n /**\n * Returns the value of the angle.\n * @memberOf Angle.prototype\n * @name Value\n * @function\n * @param {String} [unit='length'] Unit of the returned values. Possible units are\n * \n *
\n * It is sufficient to supply the first three characters of the unit, e.g. 'len'.\n * @returns {Number} angle value in various units.\n * @see Sector#L\n * @see Arc#Value\n * @example\n * var A, B, C, ang,\n * r = 0.5;\n * A = board.create(\"point\", [3, 0]);\n * B = board.create(\"point\", [0, 0]);\n * C = board.create(\"point\", [2, 2]);\n * ang = board.create(\"angle\", [A, B, C], {radius: r});\n *\n * console.log(ang.Value());\n * // Output Math.PI * 0.25\n *\n * console.log(ang.Value('radian'));\n * // Output Math.PI * 0.25\n *\n * console.log(ang.Value('degree');\n * // Output 45\n *\n * console.log(ang.Value('semicircle'));\n * // Output 0.25\n *\n * console.log(ang.Value('circle'));\n * // Output 0.125\n *\n * console.log(ang.Value('length'));\n * // Output r * Math.PI * 0.25\n *\n * console.log(ang.L());\n * // Output r * Math.PI * 0.25\n *\n */\n el.Value = function(unit) {\n unit = unit || 'radians';\n if (unit === '') {\n unit = 'radians';\n }\n return el.arc.Value(unit);\n };\n\n\n // documented in GeometryElement\n /**\n * @class\n * @ignore\n */\n el.getLabelAnchor = function () {\n var vec,\n dx = 12,\n A, B, r, d, a2, co, si, mat,\n vp_s = el.evalVisProp('selection'),\n vp_o = el.evalVisProp('orientation'),\n l_vp = this.label ? this.label.visProp : this.visProp.label,\n pos = (this.label) ?\n this.label.evalVisProp('position') : this.evalVisProp('label.position');\n\n // If this is uncommented, the angle label can not be dragged\n //if (Type.exists(this.label)) {\n // this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);\n //}\n\n if (\n !Type.isString(pos) ||\n (pos.indexOf('right') < 0 && pos.indexOf('left') < 0)\n ) {\n\n if (Type.exists(this.label) && Type.exists(this.label.visProp.fontsize)) {\n dx = this.label.evalVisProp('fontsize');\n }\n dx /= this.board.unitX;\n\n A = el.point2.coords.usrCoords;\n B = el.point1.coords.usrCoords;\n r = el.Radius();\n d = Geometry.distance(A, B, 3);\n a2 = Geometry.rad(el.point2, el.point1, el.point3);\n if ((vp_s === 'minor' && a2 > Math.PI) || (vp_s === 'major' && a2 < Math.PI) || (vp_s === 'auto' && vp_o === 'clockwise')) {\n a2 = -(2 * Math.PI - a2);\n }\n a2 *= 0.5;\n co = Math.cos(a2);\n si = Math.sin(a2);\n\n A = [1, B[1] + ((A[1] - B[1]) * r) / d, B[2] + ((A[2] - B[2]) * r) / d];\n\n mat = [\n [1, 0, 0],\n [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],\n [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5, co * 0.5]\n ];\n vec = Mat.matVecMult(mat, A);\n vec[1] /= vec[0];\n vec[2] /= vec[0];\n vec[0] /= vec[0];\n\n d = Geometry.distance(vec, B, 3);\n vec = [\n vec[0],\n B[1] + ((vec[1] - B[1]) * (r + dx)) / d,\n B[2] + ((vec[2] - B[2]) * (r + dx)) / d\n ];\n\n l_vp.position = Geometry.calcLabelQuadrant(Geometry.rad([1, 0], [0, 0], vec));\n\n return new Coords(Const.COORDS_BY_USER, vec, this.board);\n } else {\n return this.getLabelPosition(pos, this.label.evalVisProp('distance'));\n }\n };\n\n Type.extendInstanceMethodMap(el, {\n setAngle: \"setAngle\",\n Value: \"Value\",\n free: \"free\"\n });\n\n return el;\n};\n\nJXG.registerElement(\"angle\", JXG.createAngle);\n\n/**\n * @class A non-reflex angle is the instance of an angle that is at most 180°.\n * It is defined by a center, one point that\n * defines the radius, and a third point that defines the angle of the sector.\n * @pseudo\n * @name NonReflexAngle\n * @augments Angle\n * @constructor\n * @type Sector\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor sector is a sector of a circle around p1 having measure less than or equal to\n * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.\n * @example\n * // Create a non-reflex angle out of three free points\n * var p1 = board.create('point', [5.0, 3.0]),\n * p2 = board.create('point', [1.0, 0.5]),\n * p3 = board.create('point', [1.5, 5.0]),\n *\n * a = board.create('nonreflexangle', [p1, p2, p3], {radius: 2}),\n * t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);\n * \n * \n */\nJXG.createNonreflexAngle = function (board, parents, attributes) {\n var el;\n\n attributes.selection = 'minor';\n attributes = Type.copyAttributes(attributes, board.options, 'nonreflexangle');\n el = JXG.createAngle(board, parents, attributes);\n\n // Documented in createAngle\n el.Value = function (unit) {\n var rad = Geometry.rad(this.point2, this.point1, this.point3);\n unit = unit || 'radians';\n if (unit === '') {\n unit = 'radians';\n }\n rad = (rad < Math.PI) ? rad : 2.0 * Math.PI - rad;\n\n return this.arc.Value(unit, rad);\n };\n return el;\n};\n\nJXG.registerElement(\"nonreflexangle\", JXG.createNonreflexAngle);\n\n/**\n * @class A reflex angle is the instance of an angle that is larger than 180°.\n * It is defined by a center, one point that\n * defines the radius, and a third point that defines the angle of the sector.\n * @pseudo\n * @name ReflexAngle\n * @augments Angle\n * @constructor\n * @type Sector\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor sector is a sector of a circle around p1 having measure less than or equal to\n * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.\n * @example\n * // Create a non-reflex angle out of three free points\n * var p1 = board.create('point', [5.0, 3.0]),\n * p2 = board.create('point', [1.0, 0.5]),\n * p3 = board.create('point', [1.5, 5.0]),\n *\n * a = board.create('reflexangle', [p1, p2, p3], {radius: 2}),\n * t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);\n * \n * \n */\nJXG.createReflexAngle = function (board, parents, attributes) {\n var el;\n\n attributes.selection = 'major';\n attributes = Type.copyAttributes(attributes, board.options, 'reflexangle');\n el = JXG.createAngle(board, parents, attributes);\n\n // Documented in createAngle\n el.Value = function (unit) {\n var rad = Geometry.rad(this.point2, this.point1, this.point3);\n unit = unit || 'radians';\n if (unit === '') {\n unit = 'radians';\n }\n rad = (rad >= Math.PI) ? rad : 2.0 * Math.PI - rad;\n\n return this.arc.Value(unit, rad);\n };\n\n return el;\n};\n\nJXG.registerElement(\"reflexangle\", JXG.createReflexAngle);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n */\n\nimport JXG from \"../jxg.js\";\nimport Mat from \"../math/math.js\";\nimport Geometry from \"../math/geometry.js\";\nimport Numerics from \"../math/numerics.js\";\nimport Coords from \"../base/coords.js\";\nimport Type from \"../utils/type.js\";\nimport Const from \"../base/constants.js\";\n// import Point from \"../base/point.js\";\n// import Line from \"../base/line.js\";\n// import Circle from \"../base/circle.js\";\n// import Transform from \"../base/transformation.js\";\nimport Composition from \"../base/composition.js\";\n// import Curve from \"../base/curve.js\";\n// import Polygon from \"../base/polygon.js\";\n\n/**\n * @class A point that is the orthogonal projection of a point onto a line.\n * @pseudo\n * @description An orthogonal projection is given by a point and a line. It is determined by projecting the given point\n * orthogonal onto the given line.\n * @constructor\n * @name Orthogonalprojection\n * @type JXG.Point\n * @augments JXG.Point\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Line_JXG.Point} p,l The constructed point is the orthogonal projection of p onto l.\n * @example\n * var p1 = board.create('point', [0.0, 4.0]);\n * var p2 = board.create('point', [6.0, 1.0]);\n * var l1 = board.create('line', [p1, p2]);\n * var p3 = board.create('point', [3.0, 3.0]);\n *\n * var pp1 = board.create('orthogonalprojection', [p3, l1]);\n * \n * \n */\nJXG.createOrthogonalProjection = function (board, parents, attributes) {\n var l, p, t, attr;\n\n parents[0] = board.select(parents[0]);\n parents[1] = board.select(parents[1]);\n\n if (\n Type.isPointType(board, parents[0]) &&\n parents[1].elementClass === Const.OBJECT_CLASS_LINE\n ) {\n p = Type.providePoints(board, [parents[0]], attributes, 'point')[0];\n l = parents[1];\n } else if (\n Type.isPointType(board, parents[1]) &&\n parents[0].elementClass === Const.OBJECT_CLASS_LINE\n ) {\n p = Type.providePoints(board, [parents[1]], attributes, 'point')[0];\n l = parents[0];\n } else {\n throw new Error(\n \"JSXGraph: Can't create perpendicular point with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,line]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'orthogonalprojection');\n\n /**\n * @type JXG.Element\n * @ignore\n */\n t = board.create(\n \"point\",\n [\n function () {\n return Geometry.projectPointToLine(p, l, board);\n }\n ],\n attr\n );\n\n if (Type.exists(p._is_new)) {\n t.addChild(p);\n delete p._is_new;\n } else {\n p.addChild(t);\n }\n l.addChild(t);\n\n t.elType = 'orthogonalprojection';\n t.setParents([p.id, t.id]);\n\n t.update();\n\n /**\n * Used to generate a polynomial for the orthogonal projection\n * @name Orthogonalprojection#generatePolynomial\n * @returns {Array} An array containing the generated polynomial.\n * @private\n * @function\n * @ignore\n */\n t.generatePolynomial = function () {\n /*\n * Perpendicular takes point P and line L and creates point T and line M:\n *\n * | M\n * |\n * x P (p1,p2)\n * |\n * |\n * L |\n * ----------x-------------x------------------------x--------\n * A (a1,a2) |T (t1,t2) B (b1,b2)\n * |\n * |\n *\n * So we have two conditions:\n *\n * (a) AT || TB (collinearity condition)\n * (b) PT _|_ AB (orthogonality condition)\n *\n * a2-t2 t2-b2\n * ------- = ------- (1)\n * a1-t1 t1-b1\n *\n * p2-t2 a1-b1\n * ------- = - ------- (2)\n * p1-t1 a2-b2\n *\n * Multiplying (1) and (2) with denominators and simplifying gives\n *\n * a2t1 - a2b1 + t2b1 - a1t2 + a1b2 - t1b2 = 0 (1')\n *\n * p2a2 - p2b2 - t2a2 + t2b2 + p1a1 - p1b1 - t1a1 + t1b1 = 0 (2')\n *\n */\n\n var a1 = l.point1.symbolic.x,\n a2 = l.point1.symbolic.y,\n b1 = l.point2.symbolic.x,\n b2 = l.point2.symbolic.y,\n p1 = p.symbolic.x,\n p2 = p.symbolic.y,\n t1 = t.symbolic.x,\n t2 = t.symbolic.y,\n poly1 = \"(\" + a2 + \")*(\" + t1 + \")-(\" + a2 + \")*(\" + b1 + \")+(\" + t2 + \")*(\" + b1 + \")-(\" + a1 + \")*(\" + t2 + \")+(\" + a1 + \")*(\" +\n b2 + \")-(\" + t1 + \")*(\" + b2 + \")\",\n poly2 = \"(\" + p2 + \")*(\" + a2 + \")-(\" + p2 + \")*(\" + b2 + \")-(\" + t2 + \")*(\" + a2 + \")+(\" + t2 + \")*(\" + b2 + \")+(\" + p1 + \")*(\" +\n a1 + \")-(\" + p1 + \")*(\" + b1 + \")-(\" + t1 + \")*(\" + a1 + \")+(\" + t1 + \")*(\" + b1 + \")\";\n\n return [poly1, poly2];\n };\n\n return t;\n};\n\n/**\n\n * @class A perpendicular is a line orthogonal to a given line, through a given point not on the line,\n * @pseudo\n * @description A perpendicular is a composition of two elements: a line and a point. The line is orthogonal\n * to a given line and contains a given point.\n * @name Perpendicular\n * @constructor\n * @type JXG.Line\n * @augments Segment\n * @returns A {@link JXG.Line} object through the given point that is orthogonal to the given line.\n * @throws {Error} If the elements cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Line_JXG.Point} l,p The perpendicular line will be orthogonal to l and\n * will contain p.\n * @example\n * // Create a perpendicular\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n * var l1 = board.create('line', [p1, p2]);\n *\n * var p3 = board.create('point', [3.0, 3.0]);\n * var perp1 = board.create('perpendicular', [l1, p3]);\n * \n * \n */\nJXG.createPerpendicular = function (board, parents, attributes) {\n var p, l, pd, attr;\n\n parents[0] = board.select(parents[0]);\n parents[1] = board.select(parents[1]);\n\n if (\n Type.isPointType(board, parents[0]) &&\n parents[1].elementClass === Const.OBJECT_CLASS_LINE\n ) {\n l = parents[1];\n p = Type.providePoints(board, [parents[0]], attributes, 'point')[0];\n } else if (\n Type.isPointType(board, parents[1]) &&\n parents[0].elementClass === Const.OBJECT_CLASS_LINE\n ) {\n l = parents[0];\n p = Type.providePoints(board, [parents[1]], attributes, 'point')[0];\n } else {\n throw new Error(\n \"JSXGraph: Can't create perpendicular with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [line,point]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'perpendicular');\n pd = JXG.createLine(\n board,\n [\n function () {\n return l.stdform[2] * p.X() - l.stdform[1] * p.Y();\n },\n function () {\n return -l.stdform[2] * p.Z();\n },\n function () {\n return l.stdform[1] * p.Z();\n }\n ],\n attr\n );\n\n pd.elType = 'perpendicular';\n pd.setParents([l.id, p.id]);\n\n if (Type.exists(p._is_new)) {\n pd.addChild(p);\n delete p._is_new;\n } else {\n p.addChild(pd);\n }\n l.addChild(pd);\n\n return pd;\n};\n\n/**\n * @class Orthogonal projection of a point onto a line.\n * @pseudo\n * @description A perpendicular point is given by a point and a line. It is determined by projecting the given point\n * orthogonal onto the given line. This element should be used in GEONExTReader only. All other applications should\n * use orthogonal projection {@link Orthogonalprojection}.\n * @constructor\n * @name PerpendicularPoint\n * @type JXG.Point\n * @augments JXG.Point\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Line_JXG.Point} p,l The constructed point is the orthogonal projection of p onto l.\n * @example\n * var p1 = board.create('point', [0.0, 4.0]);\n * var p2 = board.create('point', [6.0, 1.0]);\n * var l1 = board.create('line', [p1, p2]);\n * var p3 = board.create('point', [3.0, 3.0]);\n *\n * var pp1 = board.create('perpendicularpoint', [p3, l1]);\n * \n * \n */\nJXG.createPerpendicularPoint = function (board, parents, attributes) {\n var l, p, t;\n\n parents[0] = board.select(parents[0]);\n parents[1] = board.select(parents[1]);\n if (\n Type.isPointType(board, parents[0]) &&\n parents[1].elementClass === Const.OBJECT_CLASS_LINE\n ) {\n p = Type.providePoints(board, [parents[0]], attributes, 'point')[0];\n l = parents[1];\n } else if (\n Type.isPointType(board, parents[1]) &&\n parents[0].elementClass === Const.OBJECT_CLASS_LINE\n ) {\n p = Type.providePoints(board, [parents[1]], attributes, 'point')[0];\n l = parents[0];\n } else {\n throw new Error(\n \"JSXGraph: Can't create perpendicular point with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,line]\"\n );\n }\n\n /**\n * @class\n * @ignore\n */\n t = board.create(\n \"point\",\n [\n function () {\n return Geometry.perpendicular(l, p, board)[0];\n }\n ],\n attributes\n );\n\n if (Type.exists(p._is_new)) {\n t.addChild(p);\n delete p._is_new;\n } else {\n p.addChild(t);\n }\n l.addChild(t);\n\n t.elType = 'perpendicularpoint';\n t.setParents([p.id, l.id]);\n\n t.update();\n\n /**\n * Used to generate a polynomial for the perpendicular point\n * @name PerpendicularPoint#generatePolynomial\n * @returns {Array} An array containing the generated polynomial.\n * @private\n * @function\n * @ignore\n */\n t.generatePolynomial = function () {\n /*\n * Perpendicular takes point P and line L and creates point T and line M:\n *\n * | M\n * |\n * x P (p1,p2)\n * |\n * |\n * L |\n * ----------x-------------x------------------------x--------\n * A (a1,a2) |T (t1,t2) B (b1,b2)\n * |\n * |\n *\n * So we have two conditions:\n *\n * (a) AT || TB (collinearity condition)\n * (b) PT _|_ AB (orthogonality condition)\n *\n * a2-t2 t2-b2\n * ------- = ------- (1)\n * a1-t1 t1-b1\n *\n * p2-t2 a1-b1\n * ------- = - ------- (2)\n * p1-t1 a2-b2\n *\n * Multiplying (1) and (2) with denominators and simplifying gives\n *\n * a2t1 - a2b1 + t2b1 - a1t2 + a1b2 - t1b2 = 0 (1')\n *\n * p2a2 - p2b2 - t2a2 + t2b2 + p1a1 - p1b1 - t1a1 + t1b1 = 0 (2')\n *\n */\n var a1 = l.point1.symbolic.x,\n a2 = l.point1.symbolic.y,\n b1 = l.point2.symbolic.x,\n b2 = l.point2.symbolic.y,\n p1 = p.symbolic.x,\n p2 = p.symbolic.y,\n t1 = t.symbolic.x,\n t2 = t.symbolic.y,\n poly1 = \"(\" + a2 + \")*(\" + t1 + \")-(\" + a2 + \")*(\" + b1 + \")+(\" + t2 + \")*(\" + b1 + \")-(\" + a1 + \")*(\" + t2 + \")+(\" + a1 + \")*(\" + b2 + \")-(\" + t1 +\n \")*(\" + b2 + \")\",\n poly2 = \"(\" + p2 + \")*(\" + a2 + \")-(\" + p2 + \")*(\" + b2 + \")-(\" + t2 + \")*(\" + a2 + \")+(\" + t2 + \")*(\" + b2 + \")+(\" + p1 + \")*(\" + a1 + \")-(\" + p1 +\n \")*(\" + b1 + \")-(\" + t1 + \")*(\" + a1 + \")+(\" + t1 + \")*(\" + b1 + \")\";\n\n return [poly1, poly2];\n };\n\n return t;\n};\n\n/**\n * @class A line segment orthogonal to a given line, through a given point not on the line,\n * @pseudo\n * @description A perpendicular is a composition of two elements: a line segment and a point. The line segment is orthogonal\n * to a given line and contains a given point and meets the given line in the perpendicular point.\n * @name PerpendicularSegment\n * @constructor\n * @type JXG.Line\n * @augments Segment\n * @returns An array containing two elements: A {@link JXG.Line} object in the first component and a\n * {@link JXG.Point} element in the second component. The line segment is orthogonal to the given line and meets it\n * in the returned point.\n * @throws {Error} If the elements cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Line_JXG.Point} l,p The perpendicular line will be orthogonal to l and\n * will contain p. The perpendicular point is the intersection point of the two lines.\n * @example\n * // Create a perpendicular\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n * var l1 = board.create('line', [p1, p2]);\n *\n * var p3 = board.create('point', [3.0, 3.0]);\n * var perp1 = board.create('perpendicularsegment', [l1, p3]);\n * \n * \n */\nJXG.createPerpendicularSegment = function (board, parents, attributes) {\n var p, l, pd, t, attr;\n\n parents[0] = board.select(parents[0]);\n parents[1] = board.select(parents[1]);\n if (\n Type.isPointType(board, parents[0]) &&\n parents[1].elementClass === Const.OBJECT_CLASS_LINE\n ) {\n l = parents[1];\n p = Type.providePoints(board, [parents[0]], attributes, 'point')[0];\n } else if (\n Type.isPointType(board, parents[1]) &&\n parents[0].elementClass === Const.OBJECT_CLASS_LINE\n ) {\n l = parents[0];\n p = Type.providePoints(board, [parents[1]], attributes, 'point')[0];\n } else {\n throw new Error(\n \"JSXGraph: Can't create perpendicular with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [line,point]\"\n );\n }\n attr = Type.copyAttributes(attributes, board.options, \"perpendicularsegment\", 'point');\n t = JXG.createPerpendicularPoint(board, [l, p], attr);\n t.dump = false;\n\n if (!Type.exists(attributes.layer)) {\n attributes.layer = board.options.layer.line;\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'perpendicularsegment');\n pd = JXG.createLine(\n board,\n [\n function () {\n return Geometry.perpendicular(l, p, board)[1] ? [t, p] : [p, t];\n }\n ],\n attr\n );\n\n /**\n * Helper point\n * @memberOf PerpendicularSegment.prototype\n * @type PerpendicularPoint\n * @name point\n */\n pd.point = t;\n\n if (Type.exists(p._is_new)) {\n pd.addChild(p);\n delete p._is_new;\n } else {\n p.addChild(pd);\n }\n l.addChild(pd);\n\n pd.elType = 'perpendicularsegment';\n pd.setParents([p.id, l.id]);\n pd.subs = {\n point: t\n };\n pd.inherits.push(t);\n\n return pd;\n};\n\n/**\n * @class Midpoint of two points.\n * @pseudo\n * @description A midpoint is given by two points. It is collinear to the given points and the distance\n * is the same to each of the given points, i.e. it is in the middle of the given points.\n * @constructor\n * @name Midpoint\n * @type JXG.Point\n * @augments JXG.Point\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point} p1,p2 The constructed point will be in the middle of p1 and p2.\n * @param {JXG.Line} l The midpoint will be in the middle of {@link JXG.Line#point1} and {@link JXG.Line#point2} of\n * the given line l.\n * @example\n * // Create base elements: 2 points and 1 line\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n * var l1 = board.create('segment', [[0.0, 3.0], [3.0, 3.0]]);\n *\n * var mp1 = board.create('midpoint', [p1, p2]);\n * var mp2 = board.create('midpoint', [l1]);\n * \n * \n */\nJXG.createMidpoint = function (board, parents, attributes) {\n var a, b, el, i, attr;\n\n for (i = 0; i < parents.length; ++i) {\n parents[i] = board.select(parents[i]);\n }\n if (\n parents.length === 2 &&\n Type.isPointType(board, parents[0]) &&\n Type.isPointType(board, parents[1])\n ) {\n parents = Type.providePoints(board, parents, attributes, 'point');\n a = parents[0];\n b = parents[1];\n } else if (parents.length === 1 && parents[0].elementClass === Const.OBJECT_CLASS_LINE) {\n a = parents[0].point1;\n b = parents[0].point2;\n } else {\n throw new Error(\n \"JSXGraph: Can't create midpoint.\" +\n \"\\nPossible parent types: [point,point], [line]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'midpoint');\n /**\n * @type JXG.Element\n * @ignore\n */\n el = board.create(\n \"point\",\n [\n function () {\n var x = a.coords.usrCoords[1] + b.coords.usrCoords[1];\n if (\n isNaN(x) ||\n Math.abs(a.coords.usrCoords[0]) < Mat.eps ||\n Math.abs(b.coords.usrCoords[0]) < Mat.eps\n ) {\n return NaN;\n }\n\n return x * 0.5;\n },\n function () {\n var y = a.coords.usrCoords[2] + b.coords.usrCoords[2];\n if (\n isNaN(y) ||\n Math.abs(a.coords.usrCoords[0]) < Mat.eps ||\n Math.abs(b.coords.usrCoords[0]) < Mat.eps\n ) {\n return NaN;\n }\n\n return y * 0.5;\n }\n ],\n attr\n );\n if (Type.exists(a._is_new)) {\n el.addChild(a);\n delete a._is_new;\n } else {\n a.addChild(el);\n }\n if (Type.exists(b._is_new)) {\n el.addChild(b);\n delete b._is_new;\n } else {\n b.addChild(el);\n }\n\n el.elType = 'midpoint';\n el.setParents([a.id, b.id]);\n\n el.prepareUpdate().update();\n\n /**\n * Used to generate a polynomial for the midpoint.\n * @name Midpoint#generatePolynomial\n * @returns {Array} An array containing the generated polynomial.\n * @private\n * @function\n * @ignore\n */\n el.generatePolynomial = function () {\n /*\n * Midpoint takes two point A and B or line L (with points P and Q) and creates point T:\n *\n * L (not necessarily)\n * ----------x------------------x------------------x--------\n * A (a1,a2) T (t1,t2) B (b1,b2)\n *\n * So we have two conditions:\n *\n * (a) AT || TB (collinearity condition)\n * (b) [AT] == [TB] (equidistant condition)\n *\n * a2-t2 t2-b2\n * ------- = ------- (1)\n * a1-t1 t1-b1\n *\n * (a1 - t1)^2 + (a2 - t2)^2 = (b1 - t1)^2 + (b2 - t2)^2 (2)\n *\n *\n * Multiplying (1) with denominators and simplifying (1) and (2) gives\n *\n * a2t1 - a2b1 + t2b1 - a1t2 + a1b2 - t1b2 = 0 (1')\n *\n * a1^2 - 2a1t1 + a2^2 - 2a2t2 - b1^2 + 2b1t1 - b2^2 + 2b2t2 = 0 (2')\n *\n */\n var a1 = a.symbolic.x,\n a2 = a.symbolic.y,\n b1 = b.symbolic.x,\n b2 = b.symbolic.y,\n t1 = el.symbolic.x,\n t2 = el.symbolic.y,\n poly1 = \"(\" + a2 + \")*(\" + t1 + \")-(\" + a2 + \")*(\" + b1 + \")+(\" + t2 + \")*(\" + b1 + \")-(\" + a1 + \")*(\" + t2 + \")+(\" + a1 + \")*(\" + b2 +\n \")-(\" + t1 + \")*(\" + b2 + \")\",\n poly2 = \"(\" + a1 + \")^2 - 2*(\" + a1 + \")*(\" + t1 + \")+(\" + a2 + \")^2-2*(\" + a2 + \")*(\" + t2 + \")-(\" + b1 + \")^2+2*(\" + b1 + \")*(\" + t1 +\n \")-(\" + b2 + \")^2+2*(\" + b2 + \")*(\" + t2 + \")\";\n\n return [poly1, poly2];\n };\n\n return el;\n};\n\n/**\n * @class Given three point, a parallel point is the point such that the four points form a parallelogram.\n * @pseudo\n * @description A parallel point is given by three points. Taking the Euclidean vector from the first to the\n * second point, the parallel point is determined by adding that vector to the third point.\n * The line determined by the first two points is parallel to the line determined by the third point and the constructed point.\n * @constructor\n * @name Parallelpoint\n * @type JXG.Point\n * @augments JXG.Point\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 Taking the Euclidean vector v=p2-p1 the parallel point is determined by\n * p4 = p3+v\n * @param {JXG.Line_JXG.Point} l,p The resulting point will together with p specify a line which is parallel to l.\n * @example\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n * var p3 = board.create('point', [3.0, 3.0]);\n *\n * var pp1 = board.create('parallelpoint', [p1, p2, p3]);\n * \n * \n */\nJXG.createParallelPoint = function (board, parents, attributes) {\n var a, b, c, p, i, attr;\n\n for (i = 0; i < parents.length; ++i) {\n parents[i] = board.select(parents[i]);\n }\n if (\n parents.length === 3 &&\n Type.isPointType(board, parents[0]) &&\n Type.isPointType(board, parents[1]) &&\n Type.isPointType(board, parents[2])\n ) {\n parents = Type.providePoints(board, parents, attributes, 'point');\n a = parents[0];\n b = parents[1];\n c = parents[2];\n } else if (\n Type.isPointType(board, parents[0]) &&\n parents[1].elementClass === Const.OBJECT_CLASS_LINE\n ) {\n c = Type.providePoints(board, [parents[0]], attributes, 'point')[0];\n a = parents[1].point1;\n b = parents[1].point2;\n } else if (\n Type.isPointType(board, parents[1]) &&\n parents[0].elementClass === Const.OBJECT_CLASS_LINE\n ) {\n c = Type.providePoints(board, [parents[1]], attributes, 'point')[0];\n a = parents[0].point1;\n b = parents[0].point2;\n } else {\n throw new Error(\n \"JSXGraph: Can't create parallel point with parent types '\" +\n typeof parents[0] +\n \"', '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [line,point], [point,point,point]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'parallelpoint');\n /**\n * @type {JXG.Element}\n * @ignore\n */\n p = board.create(\n \"point\",\n [\n function () {\n return c.coords.usrCoords[1] + b.coords.usrCoords[1] - a.coords.usrCoords[1];\n },\n function () {\n return c.coords.usrCoords[2] + b.coords.usrCoords[2] - a.coords.usrCoords[2];\n }\n ],\n attr\n );\n\n // required for algorithms requiring dependencies between elements\n if (Type.exists(a._is_new)) {\n p.addChild(a);\n delete a._is_new;\n } else {\n a.addChild(p);\n }\n if (Type.exists(b._is_new)) {\n p.addChild(b);\n delete b._is_new;\n } else {\n b.addChild(p);\n }\n if (Type.exists(c._is_new)) {\n p.addChild(c);\n delete c._is_new;\n } else {\n c.addChild(p);\n }\n\n p.elType = 'parallelpoint';\n p.setParents([a.id, b.id, c.id]);\n\n // required to set the coordinates because functions are considered as constraints. hence, the coordinates get set first after an update.\n // can be removed if the above issue is resolved.\n p.prepareUpdate().update();\n\n /**\n * @function\n * @ignore\n */\n p.generatePolynomial = function () {\n /*\n * Parallelpoint takes three points A, B and C or line L (with points B and C) and creates point T:\n *\n *\n * C (c1,c2) T (t1,t2)\n * x x\n * / /\n * / /\n * / /\n * / /\n * / /\n * / /\n * / /\n * / /\n * L (opt) / /\n * ----------x-------------------------------------x--------\n * A (a1,a2) B (b1,b2)\n *\n * So we have two conditions:\n *\n * (a) CT || AB (collinearity condition I)\n * (b) BT || AC (collinearity condition II)\n *\n * The corresponding equations are\n *\n * (b2 - a2)(t1 - c1) - (t2 - c2)(b1 - a1) = 0 (1)\n * (t2 - b2)(a1 - c1) - (t1 - b1)(a2 - c2) = 0 (2)\n *\n * Simplifying (1) and (2) gives\n *\n * b2t1 - b2c1 - a2t1 + a2c1 - t2b1 + t2a1 + c2b1 - c2a1 = 0 (1')\n * t2a1 - t2c1 - b2a1 + b2c1 - t1a2 + t1c2 + b1a2 - b1c2 = 0 (2')\n *\n */\n var a1 = a.symbolic.x,\n a2 = a.symbolic.y,\n b1 = b.symbolic.x,\n b2 = b.symbolic.y,\n c1 = c.symbolic.x,\n c2 = c.symbolic.y,\n t1 = p.symbolic.x,\n t2 = p.symbolic.y,\n poly1 = \"(\" + b2 + \")*(\" + t1 + \")-(\" + b2 + \")*(\" + c1 + \")-(\" + a2 + \")*(\" + t1 + \")+(\" + a2 + \")*(\" + c1 + \")-(\" + t2 + \")*(\" + b1 + \")+(\" + t2 + \")*(\" +\n a1 + \")+(\" + c2 + \")*(\" + b1 + \")-(\" + c2 + \")*(\" + a1 + \")\",\n poly2 = \"(\" + t2 + \")*(\" + a1 + \")-(\" + t2 + \")*(\" + c1 + \")-(\" + b2 + \")*(\" + a1 + \")+(\" + b2 + \")*(\" + c1 + \")-(\" + t1 + \")*(\" + a2 + \")+(\" + t1 + \")*(\" +\n c2 + \")+(\" + b1 + \")*(\" + a2 + \")-(\" + b1 + \")*(\" + c2 + \")\";\n\n return [poly1, poly2];\n };\n\n return p;\n};\n\n/**\n * @class A parallel is a line through a given point, parallel to a given line.\n * \n * \n * @example\n * var p1, p2, p3, l1, pl1;\n *\n * p1 = board.create('point', [0.0, 2.0]);\n * p2 = board.create('point', [2.0, 1.0]);\n * l1 = board.create('line', [p1, p2]);\n *\n * p3 = board.create('point', [1.0, 3.0]);\n * pl1 = board.create('parallel', [p1, p2, p3], {straightFirst: false, straightLast: false});\n *\n * \n * \n *\n */\nJXG.createParallel = function (board, parents, attributes) {\n var p,\n pp,\n pl,\n li,\n i,\n attr,\n ty = 1;\n\n for (i = 0; i < parents.length; ++i) {\n parents[i] = board.select(parents[i]);\n }\n p = null;\n if (parents.length === 3) {\n // Line / segment through point parents[2] which is parallel to line through parents[0] and parents[1]\n parents = Type.providePoints(board, parents, attributes, 'point');\n p = parents[2];\n ty = 0;\n } else if (Type.isPointType(board, parents[0])) {\n // Parallel to line parents[1] through point parents[0]\n p = Type.providePoints(board, [parents[0]], attributes, 'point')[0];\n /** @ignore */\n li = function () {\n return parents[1].stdform;\n };\n } else if (Type.isPointType(board, parents[1])) {\n // Parallel to line parents[0] through point parents[1]\n p = Type.providePoints(board, [parents[1]], attributes, 'point')[0];\n /** @ignore */\n li = function () {\n return parents[0].stdform;\n };\n }\n\n if (!Type.exists(attributes.layer)) {\n attributes.layer = board.options.layer.line;\n }\n\n attr = Type.copyAttributes(attributes, board.options, \"parallel\", 'point');\n if (ty === 1) {\n // Line is given by line element. The parallel line is\n // constructed as line through an ideal point.\n pp = board.create(\n \"point\",\n [\n function () {\n return Mat.crossProduct([1, 0, 0], li());\n }\n ],\n attr\n );\n } else {\n // Line is given by two points. The parallel line is\n // constructed as line through two finite point.\n pp = board.create(\"parallelpoint\", parents, attr);\n }\n pp.isDraggable = true;\n\n attr = Type.copyAttributes(attributes, board.options, 'parallel');\n // line creator also calls addChild\n pl = board.create(\"line\", [p, pp], attr);\n\n pl.elType = 'parallel';\n pl.subs = {\n point: pp\n };\n\n pl.inherits.push(pp);\n pl.setParents([parents[0].id, parents[1].id]);\n if (parents.length === 3) {\n pl.addParents(parents[2].id);\n }\n\n // p.addChild(pl);\n\n /**\n * Helper point used to create the parallel line. This point lies on the line at infinity, hence it's not visible,\n * not even with visible set to true. Creating another line through this point would make that other line\n * parallel to the create parallel.\n * @memberOf Parallel.prototype\n * @name point\n * @type JXG.Point\n */\n pl.point = pp;\n\n return pl;\n};\n\n/**\n * @class A segment with an arrow head attached thath is parallel to a given segment.\n * The segment is given by its defining two points, the arrow starts at a given point.\n * \n * \n */\nJXG.createArrowParallel = function (board, parents, attributes) {\n var p, attr;\n\n /* parallel arrow point polynomials are done in createParallelPoint */\n try {\n attr = Type.copyAttributes(attributes, board.options, 'arrowparallel');\n\n if (attr.lastArrow === false) {\n // An arrow has to have an arrow head.\n attr.lastArrow = true;\n }\n p = JXG.createParallel(board, parents, attr).setAttribute({\n straightFirst: false,\n straightLast: false\n });\n p.type = Const.OBJECT_TYPE_VECTOR;\n p.elType = 'arrowparallel';\n\n // parents are set in createParallel\n\n return p;\n } catch (e) {\n throw new Error(\n \"JSXGraph: Can't create arrowparallel with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [line,point], [point,point,point]\"\n );\n }\n};\n\n/**\n * @class A bisector is a line which divides an angle into two equal angles. It is given by three points A, B, and\n * C and divides the angle ABC into two equal sized parts.\n * @pseudo\n * @constructor\n * @name Bisector\n * @type JXG.Line\n * @augments JXG.Line\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The angle described by p1, p2 and p3 will\n * be divided into two equal angles.\n * @example\n * var p1 = board.create('point', [6.0, 4.0]);\n * var p2 = board.create('point', [3.0, 2.0]);\n * var p3 = board.create('point', [1.0, 7.0]);\n *\n * var bi1 = board.create('bisector', [p1, p2, p3]);\n * \n * \n */\nJXG.createBisector = function (board, parents, attributes) {\n var p, l, i, attr;\n\n parents = Type.providePoints(board, parents, attributes, 'point');\n if (Type.isPoint(parents[0]) && Type.isPoint(parents[1]) && Type.isPoint(parents[2])) {\n // hidden and fixed helper\n attr = Type.copyAttributes(attributes, board.options, \"bisector\", 'point');\n attr.snapToGrid = false;\n\n p = board.create(\n \"point\",\n [\n function () {\n return Geometry.angleBisector(parents[0], parents[1], parents[2], board);\n }\n ],\n attr\n );\n p.dump = false;\n\n for (i = 0; i < 3; i++) {\n // required for algorithm requiring dependencies between elements\n if (Type.exists(parents[i]._is_new)) {\n p.addChild(parents[i]);\n delete parents[i]._is_new;\n } else {\n parents[i].addChild(p);\n }\n }\n\n if (!Type.exists(attributes.layer)) {\n attributes.layer = board.options.layer.line;\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'bisector');\n l = JXG.createLine(board, [parents[1], p], attr);\n\n /**\n * Helper point\n * @memberOf Bisector.prototype\n * @type Point\n * @name point\n */\n l.point = p;\n\n l.elType = 'bisector';\n l.setParents(parents);\n l.subs = {\n point: p\n };\n l.inherits.push(p);\n\n return l;\n }\n\n throw new Error(\n \"JSXGraph: Can't create angle bisector with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point]\"\n );\n};\n\n/**\n * @class Bisector lines are similar to {@link Bisector} but take two lines as parent elements. The resulting element is\n * a composition of two lines.\n * @pseudo\n * @constructor\n * @name Bisectorlines\n * @type JXG.Composition\n * @augments JXG.Composition\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Line_JXG.Line} l1,l2 The four angles described by the lines l1 and l2 will each\n * be divided into two equal angles.\n * @example\n * var p1 = board.create('point', [6.0, 4.0]);\n * var p2 = board.create('point', [3.0, 2.0]);\n * var p3 = board.create('point', [1.0, 7.0]);\n * var p4 = board.create('point', [3.0, 0.0]);\n * var l1 = board.create('line', [p1, p2]);\n * var l2 = board.create('line', [p3, p4]);\n *\n * var bi1 = board.create('bisectorlines', [l1, l2]);\n * \n * \n */\nJXG.createAngularBisectorsOfTwoLines = function (board, parents, attributes) {\n // The angular bisectors of two line [c1,a1,b1] and [c2,a2,b2] are determined by the equation:\n // (a1*x+b1*y+c1*z)/sqrt(a1^2+b1^2) = +/- (a2*x+b2*y+c2*z)/sqrt(a2^2+b2^2)\n\n var g1,\n g2,\n attr,\n ret,\n l1 = board.select(parents[0]),\n l2 = board.select(parents[1]);\n\n if (\n l1.elementClass !== Const.OBJECT_CLASS_LINE ||\n l2.elementClass !== Const.OBJECT_CLASS_LINE\n ) {\n throw new Error(\n \"JSXGraph: Can't create angle bisectors of two lines with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [line,line]\"\n );\n }\n\n if (!Type.exists(attributes.layer)) {\n attributes.layer = board.options.layer.line;\n }\n\n attr = Type.copyAttributes(attributes, board.options, \"bisectorlines\", 'line1');\n g1 = board.create(\n \"line\",\n [\n function () {\n var d1 = Mat.hypot(l1.stdform[1], l1.stdform[2]),\n d2 = Mat.hypot(l2.stdform[1], l2.stdform[2]);\n\n return l1.stdform[0] / d1 - l2.stdform[0] / d2;\n },\n function () {\n var d1 = Mat.hypot(l1.stdform[1], l1.stdform[2]),\n d2 = Mat.hypot(l2.stdform[1], l2.stdform[2]);\n\n return l1.stdform[1] / d1 - l2.stdform[1] / d2;\n },\n function () {\n var d1 = Mat.hypot(l1.stdform[1], l1.stdform[2]),\n d2 = Mat.hypot(l2.stdform[1], l2.stdform[2]);\n\n return l1.stdform[2] / d1 - l2.stdform[2] / d2;\n }\n ],\n attr\n );\n\n if (!Type.exists(attributes.layer)) {\n attributes.layer = board.options.layer.line;\n }\n attr = Type.copyAttributes(attributes, board.options, \"bisectorlines\", 'line2');\n g2 = board.create(\n \"line\",\n [\n function () {\n var d1 = Mat.hypot(l1.stdform[1], l1.stdform[2]),\n d2 = Mat.hypot(l2.stdform[1], l2.stdform[2]);\n\n return l1.stdform[0] / d1 + l2.stdform[0] / d2;\n },\n function () {\n var d1 = Mat.hypot(l1.stdform[1], l1.stdform[2]),\n d2 = Mat.hypot(l2.stdform[1], l2.stdform[2]);\n\n return l1.stdform[1] / d1 + l2.stdform[1] / d2;\n },\n function () {\n var d1 = Mat.hypot(l1.stdform[1], l1.stdform[2]),\n d2 = Mat.hypot(l2.stdform[1], l2.stdform[2]);\n\n return l1.stdform[2] / d1 + l2.stdform[2] / d2;\n }\n ],\n attr\n );\n\n // documentation\n /**\n * First line.\n * @memberOf Bisectorlines.prototype\n * @name line1\n * @type Line\n */\n\n /**\n * Second line.\n * @memberOf Bisectorlines.prototype\n * @name line2\n * @type Line\n */\n\n ret = new Composition({ line1: g1, line2: g2 });\n\n g1.dump = false;\n g2.dump = false;\n\n ret.elType = 'bisectorlines';\n ret.setParents([l1.id, l2.id]);\n ret.subs = {\n line1: g1,\n line2: g2\n };\n // ret.inherits.push(g1, g2);\n\n return ret;\n};\n\n// /**\n// * @class An m-sector is a line which divides an angle into two angles. It is given by three points A, B, and\n// * C and a real number m, and divides an angle into two angles, an angle with amplitude m and an angle with\n// * amplitude (1-m)\n// * @pseudo\n// * @constructor\n// * @name Msector\n// * @type JXG.Line\n// * @augments JXG.Line\n// * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n// * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The angle described by p1, p2 and p3 will\n// * be divided into two angles according to the value of m.\n// * @example\n// * var p1 = board.create('point', [6.0, 4.0]);\n// * var p2 = board.create('point', [3.0, 2.0]);\n// * var p3 = board.create('point', [1.0, 7.0]);\n// *\n// * var bi1 = board.create('msector', [p1, p2, p3], 1/5);\n// * \n// * \n// */\n// JXG.createMsector = function (board, parents, attributes) {\n// var p, l, i, attr;\n\n// if (parents[0].elementClass === Const.OBJECT_CLASS_POINT &&\n// parents[1].elementClass === Const.OBJECT_CLASS_POINT &&\n// parents[2].elementClass === Const.OBJECT_CLASS_POINT) {\n// // hidden and fixed helper\n// attr = Type.copyAttributes(attributes, board.options, 'msector', 'point');\n// p = board.create('point', [\n// function () {\n// return Geometry.angleMsector(parents[0], parents[1], parents[2], parents[3], board);\n// }\n// ], attr);\n// p.dump = false;\n\n// for (i = 0; i < 3; i++) {\n// // required for algorithm requiring dependencies between elements\n// parents[i].addChild(p);\n// }\n\n// if (!Type.exists(attributes.layer)) {\n// attributes.layer = board.options.layer.line;\n// }\n\n// attr = Type.copyAttributes(attributes, board.options, 'msector');\n// l = JXG.createLine(board, [parents[1], p], attr);\n\n// /**\n// * Helper point\n// * @memberOf Msector.prototype\n// * @type Point\n// * @name point\n// */\n// l.point = p;\n\n// l.elType = 'msector';\n// l.parents = [parents[0].id, parents[1].id, parents[2].id];\n// l.subs = {\n// point: p\n// };\n// l.inherits.push(p);\n\n// return l;\n// }\n\n// throw new Error(\"JSXGraph: Can't create angle msector with parent types '\" +\n// (typeof parents[0]) + \"' and '\" + (typeof parents[1]) + \"'.\" +\n// \"\\nPossible parent types: [point,point,point,Number]\");\n// };\n\n/**\n * @class Constructs the center of a {@link Circumcircle} without creating the circle.\n * Like the circumcircle the circumcenter is constructed by providing three points.\n * @pseudo\n * @description A circumcenter is given by three points which are all lying on the circle with the\n * constructed circumcenter as the midpoint.\n * @constructor\n * @name Circumcenter\n * @type JXG.Point\n * @augments JXG.Point\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The constructed point is the midpoint of the circle determined\n * by p1, p2, and p3.\n * @example\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n * var p3 = board.create('point', [3.0, 3.0]);\n *\n * var cc1 = board.create('circumcenter', [p1, p2, p3]);\n * \n * \n */\nJXG.createCircumcenter = function (board, parents, attributes) {\n var p, i, a, b, c;\n\n parents = Type.providePoints(board, parents, attributes, 'point');\n if (Type.isPoint(parents[0]) && Type.isPoint(parents[1]) && Type.isPoint(parents[2])) {\n a = parents[0];\n b = parents[1];\n c = parents[2];\n\n p = JXG.createPoint(\n board,\n [\n function () {\n return Geometry.circumcenter(a, b, c, board);\n }\n ],\n attributes\n );\n\n for (i = 0; i < 3; i++) {\n if (Type.exists(parents[i]._is_new)) {\n p.addChild(parents[i]);\n delete parents[i]._is_new;\n } else {\n parents[i].addChild(p);\n }\n }\n\n p.elType = 'circumcenter';\n p.setParents(parents);\n\n p.generatePolynomial = function () {\n /*\n * CircumcircleMidpoint takes three points A, B and C and creates point M, which is the circumcenter of A, B, and C.\n *\n *\n * So we have two conditions:\n *\n * (a) CT == AT (distance condition I)\n * (b) BT == AT (distance condition II)\n *\n */\n var a1 = a.symbolic.x,\n a2 = a.symbolic.y,\n b1 = b.symbolic.x,\n b2 = b.symbolic.y,\n c1 = c.symbolic.x,\n c2 = c.symbolic.y,\n t1 = p.symbolic.x,\n t2 = p.symbolic.y,\n poly1 = [\"((\", t1, \")-(\", a1, \"))^2+((\", t2, \")-(\", a2, \"))^2-((\", t1, \")-(\", b1, \"))^2-((\", t2, \")-(\", b2, \"))^2\"].join(\"\"),\n poly2 = [\"((\", t1, \")-(\", a1, \"))^2+((\", t2, \")-(\", a2, \"))^2-((\", t1, \")-(\", c1, \"))^2-((\", t2, \")-(\", c2, \"))^2\"].join(\"\");\n\n return [poly1, poly2];\n };\n\n return p;\n }\n\n throw new Error(\n \"JSXGraph: Can't create circumcircle midpoint with parent types '\" +\n typeof parents[0] +\n \"', '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point]\"\n );\n};\n\n/**\n * @class The center of the incircle of the triangle described by the three given points (without\n * constructing the circle).\n * {@link https://mathworld.wolfram.com/Incenter.html}\n * @pseudo\n * @constructor\n * @name Incenter\n * @type JXG.Point\n * @augments JXG.Point\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The constructed point is the incenter of the triangle described\n * by p1, p2, and p3.\n * @example\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n * var p3 = board.create('point', [3.0, 3.0]);\n *\n * var ic1 = board.create('incenter', [p1, p2, p3]);\n * \n * \n */\nJXG.createIncenter = function (board, parents, attributes) {\n var p, A, B, C, i;\n\n parents = Type.providePoints(board, parents, attributes, 'point');\n if (\n parents.length >= 3 &&\n Type.isPoint(parents[0]) &&\n Type.isPoint(parents[1]) &&\n Type.isPoint(parents[2])\n ) {\n A = parents[0];\n B = parents[1];\n C = parents[2];\n\n p = board.create(\n \"point\",\n [\n function () {\n var a, b, c;\n\n a = Mat.hypot(B.X() - C.X(), B.Y() - C.Y());\n b = Mat.hypot(A.X() - C.X(), A.Y() - C.Y());\n c = Mat.hypot(B.X() - A.X(), B.Y() - A.Y());\n\n return new Coords(\n Const.COORDS_BY_USER,\n [\n (a * A.X() + b * B.X() + c * C.X()) / (a + b + c),\n (a * A.Y() + b * B.Y() + c * C.Y()) / (a + b + c)\n ],\n board\n );\n }\n ],\n attributes\n );\n\n for (i = 0; i < 3; i++) {\n if (Type.exists(parents[i]._is_new)) {\n p.addChild(parents[i]);\n delete parents[i]._is_new;\n } else {\n parents[i].addChild(p);\n }\n }\n\n p.elType = 'incenter';\n p.setParents(parents);\n } else {\n throw new Error(\n \"JSXGraph: Can't create incenter with parent types '\" +\n typeof parents[0] +\n \"', '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point]\"\n );\n }\n\n return p;\n};\n\n/**\n * @class A circumcircle is the unique circle through three points.\n * @pseudo\n * @constructor\n * @name Circumcircle\n * @type JXG.Circle\n * @augments JXG.Circle\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The constructed element is the circle determined by p1, p2, and p3.\n * @example\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n * var p3 = board.create('point', [3.0, 3.0]);\n *\n * var cc1 = board.create('circumcircle', [p1, p2, p3]);\n * \n * \n */\nJXG.createCircumcircle = function (board, parents, attributes) {\n var p, c, attr, i;\n\n parents = Type.providePoints(board, parents, attributes, 'point');\n if (parents === false) {\n throw new Error(\n \"JSXGraph: Can't create circumcircle with parent types '\" +\n typeof parents[0] +\n \"', '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point]\"\n );\n }\n\n try {\n attr = Type.copyAttributes(attributes, board.options, \"circumcircle\", 'center');\n p = JXG.createCircumcenter(board, parents, attr);\n\n p.dump = false;\n\n if (!Type.exists(attributes.layer)) {\n attributes.layer = board.options.layer.circle;\n }\n attr = Type.copyAttributes(attributes, board.options, 'circumcircle');\n c = JXG.createCircle(board, [p, parents[0]], attr);\n\n c.elType = 'circumcircle';\n c.setParents(parents);\n c.subs = {\n center: p\n };\n c.inherits.push(c);\n for (i = 0; i < 3; i++) {\n if (Type.exists(parents[i]._is_new)) {\n c.addChild(parents[i]);\n delete parents[i]._is_new;\n } else {\n parents[i].addChild(c);\n }\n }\n } catch (e) {\n throw new Error(\n \"JSXGraph: Can't create circumcircle with parent types '\" +\n typeof parents[0] +\n \"', '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point]\"\n );\n }\n\n // p is already stored as midpoint in c so there's no need to store it explicitly.\n\n return c;\n};\n\n/**\n * @class The circle which touches the three sides of a triangle given by three points.\n * @pseudo\n * @constructor\n * @name Incircle\n * @type JXG.Circle\n * @augments JXG.Circle\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The constructed point is the midpoint of the incircle of\n * p1, p2, and p3.\n * @example\n * var p1 = board.create('point', [0.0, 2.0]);\n * var p2 = board.create('point', [2.0, 1.0]);\n * var p3 = board.create('point', [3.0, 3.0]);\n *\n * var ic1 = board.create('incircle', [p1, p2, p3]);\n * \n * \n */\nJXG.createIncircle = function (board, parents, attributes) {\n var i, p, c, attr;\n\n parents = Type.providePoints(board, parents, attributes, 'point');\n if (parents === false) {\n throw new Error(\n \"JSXGraph: Can't create circumcircle with parent types '\" +\n typeof parents[0] +\n \"', '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point]\"\n );\n }\n try {\n attr = Type.copyAttributes(attributes, board.options, \"incircle\", 'center');\n p = JXG.createIncenter(board, parents, attr);\n\n p.dump = false;\n\n if (!Type.exists(attributes.layer)) {\n attributes.layer = board.options.layer.circle;\n }\n attr = Type.copyAttributes(attributes, board.options, 'incircle');\n c = JXG.createCircle(\n board,\n [\n p,\n function () {\n var a = Mat.hypot(parents[1].X() - parents[2].X(), parents[1].Y() - parents[2].Y()),\n b = Mat.hypot(parents[0].X() - parents[2].X(), parents[0].Y() - parents[2].Y()),\n c = Mat.hypot(parents[1].X() - parents[0].X(), parents[1].Y() - parents[0].Y()),\n s = (a + b + c) / 2;\n\n return Math.sqrt(((s - a) * (s - b) * (s - c)) / s);\n }\n ],\n attr\n );\n\n c.elType = 'incircle';\n c.setParents(parents);\n for (i = 0; i < 3; i++) {\n if (Type.exists(parents[i]._is_new)) {\n c.addChild(parents[i]);\n delete parents[i]._is_new;\n } else {\n parents[i].addChild(c);\n }\n }\n\n /**\n * The center of the incircle\n * @memberOf Incircle.prototype\n * @type Incenter\n * @name center\n */\n c.center = p;\n\n c.subs = {\n center: c.center\n };\n c.inherits.push(p);\n } catch (e) {\n throw new Error(\n \"JSXGraph: Can't create circumcircle with parent types '\" +\n typeof parents[0] +\n \"', '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point,point]\"\n );\n }\n\n // p is already stored as midpoint in c so there's no need to store it explicitly.\n\n return c;\n};\n\n/**\n * @class Reflect a point, line, circle, curve, polygon across a given line.\n * @pseudo\n * @description A reflected element (point, polygon, line or curve) is given by a given\n * object of the same type and a line of reflection.\n * It is determined by the reflection of the given element\n * across the given line.\n * @constructor\n * @name Reflection\n * @type JXG.GeometryElement\n * @augments JXG.GeometryElement\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point|JXG.Line|JXG.Curve|JXG.Polygon_JXG.Line} p,l The reflection element is the reflection of p across the line l.\n * @example\n * var p1 = board.create('point', [0.0, 4.0]);\n * var p2 = board.create('point', [6.0, 1.0]);\n * var l1 = board.create('line', [p1, p2]);\n * var p3 = board.create('point', [3.0, 3.0]);\n *\n * var rp1 = board.create('reflection', [p3, l1]);\n * \n * \n * @example\n * // Reflection of more elements\n * // reflection line\n * var li = board.create('line', [1,1,1], {strokeColor: '#aaaaaa'});\n *\n * var p1 = board.create('point', [-3,-1], {name: \"A\"});\n * var q1 = board.create('reflection', [p1, li], {name: \"A'\"});\n *\n * var l1 = board.create('line', [1,-5,1]);\n * var l2 = board.create('reflection', [l1, li]);\n *\n * var cu1 = board.create('curve', [[-3, -3, -2.5, -3, -3, -2.5], [-3, -2, -2, -2, -2.5, -2.5]], {strokeWidth:3});\n * var cu2 = board.create('reflection', [cu1, li], {strokeColor: 'red', strokeWidth:3});\n *\n * var pol1 = board.create('polygon', [[-6,-3], [-4,-5], [-5,-1.5]]);\n * var pol2 = board.create('reflection', [pol1, li]);\n *\n * var c1 = board.create('circle', [[-2,-2], [-2, -1]]);\n * var c2 = board.create('reflection', [c1, li]);\n *\n * var a1 = board.create('arc', [[1, 1], [0, 1], [1, 0]], {strokeColor: 'red'});\n * var a2 = board.create('reflection', [a1, li], {strokeColor: 'red'});\n *\n * var s1 = board.create('sector', [[-3.5,-3], [-3.5, -2], [-3.5,-4]], {\n * anglePoint: {visible:true}, center: {visible: true}, radiusPoint: {visible: true},\n * fillColor: 'yellow', strokeColor: 'black'});\n * var s2 = board.create('reflection', [s1, li], {fillColor: 'yellow', strokeColor: 'black', fillOpacity: 0.5});\n *\n * var an1 = board.create('angle', [[-4,3.9], [-3, 4], [-3, 3]]);\n * var an2 = board.create('reflection', [an1, li]);\n *\n * \n * \n *\n */\nJXG.createReflection = function (board, parents, attributes) {\n var l, org, r, r_c,\n t, i, attr, attr2,\n errStr = \"\\nPossible parent types: [point|line|curve|polygon|circle|arc|sector, line]\";\n\n for (i = 0; i < parents.length; ++i) {\n parents[i] = board.select(parents[i]);\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'reflection');\n\n if (Type.isPoint(parents[0])) {\n org = Type.providePoints(board, [parents[0]], attr2)[0];\n } else if (\n parents[0].elementClass === Const.OBJECT_CLASS_CURVE ||\n parents[0].elementClass === Const.OBJECT_CLASS_LINE ||\n parents[0].type === Const.OBJECT_TYPE_POLYGON ||\n parents[0].elementClass === Const.OBJECT_CLASS_CIRCLE\n ) {\n org = parents[0];\n } else {\n throw new Error(\n \"JSXGraph: Can't create reflection element with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n errStr\n );\n }\n\n if (parents[1].elementClass === Const.OBJECT_CLASS_LINE) {\n l = parents[1];\n } else {\n throw new Error(\n \"JSXGraph: Can't create reflected element with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n errStr\n );\n }\n t = JXG.createTransform(board, [l], { type: \"reflect\" });\n\n if (Type.isPoint(org)) {\n r = JXG.createPoint(board, [org, t], attr);\n\n // Arcs and sectors are treated as curves\n } else if (org.elementClass === Const.OBJECT_CLASS_CURVE) {\n r = JXG.createCurve(board, [org, t], attr);\n } else if (org.elementClass === Const.OBJECT_CLASS_LINE) {\n r = JXG.createLine(board, [org, t], attr);\n } else if (org.type === Const.OBJECT_TYPE_POLYGON) {\n r = JXG.createPolygon(board, [org, t], attr);\n } else if (org.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n if (attr.type.toLowerCase() === 'euclidean') {\n // Create a circle element from a circle and a Euclidean transformation\n attr2 = Type.copyAttributes(attributes, board.options, \"reflection\", 'center');\n r_c = JXG.createPoint(board, [org.center, t], attr2);\n r_c.prepareUpdate()\n .update()\n .updateVisibility(r_c.evalVisProp('visible'))\n .updateRenderer();\n r = JXG.createCircle(\n board,\n [\n r_c,\n function () {\n return org.Radius();\n }\n ],\n attr\n );\n } else {\n // Create a conic element from a circle and a projective transformation\n r = JXG.createCircle(board, [org, t], attr);\n }\n } else {\n throw new Error(\n \"JSXGraph: Can't create reflected element with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n errStr\n );\n }\n\n if (Type.exists(org._is_new)) {\n r.addChild(org);\n delete org._is_new;\n } else {\n // org.addChild(r);\n }\n l.addChild(r);\n\n r.elType = 'reflection';\n r.addParents(l);\n r.prepareUpdate().update(); //.updateVisibility(r.evalVisProp('visible')).updateRenderer();\n\n if (Type.isPoint(r)) {\n r.generatePolynomial = function () {\n /*\n * Reflection takes a point R and a line L and creates point P, which is the reflection of R on L.\n * L is defined by two points A and B.\n *\n * So we have two conditions:\n *\n * (a) RP _|_ AB (orthogonality condition)\n * (b) AR == AP (distance condition)\n *\n */\n var a1 = l.point1.symbolic.x,\n a2 = l.point1.symbolic.y,\n b1 = l.point2.symbolic.x,\n b2 = l.point2.symbolic.y,\n p1 = org.symbolic.x,\n p2 = org.symbolic.y,\n r1 = r.symbolic.x,\n r2 = r.symbolic.y,\n poly1 = [\"((\", r2, \")-(\", p2, \"))*((\", a2, \")-(\", b2, \"))+((\", a1, \")-(\", b1, \"))*((\", r1, \")-(\", p1, \"))\"].join(\"\"),\n poly2 = [\"((\", r1, \")-(\", a1, \"))^2+((\", r2, \")-(\", a2, \"))^2-((\", p1, \")-(\", a1, \"))^2-((\", p2, \")-(\", a2, \"))^2\"].join(\"\");\n\n return [poly1, poly2];\n };\n }\n\n return r;\n};\n\n/**\n * @class Reflect a point, line, circle, curve, polygon across a given point.\n * @pseudo\n * @description A mirror element is determined by the reflection of a\n * given point, line, circle, curve, polygon across another given point.\n * In contrast to generic transformations, mirror elements of circles are again circles.\n * @constructor\n * @name MirrorElement\n * @type JXG.GeometryElement\n * @augments JXG.GeometryElement\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point|JXG.Line|JXG.Curve|JXG.Ppolygon_JXG.Point} p1,p2 The constructed element is the mirror image of p2 across p1.\n * @example\n * // point of reflection\n * var mirr = board.create('point', [-1,-1], {color: '#aaaaaa'});\n *\n * var p1 = board.create('point', [-3,-1], {name: \"A\"});\n * var q1 = board.create('mirrorelement', [p1, mirr], {name: \"A'\"});\n *\n * var l1 = board.create('line', [1, -5, 1]);\n * var l2 = board.create('mirrorelement', [l1, mirr]);\n *\n * var cu1 = board.create('curve', [[-3, -3, -2.5, -3, -3, -2.5], [-3, -2, -2, -2, -2.5, -2.5]], {strokeWidth:3});\n * var cu2 = board.create('mirrorelement', [cu1, mirr], {strokeColor: 'red', strokeWidth:3});\n *\n * var pol1 = board.create('polygon', [[-6,-2], [-4,-4], [-5,-0.5]]);\n * var pol2 = board.create('mirrorelement', [pol1, mirr]);\n *\n * var c1 = board.create('circle', [[-6,-6], [-6, -5]]);\n * var c2 = board.create('mirrorelement', [c1, mirr]);\n *\n * var a1 = board.create('arc', [[1, 1], [0, 1], [1, 0]], {strokeColor: 'red'});\n * var a2 = board.create('mirrorelement', [a1, mirr], {strokeColor: 'red'});\n *\n * var s1 = board.create('sector', [[-3.5,-3], [-3.5, -2], [-3.5,-4]], {\n * anglePoint: {visible:true}, center: {visible: true}, radiusPoint: {visible: true},\n * fillColor: 'yellow', strokeColor: 'black'});\n * var s2 = board.create('mirrorelement', [s1, mirr], {fillColor: 'yellow', strokeColor: 'black', fillOpacity: 0.5});\n *\n * var an1 = board.create('angle', [[-4,3.9], [-3, 4], [-3, 3]]);\n * var an2 = board.create('mirrorelement', [an1, mirr]);\n *\n *\n * \n * \n */\nJXG.createMirrorElement = function (board, parents, attributes) {\n var org, i, m, r, r_c, t,\n attr, attr2,\n errStr = \"\\nPossible parent types: [point|line|curve|polygon|circle|arc|sector, point]\";\n\n for (i = 0; i < parents.length; ++i) {\n parents[i] = board.select(parents[i]);\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'mirrorelement');\n if (Type.isPoint(parents[0])) {\n // Create point to be mirrored if supplied by coords array.\n org = Type.providePoints(board, [parents[0]], attr)[0];\n } else if (\n parents[0].elementClass === Const.OBJECT_CLASS_CURVE ||\n parents[0].elementClass === Const.OBJECT_CLASS_LINE ||\n parents[0].type === Const.OBJECT_TYPE_POLYGON ||\n parents[0].elementClass === Const.OBJECT_CLASS_CIRCLE\n ) {\n org = parents[0];\n } else {\n throw new Error(\n \"JSXGraph: Can't create mirror element with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n errStr\n );\n }\n\n if (Type.isPoint(parents[1])) {\n attr2 = Type.copyAttributes(attributes, board.options, \"mirrorelement\", 'point');\n // Create mirror point if supplied by coords array.\n m = Type.providePoints(board, [parents[1]], attr2)[0];\n } else {\n throw new Error(\n \"JSXGraph: Can't create mirror element with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n errStr\n );\n }\n\n t = JXG.createTransform(board, [Math.PI, m], { type: \"rotate\" });\n if (Type.isPoint(org)) {\n r = JXG.createPoint(board, [org, t], attr);\n\n // Arcs and sectors are treated as curves\n } else if (org.elementClass === Const.OBJECT_CLASS_CURVE) {\n r = JXG.createCurve(board, [org, t], attr);\n } else if (org.elementClass === Const.OBJECT_CLASS_LINE) {\n r = JXG.createLine(board, [org, t], attr);\n } else if (org.type === Const.OBJECT_TYPE_POLYGON) {\n r = JXG.createPolygon(board, [org, t], attr);\n } else if (org.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n if (attr.type.toLowerCase() === 'euclidean') {\n // Create a circle element from a circle and a Euclidean transformation\n attr2 = Type.copyAttributes(attributes, board.options, \"mirrorelement\", 'center');\n r_c = JXG.createPoint(board, [org.center, t], attr2);\n r_c.prepareUpdate()\n .update()\n .updateVisibility(r_c.evalVisProp('visible'))\n .updateRenderer();\n r = JXG.createCircle(\n board,\n [\n r_c,\n function () {\n return org.Radius();\n }\n ],\n attr\n );\n } else {\n // Create a conic element from a circle and a projective transformation\n r = JXG.createCircle(board, [org, t], attr);\n }\n } else {\n throw new Error(\n \"JSXGraph: Can't create mirror element with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n errStr\n );\n }\n\n if (Type.exists(org._is_new)) {\n r.addChild(org);\n delete org._is_new;\n } else {\n // org.addChild(r);\n }\n m.addChild(r);\n\n r.elType = 'mirrorelement';\n r.addParents(m);\n r.prepareUpdate().update();\n\n return r;\n};\n\n/**\n * @class A MirrorPoint is a special case of a {@link MirrorElement}.\n * @pseudo\n * @description A mirror point is determined by the reflection of a given point against another given point.\n * @constructor\n * @name MirrorPoint\n * @type JXG.Point\n * @augments JXG.Point\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point_JXG.Point} p1,p2 The constructed point is the reflection of p2 against p1.\n *\n * This method is superseeded by the more general {@link JXG.createMirrorElement}.\n * @example\n * var p1 = board.create('point', [3.0, 3.0]);\n * var p2 = board.create('point', [6.0, 1.0]);\n *\n * var mp1 = board.create('mirrorpoint', [p1, p2]);\n * \n * \n */\nJXG.createMirrorPoint = function (board, parents, attributes) {\n var el = JXG.createMirrorElement(board, parents, attributes);\n el.elType = 'mirrorpoint';\n return el;\n};\n\n/**\n * @class The graph of the integral function of a given function in a given interval.\n * @pseudo\n * @description The Integral element is used to visualize the area under a given curve over a given interval\n * and to calculate the area's value. For that a polygon and gliders are used. The polygon displays the area,\n * the gliders are used to change the interval dynamically.\n * @constructor\n * @name Integral\n * @type JXG.Curve\n * @augments JXG.Curve\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Array_JXG.Curve} i,c The constructed element covers the area between the curve c and the x-axis\n * within the interval i.\n * @example\n * var c1 = board.create('functiongraph', [function (t) { return Math.cos(t)*t; }]);\n * var i1 = board.create('integral', [[-2.0, 2.0], c1]);\n * \n * \n */\nJXG.createIntegral = function (board, parents, attributes) {\n var interval, curve, attr, start, end,\n startx, starty, endx, endy,\n pa_on_curve, pa_on_axis, pb_on_curve, pb_on_axis,\n txt_fun,\n t = null, p;\n\n if (Type.isArray(parents[0]) && parents[1].elementClass === Const.OBJECT_CLASS_CURVE) {\n interval = parents[0];\n curve = parents[1];\n } else if (\n Type.isArray(parents[1]) &&\n parents[0].elementClass === Const.OBJECT_CLASS_CURVE\n ) {\n interval = parents[1];\n curve = parents[0];\n } else {\n throw new Error(\n \"JSXGraph: Can't create integral with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [[number|function,number|function],curve]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'integral');\n attr.withlabel = false; // There is a custom 'label' below.\n p = board.create(\"curve\", [[0], [0]], attr);\n\n // Dirty hack: the integral curve is removed from board.objectsList\n // and inserted below again after the pa_/pb_on_axis elements.\n // Otherwise, the filled area lags is updated before the\n // update of the bounds.\n board.objectsList.pop();\n\n // Correct the interval if necessary - NOT ANYMORE, GGB's fault\n start = interval[0];\n end = interval[1];\n\n if (Type.isFunction(start)) {\n startx = start;\n starty = function () {\n return curve.Y(startx());\n };\n start = startx();\n } else {\n startx = start;\n starty = curve.Y(start);\n }\n\n if (Type.isFunction(end)) {\n endx = end;\n endy = function () {\n return curve.Y(endx());\n };\n end = endx();\n } else {\n endx = end;\n endy = curve.Y(end);\n }\n\n attr = Type.copyAttributes(attributes, board.options, \"integral\", 'curveleft');\n pa_on_curve = board.create(\"glider\", [startx, starty, curve], attr);\n if (Type.isFunction(startx)) {\n pa_on_curve.hideElement();\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'integral', 'baseleft');\n pa_on_axis = board.create('point', [\n function () {\n if (p.evalVisProp('axis') === 'y') {\n return 0;\n }\n return pa_on_curve.X();\n },\n function () {\n if (p.evalVisProp('axis') === 'y') {\n return pa_on_curve.Y();\n }\n return 0;\n }\n ], attr);\n\n attr = Type.copyAttributes(attributes, board.options, \"integral\", 'curveright');\n pb_on_curve = board.create(\"glider\", [endx, endy, curve], attr);\n if (Type.isFunction(endx)) {\n pb_on_curve.hideElement();\n }\n\n attr = Type.copyAttributes(attributes, board.options, \"integral\", 'baseright');\n pb_on_axis = board.create('point', [\n function () {\n if (p.evalVisProp('axis') === 'y') {\n return 0;\n }\n return pb_on_curve.X();\n },\n function () {\n if (p.evalVisProp('axis') === 'y') {\n return pb_on_curve.Y();\n }\n\n return 0;\n }\n ], attr);\n\n // Re-insert the filled integral curve element\n p._pos = board.objectsList.length;\n board.objectsList.push(p);\n\n attr = Type.copyAttributes(attributes, board.options, 'integral');\n if (attr.withlabel !== false && attr.axis !== 'y') {\n attr = Type.copyAttributes(attributes, board.options, \"integral\", 'label');\n attr = Type.copyAttributes(attr, board.options, 'label');\n\n t = board.create('text', [\n function () {\n var off = new Coords(\n Const.COORDS_BY_SCREEN,\n [\n this.evalVisProp('offset.0') +\n this.board.origin.scrCoords[1],\n 0\n ],\n this.board,\n false\n ),\n bb = this.board.getBoundingBox(),\n dx = (bb[2] - bb[0]) * 0.1,\n x = pb_on_curve.X();\n\n if (x < bb[0]) {\n x = bb[0] + dx;\n } else if (x > bb[2]) {\n x = bb[2] - dx;\n }\n\n return x + off.usrCoords[1];\n },\n function () {\n var off = new Coords(\n Const.COORDS_BY_SCREEN,\n [\n 0,\n this.evalVisProp('offset.1') +\n this.board.origin.scrCoords[2]\n ],\n this.board,\n false\n ),\n bb = this.board.getBoundingBox(),\n dy = (bb[1] - bb[3]) * 0.1,\n y = pb_on_curve.Y();\n\n if (y > bb[1]) {\n y = bb[1] - dy;\n } else if (y < bb[3]) {\n y = bb[3] + dy;\n }\n\n return y + off.usrCoords[2];\n },\n ''\n ], attr);\n\n txt_fun = function () {\n var intSymbol = '∫',\n Int = Numerics.NewtonCotes([pa_on_axis.X(), pb_on_axis.X()], curve.Y),\n digits = t.evalVisProp('digits'),\n val;\n\n if (t.useLocale()) {\n val = t.formatNumberLocale(Int, digits);\n } else {\n val = Type.toFixed(Int, digits);\n }\n if (t.evalVisProp('usemathjax') || t.evalVisProp('usekatex')) {\n intSymbol = '\\\\int';\n }\n return intSymbol + ' = ' + val;\n };\n t.setText(txt_fun);\n t.dump = false;\n\n pa_on_curve.addChild(t);\n pb_on_curve.addChild(t);\n }\n\n // dump stuff\n pa_on_curve.dump = false;\n pa_on_axis.dump = false;\n\n pb_on_curve.dump = false;\n pb_on_axis.dump = false;\n\n p.elType = 'integral';\n p.setParents([curve.id, interval]);\n p.subs = {\n curveLeft: pa_on_curve,\n baseLeft: pa_on_axis,\n curveRight: pb_on_curve,\n baseRight: pb_on_axis\n };\n p.inherits.push(pa_on_curve, pa_on_axis, pb_on_curve, pb_on_axis);\n\n if (attr.withlabel) {\n p.subs.label = t;\n p.inherits.push(t);\n }\n\n /**\n * Returns the current value of the integral.\n * @memberOf Integral\n * @name Value\n * @function\n * @returns {Number}\n */\n p.Value = function () {\n return Numerics.I([pa_on_axis.X(), pb_on_axis.X()], curve.Y);\n };\n\n /**\n * documented in JXG.Curve\n * @class\n * @ignore\n */\n p.updateDataArray = function () {\n var x, y, i, left, right, lowx, upx, lowy, upy;\n\n if (this.evalVisProp('axis') === 'y') {\n if (pa_on_curve.Y() < pb_on_curve.Y()) {\n lowx = pa_on_curve.X();\n lowy = pa_on_curve.Y();\n upx = pb_on_curve.X();\n upy = pb_on_curve.Y();\n } else {\n lowx = pb_on_curve.X();\n lowy = pb_on_curve.Y();\n upx = pa_on_curve.X();\n upy = pa_on_curve.Y();\n }\n left = Math.min(lowx, upx);\n right = Math.max(lowx, upx);\n\n x = [0, lowx];\n y = [lowy, lowy];\n\n for (i = 0; i < curve.numberPoints; i++) {\n if (\n lowy <= curve.points[i].usrCoords[2] &&\n left <= curve.points[i].usrCoords[1] &&\n curve.points[i].usrCoords[2] <= upy &&\n curve.points[i].usrCoords[1] <= right\n ) {\n x.push(curve.points[i].usrCoords[1]);\n y.push(curve.points[i].usrCoords[2]);\n }\n }\n x.push(upx);\n y.push(upy);\n x.push(0);\n y.push(upy);\n\n // close the curve\n x.push(0);\n y.push(lowy);\n } else {\n if (pa_on_axis.X() < pb_on_axis.X()) {\n left = pa_on_axis.X();\n right = pb_on_axis.X();\n } else {\n left = pb_on_axis.X();\n right = pa_on_axis.X();\n }\n\n x = [left, left];\n y = [0, curve.Y(left)];\n\n for (i = 0; i < curve.numberPoints; i++) {\n if (\n left <= curve.points[i].usrCoords[1] &&\n curve.points[i].usrCoords[1] <= right\n ) {\n x.push(curve.points[i].usrCoords[1]);\n y.push(curve.points[i].usrCoords[2]);\n }\n }\n x.push(right);\n y.push(curve.Y(right));\n x.push(right);\n y.push(0);\n\n // close the curve\n x.push(left);\n y.push(0);\n }\n\n this.dataX = x;\n this.dataY = y;\n };\n\n pa_on_curve.addChild(p);\n pb_on_curve.addChild(p);\n pa_on_axis.addChild(p);\n pb_on_axis.addChild(p);\n\n /**\n * The point on the axis initially corresponding to the lower value of the interval.\n *\n * @name baseLeft\n * @memberOf Integral\n * @type JXG.Point\n */\n p.baseLeft = pa_on_axis;\n\n /**\n * The point on the axis initially corresponding to the higher value of the interval.\n *\n * @name baseRight\n * @memberOf Integral\n * @type JXG.Point\n */\n p.baseRight = pb_on_axis;\n\n /**\n * The glider on the curve corresponding to the lower value of the interval.\n *\n * @name curveLeft\n * @memberOf Integral\n * @type Glider\n */\n p.curveLeft = pa_on_curve;\n\n /**\n * The glider on the axis corresponding to the higher value of the interval.\n *\n * @name curveRight\n * @memberOf Integral\n * @type Glider\n */\n p.curveRight = pb_on_curve;\n\n /**\n * documented in GeometryElement\n * @ignore\n */\n p.label = t;\n\n Type.extendInstanceMethodMap(p, {\n curveLeft: \"curveLeft\",\n baseLeft: \"baseLeft\",\n curveRight: \"curveRight\",\n baseRight: \"baseRight\",\n Value: \"Value\"\n });\n\n return p;\n};\n\n/**\n * @class The area which is the set of solutions of a linear inequality or an inequality\n * of a function graph.\n * For example, an inequality of type y <= f(x).\n * @pseudo\n * @description Display the solution set of a linear inequality (less than or equal to).\n * To be precise, the solution set of the inequality y <= b/a * x + c/a is shown.\n * In case a = 0, that is if the equation of the line is bx + c = 0,\n * the area of the inequality bx + c <= 0 is shown.\n * \n * \n *\n * @example\n * // Plot the inequality\n * // y >= 2/3 x + 1\n * // or\n * // 0 >= -3y + 2x +1\n * var l = board.create('line', [1, 2, -3]),\n * ineq = board.create('inequality', [l], {inverse:true});\n * \n * \n *\n * @example\n * var f = board.create('functiongraph', ['sin(x)', -2*Math.PI, 2*Math.PI]);\n *\n * var ineq_lower = board.create('inequality', [f]);\n * var ineq_greater = board.create('inequality', [f], {inverse: true, fillColor: 'yellow'});\n *\n *\n * \n * \n *\n */\nJXG.createInequality = function (board, parents, attributes) {\n var f, a, attr;\n\n attr = Type.copyAttributes(attributes, board.options, 'inequality');\n if (parents[0].elementClass === Const.OBJECT_CLASS_LINE) {\n a = board.create(\"curve\", [[], []], attr);\n a.hasPoint = function () {\n return false;\n };\n\n /**\n * @class\n * @ignore\n */\n a.updateDataArray = function () {\n var i1,\n i2,\n // This will be the height of the area. We mustn't rely upon the board height because if we pan the view\n // such that the line is not visible anymore, the borders of the area will get visible in some cases.\n h,\n bb = board.getBoundingBox(),\n inverse = this.evalVisProp('inverse'),\n factor = inverse ? -1 : 1,\n expansion = 1.5,\n w = expansion * Math.max(bb[2] - bb[0], bb[1] - bb[3]),\n // Fake a point (for Math.Geometry.perpendicular)\n // contains centroid of the board\n dp = {\n coords: {\n usrCoords: [1, (bb[0] + bb[2]) * 0.5, inverse ? bb[1] : bb[3]]\n }\n },\n slope1 = parents[0].stdform.slice(1),\n slope2 = slope1;\n\n // Calculate the area height as\n // expansion times the distance of the line to the\n // point in the middle of the top/bottom border.\n h =\n expansion *\n Math.max(\n Geometry.perpendicular(parents[0], dp, board)[0].distance(\n Const.COORDS_BY_USER,\n dp.coords\n ),\n w\n );\n h *= factor;\n\n // reuse dp\n dp = {\n coords: {\n usrCoords: [1, (bb[0] + bb[2]) * 0.5, (bb[1] + bb[3]) * 0.5]\n }\n };\n\n // If dp is on the line, Geometry.perpendicular will return a point not on the line.\n // Since this somewhat odd behavior of Geometry.perpendicular is needed in GEONExT,\n // it is circumvented here.\n if (\n Math.abs(Mat.innerProduct(dp.coords.usrCoords, parents[0].stdform, 3)) >=\n Mat.eps\n ) {\n dp = Geometry.perpendicular(parents[0], dp, board)[0].usrCoords;\n } else {\n dp = dp.coords.usrCoords;\n }\n i1 = [1, dp[1] + slope1[1] * w, dp[2] - slope1[0] * w];\n i2 = [1, dp[1] - slope2[1] * w, dp[2] + slope2[0] * w];\n\n // One of the vectors based in i1 and orthogonal to the parent line has the direction d1 = (slope1, -1)\n // We will go from i1 to i1 + h*d1, from there to i2 + h*d2 (with d2 calculated equivalent to d1) and\n // end up in i2.\n this.dataX = [i1[1], i1[1] + slope1[0] * h, i2[1] + slope2[0] * h, i2[1], i1[1]];\n this.dataY = [i1[2], i1[2] + slope1[1] * h, i2[2] + slope2[1] * h, i2[2], i1[2]];\n };\n } else if (\n parents[0].elementClass === Const.OBJECT_CLASS_CURVE &&\n parents[0].visProp.curvetype === \"functiongraph\"\n ) {\n a = board.create(\"curve\", [[], []], attr);\n /**\n * @class\n * @ignore\n */\n a.updateDataArray = function () {\n var bbox = this.board.getBoundingBox(),\n points = [],\n infty,\n first,\n last,\n len,\n i,\n miv = Infinity,\n mav = -Infinity,\n p,\n mi = parents[0].minX(),\n ma = parents[0].maxX(),\n curve_mi,\n curve_ma,\n firstx,\n lastx,\n enlarge = (bbox[1] - bbox[3]) * 1, // enlarge the bbox vertically by this amount\n inverse = this.evalVisProp('inverse');\n\n // inverse == true <=> Fill area with y >= f(x)\n infty = inverse ? 1 : 3; // we will use either bbox[1] or bbox[3] below\n\n this.dataX = [];\n this.dataY = [];\n len = parents[0].points.length;\n if (len === 0) {\n return;\n }\n\n bbox[1] += enlarge;\n bbox[3] -= enlarge;\n\n last = -1;\n while (last < len - 1) {\n // Find the first point with real coordinates on this curve segment\n for (i = last + 1, first = len; i < len; i++) {\n if (parents[0].points[i].isReal()) {\n first = i;\n break;\n }\n }\n // No real points found -> exit\n if (first >= len) {\n break;\n }\n\n // Find the last point with real coordinates on this curve segment\n for (i = first, last = len - 1; i < len - 1; i++) {\n if (!parents[0].points[i + 1].isReal()) {\n last = i;\n break;\n }\n }\n\n firstx = parents[0].points[first].usrCoords[1];\n lastx = parents[0].points[last].usrCoords[1];\n\n // Restrict the plot interval if the function ends inside of the board\n curve_mi = bbox[0] < mi ? mi : bbox[0];\n curve_ma = bbox[2] > ma ? ma : bbox[2];\n\n // Found NaNs\n curve_mi = first === 0 ? curve_mi : Math.max(curve_mi, firstx);\n curve_ma = last === len - 1 ? curve_ma : Math.min(curve_ma, lastx);\n\n // First and last relevant x-coordinate of the curve\n curve_mi = first === 0 ? mi : firstx;\n curve_ma = last === len - 1 ? ma : lastx;\n\n // Copy the curve points\n points = [];\n\n points.push([1, curve_mi, bbox[infty]]);\n points.push([1, curve_mi, parents[0].points[first].usrCoords[2]]);\n\n for (i = first; i <= last; i++) {\n p = parents[0].points[i].usrCoords;\n points.push(parents[0].points[i].usrCoords);\n miv = (p[2] < miv) ? p[2] : miv;\n mav = (p[2] > mav) ? p[2] : mav;\n }\n\n if (infty === 1) {\n points[0][2] = mav + enlarge;\n } else {\n points[0][2] = miv - enlarge;\n }\n\n points.push([1, curve_ma, parents[0].points[last].usrCoords[2]]);\n points.push([1, curve_ma, bbox[infty]]);\n points.push(points[0]);\n\n for (i = 0; i < points.length; i++) {\n this.dataX.push(points[i][1]);\n this.dataY.push(points[i][2]);\n }\n\n if (last < len - 1) {\n this.dataX.push(NaN);\n this.dataY.push(NaN);\n }\n }\n };\n\n // Previous code:\n /**\n * @class\n * @ignore\n */\n a.hasPoint = function () {\n return false;\n };\n } else {\n // Not yet practical?\n f = Type.createFunction(parents[0]);\n a.addParentsFromJCFunctions([f]);\n\n if (!Type.exists(f)) {\n throw new Error(\n \"JSXGraph: Can't create area with the given parents.\" +\n \"\\nPossible parent types: [line], [function]\"\n );\n }\n }\n\n a.addParents(parents[0]);\n return a;\n};\n\nJXG.registerElement(\"arrowparallel\", JXG.createArrowParallel);\nJXG.registerElement(\"bisector\", JXG.createBisector);\nJXG.registerElement(\"bisectorlines\", JXG.createAngularBisectorsOfTwoLines);\nJXG.registerElement(\"msector\", JXG.createMsector);\nJXG.registerElement(\"circumcircle\", JXG.createCircumcircle);\nJXG.registerElement(\"circumcirclemidpoint\", JXG.createCircumcenter);\nJXG.registerElement(\"circumcenter\", JXG.createCircumcenter);\nJXG.registerElement(\"incenter\", JXG.createIncenter);\nJXG.registerElement(\"incircle\", JXG.createIncircle);\nJXG.registerElement(\"integral\", JXG.createIntegral);\nJXG.registerElement(\"midpoint\", JXG.createMidpoint);\nJXG.registerElement(\"mirrorelement\", JXG.createMirrorElement);\nJXG.registerElement(\"mirrorpoint\", JXG.createMirrorPoint);\nJXG.registerElement(\"orthogonalprojection\", JXG.createOrthogonalProjection);\nJXG.registerElement(\"parallel\", JXG.createParallel);\nJXG.registerElement(\"parallelpoint\", JXG.createParallelPoint);\nJXG.registerElement(\"perpendicular\", JXG.createPerpendicular);\nJXG.registerElement(\"perpendicularpoint\", JXG.createPerpendicularPoint);\nJXG.registerElement(\"perpendicularsegment\", JXG.createPerpendicularSegment);\nJXG.registerElement(\"reflection\", JXG.createReflection);\nJXG.registerElement(\"inequality\", JXG.createInequality);\n\n// export default {\n// createArrowParallel: JXG.createArrowParallel,\n// createBisector: JXG.createBisector,\n// createAngularBisectorOfTwoLines: JXG.createAngularBisectorsOfTwoLines,\n// createCircumcircle: JXG.createCircumcircle,\n// createCircumcenter: JXG.createCircumcenter,\n// createIncenter: JXG.createIncenter,\n// createIncircle: JXG.createIncircle,\n// createIntegral: JXG.createIntegral,\n// createMidpoint: JXG.createMidpoint,\n// createMirrorElement: JXG.createMirrorElement,\n// createMirrorPoint: JXG.createMirrorPoint,\n// createNormal: JXG.createNormal,\n// createOrthogonalProjection: JXG.createOrthogonalProjection,\n// createParallel: JXG.createParallel,\n// createParallelPoint: JXG.createParallelPoint,\n// createPerpendicular: JXG.createPerpendicular,\n// createPerpendicularPoint: JXG.createPerpendicularPoint,\n// createPerpendicularSegmen: JXG.createPerpendicularSegment,\n// createReflection: JXG.createReflection,\n// createInequality: JXG.createInequality\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n * @example\n * // more fancy grid\n * var g = board.create('grid', [], {\n * major: {\n * face: 'plus',\n * size: 7,\n * strokeColor: 'green',\n * strokeOpacity: 1,\n * },\n * minor: {\n * size: 4\n * },\n * minorElements: 3,\n * });\n * \n * \n *\n * @example\n * // extreme fancy grid\n * var grid = board.create('grid', [], {\n * major: {\n * face: 'regularPolygon',\n * size: 8,\n * strokeColor: 'blue',\n * fillColor: 'orange',\n * strokeOpacity: 1,\n * },\n * minor: {\n * face: 'diamond',\n * size: 4,\n * strokeColor: 'green',\n * fillColor: 'grey',\n * },\n * minorElements: 1,\n * includeBoundaries: false,\n * });\n * \n * \n *\n * @example\n * // grid with parent axes\n * var axis1 = board.create('axis', [[-1, -2.5], [1, -2.5]], {\n * ticks: {\n * strokeColor: 'green',\n * strokeWidth: 2,\n * minorticks: 2,\n * majorHeight: 10,\n * drawZero: true\n * }\n * });\n * var axis2 = board.create('axis', [[3, 0], [3, 2]], {\n * ticks: {\n * strokeColor: 'red',\n * strokeWidth: 2,\n * minorticks: 3,\n * majorHeight: 10,\n * drawZero: true\n * }\n * });\n * var grid = board.create('grid', [axis1, axis2], {\n * major: {\n * face: 'line'\n * },\n * minor: {\n * face: 'point',\n * size: 3\n * },\n * minorElements: 'auto',\n * includeBoundaries: false,\n * });\n * \n * \n */\nJXG.createGrid = function (board, parents, attributes) {\n var eps = Mat.eps, // to avoid rounding errors\n maxLines = 5000, // maximum number of vertical or horizontal grid elements (abort criterion for performance reasons)\n\n majorGrid, // main object which will be returned as grid\n minorGrid, // sub-object\n parentAxes, // {Array} array of user defined axes (allowed length 0, 1 or 2)\n\n attrGrid, // attributes for grid\n attrMajor, // attributes for major grid\n attrMinor, // attributes for minor grid\n\n majorStep, // {[Number]} distance (in usrCoords) in x- and y-direction between center of two major grid elements\n majorSize = [],\n majorRadius = [], // half of the size of major grid element\n\n createDataArrayForFace; // {Function}\n\n parentAxes = parents;\n if (\n parentAxes.length > 2 ||\n (parentAxes.length >= 1 && parentAxes[0].elType !== 'axis') ||\n (parentAxes.length >= 2 && parentAxes[1].elType !== 'axis')\n ) {\n throw new Error(\n \"JSXGraph: Can't create 'grid' with parent type '\" +\n parents[0].elType +\n \"'. Possible parent types: [axis,axis]\"\n );\n }\n if (!Type.exists(parentAxes[0]) && Type.exists(board.defaultAxes)) {\n parentAxes[0] = board.defaultAxes.x;\n }\n if (!Type.exists(parentAxes[1]) && Type.exists(board.defaultAxes)) {\n parentAxes[1] = board.defaultAxes.y;\n }\n\n /**\n * Creates for each face the right data array for updateDataArray function.\n * This functions also adapts visProps according to face.\n\n * @param {String} face Chosen face to be drawn\n * @param {Object} grid Curve/grid to be drawn\n * @param {Number} x x-coordinate of target position\n * @param {Number} y y-coordinate of target position\n * @param {Number} radiusX Half of width in x-direction of face to be drawn\n * @param {Number} radiusY Half of width in y-direction of face to be drawn\n * @param {Array} bbox boundingBox\n *\n * @returns {Array} data array of length 2 (x- and y- coordinated for curve)\n * @private\n * @ignore\n */\n createDataArrayForFace = function (face, grid, x, y, radiusX, radiusY, bbox) {\n var t, q, m, n, array, rx2, ry2;\n\n switch (face.toLowerCase()) {\n\n // filled point\n case '.':\n case 'point':\n grid.visProp.linecap = 'round';\n grid.visProp.strokewidth = radiusX * grid.board.unitX + radiusY * grid.board.unitY;\n return [\n [x, x, NaN],\n [y, y, NaN]\n ];\n\n // bezierCircle\n case 'o':\n case 'circle':\n grid.visProp.linecap = 'square';\n grid.bezierDegree = 3;\n q = 4 * Math.tan(Math.PI / 8) / 3;\n return [\n [\n x + radiusX, x + radiusX, x + q * radiusX, x,\n x - q * radiusX, x - radiusX, x - radiusX, x - radiusX,\n x - q * radiusX, x, x + q * radiusX, x + radiusX,\n x + radiusX, NaN\n ], [\n y, y + q * radiusY, y + radiusY, y + radiusY,\n y + radiusY, y + q * radiusY, y, y - q * radiusY,\n y - radiusY, y - radiusY, y - radiusY, y - q * radiusY,\n y, NaN\n ]\n ];\n\n // polygon\n case 'regpol':\n case 'regularpolygon':\n grid.visProp.linecap = 'round';\n n = grid.evalVisProp('polygonvertices');\n array = [[], []];\n // approximation of circle with variable n\n for (t = 0; t <= 2 * Math.PI; t += (2 * Math.PI) / n) {\n array[0].push(x - radiusX * Math.sin(t));\n array[1].push(y - radiusY * Math.cos(t));\n }\n array[0].push(NaN);\n array[1].push(NaN);\n return array;\n\n // square\n case '[]':\n case 'square':\n grid.visProp.linecap = 'square';\n return [\n [x - radiusX, x + radiusX, x + radiusX, x - radiusX, x - radiusX, NaN],\n [y + radiusY, y + radiusY, y - radiusY, y - radiusY, y + radiusY, NaN]\n ];\n\n // diamond\n case '<>':\n case 'diamond':\n grid.visProp.linecap = 'square';\n return [\n [x, x + radiusX, x, x - radiusX, x, NaN],\n [y + radiusY, y, y - radiusY, y, y + radiusY, NaN]\n ];\n\n // diamond2\n case '<<>>':\n case 'diamond2':\n grid.visProp.linecap = 'square';\n rx2 = radiusX * Math.sqrt(2);\n ry2 = radiusY * Math.sqrt(2);\n return [\n [x, x + rx2, x, x - rx2, x, NaN],\n [y + ry2, y, y - ry2, y, y + ry2, NaN]\n ];\n\n case 'x':\n case 'cross':\n return [\n [x - radiusX, x + radiusX, NaN, x - radiusX, x + radiusX, NaN],\n [y + radiusY, y - radiusY, NaN, y - radiusY, y + radiusY, NaN]\n ];\n\n case '+':\n case 'plus':\n return [\n [x - radiusX, x + radiusX, NaN, x, x, NaN],\n [y, y, NaN, y - radiusY, y + radiusY, NaN]\n ];\n\n case '-':\n case 'minus':\n return [\n [x - radiusX, x + radiusX, NaN],\n [y, y, NaN]\n ];\n\n case '|':\n case 'divide':\n return [\n [x, x, NaN],\n [y - radiusY, y + radiusY, NaN]\n ];\n\n case '^':\n case 'a':\n case 'A':\n case 'triangleup':\n return [\n [x - radiusX, x, x + radiusX, NaN],\n [y - radiusY, y, y - radiusY, NaN]\n ];\n\n case 'v':\n case 'triangledown':\n return [\n [x - radiusX, x, x + radiusX, NaN],\n [y + radiusY, y, y + radiusY, NaN]\n ];\n\n case '<':\n case 'triangleleft':\n return [\n [x + radiusX, x, x + radiusX, NaN],\n [y + radiusY, y, y - radiusY, NaN]\n ];\n\n case '>':\n case 'triangleright':\n return [\n [x - radiusX, x, x - radiusX, NaN],\n [y + radiusY, y, y - radiusY, NaN]\n ];\n\n case 'line':\n m = grid.evalVisProp('margin');\n return [\n // [x, x, NaN, bbox[0] + (4 / grid.board.unitX), bbox[2] - (4 / grid.board.unitX), NaN],\n [x, x, NaN, bbox[0] - m / grid.board.unitX, bbox[2] + m / grid.board.unitX, NaN],\n [bbox[1] + m / grid.board.unitY, bbox[3] - m / grid.board.unitY, NaN, y, y, NaN]\n ];\n\n default:\n return [[], []];\n }\n };\n\n // Themes\n attrGrid = Type.copyAttributes(attributes, board.options, 'grid');\n Type.mergeAttr(attrGrid, attrGrid.themes[attrGrid.theme], false);\n\n // Create majorGrid\n attrMajor = {};\n Type.mergeAttr(attrMajor, attrGrid, true, true);\n Type.mergeAttr(attrMajor, attrGrid.major, true, true);\n majorGrid = board.create('curve', [[null], [null]], attrMajor);\n majorGrid.elType = 'grid';\n majorGrid.type = Const.OBJECT_TYPE_GRID;\n\n // Create minorGrid\n attrMinor = {};\n Type.mergeAttr(attrMinor, attrGrid, true, true);\n Type.mergeAttr(attrMinor, attrGrid.minor, true, true);\n if (attrMinor.id === attrMajor.id) {\n attrMinor.id = majorGrid.id + '_minor';\n }\n if (attrMinor.name === attrMajor.name) {\n attrMinor.name = majorGrid.name + '_minor';\n }\n minorGrid = board.create('curve', [[null], [null]], attrMinor);\n minorGrid.elType = 'grid';\n minorGrid.type = Const.OBJECT_TYPE_GRID;\n\n majorGrid.minorGrid = minorGrid;\n minorGrid.majorGrid = majorGrid;\n\n majorGrid.hasPoint = function () { return false; };\n minorGrid.hasPoint = function () { return false; };\n\n majorGrid.inherits.push(minorGrid);\n\n majorGrid.updateDataArray = function () {\n var bbox = this.board.getBoundingBox(),\n startX, startY,\n x, y, m,\n dataArr,\n finite, delta,\n\n gridX = this.evalVisProp('gridx'), // for backwards compatibility\n gridY = this.evalVisProp('gridy'), // for backwards compatibility\n face = this.evalVisProp('face'),\n drawZero = this.evalVisProp('drawzero'),\n drawZeroOrigin = drawZero === true || (Type.isObject(drawZero) && this.eval(drawZero.origin) === true),\n drawZeroX = drawZero === true || (Type.isObject(drawZero) && this.eval(drawZero.x) === true),\n drawZeroY = drawZero === true || (Type.isObject(drawZero) && this.eval(drawZero.y) === true),\n\n includeBoundaries = this.evalVisProp('includeboundaries'),\n forceSquare = this.evalVisProp('forcesquare');\n\n this.dataX = [];\n this.dataY = [];\n\n // set global majorStep\n majorStep = this.evalVisProp('majorstep');\n if (!Type.isArray(majorStep)) {\n majorStep = [majorStep, majorStep];\n }\n if (majorStep.length < 2) {\n majorStep = [majorStep[0], majorStep[0]];\n }\n if (Type.exists(gridX)) {\n JXG.deprecated(\"gridX\", 'majorStep');\n majorStep[0] = gridX;\n }\n if (Type.exists(gridY)) {\n JXG.deprecated(\"gridY\", 'majorStep');\n majorStep[1] = gridY;\n }\n\n if (majorStep[0] === 'auto') {\n // majorStep[0] = 1; // parentAxes[0] may not be defined\n // Prevent too many grid lines if majorstep:'auto'\n delta = Math.pow(10, Math.floor(Math.log(50 / this.board.unitX) / Math.LN10));\n majorStep[0] = delta;\n\n if (Type.exists(parentAxes[0])) {\n majorStep[0] = parentAxes[0].ticks[0].getDistanceMajorTicks();\n }\n } else {\n // This allows the value to have unit px, abs, % or fr.\n majorStep[0] = Type.parseNumber(majorStep[0], Math.abs(bbox[1] - bbox[3]), 1 / this.board.unitX);\n }\n\n if (majorStep[1] === 'auto') {\n // majorStep[1] = 1; // parentAxes[1] may not be defined\n // Prevent too many grid lines if majorstep:'auto'\n delta = Math.pow(10, Math.floor(Math.log(50 / this.board.unitY) / Math.LN10));\n majorStep[1] = delta;\n\n if (Type.exists(parentAxes[1])) {\n majorStep[1] = parentAxes[1].ticks[0].getDistanceMajorTicks();\n }\n } else {\n // This allows the value to have unit px, abs, % or fr.\n majorStep[1] = Type.parseNumber(majorStep[1], Math.abs(bbox[0] - bbox[2]), 1 / this.board.unitY);\n }\n\n if (forceSquare === 'min' || forceSquare === true) {\n if (majorStep[0] * this.board.unitX <= majorStep[1] * this.board.unitY) { // compare px-values\n majorStep[1] = majorStep[0] / this.board.unitY * this.board.unitX;\n } else {\n majorStep[0] = majorStep[1] / this.board.unitX * this.board.unitY;\n }\n } else if (forceSquare === 'max') {\n if (majorStep[0] * this.board.unitX <= majorStep[1] * this.board.unitY) { // compare px-values\n majorStep[0] = majorStep[1] / this.board.unitX * this.board.unitY;\n } else {\n majorStep[1] = majorStep[0] / this.board.unitY * this.board.unitX;\n }\n }\n\n // Set global majorSize\n majorSize = this.evalVisProp('size');\n if (!Type.isArray(majorSize)) {\n majorSize = [majorSize, majorSize];\n }\n if (majorSize.length < 2) {\n majorSize = [majorSize[0], majorSize[0]];\n }\n\n // Here comes a hack:\n // \"majorsize\" is filled by the attribute \"size\" which is usually considered\n // as pixel value. However, usually a number value for size is\n // considered to be in pixel, while parseNumber expects user coords.\n // Therefore, we have to add 'px'.\n if (Type.isNumber(majorSize[0], true)) {\n majorSize[0] = majorSize[0] + 'px';\n }\n if (Type.isNumber(majorSize[1], true)) {\n majorSize[1] = majorSize[1] + 'px';\n }\n majorSize[0] = Type.parseNumber(majorSize[0], majorStep[0], 1 / this.board.unitX);\n majorSize[1] = Type.parseNumber(majorSize[1], majorStep[1], 1 / this.board.unitY);\n majorRadius[0] = majorSize[0] / 2;\n majorRadius[1] = majorSize[1] / 2;\n\n // calculate start position of curve\n startX = Mat.roundToStep(bbox[0], majorStep[0]);\n startY = Mat.roundToStep(bbox[1], majorStep[1]);\n\n // check if number of grid elements side by side is not too large\n finite = isFinite(startX) && isFinite(startY) &&\n isFinite(bbox[2]) && isFinite(bbox[3]) &&\n Math.abs(bbox[2]) < Math.abs(majorStep[0] * maxLines) &&\n Math.abs(bbox[3]) < Math.abs(majorStep[1] * maxLines);\n\n // POI finite = false means that no grid is drawn. Should we change this?\n // Draw grid elements\n if (face.toLowerCase() === 'line') {\n m = majorGrid.evalVisProp('margin');\n for (y = startY; finite && y >= bbox[3]; y -= majorStep[1]) {\n if (\n (!drawZeroOrigin && Math.abs(y) < eps) ||\n (!drawZeroY && Math.abs(y) < eps) ||\n (!includeBoundaries && (\n y <= bbox[3] + majorRadius[1] ||\n y >= bbox[1] - majorRadius[1]\n ))\n ) {\n continue;\n }\n\n dataArr = [\n [bbox[0] - m / majorGrid.board.unitX, bbox[2] + m / majorGrid.board.unitX, NaN],\n [y, y, NaN]\n ];\n // Push is drastically faster than concat\n Type.concat(this.dataX, dataArr[0]);\n Type.concat(this.dataY, dataArr[1]);\n }\n for (x = startX; finite && x <= bbox[2]; x += majorStep[0]) {\n if (\n (!drawZeroOrigin && Math.abs(x) < eps) ||\n (!drawZeroX && Math.abs(x) < eps) ||\n (!includeBoundaries && (\n x <= bbox[0] + majorRadius[0] ||\n x >= bbox[2] - majorRadius[0]\n ))\n ) {\n continue;\n }\n\n dataArr = [\n [x, x, NaN],\n [bbox[1] + m / majorGrid.board.unitY, bbox[3] - m / majorGrid.board.unitY, NaN]\n ];\n // Push is drastically faster than concat\n Type.concat(this.dataX, dataArr[0]);\n Type.concat(this.dataY, dataArr[1]);\n }\n } else {\n for (y = startY; finite && y >= bbox[3]; y -= majorStep[1]) {\n for (x = startX; finite && x <= bbox[2]; x += majorStep[0]) {\n\n if (\n (!drawZeroOrigin && Math.abs(y) < eps && Math.abs(x) < eps) ||\n (!drawZeroX && Math.abs(y) < eps && Math.abs(x) >= eps) ||\n (!drawZeroY && Math.abs(x) < eps && Math.abs(y) >= eps) ||\n (!includeBoundaries && (\n x <= bbox[0] + majorRadius[0] ||\n x >= bbox[2] - majorRadius[0] ||\n y <= bbox[3] + majorRadius[1] ||\n y >= bbox[1] - majorRadius[1]\n ))\n ) {\n continue;\n }\n\n dataArr = createDataArrayForFace(face, majorGrid, x, y, majorRadius[0], majorRadius[1], bbox);\n // Push is drastically faster than concat\n Type.concat(this.dataX, dataArr[0]);\n Type.concat(this.dataY, dataArr[1]);\n }\n }\n }\n };\n\n minorGrid.updateDataArray = function () {\n var bbox = this.board.getBoundingBox(),\n startX, startY,\n x, y, m,\n dataArr,\n finite,\n\n minorStep = [],\n minorRadius = [],\n XdisTo0, XdisFrom0, YdisTo0, YdisFrom0, // {Number} absolute distances of minor grid elements center to next major grid element center\n dis0To, dis1To, dis2To, dis3To, // {Number} absolute distances of borders of the boundingBox to the next major grid element.\n dis0From, dis1From, dis2From, dis3From,\n\n minorElements = this.evalVisProp('minorelements'),\n minorSize = this.evalVisProp('size'),\n minorFace = this.evalVisProp('face'),\n minorDrawZero = this.evalVisProp('drawzero'),\n minorDrawZeroX = minorDrawZero === true || (Type.isObject(minorDrawZero) && this.eval(minorDrawZero.x) === true),\n minorDrawZeroY = minorDrawZero === true || (Type.isObject(minorDrawZero) && this.eval(minorDrawZero.y) === true),\n\n majorFace = this.majorGrid.evalVisProp('face'),\n majorDrawZero = this.majorGrid.evalVisProp('drawzero'),\n majorDrawZeroOrigin = majorDrawZero === true || (Type.isObject(majorDrawZero) && this.eval(majorDrawZero.origin) === true),\n majorDrawZeroX = majorDrawZero === true || (Type.isObject(majorDrawZero) && this.eval(majorDrawZero.x) === true),\n majorDrawZeroY = majorDrawZero === true || (Type.isObject(majorDrawZero) && this.eval(majorDrawZero.y) === true),\n\n includeBoundaries = this.evalVisProp('includeboundaries');\n\n this.dataX = [];\n this.dataY = [];\n\n // set minorStep\n // minorElements can be 'auto' or a number (also a number like '20')\n if (!Type.isArray(minorElements)) {\n minorElements = [minorElements, minorElements];\n }\n if (minorElements.length < 2) {\n minorElements = [minorElements[0], minorElements[0]];\n }\n\n if (Type.isNumber(minorElements[0], true)) {\n minorElements[0] = parseFloat(minorElements[0]);\n\n } else { // minorElements[0] === 'auto'\n minorElements[0] = 3; // parentAxes[0] may not be defined\n if (Type.exists(parentAxes[0])) {\n minorElements[0] = parentAxes[0].eval(parentAxes[0].getAttribute('ticks').minorticks);\n }\n }\n minorStep[0] = majorStep[0] / (minorElements[0] + 1);\n\n if (Type.isNumber(minorElements[1], true)) {\n minorElements[1] = parseFloat(minorElements[1]);\n\n } else { // minorElements[1] === 'auto'\n minorElements[1] = 3; // parentAxes[1] may not be defined\n if (Type.exists(parentAxes[1])) {\n minorElements[1] = parentAxes[1].eval(parentAxes[1].getAttribute('ticks').minorticks);\n }\n }\n minorStep[1] = majorStep[1] / (minorElements[1] + 1);\n\n // set global minorSize\n if (!Type.isArray(minorSize)) {\n minorSize = [minorSize, minorSize];\n }\n if (minorSize.length < 2) {\n minorSize = [minorSize[0], minorSize[0]];\n }\n\n // minorRadius = [\n // Type.parseNumber(minorSize[0], minorStep[0] * 0.5, 1 / this.board.unitX),\n // Type.parseNumber(minorSize[0], minorStep[0] * 0.5, 1 / this.board.unitY)\n // ];\n\n // Here comes a hack:\n // \"minorsize\" is filled by the attribute \"size\" which is usually considered\n // as pixel value. However, usually a number value for size is\n // considered to be in pixel, while parseNumber expects user coords.\n // Therefore, we have to add 'px'.\n if (Type.isNumber(minorSize[0], true)) {\n minorSize[0] = minorSize[0] + 'px';\n }\n if (Type.isNumber(minorSize[1], true)) {\n minorSize[1] = minorSize[1] + 'px';\n }\n minorSize[0] = Type.parseNumber(minorSize[0], minorStep[0], 1 / this.board.unitX);\n minorSize[1] = Type.parseNumber(minorSize[1], minorStep[1], 1 / this.board.unitY);\n minorRadius[0] = minorSize[0] * 0.5;\n minorRadius[1] = minorSize[1] * 0.5;\n\n // calculate start position of curve\n startX = Mat.roundToStep(bbox[0], minorStep[0]);\n startY = Mat.roundToStep(bbox[1], minorStep[1]);\n\n // check if number of grid elements side by side is not too large\n finite = isFinite(startX) && isFinite(startY) &&\n isFinite(bbox[2]) && isFinite(bbox[3]) &&\n Math.abs(bbox[2]) <= Math.abs(minorStep[0] * maxLines) &&\n Math.abs(bbox[3]) < Math.abs(minorStep[1] * maxLines);\n\n // POI finite = false means that no grid is drawn. Should we change this?\n\n // draw grid elements\n if (minorFace.toLowerCase() !== 'line') {\n for (y = startY; finite && y >= bbox[3]; y -= minorStep[1]) {\n for (x = startX; finite && x <= bbox[2]; x += minorStep[0]) {\n\n /* explanation:\n |<___XdisTo0___><___________XdisFrom0___________>\n | . . .\n ____|____ . . _________\n | | | ____ ____ | |\n | | | | | | | | |\n | | | |____| |____| | |\n |____|____| | | . |_________|\n | | . \\ . .\n | \\ . minorRadius[0] . .\n | majorRadius[0] . . .\n | . . .\n |<-----------> . . .\n | \\ . . .\n | XdisTo0 - minorRadius[0] <= majorRadius[0] ? -> exclude\n | . . .\n | . <--------------------------->\n | \\\n | XdisFrom0 - minorRadius[0] <= majorRadius[0] ? -> exclude\n |\n -——---|————————-————---|----------------|---------------|-------->\n |\n |<______________________majorStep[0]_____________________>\n |\n |<__minorStep[0]____><__minorStep[0]_____><__minorStep[0]_____>\n |\n |\n */\n XdisTo0 = Mat.roundToStep(Math.abs(x), majorStep[0]);\n XdisTo0 = Math.abs(XdisTo0 - Math.abs(x));\n XdisFrom0 = majorStep[0] - XdisTo0;\n\n YdisTo0 = Mat.roundToStep(Math.abs(y), majorStep[1]);\n YdisTo0 = Math.abs(YdisTo0 - Math.abs(y));\n YdisFrom0 = majorStep[1] - YdisTo0;\n\n if (majorFace === 'line') {\n // for majorFace 'line' do not draw minor grid elements on lines\n if (\n XdisTo0 - minorRadius[0] - majorRadius[0] < eps ||\n XdisFrom0 - minorRadius[0] - majorRadius[0] < eps ||\n YdisTo0 - minorRadius[1] - majorRadius[1] < eps ||\n YdisFrom0 - minorRadius[1] - majorRadius[1] < eps\n ) {\n continue;\n }\n\n } else {\n if ((\n XdisTo0 - minorRadius[0] - majorRadius[0] < eps ||\n XdisFrom0 - minorRadius[0] - majorRadius[0] < eps\n ) && (\n YdisTo0 - minorRadius[1] - majorRadius[1] < eps ||\n YdisFrom0 - minorRadius[1] - majorRadius[1] < eps\n )) {\n // if major grid elements (on 0 or axes) are not existing, minor grid elements have to exist. Otherwise:\n if ((\n majorDrawZeroOrigin ||\n majorRadius[1] - Math.abs(y) + minorRadius[1] < eps ||\n majorRadius[0] - Math.abs(x) + minorRadius[0] < eps\n ) && (\n majorDrawZeroX ||\n majorRadius[1] - Math.abs(y) + minorRadius[1] < eps ||\n majorRadius[0] + Math.abs(x) - minorRadius[0] < eps\n ) && (\n majorDrawZeroY ||\n majorRadius[0] - Math.abs(x) + minorRadius[0] < eps ||\n majorRadius[1] + Math.abs(y) - minorRadius[1] < eps\n )) {\n continue;\n }\n }\n }\n if (\n (!minorDrawZeroY && Math.abs(x) < eps) ||\n (!minorDrawZeroX && Math.abs(y) < eps)\n ) {\n continue;\n }\n\n /* explanation of condition below:\n\n | __dis2To___> _dis2From_ // dis2To bzw. dis2From >= majorRadius[0]\n | __/_ \\/ _\\__\n | | | [] > | |\n | |____| > |____|\n | >\n | >\n | x-minorSize[0] > bbox[2]\n 0 . >/\n -——|————————-————.-.——.—>\n | . . . >\n | . . . >\n | . . . > dis2From (<= majorRadius[0])\n | . . .__/\\____\n | . . | > |\n | . [] | > \\/ |\n | . | > /\\ |\n | . |_>______|\n | . . >\n | . . >\n | . bbox[2]+dis2From-majorRadius[0]\n | . >\n | .______>_\n | | > |\n | [] | \\/ > |\n | | /\\ > |\n | |______>_|\n | . \\_/\n | . dis2To (<= majorRadius[0])\n | . >\n | . >\n | bbox[2]-dis2To-majorRadius[0]\n */\n dis0To = Math.abs(bbox[0] % majorStep[0]);\n dis1To = Math.abs(bbox[1] % majorStep[1]);\n dis2To = Math.abs(bbox[2] % majorStep[0]);\n dis3To = Math.abs(bbox[3] % majorStep[1]);\n dis0From = majorStep[0] - dis0To;\n dis1From = majorStep[1] - dis1To;\n dis2From = majorStep[0] - dis2To;\n dis3From = majorStep[1] - dis3To;\n\n if (\n !includeBoundaries && (\n (x - minorRadius[0] - bbox[0] - majorRadius[0] + dis0From < eps && dis0From - majorRadius[0] < eps) ||\n (x - minorRadius[0] - bbox[0] - majorRadius[0] - dis0To < eps && dis0To - majorRadius[0] < eps) ||\n (-x - minorRadius[0] + bbox[2] - majorRadius[0] + dis2From < eps && dis2From - majorRadius[0] < eps) ||\n (-x - minorRadius[0] + bbox[2] - majorRadius[0] - dis2To < eps && dis2To - majorRadius[0] < eps) ||\n\n (-y - minorRadius[1] + bbox[1] - majorRadius[1] + dis1From < eps && dis1From - majorRadius[1] < eps) ||\n (-y - minorRadius[1] + bbox[1] - majorRadius[1] - dis1To < eps && dis1To - majorRadius[1] < eps) ||\n (y - minorRadius[1] - bbox[3] - majorRadius[1] + dis3From < eps && dis3From - majorRadius[1] < eps) ||\n (y - minorRadius[1] - bbox[3] - majorRadius[1] - dis3To < eps && dis3To - majorRadius[1] < eps) ||\n\n (-y - minorRadius[1] + bbox[1] < eps) ||\n (x - minorRadius[0] - bbox[0] < eps) ||\n (y - minorRadius[1] - bbox[3] < eps) ||\n (-x - minorRadius[0] + bbox[2] < eps)\n )\n ) {\n continue;\n }\n\n dataArr = createDataArrayForFace(minorFace, minorGrid, x, y, minorRadius[0], minorRadius[1], bbox);\n Type.concat(this.dataX, dataArr[0]);\n Type.concat(this.dataY, dataArr[1]);\n }\n }\n } else {\n m = minorGrid.evalVisProp('margin');\n for (y = startY; finite && y >= bbox[3]; y -= minorStep[1]) {\n YdisTo0 = Mat.roundToStep(Math.abs(y), majorStep[1]);\n YdisTo0 = Math.abs(YdisTo0 - Math.abs(y));\n YdisFrom0 = majorStep[1] - YdisTo0;\n\n if (majorFace === 'line') {\n // for majorFace 'line' do not draw minor grid elements on lines\n if (\n YdisTo0 - minorRadius[1] - majorRadius[1] < eps ||\n YdisFrom0 - minorRadius[1] - majorRadius[1] < eps\n ) {\n continue;\n }\n\n } else {\n if ((\n YdisTo0 - minorRadius[1] - majorRadius[1] < eps ||\n YdisFrom0 - minorRadius[1] - majorRadius[1] < eps\n )) {\n // if major grid elements (on 0 or axes) are not existing, minor grid elements have to exist. Otherwise:\n if ((\n majorDrawZeroOrigin ||\n majorRadius[1] - Math.abs(y) + minorRadius[1] < eps\n ) && (\n majorDrawZeroX ||\n majorRadius[1] - Math.abs(y) + minorRadius[1] < eps\n ) && (\n majorDrawZeroY ||\n majorRadius[1] + Math.abs(y) - minorRadius[1] < eps\n )) {\n continue;\n }\n }\n }\n if (!minorDrawZeroX && Math.abs(y) < eps) {\n continue;\n }\n\n dis0To = Math.abs(bbox[0] % majorStep[0]);\n dis1To = Math.abs(bbox[1] % majorStep[1]);\n dis2To = Math.abs(bbox[2] % majorStep[0]);\n dis3To = Math.abs(bbox[3] % majorStep[1]);\n dis0From = majorStep[0] - dis0To;\n dis1From = majorStep[1] - dis1To;\n dis2From = majorStep[0] - dis2To;\n dis3From = majorStep[1] - dis3To;\n\n if (\n !includeBoundaries && (\n (-y - minorRadius[1] + bbox[1] - majorRadius[1] + dis1From < eps && dis1From - majorRadius[1] < eps) ||\n (-y - minorRadius[1] + bbox[1] - majorRadius[1] - dis1To < eps && dis1To - majorRadius[1] < eps) ||\n (y - minorRadius[1] - bbox[3] - majorRadius[1] + dis3From < eps && dis3From - majorRadius[1] < eps) ||\n (y - minorRadius[1] - bbox[3] - majorRadius[1] - dis3To < eps && dis3To - majorRadius[1] < eps) ||\n\n (-y - minorRadius[1] + bbox[1] < eps) ||\n (y - minorRadius[1] - bbox[3] < eps)\n )\n ) {\n continue;\n }\n\n dataArr = [\n [bbox[0] - m / minorGrid.board.unitX, bbox[2] + m / minorGrid.board.unitX, NaN],\n [y, y, NaN]\n ];\n Type.concat(this.dataX, dataArr[0]);\n Type.concat(this.dataY, dataArr[1]);\n }\n for (x = startX; finite && x <= bbox[2]; x += minorStep[0]) {\n XdisTo0 = Mat.roundToStep(Math.abs(x), majorStep[0]);\n XdisTo0 = Math.abs(XdisTo0 - Math.abs(x));\n XdisFrom0 = majorStep[0] - XdisTo0;\n\n if (majorFace === 'line') {\n // for majorFace 'line' do not draw minor grid elements on lines\n if (\n XdisTo0 - minorRadius[0] - majorRadius[0] < eps ||\n XdisFrom0 - minorRadius[0] - majorRadius[0] < eps\n ) {\n continue;\n }\n\n } else {\n if ((\n XdisTo0 - minorRadius[0] - majorRadius[0] < eps ||\n XdisFrom0 - minorRadius[0] - majorRadius[0] < eps\n )) {\n // if major grid elements (on 0 or axes) are not existing, minor grid elements have to exist. Otherwise:\n if ((\n majorDrawZeroOrigin ||\n majorRadius[0] - Math.abs(x) + minorRadius[0] < eps\n ) && (\n majorDrawZeroX ||\n majorRadius[0] + Math.abs(x) - minorRadius[0] < eps\n ) && (\n majorDrawZeroY ||\n majorRadius[0] - Math.abs(x) + minorRadius[0] < eps\n )) {\n continue;\n }\n }\n }\n if (!minorDrawZeroY && Math.abs(x) < eps) {\n continue;\n }\n\n dis0To = Math.abs(bbox[0] % majorStep[0]);\n dis1To = Math.abs(bbox[1] % majorStep[1]);\n dis2To = Math.abs(bbox[2] % majorStep[0]);\n dis3To = Math.abs(bbox[3] % majorStep[1]);\n dis0From = majorStep[0] - dis0To;\n dis1From = majorStep[1] - dis1To;\n dis2From = majorStep[0] - dis2To;\n dis3From = majorStep[1] - dis3To;\n\n if (\n !includeBoundaries && (\n (x - minorRadius[0] - bbox[0] - majorRadius[0] + dis0From < eps && dis0From - majorRadius[0] < eps) ||\n (x - minorRadius[0] - bbox[0] - majorRadius[0] - dis0To < eps && dis0To - majorRadius[0] < eps) ||\n (-x - minorRadius[0] + bbox[2] - majorRadius[0] + dis2From < eps && dis2From - majorRadius[0] < eps) ||\n (-x - minorRadius[0] + bbox[2] - majorRadius[0] - dis2To < eps && dis2To - majorRadius[0] < eps) ||\n\n (x - minorRadius[0] - bbox[0] < eps) ||\n (-x - minorRadius[0] + bbox[2] < eps)\n )\n ) {\n continue;\n }\n\n dataArr = [\n [x, x, NaN],\n [bbox[1] + m / minorGrid.board.unitY, bbox[3] - m / minorGrid.board.unitY, NaN]\n ];\n Type.concat(this.dataX, dataArr[0]);\n Type.concat(this.dataY, dataArr[1]);\n }\n }\n };\n\n board.grids.push(majorGrid);\n board.grids.push(minorGrid);\n\n minorGrid.dump = false;\n\n majorGrid.getParents = minorGrid.getParents = function() {\n return parentAxes.slice();\n };\n\n return majorGrid;\n};\n\nJXG.registerElement(\"grid\", JXG.createGrid);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n * @example\n * var p0 = board.create('point', [-3, -2]),\n * im = board.create('image', ['https://jsxgraph.org/distrib/images/uccellino.jpg',\n * [function(){ return p0.X(); }, function(){ return p0.Y(); }],\n * [3,3]]),\n * p1 = board.create('point', [1, 2]);\n *\n * im.setSize(function(){ return p1.X() - p0.X(); }, function(){ return p1.Y() - p0.Y(); });\n * board.update();\n *\n * \n * \n *\n */\n setSize: function (width, height) {\n this.W = Type.createFunction(width, this.board, \"\");\n this.H = Type.createFunction(height, this.board, \"\");\n this.addParentsFromJCFunctions([this.W, this.H]);\n // this.fullUpdate();\n\n return this;\n },\n\n /**\n * Returns the width of the image in user coordinates.\n * @returns {number} width of the image in user coordinates\n */\n W: function () {}, // Needed for docs, defined in constructor\n\n /**\n * Returns the height of the image in user coordinates.\n * @returns {number} height of the image in user coordinates\n */\n H: function () {} // Needed for docs, defined in constructor\n }\n);\n\n/**\n * @class Display of an external image.\n * @pseudo\n * @name Image\n * @type JXG.Image\n * @augments JXG.Image\n * @constructor\n * @constructor\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {string,function_Array_Array} url,coords,size url defines the location of the image data. The array coords contains the user coordinates\n * of the lower left corner of the image.\n * It can consist of two or three elements of type number, a string containing a GEONExT\n * constraint, or a function which takes no parameter and returns a number. Every element determines one coordinate. If a coordinate is\n * given by a number, the number determines the initial position of a free image. If given by a string or a function that coordinate will be constrained\n * that means the user won't be able to change the image's position directly by mouse because it will be calculated automatically depending on the string\n * or the function's return value. If two parent elements are given the coordinates will be interpreted as 2D affine Euclidean coordinates, if three such\n * parent elements are given they will be interpreted as homogeneous coordinates.\n * \n * \n */\nJXG.createImage = function (board, parents, attributes) {\n var attr,\n im,\n url = parents[0],\n coords = parents[1],\n size = parents[2];\n\n attr = Type.copyAttributes(attributes, board.options, 'image');\n im = CoordsElement.create(JXG.Image, board, coords, attr, url, size);\n if (!im) {\n throw new Error(\n \"JSXGraph: Can't create image with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [x,y], [z,x,y], [element,transformation]\"\n );\n }\n\n if (attr.rotate !== 0) {\n // This is the default value, i.e. no rotation\n im.addRotation(attr.rotate);\n }\n\n return im;\n};\n\nJXG.registerElement(\"image\", JXG.createImage);\n\nexport default JXG.Image;\n// export default {\n// Image: JXG.Image,\n// createImage: JXG.createImage\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n * @example\n * // Create a slider taking integer values between 1 and 5. Initial value is 3.\n * var s = board.create('slider', [[1, 3], [3, 1], [0, 3, 5]], {\n * snapWidth: 1,\n * minTicksDistance: 60,\n * drawLabels: false\n * });\n * \n * \n * @example\n * // Draggable slider\n * var s1 = board.create('slider', [[-3, 1], [2, 1],[-10, 1, 10]], {\n * visible: true,\n * snapWidth: 2,\n * point1: {fixed: false},\n * point2: {fixed: false},\n * baseline: {fixed: false, needsRegularUpdate: true}\n * });\n *\n * \n * \n *\n * @example\n * // Set the slider by clicking on the base line: attribute 'moveOnUp'\n * var s1 = board.create('slider', [[-3,1], [2,1],[-10,1,10]], {\n * snapWidth: 2,\n * moveOnUp: true // default value\n * });\n *\n * \n * \n *\n * @example\n * // Set colors\n * var sl = board.create('slider', [[-3, 1], [1, 1], [-10, 1, 10]], {\n *\n * baseline: { strokeColor: 'blue'},\n * highline: { strokeColor: 'red'},\n * fillColor: 'yellow',\n * label: {fontSize: 24, strokeColor: 'orange'},\n * name: 'xyz', // Not shown, if suffixLabel is set\n * suffixLabel: 'x = ',\n * postLabel: ' u'\n *\n * });\n *\n * \n * \n *\n * @example\n * // Create a \"frozen\" slider\n * var sli = board.create('slider', [[-4, 4], [-1.5, 4], [-10, 1, 10]], {\n * name:'a',\n * frozen: true\n * });\n *\n * \n * \n *\n * @example\n * // Use MathJax for slider label (don't forget to load MathJax)\n * var s = board.create('slider', [[-3, 2], [2, 2], [-10, 1, 10]], {\n * name: 'A^{(2)}',\n * suffixLabel: '\\\\(A^{(2)} = ',\n * unitLabel: ' \\\\;km/h ',\n * postLabel: '\\\\)',\n * label: {useMathJax: true}\n * });\n *\n * \n * \n * \n *\n *\n */\nJXG.createSlider = function (board, parents, attributes) {\n var pos0, pos1,\n smin, start, smax, diff,\n p1, p2, p3, l1, l2,\n ticks, ti, t,\n startx, starty,\n withText, withTicks,\n snapValues, snapValueDistance,\n snapWidth, sw, s,\n attr;\n\n attr = Type.copyAttributes(attributes, board.options, 'slider');\n withTicks = attr.withticks;\n withText = attr.withlabel;\n snapWidth = attr.snapwidth;\n snapValues = attr.snapvalues;\n snapValueDistance = attr.snapvaluedistance;\n\n // Start point\n p1 = board.create(\"point\", parents[0], attr.point1);\n\n // End point\n p2 = board.create(\"point\", parents[1], attr.point2);\n //g = board.create('group', [p1, p2]);\n\n // Base line\n l1 = board.create(\"segment\", [p1, p2], attr.baseline);\n\n // This is required for a correct projection of the glider onto the segment below\n l1.updateStdform();\n\n pos0 = p1.coords.usrCoords.slice(1);\n pos1 = p2.coords.usrCoords.slice(1);\n smin = parents[2][0];\n start = parents[2][1];\n smax = parents[2][2];\n diff = smax - smin;\n\n sw = Type.evaluate(snapWidth);\n s = sw === -1 ?\n start :\n Math.round((start - smin)/ sw) * sw + smin;\n // Math.round(start / sw) * sw;\n startx = pos0[0] + ((pos1[0] - pos0[0]) * (s - smin)) / (smax - smin);\n starty = pos0[1] + ((pos1[1] - pos0[1]) * (s - smin)) / (smax - smin);\n\n // glider point\n // attr = Type.copyAttributes(attributes, board.options, 'slider');\n // overwrite this in any case; the sliders label is a special text element, not the gliders label.\n // this will be set back to true after the text was created (and only if withlabel was true initially).\n attr.withlabel = false;\n // gliders set snapwidth=-1 by default (i.e. deactivate them)\n p3 = board.create(\"glider\", [startx, starty, l1], attr);\n p3.setAttribute({ snapwidth: snapWidth, snapvalues: snapValues, snapvaluedistance: snapValueDistance });\n\n // Segment from start point to glider point: highline\n // attr = Type.copyAttributes(attributes, board.options, \"slider\", 'highline');\n l2 = board.create(\"segment\", [p1, p3], attr.highline);\n\n /**\n * Returns the current slider value.\n * @memberOf Slider.prototype\n * @name Value\n * @function\n * @returns {Number}\n */\n p3.Value = function () {\n var d = this._smax - this._smin,\n ev_sw = this.evalVisProp('snapwidth');\n\n return ev_sw === -1\n ? this.position * d + this._smin\n : Math.round((this.position * d) / ev_sw) * ev_sw + this._smin;\n };\n\n /**\n * End value of the slider range.\n * @memberOf Slider.prototype\n * @name _smax\n * @type Number\n */\n p3._smax = smax;\n\n /**\n * Start value of the slider range.\n * @memberOf Slider.prototype\n * @name _smin\n * @type Number\n */\n p3._smin = smin;\n\n /**\n * Sets the maximum value of the slider.\n * @memberOf Slider.prototype\n * @function\n * @name setMax\n * @param {Number} val New maximum value\n * @returns {Object} this object\n */\n p3.setMax = function (val) {\n this._smax = val;\n return this;\n };\n\n /**\n * Sets the value of the slider. This call must be followed\n * by a board update call.\n * @memberOf Slider.prototype\n * @name setValue\n * @function\n * @param {Number} val New value\n * @returns {Object} this object\n */\n p3.setValue = function (val) {\n var d = this._smax - this._smin;\n\n if (Math.abs(d) > Mat.eps) {\n this.position = (val - this._smin) / d;\n } else {\n this.position = 0.0; //this._smin;\n }\n this.position = Math.max(0.0, Math.min(1.0, this.position));\n return this;\n };\n\n /**\n * Sets the minimum value of the slider.\n * @memberOf Slider.prototype\n * @name setMin\n * @function\n * @param {Number} val New minimum value\n * @returns {Object} this object\n */\n p3.setMin = function (val) {\n this._smin = val;\n return this;\n };\n\n if (withText) {\n // attr = Type.copyAttributes(attributes, board.options, 'slider', 'label');\n t = board.create('text', [\n function () {\n return (p2.X() - p1.X()) * 0.05 + p2.X();\n },\n function () {\n return (p2.Y() - p1.Y()) * 0.05 + p2.Y();\n },\n function () {\n var n,\n d = p3.evalVisProp('digits'),\n sl = p3.evalVisProp('suffixlabel'),\n ul = p3.evalVisProp('unitlabel'),\n pl = p3.evalVisProp('postlabel');\n\n if (d === 2 && p3.evalVisProp('precision') !== 2) {\n // Backwards compatibility\n d = p3.evalVisProp('precision');\n }\n\n if (sl !== null) {\n n = sl;\n } else if (p3.name && p3.name !== \"\") {\n n = p3.name + \" = \";\n } else {\n n = \"\";\n }\n\n if (p3.useLocale()) {\n n += p3.formatNumberLocale(p3.Value(), d);\n } else {\n n += Type.toFixed(p3.Value(), d);\n }\n\n if (ul !== null) {\n n += ul;\n }\n if (pl !== null) {\n n += pl;\n }\n\n return n;\n }\n ],\n attr.label\n );\n\n /**\n * The text element to the right of the slider, indicating its current value.\n * @memberOf Slider.prototype\n * @name label\n * @type JXG.Text\n */\n p3.label = t;\n\n // reset the withlabel attribute\n p3.visProp.withlabel = true;\n p3.hasLabel = true;\n p3.inherits.push(t);\n t.addParents(p3);\n p3.addChild(t);\n }\n\n /**\n * Start point of the base line.\n * @memberOf Slider.prototype\n * @name point1\n * @type JXG.Point\n */\n p3.point1 = p1;\n\n /**\n * End point of the base line.\n * @memberOf Slider.prototype\n * @name point2\n * @type JXG.Point\n */\n p3.point2 = p2;\n\n /**\n * The baseline the glider is bound to.\n * @memberOf Slider.prototype\n * @name baseline\n * @type JXG.Line\n */\n p3.baseline = l1;\n\n /**\n * A line on top of the baseline, indicating the slider's progress.\n * @memberOf Slider.prototype\n * @name highline\n * @type JXG.Line\n */\n p3.highline = l2;\n\n if (withTicks) {\n // Function to generate correct label texts\n\n // attr = Type.copyAttributes(attributes, board.options, \"slider\", 'ticks');\n if (!Type.exists(attr.generatelabeltext)) {\n attr.ticks.generateLabelText = function (tick, zero, value) {\n var labelText,\n dFull = p3.point1.Dist(p3.point2),\n smin = p3._smin,\n smax = p3._smax,\n val = (this.getDistanceFromZero(zero, tick) * (smax - smin)) / dFull + smin;\n\n if (dFull < Mat.eps || Math.abs(val) < Mat.eps) {\n // Point is zero\n labelText = '0';\n } else {\n labelText = this.formatLabelText(val);\n }\n return labelText;\n };\n }\n ticks = 2;\n ti = board.create(\n \"ticks\",\n [\n p3.baseline,\n p3.point1.Dist(p1) / ticks,\n\n function (tick) {\n var dFull = p3.point1.Dist(p3.point2),\n d = p3.point1.coords.distance(Const.COORDS_BY_USER, tick);\n\n if (dFull < Mat.eps) {\n return 0;\n }\n\n return (d / dFull) * diff + smin;\n }\n ],\n attr.ticks\n );\n\n /**\n * Ticks give a rough indication about the slider's current value.\n * @memberOf Slider.prototype\n * @name ticks\n * @type JXG.Ticks\n */\n p3.ticks = ti;\n }\n\n // override the point's remove method to ensure the removal of all elements\n p3.remove = function () {\n if (withText) {\n board.removeObject(t);\n }\n\n board.removeObject(l2);\n board.removeObject(l1);\n board.removeObject(p2);\n board.removeObject(p1);\n\n Point.prototype.remove.call(p3);\n };\n\n p1.dump = false;\n p2.dump = false;\n l1.dump = false;\n l2.dump = false;\n if (withText) {\n t.dump = false;\n }\n\n // p3.type = Const.OBJECT_TYPE_SLIDER; // No! type has to be Const.OBJECT_TYPE_GLIDER\n p3.elType = 'slider';\n p3.parents = parents;\n p3.subs = {\n point1: p1,\n point2: p2,\n baseLine: l1,\n highLine: l2\n };\n p3.inherits.push(p1, p2, l1, l2);\n // Remove inherits to avoid circular inherits.\n l1.inherits = [];\n l2.inherits = [];\n\n if (withTicks) {\n ti.dump = false;\n p3.subs.ticks = ti;\n p3.inherits.push(ti);\n }\n\n p3.getParents = function () {\n return [\n this.point1.coords.usrCoords.slice(1),\n this.point2.coords.usrCoords.slice(1),\n [this._smin, this.position * (this._smax - this._smin) + this._smin, this._smax]\n ];\n };\n\n p3.baseline.on(\"up\", function (evt) {\n var pos, c;\n\n if (p3.evalVisProp('moveonup') && !p3.evalVisProp('fixed')) {\n pos = l1.board.getMousePosition(evt, 0);\n c = new Coords(Const.COORDS_BY_SCREEN, pos, this.board);\n p3.moveTo([c.usrCoords[1], c.usrCoords[2]]);\n p3.triggerEventHandlers(['drag'], [evt]);\n }\n });\n\n // This is necessary to show baseline, highline and ticks\n // when opening the board in case the visible attributes are set\n // to 'inherit'.\n p3.prepareUpdate().update();\n if (!board.isSuspendedUpdate) {\n p3.updateVisibility().updateRenderer();\n p3.baseline.prepareUpdate().updateVisibility().updateRenderer(); // prepareUpdate needed because needsRegularUpdate==false\n p3.highline.updateVisibility().updateRenderer();\n if (withTicks) {\n p3.prepareUpdate().ticks.updateVisibility().updateRenderer();\n }\n }\n\n Type.extendInstanceMethodMap(p3, {\n Value: \"Value\",\n setValue: \"setValue\",\n smax: \"_smax\",\n // Max: \"_smax\",\n smin: \"_smin\",\n // Min: \"_smin\",\n setMax: \"setMax\",\n setMin: \"setMin\",\n point1: \"point1\",\n point2: \"point2\",\n baseline: \"baseline\",\n highline: \"highline\",\n ticks: \"ticks\",\n label: \"label\"\n });\n\n return p3;\n};\n\nJXG.registerElement(\"slider\", JXG.createSlider);\n\n// export default {\n// createSlider: JXG.createSlider\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n * \n *
\n *\n * @example\n *\n */\nimport JXG from \"../jxg.js\";\nimport Type from \"../utils/type.js\";\nimport Mat from \"../math/math.js\";\nimport Const from \"../base/constants.js\";\n\n/**\n * Prefix expression parser, i.e. a poor man's parser.\n * This is a simple prefix parser for measurements and expressions of measurements,\n * see {@link Measurement}.\n * An expression is given as\n * \n *
\n * \n *
\n * \n *
\n * @namespace\n *\n * @example\n * ['+', 100, 200]\n * @example\n * var p1 = board.create('point', [1, 1]);\n * var p2 = board.create('point', [1, 3]);\n * var seg = board.create('segment', [[-2,-3], [-2, 3]]);\n *\n * // Valid prefix expression: ['L', seg]\n *\n * @example\n * var p1 = board.create('point', [1, 1]);\n * var p2 = board.create('point', [1, 3]);\n * var seg = board.create('segment', [[-2,-3], [-2, 3]]);\n * var ci = board.create('circle', [p1, 7]);\n *\n * // Valid prefix expression: ['+', ['Radius', ci], ['L', seg]]\n *\n * @example\n * var ang = board.create('angle', [[4, 0], [0, 0], [2, 2]]);\n * // Valid prefix expression: ['V', ang, 'degrees']);\n */\nJXG.PrefixParser = {\n /**\n * Parse a prefix expression and apply an action.\n * @param {array|number} term Expression\n * @param {String} action Determines what to do. So far, the only\n * action available is 'execute', which evaluates the expression.\n * @returns {Number} What ever the action does.\n */\n parse: function (term, action) {\n var method, i, le, res, fun, v;\n\n if (Type.isNumber(term) || Type.isString(term)) {\n return term;\n }\n if (!Type.isArray(term) || term.length < 2) {\n throw new Error('prefixParser.parse: term is not an array, number or string');\n }\n\n method = term[0];\n le = term.length;\n\n if (action === 'execute') {\n if (Type.isInArray(['+', '-', '*', '/'], method)) {\n\n res = this.parse(term[1], action);\n for (i = 2; i < le; i++) {\n v = this.parse(term[i], action);\n switch (method) {\n case '+':\n res += v;\n break;\n case '-':\n res -= v;\n break;\n case '*':\n res *= v;\n break;\n case '/':\n res /= v;\n break;\n default:\n }\n }\n } else if (method === 'exec') {\n fun = term[1];\n v = [];\n for (i = 2; i < le; i++) {\n v.push(this.parse(term[i], action));\n }\n if (Type.exists(Math[fun])) {\n res = Math[fun].apply(this, v);\n } else if (Type.exists(Mat[fun])) {\n res = Mat[fun].apply(this, v);\n } else {\n throw new Error(\"PrefixParser.parse: \" + fun + \" is not allowed\");\n }\n } else {\n fun = term[0];\n\n // Allow shortcut 'V' for 'Value'\n if (fun === 'V') {\n fun = 'Value';\n }\n\n // get coords always with z\n // (its visibility is controlled by the attribute function formatCoords)\n if (fun === 'Coords') {\n term[2] = 'true';\n }\n\n if (!Type.exists(term[1][fun])) {\n throw new Error(\"PrefixParser.parse: \" + fun + \" is not a method of \" + term[1]);\n }\n v = [];\n for (i = 2; i < le; i++) {\n v.push(this.parse(term[i], action));\n }\n res = term[1][fun].apply(term[1], v);\n }\n }\n\n return res;\n },\n\n /**\n * Determine the dimension of the resulting value, i.e. ['L', obj] as well as\n * ['+', ['L', obj1], ['L', obj2]] have dimension 1.\n * \n */\nJXG.createTapemeasure = function (board, parents, attributes) {\n var pos0, pos1, attr, withTicks, withText, digits, li, p1, p2, n, ti;\n\n pos0 = parents[0];\n pos1 = parents[1];\n\n // start point\n attr = Type.copyAttributes(attributes, board.options, \"tapemeasure\", 'point1');\n p1 = board.create(\"point\", pos0, attr);\n\n // end point\n attr = Type.copyAttributes(attributes, board.options, \"tapemeasure\", 'point2');\n p2 = board.create(\"point\", pos1, attr);\n\n p1.setAttribute({ignoredSnapToPoints: [p2.id]});\n p2.setAttribute({ignoredSnapToPoints: [p1.id]});\n\n // tape measure line\n attr = Type.copyAttributes(attributes, board.options, 'tapemeasure');\n withTicks = attr.withticks;\n withText = attr.withlabel;\n digits = attr.digits;\n\n if (digits === 2 && attr.precision !== 2) {\n // Backward compatibility\n digits = attr.precision;\n }\n\n // Below, we will replace the label by the measurement function.\n if (withText) {\n attr.withlabel = true;\n }\n li = board.create(\"segment\", [p1, p2], attr);\n // p1, p2 are already added to li.inherits\n\n if (withText) {\n if (attributes.name && attributes.name !== \"\") {\n n = attributes.name + \" = \";\n } else {\n n = \"\";\n }\n li.label.setText(function () {\n var digits = li.label.evalVisProp('digits');\n\n if (li.label.useLocale()) {\n return n + li.label.formatNumberLocale(p1.Dist(p2), digits);\n }\n return n + Type.toFixed(p1.Dist(p2), digits);\n });\n }\n\n if (withTicks) {\n attr = Type.copyAttributes(attributes, board.options, \"tapemeasure\", 'ticks');\n //ticks = 2;\n ti = board.create(\"ticks\", [li, 0.1], attr);\n li.inherits.push(ti);\n }\n\n // override the segments' remove method to ensure the removal of all elements\n /** @ignore */\n li.remove = function () {\n if (withTicks) {\n li.removeTicks(ti);\n }\n\n board.removeObject(p2);\n board.removeObject(p1);\n\n GeometryElement.prototype.remove.call(this);\n };\n\n /**\n * Returns the length of the tape measure.\n * @name Value\n * @memberOf Tapemeasure.prototype\n * @function\n * @returns {Number} length of tape measure.\n */\n li.Value = function () {\n return p1.Dist(p2);\n };\n\n p1.dump = false;\n p2.dump = false;\n\n li.elType = 'tapemeasure';\n li.getParents = function () {\n return [\n [p1.X(), p1.Y()],\n [p2.X(), p2.Y()]\n ];\n };\n\n li.subs = {\n point1: p1,\n point2: p2\n };\n\n if (withTicks) {\n ti.dump = false;\n }\n\n li.prepareUpdate().update();\n if (!board.isSuspendedUpdate) {\n li.updateVisibility().updateRenderer();\n // The point updates are necessary in case of snapToGrid==true\n li.point1.updateVisibility().updateRenderer();\n li.point2.updateVisibility().updateRenderer();\n }\n\n Type.extendInstanceMethodMap(li, {\n Value: \"Value\"\n });\n\n return li;\n};\n\nJXG.registerElement(\"tapemeasure\", JXG.createTapemeasure);\n\n/**\n * @class Display measurements of geometric elements and the arithmetic operations of measurements.\n * Under the hood this is a text element which has a method Value. The text to be displayed\n * is the result of the evaluation of a prefix expression, see {@link JXG.PrefixParser}.\n * \n * \n *\n * @example\n * var p1 = board.create('point', [1, 1]);\n * var p2 = board.create('point', [1, 3]);\n * var ci1 = board.create('circle', [p1, p2]);\n * var seg = board.create('segment', [[-2,-3], [-2, 3]], { firstArrow: true, lastArrow: true});\n * var sli = board.create('slider', [[-4, 4], [-1.5, 4], [-10, 1, 10]], {name:'a'});\n *\n * var m1 = board.create('measurement', [-6, -2, ['Radius', ci1]], {\n * prefix: 'm1: ',\n * baseUnit: 'cm'\n * });\n *\n * var m2 = board.create('measurement', [-6, -4, ['L', seg]], {\n * prefix: 'm2: ',\n * baseUnit: 'cm'\n * });\n *\n * var m3 = board.create('measurement', [-6, -6, ['V', sli]], {\n * prefix: 'm3: ',\n * baseUnit: 'cm',\n * dim: 1\n * });\n *\n * var m4 = board.create('measurement', [2, -6,\n * ['+', ['V', m1], ['V', m2], ['V', m3]]\n * ], {\n * prefix: 'm4: ',\n * baseUnit: 'cm'\n * });\n *\n * \n * \n *\n */\nJXG.createMeasurement = function (board, parents, attributes) {\n var el, attr,\n x, y, term,\n i;\n\n attr = Type.copyAttributes(attributes, board.options, 'measurement');\n\n x = parents[0];\n y = parents[1];\n term = parents[2];\n\n el = board.create(\"text\", [x, y, ''], attr);\n el.type = Type.OBJECT_TYPE_MEASUREMENT;\n el.elType = 'measurement';\n\n el.Value = function () {\n return Prefix.parse(term, 'execute');\n };\n\n el.Dimension = function () {\n var d = el.evalVisProp('dim');\n\n if (d !== null) {\n return d;\n }\n return Prefix.dimension(term);\n };\n\n el.Unit = function (dimension) {\n var unit = '',\n units = el.evalVisProp('units'),\n dim = dimension,\n dims = {}, i;\n\n if (!Type.exists(dim)) {\n dim = el.Dimension();\n }\n\n if (Type.isArray(dimension)) {\n for (i = 0; i < dimension.length; i++) {\n dims['dim' + dimension[i]] = el.Unit(dimension[i]);\n }\n return dims;\n }\n\n if (Type.isObject(units) && Type.exists(units[dim]) && units[dim] !== false) {\n unit = el.eval(units[dim]);\n } else if (Type.isObject(units) && Type.exists(units['dim' + dim]) && units['dim' + dim] !== false) {\n // In some cases, object keys must not be numbers. This allows key 'dim1' instead of '1'.\n unit = el.eval(units['dim' + dim]);\n } else {\n unit = el.evalVisProp('baseUnit');\n\n if (dim === 0) {\n unit = '';\n } else if (dim > 1 && unit !== '') {\n unit = unit + '^{' + dim + '}';\n }\n }\n\n return unit;\n };\n\n el.getTerm = function () {\n return term;\n };\n\n el.getMethod = function () {\n var method = term[0];\n if (method === 'V') {\n method = 'Value';\n }\n return method;\n };\n\n el.toPrefix = function () {\n return Prefix.toPrefix(term);\n };\n\n el.getParents = function () {\n return Prefix.getParents(term);\n };\n el.addParents(el.getParents());\n for (i = 0; i < el.parents.length; i++) {\n board.select(el.parents[i]).addChild(el);\n }\n\n /**\n * @class\n * @ignore\n */\n el.setText(function () {\n var prefix = '',\n suffix = '',\n dim = el.Dimension(),\n digits = el.evalVisProp('digits'),\n unit = el.Unit(),\n val = el.Value(),\n i;\n\n if (el.evalVisProp('showPrefix')) {\n prefix = el.evalVisProp('prefix');\n }\n if (el.evalVisProp('showSuffix')) {\n suffix = el.evalVisProp('suffix');\n }\n\n if (Type.isNumber(val)) {\n if (digits === 'none') {\n // do nothing\n } else if (digits === 'auto') {\n if (el.useLocale()) {\n val = el.formatNumberLocale(val);\n } else {\n val = Type.autoDigits(val);\n }\n } else {\n if (el.useLocale()) {\n val = el.formatNumberLocale(val, digits);\n } else {\n val = Type.toFixed(val, digits);\n }\n }\n } else if (Type.isArray(val)) {\n for (i = 0; i < val.length; i++) {\n if (!Type.isNumber(val[i])) {\n continue;\n }\n if (digits === 'none') {\n // do nothing\n } else if (digits === 'auto') {\n if (el.useLocale()) {\n val[i] = el.formatNumberLocale(val[i]);\n } else {\n val[i] = Type.autoDigits(val[i]);\n }\n } else {\n if (el.useLocale()) {\n val[i] = el.formatNumberLocale(val[i], digits);\n } else {\n val[i] = Type.toFixed(val[i], digits);\n }\n }\n }\n }\n\n if (dim === 'coords' && Type.isArray(val)) {\n if (val.length === 2) {\n val.unshift(undefined);\n }\n val = el.visProp.formatcoords(el, val[1], val[2], val[0]);\n }\n\n if (dim === 'direction' && Type.isArray(val)) {\n val = el.visProp.formatdirection(el, val[0], val[1]);\n }\n\n if (Type.isString(dim)) {\n return prefix + val + suffix;\n }\n\n if (isNaN(dim)) {\n return prefix + 'NaN' + suffix;\n }\n\n return prefix + val + unit + suffix;\n });\n\n Type.extendInstanceMethodMap(el, {\n Value: \"Value\",\n V: \"Value\",\n Dimension: \"Dimension\",\n Unit: \"Unit\",\n getTerm: \"getTerm\",\n Term: \"getTerm\",\n getMethod: \"getMethod\",\n Method: \"getMethod\",\n getParents: \"getParents\",\n Parents: \"getParents\"\n });\n\n return el;\n};\n\nJXG.registerElement(\"measurement\", JXG.createMeasurement);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n *\n * @param {String|JXG.Board} board The board the chart is drawn on\n * @param {Array} x Array of x-coordinates\n * @param {Array} y Array of y-coordinates\n * @param {Object} attributes Javascript object containing attributes like colors\n * @returns {Array} Array of JXG polygons defining the bars\n */\n drawBar: function (board, x, y, attributes) {\n var i, text, w,\n xp0, xp1, xp2, yp,\n colors,\n pols = [],\n p = [],\n attr,\n attrSub,\n makeXpFun = function (i, f) {\n return function () {\n return x[i]() - f * w;\n };\n },\n hiddenPoint = {\n fixed: true,\n withLabel: false,\n visible: false,\n name: \"\"\n };\n\n attr = Type.copyAttributes(attributes, board.options, 'chart');\n\n // Determine the width of the bars\n if (attr && attr.width) {\n // width given\n w = attr.width;\n } else {\n if (x.length <= 1) {\n w = 1;\n } else {\n // Find minimum distance between to bars.\n w = x[1] - x[0];\n for (i = 1; i < x.length - 1; i++) {\n w = x[i + 1] - x[i] < w ? x[i + 1] - x[i] : w;\n }\n }\n w *= 0.8;\n }\n\n attrSub = Type.copyAttributes(attributes, board.options, \"chart\", 'label');\n\n for (i = 0; i < x.length; i++) {\n if (Type.isFunction(x[i])) {\n xp0 = makeXpFun(i, -0.5);\n xp1 = makeXpFun(i, 0);\n xp2 = makeXpFun(i, 0.5);\n } else {\n xp0 = x[i] - w * 0.5;\n xp1 = x[i];\n xp2 = x[i] + w * 0.5;\n }\n if (Type.isFunction(y[i])) {\n yp = y[i]();\n } else {\n yp = y[i];\n }\n yp = y[i];\n\n if (attr.dir === 'horizontal') {\n // horizontal bars\n p[0] = board.create(\"point\", [0, xp0], hiddenPoint);\n p[1] = board.create(\"point\", [yp, xp0], hiddenPoint);\n p[2] = board.create(\"point\", [yp, xp2], hiddenPoint);\n p[3] = board.create(\"point\", [0, xp2], hiddenPoint);\n\n if (Type.exists(attr.labels) && Type.exists(attr.labels[i])) {\n attrSub.anchorX = function (self) {\n return self.X() >= 0 ? \"left\" : 'right';\n };\n attrSub.anchorY = 'middle';\n text = board.create(\"text\", [yp, xp1, attr.labels[i]], attrSub);\n }\n } else {\n // vertical bars\n p[0] = board.create(\"point\", [xp0, 0], hiddenPoint);\n p[1] = board.create(\"point\", [xp0, yp], hiddenPoint);\n p[2] = board.create(\"point\", [xp2, yp], hiddenPoint);\n p[3] = board.create(\"point\", [xp2, 0], hiddenPoint);\n\n if (Type.exists(attr.labels) && Type.exists(attr.labels[i])) {\n attrSub.anchorX = 'middle';\n attrSub.anchorY = function (self) {\n return self.Y() >= 0 ? \"bottom\" : 'top';\n };\n text = board.create(\"text\", [xp1, yp, attr.labels[i]], attrSub);\n }\n }\n\n if (Type.isArray(attr.colors)) {\n colors = attr.colors;\n attr.fillcolor = colors[i % colors.length];\n }\n\n pols[i] = board.create(\"polygon\", p, attr);\n if (Type.exists(attr.labels) && Type.exists(attr.labels[i])) {\n pols[i].text = text;\n pols[i].addChild(text);\n }\n }\n\n return pols;\n },\n\n /**\n * Create chart consisting of JSXGraph points.\n * Attributes to change the layout of the point chart are:\n * \n *
\n *\n * @param {String|JXG.Board} board The board the chart is drawn on\n * @param {Array} x Array of x-coordinates\n * @param {Array} y Array of y-coordinates\n * @param {Object} attributes Javascript object containing attributes like colors\n * @returns {Array} Array of JSXGraph points\n */\n drawPoints: function (board, x, y, attributes) {\n var i,\n points = [],\n infoboxArray = attributes.infoboxarray;\n\n attributes.fixed = true;\n attributes.name = \"\";\n\n for (i = 0; i < x.length; i++) {\n attributes.infoboxtext = infoboxArray\n ? infoboxArray[i % infoboxArray.length]\n : false;\n points[i] = board.create(\"point\", [x[i], y[i]], attributes);\n }\n\n return points;\n },\n\n /**\n * Create pie chart.\n * Attributes to change the layout of the pie chart are:\n * \n *
\n *\n * @param {String|JXG.Board} board The board the chart is drawn on\n * @param {Array} y Array of x-coordinates\n * @param {Object} attributes Javascript object containing attributes like colors\n * @returns {Object} with keys: \"{sectors, points, midpoint}\"\n */\n drawPie: function (board, y, attributes) {\n var i,\n center,\n p = [],\n sector = [],\n // s = Statistics.sum(y),\n colorArray = attributes.colors,\n highlightColorArray = attributes.highlightcolors,\n labelArray = attributes.labels,\n r = attributes.radius || 4,\n radius = r,\n cent = attributes.center || [0, 0],\n xc = cent[0],\n yc = cent[1],\n makeRadPointFun = function (j, fun, xc) {\n return function () {\n var s,\n i,\n rad,\n t = 0;\n\n for (i = 0; i <= j; i++) {\n t += parseFloat(Type.evaluate(y[i]));\n }\n\n s = t;\n for (i = j + 1; i < y.length; i++) {\n s += parseFloat(Type.evaluate(y[i]));\n }\n rad = s !== 0 ? (2 * Math.PI * t) / s : 0;\n\n return radius() * Math[fun](rad) + xc;\n };\n },\n highlightHandleLabel = function (f, s) {\n var dx = -this.point1.coords.usrCoords[1] + this.point2.coords.usrCoords[1],\n dy = -this.point1.coords.usrCoords[2] + this.point2.coords.usrCoords[2];\n\n if (Type.exists(this.label)) {\n this.label.rendNode.style.fontSize =\n s * this.label.evalVisProp('fontsize') + 'px';\n this.label.fullUpdate();\n }\n\n this.point2.coords = new Coords(\n Const.COORDS_BY_USER,\n [\n this.point1.coords.usrCoords[1] + dx * f,\n this.point1.coords.usrCoords[2] + dy * f\n ],\n this.board\n );\n this.fullUpdate();\n },\n highlightFun = function () {\n if (!this.highlighted) {\n this.highlighted = true;\n this.board.highlightedObjects[this.id] = this;\n this.board.renderer.highlight(this);\n\n highlightHandleLabel.call(this, 1.1, 2);\n }\n },\n noHighlightFun = function () {\n if (this.highlighted) {\n this.highlighted = false;\n this.board.renderer.noHighlight(this);\n\n highlightHandleLabel.call(this, 0.9090909, 1);\n }\n },\n hiddenPoint = {\n fixed: true,\n withLabel: false,\n visible: false,\n name: \"\"\n };\n\n if (!Type.isArray(labelArray)) {\n labelArray = [];\n for (i = 0; i < y.length; i++) {\n labelArray[i] = \"\";\n }\n }\n\n if (!Type.isFunction(r)) {\n radius = function () {\n return r;\n };\n }\n\n attributes.highlightonsector = attributes.highlightonsector || false;\n attributes.straightfirst = false;\n attributes.straightlast = false;\n\n center = board.create(\"point\", [xc, yc], hiddenPoint);\n p[0] = board.create(\n \"point\",\n [\n function () {\n return radius() + xc;\n },\n function () {\n return yc;\n }\n ],\n hiddenPoint\n );\n\n for (i = 0; i < y.length; i++) {\n p[i + 1] = board.create(\n \"point\",\n [makeRadPointFun(i, \"cos\", xc), makeRadPointFun(i, \"sin\", yc)],\n hiddenPoint\n );\n\n attributes.name = labelArray[i];\n attributes.withlabel = attributes.name !== \"\";\n attributes.fillcolor = colorArray && colorArray[i % colorArray.length];\n attributes.labelcolor = colorArray && colorArray[i % colorArray.length];\n attributes.highlightfillcolor =\n highlightColorArray && highlightColorArray[i % highlightColorArray.length];\n\n sector[i] = board.create(\"sector\", [center, p[i], p[i + 1]], attributes);\n\n if (attributes.highlightonsector) {\n // overwrite hasPoint so that the whole sector is used for highlighting\n sector[i].hasPoint = sector[i].hasPointSector;\n }\n if (attributes.highlightbysize) {\n sector[i].highlight = highlightFun;\n\n sector[i].noHighlight = noHighlightFun;\n }\n }\n\n // Not enough! We need points, but this gives an error in setAttribute.\n return { sectors: sector, points: p, midpoint: center };\n },\n\n /**\n * Create radar chart.\n * Attributes to change the layout of the pie chart are:\n * \n *
\n *\n * @param {String|JXG.Board} board The board the chart is drawn on\n * @param {Array} parents Array of coordinates, e.g. [[x1, y1, z1], [x2, y2, z2], [x3, y3, z3]]\n * @param {Object} attributes Javascript object containing attributes like colors\n * @returns {Object} with keys \"{circles, lines, points, midpoint, polygons}\"\n */\n drawRadar: function (board, parents, attributes) {\n var i,\n j,\n paramArray,\n numofparams,\n maxes,\n mins,\n la,\n pdata,\n ssa,\n esa,\n ssratio,\n esratio,\n sshifts,\n eshifts,\n starts,\n ends,\n labelArray,\n colorArray,\n // highlightColorArray,\n radius,\n myAtts,\n cent,\n xc,\n yc,\n center,\n start_angle,\n rad,\n p,\n line,\n t,\n xcoord,\n ycoord,\n polygons,\n legend_position,\n circles,\n lxoff,\n lyoff,\n cla,\n clabelArray,\n ncircles,\n pcircles,\n angle,\n dr,\n sw,\n data,\n len = parents.length,\n get_anchor = function () {\n var x1, x2, y1, y2,\n relCoords = this.evalVisProp('label.offset').slice(0);\n\n x1 = this.point1.X();\n x2 = this.point2.X();\n y1 = this.point1.Y();\n y2 = this.point2.Y();\n if (x2 < x1) {\n relCoords[0] = -relCoords[0];\n }\n\n if (y2 < y1) {\n relCoords[1] = -relCoords[1];\n }\n\n this.setLabelRelativeCoords(relCoords);\n\n return new Coords(\n Const.COORDS_BY_USER,\n [this.point2.X(), this.point2.Y()],\n this.board\n );\n },\n get_transform = function (angle, i) {\n var t, tscale, trot;\n\n t = board.create(\"transform\", [-(starts[i] - sshifts[i]), 0], {\n type: \"translate\"\n });\n tscale = board.create(\n \"transform\",\n [radius / (ends[i] + eshifts[i] - (starts[i] - sshifts[i])), 1],\n { type: \"scale\" }\n );\n t.melt(tscale);\n trot = board.create(\"transform\", [angle], { type: \"rotate\" });\n t.melt(trot);\n\n return t;\n };\n\n if (len <= 0) {\n throw new Error(\"JSXGraph radar chart: no data\");\n }\n // labels for axes\n paramArray = attributes.paramarray;\n if (!Type.exists(paramArray)) {\n throw new Error(\"JSXGraph radar chart: need paramArray attribute\");\n }\n numofparams = paramArray.length;\n if (numofparams <= 1) {\n throw new Error(\"JSXGraph radar chart: need more than one param in paramArray\");\n }\n\n for (i = 0; i < len; i++) {\n if (numofparams !== parents[i].length) {\n throw new Error(\n \"JSXGraph radar chart: use data length equal to number of params (\" +\n parents[i].length +\n \" != \" +\n numofparams +\n \")\"\n );\n }\n }\n\n maxes = [];\n mins = [];\n\n for (j = 0; j < numofparams; j++) {\n maxes[j] = parents[0][j];\n mins[j] = maxes[j];\n }\n\n for (i = 1; i < len; i++) {\n for (j = 0; j < numofparams; j++) {\n if (parents[i][j] > maxes[j]) {\n maxes[j] = parents[i][j];\n }\n\n if (parents[i][j] < mins[j]) {\n mins[j] = parents[i][j];\n }\n }\n }\n\n la = [];\n pdata = [];\n\n for (i = 0; i < len; i++) {\n la[i] = \"\";\n pdata[i] = [];\n }\n\n ssa = [];\n esa = [];\n\n // 0 <= Offset from chart center <=1\n ssratio = attributes.startshiftratio || 0;\n // 0 <= Offset from chart radius <=1\n esratio = attributes.endshiftratio || 0;\n\n for (i = 0; i < numofparams; i++) {\n ssa[i] = (maxes[i] - mins[i]) * ssratio;\n esa[i] = (maxes[i] - mins[i]) * esratio;\n }\n\n // Adjust offsets per each axis\n sshifts = attributes.startshiftarray || ssa;\n eshifts = attributes.endshiftarray || esa;\n // Values for inner circle, minimums by default\n starts = attributes.startarray || mins;\n\n if (Type.exists(attributes.start)) {\n for (i = 0; i < numofparams; i++) {\n starts[i] = attributes.start;\n }\n }\n\n // Values for outer circle, maximums by default\n ends = attributes.endarray || maxes;\n if (Type.exists(attributes.end)) {\n for (i = 0; i < numofparams; i++) {\n ends[i] = attributes.end;\n }\n }\n\n if (sshifts.length !== numofparams) {\n throw new Error(\n \"JSXGraph radar chart: start shifts length is not equal to number of parameters\"\n );\n }\n\n if (eshifts.length !== numofparams) {\n throw new Error(\n \"JSXGraph radar chart: end shifts length is not equal to number of parameters\"\n );\n }\n\n if (starts.length !== numofparams) {\n throw new Error(\n \"JSXGraph radar chart: starts length is not equal to number of parameters\"\n );\n }\n\n if (ends.length !== numofparams) {\n throw new Error(\n \"JSXGraph radar chart: snds length is not equal to number of parameters\"\n );\n }\n\n // labels for legend\n labelArray = attributes.labelarray || la;\n colorArray = attributes.colors;\n // highlightColorArray = attributes.highlightcolors;\n radius = attributes.radius || 10;\n sw = attributes.strokewidth || 1;\n\n if (!Type.exists(attributes.highlightonsector)) {\n attributes.highlightonsector = false;\n }\n\n myAtts = {\n name: attributes.name,\n id: attributes.id,\n strokewidth: sw,\n polystrokewidth: attributes.polystrokewidth || sw,\n strokecolor: attributes.strokecolor || \"black\",\n straightfirst: false,\n straightlast: false,\n fillcolor: attributes.fillColor || \"#FFFF88\",\n fillopacity: attributes.fillOpacity || 0.4,\n highlightfillcolor: attributes.highlightFillColor || \"#FF7400\",\n highlightstrokecolor: attributes.highlightStrokeColor || \"black\",\n gradient: attributes.gradient || \"none\"\n };\n\n cent = attributes.center || [0, 0];\n xc = cent[0];\n yc = cent[1];\n center = board.create(\"point\", [xc, yc], {\n name: \"\",\n fixed: true,\n withlabel: false,\n visible: false\n });\n start_angle = Math.PI / 2 - Math.PI / numofparams;\n start_angle = attributes.startangle || 0;\n rad = start_angle;\n p = [];\n line = [];\n\n for (i = 0; i < numofparams; i++) {\n rad += (2 * Math.PI) / numofparams;\n xcoord = radius * Math.cos(rad) + xc;\n ycoord = radius * Math.sin(rad) + yc;\n\n p[i] = board.create(\"point\", [xcoord, ycoord], {\n name: \"\",\n fixed: true,\n withlabel: false,\n visible: false\n });\n line[i] = board.create(\"line\", [center, p[i]], {\n name: paramArray[i],\n strokeColor: myAtts.strokecolor,\n strokeWidth: myAtts.strokewidth,\n strokeOpacity: 1.0,\n straightFirst: false,\n straightLast: false,\n withLabel: true,\n highlightStrokeColor: myAtts.highlightstrokecolor\n });\n line[i].getLabelAnchor = get_anchor;\n t = get_transform(rad, i);\n\n for (j = 0; j < parents.length; j++) {\n data = parents[j][i];\n pdata[j][i] = board.create(\"point\", [data, 0], {\n name: \"\",\n fixed: true,\n withlabel: false,\n visible: false\n });\n pdata[j][i].addTransform(pdata[j][i], t);\n }\n }\n\n polygons = [];\n for (i = 0; i < len; i++) {\n myAtts.labelcolor = colorArray && colorArray[i % colorArray.length];\n myAtts.strokecolor = colorArray && colorArray[i % colorArray.length];\n myAtts.fillcolor = colorArray && colorArray[i % colorArray.length];\n polygons[i] = board.create(\"polygon\", pdata[i], {\n withLines: true,\n withLabel: false,\n fillColor: myAtts.fillcolor,\n fillOpacity: myAtts.fillopacity,\n highlightFillColor: myAtts.highlightfillcolor\n });\n\n for (j = 0; j < numofparams; j++) {\n polygons[i].borders[j].setAttribute(\n \"strokecolor:\" + colorArray[i % colorArray.length]\n );\n polygons[i].borders[j].setAttribute(\n \"strokewidth:\" + myAtts.polystrokewidth\n );\n }\n }\n\n legend_position = attributes.legendposition || 'none';\n switch (legend_position) {\n case \"right\":\n lxoff = attributes.legendleftoffset || 2;\n lyoff = attributes.legendtopoffset || 1;\n\n this.legend = board.create(\n \"legend\",\n [xc + radius + lxoff, yc + radius - lyoff],\n {\n labels: labelArray,\n colors: colorArray\n }\n );\n break;\n case \"none\":\n break;\n default:\n JXG.debug(\"Unknown legend position\");\n }\n\n circles = [];\n if (attributes.showcircles) {\n cla = [];\n for (i = 0; i < 6; i++) {\n cla[i] = 20 * i;\n }\n cla[0] = '0';\n clabelArray = attributes.circlelabelarray || cla;\n ncircles = clabelArray.length;\n\n if (ncircles < 2) {\n throw new Error(\n \"JSXGraph radar chart: too less circles in circleLabelArray\"\n );\n }\n\n pcircles = [];\n angle = start_angle + Math.PI / numofparams;\n t = get_transform(angle, 0);\n\n myAtts.fillcolor = 'none';\n myAtts.highlightfillcolor = 'none';\n myAtts.strokecolor = attributes.strokecolor || 'black';\n myAtts.strokewidth = attributes.circlestrokewidth || 0.5;\n myAtts.layer = 0;\n\n // we have ncircles-1 intervals between ncircles circles\n dr = (ends[0] - starts[0]) / (ncircles - 1);\n\n for (i = 0; i < ncircles; i++) {\n pcircles[i] = board.create(\"point\", [starts[0] + i * dr, 0], {\n name: clabelArray[i],\n size: 0,\n fixed: true,\n withLabel: true,\n visible: true\n });\n pcircles[i].addTransform(pcircles[i], t);\n circles[i] = board.create(\"circle\", [center, pcircles[i]], myAtts);\n }\n }\n this.rendNode = polygons[0].rendNode;\n return {\n circles: circles,\n lines: line,\n points: pdata,\n midpoint: center,\n polygons: polygons\n };\n },\n\n /**\n * Uses the boards renderer to update the chart.\n * @private\n */\n updateRenderer: function () {\n return this;\n },\n\n // documented in base/element\n update: function () {\n if (this.needsUpdate) {\n this.updateDataArray();\n }\n\n return this;\n },\n\n /**\n * Template for dynamic charts update.\n * This method is used to compute new entries\n * for the arrays this.dataX and\n * this.dataY. It is used in update.\n * Default is an empty method, can be overwritten\n * by the user.\n *\n * @returns {JXG.Chart} Reference to this chart object.\n */\n updateDataArray: function () {\n return this;\n }\n }\n);\n\n/**\n * @class Various types of charts for data visualization.\n * @pseudo\n * @name Chart\n * @augments JXG.Chart\n * @constructor\n * @type JXG.Chart\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Array} x Array of x-coordinates (default case, see below for alternatives)\n * @param {Array} y Array of y-coordinates (default case, see below for alternatives)\n * \n *
\n *\n * The attribute value for the key 'chartStyle' determines the type(s) of the chart. 'chartStyle' is a comma\n * separated list of strings of the possible chart types\n * 'bar', 'fit', 'line', 'pie', 'point', 'radar', 'spline'.\n *\n * @see JXG.Chart#drawBar\n * @see JXG.Chart#drawFit\n * @see JXG.Chart#drawLine\n * @see JXG.Chart#drawPie\n * @see JXG.Chart#drawPoints\n * @see JXG.Chart#drawRadar\n * @see JXG.Chart#drawSpline\n *\n * @example\n * board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-0.5,8,9,-2],axis:true});\n *\n * var f = [4, 2, -1, 3, 6, 7, 2];\n * var chart = board.create('chart', f,\n * {chartStyle:'bar',\n * width:0.8,\n * labels:f,\n * colorArray:['#8E1B77','#BE1679','#DC1765','#DA2130','#DB311B','#DF4917','#E36317','#E87F1A',\n * '#F1B112','#FCF302','#C1E212'],\n * label: {fontSize:30, display:'internal', anchorX:'left', rotate:90}\n * });\n *\n * \n * \n *\n * @example\n * board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 9, 13, -3], axis:true});\n *\n * var s = board.create('slider', [[4,7],[8,7],[1,1,1.5]], {name:'S', strokeColor:'black', fillColor:'white'});\n * var f = [function(){return (s.Value()*4.5).toFixed(2);},\n * function(){return (s.Value()*(-1)).toFixed(2);},\n * function(){return (s.Value()*3).toFixed(2);},\n * function(){return (s.Value()*2).toFixed(2);},\n * function(){return (s.Value()*(-0.5)).toFixed(2);},\n * function(){return (s.Value()*5.5).toFixed(2);},\n * function(){return (s.Value()*2.5).toFixed(2);},\n * function(){return (s.Value()*(-0.75)).toFixed(2);},\n * function(){return (s.Value()*3.5).toFixed(2);},\n * function(){return (s.Value()*2).toFixed(2);},\n * function(){return (s.Value()*(-1.25)).toFixed(2);}\n * ];\n * var chart = board.create('chart', [f],\n * {chartStyle:'bar',width:0.8,labels:f,\n * colorArray:['#8E1B77','#BE1679','#DC1765','#DA2130','#DB311B','#DF4917','#E36317','#E87F1A',\n * '#F1B112','#FCF302','#C1E212']});\n *\n * var dataArr = [4,1,3,2,5,6.5,1.5,2,0.5,1.5,-1];\n * var chart2 = board.create('chart', dataArr, {chartStyle:'line,point'});\n * chart2[0].setAttribute('strokeColor:black','strokeWidth:2pt');\n * for(var i=0; i<11;i++) {\n * chart2[1][i].setAttribute({strokeColor:'black',fillColor:'white',face:'[]', size:4, strokeWidth:'2pt'});\n * }\n * board.unsuspendUpdate();\n *\n * \n * \n *\n * @example\n * var dataArr = [4, 1.2, 3, 7, 5, 4, 1.54, function () { return 2; }];\n * var a = board.create('chart', dataArr, {\n * chartStyle:'pie', colors:['#B02B2C','#3F4C6B','#C79810','#D15600'],\n * fillOpacity:0.9,\n * center:[5,2],\n * strokeColor:'#ffffff',\n * strokeWidth:6,\n * highlightBySize:true,\n * highlightOnSector:true\n * });\n *\n * \n * \n *\n * @example\n * board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-12, 12, 20, -12], axis: false});\n * board.suspendUpdate();\n * // See labelArray and paramArray\n * var dataArr = [[23, 14, 15.0], [60, 8, 25.0], [0, 11.0, 25.0], [10, 15, 20.0]];\n *\n * var a = board.create('chart', dataArr, {\n * chartStyle:'radar',\n * colorArray:['#0F408D','#6F1B75','#CA147A','#DA2228','#E8801B','#FCF302','#8DC922','#15993C','#87CCEE','#0092CE'],\n * //fillOpacity:0.5,\n * //strokeColor:'black',\n * //strokeWidth:1,\n * //polyStrokeWidth:1,\n * paramArray:['Speed','Flexibility', 'Costs'],\n * labelArray:['Ruby','JavaScript', 'PHP', 'Python'],\n * //startAngle:Math.PI/4,\n * legendPosition:'right',\n * //\"startShiftRatio\": 0.1,\n * //endShiftRatio:0.1,\n * //startShiftArray:[0,0,0],\n * //endShiftArray:[0.5,0.5,0.5],\n * start:0\n * //end:70,\n * //startArray:[0,0,0],\n * //endArray:[7,7,7],\n * //radius:3,\n * //showCircles:true,\n * //circleLabelArray:[1,2,3,4,5],\n * //highlightColorArray:['#E46F6A','#F9DF82','#F7FA7B','#B0D990','#69BF8E','#BDDDE4','#92C2DF','#637CB0','#AB91BC','#EB8EBF'],\n * });\n * board.unsuspendUpdate();\n *\n * \n * \n *\n * For more examples see\n *
\n *
\n */\nJXG.createChart = function (board, parents, attributes) {\n var data,\n row,\n i,\n j,\n col,\n charts = [],\n w,\n x,\n showRows,\n attr,\n originalWidth,\n name,\n strokeColor,\n fillColor,\n hStrokeColor,\n hFillColor,\n len,\n table = Env.isBrowser ? board.document.getElementById(parents[0]) : null;\n\n if (parents.length === 1 && Type.isString(parents[0])) {\n if (Type.exists(table)) {\n // extract the data\n attr = Type.copyAttributes(attributes, board.options, 'chart');\n\n table = new DataSource().loadFromTable(\n parents[0],\n attr.withheaders,\n attr.withheaders\n );\n data = table.data;\n col = table.columnHeaders;\n row = table.rowHeaders;\n\n originalWidth = attr.width;\n name = attr.name;\n strokeColor = attr.strokecolor;\n fillColor = attr.fillcolor;\n hStrokeColor = attr.highlightstrokecolor;\n hFillColor = attr.highlightfillcolor;\n\n board.suspendUpdate();\n\n len = data.length;\n showRows = [];\n if (attr.rows && Type.isArray(attr.rows)) {\n for (i = 0; i < len; i++) {\n for (j = 0; j < attr.rows.length; j++) {\n if (\n attr.rows[j] === i ||\n (attr.withheaders && attr.rows[j] === row[i])\n ) {\n showRows.push(data[i]);\n break;\n }\n }\n }\n } else {\n showRows = data;\n }\n\n len = showRows.length;\n\n for (i = 0; i < len; i++) {\n x = [];\n if (attr.chartstyle && attr.chartstyle.indexOf('bar') !== -1) {\n if (originalWidth) {\n w = originalWidth;\n } else {\n w = 0.8;\n }\n\n x.push(1 - w / 2 + ((i + 0.5) * w) / len);\n\n for (j = 1; j < showRows[i].length; j++) {\n x.push(x[j - 1] + 1);\n }\n\n attr.width = w / len;\n }\n\n if (name && name.length === len) {\n attr.name = name[i];\n } else if (attr.withheaders) {\n attr.name = col[i];\n }\n\n if (strokeColor && strokeColor.length === len) {\n attr.strokecolor = strokeColor[i];\n } else {\n attr.strokecolor = Color.hsv2rgb(((i + 1) / len) * 360, 0.9, 0.6);\n }\n\n if (fillColor && fillColor.length === len) {\n attr.fillcolor = fillColor[i];\n } else {\n attr.fillcolor = Color.hsv2rgb(((i + 1) / len) * 360, 0.9, 1.0);\n }\n\n if (hStrokeColor && hStrokeColor.length === len) {\n attr.highlightstrokecolor = hStrokeColor[i];\n } else {\n attr.highlightstrokecolor = Color.hsv2rgb(((i + 1) / len) * 360, 0.9, 1.0);\n }\n\n if (hFillColor && hFillColor.length === len) {\n attr.highlightfillcolor = hFillColor[i];\n } else {\n attr.highlightfillcolor = Color.hsv2rgb(((i + 1) / len) * 360, 0.9, 0.6);\n }\n\n if (attr.chartstyle && attr.chartstyle.indexOf('bar') !== -1) {\n charts.push(new JXG.Chart(board, [x, showRows[i]], attr));\n } else {\n charts.push(new JXG.Chart(board, [showRows[i]], attr));\n }\n }\n\n board.unsuspendUpdate();\n }\n return charts;\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'chart');\n return new JXG.Chart(board, parents, attr);\n};\n\nJXG.registerElement(\"chart\", JXG.createChart);\n\n/**\n * Legend for chart\n *\n * The Legend class is a basic class for legends.\n * @class Creates a new Legend object. Do not use this constructor to create a legend.\n * Use {@link JXG.Board#create} with type {@link Legend} instead.\n * \n *
\n *\n * @pseudo\n * @name Legend\n * @augments JXG.Legend\n * @constructor\n * @type JXG.Legend\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Number} x Horizontal coordinate of the left top point of the legend\n * @param {Number} y Vertical coordinate of the left top point of the legend\n *\n * @example\n * var board = JXG.JSXGraph.initBoard('jxgbox', {axis:true,boundingbox:[-4,48.3,12.0,-2.3]});\n * var x = [-3,-2,-1,0,1,2,3,4,5,6,7,8];\n * var dataArr = [4,7,7,27,33,37,46,22,11,4,1,0];\n *\n * colors = ['green', 'yellow', 'red', 'blue'];\n * board.create('chart', [x,dataArr], {chartStyle:'bar', width:1.0, labels:dataArr, colors: colors} );\n * board.create('legend', [8, 45], {labels:dataArr, colors: colors, strokeWidth:5} );\n *\n * \n * \n *\n * @example\n * var inputFun, cf = [], cf2 = [], niveaunum,\n * niveauline = [], niveauopac = [],legend;\n *\n * inputFun = \"x^2/2-2*x*y+y^2/2\";\n * niveauline = [-3,-2,-1,-0.5, 0, 1,2,3];\n * niveaunum = niveauline.length;\n * for (let i = 0; JXG.Math.lt(i, niveaunum); i++) {\n * let niveaui = niveauline[i];\n * niveauopac.push(((i + 1) / (niveaunum + 1)));\n * cf.push(board.create(\"implicitcurve\", [\n * inputFun + \"-(\" + niveaui.toFixed(2) + \")\", [-2, 2], [-2, 2]], {\n * strokeWidth: 2,\n * strokeColor: JXG.palette.red,\n * strokeOpacity: niveauopac[i],\n * needsRegularUpdate: false,\n * name: \"niveau\"+i,\n * visible: true\n * }));\n * }\n * legend = board.create('legend', [-1.75, 1.75], {\n * labels: niveauline,\n * colors: [cf[0].visProp.strokecolor],\n * strokeOpacity: niveauopac,\n * linelength: 0.2,\n * frozen:true\n * }\n * );\n *\n *\n * \n * \n *\n *\n */\nJXG.createLegend = function (board, parents, attributes) {\n //parents are coords of left top point of the legend\n var start_from = [0, 0];\n\n if (Type.exists(parents) && parents.length === 2) {\n start_from = parents;\n } else {\n throw new Error(\"JSXGraph: Legend element needs two numbers as parameters\");\n }\n\n return new JXG.Legend(board, start_from, attributes);\n};\n\nJXG.registerElement(\"legend\", JXG.createLegend);\n\nexport default {\n Chart: JXG.Chart,\n Legend: JXG.Legend\n // createChart: JXG.createChart,\n // createLegend: JXG.createLegend\n};\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see
\n * @param {Object} params The parameters depend on the transformation type\n *\n * \n * ( 1 0 0) ( z )\n * ( a 1 0) * ( x )\n * ( b 0 1) ( y )\n *
\n *\n * \n * ( 1 0 0) ( z )\n * ( 0 a 0) * ( x )\n * ( 0 0 b) ( y )\n *
\n *\n * \n * ( 1 0 0 ) ( z )\n * ( 0 cos(a) -sin(a) ) * ( x )\n * ( 0 sin(a) cos(a) ) ( y )\n *
\n *\n * \n * ( 1 0 0) ( z )\n * ( 0 1 a) * ( x )\n * ( 0 b 1) ( y )\n *
\n *\n * \n * ( 1 0 0 ) ( z )\n * ( 0 a b ) * ( x )\n * ( 0 c d ) ( y )\n *
\n *\n * \n * ( 1 0 0 ) ( z )\n * ( 0 M ) * ( x )\n * ( 0 ) ( y )\n *
\n *\n * \n * ( a b c ) ( z )\n * ( d e f ) * ( x )\n * ( g h i ) ( y )\n *
\n *\n * \n * ( ) ( z )\n * ( M ) * ( x )\n * ( ) ( y )\n *
\n */\nJXG.Transformation = function (board, type, params, is3D) {\n this.elementClass = Const.OBJECT_CLASS_OTHER;\n this.type = Const.OBJECT_TYPE_TRANSFORMATION;\n this.elType = '';\n\n this.transformationType = 'none'; // will be set by setMatrix or setMatrix3D\n\n if (is3D) {\n this.is3D = true;\n this.matrix = [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1]\n ];\n } else {\n this.is3D = false;\n this.matrix = [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1]\n ];\n }\n\n this.board = board;\n this.isNumericMatrix = false;\n if (this.is3D) {\n this.setMatrix3D(params[0] /* view3d */, type, params.slice(1));\n } else {\n this.setMatrix(board, type, params);\n }\n};\n\nJXG.Transformation.prototype = {};\n\nType.copyMethodMap(JXG.Transformation, {\n apply: \"apply\",\n applyOnce: \"applyOnce\",\n bindTo: \"bindTo\",\n bind: \"bindTo\",\n melt: \"melt\",\n meltTo: \"meltTo\"\n});\n\nJXG.extend(\n JXG.Transformation.prototype,\n /** @lends JXG.Transformation.prototype */ {\n /**\n * Updates the numerical data for the transformation, i.e. the entry of the subobject matrix.\n * @returns {JXG.Transform} returns pointer to itself\n */\n update: function () {\n return this;\n },\n\n /**\n * Set the transformation matrix for different types of standard transforms.\n * @param {JXG.Board} board\n * @param {String} type Transformation type, possible values are\n * 'translate',\n * 'scale',\n * 'reflect',\n * 'rotate',\n * 'shear',\n * 'affine',\n * 'affinematrix',\n * 'generic',\n * 'matrix'.\n * @param {Array} params Parameters for the various transformation types.\n *\n * \n * ( a b c ) ( z )\n * ( d e f ) * ( x )\n * ( g h i ) ( y )\n *
\n *\n * The transformation matrix then looks like:\n * \n * ( 1 0 0) ( z )\n * ( a 1 0) * ( x )\n * ( b 0 1) ( y )\n *
\n *\n * \n * ( 1 0 0) ( z )\n * ( 0 a 0) * ( x )\n * ( 0 0 b) ( y )\n *
\n *\n * \n * ( 1 0 0 ) ( z )\n * ( 0 cos(a) -sin(a) ) * ( x )\n * ( 0 sin(a) cos(a) ) ( y )\n *
\n *\n * \n * ( 1 0 0) ( z )\n * ( 0 1 a) * ( x )\n * ( 0 b 1) ( y )\n *
\n *\n * \n * ( 1 0 0 ) ( z )\n * ( 0 a b ) * ( x )\n * ( 0 c d ) ( y )\n *
\n *\n * \n * ( 1 0 0 ) ( z )\n * ( 0 M ) * ( x )\n * ( 0 ) ( y )\n *
\n *\n * \n * ( a b c ) ( z )\n * ( d e f ) * ( x )\n * ( g h i ) ( y )\n *
\n *\n * \n * ( ) ( z )\n * ( M ) * ( x )\n * ( ) ( y )\n *
\n */\n setMatrix: function (board, type, params) {\n var i;\n\n this.isNumericMatrix = true;\n for (i = 0; i < params.length; i++) {\n if (typeof params[i] !== 'number') {\n this.isNumericMatrix = false;\n break;\n }\n }\n\n if (type === 'translate') {\n if (params.length !== 2) {\n throw new Error(\"JSXGraph: translate transformation needs 2 parameters.\");\n }\n this.evalParam = Type.createEvalFunction(board, params, 2);\n this.update = function () {\n this.matrix[1][0] = this.evalParam(0);\n this.matrix[2][0] = this.evalParam(1);\n };\n } else if (type === 'scale') {\n if (params.length !== 2) {\n throw new Error(\"JSXGraph: scale transformation needs 2 parameters.\");\n }\n this.evalParam = Type.createEvalFunction(board, params, 2);\n this.update = function () {\n this.matrix[1][1] = this.evalParam(0); // x\n this.matrix[2][2] = this.evalParam(1); // y\n };\n // Input: line or two points\n } else if (type === 'reflect') {\n // line or two points\n if (params.length < 4) {\n params[0] = board.select(params[0]);\n }\n\n // two points\n if (params.length === 2) {\n params[1] = board.select(params[1]);\n }\n\n // 4 coordinates [px,py,qx,qy]\n if (params.length === 4) {\n this.evalParam = Type.createEvalFunction(board, params, 4);\n }\n\n this.update = function () {\n var x, y, z, xoff, yoff, d, v, p;\n // Determine homogeneous coordinates of reflections axis\n // line\n if (params.length === 1) {\n v = params[0].stdform;\n } else if (params.length === 2) {\n // two points\n v = Mat.crossProduct(\n params[1].coords.usrCoords,\n params[0].coords.usrCoords\n );\n } else if (params.length === 4) {\n // two points coordinates [px,py,qx,qy]\n v = Mat.crossProduct(\n [1, this.evalParam(2), this.evalParam(3)],\n [1, this.evalParam(0), this.evalParam(1)]\n );\n }\n\n // Project origin to the line. This gives a finite point p\n x = v[1];\n y = v[2];\n z = v[0];\n p = [-z * x, -z * y, x * x + y * y];\n d = p[2];\n\n // Normalize p\n xoff = p[0] / p[2];\n yoff = p[1] / p[2];\n\n // x, y is the direction of the line\n x = -v[2];\n y = v[1];\n\n this.matrix[1][1] = (x * x - y * y) / d;\n this.matrix[1][2] = (2 * x * y) / d;\n this.matrix[2][1] = this.matrix[1][2];\n this.matrix[2][2] = -this.matrix[1][1];\n this.matrix[1][0] =\n xoff * (1 - this.matrix[1][1]) - yoff * this.matrix[1][2];\n this.matrix[2][0] =\n yoff * (1 - this.matrix[2][2]) - xoff * this.matrix[2][1];\n };\n } else if (type === 'rotate') {\n if (params.length === 3) {\n // angle, x, y\n this.evalParam = Type.createEvalFunction(board, params, 3);\n } else if (params.length > 0 && params.length <= 2) {\n // angle, p or angle\n this.evalParam = Type.createEvalFunction(board, params, 1);\n\n if (params.length === 2 && !Type.isArray(params[1])) {\n params[1] = board.select(params[1]);\n }\n }\n\n this.update = function () {\n var x,\n y,\n beta = this.evalParam(0),\n co = Math.cos(beta),\n si = Math.sin(beta);\n\n this.matrix[1][1] = co;\n this.matrix[1][2] = -si;\n this.matrix[2][1] = si;\n this.matrix[2][2] = co;\n\n // rotate around [x,y] otherwise rotate around [0,0]\n if (params.length > 1) {\n if (params.length === 3) {\n x = this.evalParam(1);\n y = this.evalParam(2);\n } else {\n if (Type.isArray(params[1])) {\n x = params[1][0];\n y = params[1][1];\n } else {\n x = params[1].X();\n y = params[1].Y();\n }\n }\n this.matrix[1][0] = x * (1 - co) + y * si;\n this.matrix[2][0] = y * (1 - co) - x * si;\n }\n };\n } else if (type === 'shear') {\n if (params.length !== 2) {\n throw new Error(\"JSXGraph: shear transformation needs 2 parameters.\");\n }\n\n this.evalParam = Type.createEvalFunction(board, params, 2);\n this.update = function () {\n this.matrix[1][2] = this.evalParam(0);\n this.matrix[2][1] = this.evalParam(1);\n };\n } else if (type === 'affine') {\n if (params.length !== 4) {\n throw new Error(\"JSXGraph: affine transformation needs 4 parameters.\");\n }\n\n this.evalParam = Type.createEvalFunction(board, params, 9);\n\n this.update = function () {\n this.matrix[1][1] = this.evalParam(0);\n this.matrix[1][2] = this.evalParam(1);\n this.matrix[2][1] = this.evalParam(2);\n this.matrix[2][2] = this.evalParam(3);\n };\n } else if (type === 'affinematrix') {\n if (params.length !== 1) {\n throw new Error(\"JSXGraph: transformation of type 'matrix' needs 1 parameter.\");\n }\n\n this.evalParam = params[0].slice();\n this.update = function () {\n var i, j;\n for (i = 0; i < 2; i++) {\n for (j = 0; j < 2; j++) {\n this.matrix[i + 1][j + 1] = Type.evaluate(this.evalParam[i][j]);\n }\n }\n };\n } else if (type === 'generic') {\n if (params.length !== 9) {\n throw new Error(\"JSXGraph: generic transformation needs 9 parameters.\");\n }\n\n this.evalParam = Type.createEvalFunction(board, params, 9);\n\n this.update = function () {\n this.matrix[0][0] = this.evalParam(0);\n this.matrix[0][1] = this.evalParam(1);\n this.matrix[0][2] = this.evalParam(2);\n this.matrix[1][0] = this.evalParam(3);\n this.matrix[1][1] = this.evalParam(4);\n this.matrix[1][2] = this.evalParam(5);\n this.matrix[2][0] = this.evalParam(6);\n this.matrix[2][1] = this.evalParam(7);\n this.matrix[2][2] = this.evalParam(8);\n };\n } else if (type === 'matrix') {\n if (params.length !== 1) {\n throw new Error(\"JSXGraph: transformation of type 'matrix' needs 1 parameter.\");\n }\n\n this.evalParam = params[0].slice();\n this.update = function () {\n var i, j;\n for (i = 0; i < 3; i++) {\n for (j = 0; j < 3; j++) {\n this.matrix[i][j] = Type.evaluate(this.evalParam[i][j]);\n }\n }\n };\n } else {\n return;\n }\n this.transformationType = type;\n\n // Handle dependencies\n // NO: transformations do not have method addParents\n // if (Type.exists(this.evalParam)) {\n // for (e in this.evalParam.deps) {\n // obj = this.evalParam.deps[e];\n // this.addParents(obj);\n // obj.addChild(this);\n // }\n // }\n },\n\n /**\n * Set the 3D transformation matrix for different types of standard transforms.\n * @param {JXG.Board} board\n * @param {String} type Transformation type, possible values are\n * 'translate',\n * 'scale',\n * 'rotateX',\n * 'rotateY',\n * 'rotateZ',\n * 'rotate',\n * 'affine',\n * 'affinematrix',\n * 'generic',\n * 'matrix'.\n * @param {Array} params Parameters for the various transformation types.\n *\n * \n * ( a b c d) ( w )\n * ( e f g h) * ( x )\n * ( i j k l) ( y )\n * ( m n o p) ( z )\n *
\n *\n * The transformation matrix then looks like:\n * \n * ( 1 0 0 0) ( w )\n * ( a 1 0 0) * ( x )\n * ( b 0 1 0) ( y )\n * ( c 0 0 1) ( z )\n *
\n *\n * \n * ( 1 0 0 0) ( w )\n * ( 0 a 0 0) * ( x )\n * ( 0 0 b 0) ( y )\n * ( 0 0 0 c) ( z )\n *
\n *\n * \n * ( 1 0 0 ) ( w )\n * ( 0 1 0 0 ) * ( x )\n * ( 0 0 cos(a) -sin(a) ) ( y )\n * ( 0 0 sin(a) cos(a) ) ( z )\n *
\n *\n * \n * ( 1 0 0 ) ( w )\n * ( 0 cos(a) 0 -sin(a) ) * ( x )\n * ( 0 0 1 0 ) ( y )\n * ( 0 sin(a) 0 cos(a) ) ( z )\n *
\n *\n * \n * ( 1 0 0 ) ( w )\n * ( 0 cos(a) -sin(a) 0 ) * ( x )\n * ( 0 sin(a) cos(a) 0 ) ( y )\n * ( 0 0 0 1 ) ( z )\n *
\n *\n * \n * ( 1 0 0 0 ) ( w )\n * ( 0 a b c ) * ( x )\n * ( 0 d e f ) ( y )\n * ( 0 g h i ) ( z )\n *
\n *\n * \n * ( 1 0 0 0 ) ( w )\n * ( 0 ) * ( x )\n * ( 0 M ) ( y )\n * ( 0 ) ( z )\n *
\n *\n * \n * ( a b c d ) ( w )\n * ( e f ... ) * ( x )\n * ( ... ) ( y )\n * ( ... p ) ( z )\n *
\n *\n * \n * ( ) ( w )\n * ( M ) * ( x )\n * ( ) ( y )\n * ( ) ( z )\n *
\n *\n */\n setMatrix3D: function (view, type, params) {\n var i,\n board = view.board;\n\n this.isNumericMatrix = true;\n for (i = 0; i < params.length; i++) {\n if (typeof params[i] !== 'number') {\n this.isNumericMatrix = false;\n break;\n }\n }\n\n if (type === 'translate') {\n if (params.length !== 3) {\n throw new Error(\"JSXGraph: 3D translate transformation needs 3 parameters.\");\n }\n this.evalParam = Type.createEvalFunction(board, params, 3);\n this.update = function () {\n this.matrix[1][0] = this.evalParam(0);\n this.matrix[2][0] = this.evalParam(1);\n this.matrix[3][0] = this.evalParam(2);\n };\n } else if (type === 'scale') {\n if (params.length !== 3 && params.length !== 4) {\n throw new Error(\"JSXGraph: 3D scale transformation needs either 3 or 4 parameters.\");\n }\n this.evalParam = Type.createEvalFunction(board, params, 3);\n this.update = function () {\n var x = this.evalParam(0),\n y = this.evalParam(1),\n z = this.evalParam(2);\n\n this.matrix[1][1] = x;\n this.matrix[2][2] = y;\n this.matrix[3][3] = z;\n };\n } else if (type === 'rotateX') {\n params.splice(1, 0, [1, 0, 0]);\n this.setMatrix3D(view, 'rotate', params);\n } else if (type === 'rotateY') {\n params.splice(1, 0, [0, 1, 0]);\n this.setMatrix3D(view, 'rotate', params);\n } else if (type === 'rotateZ') {\n params.splice(1, 0, [0, 0, 1]);\n this.setMatrix3D(view, 'rotate', params);\n } else if (type === 'rotate') {\n if (params.length < 2) {\n throw new Error(\"JSXGraph: 3D rotate transformation needs 2 or 3 parameters.\");\n }\n if (params.length === 3 && !Type.isFunction(params[2]) && !Type.isArray(params[2])) {\n this.evalParam = Type.createEvalFunction(board, params, 2);\n params[2] = view.select(params[2]);\n } else {\n this.evalParam = Type.createEvalFunction(board, params, params.length);\n }\n this.update = function () {\n var a = this.evalParam(0), // angle\n n = this.evalParam(1), // normal\n p = [1, 0, 0, 0],\n co = Math.cos(a),\n si = Math.sin(a),\n n1, n2, n3,\n m1 = [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1]\n ],\n m2 = [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1]\n ],\n nrm = Mat.norm(n);\n\n if (n.length === 3) {\n n1 = n[0] / nrm;\n n2 = n[1] / nrm;\n n3 = n[2] / nrm;\n } else {\n n1 = n[1] / nrm;\n n2 = n[2] / nrm;\n n3 = n[3] / nrm;\n }\n if (params.length === 3) {\n if (params.length === 3 && Type.exists(params[2].is3D)) {\n p = params[2].coords.slice();\n } else {\n p = this.evalParam(2);\n }\n if (p.length === 3) {\n p.unshift(1);\n }\n m1[1][0] = -p[1];\n m1[2][0] = -p[2];\n m1[3][0] = -p[3];\n\n m2[1][0] = p[1];\n m2[2][0] = p[2];\n m2[3][0] = p[3];\n }\n\n this.matrix = [\n [1, 0, 0, 0],\n [0, n1 * n1 * (1 - co) + co, n1 * n2 * (1 - co) - n3 * si, n1 * n3 * (1 - co) + n2 * si],\n [0, n2 * n1 * (1 - co) + n3 * si, n2 * n2 * (1 - co) + co, n2 * n3 * (1 - co) - n1 * si],\n [0, n3 * n1 * (1 - co) - n2 * si, n3 * n2 * (1 - co) + n1 * si, n3 * n3 * (1 - co) + co]\n ];\n this.matrix = Mat.matMatMult(this.matrix, m1);\n this.matrix = Mat.matMatMult(m2, this.matrix);\n };\n } else if (type === 'affine') {\n if (params.length !== 9) {\n throw new Error(\"JSXGraph: 3D transformation of type 'affine' needs 9 parameters.\");\n }\n\n this.evalParam = Type.createEvalFunction(board, params, 9);\n this.update = function () {\n this.matrix[1][1] = this.evalParam(0);\n this.matrix[1][2] = this.evalParam(1);\n this.matrix[1][3] = this.evalParam(2);\n this.matrix[2][1] = this.evalParam(3);\n this.matrix[2][2] = this.evalParam(4);\n this.matrix[2][3] = this.evalParam(5);\n this.matrix[3][1] = this.evalParam(6);\n this.matrix[3][2] = this.evalParam(7);\n this.matrix[3][3] = this.evalParam(8);\n };\n } else if (type === 'affinematrix') {\n if (params.length !== 1) {\n throw new Error(\"JSXGraph: 3D transformation of type 'affinematrix' needs 1 parameter.\");\n }\n\n this.evalParam = params[0].slice();\n this.update = function () {\n var i, j;\n for (i = 0; i < 3; i++) {\n for (j = 0; j < 3; j++) {\n this.matrix[i + 1][j + 1] = Type.evaluate(this.evalParam[i][j]);\n }\n }\n };\n } else if (type === 'generic') {\n if (params.length !== 16) {\n throw new Error(\"JSXGraph: 3D transformation of type 'generic' needs 16 parameters.\");\n }\n\n this.evalParam = Type.createEvalFunction(board, params, 6);\n this.update = function () {\n this.matrix[0][0] = this.evalParam(0);\n this.matrix[0][1] = this.evalParam(1);\n this.matrix[0][2] = this.evalParam(2);\n this.matrix[0][3] = this.evalParam(3);\n this.matrix[1][0] = this.evalParam(4);\n this.matrix[1][1] = this.evalParam(5);\n this.matrix[1][2] = this.evalParam(6);\n this.matrix[1][3] = this.evalParam(7);\n this.matrix[2][0] = this.evalParam(8);\n this.matrix[2][1] = this.evalParam(9);\n this.matrix[2][2] = this.evalParam(10);\n this.matrix[2][3] = this.evalParam(11);\n this.matrix[3][0] = this.evalParam(12);\n this.matrix[3][1] = this.evalParam(13);\n this.matrix[3][2] = this.evalParam(14);\n this.matrix[3][3] = this.evalParam(15);\n };\n } else if (type === 'matrix') {\n if (params.length !== 1) {\n throw new Error(\"JSXGraph: 3D transformation of type 'matrix' needs 1 parameter.\");\n }\n\n this.evalParam = params[0].slice();\n this.update = function () {\n var i, j;\n for (i = 0; i < 4; i++) {\n for (j = 0; j < 4; j++) {\n this.matrix[i][j] = Type.evaluate(this.evalParam[i][j]);\n }\n }\n };\n } else {\n return;\n }\n this.transformationType = type;\n },\n\n /**\n * Transform a point element, that are: {@link Point}, {@link Text}, {@link Image}, {@link Point3D}.\n * First, the transformation matrix is updated, then do the matrix-vector-multiplication.\n * \n * ( a b c ) ( z )\n * ( d e f ) * ( x )\n * ( g h i ) ( y )\n *
\n * where in general a=1. If b = c = 0, the transformation is called affine.\n * In this case, finite points will stay finite. This is not the case for general projective coordinates.\n * \n *
\n * \n *
\n *\n *\n * @see JXG.Transformation#setMatrix\n *\n * @example\n * // The point B is determined by taking twice the vector A from the origin\n *\n * var p0 = board.create('point', [0, 3], {name: 'A'}),\n * t = board.create('transform', [function(){ return p0.X(); }, \"Y(A)\"], {type: 'translate'}),\n * p1 = board.create('point', [p0, t], {color: 'blue'});\n *\n * \n * \n * ( 1 0 0) ( z )\n * ( a 1 0) * ( x )\n * ( b 0 1) ( y )\n *
\n * \n * ( 1 0 0) ( z )\n * ( 0 a 0) * ( x )\n * ( 0 0 b) ( y )\n *
\n * \n * ( 1 0 0 ) ( z )\n * ( 0 cos(a) -sin(a) ) * ( x )\n * ( 0 sin(a) cos(a) ) ( y )\n *
\n * \n * ( 1 0 0) ( z )\n * ( 0 1 a) * ( x )\n * ( 0 b 1) ( y )\n *
\n * \n *
\n * \n * ( 1 0 0 ) ( z )\n * ( 0 a b ) * ( x )\n * ( 0 c d ) ( y )\n *
\n * \n * ( 1 0 0 ) ( z )\n * ( 0 M ) * ( x )\n * ( 0 ) ( y )\n *
\n * \n * ( a b c ) ( z )\n * ( d e f ) * ( x )\n * ( g h i ) ( y )\n *
\n * \n *\n * @example\n * // The point B is the result of scaling the point A with factor 2 in horizontal direction\n * // and with factor 0.5 in vertical direction.\n *\n * var p1 = board.create('point', [1, 1]),\n * t = board.create('transform', [2, 0.5], {type: 'scale'}),\n * p2 = board.create('point', [p1, t], {color: 'blue'});\n *\n * \n * \n *\n * @example\n * // The point B is rotated around C which gives point D. The angle is determined\n * // by the vertical height of point A.\n *\n * var p0 = board.create('point', [0, 3], {name: 'A'}),\n * p1 = board.create('point', [1, 1]),\n * p2 = board.create('point', [2, 1], {name:'C', fixed: true}),\n *\n * // angle, rotation center:\n * t = board.create('transform', ['Y(A)', p2], {type: 'rotate'}),\n * p3 = board.create('point', [p1, t], {color: 'blue'});\n *\n * \n * \n *\n * @example\n * // A concatenation of several transformations.\n * var p1 = board.create('point', [1, 1]),\n * t1 = board.create('transform', [-2, -1], {type: 'translate'}),\n * t2 = board.create('transform', [Math.PI/4], {type: 'rotate'}),\n * t3 = board.create('transform', [2, 1], {type: 'translate'}),\n * p2 = board.create('point', [p1, [t1, t2, t3]], {color: 'blue'});\n *\n * \n * \n *\n * @example\n * // Reflection of point A\n * var p1 = board.create('point', [1, 1]),\n * p2 = board.create('point', [1, 3]),\n * p3 = board.create('point', [-2, 0]),\n * l = board.create('line', [p2, p3]),\n * t = board.create('transform', [l], {type: 'reflect'}), // Possible are l, l.id, l.name\n * p4 = board.create('point', [p1, t], {color: 'blue'});\n *\n * \n * \n *\n * @example\n * // Type: 'matrix'\n * var y = board.create('slider', [[-3, 1], [-3, 4], [0, 1, 6]]);\n * var t1 = board.create('transform', [\n * [\n * [1, 0, 0],\n * [0, 1, 0],\n * [() => y.Value(), 0, 1]\n * ]\n * ], {type: 'matrix'});\n *\n * var A = board.create('point', [2, -3]);\n * var B = board.create('point', [A, t1]);\n *\n * \n * \n *\n * @example\n * // One time application of a transform to points A, B\n * var p1 = board.create('point', [1, 1]),\n * p2 = board.create('point', [-1, -2]),\n * t = board.create('transform', [3, 2], {type: 'shear'});\n * t.applyOnce([p1, p2]);\n *\n * \n * \n *\n * @example\n * // Construct a square of side length 2 with the\n * // help of transformations\n * var sq = [],\n * right = board.create('transform', [2, 0], {type: 'translate'}),\n * up = board.create('transform', [0, 2], {type: 'translate'}),\n * pol, rot, p0;\n *\n * // The first point is free\n * sq[0] = board.create('point', [0, 0], {name: 'Drag me'}),\n *\n * // Construct the other free points by transformations\n * sq[1] = board.create('point', [sq[0], right]),\n * sq[2] = board.create('point', [sq[0], [right, up]]),\n * sq[3] = board.create('point', [sq[0], up]),\n *\n * // Polygon through these four points\n * pol = board.create('polygon', sq, {\n * fillColor:'blue',\n * gradient:'radial',\n * gradientsecondcolor:'white',\n * gradientSecondOpacity:'0'\n * }),\n *\n * p0 = board.create('point', [0, 3], {name: 'angle'}),\n * // Rotate the square around point sq[0] by dragging A vertically.\n * rot = board.create('transform', ['Y(angle)', sq[0]], {type: 'rotate'});\n *\n * // Apply the rotation to all but the first point of the square\n * rot.bindTo(sq.slice(1));\n *\n * \n * \n *\n * @example\n * // Text transformation\n * var p0 = board.create('point', [0, 0], {name: 'p_0'});\n * var p1 = board.create('point', [3, 0], {name: 'p_1'});\n * var txt = board.create('text',[0.5, 0, 'Hello World'], {display:'html'});\n *\n * // If p_0 is dragged, translate p_1 and text accordingly\n * var tOff = board.create('transform', [() => p0.X(), () => p0.Y()], {type:'translate'});\n * tOff.bindTo(txt);\n * tOff.bindTo(p1);\n *\n * // Rotate text around p_0 by dragging point p_1\n * var tRot = board.create('transform', [\n * () => Math.atan2(p1.Y() - p0.Y(), p1.X() - p0.X()), p0], {type:'rotate'});\n * tRot.bindTo(txt);\n *\n * // Scale text by dragging point \"p_1\"\n * // We do this by\n * // - moving text by -p_0 (inverse of transformation tOff),\n * // - scale the text (because scaling is relative to (0,0))\n * // - move the text back by +p_0\n * var tOffInv = board.create('transform', [\n * () => -p0.X(),\n * () => -p0.Y()\n * ], {type:'translate'});\n * var tScale = board.create('transform', [\n * // Some scaling factor\n * () => p1.Dist(p0) / 3,\n * () => p1.Dist(p0) / 3\n * ], {type:'scale'});\n * tOffInv.bindTo(txt); tScale.bindTo(txt); tOff.bindTo(txt);\n *\n * \n * \n *\n */\nJXG.createTransform = function (board, parents, attributes) {\n return new JXG.Transformation(board, attributes.type, parents);\n};\n\nJXG.registerElement('transform', JXG.createTransform);\n\n/**\n * @class Define projective 3D transformations like translation, rotation, reflection.\n * @pseudo\n * @description A transformation consists of a 4x4 matrix, i.e. it is a projective transformation.\n * \n * ( a b c d) ( w )\n * ( e f g h) * ( x )\n * ( i j k l) ( y )\n * ( m n o p) ( z )\n *
\n * where in general a=1. If b = c = d = 0, the transformation is called affine.\n * In this case, finite points will stay finite. This is not the case for general projective coordinates.\n * \n *
\n * \n *
\n *\n * @example\n * var bound = [-5, 5];\n * var view = board.create('view3d',\n * [\n * [-5, -5], [8, 8],\n * [bound, bound, bound]\n * ], {\n * projection: \"central\",\n * depthOrder: { enabled: true },\n * axesPosition: 'border' // 'center', 'none'\n * }\n * );\n *\n * var slider = board.create('slider', [[-4, 6], [0, 6], [0, 0, 5]]);\n *\n * var p1 = view.create('point3d', [1, 2, 2], { name: 'drag me', size: 5 });\n *\n * // Translate from p1 by fixed amount\n * var t1 = view.create('transform3d', [2, 3, 2], { type: 'translate' });\n * // Translate from p1 by dynamic amount\n * var t2 = view.create('transform3d', [() => slider.Value() + 3, 0, 0], { type: 'translate' });\n *\n * view.create('point3d', [p1, t1], { name: 'translate fixed', size: 5 });\n * view.create('point3d', [p1, t2], { name: 'translate by func', size: 5 });\n *\n * \n * \n * ( 1 0 0 0) ( w )\n * ( a 1 0 0) * ( x )\n * ( b 0 1 0) ( y )\n * ( c 0 0 c) ( z )\n *
\n * \n * ( 1 0 0 0) ( w )\n * ( 0 a 0 0) * ( x )\n * ( 0 0 b 0) ( y )\n * ( 0 0 0 c) ( z )\n *
\n * \n * ( 1 0 0 0 ) ( w )\n * ( 0 a b c ) * ( x )\n * ( 0 d e f ) ( y )\n * ( 0 g h i ) ( z )\n *
\n * \n * ( 1 0 0 0 ) ( w )\n * ( 0 ) * ( x )\n * ( 0 M ) ( y )\n * ( 0 ) ( z )\n *
\n * \n * ( a b c d ) ( w )\n * ( e f ... ) * ( x )\n * ( ... ) ( y )\n * ( ... p ) ( z )\n *
\n * \n * ( ) ( w )\n * ( M ) * ( x )\n * ( ) ( y )\n * ( ) ( z )\n *
\n * \n *\n */\nJXG.createTransform3D = function (board, parents, attributes) {\n return new JXG.Transformation(board, attributes.type, parents, true);\n};\n\nJXG.registerElement('transform3d', JXG.createTransform3D);\n\nexport default JXG.Transformation;\n\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n */\nJXG.Turtle = function (board, parents, attributes) {\n var x, y, dir;\n\n this.constructor(board, attributes, Const.OBJECT_TYPE_TURTLE, Const.OBJECT_CLASS_OTHER);\n\n this.turtleIsHidden = false;\n this.board = board;\n this.visProp.curveType = 'plot';\n\n // Store visProp in this._attributes.\n // this._attributes is overwritten by setPenSize, setPenColor...\n // Setting the color or size affects the turtle from the time of\n // calling the method,\n // whereas Turtle.setAttribute affects all turtle curves.\n this._attributes = Type.copyAttributes(this.visProp, board.options, 'turtle');\n delete this._attributes.id;\n\n x = 0;\n y = 0;\n dir = 90;\n\n if (parents.length !== 0) {\n // [x,y,dir]\n if (parents.length === 3) {\n // Only numbers are accepted at the moment\n x = parents[0];\n y = parents[1];\n dir = parents[2];\n } else if (parents.length === 2) {\n // [[x,y],dir]\n if (Type.isArray(parents[0])) {\n x = parents[0][0];\n y = parents[0][1];\n dir = parents[1];\n // [x,y]\n } else {\n x = parents[0];\n y = parents[1];\n }\n // [[x,y]]\n } else {\n x = parents[0][0];\n y = parents[0][1];\n }\n }\n\n this.init(x, y, dir);\n\n return this;\n};\n\nJXG.Turtle.prototype = new GeometryElement();\n\nType.copyMethodMap(JXG.Turtle, {\n forward: 'forward',\n fd: 'forward',\n back: 'back',\n bk: 'back',\n right: 'right',\n rt: 'right',\n left: 'left',\n lt: 'left',\n penUp: 'penUp',\n pu: 'penUp',\n up: 'penUp',\n penDown: 'penDown',\n pd: 'penDown',\n down: 'penDown',\n clearScreen: 'clearScreen',\n cs: 'clearScreen',\n clean: 'clean',\n setPos: 'setPos',\n home: 'home',\n hideTurtle: 'hideTurtle',\n ht: 'hideTurtle',\n hide: 'hideTurtle',\n showTurtle: 'showTurtle',\n st: 'showTurtle',\n show: 'showTurtle',\n penSize: 'setPenSize',\n setPenSize: 'setPenSize',\n penColor: 'setPenColor',\n setPenColor: 'setPenColor',\n highlightPenColor: 'setHighlightPenColor',\n setHighlightPenColor: 'setHighlightPenColor',\n getPenColor: 'getPenColor',\n Color: 'getPenColor',\n getHighlightPenColor: 'getHighlightPenColor',\n HighlightColor: 'getHighlightPenColor',\n getPenSize: 'getPenSize',\n Size: 'getPenSize',\n pushTurtle: 'pushTurtle',\n push: 'pushTurtle',\n popTurtle: 'popTurtle',\n pop: 'popTurtle',\n lookTo: 'lookTo',\n pos: 'pos',\n Pos: 'pos',\n moveTo: 'moveTo',\n X: 'X',\n Y: 'Y'\n});\n\nJXG.extend(\n JXG.Turtle.prototype,\n /** @lends JXG.Turtle.prototype */ {\n /**\n * Initialize a new turtle or reinitialize a turtle after {@link JXG.Turtle#clearScreen}.\n * @private\n */\n init: function (x, y, dir) {\n var hiddenPointAttr = {\n fixed: true,\n name: \"\",\n visible: false,\n withLabel: false\n };\n\n this.arrowLen =\n 20 / Mat.hypot(this.board.unitX, this.board.unitY);\n\n this.pos = [x, y];\n this.isPenDown = true;\n this.dir = 90;\n this.stack = [];\n this.objects = [];\n this.curve = this.board.create(\n \"curve\",\n [[this.pos[0]], [this.pos[1]]],\n this._attributes\n );\n this.objects.push(this.curve);\n\n this.turtle = this.board.create(\"point\", this.pos, hiddenPointAttr);\n this.objects.push(this.turtle);\n\n this.turtle2 = this.board.create(\n \"point\",\n [this.pos[0], this.pos[1] + this.arrowLen],\n hiddenPointAttr\n );\n this.objects.push(this.turtle2);\n\n this.visProp.arrow.lastArrow = true;\n this.visProp.arrow.straightFirst = false;\n this.visProp.arrow.straightLast = false;\n this.arrow = this.board.create(\n \"line\",\n [this.turtle, this.turtle2],\n this.visProp.arrow\n );\n this.objects.push(this.arrow);\n\n this.subs = {\n arrow: this.arrow\n };\n this.inherits.push(this.arrow);\n\n this.right(90 - dir);\n this.board.update();\n },\n\n /**\n * Move the turtle forward.\n * @param {Number} len of forward move in user coordinates\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n forward: function (len) {\n if (len === 0) {\n return this;\n }\n\n var t,\n dx = len * Math.cos((this.dir * Math.PI) / 180),\n dy = len * Math.sin((this.dir * Math.PI) / 180);\n\n if (!this.turtleIsHidden) {\n t = this.board.create(\"transform\", [dx, dy], { type: \"translate\" });\n\n t.applyOnce(this.turtle);\n t.applyOnce(this.turtle2);\n }\n\n if (this.isPenDown) {\n // IE workaround\n if (this.curve.dataX.length >= 8192) {\n this.curve = this.board.create(\n \"curve\",\n [[this.pos[0]], [this.pos[1]]],\n this._attributes\n );\n this.objects.push(this.curve);\n }\n }\n\n this.pos[0] += dx;\n this.pos[1] += dy;\n\n if (this.isPenDown) {\n this.curve.dataX.push(this.pos[0]);\n this.curve.dataY.push(this.pos[1]);\n }\n\n this.board.update();\n return this;\n },\n\n /**\n * Move the turtle backwards.\n * @param {Number} len of backwards move in user coordinates\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n back: function (len) {\n return this.forward(-len);\n },\n\n /**\n * Rotate the turtle direction to the right\n * @param {Number} angle of the rotation in degrees\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n right: function (angle) {\n this.dir -= angle;\n this.dir %= 360;\n\n if (!this.turtleIsHidden) {\n var t = this.board.create(\n \"transform\",\n [(-angle * Math.PI) / 180, this.turtle],\n { type: \"rotate\" }\n );\n t.applyOnce(this.turtle2);\n }\n\n this.board.update();\n return this;\n },\n\n /**\n * Rotate the turtle direction to the right.\n * @param {Number} angle of the rotation in degrees\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n left: function (angle) {\n return this.right(-angle);\n },\n\n /**\n * Pen up, stops visible drawing\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n penUp: function () {\n this.isPenDown = false;\n return this;\n },\n\n /**\n * Pen down, continues visible drawing\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n penDown: function () {\n this.isPenDown = true;\n this.curve = this.board.create(\n \"curve\",\n [[this.pos[0]], [this.pos[1]]],\n this._attributes\n );\n this.objects.push(this.curve);\n\n return this;\n },\n\n /**\n * Removes the turtle curve from the board. The turtle stays in its position.\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n clean: function () {\n var i, el;\n\n for (i = 0; i < this.objects.length; i++) {\n el = this.objects[i];\n if (el.type === Const.OBJECT_TYPE_CURVE) {\n this.board.removeObject(el);\n this.objects.splice(i, 1);\n }\n }\n\n this.curve = this.board.create(\n \"curve\",\n [[this.pos[0]], [this.pos[1]]],\n this._attributes\n );\n this.objects.push(this.curve);\n this.board.update();\n\n return this;\n },\n\n /**\n * Removes the turtle completely and resets it to its initial position and direction.\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n clearScreen: function () {\n // var i,\n // el,\n // len = this.objects.length;\n // for (i = len - 1; i >= 0; i--) {\n // el = this.objects[i];\n // this.board.removeObject(el);\n // }\n // It is much faster to remove the whole array of pathes.\n this.board.removeObject(this.objects);\n this.objects = [];\n\n this.init(0, 0, 90);\n return this;\n },\n\n /**\n * Moves the turtle without drawing to a new position\n * @param {Number} x new x- coordinate\n * @param {Number} y new y- coordinate\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n setPos: function (x, y) {\n var t;\n\n if (Type.isArray(x)) {\n this.pos = x;\n } else {\n this.pos = [x, y];\n }\n\n if (!this.turtleIsHidden) {\n this.turtle.setPositionDirectly(Const.COORDS_BY_USER, [x, y]);\n this.turtle2.setPositionDirectly(Const.COORDS_BY_USER, [x, y + this.arrowLen]);\n t = this.board.create(\n \"transform\",\n [(-(this.dir - 90) * Math.PI) / 180, this.turtle],\n { type: \"rotate\" }\n );\n t.applyOnce(this.turtle2);\n }\n\n this.curve = this.board.create(\n \"curve\",\n [[this.pos[0]], [this.pos[1]]],\n this._attributes\n );\n this.objects.push(this.curve);\n this.board.update();\n\n return this;\n },\n\n /**\n * Sets the pen size. Equivalent to setAttribute({strokeWidth:size})\n * but affects only the future turtle.\n * @param {Number} size\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n setPenSize: function (size) {\n //this.visProp.strokewidth = size;\n this.curve = this.board.create(\n \"curve\",\n [[this.pos[0]], [this.pos[1]]],\n this.copyAttr(\"strokeWidth\", size)\n );\n this.objects.push(this.curve);\n return this;\n },\n\n /**\n * Sets the pen color. Equivalent to setAttribute({strokeColor:color})\n * but affects only the future turtle.\n * @param {String} color\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n setPenColor: function (color) {\n this.curve = this.board.create(\n \"curve\",\n [[this.pos[0]], [this.pos[1]]],\n this.copyAttr(\"strokeColor\", color)\n );\n this.objects.push(this.curve);\n\n return this;\n },\n\n /**\n * Get attribute of the last turtle curve object.\n *\n * @param {String} key\n * @returns attribute value\n * @private\n */\n getPenAttribute: function(key) {\n var pos, le = this.objects.length;\n if (le === 4) {\n // No new turtle objects have been created\n pos = 0;\n } else {\n pos = le - 1;\n }\n return this.objects[pos].evalVisProp(key);\n },\n\n /**\n * Get most recently set turtle size (in pixel).\n * @returns Number Size of the last turtle segment in pixel.\n */\n getPenSize: function() {\n return this.getPenAttribute('strokewidth');\n },\n\n /**\n * Get most recently set turtle color.\n * @returns String RGB color value of the last turtle segment.\n */\n getPenColor: function() {\n return this.getPenAttribute('strokecolor');\n },\n\n /**\n * Get most recently set turtle color.\n * @returns String RGB highlight color value of the last turtle segment.\n */\n getHighlightPenColor: function() {\n return this.getPenAttribute('highlightstrokecolor');\n },\n\n /**\n * Sets the highlight pen color. Equivalent to setAttribute({highlightStrokeColor:color})\n * but affects only the future turtle.\n * @param {String} color\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n setHighlightPenColor: function (color) {\n //this.visProp.highlightstrokecolor = colStr;\n this.curve = this.board.create(\n \"curve\",\n [[this.pos[0]], [this.pos[1]]],\n this.copyAttr(\"highlightStrokeColor\", color)\n );\n this.objects.push(this.curve);\n return this;\n },\n\n /**\n * Sets properties of the turtle, see also {@link JXG.GeometryElement#setAttribute}.\n * Sets the property for all curves of the turtle in the past and in the future.\n * @param {Object} attributes key:value pairs\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n setAttribute: function (attributes) {\n var i,\n el,\n tmp,\n len = this.objects.length;\n\n for (i = 0; i < len; i++) {\n el = this.objects[i];\n if (el.type === Const.OBJECT_TYPE_CURVE) {\n el.setAttribute(attributes);\n }\n }\n\n // Set visProp of turtle\n tmp = this.visProp.id;\n this.visProp = Type.deepCopy(this.curve.visProp);\n this.visProp.id = tmp;\n this._attributes = Type.deepCopy(this.visProp);\n delete this._attributes.id;\n\n return this;\n },\n\n /**\n * Set a future attribute of the turtle.\n * @private\n * @param {String} key\n * @param {Number|String} val\n * @returns {Object} pointer to the attributes object\n */\n copyAttr: function (key, val) {\n this._attributes[key.toLowerCase()] = val;\n return this._attributes;\n },\n\n /**\n * Sets the visibility of the turtle head to true,\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n showTurtle: function () {\n this.turtleIsHidden = false;\n this.arrow.setAttribute({ visible: true });\n this.visProp.arrow.visible = false;\n this.setPos(this.pos[0], this.pos[1]);\n this.board.update();\n\n return this;\n },\n\n /**\n * Sets the visibility of the turtle head to false,\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n hideTurtle: function () {\n this.turtleIsHidden = true;\n this.arrow.setAttribute({ visible: false });\n this.visProp.arrow.visible = false;\n this.board.update();\n\n return this;\n },\n\n /**\n * Moves the turtle to position [0,0].\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n home: function () {\n this.pos = [0, 0];\n this.setPos(this.pos[0], this.pos[1]);\n\n return this;\n },\n\n /**\n * Pushes the position of the turtle on the stack.\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n pushTurtle: function () {\n this.stack.push([this.pos[0], this.pos[1], this.dir]);\n\n return this;\n },\n\n /**\n * Gets the last position of the turtle on the stack, sets the turtle to this position and removes this\n * position from the stack.\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n popTurtle: function () {\n var status = this.stack.pop();\n this.pos[0] = status[0];\n this.pos[1] = status[1];\n this.dir = status[2];\n this.setPos(this.pos[0], this.pos[1]);\n\n return this;\n },\n\n /**\n * Rotates the turtle into a new direction.\n * There are two possibilities:\n * @param {Number|Array} target If a number is given, it is interpreted as the new direction to look to; If an array\n * consisting of two Numbers is given targeted is used as a pair coordinates.\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n lookTo: function (target) {\n var ax, ay, bx, by, beta;\n\n if (Type.isArray(target)) {\n ax = this.pos[0];\n ay = this.pos[1];\n bx = target[0];\n by = target[1];\n\n // Rotate by the slope of the line [this.pos, target]\n beta = Math.atan2(by - ay, bx - ax);\n this.right(this.dir - (beta * 180) / Math.PI);\n } else if (Type.isNumber(target)) {\n this.right(this.dir - target);\n }\n return this;\n },\n\n /**\n * Moves the turtle to a given coordinate pair.\n * The direction is not changed.\n * @param {Array} target Coordinates of the point where the turtle looks to.\n * @returns {JXG.Turtle} pointer to the turtle object\n */\n moveTo: function (target) {\n var dx, dy, t;\n\n if (Type.isArray(target)) {\n dx = target[0] - this.pos[0];\n dy = target[1] - this.pos[1];\n\n if (!this.turtleIsHidden) {\n t = this.board.create(\"transform\", [dx, dy], { type: \"translate\" });\n t.applyOnce(this.turtle);\n t.applyOnce(this.turtle2);\n }\n\n if (this.isPenDown) {\n // IE workaround\n if (this.curve.dataX.length >= 8192) {\n this.curve = this.board.create(\n \"curve\",\n [[this.pos[0]], [this.pos[1]]],\n this._attributes\n );\n this.objects.push(this.curve);\n }\n }\n\n this.pos[0] = target[0];\n this.pos[1] = target[1];\n\n if (this.isPenDown) {\n this.curve.dataX.push(this.pos[0]);\n this.curve.dataY.push(this.pos[1]);\n }\n this.board.update();\n }\n\n return this;\n },\n\n /**\n * Alias for {@link JXG.Turtle#forward}\n */\n fd: function (len) {\n return this.forward(len);\n },\n /**\n * Alias for {@link JXG.Turtle#back}\n */\n bk: function (len) {\n return this.back(len);\n },\n /**\n * Alias for {@link JXG.Turtle#left}\n */\n lt: function (angle) {\n return this.left(angle);\n },\n /**\n * Alias for {@link JXG.Turtle#right}\n */\n rt: function (angle) {\n return this.right(angle);\n },\n /**\n * Alias for {@link JXG.Turtle#penUp}\n */\n pu: function () {\n return this.penUp();\n },\n /**\n * Alias for {@link JXG.Turtle#penDown}\n */\n pd: function () {\n return this.penDown();\n },\n /**\n * Alias for {@link JXG.Turtle#hideTurtle}\n */\n ht: function () {\n return this.hideTurtle();\n },\n /**\n * Alias for {@link JXG.Turtle#showTurtle}\n */\n st: function () {\n return this.showTurtle();\n },\n /**\n * Alias for {@link JXG.Turtle#clearScreen}\n */\n cs: function () {\n return this.clearScreen();\n },\n /**\n * Alias for {@link JXG.Turtle#pushTurtle}\n */\n push: function () {\n return this.pushTurtle();\n },\n /**\n * Alias for {@link JXG.Turtle#popTurtle}\n */\n pop: function () {\n return this.popTurtle();\n },\n\n /**\n * The \"co\"-coordinate of the turtle curve at position t is returned.\n *\n * @param {Number} t parameter\n * @param {String} co. Either 'X' or 'Y'.\n * @returns {Number} x-coordinate of the turtle position or x-coordinate of turtle at position t\n */\n evalAt: function (t, co) {\n var i,\n j,\n el,\n tc,\n len = this.objects.length;\n\n for (i = 0, j = 0; i < len; i++) {\n el = this.objects[i];\n\n if (el.elementClass === Const.OBJECT_CLASS_CURVE) {\n if (j <= t && t < j + el.numberPoints) {\n tc = t - j;\n return el[co](tc);\n }\n j += el.numberPoints;\n }\n }\n\n return this[co]();\n },\n\n /**\n * if t is not supplied the x-coordinate of the turtle is returned. Otherwise\n * the x-coordinate of the turtle curve at position t is returned.\n * @param {Number} t parameter\n * @returns {Number} x-coordinate of the turtle position or x-coordinate of turtle at position t\n */\n X: function (t) {\n if (!Type.exists(t)) {\n return this.pos[0];\n }\n\n return this.evalAt(t, 'X');\n },\n\n /**\n * if t is not supplied the y-coordinate of the turtle is returned. Otherwise\n * the y-coordinate of the turtle curve at position t is returned.\n * @param {Number} t parameter\n * @returns {Number} x-coordinate of the turtle position or x-coordinate of turtle at position t\n */\n Y: function (t) {\n if (!Type.exists(t)) {\n return this.pos[1];\n }\n return this.evalAt(t, 'Y');\n },\n\n /**\n * @returns {Number} z-coordinate of the turtle position\n */\n Z: function (t) {\n return 1.0;\n },\n\n /**\n * Gives the lower bound of the parameter if the turtle is treated as parametric curve.\n */\n minX: function () {\n return 0;\n },\n\n /**\n * Gives the upper bound of the parameter if the turtle is treated as parametric curve.\n * May be overwritten in @see generateTerm.\n */\n maxX: function () {\n var i,\n el,\n len = this.objects.length,\n np = 0;\n\n for (i = 0; i < len; i++) {\n el = this.objects[i];\n if (el.elementClass === Const.OBJECT_CLASS_CURVE) {\n np += this.objects[i].numberPoints;\n }\n }\n return np;\n },\n\n /**\n * Checks whether (x,y) is near the curve.\n * @param {Number} x Coordinate in x direction, screen coordinates.\n * @param {Number} y Coordinate in y direction, screen coordinates.\n * @returns {Boolean} True if (x,y) is near the curve, False otherwise.\n */\n hasPoint: function (x, y) {\n var i, el;\n\n // run through all curves of this turtle\n for (i = 0; i < this.objects.length; i++) {\n el = this.objects[i];\n\n if (el.type === Const.OBJECT_TYPE_CURVE) {\n if (el.hasPoint(x, y)) {\n // So what??? All other curves have to be notified now (for highlighting)\n return true;\n // This has to be done, yet.\n }\n }\n }\n return false;\n }\n }\n);\n\n/**\n * @class A turtle is a graphic paradigm similar to the programming languages Logo or PostScript.\n * @pseudo\n * @description Creates a new turtle\n * @name Turtle\n * @augments JXG.Turtle\n * @constructor\n * @type JXG.Turtle\n *\n * @param {JXG.Board} board The board the turtle is put on.\n * @param {Array} parents\n * @param {Object} attributes Object containing properties for the element such as stroke-color and visibility. See {@link JXG.GeometryElement#setAttribute}\n * @returns {JXG.Turtle} Reference to the created turtle object.\n */\nJXG.createTurtle = function (board, parents, attributes) {\n var attr;\n parents = parents || [];\n\n attr = Type.copyAttributes(attributes, board.options, 'turtle');\n return new JXG.Turtle(board, parents, attr);\n};\n\nJXG.registerElement(\"turtle\", JXG.createTurtle);\n\nexport default JXG.Turtle;\n// export default {\n// Turtle: JXG.Turtle,\n// createTurtle: JXG.createTurtle\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see
\n * The first case is needed to determine which ticks are displayed, i.e. where to stop.\n * The second case is to determine the distance between ticks in case of 'insertTicks:true'.\n * @returns {Object} {lower: Number, upper: Number } containing the lower and upper bounds in user units.\n *\n * @private\n */\n getLowerAndUpperBounds: function (coordsZero, type) {\n var lowerBound, upperBound,\n fA, lA,\n point1, point2,\n isPoint1inBoard, isPoint2inBoard,\n // We use the distance from zero to P1 and P2 to establish lower and higher points\n dZeroPoint1, dZeroPoint2,\n arrowData,\n // angle,\n a1, a2, m1, m2,\n eps = Mat.eps * 10,\n ev_sf = this.line.evalVisProp('straightfirst'),\n ev_sl = this.line.evalVisProp('straightlast'),\n ev_i = this.evalVisProp('includeboundaries');\n\n // The line's defining points that will be adjusted to be within the board limits\n if (this.line.elementClass === Const.OBJECT_CLASS_CURVE) {\n return {\n lower: this.line.minX(),\n upper: this.line.maxX()\n };\n }\n\n point1 = new Coords(Const.COORDS_BY_USER, this.line.point1.coords.usrCoords, this.board);\n point2 = new Coords(Const.COORDS_BY_USER, this.line.point2.coords.usrCoords, this.board);\n\n // Are the original defining points within the board?\n isPoint1inBoard =\n Math.abs(point1.usrCoords[0]) >= Mat.eps &&\n point1.scrCoords[1] >= 0.0 &&\n point1.scrCoords[1] <= this.board.canvasWidth &&\n point1.scrCoords[2] >= 0.0 &&\n point1.scrCoords[2] <= this.board.canvasHeight;\n isPoint2inBoard =\n Math.abs(point2.usrCoords[0]) >= Mat.eps &&\n point2.scrCoords[1] >= 0.0 &&\n point2.scrCoords[1] <= this.board.canvasWidth &&\n point2.scrCoords[2] >= 0.0 &&\n point2.scrCoords[2] <= this.board.canvasHeight;\n\n // Adjust line limit points to be within the board\n if (Type.exists(type) && type === 'ticksdistance') {\n // The good old calcStraight is needed for determining the distance between major ticks.\n // Here, only the visual area is of importance\n Geometry.calcStraight(this.line, point1, point2, 0);\n m1 = this.getDistanceFromZero(coordsZero, point1);\n m2 = this.getDistanceFromZero(coordsZero, point2);\n Geometry.calcStraight(this.line, point1, point2, this.line.evalVisProp('margin'));\n m1 = this.getDistanceFromZero(coordsZero, point1) - m1;\n m2 = this.getDistanceFromZero(coordsZero, point2).m2;\n } else {\n // This function projects the corners of the board to the line.\n // This is important for diagonal lines with infinite tick lines.\n Geometry.calcLineDelimitingPoints(this.line, point1, point2);\n }\n\n // Shorten ticks bounds such that ticks are not through arrow heads\n fA = this.line.evalVisProp('firstarrow');\n lA = this.line.evalVisProp('lastarrow');\n\n a1 = this.getDistanceFromZero(coordsZero, point1);\n a2 = this.getDistanceFromZero(coordsZero, point2);\n if (fA || lA) {\n // Do not display ticks at through arrow heads.\n // In arrowData we ignore the highlighting status.\n // Ticks would appear to be too nervous.\n arrowData = this.board.renderer.getArrowHeadData(\n this.line,\n this.line.evalVisProp('strokewidth'),\n ''\n );\n\n this.board.renderer.getPositionArrowHead(\n this.line,\n point1,\n point2,\n arrowData\n );\n }\n // Calculate (signed) distance from Zero to P1 and to P2\n dZeroPoint1 = this.getDistanceFromZero(coordsZero, point1);\n dZeroPoint2 = this.getDistanceFromZero(coordsZero, point2);\n\n // Recompute lengths of arrow heads\n a1 = dZeroPoint1 - a1;\n a2 = dZeroPoint1 - a2;\n\n // We have to establish if the direction is P1->P2 or P2->P1 to set the lower and upper\n // bounds appropriately. As the distances contain also a sign to indicate direction,\n // we can compare dZeroPoint1 and dZeroPoint2 to establish the line direction\n if (dZeroPoint1 < dZeroPoint2) {\n // Line goes P1->P2\n lowerBound = dZeroPoint1;\n upperBound = dZeroPoint2;\n\n if (!ev_sf && isPoint1inBoard && !ev_i) {\n lowerBound += eps;\n }\n if (!ev_sl && isPoint2inBoard && !ev_i) {\n upperBound -= eps;\n }\n } else if (dZeroPoint2 < dZeroPoint1) {\n // Line goes P2->P1\n // Does this happen at all?\n lowerBound = dZeroPoint2;\n upperBound = dZeroPoint1;\n\n if (!ev_sl && isPoint2inBoard && !ev_i) {\n lowerBound += eps;\n }\n if (!ev_sf && isPoint1inBoard && !ev_i) {\n upperBound -= eps;\n }\n } else {\n // P1 = P2 = Zero, we can't do a thing\n lowerBound = 0;\n upperBound = 0;\n }\n\n return {\n lower: lowerBound,\n upper: upperBound,\n a1: a1,\n a2: a2,\n m1: m1,\n m2: m2\n };\n },\n\n /**\n * Calculates the signed distance in user coordinates from zero to a given point.\n * Sign is positive, if the direction from zero to point is the same as the direction\n * zero to point2 of the line.\n *\n * @param {JXG.Coords} zero coordinates of the point considered zero\n * @param {JXG.Coords} point coordinates of the point to find out the distance\n * @returns {Number} distance between zero and point, including its sign\n * @private\n */\n getDistanceFromZero: function (zero, point) {\n var p1, p2, dirLine, dirPoint, distance;\n\n p1 = this.line.point1.coords;\n p2 = this.line.point2.coords;\n distance = zero.distance(Const.COORDS_BY_USER, point);\n\n // Establish sign\n dirLine = [\n p2.usrCoords[0] - p1.usrCoords[0],\n p2.usrCoords[1] - p1.usrCoords[1],\n p2.usrCoords[2] - p1.usrCoords[2]\n ];\n dirPoint = [\n point.usrCoords[0] - zero.usrCoords[0],\n point.usrCoords[1] - zero.usrCoords[1],\n point.usrCoords[2] - zero.usrCoords[2]\n ];\n if (Mat.innerProduct(dirLine, dirPoint, 3) < 0) {\n distance *= -1;\n }\n\n return distance;\n },\n\n /**\n * Creates ticks coordinates and labels automatically.\n * The frequency of ticks is affected by the values of {@link JXG.Ticks#insertTicks}, {@link JXG.Ticks#minTicksDistance},\n * and {@link JXG.Ticks#ticksDistance}\n *\n * @param {JXG.Coords} coordsZero coordinates of the point considered zero\n * @param {Object} bounds contains the lower and upper bounds for ticks placement\n * @private\n */\n generateEquidistantTicks: function (coordsZero, bounds) {\n var tickPosition,\n eps = Mat.eps,\n deltas, ticksDelta,\n // ev_mia = this.evalVisProp('minorticksinarrow'),\n // ev_maa = this.evalVisProp('minorticksinarrow'),\n // ev_mla = this.evalVisProp('minorticksinarrow'),\n ev_mt = this.evalVisProp('minorticks');\n\n // Determine a proposed distance between major ticks in user units\n ticksDelta = this.getDistanceMajorTicks();\n\n // Obsolete, since this.equidistant is always true at this point\n // ticksDelta = this.equidistant ? this.ticksFunction(1) : this.ticksDelta;\n\n if (this.line.elementClass === Const.OBJECT_CLASS_LINE) {\n // Calculate x and y distances between two points on the line which are 1 unit apart\n // In essence, these are cosine and sine.\n deltas = this.getXandYdeltas();\n }\n\n ticksDelta *= this.evalVisProp('scale');\n\n // In case of insertTicks, adjust ticks distance to satisfy the minTicksDistance restriction.\n // if (ev_it) { // } && this.minTicksDistance > Mat.eps) {\n // ticksDelta = this.adjustTickDistance(ticksDelta, coordsZero, deltas);\n // }\n\n // Convert ticksdelta to the distance between two minor ticks\n ticksDelta /= (ev_mt + 1);\n this.ticksDelta = ticksDelta;\n\n if (ticksDelta < Mat.eps) {\n return;\n }\n if (Math.abs(bounds.upper - bounds.lower) > ticksDelta * 2048) {\n JXG.warn(\"JSXGraph ticks: too many ticks (>2048). Please increase ticksDistance.\");\n return;\n }\n\n // Position ticks from zero to the positive side while not reaching the upper boundary\n tickPosition = 0;\n if (!this.evalVisProp('drawzero')) {\n tickPosition = ticksDelta;\n }\n if (tickPosition < bounds.lower) {\n // Jump from 0 to bounds.lower\n tickPosition = Math.floor((bounds.lower - eps) / ticksDelta) * ticksDelta;\n }\n while (tickPosition <= bounds.upper + eps) {\n // Only draw ticks when we are within bounds, ignore case where tickPosition < lower < upper\n if (tickPosition >= bounds.lower - eps) {\n this.processTickPosition(coordsZero, tickPosition, ticksDelta, deltas);\n }\n tickPosition += ticksDelta;\n\n // Emergency out (probably obsolete)\n if (bounds.upper - tickPosition > ticksDelta * 10000) {\n break;\n }\n }\n\n // Position ticks from zero (not inclusive) to the negative side while not reaching the lower boundary\n tickPosition = -ticksDelta;\n if (tickPosition > bounds.upper) {\n // Jump from -ticksDelta to bounds.upper\n tickPosition = Math.ceil((bounds.upper + eps) / (-ticksDelta)) * (-ticksDelta);\n }\n while (tickPosition >= bounds.lower - eps) {\n // Only draw ticks when we are within bounds, ignore case where lower < upper < tickPosition\n if (tickPosition <= bounds.upper + eps) {\n this.processTickPosition(coordsZero, tickPosition, ticksDelta, deltas);\n }\n tickPosition -= ticksDelta;\n\n // Emergency out (probably obsolete)\n if (tickPosition - bounds.lower > ticksDelta * 10000) {\n break;\n }\n }\n },\n\n /**\n * Calculates the distance between two major ticks in user units.\n * \n *
\n * @returns Number\n * @private\n */\n getDistanceMajorTicks: function () {\n var delta, delta2,\n b, d, dist,\n scale,\n numberMajorTicks = 5,\n maxDist, minDist, ev_mt;\n\n if (this.evalVisProp('insertticks')) {\n // Case of insertTicks==true:\n // Here, we ignore the attribute 'margin'\n b = this.getLowerAndUpperBounds(this.getZeroCoordinates(), '');\n\n dist = (b.upper - b.lower);\n scale = this.evalVisProp('scale');\n\n maxDist = dist / (numberMajorTicks + 1) / scale;\n minDist = this.evalVisProp('minticksdistance') / scale;\n ev_mt = this.evalVisProp('minorticks');\n\n d = this.getXandYdeltas();\n d.x *= this.board.unitX;\n d.y *= this.board.unitY;\n minDist /= Mat.hypot(d.x, d.y);\n minDist *= (ev_mt + 1);\n\n // Determine minimal delta to fulfill the minTicksDistance constraint\n delta = Math.pow(10, Math.floor(Math.log(minDist) / Math.LN10));\n if (2 * delta >= minDist) {\n delta *= 2;\n } else if (5 * delta >= minDist) {\n delta *= 5;\n }\n\n // Determine maximal delta to fulfill the constraint to have approx. \"numberMajorTicks\" majorTicks\n delta2 = Math.pow(10, Math.floor(Math.log(maxDist) / Math.LN10));\n if (5 * delta2 < maxDist) {\n delta2 *= 5;\n } else if (2 * delta2 < maxDist) {\n delta2 *= 2;\n }\n\n // Take the larger value of the two delta's, that is\n // minTicksDistance has priority over numberMajorTicks\n delta = Math.max(delta, delta2);\n\n // < v1.6.0:\n // delta = Math.pow(10, Math.floor(Math.log(0.6 * dist) / Math.LN10));\n // if (false && dist <= 6 * delta) {\n // delta *= 0.5;\n // }\n return delta;\n }\n\n // Case of insertTicks==false\n return this.evalVisProp('ticksdistance');\n },\n\n // /**\n // * Auxiliary method used by {@link JXG.Ticks#generateEquidistantTicks} to adjust the\n // * distance between two ticks depending on {@link JXG.Ticks#minTicksDistance} value\n // *\n // * @param {Number} ticksDelta distance between two major ticks in user coordinates\n // * @param {JXG.Coords} coordsZero coordinates of the point considered zero\n // * @param {Object} deltas x and y distance in pixel between two user units\n // * @param {Object} bounds upper and lower bound of the tick positions in user units.\n // * @private\n // */\n // adjustTickDistance: function (ticksDelta, coordsZero, deltas) {\n // var nx,\n // ny,\n // // bounds,\n // distScr,\n // sgn = 1,\n // ev_mintd = this.evalVisProp('minticksdistance'),\n // ev_minti = this.evalVisProp('minorticks');\n\n // if (this.line.elementClass === Const.OBJECT_CLASS_CURVE) {\n // return ticksDelta;\n // }\n // // Seems to be ignored:\n // // bounds = this.getLowerAndUpperBounds(coordsZero, 'ticksdistance');\n\n // // distScr is the distance between two major Ticks in pixel\n // nx = coordsZero.usrCoords[1] + deltas.x * ticksDelta;\n // ny = coordsZero.usrCoords[2] + deltas.y * ticksDelta;\n // distScr = coordsZero.distance(\n // Const.COORDS_BY_SCREEN,\n // new Coords(Const.COORDS_BY_USER, [nx, ny], this.board)\n // );\n // // console.log(deltas, distScr, this.board.unitX, this.board.unitY, \"ticksDelta:\", ticksDelta);\n\n // if (ticksDelta === 0.0) {\n // return 0.0;\n // }\n\n // // console.log(\":\", distScr, ev_minti + 1, distScr / (ev_minti + 1), ev_mintd)\n // while (false && distScr / (ev_minti + 1) < ev_mintd) {\n // if (sgn === 1) {\n // ticksDelta *= 2;\n // } else {\n // ticksDelta *= 5;\n // }\n // sgn *= -1;\n\n // nx = coordsZero.usrCoords[1] + deltas.x * ticksDelta;\n // ny = coordsZero.usrCoords[2] + deltas.y * ticksDelta;\n // distScr = coordsZero.distance(\n // Const.COORDS_BY_SCREEN,\n // new Coords(Const.COORDS_BY_USER, [nx, ny], this.board)\n // );\n // }\n\n // return ticksDelta;\n // },\n\n /**\n * Auxiliary method used by {@link JXG.Ticks#generateEquidistantTicks} to create a tick\n * in the line at the given tickPosition.\n *\n * @param {JXG.Coords} coordsZero coordinates of the point considered zero\n * @param {Number} tickPosition current tick position relative to zero\n * @param {Number} ticksDelta distance between two major ticks in user coordinates\n * @param {Object} deltas x and y distance between two major ticks\n * @private\n */\n processTickPosition: function (coordsZero, tickPosition, ticksDelta, deltas) {\n var x,\n y,\n tickCoords,\n ti,\n ev_mt,\n isLabelPosition,\n ticksPerLabel = this.evalVisProp('ticksperlabel'),\n labelVal = null;\n\n // Calculates tick coordinates\n if (this.line.elementClass === Const.OBJECT_CLASS_LINE) {\n x = coordsZero.usrCoords[1] + tickPosition * deltas.x;\n y = coordsZero.usrCoords[2] + tickPosition * deltas.y;\n } else {\n x = this.line.X(coordsZero + tickPosition);\n y = this.line.Y(coordsZero + tickPosition);\n }\n tickCoords = new Coords(Const.COORDS_BY_USER, [x, y], this.board);\n if (this.line.elementClass === Const.OBJECT_CLASS_CURVE) {\n labelVal = coordsZero + tickPosition;\n this.setTicksSizeVariables(labelVal);\n }\n\n ev_mt = this.evalVisProp('minorticks');\n // Test if tick is a major tick.\n // This is the case if tickPosition/ticksDelta is\n // a multiple of the number of minorticks+1\n tickCoords.major =\n Math.round(tickPosition / ticksDelta) % (ev_mt + 1) === 0;\n\n if (!ticksPerLabel) {\n // In case of null, 0 or false, majorTicks are labelled\n ticksPerLabel = ev_mt + 1;\n }\n isLabelPosition = Math.round(tickPosition / ticksDelta) % ticksPerLabel === 0;\n\n // Compute the start position and the end position of a tick.\n // If both positions are out of the canvas, ti is empty.\n ti = this.createTickPath(tickCoords, tickCoords.major);\n if (ti.length === 3) {\n this.ticks.push(ti);\n if (isLabelPosition && this.evalVisProp('drawlabels')) {\n // Create a label at this position\n this.labelsData.push(\n this.generateLabelData(\n this.generateLabelText(tickCoords, coordsZero, labelVal),\n tickCoords,\n this.ticks.length\n )\n );\n } else {\n // minor ticks have no labels\n this.labelsData.push(null);\n }\n }\n },\n\n /**\n * Creates ticks coordinates and labels based on {@link JXG.Ticks#fixedTicks} and {@link JXG.Ticks#labels}.\n *\n * @param {JXG.Coords} coordsZero Coordinates of the point considered zero\n * @param {Object} bounds contains the lower and upper bounds for ticks placement\n * @private\n */\n generateFixedTicks: function (coordsZero, bounds) {\n var tickCoords,\n labelText,\n i,\n ti,\n x,\n y,\n eps2 = Mat.eps,\n fixedTick,\n hasLabelOverrides = Type.isArray(this.visProp.labels),\n deltas,\n ev_dl = this.evalVisProp('drawlabels');\n\n if (this.line.elementClass === Const.OBJECT_CLASS_LINE) {\n // Calculate x and y distances between two points on the line which are 1 unit apart\n // In essence, these are cosine and sine.\n deltas = this.getXandYdeltas();\n }\n for (i = 0; i < this.fixedTicks.length; i++) {\n if (this.line.elementClass === Const.OBJECT_CLASS_LINE) {\n fixedTick = this.fixedTicks[i];\n x = coordsZero.usrCoords[1] + fixedTick * deltas.x;\n y = coordsZero.usrCoords[2] + fixedTick * deltas.y;\n } else {\n fixedTick = coordsZero + this.fixedTicks[i];\n x = this.line.X(fixedTick);\n y = this.line.Y(fixedTick);\n }\n tickCoords = new Coords(Const.COORDS_BY_USER, [x, y], this.board);\n\n if (this.line.elementClass === Const.OBJECT_CLASS_CURVE) {\n this.setTicksSizeVariables(fixedTick);\n }\n\n // Compute the start position and the end position of a tick.\n // If tick is out of the canvas, ti is empty.\n ti = this.createTickPath(tickCoords, true);\n if (\n ti.length === 3 &&\n fixedTick >= bounds.lower - eps2 &&\n fixedTick <= bounds.upper + eps2\n ) {\n this.ticks.push(ti);\n\n if (ev_dl && (hasLabelOverrides || Type.exists(this.visProp.labels[i]))) {\n labelText = hasLabelOverrides\n ? this.evalVisProp('labels.' + i)\n : fixedTick;\n this.labelsData.push(\n this.generateLabelData(\n this.generateLabelText(tickCoords, coordsZero, labelText),\n tickCoords,\n i\n )\n );\n } else {\n this.labelsData.push(null);\n }\n }\n }\n },\n\n /**\n * Calculates the x and y distances in user coordinates between two units in user space.\n * In essence, these are cosine and sine. The only work to be done is to determine\n * the direction of the line.\n *\n * @returns {Object}\n * @private\n */\n getXandYdeltas: function () {\n var // Auxiliary points to store the start and end of the line according to its direction\n point1UsrCoords,\n point2UsrCoords,\n distP1P2 = this.line.point1.Dist(this.line.point2);\n\n // if (this.line.type === Const.OBJECT_TYPE_AXIS) {\n // // When line is an Axis, direction depends on board coordinates system\n // // Assume line.point1 and line.point2 are in correct order\n // point1UsrCoords = this.line.point1.coords.usrCoords;\n // point2UsrCoords = this.line.point2.coords.usrCoords;\n // // Check if direction is incorrect, then swap\n // if (\n // point1UsrCoords[1] > point2UsrCoords[1] ||\n // (Math.abs(point1UsrCoords[1] - point2UsrCoords[1]) < Mat.eps &&\n // point1UsrCoords[2] > point2UsrCoords[2])\n // ) {\n // point1UsrCoords = this.line.point2.coords.usrCoords;\n // point2UsrCoords = this.line.point1.coords.usrCoords;\n // }\n // } /* if (this.line.elementClass === Const.OBJECT_CLASS_LINE)*/ else {\n // Line direction is always from P1 to P2 for non axis types\n point1UsrCoords = this.line.point1.coords.usrCoords;\n point2UsrCoords = this.line.point2.coords.usrCoords;\n // }\n return {\n x: (point2UsrCoords[1] - point1UsrCoords[1]) / distP1P2,\n y: (point2UsrCoords[2] - point1UsrCoords[2]) / distP1P2\n };\n },\n\n /**\n * Check if (parts of) the tick is inside the canvas. The tick intersects the boundary\n * at two positions: [x[0], y[0]] and [x[1], y[1]] in screen coordinates.\n * @param {Array} x Array of length two\n * @param {Array} y Array of length two\n * @param {Number} [m=0] Optional margin\n * @return {Boolean} true if parts of the tick are inside of the canvas or on the boundary.\n */\n _isInsideCanvas: function (x, y, m) {\n var cw = this.board.canvasWidth,\n ch = this.board.canvasHeight;\n\n if (m === undefined) {\n m = 0;\n }\n return (\n (x[0] >= m && x[0] <= cw - m && y[0] >= m && y[0] <= ch - m) ||\n (x[1] >= m && x[1] <= cw - m && y[1] >= m && y[1] <= ch - m)\n );\n },\n\n /**\n * @param {JXG.Coords} coords Coordinates of the tick on the line.\n * @param {Boolean} major True if tick is major tick.\n * @returns {Array} Array of length 3 containing path coordinates in screen coordinates\n * of the tick (arrays of length 2). 3rd entry is true if major tick otherwise false.\n * If the tick is outside of the canvas, the return array is empty.\n * @private\n */\n createTickPath: function (coords, major) {\n var c,\n lineStdForm,\n intersection,\n dxs,\n dys,\n dxr,\n dyr,\n alpha,\n style,\n x = [-2000000, -2000000],\n y = [-2000000, -2000000],\n i, r, r_max, bb, full, delta,\n // Used for infinite ticks\n te0, te1, // Tick ending visProps\n dists; // 'signed' distances of intersections to the parent line\n\n c = coords.scrCoords;\n if (major) {\n dxs = this.dxMaj;\n dys = this.dyMaj;\n style = this.majStyle;\n te0 = this.evalVisProp('majortickendings.0') > 0;\n te1 = this.evalVisProp('majortickendings.1') > 0;\n } else {\n dxs = this.dxMin;\n dys = this.dyMin;\n style = this.minStyle;\n te0 = this.evalVisProp('tickendings.0') > 0;\n te1 = this.evalVisProp('tickendings.1') > 0;\n }\n lineStdForm = [-dys * c[1] - dxs * c[2], dys, dxs];\n\n // For all ticks regardless if of finite or infinite\n // tick length the intersection with the canvas border is\n // computed.\n if (major && this.evalVisProp('type') === 'polar') {\n // polar style\n bb = this.board.getBoundingBox();\n full = 2.0 * Math.PI;\n delta = full / 180;\n //ratio = this.board.unitY / this.board.X;\n\n // usrCoords: Test if 'circle' is inside of the canvas\n c = coords.usrCoords;\n r = Mat.hypot(c[1], c[2]);\n r_max = Math.max(\n Mat.hypot(bb[0], bb[1]),\n Mat.hypot(bb[2], bb[3])\n );\n\n if (r < r_max) {\n // Now, switch to screen coords\n x = [];\n y = [];\n for (i = 0; i <= full; i += delta) {\n x.push(\n this.board.origin.scrCoords[1] + r * Math.cos(i) * this.board.unitX\n );\n y.push(\n this.board.origin.scrCoords[2] + r * Math.sin(i) * this.board.unitY\n );\n }\n return [x, y, major];\n }\n } else {\n // line style\n if (style === 'infinite') {\n // Problematic are infinite ticks which have set tickendings:[0,1].\n // For example, this is the default setting for minor ticks\n if (this.evalVisProp('ignoreinfinitetickendings')) {\n te0 = te1 = true;\n }\n intersection = Geometry.meetLineBoard(lineStdForm, this.board);\n\n if (te0 && te1) {\n x[0] = intersection[0].scrCoords[1];\n x[1] = intersection[1].scrCoords[1];\n y[0] = intersection[0].scrCoords[2];\n y[1] = intersection[1].scrCoords[2];\n } else {\n // Assuming the usrCoords of both intersections are normalized, a 'signed distance'\n // with respect to the parent line is computed for the intersections. The sign is\n // used to conclude whether the point is either at the left or right side of the\n // line. The magnitude can be used to compare the points and determine which point\n // is closest to the line.\n dists = [\n Mat.innerProduct(\n intersection[0].usrCoords.slice(1, 3),\n this.line.stdform.slice(1, 3)\n ) + this.line.stdform[0],\n Mat.innerProduct(\n intersection[1].usrCoords.slice(1, 3),\n this.line.stdform.slice(1, 3)\n ) + this.line.stdform[0]\n ];\n\n // Reverse intersection array order if first intersection is not the leftmost one.\n if (dists[0] < dists[1]) {\n intersection.reverse();\n dists.reverse();\n }\n\n if (te0) { // Left-infinite tick\n if (dists[0] < 0) { // intersections at the wrong side of line\n return [];\n } else if (dists[1] < 0) { // 'default' case, tick drawn from line to board bounds\n x[0] = intersection[0].scrCoords[1];\n y[0] = intersection[0].scrCoords[2];\n x[1] = c[1];\n y[1] = c[2];\n } else { // tick visible, but coords of tick on line are outside the visible area\n x[0] = intersection[0].scrCoords[1];\n y[0] = intersection[0].scrCoords[2];\n x[1] = intersection[1].scrCoords[1];\n y[1] = intersection[1].scrCoords[2];\n }\n } else if (te1) { // Right-infinite tick\n if (dists[1] > 0) { // intersections at the wrong side of line\n return [];\n } else if (dists[0] > 0) { // 'default' case, tick drawn from line to board bounds\n x[0] = c[1];\n y[0] = c[2];\n x[1] = intersection[1].scrCoords[1];\n y[1] = intersection[1].scrCoords[2];\n } else { // tick visible, but coords of tick on line are outside the visible area\n x[0] = intersection[0].scrCoords[1];\n y[0] = intersection[0].scrCoords[2];\n x[1] = intersection[1].scrCoords[1];\n y[1] = intersection[1].scrCoords[2];\n }\n }\n }\n } else {\n if (this.evalVisProp('face') === \">\") {\n alpha = Math.PI / 4;\n } else if (this.evalVisProp('face') === \"<\") {\n alpha = -Math.PI / 4;\n } else {\n alpha = 0;\n }\n dxr = Math.cos(alpha) * dxs - Math.sin(alpha) * dys;\n dyr = Math.sin(alpha) * dxs + Math.cos(alpha) * dys;\n\n x[0] = c[1] + dxr * te0;\n y[0] = c[2] - dyr * te0;\n x[1] = c[1];\n y[1] = c[2];\n\n alpha = -alpha;\n dxr = Math.cos(alpha) * dxs - Math.sin(alpha) * dys;\n dyr = Math.sin(alpha) * dxs + Math.cos(alpha) * dys;\n\n x[2] = c[1] - dxr * te1;\n y[2] = c[2] + dyr * te1;\n }\n\n // Check if (parts of) the tick is inside the canvas.\n if (!this.evalVisProp('clip') || this._isInsideCanvas(x, y)) {\n return [x, y, major];\n }\n }\n\n return [];\n },\n\n /**\n * Format label texts. Show the desired number of digits\n * and use utf-8 minus sign.\n * @param {Number} value Number to be displayed\n * @return {String} The value converted into a string.\n * @private\n */\n formatLabelText: function (value) {\n var labelText,\n digits,\n ev_um = this.evalVisProp('label.usemathjax'),\n ev_uk = this.evalVisProp('label.usekatex'),\n ev_s = this.evalVisProp('scalesymbol');\n\n if (Type.isNumber(value)) {\n if (this.evalVisProp('label.tofraction')) {\n if (ev_um) {\n labelText = '\\\\(' + Type.toFraction(value, true) + '\\\\)';\n } else {\n labelText = Type.toFraction(value, ev_uk);\n }\n } else {\n digits = this.evalVisProp('digits');\n if (this.useLocale()) {\n labelText = this.formatNumberLocale(value, digits);\n } else {\n labelText = (Math.round(value * 1e11) / 1e11).toString();\n\n if (\n labelText.length > this.evalVisProp('maxlabellength') ||\n labelText.indexOf('e') !== -1\n ) {\n if (this.evalVisProp('precision') !== 3 && digits === 3) {\n // Use the deprecated attribute \"precision\"\n digits = this.evalVisProp('precision');\n }\n\n //labelText = value.toPrecision(digits).toString();\n labelText = value.toExponential(digits).toString();\n }\n }\n }\n\n if (this.evalVisProp('beautifulscientificticklabels')) {\n labelText = this.beautifyScientificNotationLabel(labelText);\n }\n\n if (labelText.indexOf('.') > -1 && labelText.indexOf('e') === -1) {\n // trim trailing zeros\n labelText = labelText.replace(/0+$/, \"\");\n // trim trailing .\n labelText = labelText.replace(/\\.$/, \"\");\n }\n } else {\n labelText = value.toString();\n }\n\n if (ev_s.length > 0) {\n if (labelText === '1') {\n labelText = ev_s;\n } else if (labelText === \"-1\") {\n labelText = \"-\" + ev_s;\n } else if (labelText !== '0') {\n labelText = labelText + ev_s;\n }\n }\n\n if (this.evalVisProp('useunicodeminus')) {\n labelText = labelText.replace(/-/g, \"\\u2212\");\n }\n return labelText;\n },\n\n /**\n * Formats label texts to make labels displayed in scientific notation look beautiful.\n * For example, label 5.00e+6 will become 5•10⁶, label -1.00e-7 will become into -1•10⁻⁷\n * @param {String} labelText - The label that we want to convert\n * @returns {String} If labelText was not in scientific notation, return labelText without modifications.\n * Otherwise returns beautified labelText with proper superscript notation.\n */\n beautifyScientificNotationLabel: function (labelText) {\n var returnString;\n\n if (labelText.indexOf('e') === -1) {\n return labelText;\n }\n\n // Clean up trailing 0's, so numbers like 5.00e+6.0 for example become into 5e+6\n returnString =\n parseFloat(labelText.substring(0, labelText.indexOf('e'))) +\n labelText.substring(labelText.indexOf('e'));\n\n // Replace symbols like -,0,1,2,3,4,5,6,7,8,9 with their superscript version.\n // Gets rid of + symbol since there is no need for it anymore.\n returnString = returnString.replace(/e(.*)$/g, function (match, $1) {\n var temp = \"\\u2022\" + '10';\n // Note: Since board ticks do not support HTTP elements like , we need to replace\n // all the numbers with superscript Unicode characters.\n temp += $1\n .replace(/-/g, \"\\u207B\")\n .replace(/\\+/g, \"\")\n .replace(/0/g, \"\\u2070\")\n .replace(/1/g, \"\\u00B9\")\n .replace(/2/g, \"\\u00B2\")\n .replace(/3/g, \"\\u00B3\")\n .replace(/4/g, \"\\u2074\")\n .replace(/5/g, \"\\u2075\")\n .replace(/6/g, \"\\u2076\")\n .replace(/7/g, \"\\u2077\")\n .replace(/8/g, \"\\u2078\")\n .replace(/9/g, \"\\u2079\");\n\n return temp;\n });\n\n return returnString;\n },\n\n /**\n * Creates the label text for a given tick. A value for the text can be provided as a number or string\n *\n * @param {JXG.Coords} tick The Coords-object of the tick to create a label for\n * @param {JXG.Coords} zero The Coords-object of line's zero\n * @param {Number|String} value A predefined value for this tick\n * @returns {String}\n * @private\n */\n generateLabelText: function (tick, zero, value) {\n var labelText, distance;\n\n // No value provided, equidistant, so assign distance as value\n if (!Type.exists(value)) {\n // could be null or undefined\n distance = this.getDistanceFromZero(zero, tick);\n if (Math.abs(distance) < Mat.eps) {\n // Point is zero\n return '0';\n }\n value = distance / this.evalVisProp('scale');\n }\n labelText = this.formatLabelText(value);\n\n return labelText;\n },\n\n /**\n * Create a tick label data, i.e. text and coordinates\n * @param {String} labelText\n * @param {JXG.Coords} tick\n * @param {Number} tickNumber\n * @returns {Object} with properties 'x', 'y', 't' (text), 'i' (tick number) or null in case of o label\n * @private\n */\n generateLabelData: function (labelText, tick, tickNumber) {\n var xa, ya, m, fs;\n\n // Test if large portions of the label are inside of the canvas\n // This is the last chance to abandon the creation of the label if it is mostly\n // outside of the canvas.\n fs = this.evalVisProp('label.fontsize');\n xa = [tick.scrCoords[1], tick.scrCoords[1]];\n ya = [tick.scrCoords[2], tick.scrCoords[2]];\n m = fs === undefined ? 12 : fs;\n m *= 0.5;\n if (!this.evalVisProp('clip') || !this._isInsideCanvas(xa, ya, m)) {\n return null;\n }\n\n xa = this.evalVisProp('label.offset')[0];\n ya = this.evalVisProp('label.offset')[1];\n\n return {\n x: tick.usrCoords[1] + xa / this.board.unitX,\n y: tick.usrCoords[2] + ya / this.board.unitY,\n t: labelText,\n i: tickNumber\n };\n },\n\n /**\n * Recalculate the tick positions and the labels.\n * @returns {JXG.Ticks}\n */\n update: function () {\n if (this.needsUpdate) {\n //this.visPropCalc.visible = this.evalVisProp('visible');\n // A canvas with no width or height will create an endless loop, so ignore it\n if (this.board.canvasWidth !== 0 && this.board.canvasHeight !== 0) {\n this.calculateTicksCoordinates();\n }\n // this.updateVisibility(this.line.visPropCalc.visible);\n //\n // for (var i = 0; i < this.labels.length; i++) {\n // if (this.labels[i] !== null) {\n // this.labels[i].prepareUpdate()\n // .updateVisibility(this.line.visPropCalc.visible)\n // .updateRenderer();\n // }\n // }\n }\n\n return this;\n },\n\n /**\n * Uses the boards renderer to update the arc.\n * @returns {JXG.Ticks} Reference to the object.\n */\n updateRenderer: function () {\n if (!this.needsUpdate) {\n return this;\n }\n\n if (this.visPropCalc.visible) {\n this.board.renderer.updateTicks(this);\n }\n this.updateRendererLabels();\n\n this.setDisplayRendNode();\n // if (this.visPropCalc.visible != this.visPropOld.visible) {\n // this.board.renderer.display(this, this.visPropCalc.visible);\n // this.visPropOld.visible = this.visPropCalc.visible;\n // }\n\n this.needsUpdate = false;\n return this;\n },\n\n /**\n * Updates the label elements of the major ticks.\n *\n * @private\n * @returns {JXG.Ticks} Reference to the object.\n */\n updateRendererLabels: function () {\n var i, j, lenData, lenLabels, attr, label, ld, visible;\n\n // The number of labels needed\n lenData = this.labelsData.length;\n // The number of labels which already exist\n // The existing labels are stored in this.labels[]\n // The new label positions and label values are stored in this.labelsData[]\n lenLabels = this.labels.length;\n\n for (i = 0, j = 0; i < lenData; i++) {\n if (this.labelsData[i] === null) {\n // This is a tick without label\n continue;\n }\n\n ld = this.labelsData[i];\n if (j < lenLabels) {\n // Take an already existing text element\n label = this.labels[j];\n label.setText(ld.t);\n label.setCoords(ld.x, ld.y);\n j++;\n } else {\n // A new text element is needed\n this.labelCounter += 1;\n\n attr = Type.deepCopy(this.visProp.label);\n attr.isLabel = true;\n attr.priv = this.visProp.priv;\n attr.id = this.id + ld.i + \"Label\" + this.labelCounter;\n\n label = JXG.createText(this.board, [ld.x, ld.y, ld.t], attr);\n this.addChild(label);\n label.setParents(this);\n label.elType = 'label';\n label.isDraggable = false;\n label.dump = false;\n this.labels.push(label);\n }\n\n // Look-ahead if the label inherits visibility.\n // If yes, update label.\n visible = this.evalVisProp('label.visible');\n if (visible === 'inherit') {\n visible = this.visPropCalc.visible;\n }\n\n label.prepareUpdate().updateVisibility(visible).updateRenderer();\n\n label.distanceX = this.evalVisProp('label.offset')[0];\n label.distanceY = this.evalVisProp('label.offset')[1];\n }\n\n // Hide unused labels\n lenData = j;\n for (j = lenData; j < lenLabels; j++) {\n this.board.renderer.display(this.labels[j], false);\n // Tick labels have the attribute \"visible: 'inherit'\"\n // This must explicitly set to false, otherwise\n // this labels would be set to visible in the upcoming\n // update of the labels.\n this.labels[j].visProp.visible = this.labels[j].visPropCalc.visible = false;\n }\n\n return this;\n },\n\n hideElement: function () {\n var i;\n\n JXG.deprecated(\"Element.hideElement()\", \"Element.setDisplayRendNode()\");\n\n this.visPropCalc.visible = false;\n this.board.renderer.display(this, false);\n for (i = 0; i < this.labels.length; i++) {\n if (Type.exists(this.labels[i])) {\n this.labels[i].hideElement();\n }\n }\n\n return this;\n },\n\n showElement: function () {\n var i;\n\n JXG.deprecated(\"Element.showElement()\", \"Element.setDisplayRendNode()\");\n\n this.visPropCalc.visible = true;\n this.board.renderer.display(this, false);\n\n for (i = 0; i < this.labels.length; i++) {\n if (Type.exists(this.labels[i])) {\n this.labels[i].showElement();\n }\n }\n\n return this;\n }\n }\n);\n\n/**\n * @class Ticks are used as distance markers on a line or curve.\n * They are mainly used for axis elements and slider elements. Ticks may stretch infinitely\n * or finitely, which can be set with {@link Ticks#majorHeight} and {@link Ticks#minorHeight}.\n * \n *
\n *
\n * \n *
\n * The distance between two major ticks is a value of the form\n * a 10i, where a is one of {1, 2, 5} and\n * the number a 10i is maximized such that there are approximately\n * 6 major ticks and there are at least \"minTicksDistance\" pixel between minor ticks.\n * \n * @example\n * // Create ticks labels as fractions\n * board.create('axis', [[0,1], [1,1]], {\n * ticks: {\n * label: {\n * toFraction: true,\n * useMathjax: true,\n * display: 'html',\n * anchorX: 'middle',\n * offset: [0, -10]\n * }\n * }\n * });\n *\n * \n * \n * \n *\n * @example\n * // TODO\n *\n */\nJXG.createTicks = function (board, parents, attributes) {\n var el,\n dist,\n attr = Type.copyAttributes(attributes, board.options, 'ticks');\n\n if (parents.length < 2) {\n dist = attr.ticksdistance; // Will be ignored anyhow and attr.ticksDistance will be used instead\n } else {\n dist = parents[1];\n }\n\n if (\n parents[0].elementClass === Const.OBJECT_CLASS_LINE ||\n parents[0].elementClass === Const.OBJECT_CLASS_CURVE\n ) {\n el = new JXG.Ticks(parents[0], dist, attr);\n } else {\n throw new Error(\n \"JSXGraph: Can't create Ticks with parent types '\" + typeof parents[0] + \"'.\"\n );\n }\n\n // deprecated\n if (Type.isFunction(attr.generatelabelvalue)) {\n el.generateLabelText = attr.generatelabelvalue;\n }\n if (Type.isFunction(attr.generatelabeltext)) {\n el.generateLabelText = attr.generatelabeltext;\n }\n\n el.setParents(parents[0]);\n el.isDraggable = true;\n el.fullUpdate(parents[0].visPropCalc.visible);\n\n return el;\n};\n\n/**\n * @class Hatches are collections of short line segments used to mark congruent lines or curves.\n * @pseudo\n * @name Hatch\n * @augments JXG.Ticks\n * @constructor\n * @type JXG.Ticks\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Line|JXG.curve} line The line or curve the hatch marks are going to be attached to.\n * @param {Number} numberofhashes Number of dashes. The distance of the hashes can be controlled with the attribute ticksDistance.\n * @example\n * // Create an axis providing two coords pairs.\n * var p1 = board.create('point', [0, 3]);\n * var p2 = board.create('point', [1, 3]);\n * var l1 = board.create('line', [p1, p2]);\n * var t = board.create('hatch', [l1, 3]);\n * \n * \n *\n * @example\n * // Alter the position of the hatch\n *\n * var p = board.create('point', [-5, 0]);\n * var q = board.create('point', [5, 0]);\n * var li = board.create('line', [p, q]);\n * var h = board.create('hatch', [li, 2], {anchor: 0.2, ticksDistance:0.4});\n *\n * \n * \n *\n * @example\n * // Alternative hatch faces\n *\n * var li = board.create('line', [[-6,0], [6,3]]);\n * var h1 = board.create('hatch', [li, 2], {tickEndings: [1,1], face:'|'});\n * var h2 = board.create('hatch', [li, 2], {tickEndings: [1,1], face:'>', anchor: 0.3});\n * var h3 = board.create('hatch', [li, 2], {tickEndings: [1,1], face:'<', anchor: 0.7});\n *\n * \n * \n *\n */\nJXG.createHatchmark = function (board, parents, attributes) {\n var num, i, base, width, totalwidth, el,\n pos = [],\n attr = Type.copyAttributes(attributes, board.options, 'hatch');\n\n if (\n (parents[0].elementClass !== Const.OBJECT_CLASS_LINE &&\n parents[0].elementClass !== Const.OBJECT_CLASS_CURVE) ||\n typeof parents[1] !== \"number\"\n ) {\n throw new Error(\n \"JSXGraph: Can't create Hatch mark with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \" and ''\" +\n typeof parents[2] +\n \"'.\"\n );\n }\n\n num = parents[1];\n width = attr.ticksdistance;\n totalwidth = (num - 1) * width;\n base = -totalwidth * 0.5;\n\n for (i = 0; i < num; i++) {\n pos[i] = base + i * width;\n }\n\n el = board.create('ticks', [parents[0], pos], attr);\n el.elType = 'hatch';\n parents[0].inherits.push(el);\n\n return el;\n};\n\nJXG.registerElement(\"ticks\", JXG.createTicks);\nJXG.registerElement(\"hash\", JXG.createHatchmark);\nJXG.registerElement(\"hatch\", JXG.createHatchmark);\n\nexport default JXG.Ticks;\n// export default {\n// Ticks: JXG.Ticks,\n// createTicks: JXG.createTicks,\n// createHashmark: JXG.createHatchmark,\n// createHatchmark: JXG.createHatchmark\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph and JSXCompressor.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n JSXCompressor is free software dual licensed under the GNU LGPL or Apache License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n OR\n * Apache License Version 2.0\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License, Apache\n License, and the MIT License along with JSXGraph. If not, see\n \n * \n *\n * @example\n * var p1 = board.create('glider', [-3, 0, board.defaultAxes.x]);\n * var p2 = board.create('glider', [-1, 0, board.defaultAxes.x]);\n * var c1 = board.create('comb', [p1, p2], {width: 0.2, frequency: 0.1, angle: Math.PI / 4});\n *\n * \n * \n *\n * @example\n * var s = board.create('slider', [[1,3], [4,3], [0.1, 0.3, 0.8]]);\n * var p1 = board.create('glider', [-3, 0, board.defaultAxes.x]);\n * var p2 = board.create('glider', [-1, 0, board.defaultAxes.x]);\n * var c1 = board.create('comb', [p1, p2], {\n * width: function(){ return 4*s.Value(); },\n * reverse: function(){ return (s.Value()<0.5) ? false : true; },\n * frequency: function(){ return s.Value(); },\n * angle: function(){ return s.Value() * Math.PI / 2; },\n * curve: {\n * strokeColor: 'red'\n * }\n * });\n *\n * \n * \n *\n */\nJXG.createComb = function (board, parents, attributes) {\n var p1, p2, c, attr, parent_types;\n //ds, angle, width, p;\n\n if (parents.length === 2) {\n // point 1 given by coordinates\n if (Type.isArray(parents[0]) && parents[0].length > 1) {\n attr = Type.copyAttributes(attributes, board.options, \"comb\", 'point1');\n p1 = board.create(\"point\", parents[0], attr);\n } else if (Type.isString(parents[0]) || Type.isPoint(parents[0])) {\n p1 = board.select(parents[0]);\n } else if (Type.isFunction(parents[0]) && Type.isPoint(parents[0]())) {\n p1 = parents[0]();\n } else if (\n Type.isFunction(parents[0]) &&\n parents[0]().length &&\n parents[0]().length >= 2\n ) {\n attr = Type.copyAttributes(attributes, board.options, \"comb\", 'point1');\n p1 = JXG.createPoint(board, parents[0](), attr);\n } else {\n throw new Error(\n \"JSXGraph: Can't create comb with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,point], [[x1,y1],[x2,y2]]\"\n );\n }\n\n // point 2 given by coordinates\n if (Type.isArray(parents[1]) && parents[1].length > 1) {\n attr = Type.copyAttributes(attributes, board.options, \"comb\", 'point2');\n p2 = board.create(\"point\", parents[1], attr);\n } else if (Type.isString(parents[1]) || Type.isPoint(parents[1])) {\n p2 = board.select(parents[1]);\n } else if (Type.isFunction(parents[1]) && Type.isPoint(parents[1]())) {\n p2 = parents[1]();\n } else if (\n Type.isFunction(parents[1]) &&\n parents[1]().length &&\n parents[1]().length >= 2\n ) {\n attr = Type.copyAttributes(attributes, board.options, \"comb\", 'point2');\n p2 = JXG.createPoint(board, parents[1](), attr);\n } else {\n throw new Error(\n \"JSXGraph: Can't create comb with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [point,point], [[x1,y1],[x2,y2]]\"\n );\n }\n } else {\n parent_types = parents.map(function (parent) {\n return \"'\" + typeof parent + \"'\";\n });\n throw new Error(\n \"JSXGraph: Can't create comb with parent types \" +\n parent_types.join(\", \") +\n \".\" +\n \"\\nPossible parent types: [point,point], [[x1,y1],[x2,y2]]\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'comb');\n // Type.merge(attr, Type.copyAttributes(attributes, board.options, 'comb', 'curve'));\n c = board.create('curve', [[0], [0]], attr);\n\n /**\n * @class\n * @ignore\n */\n c.updateDataArray = function () {\n var s = 0,\n max_s = p1.Dist(p2),\n cs, sn, dx, dy, x, y, f,\n p1_inner = p1,\n p2_inner = p2,\n ds, angle, width;\n\n ds = c.evalVisProp('frequency');\n angle = -c.evalVisProp('angle');\n width = c.evalVisProp('width');\n if (c.evalVisProp('reverse')) {\n p1_inner = p2;\n p2_inner = p1;\n angle = -angle;\n }\n cs = Math.cos(angle);\n sn = Math.sin(angle);\n dx = (p2_inner.X() - p1_inner.X()) / max_s;\n dy = (p2_inner.Y() - p1_inner.Y()) / max_s;\n\n // But instead of lifting by sin(angle), we want lifting by width.\n cs *= width / Math.abs(sn);\n sn *= width / Math.abs(sn);\n\n this.dataX = [];\n this.dataY = [];\n // TODO Handle infinite bounds?\n while (s < max_s) {\n x = p1_inner.X() + dx * s;\n y = p1_inner.Y() + dy * s;\n\n // We may need to cut the last piece of a comb.\n f = Math.min(cs, max_s - s) / Math.abs(cs);\n sn *= f;\n cs *= f;\n\n this.dataX.push(x);\n this.dataY.push(y);\n\n this.dataX.push(x + dx * cs + dy * sn);\n this.dataY.push(y - dx * sn + dy * cs);\n\n this.dataX.push(NaN); // Force a jump\n this.dataY.push(NaN);\n s += ds;\n }\n };\n\n return c;\n};\n\nJXG.registerElement(\"comb\", JXG.createComb);\n\n// export default {\n// createComb: JXG.createComb\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n * @example\n * // Create a on a line and a point on that line\n * var p1 = board.create('point', [-2, 3]),\n * p2 = board.create('point', [2, -3]),\n * li = board.create('line', [p1, p2]),\n * p = board.create('glider', [0, 0, li]),\n *\n * st = board.create('slopetriangle', [li, p]);\n *\n * \n * \n */\nJXG.createSlopeTriangle = function (board, parents, attributes) {\n var el, tangent, tglide, glider,\n toppoint, baseline, basepoint,\n label, attr,\n isPrivateTangent = false;\n\n if (parents.length === 1 && parents[0].type === Const.OBJECT_TYPE_TANGENT) {\n tangent = parents[0];\n tglide = tangent.glider;\n } else if (parents.length === 1 && parents[0].type === Const.OBJECT_TYPE_GLIDER) {\n tglide = parents[0];\n attr = Type.copyAttributes(attributes, board.options, \"slopetriangle\", 'tangent');\n tangent = board.create(\"tangent\", [tglide], attr);\n isPrivateTangent = true;\n } else if (\n parents.length === 2 &&\n parents[0].elementClass === Const.OBJECT_CLASS_LINE &&\n Type.isPoint(parents[1])\n ) {\n tangent = parents[0];\n tglide = parents[1];\n } else {\n throw new Error(\n \"JSXGraph: Can't create slope triangle with parent types '\" +\n typeof parents[0] +\n \"'.\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, \"slopetriangle\", 'basepoint');\n basepoint = board.create(\n \"point\",\n [\n function () {\n return [tglide.X() + 1, tglide.Y()];\n }\n ],\n attr\n );\n\n attr = Type.copyAttributes(attributes, board.options, \"slopetriangle\", 'baseline');\n baseline = board.create(\"line\", [tglide, basepoint], attr);\n\n attr = Type.copyAttributes(attributes, board.options, \"slopetriangle\", 'glider');\n glider = board.create(\"glider\", [tglide.X() + 1, tglide.Y(), baseline], attr);\n\n attr = Type.copyAttributes(attributes, board.options, \"slopetriangle\", 'toppoint');\n toppoint = board.create(\n \"point\",\n [\n function () {\n return [\n glider.X(),\n glider.Y() + (glider.X() - tglide.X()) * tangent.getSlope()\n ];\n }\n ],\n attr\n );\n\n attr = Type.copyAttributes(attributes, board.options, 'slopetriangle');\n // attr.borders = Type.copyAttributes(attr.borders, board.options, \"slopetriangle\", 'borders');\n el = board.create(\"polygon\", [tglide, glider, toppoint], attr);\n el.elType = 'slopetriangle';\n\n /**\n * Returns the slope of the tangent.\n * @name Slope\n * @memberOf Slopetriangle.prototype\n * @function\n * @returns {Number} slope of the tangent.\n */\n el.Slope = priv.Slope;\n\n /**\n * Returns the angle between the tangent and the x-axis.\n * @name getAngle\n * @memberOf Slopetriangle.prototype\n * @function\n * @param {String} [unit='radians'] Unit of the returned values. Possible units are\n * \n *
\n * @returns {Number}\n */\n el.getAngle = priv.getAngle;\n\n /**\n * Returns δx of the slope triangle, that is the slope of the tangent.\n * This value is less than 0 if the line points to the left.\n * @name DeltaX\n * @memberOf Slopetriangle.prototype\n * @function\n * @returns {Number}\n */\n el.DeltaX = priv.DeltaX;\n\n /**\n * Returns δy of the slope triangle, that is the slope of the tangent.\n * This value is less than 0 if the line points to the bottom.\n * @name DeltaY\n * @memberOf Slopetriangle.prototype\n * @function\n * @returns {Number}\n */\n el.DeltaY = priv.DeltaY;\n\n /**\n * Returns the direction of the slope triangle, that is the direction of the tangent.\n * @name Direction\n * @memberOf Slopetriangle.prototype\n * @see Line#Direction\n * @function\n * @returns {Number} slope of the tangent.\n */\n el.Direction = priv.Direction;\n el.tangent = tangent;\n el._isPrivateTangent = isPrivateTangent;\n\n el.borderHorizontal = el.borders[0];\n el.borderVertical = el.borders[1];\n el.borderParallel = el.borders[2];\n\n //el.borderHorizontal.setArrow(false, {type: 2, size: 10});\n //el.borderVertical.setArrow(false, {type: 2, size: 10});\n el.borderParallel.setArrow(false, false);\n\n attr = Type.copyAttributes(attributes, board.options, \"slopetriangle\", 'label');\n //label = board.create(\"text\", [\n // function () {\n // return glider.X() + 0.1;\n // },\n // function () {\n // return (glider.Y() + toppoint.Y()) * 0.5;\n // },\n // function () {\n // return \"\";\n // }\n // ],\n // attr\n // );\n\n attr = Type.copyAttributes(attr, board.options, 'label');\n // Add label to vertical polygon edge\n attr.isLabel = true;\n attr.anchor = el.borderVertical;\n attr.priv = el.borderVertical.visProp.priv;\n attr.id = el.borderVertical.id + 'Label';\n\n label = board.create(\"text\", [0, 0, function () { return \"\"; }], attr);\n label.elType = 'label';\n label.needsUpdate = true;\n label.dump = false;\n el.borderVertical.label = label;\n el.borderVertical.hasLabel = true;\n el.borderVertical.visProp.withlabel = true;\n\n el.borderVertical.slopetriangle = el;\n el.borderHorizontal.slopetriangle = el;\n glider.slopetriangle = el;\n basepoint.slopetriangle = el;\n baseline.slopetriangle = el;\n toppoint.slopetriangle = el;\n label.slopetriangle = el;\n\n label.setText(function () {\n var prefix = '',\n suffix = '',\n digits = label.evalVisProp('digits'),\n val = el.Slope();\n\n if (label.evalVisProp('showprefix')) {\n prefix = label.evalVisProp('prefix');\n }\n if (label.evalVisProp('showsuffix')) {\n suffix = label.evalVisProp('suffix');\n }\n\n if (digits === 'none') {\n // do nothing\n } else if (digits === 'auto') {\n if (label.useLocale()) {\n val = label.formatNumberLocale(val);\n } else {\n val = Type.autoDigits(val);\n }\n } else {\n if (label.useLocale()) {\n val = label.formatNumberLocale(val, digits);\n } else {\n val = Type.toFixed(val, digits);\n }\n }\n\n if (Type.isFunction(el.visProp.formatvalue)) {\n val = el.visProp.formatvalue(el, val);\n }\n\n return prefix + val + suffix;\n });\n label.fullUpdate();\n\n el.glider = glider;\n el.basepoint = basepoint;\n el.baseline = baseline;\n el.toppoint = toppoint;\n el.label = label;\n\n el.subs = {\n glider: glider,\n basePoint: basepoint,\n baseLine: baseline,\n topPoint: toppoint,\n label: label\n };\n el.inherits.push(glider, basepoint, baseline, toppoint, label);\n\n el.remove = priv.removeSlopeTriangle;\n\n Type.extendInstanceMethodMap(el, {\n tangent: \"tangent\",\n glider: \"glider\",\n basepoint: \"basepoint\",\n baseline: \"baseline\",\n toppoint: \"toppoint\",\n borderHorizontal: \"borderHorizontal\",\n borderVertical: \"borderVertical\",\n borderParallel: \"borderParallel\",\n label: \"label\",\n Value: \"Slope\",\n V: \"Slope\",\n Slope: \"Slope\",\n Angle: \"getAngle\",\n getAngle: \"getAngle\",\n DeltaX: \"DeltaX\",\n DeltaY: \"DeltaY\",\n Direction: \"Direction\"\n });\n\n return el;\n};\n\nJXG.registerElement(\"slopetriangle\", JXG.createSlopeTriangle);\n\n// export default {\n// createSlopeTriangle: JXG.createSlopeTriangle\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *\n * The checkbox can be supplied with custom-made events by using the property rendNodeCheckbox.\n * @example\n * var checkbox = board.create('checkbox', [0, 4, 'Click me']),\n * p = board.create('point', [1, 1]);\n *\n * JXG.addEvent(checkbox.rendNodeCheckbox, 'change', function() {\n * if (this.Value()) {\n * p.moveTo([4, 1]);\n * } else {\n * p.moveTo([1, 1]);\n * }\n * }, checkbox);\n * \n * \n * @example\n * var i1 = board.create('input', [1, 5, 'sin(x)', 'f(x)='], {cssStyle: 'width:4em', maxlength: 2});\n * var c1 = board.create('checkbox', [1, 3, 'label 1'], {});\n * var b1 = board.create('button', [1, 1, 'Change texts', function () {\n * i1.setText('g(x)=');\n * i1.set('cos(x)');\n * c1.setText('label 2');\n * b1.setText('Texts are changed');\n * }],\n * {cssStyle: 'width:200px'});\n *\n * \n * \n *\n */\nJXG.createCheckbox = function (board, parents, attributes) {\n var t,\n par,\n setTextBackup,\n attr = Type.copyAttributes(attributes, board.options, 'checkbox');\n\n //if (parents.length !== 3) {\n //throw new Error(\"JSXGraph: Can't create checkbox with parent types '\" +\n // (typeof parents[0]) + \"' and '\" + (typeof parents[1]) + \"'.\" +\n // \"\\nPossible parents are: [[x,y], label]\");\n //}\n\n par = [\n parents[0],\n parents[1],\n '' +\n '' +\n \"\"\n ];\n\n // Make sure the setText method is the original one. The JessieCode parser changes it during parsing.\n setTextBackup = Text.prototype.setText;\n Text.prototype.setText = Text.prototype._setText;\n\n // 1. Create checkbox element with empty label\n t = board.create(\"text\", par, attr);\n t.type = Type.OBJECT_TYPE_CHECKBOX;\n\n // Restore whichever setText method was set before this contructor was called.\n Text.prototype.setText = setTextBackup;\n\n\n t.rendNodeCheckbox = t.rendNode.childNodes[0].childNodes[0];\n t.rendNodeLabel = t.rendNode.childNodes[0].childNodes[1];\n\n t.rendNodeTag = t.rendNodeCheckbox; // Needed for unified treatment in setAttribute\n t.rendNodeTag.disabled = !!attr.disabled;\n\n t.rendNodeCheckbox.id = t.rendNode.id + \"_checkbox\";\n t.rendNodeLabel.id = t.rendNode.id + \"_label\";\n t.rendNodeLabel.setAttribute(\"for\", t.rendNodeCheckbox.id);\n\n // 2. Set parents[2] (string|function) as label of the checkbox element.\n // abstract.js selects the correct DOM element for the update\n t.setText(parents[2]);\n\n // This sets the font-size of the checkbox itself\n t.visPropOld.fontsize = '0px';\n board.renderer.updateTextStyle(t, false);\n\n t.rendNodeCheckbox.checked = attr.checked;\n\n t._value = attr.checked;\n\n /**\n * Returns the value of the checkbox element\n * @name Value\n * @memberOf Checkbox.prototype\n * @function\n * @returns {String} value of the checkbox.\n */\n t.Value = function () {\n return this._value;\n };\n\n /**\n * @class\n * @ignore\n */\n t.update = function () {\n if (this.needsUpdate) {\n JXG.Text.prototype.update.call(this);\n this._value = this.rendNodeCheckbox.checked;\n }\n return this;\n };\n\n Env.addEvent(t.rendNodeCheckbox, \"change\", priv.CheckboxChangeEventHandler, t);\n\n return t;\n};\n\nJXG.registerElement(\"checkbox\", JXG.createCheckbox);\n\n// export default {\n// createCheckbox: JXG.createCheckbox\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n * @example\n * // Add the `keyup` event to an input field\n * var A = board.create('point', [3, -2]);\n * var i = board.create('input', [-4, -4, \"1\", \"x \"]);\n *\n * i.rendNodeInput.addEventListener(\"keyup\", ( function () {\n * var x = parseFloat(this.value);\n * if (!isNaN(x)) {\n * \t A.moveTo([x, 3], 100);\n * }\n * }));\n *\n * \n * \n *\n * @example\n * // Add the `change` event to an input field\n * var A = board.create('point', [3, -2]);\n * var i = board.create('input', [-4, -4, \"1\", \"x \"]);\n *\n * i.rendNodeInput.addEventListener(\"change\", ( function () {\n * var x = parseFloat(i.Value());\n * A.moveTo([x, 2], 100);\n * }));\n *\n * \n * \n *\n * @example\n * // change the width of an input field\n * let s = board.create('slider', [[-3, 3], [2, 3], [50, 100, 300]]);\n * let inp = board.create('input', [-6, 1, 'Math.sin(x)*x', 'f(x)='],{cssStyle:()=>'width:'+s.Value()+'px'});\n *\n * \n * \n *\n * @example\n * Apply CSS classes to label and input tag\n * <style>\n * div.JXGtext_inp {\n * font-weight: bold;\n * }\n *\n * // Label\n * div.JXGtext_inp > span > span {\n * padding: 3px;\n * }\n *\n * // Input field\n * div.JXGtext_inp > span > input {\n * width: 100px;\n * border: solid 4px red;\n * border-radius: 25px;\n * }\n * </style>\n *\n * var inp = board.create('input', [-6, 1, 'x', 'y'], {\n * CssClass: 'JXGtext_inp', HighlightCssClass: 'JXGtext_inp'\n * });\n *\n * \n * \n * \n * \n *\n */\nJXG.createInput = function (board, parents, attributes) {\n var t,\n par,\n setTextBackup,\n attr = Type.copyAttributes(attributes, board.options, 'input');\n\n par = [\n parents[0],\n parents[1],\n '' +\n '' +\n \"\"\n ];\n\n // Make sure the setText method is the original one. The JessieCode parser changes it during parsing.\n setTextBackup = Text.prototype.setText;\n Text.prototype.setText = Text.prototype._setText;\n\n // 1. Create input element with empty label\n t = board.create(\"text\", par, attr);\n t.type = Type.OBJECT_TYPE_INPUT;\n\n // Restore whichever setText method was set before this contructor was called.\n Text.prototype.setText = setTextBackup;\n\n t.rendNodeLabel = t.rendNode.childNodes[0].childNodes[0];\n t.rendNodeInput = t.rendNode.childNodes[0].childNodes[1];\n t.rendNodeInput.value = parents[2];\n t.rendNodeTag = t.rendNodeInput; // Needed for unified treatment in setAttribute\n t.rendNodeTag.disabled = !!attr.disabled;\n t.rendNodeLabel.id = t.rendNode.id + \"_label\";\n t.rendNodeInput.id = t.rendNode.id + \"_input\";\n t.rendNodeInput.setAttribute(\"aria-labelledby\", t.rendNodeLabel.id);\n\n // 2. Set parents[3] (string|function) as label of the input element.\n // abstract.js selects the correct DOM element for the update\n t.setText(parents[3]);\n\n t._value = parents[2];\n\n // 3. capture keydown events on the input, and do not let them propagate. The problem is that\n // elevation controls on view3D use left and right, so editing the input triggers 3D pan.\n t.rendNodeInput.addEventListener(\"keydown\", (event) => {\n // only trap left-and-right in case user wants input editing events\n if (event.key === 'ArrowLeft' || event.key === 'ArrowRight') {\n event.stopPropagation();\n }\n });\n\n\n\n\n /**\n * @class\n * @ignore\n */\n t.update = function () {\n if (this.needsUpdate) {\n JXG.Text.prototype.update.call(this);\n this._value = this.rendNodeInput.value;\n }\n return this;\n };\n\n /**\n * Returns the value (content) of the input element\n * @name Value\n * @memberOf Input.prototype\n * @function\n * @returns {String} content of the input field.\n */\n t.Value = function () {\n return this._value;\n };\n\n /**\n * Sets value of the input element.\n * @name set\n * @memberOf Input.prototype\n * @function\n *\n * @param {String} val\n * @returns {JXG.GeometryElement} Reference to the element.\n *\n * @example\n * var i1 = board.create('input', [-3, 4, 'sin(x)', 'f(x)='], {cssStyle: 'width:4em', maxlength: 2});\n * var c1 = board.create('checkbox', [-3, 2, 'label 1'], {});\n * var b1 = board.create('button', [-3, -1, 'Change texts', function () {\n * i1.setText('g(x)');\n * i1.set('cos(x)');\n * c1.setText('label 2');\n * b1.setText('Texts are changed');\n * }],\n * {cssStyle: 'width:400px'});\n *\n * \n * \n *\n */\n\n /**\n * @class\n * @ignore\n */\n\n t.set = function (val) {\n this._value = val;\n this.rendNodeInput.value = val;\n return this;\n };\n\n Env.addEvent(t.rendNodeInput, \"input\", priv.InputInputEventHandler, t);\n Env.addEvent(\n t.rendNodeInput,\n \"mousedown\",\n function (evt) {\n if (Type.exists(evt.stopPropagation)) {\n evt.stopPropagation();\n }\n },\n t\n );\n Env.addEvent(\n t.rendNodeInput,\n \"touchstart\",\n function (evt) {\n if (Type.exists(evt.stopPropagation)) {\n evt.stopPropagation();\n }\n },\n t\n );\n Env.addEvent(\n t.rendNodeInput,\n \"pointerdown\",\n function (evt) {\n if (Type.exists(evt.stopPropagation)) {\n evt.stopPropagation();\n }\n },\n t\n );\n\n // This sets the font-size of the input HTML element\n t.visPropOld.fontsize = '0px';\n board.renderer.updateTextStyle(t, false);\n\n return t;\n};\n\nJXG.registerElement(\"input\", JXG.createInput);\n\n// export default {\n// createInput: JXG.createInput\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n * @example\n * // A toggle button\n * var butt = board.create('button', [-2, -2, 'Off', function() {\n * var txt;\n * butt.value = !butt.value;\n * if (butt.value) {\n * \ttxt = 'On';\n * } else {\n * \ttxt = 'Off';\n * }\n * \tbutt.rendNodeButton.innerHTML = txt;\n * }]);\n *\n * // Set initial value for the button\n * if (!JXG.exists(butt.value)) {\n * \tbutt.value = false;\n * }\n *\n * var p = board.create('point', [2, -2], {\n * \tvisible: () => butt.value\n * });\n *\n *\n *\n * \n * \n *\n * @example\n * var i1 = board.create('input', [-3, 4, 'sin(x)', 'f(x)='], {cssStyle: 'width:4em', maxlength: 2});\n * var c1 = board.create('checkbox', [-3, 2, 'label 1'], {});\n * var b1 = board.create('button', [-3, -1, 'Change texts', function () {\n * i1.setText('g(x)');\n * i1.set('cos(x)');\n * c1.setText('label 2');\n * b1.setText('Texts are changed');\n * }],\n * {cssStyle: 'width:200px'});\n *\n * \n * \n *\n * @example\n * // Set the CSS class of the button\n *\n * // CSS:\n * <style>\n * .mybutton > button {\n * background-color: #04AA6D;\n * border: none;\n * color: white;\n * padding: 1px 3px;\n * text-align: center;\n * text-decoration: none;\n * display: inline-block;\n * font-size: 16px;\n * }\n * </style>\n *\n * // JavaScript:\n * var button = board.create('button',\n * [1, 4, 'answers', function () {}],\n * {cssClass:'mybutton', highlightCssClass: 'mybutton'});\n *\n * \n * \n * \n * \n *\n */\nJXG.createButton = function (board, parents, attributes) {\n var t,\n par,\n setTextBackup,\n attr = Type.copyAttributes(attributes, board.options, 'button');\n\n //if (parents.length < 3) {\n //throw new Error(\"JSXGraph: Can't create button with parent types '\" +\n // (typeof parents[0]) + \"' and '\" + (typeof parents[1]) + \"'.\" +\n // \"\\nPossible parents are: [x, y, label, handler]\");\n //}\n\n // Make sure the setText method is the original one. The JessieCode parser changes it during parsing.\n setTextBackup = Text.prototype.setText;\n Text.prototype.setText = Text.prototype._setText;\n\n // 1. Create empty button\n par = [parents[0], parents[1], ''];\n t = board.create(\"text\", par, attr);\n t.type = Type.OBJECT_TYPE_BUTTON;\n\n // Restore whichever setText method was set before this contructor was called.\n Text.prototype.setText = setTextBackup;\n\n t.rendNodeButton = t.rendNode.childNodes[0];\n t.rendNodeButton.id = t.rendNode.id + \"_button\";\n\n t.rendNodeTag = t.rendNodeButton; // Needed for unified treatment in setAttribute\n t.rendNodeTag.disabled = !!attr.disabled;\n\n // 2. Set parents[2] (string|function) as content of the button.\n // abstract.js selects the correct DOM element for the update\n t.setText(parents[2]);\n\n // This sets the font size of the button text\n t.visPropOld.fontsize = '0px';\n board.renderer.updateTextStyle(t, false);\n\n if (parents[3]) {\n if (Type.isString(parents[3])) {\n t._jc = new JXG.JessieCode();\n t._jc.use(board);\n t._handler = function () {\n t._jc.parse(parents[3]);\n };\n } else {\n t._handler = parents[3];\n }\n }\n\n Env.addEvent(t.rendNodeButton, \"click\", priv.ButtonClickEventHandler, t);\n Env.addEvent(\n t.rendNodeButton,\n \"mousedown\",\n function (evt) {\n if (Type.exists(evt.stopPropagation)) {\n evt.stopPropagation();\n }\n },\n t\n );\n Env.addEvent(\n t.rendNodeButton,\n \"touchstart\",\n function (evt) {\n if (Type.exists(evt.stopPropagation)) {\n evt.stopPropagation();\n }\n },\n t\n );\n Env.addEvent(\n t.rendNodeButton,\n \"pointerdown\",\n function (evt) {\n if (Type.exists(evt.stopPropagation)) {\n evt.stopPropagation();\n }\n },\n t\n );\n\n return t;\n};\n\nJXG.registerElement(\"button\", JXG.createButton);\n\n// export default {\n// createButton: JXG.createButton\n// };\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n * @example\n * // Slider to control length of vectors\n * var s = board.create('slider', [[-3, 7], [3, 7], [0, 0.33, 1]], {name: 'length'});\n * // Slider to control number of steps\n * var stepsize = board.create('slider', [[-3, 6], [3, 6], [1, 20, 100]], {name: 'steps', snapWidth: 1});\n *\n * // Defining functions\n * var fx = (x, y) => 0.2 * y;\n * var fy = (x, y) => 0.2 * (Math.cos(x) - 2) * Math.sin(x);\n *\n * var field = board.create('vectorfield', [\n * [fx, fy], // Defining function\n * [-6, () => stepsize.Value(), 6], // Horizontal mesh\n * [-5, () => stepsize.Value(), 5], // Vertical mesh\n * ], {\n * highlightStrokeColor: JXG.palette.blue, // Make highlighting invisible\n *\n * scale: () => s.Value(), // Scaling of vectors\n *\n * arrowHead: {\n * enabled: true,\n * size: 8, // Pixel length of arrow head\n * angle: Math.PI / 16\n * }\n * });\n *\n * \n * \n *\n */\nJXG.createVectorField = function (board, parents, attributes) {\n var el, attr;\n\n if (!(parents.length >= 3 &&\n (Type.isArray(parents[0]) || Type.isFunction(parents[0]) || Type.isString(parents[0])) &&\n (Type.isArray(parents[1]) && parents[1].length === 3) &&\n (Type.isArray(parents[2]) && parents[2].length === 3)\n )) {\n throw new Error(\n \"JSXGraph: Can't create vector field with parent types \" +\n \"'\" + typeof parents[0] + \"', \" +\n \"'\" + typeof parents[1] + \"', \" +\n \"'\" + typeof parents[2] + \"'.\"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'vectorfield');\n\n /**\n * @type {JXG.Curve}\n * @ignore\n */\n el = board.create('curve', [[], []], attr);\n el.elType = 'vectorfield';\n\n /**\n * Set the defining functions of vector field.\n * @memberOf Vectorfield\n * @name setF\n * @function\n * @param {Array|Function} func Either an array containing two functions f1(x, y) and f2(x, y) or function f(x, y) returning an array of length 2.\n * @returns {Object} Reference to the vector field object.\n *\n * @example\n * field.setF([(x, y) => Math.sin(y), (x, y) => Math.cos(x)]);\n * board.update();\n *\n */\n el.setF = function (func, varnames) {\n var f0, f1;\n if (Type.isArray(func)) {\n f0 = Type.createFunction(func[0], this.board, varnames);\n f1 = Type.createFunction(func[1], this.board, varnames);\n /**\n * @ignore\n */\n this.F = function (x, y) { return [f0(x, y), f1(x, y)]; };\n } else {\n this.F = Type.createFunction(func, el.board, varnames);\n }\n return this;\n };\n\n el.setF(parents[0], 'x, y');\n el.xData = parents[1];\n el.yData = parents[2];\n\n el.updateDataArray = function () {\n var x, y, i, j,\n scale = this.evalVisProp('scale'),\n start_x = Type.evaluate(this.xData[0]),\n steps_x = Type.evaluate(this.xData[1]),\n end_x = Type.evaluate(this.xData[2]),\n delta_x = (end_x - start_x) / steps_x,\n\n start_y = Type.evaluate(this.yData[0]),\n steps_y = Type.evaluate(this.yData[1]),\n end_y = Type.evaluate(this.yData[2]),\n delta_y = (end_y - start_y) / steps_y,\n v, theta, phi1, phi2,\n\n showArrow = this.evalVisProp('arrowhead.enabled'),\n leg, leg_x, leg_y, alpha;\n\n\n if (showArrow) {\n // Arrow head style\n leg = this.evalVisProp('arrowhead.size');\n leg_x = leg / board.unitX;\n leg_y = leg / board.unitY;\n alpha = this.evalVisProp('arrowhead.angle');\n }\n\n this.dataX = [];\n this.dataY = [];\n\n for (i = 0, x = start_x; i <= steps_x; x += delta_x, i++) {\n for (j = 0, y = start_y; j <= steps_y; y += delta_y, j++) {\n v = this.F(x, y);\n v[0] *= scale;\n v[1] *= scale;\n\n Type.concat(this.dataX, [x, x + v[0], NaN]);\n Type.concat(this.dataY, [y, y + v[1], NaN]);\n\n if (showArrow && Math.abs(v[0]) + Math.abs(v[1]) > 0.0) {\n // Arrow head\n theta = Math.atan2(v[1], v[0]);\n phi1 = theta + alpha;\n phi2 = theta - alpha;\n Type.concat(this.dataX, [x + v[0] - Math.cos(phi1) * leg_x, x + v[0], x + v[0] - Math.cos(phi2) * leg_x, NaN]);\n Type.concat(this.dataY, [y + v[1] - Math.sin(phi1) * leg_y, y + v[1], y + v[1] - Math.sin(phi2) * leg_y, NaN]);\n }\n }\n }\n };\n\n Type.extendInstanceMethodMap(el, {\n setF: \"setF\"\n });\n\n return el;\n};\n\nJXG.registerElement(\"vectorfield\", JXG.createVectorField);\n\n/**\n * @class A slope field is a graphical representation of the solutions\n * to a first-order differential equation of a scalar function.\n * \n * \n *\n * @example\n * // Slider to control length of vectors\n * var s = board.create('slider', [[-3, 7], [3, 7], [0, 0.33, 1]], {name: 'length'});\n * // Slider to control number of steps\n * var stepsize = board.create('slider', [[-3, 6], [3, 6], [1, 20, 100]], {name: 'steps', snapWidth: 1});\n *\n * var field = board.create('slopefield', [\n * (x, y) => x * x - y * y,\n * [-6, () => stepsize.Value(), 6],\n * [-5, () => stepsize.Value(), 5]],\n * {\n * strokeWidth: 1.5,\n * highlightStrokeWidth: 0.5,\n * highlightStrokeColor: JXG.palette.blue,\n *\n * scale: () => s.Value(),\n *\n * arrowHead: {\n * enabled: false,\n * size: 8,\n * angle: Math.PI / 16\n * }\n * });\n *\n * \n * \n *\n */\nJXG.createSlopeField = function (board, parents, attributes) {\n var el, f, attr;\n\n if (!(parents.length >= 3 &&\n (Type.isFunction(parents[0]) || Type.isString(parents[0])) &&\n (Type.isArray(parents[1]) && parents[1].length === 3) &&\n (Type.isArray(parents[2]) && parents[2].length === 3)\n )) {\n throw new Error(\n \"JSXGraph: Can't create slope field with parent types \" +\n \"'\" + typeof parents[0] + \"', \" +\n \"'\" + typeof parents[1] + \"', \" +\n \"'\" + typeof parents[2] + \"'.\"\n );\n }\n\n f = Type.createFunction(parents[0], board, 'x, y');\n parents[0] = function (x, y) {\n var z = f(x, y),\n nrm = Math.sqrt(1 + z * z);\n return [1 / nrm, z / nrm];\n };\n attr = Type.copyAttributes(attributes, board.options, 'slopefield');\n /**\n * @type {JXG.Curve}\n * @ignore\n */\n el = board.create('vectorfield', parents, attr);\n el.elType = 'slopefield';\n\n /**\n * Set the defining functions of slope field.\n * @name Slopefield#setF\n * @function\n * @param {Function} func Function f(x, y) returning a number.\n * @returns {Object} Reference to the slope field object.\n *\n * @example\n * field.setF((x, y) => x * x + y * y);\n * board.update();\n *\n */\n el.setF = function (func, varnames) {\n var f = Type.createFunction(func, el.board, varnames);\n\n /**\n * @ignore\n */\n this.F = function (x, y) {\n var z = f(x, y),\n nrm = Math.sqrt(1 + z * z);\n return [1 / nrm, z / nrm];\n };\n };\n\n Type.extendInstanceMethodMap(el, {\n setF: \"setF\"\n });\n\n return el;\n};\n\nJXG.registerElement(\"slopefield\", JXG.createSlopeField);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n *\n *\n * @pseudo\n * @name Smartlabel\n * @augments JXG.Text\n * @constructor\n * @type JXG.Text\n * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.GeometryElement} Parent parent object: point, line, circle, polygon, angle.\n * @param {String|Function} Txt Optional text. In case, this content is not the empty string,\n * the measurement is overwritten by this text.\n *\n * @example\n * var p1 = board.create('point', [3, 4], {showInfobox: false, withLabel: false});\n * board.create('smartlabel', [p1], {digits: 1, baseUnit: 'm', dir: 'col', useMathJax: false});\n *\n * \n * \n *\n * @example\n * var s1 = board.create('line', [[-7, 2], [6, -6]], {point1: {visible:true}, point2: {visible:true}});\n * board.create('smartlabel', [s1], {baseUnit: 'm', measure: 'length', prefix: 'L = ', useMathJax: false});\n * board.create('smartlabel', [s1], {baseUnit: 'm', measure: 'slope', prefix: 'Δ = ', useMathJax: false});\n *\n *\n * \n * \n *\n * @example\n * var c1 = board.create('circle', [[0, 1], [4, 1]], {point2: {visible: true}});\n * board.create('smartlabel', [c1], {baseUnit: 'm', measure: 'perimeter', prefix: 'U = ', useMathJax: false});\n * board.create('smartlabel', [c1], {baseUnit: 'm', measure: 'area', prefix: 'A = ', useMathJax: false});\n * board.create('smartlabel', [c1], {baseUnit: 'm', measure: 'radius', prefix: 'R = ', useMathJax: false});\n *\n *\n * \n * \n *\n * @example\n * var p2 = board.create('polygon', [[-6, -5], [7, -7], [-4, 3]], {});\n * board.create('smartlabel', [p2], {\n * baseUnit: 'm',\n * measure: 'area',\n * prefix: 'A = ',\n * cssClass: 'smart-label-pure smart-label-polygon',\n * highlightCssClass: 'smart-label-pure smart-label-polygon',\n * useMathJax: false\n * });\n * board.create('smartlabel', [p2, () => 'X: ' + p2.vertices[0].X().toFixed(1)], {\n * measure: 'perimeter',\n * cssClass: 'smart-label-outline smart-label-polygon',\n * highlightCssClass: 'smart-label-outline smart-label-polygon',\n * useMathJax: false\n * });\n *\n * \n * \n *\n * @example\n * var a1 = board.create('angle', [[1, -1], [1, 2], [1, 5]], {name: 'β', withLabel: false});\n * var sma = board.create('smartlabel', [a1], {digits: 1, prefix: a1.name + '=', baseUnit: '°', useMathJax: false});\n *\n * \n * \n *\n */\nJXG.createSmartLabel = function (board, parents, attributes) {\n var el, attr,\n p, user_supplied_text;\n\n if (parents.length === 0 || (\n [Const.OBJECT_CLASS_POINT, Const.OBJECT_CLASS_LINE, Const.OBJECT_CLASS_CIRCLE].indexOf(parents[0].elementClass) < 0 &&\n [Const.OBJECT_TYPE_POLYGON, Const.OBJECT_TYPE_ANGLE].indexOf(parents[0].type) < 0\n )) {\n throw new Error(\n \"JSXGraph: Can't create smartlabel with parent types \" +\n \"'\" + typeof parents[0] + \"', \" +\n \"'\" + typeof parents[1] + \"'.\"\n );\n }\n\n p = parents[0];\n user_supplied_text = parents[1] || '';\n\n attr = Type.copyAttributes(attributes, board.options, 'smartlabel');\n\n if (p.elementClass === Const.OBJECT_CLASS_POINT) {\n attr = Type.merge(attr, Type.copyAttributes(attributes, board.options, 'smartlabelpoint'));\n\n } else if (p.elementClass === Const.OBJECT_CLASS_LINE) {\n attr = Type.merge(attr, Type.copyAttributes(attributes, board.options, 'smartlabelline'));\n /**\n * @class\n * @ignore\n */\n attr.rotate = function (self) {\n var orientation = self.evalVisProp('orientation'),\n add;\n switch (orientation) {\n case 'none':\n return 0;\n case 'orthogonal':\n add = 270;\n break;\n case 'orthogonal-inverted':\n add = 90;\n break;\n case 'parallel-inverted':\n case 'inverted':\n add = 0;\n break;\n default:\n add = 360;\n }\n return (Math.atan(p.getSlope()) * 180 / Math.PI + add) % 360;\n };\n /**\n * @class\n * @ignore\n */\n attr.visible = function (self) {\n var orientation = self.evalVisProp('orientation'),\n thres = self.evalVisProp('visibleThreshold'),\n sizeLabel = self.getSize(),\n sizeParent,\n c1, c2,\n dx, dy;\n\n c1 = p.point1.coords.scrCoords;\n c2 = p.point2.coords.scrCoords;\n dx = c2[1] - c1[1];\n dy = c2[2] - c1[2];\n sizeParent = Math.floor(Math.sqrt(dx * dx + dy * dy));\n\n switch (orientation) {\n case 'parallel':\n case 'parallel-inverted':\n case 'inverted':\n return sizeLabel[0] < sizeParent * thres;\n\n case 'orthogonal':\n case 'orthogonal-inverted':\n return sizeLabel[1] < sizeParent * thres;\n\n case 'none':\n default:\n return p.L() >= 1.5;\n }\n };\n\n } else if (p.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n attr = Type.merge(attr, Type.copyAttributes(attributes, board.options, 'smartlabelcircle'));\n /**\n * @class\n * @ignore\n */\n attr.visible = function (self) {\n var sizeLabel = self.getSize(),\n thres = self.evalVisProp('visibleThreshold'),\n sizeParent,\n c1, c2,\n dx, dy;\n\n c1 = p.center.coords.scrCoords;\n if (p.point2) {\n c2 = p.point2.coords.scrCoords;\n } else {\n c2 = new JXG.Coords(JXG.COORDS_BY_USER, [p.center.coords.usrCoords[0], p.center.coords.usrCoords[1] + p.Radius()], p.board).scrCoords;\n }\n dx = c2[1] - c1[1];\n dy = c2[2] - c1[2];\n sizeParent = Math.floor(Math.sqrt(dx * dx + dy * dy)) * 2;\n\n return sizeLabel[0] < sizeParent * thres;\n };\n\n } else if (p.type === Const.OBJECT_TYPE_POLYGON) {\n attr = Type.merge(attr, Type.copyAttributes(attributes, board.options, 'smartlabelpolygon'));\n } else if (p.type === Const.OBJECT_TYPE_ANGLE) {\n attr = Type.merge(attr, Type.copyAttributes(attributes, board.options, 'smartlabelangle'));\n /**\n * @class\n * @ignore\n */\n attr.rotate = function () {\n var c1 = p.center.coords.usrCoords,\n c2 = p.getLabelAnchor().usrCoords,\n v = (Math.atan2(c2[2] - c1[2], c2[1] - c1[1]) * 180 / Math.PI + 360) % 360;\n return (v > 90 && v < 270) ? v + 180 : v;\n };\n /**\n * @class\n * @ignore\n */\n attr.anchorX = function () {\n var c1 = p.center.coords.usrCoords,\n c2 = p.getLabelAnchor().usrCoords,\n v = (Math.atan2(c2[2] - c1[2], c2[1] - c1[1]) * 180 / Math.PI + 360) % 360;\n return (v > 90 && v < 270) ? 'right' : 'left';\n };\n }\n\n if (p.elementClass === Const.OBJECT_CLASS_POINT) {\n el = board.create('text', [\n function () { return p.X(); },\n function () { return p.Y(); },\n ''\n ], attr);\n\n } else if (p.elementClass === Const.OBJECT_CLASS_LINE) {\n\n if (attr.measure === 'length') {\n el = board.create('text', [\n function () { return (p.point1.X() + p.point2.X()) * 0.5; },\n function () { return (p.point1.Y() + p.point2.Y()) * 0.5; },\n ''\n ], attr);\n\n } else if (attr.measure === 'slope') {\n el = board.create('text', [\n function () { return (p.point1.X() * 0.25 + p.point2.X() * 0.75); },\n function () { return (p.point1.Y() * 0.25 + p.point2.Y() * 0.75); },\n ''\n ], attr);\n }\n\n } else if (p.elementClass === Const.OBJECT_CLASS_CIRCLE) {\n if (attr.measure === 'radius') {\n el = board.create('text', [\n function () { return p.center.X() + p.Radius() * 0.5; },\n function () { return p.center.Y(); },\n ''\n ], attr);\n\n } else if (attr.measure === 'area') {\n el = board.create('text', [\n function () { return p.center.X(); },\n function () { return p.center.Y() + p.Radius() * 0.5; },\n ''\n ], attr);\n\n } else if (attr.measure === 'circumference' || attr.measure === 'perimeter') {\n el = board.create('text', [\n function () { return p.getLabelAnchor(); },\n ''\n ], attr);\n\n }\n } else if (p.type === Const.OBJECT_TYPE_POLYGON) {\n if (attr.measure === 'area') {\n el = board.create('text', [\n function () { return p.getTextAnchor(); },\n ''\n ], attr);\n\n } else if (attr.measure === 'perimeter') {\n el = board.create('text', [\n function () {\n var last = p.borders.length - 1;\n if (last >= 0) {\n return [\n (p.borders[last].point1.X() + p.borders[last].point2.X()) * 0.5,\n (p.borders[last].point1.Y() + p.borders[last].point2.Y()) * 0.5\n ];\n } else {\n return p.getTextAnchor();\n }\n },\n ''\n ], attr);\n }\n\n } else if (p.type === Const.OBJECT_TYPE_ANGLE) {\n el = board.create('text', [\n function () {\n return p.getLabelAnchor();\n },\n ''\n ], attr);\n }\n\n if (!Type.exists(el)) {\n return null;\n }\n\n el.elType = 'smartlabel';\n\n el.parentObject = p;\n\n el.Value = function () {\n var mType = this.evalVisProp('measure');\n\n switch (mType) {\n case 'length':\n return p.L();\n\n case 'slope':\n return p.Slope();\n\n case 'area':\n return p.Area();\n\n case 'radius':\n return p.Radius();\n\n case 'perimeter':\n case 'circumference':\n return p.Perimeter();\n\n case 'rad':\n return p.Value();\n\n case 'deg':\n return p.Value() * 180 / Math.PI;\n\n case 'coords':\n return [p.X(), p.Y()];\n\n default:\n return 0.0;\n }\n };\n\n el.Dimension = function () {\n var mType = this.evalVisProp('measure');\n\n switch (mType) {\n case 'area':\n return 2;\n\n case 'length':\n case 'radius':\n case 'perimeter':\n case 'circumference':\n return 1;\n\n case 'slope':\n return 0;\n\n case 'rad':\n case 'deg':\n // Angles in various units has dimension 0\n return 0;\n\n case 'coords':\n return 1;\n\n default:\n return 0;\n }\n };\n\n el.Unit = function (dimension) {\n var unit = '',\n units = el.evalVisProp('units'),\n dim = dimension,\n dims = {}, i;\n\n if (!Type.exists(dim)) {\n dim = el.Dimension();\n }\n\n if (Type.isArray(dimension)) {\n for (i = 0; i < dimension.length; i++) {\n dims['dim' + dimension[i]] = el.Unit(dimension[i]);\n }\n return dims;\n }\n\n if (Type.isObject(units) && Type.exists(units[dim]) && units[dim] !== false) {\n unit = el.eval(units[dim]);\n } else if (Type.isObject(units) && Type.exists(units['dim' + dim]) && units['dim' + dim] !== false) {\n // In some cases, object keys must not be numbers. This allows key 'dim1' instead of '1'.\n unit = el.eval(units['dim' + dim]);\n } else {\n unit = el.evalVisProp('baseUnit');\n\n if (unit === '' && el.evalVisProp('unit') !== '') {\n // Backwards compatibility\n unit = el.evalVisProp('unit');\n }\n\n if (dim === 0) {\n unit = '';\n } else if (dim > 1 && unit !== '') {\n unit = unit + '^{' + dim + '}';\n }\n }\n\n return unit;\n };\n\n el.setText(function () {\n var digits, val, u,\n txt = Type.evaluate(user_supplied_text),\n str = '',\n pre = '',\n suf = '',\n dir,\n mj,\n i;\n\n if (txt !== '') {\n return txt;\n }\n\n val = el.Value();\n digits = el.evalVisProp('digits');\n u = el.Unit();\n pre = '';\n suf = '';\n dir = el.evalVisProp('dir');\n mj = el.evalVisProp('usemathjax') || el.evalVisProp('usekatex');\n\n if (el.evalVisProp('showPrefix')) {\n pre = el.evalVisProp('prefix');\n }\n if (el.evalVisProp('showSuffix')) {\n suf = el.evalVisProp('suffix');\n }\n\n if (el.useLocale()) {\n if (Type.isArray(val)) {\n for (i = 0; i < val.length; i++) {\n val[i] = el.formatNumberLocale(val[i], digits);\n }\n } else {\n val = el.formatNumberLocale(val, digits);\n }\n } else {\n if (Type.isArray(val)) {\n for (i = 0; i < val.length; i++) {\n val[i] = Type.toFixed(val[i], digits);\n }\n } else {\n val = Type.toFixed(val, digits);\n }\n }\n\n if (Type.isFunction(el.visProp.formatvalue)) {\n val = el.visProp.formatvalue(el, val);\n }\n\n if (Type.isArray(val)) {\n if (dir === 'row') {\n str = [];\n if (mj) {\n str.push('\\\\(', pre);\n for (i = 0; i < val.length; i++) {\n str.push(val[i], '\\\\,', u);\n if (i < val.length - 1) {\n str.push(' / ');\n }\n }\n str.push(suf, '\\\\)');\n } else {\n str.push(pre);\n for (i = 0; i < val.length; i++) {\n str.push(val[i], ' ', u);\n if (i < val.length - 1) {\n str.push(' / ');\n }\n }\n str.push(suf);\n }\n str = str.join('');\n } else if (dir.indexOf('col') === 0) { // Starts with 'col'\n str = [];\n if (mj) {\n str.push('\\\\(', pre, '\\\\left(\\\\array{');\n for (i = 0; i < val.length; i++) {\n str.push(val[i], '\\\\,', u);\n if (i < val.length - 1) {\n str.push('\\\\\\\\ ');\n }\n }\n str.push('}\\\\right)', suf, '\\\\)');\n\n } else {\n str.push(pre);\n for (i = 0; i < val.length; i++) {\n str.push(val[i], ' ', u);\n if (i < val.length - 1) {\n str.push('\n *
');\n }\n }\n str.push(suf);\n }\n str = str.join('');\n }\n } else {\n if (mj) {\n str = ['\\\\(', pre, val, '\\\\,', u, suf, '\\\\)'].join('');\n } else {\n str = [pre, val, u, suf].join('');\n }\n }\n\n return str;\n });\n\n p.addChild(el);\n el.setParents([p]);\n\n Type.extendInstanceMethodMap(el, {\n Value: \"Value\",\n V: \"Value\",\n Dimension: \"Dimension\",\n Unit: \"Unit\",\n parent: \"parentObject\",\n parentObject: \"parentObject\"\n });\n\n return el;\n};\n\nJXG.registerElement(\"smartlabel\", JXG.createSmartLabel);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Michael Gerhaeuser,\n Carsten Miller,\n Bianca Valentin,\n Alfred Wassermann,\n Peter Wilfahrt\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *\n * @example\n * var p = board.create('point', [1, 7], {size: 16});\n * var fo = board.create('fo', [\n * '<div style=\"background-color:blue; color: yellow; padding:20px; width:200px; height:50px; \">Hello</div>',\n * [-7, -6]],\n * {layer: 1, fixed: false}\n * );\n *\n * \n * \n *\n * @example\n * board.renderer.container.style.backgroundColor = 'lightblue';\n * var points = [];\n * points.push( board.create('point', [-2, 3.5], {fixed:false,color: 'yellow', size: 6,name:'6 am'}) );\n * points.push( board.create('point', [0, 3.5], {fixed:false,color: 'yellow', size: 6,name:'12 pm'}) );\n * points.push( board.create('point', [2, 3.5], {fixed:false,color: 'yellow', size: 6,name:'6 pm'}) );\n *\n * var fo = board.create('fo', [\n * '<video width=\"100%\" height=\"100%\" src=\"https://benedu.net/moodle/aaimg/ajx_img/astro/tr/1vd.mp4\" type=\"html5video\" controls>',\n * [-6, -4], [12, 8]],\n * {layer: 0, fixed: true}\n * );\n *\n * var f = JXG.Math.Numerics.lagrangePolynomial(points);\n * var graph = board.create('functiongraph', [f, -10, 10], {fixed:true,strokeWidth:3, layer: 8});\n *\n * \n * \n *\n * Video \"24-hour time-lapse in Cascais, Portugal. Produced by Nuno Miguel Duarte\" adapted from\n * https://www.pbslearningmedia.org/resource/buac18-k2-sci-ess-sunposition/changing-position-of-the-sun-in-the-sky/,\n * ©2016 Nuno Miguel Duarte.\n *\n */\nJXG.createForeignObject = function (board, parents, attributes) {\n var attr,\n fo,\n content = parents[0],\n coords = parents[1],\n size = [];\n\n if (parents.length >= 2) {\n size = parents[2];\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'foreignobject');\n fo = CoordsElement.create(JXG.ForeignObject, board, coords, attr, content, size);\n if (!fo) {\n throw new Error(\n \"JSXGraph: Can't create foreignObject with parent types '\" +\n typeof parents[0] +\n \"' and '\" +\n typeof parents[1] +\n \"'.\" +\n \"\\nPossible parent types: [string, [x, y], [w, h]], [string, [x, y]], [element,transformation]\"\n );\n }\n\n return fo;\n};\n\nJXG.registerElement(\"foreignobject\", JXG.createForeignObject);\nJXG.registerElement(\"fo\", JXG.createForeignObject);\n\nexport default JXG.ForeignObject;\n// export default {\n// ForeignObject: JXG.ForeignObject,\n// createForeignobject: JXG.createForeignObject\n// };\n","/*global JXG:true, define: true*/\n\nimport JXG from \"./jxg.js\";\nimport Options from \"./options.js\";\n\nJXG.extend(Options, {\n // infobox: {\n // // strokeColor: 'black',\n // // useKatex: false,\n // // useMathjax: false\n // },\n\n axes3d: {\n /**#@+\n * @visprop\n */\n\n /**\n * Position of the main axes in a View3D element. Possible values are\n * 'center', 'border' or 'none'. This attribute is immutable, i.e.\n * can not be changed during the lifetime of the construction.\n *\n * @type String\n * @name View3D#axesPosition\n * @default 'center'\n */\n axesPosition: \"center\", // Possible values: 'center', 'border', 'none'\n\n // Main axes\n /**\n * Attributes of the centered 3D x-axis.\n * Suppress label with `withLabel: false`.\n *\n * @type Line3D\n * @name View3D#xAxis\n * @see View3D#axesPosition\n */\n xAxis: {\n name: 'X',\n withlabel: true,\n visible: true,\n layer: 12,\n point2: { name: 'x' }, // Obsolete\n strokeColor: JXG.palette.red\n },\n\n /**\n * Attributes of the centered 3D y-axis.\n * Suppress label with `withLabel: false`.\n *\n * @type Line3D\n * @name View3D#yAxis\n * @see View3D#axesPosition\n */\n yAxis: {\n name: 'Y',\n withlabel: true,\n visible: true,\n layer: 12,\n point2: { name: 'y' }, // Obsolete\n strokeColor: JXG.palette.green\n },\n\n /**\n * Attributes of the centered 3D z-axis.\n * Suppress label with `withLabel: false`.\n *\n * @type Line3D\n * @name View3D#zAxis\n * @see View3D#axesPosition\n */\n zAxis: {\n name: 'Z',\n visible: true,\n withlabel: true,\n layer: 12,\n point2: { name: '' }, // Obsolete\n strokeColor: JXG.palette.blue\n },\n\n /**\n * Attributes of the 3D x-axis at the border.\n *\n * @type Line3D\n * @name View3D#xAxisBorder\n * @see View3D#axesPosition\n * @default
\n * {\n * name: 'x',\n * withLabel: false,\n * label: {\n * position: '50% left',\n * offset: [30, 0],\n * fontsize: 15\n * },\n * strokeWidth: 1,\n * lastArrow: false,\n * ticks3d: {\n * label: {\n * anchorX: 'middle',\n * anchorY: 'middle'\n * }\n * }\n *}\n *\n */\n xAxisBorder: {\n name: 'x',\n visible: 'ìnherit',\n withLabel: false,\n label: {\n position: '50% left',\n offset: [30, 0],\n fontsize: 15\n },\n strokeWidth: 1,\n lastArrow: false,\n ticks3d: {\n visible: 'ìnherit',\n label: {\n anchorX: 'middle',\n anchorY: 'middle'\n }\n\n }\n },\n\n /**\n * Attributes of the 3D y-axis at the border.\n *\n * @type Line3D\n * @name View3D#yAxisBorder\n * @see View3D#axesPosition\n * @default {\n * name: 'x',\n * withLabel: false,\n * label: {\n * position: '50% right',\n * offset: [0, -30],\n * fontsize: 15\n * },\n * strokeWidth: 1,\n * lastArrow: false,\n * ticks3d: {\n * label: {\n * anchorX: 'middle',\n * }\n * }\n *}\n *\n */\n yAxisBorder: {\n name: 'y',\n visible: 'ìnherit',\n withLabel: false,\n label: {\n position: '50% right',\n offset: [0, -30],\n fontsize: 15\n },\n strokeWidth: 1,\n lastArrow: false,\n ticks3d: {\n visible: 'ìnherit',\n label: {\n anchorX: 'middle'\n }\n }\n },\n\n /**\n * Attributes of the 3D z-axis at the border.\n *\n * @type Line3D\n * @name View3D#zAxisBorder\n * @see View3D#axesPosition\n * @default {\n * name: 'z',\n * withLabel: false,\n * label: {\n * position: '50% right',\n * offset: [30, 0],\n * fontsize: 15\n * },\n * strokeWidth: 1,\n * lastArrow: false,\n * ticks3d: {\n * label: {\n * anchorX: 'middle',\n * anchorY: 'middle'\n * }\n * }\n *}\n *\n */\n zAxisBorder: {\n name: 'z',\n visible: 'ìnherit',\n withLabel: false,\n label: {\n position: '50% right',\n offset: [30, 0],\n fontsize: 15\n },\n strokeWidth: 1,\n lastArrow: false,\n ticks3d: {\n visible: 'ìnherit',\n label: {\n anchorX: 'middle',\n anchorY: 'middle'\n }\n }\n },\n\n // Planes\n /**\n * Attributes of the 3D plane orthogonal to the x-axis at the \"rear\" of the cube.\n * @type Plane3D\n * @name View3D#xPlaneRear\n */\n xPlaneRear: {\n visible: true,\n layer: 0,\n strokeWidth: 1,\n strokeColor: '#dddddd',\n fillColor: '#dddddd',\n mesh3d: { layer: 1 },\n\n stepsU: 10,\n stepsV: 10,\n tiling: 'rectangle',\n polyhedron: {\n visible: 'inherit',\n strokeWidth: 0.5,\n strokeOpacity: 0.7,\n strokeColor: '#cccccc',\n fillOpacity: 0.30,\n fillColorArray: ['#e7e7e7'],\n shader: {\n enabled: true,\n fixed: true,\n type: 'zIndex',\n hue: 0,\n saturation: 0,\n minlightness: 65,\n maxLightness: 98\n }\n }\n },\n\n /**\n * Attributes of the 3D plane orthogonal to the y-axis at the \"rear\" of the cube.\n * @type Plane3D\n * @name View3D#yPlaneRear\n */\n yPlaneRear: {\n visible: true,\n strokeWidth: 1,\n strokeColor: '#dddddd',\n fillColor: '#dddddd',\n layer: 0,\n mesh3d: { layer: 1 },\n\n stepsU: 10,\n stepsV: 10,\n tiling: 'rectangle',\n polyhedron: {\n visible: 'inherit',\n strokeWidth: 0.5,\n strokeOpacity: 0.7,\n strokeColor: '#cccccc',\n fillOpacity: 0.30,\n fillColorArray: ['#e7e7e7'],\n shader: {\n enabled: true,\n fixed: true,\n type: 'zIndex',\n hue: 0,\n saturation: 0,\n minlightness: 65,\n maxLightness: 98\n }\n }\n },\n\n /**\n * Attributes of the 3D plane orthogonal to the z-axis at the \"rear\" of the cube.\n * @type Plane3D\n * @name View3D#zPlaneRear\n */\n zPlaneRear: {\n visible: true,\n strokeWidth: 1,\n strokeColor: '#dddddd',\n fillColor: '#dddddd',\n layer: 0,\n mesh3d: { layer: 1 },\n\n stepsU: 10,\n stepsV: 10,\n tiling: 'rectangle',\n polyhedron: {\n visible: 'inherit',\n strokeWidth: 0.5,\n strokeOpacity: 0.7,\n strokeColor: '#cccccc',\n fillOpacity: 0.30,\n fillColorArray: ['#e7e7e7'],\n shader: {\n enabled: true,\n fixed: true,\n type: 'zIndex',\n hue: 0,\n saturation: 0,\n minlightness: 65,\n maxLightness: 98\n }\n }\n },\n\n /**\n * Attributes of the 3D plane orthogonal to the x-axis at the \"front\" of the cube.\n * @type Plane3D\n * @name View3D#xPlaneFront\n */\n xPlaneFront: {\n visible: false,\n type: 'wireframe',\n strokeWidth: 1,\n strokeColor: '#dddddd',\n fillColor: 'none',\n layer: 0,\n mesh3d: {\n layer: 1,\n visible: false\n },\n\n stepsU: 10,\n stepsV: 10,\n tiling: 'rectangle',\n polyhedron: {\n visible: 'inherit',\n strokeWidth: 0.5,\n strokeOpacity: 0.7,\n strokeColor: '#cccccc',\n fillOpacity: 0.30,\n fillColorArray: ['#e7e7e7'],\n shader: {\n enabled: true,\n fixed: true,\n type: 'zIndex',\n hue: 0,\n saturation: 0,\n minlightness: 65,\n maxLightness: 98\n }\n }\n },\n /**\n * Attributes of the 3D plane orthogonal to the y-axis at the \"front\" of the cube.\n * @type Plane3D\n * @name View3D#yPlaneFront\n */\n yPlaneFront: {\n visible: false,\n type: 'wireframe',\n strokeWidth: 1,\n strokeColor: '#dddddd',\n fillColor: 'none',\n layer: 0,\n mesh3d: {\n layer: 1,\n visible: false\n },\n\n stepsU: 10,\n stepsV: 10,\n tiling: 'rectangle',\n polyhedron: {\n visible: 'inherit',\n strokeWidth: 0.5,\n strokeOpacity: 0.7,\n strokeColor: '#cccccc',\n fillOpacity: 0.30,\n fillColorArray: ['#e7e7e7'],\n shader: {\n enabled: true,\n fixed: true,\n type: 'zIndex',\n hue: 0,\n saturation: 0,\n minlightness: 65,\n maxLightness: 98\n }\n }\n },\n /**\n * Attributes of the 3D plane orthogonal to the z-axis at the \"front\" of the cube.\n * @type Plane3D\n * @name View3D#zPlaneFront\n */\n zPlaneFront: {\n visible: false,\n type: 'wireframe',\n strokeWidth: 1,\n strokeColor: '#dddddd',\n fillColor: 'none',\n layer: 0,\n mesh3d: {\n layer: 1,\n visible: false\n },\n\n stepsU: 10,\n stepsV: 10,\n tiling: 'rectangle',\n polyhedron: {\n visible: 'inherit',\n strokeWidth: 0.5,\n strokeOpacity: 0.7,\n strokeColor: '#cccccc',\n fillOpacity: 0.30,\n fillColorArray: ['#e7e7e7'],\n shader: {\n enabled: true,\n fixed: true,\n type: 'zIndex',\n hue: 0,\n saturation: 0,\n minlightness: 65,\n maxLightness: 98\n }\n }\n },\n\n // Axes on the planes\n /**\n * Attributes of the 3D y-axis on the 3D plane orthogonal to the x-axis at the \"rear\" of the cube.\n * @type Plane3D\n * @name View3D#xPlaneRearYAxis\n */\n xPlaneRearYAxis: {\n visible: 'inherit',\n strokeColor: \"#aaaaaa\",\n strokeWidth: 1.2,\n layer: 12\n },\n /**\n * Attributes of the 3D z-axis on the 3D plane orthogonal to the x-axis at the \"rear\" of the cube.\n * @type Plane3D\n * @name View3D#xPlaneRearZAxis\n */\n xPlaneRearZAxis: {\n visible: 'inherit',\n strokeColor: \"#888888\",\n strokeWidth: 1.2,\n layer: 12\n },\n /**\n * Attributes of the 3D y-axis on the 3D plane orthogonal to the x-axis at the \"front\" of the cube.\n * @type Plane3D\n * @name View3D#xPlaneFrontYAxis\n */\n xPlaneFrontYAxis: {\n visible: false,\n strokeColor: \"#888888\",\n strokeWidth: 1.2,\n layer: 12\n },\n /**\n * Attributes of the 3D z-axis on the 3D plane orthogonal to the x-axis at the \"front\" of the cube.\n * @type Plane3D\n * @name View3D#xPlaneFrontZAxis\n */\n xPlaneFrontZAxis: {\n visible: false,\n strokeColor: \"#888888\",\n strokeWidth: 1.2,\n layer: 12\n },\n /**\n * Attributes of the 3D x-axis on the 3D plane orthogonal to the y-axis at the \"rear\" of the cube.\n * @type Plane3D\n * @name View3D#yPlaneRearXAxis\n */\n yPlaneRearXAxis: {\n visible: 'inherit',\n strokeColor: \"#888888\",\n strokeWidth: 1.2,\n layer: 12\n },\n /**\n * Attributes of the 3D z-axis on the 3D plane orthogonal to the y-axis at the \"rear\" of the cube.\n * @type Plane3D\n * @name View3D#yPlaneRearZAxis\n */\n yPlaneRearZAxis: {\n visible: 'inherit',\n strokeColor: \"#888888\",\n strokeWidth: 1.2,\n layer: 12\n },\n /**\n * Attributes of the 3D x-axis on the 3D plane orthogonal to the y-axis at the \"front\" of the cube.\n * @type Plane3D\n * @name View3D#yPlaneFrontXAxis\n */\n yPlaneFrontXAxis: {\n visible: false,\n strokeColor: \"#888888\",\n strokeWidth: 1.2,\n layer: 12\n },\n /**\n * Attributes of the 3D z-axis on the 3D plane orthogonal to the y-axis at the \"front\" of the cube.\n * @type Plane3D\n * @name View3D#yPlaneFrontZAxis\n */\n yPlaneFrontZAxis: {\n visible: false,\n strokeColor: \"#888888\",\n strokeWidth: 1.2,\n layer: 12\n },\n\n /**\n * Attributes of the 3D x-axis on the 3D plane orthogonal to the z-axis at the \"rear\" of the cube.\n * @type Plane3D\n * @name View3D#zPlaneRearXAxis\n */\n zPlaneRearXAxis: {\n visible: 'inherit',\n strokeColor: \"#888888\",\n strokeWidth: 1.2,\n layer: 12\n },\n /**\n * Attributes of the 3D y-axis on the 3D plane orthogonal to the z-axis at the \"rear\" of the cube.\n * @type Plane3D\n * @name View3D#zPlaneRearYAxis\n */\n zPlaneRearYAxis: {\n visible: 'inherit',\n strokeColor: \"#888888\",\n strokeWidth: 1.2,\n layer: 12\n },\n /**\n * Attributes of the 3D x-axis on the 3D plane orthogonal to the z-axis at the \"front\" of the cube.\n * @type Plane3D\n * @name View3D#zPlaneFrontXAxis\n */\n zPlaneFrontXAxis: {\n visible: false,\n strokeColor: \"#888888\",\n strokeWidth: 1.2,\n layer: 12\n },\n /**\n * Attributes of the 3D y-axis on the 3D plane orthogonal to the z-axis at the \"front\" of the cube.\n * @type Plane3D\n * @name View3D#zPlaneFrontYAxis\n */\n zPlaneFrontYAxis: {\n visible: false,\n strokeColor: \"#888888\",\n strokeWidth: 1.2,\n layer: 12\n }\n\n /**#@-*/\n },\n\n axis3d: {\n highlight: false,\n fixed: true,\n strokeColor: \"black\",\n strokeWidth: 1,\n lastArrow: true,\n tabindex: null,\n label: {\n position: '103% left',\n offset: [0, 0]\n },\n\n point1: { visible: false, name: \"\", withLabel: false },\n point2: { visible: false, name: \"\", withLabel: false, label: { visible: true } }\n },\n\n circle3d: {\n\n layer: 12,\n point: { visible: false, name: \"\" },\n needsRegularUpdate: true\n\n },\n\n curve3d: {\n /**#@+\n * @visprop\n */\n\n layer: 12,\n highlight: false,\n tabindex: -1,\n strokeWidth: 1,\n numberPointsHigh: 200,\n needsRegularUpdate: true\n\n /**#@-*/\n },\n\n face3d: {\n /**#@+\n * @visprop\n */\n\n transitionProperties: [],\n layer: 12,\n highlight: false,\n tabindex: null,\n strokeWidth: 1,\n fillColor: JXG.palette.yellow,\n fillOpacity: 0.4,\n needsRegularUpdate: true,\n visible: true, // TODO: why not inherited from GeometryElement\n\n /**\n * Shading of faces. For this, the HSL color scheme is used.\n * Two types are possible: either by 'angle' or by 'zIndex'.\n * By default (i.e. type:'angle'), the angle between the camera axis and the normal of the\n * face determines the lightness value of the HSL color. Otherwise, the\n * zIndex of the face determines the lightness value of the HSL color.\n * shader: {\n * enabled: false,\n * fixed: true, // If false, update shading during rotation of viewport\n * type: 'angle', // 'angle', otherwise zIndex\n * hue: 60, // yellow\n * saturation: 90,\n * minLightness: 30,\n * maxLightness: 90,\n *\n * light: {\n * type: 1,// 1: lighting==camera,\n * // 2: Fixed: angle(light, object),\n * // 3: Fixed: angle(light, camera) (default)\n * az: -45, // TODO use radians, ignored for type==1\n * el: 20, // TODO use radians, ignored for type==1\n * bank: 0, // TODO use radians, ignored for type==1, type==3\n * dir: -1 // -1 (reverse), 0 (use abs), 1. Default: -1\n * }\n * }\n *\n * @example\n * var view = board.create(\n * 'view3d',\n * [[-5, -3], [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]],\n * {\n * projection: 'central',\n * trackball: { enabled: true },\n * depthOrder: {\n * enabled: true\n * },\n * xPlaneRear: { visible: false },\n * yPlaneRear: { visible: false },\n * zPlaneRear: { fillOpacity: 0.2, visible: true }\n * }\n * );\n *\n * let rho = 1.6180339887;\n * let vertexList = [\n * [0, -1, -rho], [0, +1, -rho], [0, -1, rho], [0, +1, rho],\n * [1, rho, 0], [-1, rho, 0], [1, -rho, 0], [-1, -rho, 0],\n * [-rho, 0, 1], [-rho, 0, -1], [rho, 0, 1], [rho, 0, -1]\n * ];\n * let faceArray = [\n * [4, 1, 11],\n * [11, 1, 0],\n * [6, 11, 0],\n * [0, 1, 9],\n * [11, 10, 4],\n * [9, 1, 5],\n * [8, 9, 5],\n * [5, 3, 8],\n * [6, 10, 11],\n * [2, 3, 10],\n * [2, 10, 6],\n * [8, 3, 2],\n * [3, 4, 10],\n * [7, 8, 2],\n * [9, 8, 7],\n * [0, 9, 7],\n * [4, 3, 5],\n * [5, 1, 4],\n * [0, 7, 6],\n * [7, 2, 6]\n * ];\n * var ico = view.create('polyhedron3d', [vertexList, faceArray], {\n * fillColorArray: [],\n * fillOpacity: 1,\n * strokeWidth: 0.1,\n * layer: 12,\n * shader: {\n * enabled: true,\n * type: 'angle',\n * hue: 0,\n * saturation: 90,\n * minlightness: 60,\n * maxLightness: 80\n * }\n * });\n *\n * \n *\n */\n shader: {\n enabled: false,\n fixed: true, // If false, update shading during rotation of viewport\n type: 'angle', // 'angle', otherwise zIndex\n hue: 60, // yellow\n saturation: 90,\n minLightness: 30,\n maxLightness: 90,\n\n light: {\n type: 1,// 1: lighting==camera,\n // 2: Fixed: angle(light, object),\n // 3: Fixed: angle(light, camera) (default)\n az: -45, // TODO use radians, ignored for type==1\n el: 20, // TODO use radians, ignored for type==1\n bank: 0, // TODO use radians, ignored for type==1, type==3\n dir: -1 // -1 (reverse), 0 (use abs), 1. Default: -1\n }\n }\n\n /**#@-*/\n },\n\n intersectionline3d: {\n point1: { visible: false, name: \"\" }, // Used in point/point\n point2: { visible: false, name: \"\" }\n },\n\n line3d: {\n /**#@+\n * @visprop\n */\n\n layer: 12,\n strokeWidth: 1,\n strokeColor: \"black\",\n fixed: true,\n tabindex: null,\n // gradient: \"linear\",\n // gradientSecondColor: \"#ffffff\",\n needsRegularUpdate: true,\n\n /**\n * Attributes of the defining point in case the line is defined by [point, vector, [range]]\n * @type Point3D\n * @name Line3D#point\n * @default \n * visible: false, name: \"\"
\n */\n point: { visible: false, name: \"\" }, // Used in cases of point/direction/range\n\n /**\n * Attributes of the first point in case the line is defined by [point, point].\n * @type Point3D\n * @name Line3D#point1\n * @default visible: false, name: \"\"
\n */\n point1: { visible: false, name: \"\" }, // Used in point/point\n\n /**\n * Attributes of the second point in case the line is defined by [point, point].\n * @type Point3D\n * @name Line3D#point2\n * @default visible: false, name: \"\"
\n */\n point2: { visible: false, name: \"\" },\n\n /**\n * If the 3D line is defined by two points and if this attribute is true,\n * the 3D line stretches infinitely in direction of its first point.\n * Otherwise it ends at point1.\n *\n * @name Line3D#straightFirst\n * @see Line3D#straightLast\n * @type Boolean\n * @default false\n */\n straightFirst: false,\n\n\n /**\n * If the 3D line is defined by two points and if this attribute is true,\n * the 3D line stretches infinitely in direction of its second point.\n * Otherwise it ends at point2.\n *\n * @name Line3D#straightLast\n * @see Line3D#straightFirst\n * @type Boolean\n * @default false\n */\n straightLast: false\n\n /**#@-*/\n },\n\n mesh3d: {\n /**#@+\n * @visprop\n */\n\n layer: 12,\n strokeWidth: 1,\n strokeColor: \"#9a9a9a\",\n strokeOpacity: 0.6,\n highlight: false,\n tabindex: null,\n needsRegularUpdate: true,\n\n /**\n * Step width of the mesh in the direction of the first spanning vector.\n * @type {Number}\n * @name Mesh3D#stepWidthU\n * @default 1\n *\n */\n stepWidthU: 1,\n\n /**\n * Step width of the mesh in the direction of the second spanning vector.\n *\n * @type {Number}\n * @name Mesh3D#stepWidthV\n * @default 1\n *\n */\n stepWidthV: 1\n\n /**#@-*/\n },\n\n plane3d: {\n /**#@+\n * @visprop\n */\n\n layer: 12,\n strokeWidth: 1,\n strokeColor: \"black\",\n strokeOpacity: 1,\n highlight: false,\n tabindex: null,\n needsRegularUpdate: true,\n visible: true,\n\n gradient: \"linear\",\n gradientSecondColor: \"#ffffff\",\n gradientAngle: Math.PI,\n fillColor: \"#bbbbbb\",\n fillOpacity: 0.3,\n\n type: 'shader', // 'wireframe', 'shader', 'colormap', 'colorarray'\n tiling: 'rectangle', // 'triangle', 'rectangle'\n\n /**\n * Optional 3D mesh of a finite plane.\n * It is not available if the plane is infinite (at initialization time) in any direction.\n *\n * @type Mesh3D\n * @name Plane3D#mesh3d\n * @default see {@link Mesh3D}\n */\n mesh3d: {\n visible: 'inherit'\n },\n\n stepsU: 6,\n stepsV: 6,\n\n colormap: {\n min: [-5, 190],\n max: [5, 0],\n s: 0.9,\n v: 0.9\n },\n\n // From surface3d\n polyhedron: {\n layer: 12,\n visible: 'inherit',\n strokeWidth: 0.1,\n fillOpacity: 0.8,\n fillColorArray: ['white', JXG.palette.blue],\n shader: {\n enabled: false,\n fixed: true,\n hue: 60, // yellow\n saturation: 90,\n minLightness: 55,\n maxLightness: 90,\n\n light: {\n dir: -1\n }\n }\n },\n\n /**\n * If the second parameter and the third parameter are given as arrays or functions and threePoints:true\n * then the second and third parameter are interpreted as point coordinates and not as directions, i.e.\n * the plane is defined by three points.\n *\n * @name Plane3D#threePoints\n * @type Boolean\n * @default false\n */\n threePoints: false,\n\n /**\n * Attributes of the defining point in case the plane is defined by [point, direction1, direction2, [range1, [range2]]].\n * @type Point3D\n * @name Plane3D#point\n * @default visible: false, name: \"\", fixed: true
\n */\n point: { visible: false, name: \"\", fixed: true },\n\n /**\n * Attributes of the first point in case the plane is defined by [point, point, point].\n * @type Point3D\n * @name Plane3D#point1\n * @default visible: false, name: \"\"
\n */\n point1: { visible: false, name: \"\" }, // Used in point/point/point\n\n /**\n * Attributes of the second point in case the plane is defined by [point, point, point].\n * @type Point3D\n * @name Plane3D#point2\n * @default visible: false, name: \"\"
\n */\n point2: { visible: false, name: \"\" }, // Used in point/point/point\n\n /**\n * Attributes of the third point in case the plane is defined by [point, point, point].\n * @type Point3D\n * @name Plane3D#point3\n * @default visible: false, name: \"\"
\n */\n point3: { visible: false, name: \"\" } // Used in point/point/point\n\n /**#@-*/\n },\n\n point3d: {\n layer: 13,\n infoboxDigits: \"auto\",\n strokeWidth: 0,\n gradient: \"radial\",\n gradientSecondColor: \"#555555\",\n fillColor: \"yellow\",\n highlightStrokeColor: \"#555555\",\n gradientFX: 0.7,\n gradientFY: 0.3,\n needsRegularUpdate: true,\n\n /**\n * If the point is bound to another element (\"glides\" on that element)\n * and if the bound reaches the boundary, the point may start cyclically\n * at the ozher side of the boundary - like one expects from a glider on a sphere.\n * For this, set cyclic to true.\n * @type Boolean\n * @name Point3D#cyclic\n * @default false\n */\n cyclic: false\n },\n\n polygon3d: {\n /**#@+\n * @visprop\n */\n\n layer: 12,\n highlight: false,\n tabindex: -1,\n strokeWidth: 1,\n fillColor: 'none',\n needsRegularUpdate: true\n\n\n /**#@-*/\n },\n\n polyhedron3d: {\n /**#@+\n * @visprop\n */\n\n /**\n * Color array to define fill colors of faces cyclically.\n * Alternatively, the fill color can be defined for each face individually.\n *\n * @type Array\n * @name Polyhedron3D#fillColorArray\n * @default ['white', 'black']\n */\n fillColorArray: ['white', 'black'],\n\n needsRegularUpdate: true\n\n /**#@-*/\n },\n\n sphere3d: {\n /**#@+\n * @visprop\n */\n\n layer: 12,\n highlight: false,\n\n strokeWidth: 1,\n strokeColor: '#00ff80',\n fillColor: 'white',\n gradient: 'radial',\n gradientSecondColor: '#00ff80',\n gradientFX: 0.7,\n gradientFY: 0.3,\n fillOpacity: 0.4,\n needsRegularUpdate: true\n\n /**#@-*/\n },\n\n surface3d: {\n /**#@+\n * @visprop\n */\n\n visible: true,\n layer: 12,\n highlight: false,\n tabindex: -1,\n\n /**\n * Description of how the mesh is visualized. Possible values are 'wireframe', 'rectangle', 'triangle'.\n * In case of `tiling:'wireframe'`, a rectangular mesh is displayed, the number of steps is determined by\n * the attributes `stepsU` and `stepsV`. Further, the attributes `strokeWidth` and `strokeColor`, ...\n * determine the style of the mesh.\n * \n *\n * @example\n *\n * var view = board.create('view3d',\n * [\n * [-6, -3], [8, 8],\n * [[-5, 5], [-5, 5], [-5, 5]]\n * ],\n * {\n * xPlaneRear: {visible: false},\n * yPlaneRear: {visible: false},\n * });\n *\n * // Function F to be plotted\n * var F = (x, y) => Math.cos(x * y / 4);\n *\n * // 3D surface\n * var c = view.create('functiongraph3d', [\n * F,\n * [-5, 5],\n * [-5, 5],\n * ], {\n * stepsU: 15,\n * stepsV: 15,\n * tiling:'triangle'\n * });\n *\n * \n * \n *\n * @example\n *\n * var view = board.create('view3d',\n * [\n * [-6, -3], [8, 8],\n * [[-5, 5], [-5, 5], [-5, 5]]\n * ],\n * {\n * xPlaneRear: {visible: false},\n * yPlaneRear: {visible: false},\n * });\n *\n * // Function F to be plotted\n * var F = (x, y) => Math.cos(x * y / 4);\n *\n * // 3D surface\n * var c = view.create('functiongraph3d', [\n * F,\n * [-5, 5],\n * [-5, 5],\n * ], {\n * stepsU: 15,\n * stepsV: 15,\n * tiling: 'rectangle'\n * });\n *\n * \n * \n */\n type: 'wireframe', // 'colormap', 'shader', 'colorarray'\n tiling: 'rectangle', // 'triangle'\n\n // Wireframe\n strokeWidth: 0.75,\n // --- end wireframe\n\n /**\n * HSV color range for colormap. Supply lower bound [z_min, hue_min] on z-value and corresponding hue value, as well\n * as upper bound [z_max, hue_max] on z-value and corresponding hue value. Further, give constant values for\n * \"saturation\" and \"value\" of HSV.\n *\n * @type {object}\n * @name ParametricSurface3D#colormap\n * @default {\n * min: [-5, 190],\n * max: [5, 0],\n * s: 0.9,\n * v: 0.9\n * }\n */\n colormap: {\n min: [-5, 190],\n max: [5, 0],\n s: 0.9,\n v: 0.9\n },\n\n /**\n * Attributes for the polyhedron3d in case `style='triangle'` or `style='rectangle'`.\n * Specifications are e.g.\n * \n *
\n * @type {object}\n * @name ParametricSurface3D#polyhedron\n * @default {strokewidth: 0, fillColorArray: ['white', 'black'] }\n * @see ParametricSurface3D#style\n *\n * @example\n * var F = (x, y) => Math.cos(x * y / 4);\n *\n * var view = board.create('view3d', [\n * [-6, -3], [8, 8],\n * [[-5, 5], [-5, 5], [-5, 5]]\n * ], {\n * xPlaneRear: {visible: false},\n * yPlaneRear: {visible: false},\n * depthOrder: {enabled: true}\n * });\n *\n * // 3D surface\n * var c = view.create('functiongraph3d', [F, [-5, 5], [-5, 5]], {\n * strokeWidth: 1, // ignored\n * stepsU: 10,\n * stepsV: 10,\n * tiling: 'triangle',\n * polyhedron: {\n * strokeWidth: 0, // has priority\n * fillOpacity: 0.9,\n * shader: {\n * enabled: true,\n * hue: 20,\n * saturation: 90,\n * minlightness: 50,\n * maxLightness: 80\n * }\n * }\n * });\n *\n * \n * \n *\n * @example\n *\n * var view = board.create('view3d',\n * [\n * [-6, -3], [8, 8],\n * [[-5, 5], [-5, 5], [-5, 5]]\n * ], {\n * xPlaneRear: {visible: false},\n * yPlaneRear: {visible: false}\n * });\n *\n * // Function F to be plotted\n * var F = (x, y) => y - x;\n *\n * // 3D surface\n * var c = view.create('functiongraph3d', [F, [-5, 5], [-5, 5]], {\n * stepsU: 9,\n * stepsV: 9,\n * tiling: 'rectangle'\n * });\n *\n * \n * \n */\n polyhedron: {\n visible: 'inherit',\n strokeWidth: 0.1,\n fillOpacity: 0.8,\n fillColorArray: ['white', JXG.palette.blue],\n shader: {\n enabled: false,\n fixed: true,\n hue: 60, // yellow\n saturation: 90,\n minLightness: 55,\n maxLightness: 90,\n\n light: {\n dir: -1\n }\n }\n },\n\n /**\n * Number of intervals the mesh is divided into in direction of parameter u.\n * If stepsU = 0 and type is 'wireframe' a 3D wireframe plot in one direction is created.\n * @type Number\n * @name ParametricSurface3D#stepsU\n */\n stepsU: 30,\n\n /**\n * Number of intervals the mesh is divided into in direction of parameter v.\n * If stepsV = 0 and type is 'wireframe' a 3D wireframe plot in one direction is created.\n * @type Number\n * @name ParametricSurface3D#stepsV\n */\n stepsV: 30,\n\n needsRegularUpdate: true\n\n /**#@-*/\n },\n\n text3d: {\n /**#@+\n * @visprop\n */\n\n withLabel: false,\n needsRegularUpdate: true\n\n /**#@-*/\n },\n\n ticks3d: {\n /**#@+\n * @visprop\n */\n\n visible: true,\n\n ticksDistance: 1,\n majorHeight: 10,\n minorTicks: 0,\n tickEndings: [0, 1],\n drawLabels: true,\n needsRegularUpdate: true,\n\n label: {\n visible: true,\n withLabel: false\n }\n\n /**#@-*/\n },\n\n vectorfield3d: {\n /**#@+\n * @visprop\n */\n\n /**\n * Scaling factor of the vectors. This in contrast to slope fields, where this attribute sets the vector to the given length.\n * @name scale\n * @memberOf Vectorfield3D.prototype\n * @type {Number|Function}\n * @see Slopefield.scale\n * @default 1\n */\n scale: 1,\n\n /**\n * Customize arrow heads of vectors. Be careful! If enabled this will slow down the performance.\n * Fields are:\n * \n *
\n * @name arrowhead\n * @memberOf Vectorfield3D.prototype\n * @type {Object}\n * @default {enabled: true, size: 5, angle: Math.PI * 0.125}\n */\n arrowhead: {\n enabled: true,\n size: 5,\n angle: Math.PI * 0.125\n },\n needsRegularUpdate: true\n\n /**#@-*/\n },\n\n view3d: {\n /**#@+\n * @visprop\n */\n\n needsRegularUpdate: true,\n\n /**\n * When this attribute is enabled, elements closer to the screen are drawn\n * over elements further from the screen within the 3D layer. This affects\n * all elements which are in one of the layer specified in the sub-attribute 'layers'.\n * \n *
\n *\n * @name View3D#depthOrder\n * @type Object\n * @default {\n * enabled: false,\n * layers: [12, 13]\n * }\n * \n */\n depthOrder: {\n enabled: true,\n layers: [12, 13]\n },\n\n /**\n * Choose the projection type to be used: `parallel` or `central`.\n * \n *
\n *\n *\n * @name View3D#projection\n * @type String\n * @default 'parallel'\n * @example\n * var bound = [-5, 5];\n * var view = board.create('view3d',\n * [[-6, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'parallel'\n * });\n *\n * \n * \n *\n * @example\n * var bound = [-5, 5];\n * var view = board.create('view3d',\n * [[-6, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'central'\n * });\n *\n * \n * \n *\n */\n projection: 'parallel',\n\n /**\n * Allow vertical dragging of objects, i.e. in direction of the z-axis.\n * Subobjects are\n *
\n *
\n * \n *
\n *\n * @name View3D#az\n * @type Object\n * @default \n *
\n * \n *
\n * \n *
\n * 'min' and 'max' are used only if trackball is not enabled.\n * Additionally, the attributes 'slider.point1.pos' and 'slider.point2.pos' control the position of the slider. Possible\n * values are 'auto' or an array [x, y] of length 2 for the position in user coordinates (or a function returning such an array).\n * {\n * pointer: {enabled: true, speed: 1, outside: true, button: -1, key: 'none'},\n * keyboard: {enabled: true, step: 10, key: 'ctrl'},\n * continuous: true,\n * slider: {\n * visible: true,\n * style: 6,\n * point1: {\n * pos: 'auto',\n * frozen: false\n * },\n * point2: {\n * pos: 'auto',\n * frozen: false\n * },\n * min: 0,\n * max: 2 * Math.PI,\n * start: 1.0\n * },\n * }\n *\n * @example\n * var bound = [-4, 6];\n * var view = board.create('view3d',\n * [[-4, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'parallel',\n * az: {\n * slider: {visible: true, start: 0.75 * Math.PI}\n * }\n * });\n *\n * \n * \n *\n */\n az: {\n pointer: {\n enabled: true,\n speed: 1,\n outside: true,\n button: -1,\n key: 'none'\n },\n keyboard: {\n enabled: true,\n step: 10,\n key: 'ctrl'\n },\n continuous: true,\n slider: {\n visible: 'inherit',\n style: 6,\n point1: {\n pos: 'auto',\n frozen: false\n },\n point2: {\n pos: 'auto',\n frozen: false\n },\n min: 0,\n max: 2 * Math.PI,\n start: 1.0\n }\n },\n\n /**\n * Specify the user handling of the elevation.\n * \n *
\n *\n * @name View3D#el\n * @type Object\n * @default \n *
\n * \n *
\n * \n *
\n * 'min' and 'max' are used only if trackball is not enabled.\n * Additionally, the attributes 'slider.point1.pos' and 'slider.point2.pos' control the position of the slider. Possible\n * values are 'auto' or an array [x, y] of length 2 for the position in user coordinates (or a function returning such an array).\n * {\n * pointer: {enabled: true, speed: 1, outside: true, button: -1, key: 'none'},\n * keyboard: {enabled: true, step: 10, key: 'ctrl'},\n * continuous: true,\n * slider: {\n * visible: true,\n * style: 6,\n * point1: {\n * pos: 'auto',\n * frozen: false\n * },\n * point2: {\n * pos: 'auto',\n * frozen: false\n * },\n * min: 0,\n * max: 2 * Math.PI,\n * start: 0.3\n * },\n * }\n * @example\n * var bound = [-4, 6];\n * var view = board.create('view3d',\n * [[-4, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'parallel',\n * el: {\n * slider: {visible: true}\n * }\n * });\n *\n * \n * \n *\n */\n el: {\n pointer: {\n enabled: true,\n speed: 1,\n outside: true,\n button: -1,\n key: 'none'\n },\n keyboard: {\n enabled: true,\n step: 10,\n key: 'ctrl'\n },\n continuous: true,\n slider: {\n visible: 'inherit',\n style: 6,\n point1: {\n frozen: false,\n pos: 'auto'\n },\n point2: {\n frozen: false,\n pos: 'auto'\n },\n min: 0,\n max: 2 * Math.PI,\n start: 0.3\n }\n },\n\n /**\n * Specify the user handling of the bank angle.\n * \n *
\n *\n * @name View3D#bank\n * @type Object\n * @default \n *
\n * \n *
\n * \n *
\n * 'min' and 'max' are used only if trackball is not enabled.\n * Additionally, the attributes 'slider.point1.pos' and 'slider.point2.pos' control the position of the slider. Possible\n * values are 'auto' or an array [x, y] of length 2 for the position in user coordinates (or a function returning such an array).\n * {\n * pointer: {enabled: true, speed: 1, outside: true, button: -1, key: 'none'},\n * keyboard: {enabled: true, step: 10, key: 'ctrl'},\n * continuous: true,\n * slider: {\n * visible: true,\n * style: 6,\n * point1: {\n * pos: 'auto',\n * frozen: false\n * },\n * point2: {\n * pos: 'auto',\n * frozen: false\n * },\n * min: 0,\n * max: 2 * Math.PI,\n * start: 0.3\n * },\n * }\n * @example\n * var bound = [-4, 6];\n * var view = board.create('view3d',\n * [[-4, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'parallel',\n * bank: {\n * slider: {visible: true}\n * }\n * });\n *\n * \n * \n *\n */\n bank: {\n pointer: {\n enabled: true,\n speed: 0.08,\n outside: true,\n button: -1,\n key: 'none'\n },\n keyboard: {\n enabled: true,\n step: 10,\n key: 'ctrl'\n },\n continuous: true,\n slider: {\n visible: 'inherit',\n style: 6,\n point1: {\n frozen: false,\n pos: 'auto'\n },\n point2: {\n frozen: false,\n pos: 'auto'\n },\n min: -Math.PI,\n max: Math.PI,\n start: 0.0\n }\n },\n\n /**\n * Distance of the camera to the center of the view. Expects values\n * larger than zero. If set to 'auto', r will be set to 1.01.\n * \n *
\n *\n * @name View3D#trackball\n * @type Object\n * @default {\n * enabled: false,\n * outside: true,\n * button: -1,\n * key: 'none'\n * }\n * \n */\n trackball: {\n enabled: false,\n outside: true,\n button: -1,\n key: 'none'\n },\n\n /**\n * Field of View defines the angle of view (in radians) of the camera, determining how much of the scene is captured within the frame.\n *\n * @type Number\n * @default 2/5*Math.PI\n */\n fov: 1 / 5 * 2 * Math.PI,\n\n /**\n * Fixed values for the view, which can be changed using keyboard keys `picture-up` and `picture-down`.\n * Array of the form: [[el0, az0, r0], [el1, az1, r1, ...[eln, azn, rn]]\n *\n * @name View3D#values\n * @type Array\n * @default {[[0, 1.57], [0.78, 0.62], [0, 0], [5.49, 0.62], [4.71, 0], [3.93, 0.62], [3.14, 0], [2.36, 0.62], [1.57, 1.57]]}\n */\n values: [\n [0, 1.57],\n [0.78, 0.62],\n [0, 0],\n [5.49, 0.62],\n [4.71, 0],\n [3.93, 0.62],\n [3.14, 0],\n [2.36, 0.62],\n [1.57, 1.57]\n ],\n\n infobox: {\n // strokeColor: '#888888',\n strokeColor: '#000000',\n fontSize: 16,\n useKatex: false,\n useMathjax: false,\n intl: {\n enabled: true,\n options: {\n minimumFractionDigits: 2,\n maximumFractionDigits: 3\n }\n }\n },\n\n /**\n * @class\n * @ignore\n */\n _currentView: -1\n\n /**#@-*/\n }\n});\n\nexport default JXG.Options;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n * The x, y plane is the screen, the origin is the\n * center of the screen, and the z axis points out of the\n * screen, toward the viewer.\n * boxToCam transformation is exposed to help 3D elements\n * manage their 2D representations in central projection mode. To map world\n * coordinates to focal coordinates, use the\n * {@link JXG.View3D#worldToFocal} method.\n * @type {Array}\n */\n this.boxToCam = [];\n\n /**\n * @type array\n * @private\n */\n // Lower left corner [x, y] of the 3D view if elevation and azimuth are set to 0.\n this.llftCorner = parents[0];\n\n /**\n * Width and height [w, h] of the 3D view if elevation and azimuth are set to 0.\n * @type array\n * @private\n */\n this.size = parents[1];\n\n /**\n * Bounding box (cube) [[x1, x2], [y1,y2], [z1,z2]] of the 3D view\n * @type array\n */\n this.bbox3D = parents[2];\n\n /**\n * The distance from the camera to the origin. In other words, the\n * radius of the sphere where the camera sits.\n * @type Number\n * @default null\n */\n this.r = null;\n\n /**\n * The distance from the camera to the screen. Computed automatically from\n * the `fov` property.\n * @type Number\n */\n this.focalDist = -1;\n\n /**\n * Type of projection. Is set in in update().\n * @type String\n */\n this.projectionType = 'parallel';\n\n /**\n * Whether trackball navigation is currently enabled.\n * @type String\n */\n this.trackballEnabled = false;\n\n /**\n * Store last position of pointer.\n * This is the successor to use evt.movementX/Y which caused problems on firefox\n * @type Object\n * @private\n */\n this._lastPos = {\n x: 0,\n y: 0\n };\n\n this.timeoutAzimuth = null;\n\n this.zIndexMin = Infinity;\n this.zIndexMax = -Infinity;\n\n this.id = this.board.setId(this, 'V');\n this.board.finalizeAdding(this);\n this.elType = 'view3d';\n};\n\nJXG.View3D.prototype = new GeometryElement();\nType.copyMethodMap(JXG.View3D, {\n // TODO\n});\n\nJXG.extend(\n JXG.View3D.prototype, /** @lends JXG.View3D.prototype */ {\n\n /**\n * Creates a new 3D element of type elementType.\n * @param {String} elementType Type of the element to be constructed given as a string e.g. 'point3d' or 'surface3d'.\n * @param {Array} parents Array of parent elements needed to construct the element e.g. coordinates for a 3D point or two\n * 3D points to construct a line. This highly depends on the elementType that is constructed. See the corresponding JXG.create*\n * methods for a list of possible parameters.\n * @param {Object} [attributes] An object containing the attributes to be set. This also depends on the elementType.\n * Common attributes are name, visible, strokeColor.\n * @returns {Object} Reference to the created element. This is usually a GeometryElement3D, but can be an array containing\n * two or more elements.\n */\n create: function (elementType, parents, attributes) {\n var prefix = [],\n el;\n\n if (elementType.indexOf('3d') > 0) {\n // is3D = true;\n prefix.push(this);\n }\n el = this.board.create(elementType, prefix.concat(parents), attributes);\n\n return el;\n },\n\n /**\n * Select a single or multiple elements at once.\n * @param {String|Object|function} str The name, id or a reference to a JSXGraph 3D element in the 3D view. An object will\n * be used as a filter to return multiple elements at once filtered by the properties of the object.\n * @param {Boolean} onlyByIdOrName If true (default:false) elements are only filtered by their id, name or groupId.\n * The advanced filters consisting of objects or functions are ignored.\n * @returns {JXG.GeometryElement3D|JXG.Composition}\n * @example\n * // select the element with name A\n * view.select('A');\n *\n * // select all elements with strokecolor set to 'red' (but not '#ff0000')\n * view.select({\n * strokeColor: 'red'\n * });\n *\n * // select all points on or below the x/y plane and make them black.\n * view.select({\n * elType: 'point3d',\n * Z: function (v) {\n * return v <= 0;\n * }\n * }).setAttribute({color: 'black'});\n *\n * // select all elements\n * view.select(function (el) {\n * return true;\n * });\n */\n select: function (str, onlyByIdOrName) {\n var flist,\n olist,\n i,\n l,\n s = str;\n\n if (s === null) {\n return s;\n }\n\n if (Type.isString(s) && s !== '') {\n // It's a string, most likely an id or a name.\n // Search by ID\n if (Type.exists(this.objects[s])) {\n s = this.objects[s];\n // Search by name\n } else if (Type.exists(this.elementsByName[s])) {\n s = this.elementsByName[s];\n // // Search by group ID\n // } else if (Type.exists(this.groups[s])) {\n // s = this.groups[s];\n }\n\n } else if (\n !onlyByIdOrName &&\n (Type.isFunction(s) || (Type.isObject(s) && !Type.isFunction(s.setAttribute)))\n ) {\n // It's a function or an object, but not an element\n flist = Type.filterElements(this.objectsList, s);\n\n olist = {};\n l = flist.length;\n for (i = 0; i < l; i++) {\n olist[flist[i].id] = flist[i];\n }\n s = new Composition(olist);\n\n } else if (\n Type.isObject(s) &&\n Type.exists(s.id) &&\n !Type.exists(this.objects[s.id])\n ) {\n // It's an element which has been deleted (and still hangs around, e.g. in an attractor list)\n s = null;\n }\n\n return s;\n },\n\n // set the Tait-Bryan angles to specify the current view rotation matrix\n setAnglesFromRotation: function () {\n var rem = this.matrix3DRot, // rotation remaining after angle extraction\n rBank, cosBank, sinBank,\n cosEl, sinEl,\n cosAz, sinAz;\n\n // extract bank by rotating the view box z axis onto the camera yz plane\n rBank = Math.sqrt(rem[1][3] * rem[1][3] + rem[2][3] * rem[2][3]);\n if (rBank > Mat.eps) {\n cosBank = rem[2][3] / rBank;\n sinBank = rem[1][3] / rBank;\n } else {\n // if the z axis is pointed almost exactly at the screen, we\n // keep the current bank value\n cosBank = Math.cos(this.angles.bank);\n sinBank = Math.sin(this.angles.bank);\n }\n rem = Mat.matMatMult([\n [1, 0, 0, 0],\n [0, cosBank, -sinBank, 0],\n [0, sinBank, cosBank, 0],\n [0, 0, 0, 1]\n ], rem);\n this.angles.bank = Math.atan2(sinBank, cosBank);\n\n // extract elevation by rotating the view box z axis onto the camera\n // y axis\n cosEl = rem[2][3];\n sinEl = rem[3][3];\n rem = Mat.matMatMult([\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, cosEl, sinEl],\n [0, 0, -sinEl, cosEl]\n ], rem);\n this.angles.el = Math.atan2(sinEl, cosEl);\n\n // extract azimuth\n cosAz = -rem[1][1];\n sinAz = rem[3][1];\n this.angles.az = Math.atan2(sinAz, cosAz);\n if (this.angles.az < 0) this.angles.az += 2 * Math.PI;\n\n this.setSlidersFromAngles();\n },\n\n anglesHaveMoved: function () {\n return (\n this._hasMoveAz || this._hasMoveEl ||\n Math.abs(this.angles.az - this.az_slide.Value()) > Mat.eps ||\n Math.abs(this.angles.el - this.el_slide.Value()) > Mat.eps ||\n Math.abs(this.angles.bank - this.bank_slide.Value()) > Mat.eps\n );\n },\n\n getAnglesFromSliders: function () {\n this.angles.az = this.az_slide.Value();\n this.angles.el = this.el_slide.Value();\n this.angles.bank = this.bank_slide.Value();\n },\n\n setSlidersFromAngles: function () {\n this.az_slide.setValue(this.angles.az);\n this.el_slide.setValue(this.angles.el);\n this.bank_slide.setValue(this.angles.bank);\n },\n\n // return the rotation matrix specified by the current Tait-Bryan angles\n getRotationFromAngles: function () {\n var a, e, b, f,\n cosBank, sinBank,\n mat = [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1]\n ];\n\n // mat projects homogeneous 3D coords in View3D\n // to homogeneous 2D coordinates in the board\n a = this.angles.az;\n e = this.angles.el;\n b = this.angles.bank;\n f = -Math.sin(e);\n\n mat[1][1] = -Math.cos(a);\n mat[1][2] = Math.sin(a);\n mat[1][3] = 0;\n\n mat[2][1] = f * Math.sin(a);\n mat[2][2] = f * Math.cos(a);\n mat[2][3] = Math.cos(e);\n\n mat[3][1] = Math.cos(e) * Math.sin(a);\n mat[3][2] = Math.cos(e) * Math.cos(a);\n mat[3][3] = Math.sin(e);\n\n cosBank = Math.cos(b);\n sinBank = Math.sin(b);\n mat = Mat.matMatMult([\n [1, 0, 0, 0],\n [0, cosBank, sinBank, 0],\n [0, -sinBank, cosBank, 0],\n [0, 0, 0, 1]\n ], mat);\n\n return mat;\n\n /* this code, originally from `_updateCentralProjection`, is an\n * alternate implementation of the azimuth-elevation matrix\n * computation above. using this implementation instead of the\n * current one might lead to simpler code in a future refactoring\n var a, e, up,\n ax, ay, az, v, nrm,\n eye, d,\n func_sphere;\n\n // finds the point on the unit sphere with the given azimuth and\n // elevation, and returns its affine coordinates\n func_sphere = function (az, el) {\n return [\n Math.cos(az) * Math.cos(el),\n -Math.sin(az) * Math.cos(el),\n Math.sin(el)\n ];\n };\n\n a = this.az_slide.Value() + (3 * Math.PI * 0.5); // Sphere\n e = this.el_slide.Value();\n\n // create an up vector and an eye vector which are 90 degrees out of phase\n up = func_sphere(a, e + Math.PI / 2);\n eye = func_sphere(a, e);\n d = [eye[0], eye[1], eye[2]];\n\n nrm = Mat.norm(d, 3);\n az = [d[0] / nrm, d[1] / nrm, d[2] / nrm];\n\n nrm = Mat.norm(up, 3);\n v = [up[0] / nrm, up[1] / nrm, up[2] / nrm];\n\n ax = Mat.crossProduct(v, az);\n ay = Mat.crossProduct(az, ax);\n\n this.matrix3DRot[1] = [0, ax[0], ax[1], ax[2]];\n this.matrix3DRot[2] = [0, ay[0], ay[1], ay[2]];\n this.matrix3DRot[3] = [0, az[0], az[1], az[2]];\n */\n },\n\n /**\n * Project 2D point (x,y) to the virtual trackpad sphere,\n * see Bell's virtual trackpad, and return z-component of the\n * number.\n *\n * @param {Number} r\n * @param {Number} x\n * @param {Number} y\n * @returns Number\n * @private\n */\n _projectToSphere: function (r, x, y) {\n var d = Mat.hypot(x, y),\n t, z;\n\n if (d < r * 0.7071067811865475) { // Inside sphere\n z = Math.sqrt(r * r - d * d);\n } else { // On hyperbola\n t = r / 1.414213562373095;\n z = t * t / d;\n }\n return z;\n },\n\n /**\n * Determine 4x4 rotation matrix with Bell's virtual trackball.\n *\n * @returns {Array} 4x4 rotation matrix\n * @private\n */\n updateProjectionTrackball: function (Pref) {\n var R = 100,\n dx, dy, dr2,\n p1, p2, x, y, theta, t, d,\n c, s, n,\n mat = [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1]\n ];\n\n if (!Type.exists(this._trackball)) {\n return this.matrix3DRot;\n }\n\n dx = this._trackball.dx;\n dy = this._trackball.dy;\n dr2 = dx * dx + dy * dy;\n if (dr2 > Mat.eps) {\n // // Method by Hanson, \"The rolling ball\", Graphics Gems III, p.51\n // // Rotation axis:\n // // n = (-dy/dr, dx/dr, 0)\n // // Rotation angle around n:\n // // theta = atan(dr / R) approx dr / R\n // dr = Math.sqrt(dr2);\n // c = R / Math.hypot(R, dr); // cos(theta)\n // t = 1 - c; // 1 - cos(theta)\n // s = dr / Math.hypot(R, dr); // sin(theta)\n // n = [-dy / dr, dx / dr, 0];\n\n // Bell virtual trackpad, see\n // https://opensource.apple.com/source/X11libs/X11libs-60/mesa/Mesa-7.8.2/progs/util/trackball.c.auto.html\n // http://scv.bu.edu/documentation/presentations/visualizationworkshop08/materials/opengl/trackball.c.\n // See also Henriksen, Sporring, Hornaek, \"Virtual Trackballs revisited\".\n //\n R = (this.size[0] * this.board.unitX + this.size[1] * this.board.unitY) * 0.25;\n x = this._trackball.x;\n y = this._trackball.y;\n\n p2 = [x, y, this._projectToSphere(R, x, y)];\n x -= dx;\n y -= dy;\n p1 = [x, y, this._projectToSphere(R, x, y)];\n\n n = Mat.crossProduct(p1, p2);\n d = Mat.hypot(n[0], n[1], n[2]);\n n[0] /= d;\n n[1] /= d;\n n[2] /= d;\n\n t = Geometry.distance(p2, p1, 3) / (2 * R);\n t = (t > 1.0) ? 1.0 : t;\n t = (t < -1.0) ? -1.0 : t;\n theta = 2.0 * Math.asin(t);\n c = Math.cos(theta);\n t = 1 - c;\n s = Math.sin(theta);\n\n // Rotation by theta about the axis n. See equation 9.63 of\n //\n // Ian Richard Cole. \"Modeling CPV\" (thesis). Loughborough\n // University. https://hdl.handle.net/2134/18050\n //\n mat[1][1] = c + n[0] * n[0] * t;\n mat[2][1] = n[1] * n[0] * t + n[2] * s;\n mat[3][1] = n[2] * n[0] * t - n[1] * s;\n\n mat[1][2] = n[0] * n[1] * t - n[2] * s;\n mat[2][2] = c + n[1] * n[1] * t;\n mat[3][2] = n[2] * n[1] * t + n[0] * s;\n\n mat[1][3] = n[0] * n[2] * t + n[1] * s;\n mat[2][3] = n[1] * n[2] * t - n[0] * s;\n mat[3][3] = c + n[2] * n[2] * t;\n }\n\n mat = Mat.matMatMult(mat, this.matrix3DRot);\n return mat;\n },\n\n updateAngleSliderBounds: function () {\n var az_smax, az_smin,\n el_smax, el_smin, el_cover,\n el_smid, el_equiv, el_flip_equiv,\n el_equiv_loss, el_flip_equiv_loss, el_interval_loss,\n bank_smax, bank_smin;\n\n // update stored trackball toggle\n this.trackballEnabled = this.evalVisProp('trackball.enabled');\n\n // set slider bounds\n if (this.trackballEnabled) {\n this.az_slide.setMin(0);\n this.az_slide.setMax(2 * Math.PI);\n this.el_slide.setMin(-0.5 * Math.PI);\n this.el_slide.setMax(0.5 * Math.PI);\n this.bank_slide.setMin(-Math.PI);\n this.bank_slide.setMax(Math.PI);\n } else {\n this.az_slide.setMin(this.visProp.az.slider.min);\n this.az_slide.setMax(this.visProp.az.slider.max);\n this.el_slide.setMin(this.visProp.el.slider.min);\n this.el_slide.setMax(this.visProp.el.slider.max);\n this.bank_slide.setMin(this.visProp.bank.slider.min);\n this.bank_slide.setMax(this.visProp.bank.slider.max);\n }\n\n // get new slider bounds\n az_smax = this.az_slide._smax;\n az_smin = this.az_slide._smin;\n el_smax = this.el_slide._smax;\n el_smin = this.el_slide._smin;\n bank_smax = this.bank_slide._smax;\n bank_smin = this.bank_slide._smin;\n\n // wrap and restore angle values\n if (this.trackballEnabled) {\n // if we're upside-down, flip the bank angle to reach the same\n // orientation with an elevation between -pi/2 and pi/2\n el_cover = Mat.mod(this.angles.el, 2 * Math.PI);\n if (0.5 * Math.PI < el_cover && el_cover < 1.5 * Math.PI) {\n this.angles.el = Math.PI - el_cover;\n this.angles.az = Mat.wrap(this.angles.az + Math.PI, az_smin, az_smax);\n this.angles.bank = Mat.wrap(this.angles.bank + Math.PI, bank_smin, bank_smax);\n }\n\n // wrap the azimuth and bank angle\n this.angles.az = Mat.wrap(this.angles.az, az_smin, az_smax);\n this.angles.el = Mat.wrap(this.angles.el, el_smin, el_smax);\n this.angles.bank = Mat.wrap(this.angles.bank, bank_smin, bank_smax);\n } else {\n // wrap and clamp the elevation into the slider range. if\n // flipping the elevation gets us closer to the slider interval,\n // do that, inverting the azimuth and bank angle to compensate\n el_interval_loss = function (t) {\n if (t < el_smin) {\n return el_smin - t;\n } else if (el_smax < t) {\n return t - el_smax;\n } else {\n return 0;\n }\n };\n el_smid = 0.5 * (el_smin + el_smax);\n el_equiv = Mat.wrap(\n this.angles.el,\n el_smid - Math.PI,\n el_smid + Math.PI\n );\n el_flip_equiv = Mat.wrap(\n Math.PI - this.angles.el,\n el_smid - Math.PI,\n el_smid + Math.PI\n );\n el_equiv_loss = el_interval_loss(el_equiv);\n el_flip_equiv_loss = el_interval_loss(el_flip_equiv);\n if (el_equiv_loss <= el_flip_equiv_loss) {\n this.angles.el = Mat.clamp(el_equiv, el_smin, el_smax);\n } else {\n this.angles.el = Mat.clamp(el_flip_equiv, el_smin, el_smax);\n this.angles.az = Mat.wrap(this.angles.az + Math.PI, az_smin, az_smax);\n this.angles.bank = Mat.wrap(this.angles.bank + Math.PI, bank_smin, bank_smax);\n }\n\n // wrap and clamp the azimuth and bank angle into the slider range\n this.angles.az = Mat.wrapAndClamp(this.angles.az, az_smin, az_smax, 2 * Math.PI);\n this.angles.bank = Mat.wrapAndClamp(this.angles.bank, bank_smin, bank_smax, 2 * Math.PI);\n\n // since we're using `clamp`, angles may have changed\n this.matrix3DRot = this.getRotationFromAngles();\n }\n\n // restore slider positions\n this.setSlidersFromAngles();\n },\n\n /**\n * Get distance from view box center to camera.\n * In other words, the radius of the sphere where the camera sits.\n * Distinguishes between projection tpye 'central' and 'parallel'.\n * Uses the value of attribute 'r'.\n *\n * @returns Number\n * @private\n * @see View3D#r\n */\n getCameraDistance: function() {\n var rs, r, rr, diam;\n\n rr = Type.evaluate(this.r);\n if (rr === null || rr === 0) {\n // Use attribute r\n rs = this.evalVisProp('r');\n } else {\n // Use previously set value in this.r\n rs = rr;\n }\n\n if (rs === 'auto') {\n r = 1.01;\n } else {\n r = (this.projectionType === 'central') ? rs : (1 / rs);\n }\n\n if (this.projectionType === 'central') {\n diam = Mat.hypot(\n this.bbox3D[0][0] - this.bbox3D[0][1],\n this.bbox3D[1][0] - this.bbox3D[1][1],\n this.bbox3D[2][0] - this.bbox3D[2][1]\n );\n r = diam * r;\n }\n\n return r;\n },\n\n /**\n * @private\n * @returns {Array}\n */\n _updateCentralProjection: function () {\n var zf = 20, // near clip plane\n zn = 8, // far clip plane\n\n // See https://www.mathematik.uni-marburg.de/~thormae/lectures/graphics1/graphics_6_1_eng_web.html\n // bbox3D is always at the world origin, i.e. T_obj is the unit matrix.\n // All vectors contain affine coordinates and have length 3\n // The matrices are of size 4x4.\n r, A;\n\n // Set distance from view box center to camera\n r = this.getCameraDistance();\n\n // Compute camera transformation\n // this.boxToCam = this.matrix3DRot.map((row) => row.slice());\n this.boxToCam = this.matrix3DRot.map(function (row) { return row.slice(); });\n this.boxToCam[3][0] = -r;\n\n // compute focal distance and clip space transformation\n this.focalDist = 1 / Math.tan(0.5 * this.evalVisProp('fov'));\n A = [\n [0, 0, 0, -1],\n [0, this.focalDist, 0, 0],\n [0, 0, this.focalDist, 0],\n [2 * zf * zn / (zn - zf), 0, 0, (zf + zn) / (zn - zf)]\n ];\n\n return Mat.matMatMult(A, this.boxToCam);\n },\n\n // Update 3D-to-2D transformation matrix with the actual azimuth and elevation angles.\n // Called in board.updateElements()\n update: function () {\n var r, stretch,\n mat2D, objectToClip, size,\n dx, dy;\n // objectsList;\n\n if (\n !Type.exists(this.el_slide) ||\n !Type.exists(this.az_slide) ||\n !Type.exists(this.bank_slide) ||\n !this.needsUpdate\n ) {\n this.needsUpdate = false;\n return this;\n }\n\n mat2D = [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1]\n ];\n\n this.projectionType = this.evalVisProp('projection').toLowerCase();\n\n // override angle slider bounds when trackball navigation is enabled\n if (this.trackballEnabled !== this.evalVisProp('trackball.enabled')) {\n this.updateAngleSliderBounds();\n }\n\n if (this._hasMoveTrackball) {\n // The trackball has been moved since the last update, so we do\n // trackball navigation. When the trackball is enabled, a drag\n // event is interpreted as a trackball movement unless it's\n // caught by something else, like point dragging. When the\n // trackball is disabled, the trackball movement flag should\n // never be set\n this.matrix3DRot = this.updateProjectionTrackball();\n this.setAnglesFromRotation();\n } else if (this.anglesHaveMoved()) {\n // The trackball hasn't been moved since the last up date, but\n // the Tait-Bryan angles have been, so we do angle navigation\n this.getAnglesFromSliders();\n this.matrix3DRot = this.getRotationFromAngles();\n }\n\n /**\n * The translation that moves the center of the view box to the origin.\n */\n this.shift = [\n [1, 0, 0, 0],\n [-0.5 * (this.bbox3D[0][0] + this.bbox3D[0][1]), 1, 0, 0],\n [-0.5 * (this.bbox3D[1][0] + this.bbox3D[1][1]), 0, 1, 0],\n [-0.5 * (this.bbox3D[2][0] + this.bbox3D[2][1]), 0, 0, 1]\n ];\n\n switch (this.projectionType) {\n case 'central': // Central projection\n\n // Add a final transformation to scale and shift the projection\n // on the board, usually called viewport.\n size = 2 * 0.4;\n mat2D[1][1] = this.size[0] / size; // w / d_x\n mat2D[2][2] = this.size[1] / size; // h / d_y\n mat2D[1][0] = this.llftCorner[0] + mat2D[1][1] * 0.5 * size; // llft_x\n mat2D[2][0] = this.llftCorner[1] + mat2D[2][2] * 0.5 * size; // llft_y\n // The transformations this.matrix3D and mat2D can not be combined at this point,\n // since the projected vectors have to be normalized in between in project3DTo2D\n this.viewPortTransform = mat2D;\n objectToClip = this._updateCentralProjection();\n // this.matrix3D is a 4x4 matrix\n this.matrix3D = Mat.matMatMult(objectToClip, this.shift);\n break;\n\n case 'parallel': // Parallel projection\n default:\n r = this.getCameraDistance();\n stretch = [\n [1, 0, 0, 0],\n [0, r, 0, 0],\n [0, 0, r, 0],\n [0, 0, 0, r]\n ];\n\n // Add a final transformation to scale and shift the projection\n // on the board, usually called viewport.\n dx = this.bbox3D[0][1] - this.bbox3D[0][0];\n dy = this.bbox3D[1][1] - this.bbox3D[1][0];\n mat2D[1][1] = this.size[0] / dx; // w / d_x\n mat2D[2][2] = this.size[1] / dy; // h / d_y\n mat2D[1][0] = this.llftCorner[0] + mat2D[1][1] * 0.5 * dx; // llft_x\n mat2D[2][0] = this.llftCorner[1] + mat2D[2][2] * 0.5 * dy; // llft_y\n\n // Combine all transformations, this.matrix3D is a 3x4 matrix\n this.matrix3D = Mat.matMatMult(\n mat2D,\n Mat.matMatMult(Mat.matMatMult(this.matrix3DRot, stretch), this.shift).slice(0, 3)\n );\n }\n\n // Used for zIndex in dept ordering in subsequent update methods of the\n // 3D elements and in view3d.updateRenderer\n this.matrix3DRotShift = Mat.matMatMult(this.matrix3DRot, this.shift);\n\n return this;\n },\n\n /**\n * Compares 3D elements according to their z-Index.\n * @param {JXG.GeometryElement3D} a\n * @param {JXG.GeometryElement3D} b\n * @returns Number\n */\n compareDepth: function (a, b) {\n // return a.zIndex - b.zIndex;\n // if (a.type !== Const.OBJECT_TYPE_PLANE3D && b.type !== Const.OBJECT_TYPE_PLANE3D) {\n // return a.zIndex - b.zIndex;\n // } else if (a.type === Const.OBJECT_TYPE_PLANE3D) {\n // let bHesse = Mat.innerProduct(a.point.coords, a.normal, 4);\n // let po = Mat.innerProduct(b.coords, a.normal, 4);\n // let pos = Mat.innerProduct(this.boxToCam[3], a.normal, 4);\n // console.log(this.boxToCam[3])\n // return pos - po;\n // } else if (b.type === Const.OBJECT_TYPE_PLANE3D) {\n // let bHesse = Mat.innerProduct(b.point.coords, b.normal, 4);\n // let po = Mat.innerProduct(a.coords, a.normal, 4);\n // let pos = Mat.innerProduct(this.boxToCam[3], b.normal, 4);\n // console.log('b', pos, po, bHesse)\n // return -pos;\n // }\n return a.zIndex - b.zIndex;\n },\n\n updateZIndices: function() {\n var id, el;\n for (id in this.objects) {\n if (this.objects.hasOwnProperty(id)) {\n el = this.objects[id];\n // Update zIndex of less frequent objects line3d and polygon3d\n // The other elements (point3d, face3d) do this in their update method.\n if ((\n el.type === Const.OBJECT_TYPE_LINE3D ||\n el.type === Const.OBJECT_TYPE_POLYGON3D\n ) &&\n Type.exists(el.element2D) &&\n el.element2D.evalVisProp('visible')\n ) {\n el.updateZIndex();\n }\n }\n }\n },\n\n updateShaders: function() {\n var id, el, v;\n for (id in this.objects) {\n if (this.objects.hasOwnProperty(id)) {\n el = this.objects[id];\n\n if (el.visPropCalc.visible && Type.exists(el.shader)) {\n if (this.board._change3DView && el.evalVisProp('shader.fixed')) {\n // In case, 3D view is rotated and the shader is fixed\n // we can avoid the call of shader()\n v = el.zIndex;\n } else {\n v = el.shader();\n }\n if (v < this.zIndexMin) {\n this.zIndexMin = v;\n } else if (v > this.zIndexMax) {\n this.zIndexMax = v;\n }\n }\n }\n }\n },\n\n updateDepthOrdering: function () {\n var id, el,\n i, j, l, layers, lay;\n\n // Collect elements for depth ordering layer-wise\n layers = this.evalVisProp('depthorder.layers');\n for (i = 0; i < layers.length; i++) {\n this.depthOrdered[layers[i]] = [];\n }\n\n for (id in this.objects) {\n if (this.objects.hasOwnProperty(id)) {\n el = this.objects[id];\n if ((el.type === Const.OBJECT_TYPE_FACE3D ||\n el.type === Const.OBJECT_TYPE_LINE3D ||\n // el.type === Const.OBJECT_TYPE_PLANE3D ||\n el.type === Const.OBJECT_TYPE_POINT3D ||\n el.type === Const.OBJECT_TYPE_POLYGON3D\n ) &&\n Type.exists(el.element2D) &&\n el.element2D.visPropCalc.visible\n // el.element2D.evalVisProp('visible')\n ) {\n lay = el.element2D.evalVisProp('layer');\n if (layers.indexOf(lay) >= 0) {\n this.depthOrdered[lay].push(el);\n }\n }\n }\n }\n\n if (this.board.renderer && this.board.renderer.type === 'svg') {\n for (i = 0; i < layers.length; i++) {\n lay = layers[i];\n this.depthOrdered[lay].sort(this.compareDepth.bind(this));\n // DEBUG\n // if (this.depthOrdered[lay].length > 0) {\n // for (let k = 0; k < this.depthOrdered[lay].length; k++) {\n // let o = this.depthOrdered[lay][k]\n // console.log(o.visProp.fillcolor, o.zIndex)\n // }\n // }\n l = this.depthOrdered[lay];\n for (j = 0; j < l.length; j++) {\n this.board.renderer.setLayer(l[j].element2D, lay);\n }\n // this.depthOrdered[lay].forEach((el) => this.board.renderer.setLayer(el.element2D, lay));\n // Attention: forEach prevents deleting an element\n }\n }\n\n return this;\n },\n\n updateRenderer: function () {\n if (!this.needsUpdate) {\n return this;\n }\n\n // console.time('update')\n // Handle depth ordering\n this.depthOrdered = {};\n\n if (this.shift !== undefined && this.evalVisProp('depthorder.enabled')) {\n // Update the zIndices of certain element types.\n // We do it here in updateRenderer, because the elements' positions\n // are meanwhile updated.\n this.updateZIndices();\n\n this.updateShaders();\n\n if (this.board.renderer && this.board.renderer.type === 'svg') {\n // For SVG we update the DOM order here.\n // In canvas we sort the elements in board.updateRendererCanvas\n this.updateDepthOrdering();\n }\n }\n // console.timeEnd('update')\n\n this.needsUpdate = false;\n return this;\n },\n\n removeObject: function (object, saveMethod) {\n var i, el, le, o, fst, face;\n\n // this.board.removeObject(object, saveMethod);\n if (Type.isArray(object)) {\n for (i = 0; i < object.length; i++) {\n this.removeObject(object[i]);\n }\n return this;\n }\n\n object = this.select(object);\n\n // // If the object which is about to be removed unknown or a string, do nothing.\n // // it is a string if a string was given and could not be resolved to an element.\n if (!Type.exists(object) || Type.isString(object)) {\n return this;\n }\n\n try {\n // Remove all children.\n for (el in object.childElements) {\n if (object.childElements.hasOwnProperty(el)) {\n this.removeObject(object.childElements[el]);\n }\n }\n if (object.type === Const.OBJECT_TYPE_POLYHEDRON3D) {\n // Special treatment for polyhedron3d.\n // With this we can avoid the time consuming addChild() calls.\n le = object.faces.length;\n if (le > 0) {\n fst = object.faces[0]._pos;\n fst = (object.faces[0].element2D._pos < fst) ? object.faces[0].element2D._pos : fst;\n }\n for (i = 0; i < le; i++) {\n face = object.faces[i];\n delete this.objects[face.id];\n\n // this.board.removeObject(face.element2D, saveMethod);\n delete this.board.objects[face.element2D.id];\n delete this.board.elementsByName[face.element2D.name];\n face.element2D.remove();\n this.board.objectsList.splice(face.element2D._pos, 1);\n\n delete this.board.objects[face.id];\n delete this.board.elementsByName[face.name];\n face.remove();\n this.board.objectsList.splice(face._pos, 1);\n }\n le = this.board.objectsList.length;\n // Reindex the positions\n for (i = fst; i < this.board.objectsList.length; i++) {\n o = this.board.objectsList[i];\n if (o._pos > -1) { o._pos = i; }\n }\n object.faces = [];\n }\n\n delete this.objects[object.id];\n } catch (e) {\n JXG.debug('View3D ' + object.id + ': Could not be removed: ' + e);\n }\n\n // this.update();\n\n this.board.removeObject(object, saveMethod);\n\n return this;\n },\n\n /**\n * Map world coordinates to focal coordinates. These coordinate systems\n * are explained in the {@link JXG.View3D#boxToCam} matrix\n * documentation.\n *\n * @param {Array} pWorld A world space point, in homogeneous coordinates.\n * @param {Boolean} [homog=true] Whether to return homogeneous coordinates.\n * If false, projects down to ordinary coordinates.\n */\n worldToFocal: function (pWorld, homog = true) {\n var k,\n pView = Mat.matVecMult(this.boxToCam, Mat.matVecMult(this.shift, pWorld));\n\n pView[3] -= pView[0] * this.focalDist;\n if (homog) {\n return pView;\n } else {\n for (k = 1; k < 4; k++) {\n pView[k] /= pView[0];\n }\n return pView.slice(1, 4);\n }\n },\n\n /**\n * Project 3D coordinates to 2D board coordinates\n * The 3D coordinates are provides as three numbers x, y, z or one array of length 3.\n *\n * @param {Number|Array} x\n * @param {Number[]} y\n * @param {Number[]} z\n * @returns {Array} Array of length 3 containing the projection on to the board\n * in homogeneous user coordinates.\n */\n project3DTo2D: function (x, y, z) {\n var vec, w;\n if (arguments.length === 3) {\n vec = [1, x, y, z];\n } else {\n // Argument is an array\n if (x.length === 3) {\n // vec = [1].concat(x);\n vec = x.slice();\n vec.unshift(1);\n } else {\n vec = x;\n }\n }\n\n w = Mat.matVecMult(this.matrix3D, vec);\n\n switch (this.projectionType) {\n case 'central':\n w[1] /= w[0];\n w[2] /= w[0];\n w[3] /= w[0];\n w[0] /= w[0];\n return Mat.matVecMult(this.viewPortTransform, w.slice(0, 3));\n\n case 'parallel':\n default:\n return w;\n }\n },\n\n /**\n * We know that v2d * w0 = mat * (1, x, y, d)^T where v2d = (1, b, c, h)^T with unknowns w0, h, x, y.\n * Setting R = mat^(-1) gives\n * 1/ w0 * (1, x, y, d)^T = R * v2d.\n * The first and the last row of this equation allows to determine 1/w0 and h.\n *\n * @param {Array} mat\n * @param {Array} v2d\n * @param {Number} d\n * @returns Array\n * @private\n */\n _getW0: function (mat, v2d, d) {\n var R = Mat.inverse(mat),\n R1 = R[0][0] + v2d[1] * R[0][1] + v2d[2] * R[0][2],\n R2 = R[3][0] + v2d[1] * R[3][1] + v2d[2] * R[3][2],\n w, h, det;\n\n det = d * R[0][3] - R[3][3];\n w = (R2 * R[0][3] - R1 * R[3][3]) / det;\n h = (R2 - R1 * d) / det;\n return [1 / w, h];\n },\n\n /**\n * Project a 2D coordinate to the plane defined by point \"foot\"\n * and the normal vector `normal`.\n *\n * @param {JXG.Point} point2d\n * @param {Array} normal Normal of plane\n * @param {Array} foot Foot point of plane\n * @returns {Array} of length 4 containing the projected\n * point in homogeneous coordinates.\n */\n project2DTo3DPlane: function (point2d, normal, foot) {\n var mat, rhs, d, le, sol,\n f = foot.slice(1) || [0, 0, 0],\n n = normal.slice(1),\n v2d, w0, res;\n\n le = Mat.norm(n, 3);\n d = Mat.innerProduct(f, n, 3) / le;\n\n if (this.projectionType === 'parallel') {\n mat = this.matrix3D.slice(0, 3); // Copy each row by reference\n mat.push([0, n[0], n[1], n[2]]);\n\n // 2D coordinates of point\n rhs = point2d.coords.usrCoords.slice();\n rhs.push(d);\n try {\n // Prevent singularity in case elevation angle is zero\n if (mat[2][3] === 1.0) {\n mat[2][1] = mat[2][2] = Mat.eps * 0.001;\n }\n sol = Mat.Numerics.Gauss(mat, rhs);\n } catch (e) {\n sol = [0, NaN, NaN, NaN];\n }\n } else {\n mat = this.matrix3D;\n\n // 2D coordinates of point:\n rhs = point2d.coords.usrCoords.slice();\n\n v2d = Mat.Numerics.Gauss(this.viewPortTransform, rhs);\n res = this._getW0(mat, v2d, d);\n w0 = res[0];\n rhs = [\n v2d[0] * w0,\n v2d[1] * w0,\n v2d[2] * w0,\n res[1] * w0\n ];\n try {\n // Prevent singularity in case elevation angle is zero\n if (mat[2][3] === 1.0) {\n mat[2][1] = mat[2][2] = Mat.eps * 0.001;\n }\n\n sol = Mat.Numerics.Gauss(mat, rhs);\n sol[1] /= sol[0];\n sol[2] /= sol[0];\n sol[3] /= sol[0];\n // sol[3] = d;\n sol[0] /= sol[0];\n } catch (err) {\n sol = [0, NaN, NaN, NaN];\n }\n }\n\n return sol;\n },\n\n /**\n * Project a point on the screen to the nearest point, in screen\n * distance, on a line segment in 3d space. The inputs and outputs\n * are in homogeneous coordinates.\n * \n * pan: {enabled: false}\n * \n * Otherwise users will not be able to rotate the scene with their fingers on a touch device.\n * \n *\n * @example\n * var bound = [-4, 6];\n * var view = board.create('view3d',\n * [[-4, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'central',\n * trackball: {enabled:true},\n *\n * xPlaneRear: { visible: false },\n * yPlaneRear: { visible: false }\n *\n * });\n *\n * var curve = view.create('curve3d', [\n * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),\n * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),\n * (t) => Math.sin(3 * t),\n * [-Math.PI, Math.PI]\n * ], { strokeWidth: 4 });\n *\n * \n * \n *\n* @example\n * var bound = [-4, 6];\n * var view = board.create('view3d',\n * [[-4, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'central',\n * trackball: {enabled:true},\n *\n * // Main axes\n * axesPosition: 'border',\n *\n * // Axes at the border\n * xAxisBorder: { ticks3d: { ticksDistance: 2} },\n * yAxisBorder: { ticks3d: { ticksDistance: 2} },\n * zAxisBorder: { ticks3d: { ticksDistance: 2} },\n *\n * // No axes on planes\n * xPlaneRearYAxis: {visible: false},\n * xPlaneRearZAxis: {visible: false},\n * yPlaneRearXAxis: {visible: false},\n * yPlaneRearZAxis: {visible: false},\n * zPlaneRearXAxis: {visible: false},\n * zPlaneRearYAxis: {visible: false}\n * });\n *\n * var curve = view.create('curve3d', [\n * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),\n * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),\n * (t) => Math.sin(3 * t),\n * [-Math.PI, Math.PI]\n * ], { strokeWidth: 4 });\n *\n * \n * \n *\n * @example\n * var bound = [-4, 6];\n * var view = board.create('view3d',\n * [[-4, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'central',\n * trackball: {enabled:true},\n *\n * axesPosition: 'none'\n * });\n *\n * var curve = view.create('curve3d', [\n * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),\n * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),\n * (t) => Math.sin(3 * t),\n * [-Math.PI, Math.PI]\n * ], { strokeWidth: 4 });\n *\n * \n * \n *\n * @example\n * var bound = [-4, 6];\n * var view = board.create('view3d',\n * [[-4, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'central',\n * trackball: {enabled:true},\n *\n * // Main axes\n * axesPosition: 'border',\n *\n * // Axes at the border\n * xAxisBorder: { ticks3d: { ticksDistance: 2} },\n * yAxisBorder: { ticks3d: { ticksDistance: 2} },\n * zAxisBorder: { ticks3d: { ticksDistance: 2} },\n *\n * xPlaneRear: {\n * fillColor: '#fff',\n * mesh3d: {visible: false}\n * },\n * yPlaneRear: {\n * fillColor: '#fff',\n * mesh3d: {visible: false}\n * },\n * zPlaneRear: {\n * fillColor: '#fff',\n * mesh3d: {visible: false}\n * },\n * xPlaneFront: {\n * visible: true,\n * fillColor: '#fff',\n * mesh3d: {visible: false}\n * },\n * yPlaneFront: {\n * visible: true,\n * fillColor: '#fff',\n * mesh3d: {visible: false}\n * },\n * zPlaneFront: {\n * visible: true,\n * fillColor: '#fff',\n * mesh3d: {visible: false}\n * },\n *\n * // No axes on planes\n * xPlaneRearYAxis: {visible: false},\n * xPlaneRearZAxis: {visible: false},\n * yPlaneRearXAxis: {visible: false},\n * yPlaneRearZAxis: {visible: false},\n * zPlaneRearXAxis: {visible: false},\n * zPlaneRearYAxis: {visible: false},\n * xPlaneFrontYAxis: {visible: false},\n * xPlaneFrontZAxis: {visible: false},\n * yPlaneFrontXAxis: {visible: false},\n * yPlaneFrontZAxis: {visible: false},\n * zPlaneFrontXAxis: {visible: false},\n * zPlaneFrontYAxis: {visible: false}\n *\n * });\n *\n * var curve = view.create('curve3d', [\n * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),\n * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),\n * (t) => Math.sin(3 * t),\n * [-Math.PI, Math.PI]\n * ], { strokeWidth: 4 });\n *\n * \n * \n *\n * @example\n * var bound = [-5, 5];\n * var view = board.create('view3d',\n * [[-6, -3],\n * [8, 8],\n * [bound, bound, bound]],\n * {\n * // Main axes\n * axesPosition: 'center',\n * xAxis: { strokeColor: 'blue', strokeWidth: 3},\n *\n * // Planes\n * xPlaneRear: { fillColor: 'yellow', mesh3d: {visible: false}},\n * yPlaneFront: { visible: true, fillColor: 'blue'},\n *\n * // Axes on planes\n * xPlaneRearYAxis: {strokeColor: 'red'},\n * xPlaneRearZAxis: {strokeColor: 'red'},\n *\n * yPlaneFrontXAxis: {strokeColor: 'blue'},\n * yPlaneFrontZAxis: {strokeColor: 'blue'},\n *\n * zPlaneFrontXAxis: {visible: false},\n * zPlaneFrontYAxis: {visible: false}\n * });\n *\n * \n * \n * @example\n * var bound = [-5, 5];\n * var view = board.create('view3d',\n * [[-6, -3], [8, 8],\n * [bound, bound, bound]],\n * {\n * projection: 'central',\n * az: {\n * slider: {\n * visible: true,\n * point1: {\n * pos: [5, -4]\n * },\n * point2: {\n * pos: [5, 4]\n * },\n * label: {anchorX: 'middle'}\n * }\n * },\n * el: {\n * slider: {\n * visible: true,\n * point1: {\n * pos: [6, -5]\n * },\n * point2: {\n * pos: [6, 3]\n * },\n * label: {anchorX: 'middle'}\n * }\n * },\n * bank: {\n * slider: {\n * visible: true,\n * point1: {\n * pos: [7, -6]\n * },\n * point2: {\n * pos: [7, 2]\n * },\n * label: {anchorX: 'middle'}\n * }\n * }\n * });\n *\n *\n * \n * \n *\n *\n */\nJXG.createView3D = function (board, parents, attributes) {\n var view, attr, attr_az, attr_el, attr_bank,\n x, y, w, h,\n p1, p2, v,\n coords = parents[0], // llft corner\n size = parents[1]; // [w, h]\n\n attr = Type.copyAttributes(attributes, board.options, 'view3d');\n view = new JXG.View3D(board, parents, attr);\n view.defaultAxes = view.create('axes3d', [], attr);\n\n x = coords[0];\n y = coords[1];\n w = size[0];\n h = size[1];\n\n attr_az = Type.copyAttributes(attr, board.options, 'view3d', 'az', 'slider');\n attr_az.name = 'az';\n\n attr_el = Type.copyAttributes(attr, board.options, 'view3d', 'el', 'slider');\n attr_el.name = 'el';\n\n attr_bank = Type.copyAttributes(attr, board.options, 'view3d', 'bank', 'slider');\n attr_bank.name = 'bank';\n\n v = Type.evaluate(attr_az.point1.pos);\n if (!Type.isArray(v)) {\n // 'auto'\n p1 = [x - 1, y - 2];\n } else {\n p1 = v;\n }\n v = Type.evaluate(attr_az.point2.pos);\n if (!Type.isArray(v)) {\n // 'auto'\n p2 = [x + w + 1, y - 2];\n } else {\n p2 = v;\n }\n\n /**\n * Slider to adapt azimuth angle\n * @name JXG.View3D#az_slide\n * @type {Slider}\n */\n view.az_slide = board.create(\n 'slider',\n [\n p1, p2,\n [\n Type.evaluate(attr_az.min),\n Type.evaluate(attr_az.start),\n Type.evaluate(attr_az.max)\n ]\n ],\n attr_az\n );\n view.inherits.push(view.az_slide);\n view.az_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate()\n\n v = Type.evaluate(attr_el.point1.pos);\n if (!Type.isArray(v)) {\n // 'auto'\n p1 = [x - 1, y];\n } else {\n p1 = v;\n }\n v = Type.evaluate(attr_el.point2.pos);\n if (!Type.isArray(v)) {\n // 'auto'\n p2 = [x - 1, y + h];\n } else {\n p2 = v;\n }\n\n /**\n * Slider to adapt elevation angle\n *\n * @name JXG.View3D#el_slide\n * @type {Slider}\n */\n view.el_slide = board.create(\n 'slider',\n [\n p1, p2,\n [\n Type.evaluate(attr_el.min),\n Type.evaluate(attr_el.start),\n Type.evaluate(attr_el.max)]\n ],\n attr_el\n );\n view.inherits.push(view.el_slide);\n view.el_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate()\n\n v = Type.evaluate(attr_bank.point1.pos);\n if (!Type.isArray(v)) {\n // 'auto'\n p1 = [x - 1, y + h + 2];\n } else {\n p1 = v;\n }\n v = Type.evaluate(attr_bank.point2.pos);\n if (!Type.isArray(v)) {\n // 'auto'\n p2 = [x + w + 1, y + h + 2];\n } else {\n p2 = v;\n }\n\n /**\n * Slider to adjust bank angle\n *\n * @name JXG.View3D#bank_slide\n * @type {Slider}\n */\n view.bank_slide = board.create(\n 'slider',\n [\n p1, p2,\n [\n Type.evaluate(attr_bank.min),\n Type.evaluate(attr_bank.start),\n Type.evaluate(attr_bank.max)\n ]\n ],\n attr_bank\n );\n view.inherits.push(view.bank_slide);\n view.bank_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate()\n\n // Set special infobox attributes of view3d.infobox\n // Using setAttribute() is not possible here, since we have to\n // avoid a call of board.update().\n // The drawback is that we can not use shortcuts\n view.board.infobox.visProp = Type.merge(view.board.infobox.visProp, attr.infobox);\n\n // 3d infobox: drag direction and coordinates\n view.board.highlightInfobox = function (x, y, el) {\n var d, i, c3d, foot,\n pre = '',\n brd = el.board,\n arr, infobox,\n p = null;\n\n if (this.mode === this.BOARD_MODE_DRAG) {\n // Drag direction is only shown during dragging\n if (view.isVerticalDrag()) {\n pre = '\\u21C5 ';\n } else {\n pre = '\\u21C4 ';\n }\n }\n\n // Search 3D parent\n for (i = 0; i < el.parents.length; i++) {\n p = brd.objects[el.parents[i]];\n if (p.is3D) {\n break;\n }\n }\n\n if (p && Type.exists(p.element2D)) {\n foot = [1, 0, 0, p.coords[3]];\n view._w0 = Mat.innerProduct(view.matrix3D[0], foot, 4);\n\n c3d = view.project2DTo3DPlane(p.element2D, [1, 0, 0, 1], foot);\n if (!view.isInCube(c3d)) {\n view.board.highlightCustomInfobox('', p);\n return;\n }\n d = p.evalVisProp('infoboxdigits');\n infobox = view.board.infobox;\n if (d === 'auto') {\n if (infobox.useLocale()) {\n arr = [pre, '(', infobox.formatNumberLocale(p.X()), ' | ', infobox.formatNumberLocale(p.Y()), ' | ', infobox.formatNumberLocale(p.Z()), ')'];\n } else {\n arr = [pre, '(', Type.autoDigits(p.X()), ' | ', Type.autoDigits(p.Y()), ' | ', Type.autoDigits(p.Z()), ')'];\n }\n\n } else {\n if (infobox.useLocale()) {\n arr = [pre, '(', infobox.formatNumberLocale(p.X(), d), ' | ', infobox.formatNumberLocale(p.Y(), d), ' | ', infobox.formatNumberLocale(p.Z(), d), ')'];\n } else {\n arr = [pre, '(', Type.toFixed(p.X(), d), ' | ', Type.toFixed(p.Y(), d), ' | ', Type.toFixed(p.Z(), d), ')'];\n }\n }\n view.board.highlightCustomInfobox(arr.join(''), p);\n } else {\n view.board.highlightCustomInfobox('(' + x + ', ' + y + ')', el);\n }\n };\n\n // Hack needed to enable addEvent for view3D:\n view.BOARD_MODE_NONE = 0x0000;\n\n // Add events for the keyboard navigation\n Env.addEvent(board.containerObj, 'keydown', function (event) {\n var neededKey,\n catchEvt = false;\n\n // this.board._change3DView = true;\n if (view.evalVisProp('el.keyboard.enabled') &&\n (event.key === 'ArrowUp' || event.key === 'ArrowDown')\n ) {\n neededKey = view.evalVisProp('el.keyboard.key');\n if (neededKey === 'none' ||\n (neededKey.indexOf('shift') > -1 && event.shiftKey) ||\n (neededKey.indexOf('ctrl') > -1 && event.ctrlKey)) {\n view._elEventHandler(event);\n catchEvt = true;\n }\n\n }\n\n if (view.evalVisProp('az.keyboard.enabled') &&\n (event.key === 'ArrowLeft' || event.key === 'ArrowRight')\n ) {\n neededKey = view.evalVisProp('az.keyboard.key');\n if (neededKey === 'none' ||\n (neededKey.indexOf('shift') > -1 && event.shiftKey) ||\n (neededKey.indexOf('ctrl') > -1 && event.ctrlKey)\n ) {\n view._azEventHandler(event);\n catchEvt = true;\n }\n }\n\n if (view.evalVisProp('bank.keyboard.enabled') && (event.key === ',' || event.key === '<' || event.key === '.' || event.key === '>')) {\n neededKey = view.evalVisProp('bank.keyboard.key');\n if (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && event.shiftKey) || (neededKey.indexOf('ctrl') > -1 && event.ctrlKey)) {\n view._bankEventHandler(event);\n catchEvt = true;\n }\n }\n\n if (event.key === 'PageUp') {\n view.nextView();\n catchEvt = true;\n } else if (event.key === 'PageDown') {\n view.previousView();\n catchEvt = true;\n }\n\n if (catchEvt) {\n // We stop event handling only in the case if the keypress could be\n // used for the 3D view. If this is not done, input fields et al\n // can not be used any more.\n event.preventDefault();\n }\n this.board._change3DView = false;\n\n }, view);\n\n // Add events for the pointer navigation\n Env.addEvent(board.containerObj, 'pointerdown', view.pointerDownHandler, view);\n\n // Initialize view rotation matrix\n view.getAnglesFromSliders();\n view.matrix3DRot = view.getRotationFromAngles();\n\n // override angle slider bounds when trackball navigation is enabled\n view.updateAngleSliderBounds();\n\n view.board.update();\n\n return view;\n};\n\nJXG.registerElement(\"view3d\", JXG.createView3D);\n\nexport default JXG.View3D;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n *\n * @name Axes3D\n * @constructor\n * @type Object\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n *\n */\nJXG.createAxes3D = function (board, parents, attributes) {\n var view = parents[0],\n directions = [\"x\", \"y\", \"z\"],\n suffixAxis = \"Axis\",\n sides = [\"Rear\", \"Front\"],\n rear = [0, 0, 0], // x, y, z\n front = [0, 0, 0], // x, y, z\n i, j, k, i1, i2, attr, pos,\n dir, dir1, len,\n from, to, vec1, vec2,\n range1, range2,\n na, na_parent,\n ticks_attr,\n axes = {};\n\n if (Type.exists(view.bbox3D)) {\n for (i = 0; i < directions.length; i++) {\n rear[i] = view.bbox3D[i][0];\n front[i] = view.bbox3D[i][1];\n }\n } else {\n for (i = 0; i < directions.length; i++) {\n rear[i] = parents[1][i];\n front[i] = parents[2][i];\n }\n }\n\n // Main 3D axes\n attr = Type.copyAttributes(attributes, board.options, 'axes3d');\n\n // Position of the main axes can not be changed during run time\n pos = attr.axesposition;\n\n for (i = 0; i < directions.length; i++) {\n // Run through ['x', 'y', 'z']\n dir = directions[i];\n na = dir + suffixAxis;\n\n if (pos === 'center') {\n // Axes centered\n from = [0, 0, 0];\n to = [0, 0, 0];\n to[i] = front[i];\n axes[na] = view.create('axis3d', [from, to], attr[na.toLowerCase()]);\n axes[na].view = view;\n } else if (pos === 'border') {\n // Axes bordered\n na += 'Border';\n from = rear.slice();\n to = front.slice();\n if (dir === 'z') {\n from[1] = front[1];\n to[0] = rear[0];\n } else if (dir === 'x') {\n from = [rear[0], front[1], rear[2]];\n to = [front[0], front[1], rear[2]];\n } else {\n from = [front[0], rear[1], rear[2]];\n to = [front[0], front[1], rear[2]];\n }\n to[i] = front[i];\n // attr[na.toLowerCase()].lastArrow = false;\n axes[na] = view.create('axis3d', [from, to], attr[na.toLowerCase()]);\n axes[na].view = view;\n\n ticks_attr = attr[na.toLowerCase()].ticks3d;\n ticks_attr.element3d = true; // Needed to avoid update during change of view\n len = front[i] - rear[i];\n if (dir === 'x') {\n axes[na + \"Ticks\"] = view.create(\"ticks3d\", [from, [1, 0, 0], len, [0, 1, 0]], ticks_attr);\n } else if (dir === 'y') {\n axes[na + \"Ticks\"] = view.create(\"ticks3d\", [from, [0, 1, 0], len, [1, 0, 0]], ticks_attr);\n } else {\n axes[na + \"Ticks\"] = view.create(\"ticks3d\", [from, [0, 0, 1], len, [0, 1, 0]], ticks_attr);\n }\n axes[na + \"Ticks\"].view = view;\n }\n }\n\n if (pos === 'center') {\n // Origin (2D point)\n axes.O = view.create(\n \"intersection\",\n [axes[directions[0] + suffixAxis], axes[directions[1] + suffixAxis]],\n {\n name: \"\",\n visible: false,\n withLabel: false\n }\n );\n axes.O.view = view;\n } else {\n axes.O = null;\n }\n\n // Front and rear planes\n for (i = 0; i < directions.length; i++) {\n // Run through ['x', 'y', 'z']\n i1 = (i + 1) % 3;\n i2 = (i + 2) % 3;\n\n dir = directions[i];\n for (j = 0; j < sides.length; j++) {\n // Run through ['Rear', 'Front']\n // attr = Type.copyAttributes(attributes, board.options, 'axes3d');\n\n na = dir + \"Plane\" + sides[j];\n\n from = [0, 0, 0];\n from[i] = j === 0 ? rear[i] : front[i];\n vec1 = [0, 0, 0];\n vec2 = [0, 0, 0];\n vec1[i1] = 1;\n vec2[i2] = 1;\n range1 = [rear[i1], front[i1]];\n range2 = [rear[i2], front[i2]];\n\n attr = Type.copyAttributes(attributes, board.options, \"axes3d\", na);\n axes[na] = view.create('plane3d', [from, vec1, vec2, range1, range2], attr);\n axes[na].elType = 'axisplane3d';\n }\n }\n\n // Axes on front and rear planes\n for (i = 0; i < directions.length; i++) {\n // Run through ['x', 'y', 'z']\n dir = directions[i];\n for (j = 0; j < sides.length; j++) {\n for (k = 1; k <= 2; k++) {\n i1 = (i + k) % 3;\n dir1 = directions[i1];\n na = dir + \"Plane\" + sides[j] + dir1.toUpperCase() + 'Axis';\n na_parent = dir + \"Plane\" + sides[j];\n\n from = [0, 0, 0];\n to = [0, 0, 0];\n from[i] = to[i] = j === 0 ? rear[i] : front[i];\n\n from[i1] = rear[i1];\n to[i1] = front[i1];\n\n attr = Type.copyAttributes(attributes, board.options, \"axes3d\", na);\n axes[na] = view.create(\"axis3d\", [from, to], attr);\n axes[na].view = view;\n axes[na_parent].addChild(axes[na]);\n //if (Type.exists(axes[na_parent].element2D)) {\n // TODO: Access of element2D is not nice\n axes[na_parent].element2D.inherits.push(axes[na]);\n //}\n\n }\n }\n }\n\n return axes;\n};\nJXG.registerElement(\"axes3d\", JXG.createAxes3D);\n\n/**\n * @class A 3D axis element is a line together with optional ticks and labels.\n * @pseudo\n * @description Simple element 3d axis as used with \"axesPosition:center\". No ticks and no label (yet).\n * \n *\n */\nJXG.createIntersectionCircle3D = function (board, parents, attributes) {\n var view = parents[0],\n el1 = parents[1],\n el2 = parents[2],\n ixnCircle, center, func,\n attr = Type.copyAttributes(attributes, board.options, 'intersectioncircle3d');\n\n try {\n func = Geometry.intersectionFunction3D(view, el1, el2);\n center = view.create('point3d', func[0], { visible: false });\n ixnCircle = view.create('circle3d', [center, func[1], func[2]], attr);\n\n el1.addChild(ixnCircle);\n el2.addChild(ixnCircle);\n } catch (e) {\n throw new Error(\n \"JSXGraph: Can't create 'intersection' with parent types '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\"\n );\n }\n\n ixnCircle.type = Const.OBJECT_TYPE_INTERSECTION_CIRCLE3D;\n ixnCircle.elType = 'intersectioncircle3d';\n ixnCircle.setParents([el1.id, el2.id]);\n\n return ixnCircle;\n};\n\nJXG.registerElement('intersectioncircle3d', JXG.createIntersectionCircle3D);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n */\n moveTo: function (where, time, options) {\n options = options || {};\n\n var i,\n steps = Math.ceil(time / this.board.attr.animationdelay),\n X = where[0],\n Y = where[1],\n Z = where[2],\n dX = this.coords[1] - X,\n dY = this.coords[2] - Y,\n dZ = this.coords[3] - Z,\n doneCallback = () => { },\n stepFun;\n\n if (options.callback)\n doneCallback = options.callback; // unload\n\n\n /** @ignore */\n stepFun = function (i) {\n var x = i / steps; // absolute progress of the animatin\n\n if (options.effect) {\n if (options.effect === \"<>\") {\n return Math.pow(Math.sin((x * Math.PI) / 2), 2);\n }\n if (options.effect === \"<\") { // cubic ease in\n return x * x * x;\n }\n if (options.effect === \">\") { // cubic ease out\n return 1 - Math.pow(1 - x, 3);\n }\n if (options.effect === \"==\") {\n return i / steps; // linear\n }\n throw new Error(\"valid effects are '==', '<>', '>', and '<'.\");\n }\n return i / steps; // default\n };\n\n // immediate move, no time\n if (\n !Type.exists(time) ||\n time === 0\n // check for tiny move, is this necessary?\n // Math.abs(where.usrCoords[0] - this.coords.usrCoords[0]) > Mat.eps\n ) {\n this.setPosition([X, Y, Z], true); // no event here\n return this.board.update(this);\n }\n\n // In case there is no callback and we are already at the endpoint we can stop here\n if (\n !Type.exists(options.callback) &&\n Math.abs(dX) < Mat.eps &&\n Math.abs(dY) < Mat.eps &&\n Math.abs(dZ) < Mat.eps\n ) {\n return this;\n }\n\n this.animationPath = [];\n for (i = steps; i >= 0; i--) {\n this.animationPath[steps - i] = [\n X + dX * stepFun(i),\n Y + dY * stepFun(i),\n Z + dZ * stepFun(i)\n ];\n }\n\n return this.moveAlong(this.animationPath, time,\n { callback: doneCallback });\n\n },\n\n /**\n * Move along a path defined by an array of coordinates\n * @param {number[][]} [traversePath] Array of path coordinates (either cartesian or homogenous).\n * @param {number} [time] Number of milliseconds the animation should last.\n * @param {Object} [options] 'callback' and 'interpolate'. see {@link JXG.CoordsElement#moveAlong},\n * @example\n *const board = JXG.JSXGraph.initBoard('jxgbox')\n *var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]]);\n *\n * board.create('button', [-4, 4.5, 'start', () => {\n * let A = view.create('point3d', [0, 0, 0]);\n * A.moveAlong([[3, 3, 3], [-2, -1, -2], [-1, -1, -1], [-1, -2, 1]], 3000,\n * { callback: () => board.create('text', [-4, 4, 'done!']) })\n *}])\n *\n * \n * \n *\n */\n moveAlong: function (traversePath, time, options) {\n let stepTime = time/traversePath.length; // will be same as this.board.attr.animationdelay if called by MoveTo\n\n\n // unload the options\n if (Type.isObject(options)) {\n if ('callback' in options)\n this.moveCallback = options.callback;\n // TODO:add interpolation using Neville. How? easiest is add interpolation to path before start\n // if ('interpolate' in options) interpolate = options.interpolate;\n }\n\n\n if (this.movePath.length > 0) { // existing move in progress\n this.movePath = traversePath; // set the new path and return ??\n return; // promise is still outstanding\n }\n\n // no move currently in progress\n this.movePath = traversePath; // set the new path and return a promise\n return new Promise((resolve, reject) => {\n this.moveInterval = setInterval(() => {\n if (this.movePath.length > 0) {\n let coord = this.movePath.shift();\n this.setPosition(coord, true); // no events during transit\n this.board.update(this);\n }\n if (this.movePath.length === 0) { // now shorter than previous test\n clearInterval(this.moveInterval);\n resolve();\n if (Type.isFunction(this.moveCallback)) {\n this.moveCallback(); // invoke the callback\n }\n }\n }, stepTime);\n });\n },\n\n\n\n\n // Not yet working\n __evt__update3D: function (oc) { }\n }\n);\n\n/**\n * @class A Point3D object is defined by three coordinates [x,y,z], or a function returning an array with three numbers.\n * Alternatively, all numbers can also be provided as functions returning a number.\n *\n * @pseudo\n * @name Point3D\n * @augments JXG.Point3D\n * @constructor\n * @throws {Exception} If the element cannot be constructed with the given parent\n * objects an exception is thrown.\n * @param {number,function_number,function_number,function_JXG.GeometryElement3D} x,y,z,[slide=undefined] The coordinates are given as x, y, z consisting of numbers or functions.\n * If an optional 3D element \"slide\" is supplied, the point is a glider on that element. At the time of version v1.11, only elements of type line3d are supperted as glider hosts.\n * @param {array,function_JXG.GeometryElement3D} F,[slide=null] Alternatively, the coordinates can be supplied as\n * \n *
\n * If an optional 3D element \"slide\" is supplied, the point is a glider on that element.\n *\n * @example\n * var bound = [-5, 5];\n * var view = board.create('view3d',\n * [[-6, -3], [8, 8],\n * [bound, bound, bound]],\n * {});\n * var p = view.create('point3d', [1, 2, 2], { name:'A', size: 5 });\n * var q = view.create('point3d', function() { return [p.X(), p.Y(), p.Z() - 3]; }, { name:'B', size: 3, fixed: true });\n * var w = view.create('point3d', [ () => p.X() + 3, () => p.Y(), () => p.Z() - 2], { name:'C', size: 3, fixed: true });\n *\n * \n * \n *\n * @example\n * // Glider on sphere\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]],\n * {\n * depthOrder: {\n * enabled: true\n * },\n * projection: 'central',\n * xPlaneRear: {fillOpacity: 0.2, gradient: null},\n * yPlaneRear: {fillOpacity: 0.2, gradient: null},\n * zPlaneRear: {fillOpacity: 0.2, gradient: null}\n * }\n * );\n *\n * // Two points\n * var center = view.create('point3d', [0, 0, 0], {withLabel: false, size: 2});\n * var point = view.create('point3d', [2, 0, 0], {withLabel: false, size: 2});\n *\n * // Sphere\n * var sphere = view.create('sphere3d', [center, point], {fillOpacity: 0.8});\n *\n * // Glider on sphere\n * var glide = view.create('point3d', [2, 2, 0, sphere], {withLabel: false, color: 'red', size: 4});\n * var l1 = view.create('line3d', [glide, center], { strokeWidth: 2, dash: 2 });\n *\n * \n * \n *\n */\nJXG.createPoint3D = function (board, parents, attributes) {\n // parents[0]: view\n // followed by\n // parents[1]: function or array\n // or\n // parents[1..3]: coordinates\n\n var view = parents[0],\n attr, F, slide, c2d, el,\n base = null,\n transform = null;\n\n // If the last element of `parents` is a 3D object,\n // the point is a glider on that element.\n if (parents.length > 2 &&\n Type.exists(parents[parents.length - 1].is3D) &&\n !Type.isTransformationOrArray(parents[parents.length - 1])\n ) {\n slide = parents.pop();\n } else {\n slide = null;\n }\n\n if (parents.length === 2) {\n // [view, array|fun] (Array [x, y, z] | function) returning [x, y, z]\n F = parents[1];\n } else if (parents.length === 3 &&\n Type.isPoint3D(parents[1]) &&\n Type.isTransformationOrArray(parents[2])\n ) {\n F = [0, 0, 0];\n base = parents[1];\n transform = parents[2];\n } else if (parents.length === 4) {\n // [view, x, y, z], (3 numbers | functions)\n F = parents.slice(1);\n } else if (parents.length === 5) {\n // [view, w, x, y, z], (4 numbers | functions)\n F = parents.slice(1);\n } else {\n throw new Error(\n \"JSXGraph: Can't create point3d with parent types '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [[x,y,z]], [x,y,z], or [[x,y,z], slide], () => [x, y, z], or [point, transformation(s)]\"\n );\n // \"\\nPossible parent types: [[x,y,z]], [x,y,z], [element,transformation]\"); // TODO\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'point3d');\n el = new JXG.Point3D(view, F, slide, attr);\n el.initCoords();\n if (base !== null && transform !== null) {\n el.addTransform(base, transform);\n }\n\n c2d = view.project3DTo2D(el.coords);\n\n attr = el.setAttr2D(attr);\n el.element2D = view.create('point', c2d, attr);\n el.element2D.view = view;\n el.element2D.dump = false;\n el.addChild(el.element2D);\n el.inherits.push(el.element2D);\n el.element2D.setParents(el);\n\n // If this point is a glider, record that in the update tree\n if (el.slide) {\n el.slide.addChild(el);\n el.setParents(el.slide);\n }\n if (base) {\n el.setParents(base);\n }\n\n el._c2d = el.element2D.coords.usrCoords.slice(); // Store a copy of the coordinates to detect dragging\n\n return el;\n};\n\nJXG.registerElement(\"point3d\", JXG.createPoint3D);\n\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n */\nJXG.createCurve3D = function (board, parents, attributes) {\n var view = parents[0],\n F, X, Y, Z, range, attr, el,\n mat,\n base = null,\n transform = null;\n\n if (parents.length === 3) {\n if (Type.isTransformationOrArray(parents[2]) && parents[1].type === Const.OBJECT_TYPE_CURVE3D) {\n // [curve, transformation(s)]\n // This might be adopted to the type of the base element (data plot or function)\n base = parents[1];\n transform = parents[2];\n F = null;\n X = [];\n Y = [];\n Z = [];\n } else {\n // [F, range]\n F = parents[1];\n range = parents[2];\n X = null;\n Y = null;\n Z = null;\n }\n } else if (parents.length === 2 && Type.isArray(parents[1])) {\n mat = Mat.transpose(parents[1]);\n X = mat[0];\n Y = mat[1];\n Z = mat[2];\n F = null;\n } else {\n // [X, Y, Z, range]\n X = parents[1];\n Y = parents[2];\n Z = parents[3];\n range = parents[4];\n F = null;\n }\n // TODO Throw new Error\n\n attr = Type.copyAttributes(attributes, board.options, 'curve3d');\n el = new JXG.Curve3D(view, F, X, Y, Z, range, attr);\n\n attr = el.setAttr2D(attr);\n el.element2D = view.create(\"curve\", [[], []], attr);\n el.element2D.view = view;\n el.element2D.dump = false;\n if (base !== null) {\n el.addTransform(base, transform);\n el.addParents(base);\n }\n\n /**\n * @class\n * @ignore\n */\n el.element2D.updateDataArray = function () {\n var ret = el.updateDataArray2D();\n this.dataX = ret.X;\n this.dataY = ret.Y;\n };\n el.addChild(el.element2D);\n el.inherits.push(el.element2D);\n el.element2D.setParents(el);\n\n el.element2D.prepareUpdate().update();\n if (!board.isSuspendedUpdate) {\n el.element2D.updateVisibility().updateRenderer();\n }\n\n return el;\n};\n\nJXG.registerElement(\"curve3d\", JXG.createCurve3D);\n\n/**\n * @class A vector field is an assignment of a vector to each point in 3D space.\n * \n * \n *\n */\nJXG.createVectorfield3D = function (board, parents, attributes) {\n var view = parents[0],\n el, attr;\n\n if (!(parents.length >= 5 &&\n (Type.isArray(parents[1]) || Type.isFunction(parents[1]) || Type.isString(parents[1])) &&\n (Type.isArray(parents[2]) && parents[1].length === 3) &&\n (Type.isArray(parents[3]) && parents[2].length === 3) &&\n (Type.isArray(parents[4]) && parents[3].length === 3)\n )) {\n throw new Error(\n \"JSXGraph: Can't create vector field 3D with parent types \" +\n \"'\" + typeof parents[1] + \"', \" +\n \"'\" + typeof parents[2] + \"', \" +\n \"'\" + typeof parents[3] + \"'.\" +\n \"'\" + typeof parents[4] + \"', \"\n );\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'vectorfield3d');\n el = view.create('curve3d', [[], [], []], attr);\n\n /**\n * Set the defining functions of 3D vector field.\n * @memberOf Vectorfield3D\n * @name setF\n * @function\n * @param {Array|Function} func Either an array containing three functions f1(x, y, z),\n * f2(x, y, z), and f3(x, y, z) or function f(x, y, z) returning an array of length 3.\n * @returns {Object} Reference to the 3D vector field object.\n *\n * @example\n * field.setF([(x, y, z) => Math.sin(y), (x, y, z) => Math.cos(x), (x, y, z) => z]);\n * board.update();\n *\n */\n el.setF = function (func, varnames) {\n var f0, f1, f2;\n if (Type.isArray(func)) {\n f0 = Type.createFunction(func[0], this.board, varnames);\n f1 = Type.createFunction(func[1], this.board, varnames);\n f2 = Type.createFunction(func[2], this.board, varnames);\n /**\n * @ignore\n */\n this.F = function (x, y, z) {\n return [f0(x, y, z), f1(x, y, z), f2(x, y, z)];\n };\n } else {\n this.F = Type.createFunction(func, el.board, varnames);\n }\n return this;\n };\n\n el.setF(parents[1], 'x, y, z');\n el.xData = parents[2];\n el.yData = parents[3];\n el.zData = parents[4];\n\n el.updateDataArray = function () {\n var k, i, j,\n v, nrm,\n x, y, z,\n scale = this.evalVisProp('scale'),\n start = [\n Type.evaluate(this.xData[0]),\n Type.evaluate(this.yData[0]),\n Type.evaluate(this.zData[0])\n ],\n steps = [\n Type.evaluate(this.xData[1]),\n Type.evaluate(this.yData[1]),\n Type.evaluate(this.zData[1])\n ],\n end = [\n Type.evaluate(this.xData[2]),\n Type.evaluate(this.yData[2]),\n Type.evaluate(this.zData[2])\n ],\n delta = [\n (end[0] - start[0]) / steps[0],\n (end[1] - start[1]) / steps[1],\n (end[2] - start[2]) / steps[2]\n ],\n phi, theta1, theta2, theta,\n showArrow = this.evalVisProp('arrowhead.enabled'),\n leg, leg_x, leg_y, leg_z, alpha;\n\n if (showArrow) {\n // Arrow head style\n // leg = 8;\n // alpha = Math.PI * 0.125;\n leg = this.evalVisProp('arrowhead.size');\n alpha = this.evalVisProp('arrowhead.angle');\n leg_x = leg / board.unitX;\n leg_y = leg / board.unitY;\n leg_z = leg / Math.sqrt(board.unitX * board.unitY);\n }\n\n this.dataX = [];\n this.dataY = [];\n this.dataZ = [];\n for (i = 0, x = start[0]; i <= steps[0]; x += delta[0], i++) {\n for (j = 0, y = start[1]; j <= steps[1]; y += delta[1], j++) {\n for (k = 0, z = start[2]; k <= steps[2]; z += delta[2], k++) {\n v = this.F(x, y, z);\n nrm = Mat.norm(v);\n if (nrm < Number.EPSILON) {\n continue;\n }\n\n v[0] *= scale;\n v[1] *= scale;\n v[2] *= scale;\n Type.concat(this.dataX, [x, x + v[0], NaN]);\n Type.concat(this.dataY, [y, y + v[1], NaN]);\n Type.concat(this.dataZ, [z, z + v[2], NaN]);\n\n if (showArrow) {\n // Arrow head\n nrm *= scale;\n phi = Math.atan2(v[1], v[0]);\n theta = Math.asin(v[2] / nrm);\n theta1 = theta - alpha;\n theta2 = theta + alpha;\n Type.concat(this.dataX, [\n x + v[0] - leg_x * Math.cos(phi) * Math.cos(theta1),\n x + v[0],\n x + v[0] - leg_x * Math.cos(phi) * Math.cos(theta2),\n NaN]);\n Type.concat(this.dataY, [\n y + v[1] - leg_y * Math.sin(phi) * Math.cos(theta1),\n y + v[1],\n y + v[1] - leg_y * Math.sin(phi) * Math.cos(theta2),\n NaN]);\n Type.concat(this.dataZ, [\n z + v[2] - leg_z * Math.sin(theta2),\n z + v[2],\n z + v[2] - leg_z * Math.sin(theta1),\n NaN]);\n }\n }\n }\n }\n };\n\n Type.extendInstanceMethodMap(el, {\n setF: \"setF\"\n });\n\n return el;\n};\n\nJXG.registerElement(\"vectorfield3D\", JXG.createVectorfield3D);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Aaron Fenyes,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n * All numbers can also be provided as functions returning a number.\n * The case [point, array] is ambiguous, it is not clear if 'array' contains the coordinates of a point\n * or of a direction. In that case, 'array' is interpreted as the coordinate array of a point,\n * i.e. the line is defined by two points.\n *\n * @pseudo\n * @name Line3D\n * @augments JXG.GeometryElement3D\n * @constructor\n * @type JXG.Line3D\n * @throws {Exception} If the element cannot be constructed with the given parent\n * objects an exception is thrown.\n * @param {JXG.Point3D,array,function_JXG.Point3D,array,function} point1,point2 First and second defining point of the line.\n * The attributes {@link Line3D#straightFirst} and {@link Line3D#straightLast} control if the line is displayed as\n * segment, ray or infinite line.\n * @param {JXG.Point3D,array,function_JXG.Line3D,array,function_array,function} point,direction,range The line is defined by point, direction and range.\n * \n *
\n *\n * @example\n * var bound = [-5, 5];\n * var view = board.create('view3d',\n * [[-6, -3], [8, 8],\n * [bound, bound, bound]],\n * {});\n * var p = view.create('point3d', [1, 2, 2], { name:'A', size: 5 });\n * // Lines through 2 points\n * var l1 = view.create('line3d', [[1, 3, 3], [-3, -3, -3]], {point1: {visible: true}, point2: {visible: true} });\n * var l2 = view.create('line3d', [p, l1.point1]);\n *\n * // Line by point, direction, range\n * var l3 = view.create('line3d', [p, [0, 0, 1], [-2, 4]]);\n *\n * \n * \n *\n * @example\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]],\n * {\n * depthOrder: {\n * enabled: true\n * },\n * projection: 'central',\n * xPlaneRear: {fillOpacity: 0.2},\n * yPlaneRear: {fillOpacity: 0.2},\n * zPlaneRear: {fillOpacity: 0.2}\n * }\n * );\n *\n * var A = view.create('point3d', [0, 0, 0], {size: 2});\n * var B = view.create('point3d', [2, 1, 1], {size: 2});\n * var C = view.create('point3d', [-2.5, 2.5, 1.5], {size: 2});\n *\n * // Draggable line by two points\n * var line1 = view.create('line3d', [A, B], {\n * fixed: false,\n * straightFirst: true,\n * straightLast: true,\n * dash: 2\n * });\n *\n * // Line by point, direction, and range\n * var line2 = view.create('line3d', [C, [1, 0, 0], [-1, Infinity]], {\n * strokeColor: 'blue'\n * });\n *\n * // Line by point and array\n * var line3 = view.create('line3d', [C, [-2.5, -1, 1.5]], {\n * point2: { visible: true},\n * strokeColor: 'red'\n * });\n *\n * \n * \n *\n * @example\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]],\n * {\n * depthOrder: {\n * enabled: true\n * },\n * projection: 'parallel',\n * xPlaneRear: { fillOpacity: 0.2 },\n * yPlaneRear: { fillOpacity: 0.2 },\n * zPlaneRear: { fillOpacity: 0.2 }\n * }\n * );\n *\n *\n * var A = view.create('point3d', [-2, 0, 1], { size: 2 });\n * var B = view.create('point3d', [-2, 0, 2], { size: 2 });\n * var line1 = view.create('line3d', [A, B], {\n * fixed: false,\n * strokeColor: 'blue',\n * straightFirst: true,\n * straightLast: true\n * });\n *\n * var C = view.create('point3d', [2, 0, 1], { size: 2 });\n * var line2 = view.create('line3d', [C, line1, [-Infinity, Infinity]], { strokeColor: 'red' });\n *\n * \n * \n *\n */\nJXG.createLine3D = function (board, parents, attributes) {\n var view = parents[0],\n attr, points,\n point, direction, range,\n point1, point2, endpoints,\n el,\n base = null,\n transform = null;\n\n attr = Type.copyAttributes(attributes, board.options, 'line3d');\n\n // In any case, parents[1] contains a point or point coordinates\n\n if (parents[1].type === Const.OBJECT_TYPE_LINE3D &&\n Type.isTransformationOrArray(parents[2])\n ) {\n base = parents[1];\n transform = parents[2];\n\n points = Type.providePoints3D(\n view,\n [\n [0, 0, 0, 0],\n [0, 0, 0, 0]\n ],\n attributes,\n 'line3d',\n ['point1', 'point2']\n );\n }\n\n if (base === null && // No transformation\n (Type.isPoint3D(parents[2]) ||\n ( parents.length === 3 && (Type.isArray(parents[2]) || Type.isFunction(parents[2])) )\n )\n ) {\n // Line defined by two points; [view, point1, point2]\n point1 = Type.providePoints3D(view, [parents[1]], attributes, 'line3d', ['point1'])[0];\n point2 = Type.providePoints3D(view, [parents[2]], attributes, 'line3d', ['point2'])[0];\n direction = function () {\n return [0, point2.X() - point1.X(), point2.Y() - point1.Y(), point2.Z() - point1.Z()];\n };\n range = [0, 1]; // Segment by default\n el = new JXG.Line3D(view, point1, direction, range, attr);\n el.prepareUpdate().update();\n\n // Create two shadow points that are the end points of the visible line.\n // This is of relevance if the line has straightFirst or straightLast set to true, then\n // endpoints differ from point1, point2.\n // In such a case, the endpoints are the intersection of the line with the cube.\n endpoints = Type.providePoints3D(\n view,\n [\n [1, 0, 0, 0],\n [1, 0, 0, 0]\n ],\n { visible: true },\n 'line3d',\n ['point1', 'point2']\n );\n\n /**\n * @ignore\n */\n endpoints[0].F = function () {\n var r = 0;\n if (el.evalVisProp('straightfirst')) {\n r = -Infinity;\n }\n return el.getPointCoords(r);\n };\n\n /**\n * @ignore\n */\n endpoints[1].F = function () {\n var r = 1;\n if (el.evalVisProp('straightlast')) {\n r = Infinity;\n }\n return el.getPointCoords(r);\n };\n endpoints[0].prepareUpdate().update();\n endpoints[1].prepareUpdate().update();\n\n // The 2D line is always a segment.\n attr = el.setAttr2D(attr);\n attr.straightfirst = false;\n attr.straightlast = false;\n el.element2D = view.create('segment', [endpoints[0].element2D, endpoints[1].element2D], attr);\n el.element2D.view = view;\n el.element2D.dump = false;\n\n /**\n * Shadow points that determine the visible line.\n * This is of relevance if the line is defined by two points and has straightFirst or straightLast set to true.\n * In such a case, the shadow points are the intersection of the line with the cube.\n *\n * @name JXG.Point3D.endpoints\n * @type Array\n * @private\n */\n el.endpoints = endpoints;\n el.addChild(endpoints[0]);\n el.addChild(endpoints[1]);\n // el.setParents(endpoints);\n el.addParents([point1, point2]);\n\n } else {\n // Line defined by point, direction and range\n\n // Directions are handled as arrays of length 4, i.e. with homogeneous coordinates.\n if (base !== null) {\n point = Type.providePoints3D(view, [[0, 0, 0]], attributes, 'line3d', ['point'])[0];\n direction = [0, 0, 0, 0.0001];\n range = parents[3] || [-Infinity, Infinity];\n } else if (\n (Type.exists(parents[2].view) && parents[2].type === Const.OBJECT_TYPE_LINE3D) || // direction given by another line\n Type.isFunction(parents[2]) || (parents[2].length === 3) || (parents[2].length === 4) // direction given as function or array\n ) {\n point = Type.providePoints3D(view, [parents[1]], attributes, 'line3d', ['point'])[0];\n direction = parents[2];\n range = parents[3];\n } else {\n throw new Error(\n \"JSXGraph: Can't create line3d with parents of type '\" +\n typeof parents[1] + \", \" +\n typeof parents[2] + \", \" +\n typeof parents[3] + \"'.\"\n );\n }\n\n points = Type.providePoints3D(\n view,\n [\n [1, 0, 0, 0],\n [1, 0, 0, 0]\n ],\n attributes,\n 'line3d',\n ['point1', 'point2']\n );\n\n // Create a line3d with two dummy points\n el = new JXG.Line3D(view, point, direction, range, attr);\n el.prepareUpdate().update();\n\n // Now set the real points which define the line\n /**\n * @ignore\n */\n points[0].F = function () {\n return el.getPointCoords(Type.evaluate(el.range[0]));\n };\n points[0].prepareUpdate().update();\n point1 = points[0];\n\n /**\n * @ignore\n */\n points[1].F = function () {\n return el.getPointCoords(Type.evaluate(el.range[1]));\n };\n points[1].prepareUpdate().update();\n point2 = points[1];\n\n attr = el.setAttr2D(attr);\n attr.straightfirst = false;\n attr.straightlast = false;\n el.element2D = view.create('segment', [point1.element2D, point2.element2D], attr);\n el.element2D.view = view;\n el.element2D.dump = false;\n\n /**\n * Array of length 2 containing the endings of the Line3D element. These are the defining points,\n * the intersections of the line with the bounding box, or the endings defined by the range.\n * @name Line3D#endpoints\n * @type {Array}\n */\n el.endpoints = points;\n\n el.addParents(point);\n\n if (base !== null && transform !== null) {\n el.addTransform(base, transform);\n el.addParents(base);\n }\n }\n\n el.addChild(el.element2D);\n el.inherits.push(el.element2D);\n el.element2D.addParents(el);\n\n el.point1 = point1;\n el.point2 = point2;\n if (el.point1._is_new) {\n el.addChild(el.point1);\n delete el.point1._is_new;\n } else {\n el.point1.addChild(el);\n }\n if (el.point2._is_new) {\n el.addChild(el.point2);\n delete el.point2._is_new;\n } else {\n el.point2.addChild(el);\n }\n if (Type.exists(point)) {\n if (point._is_new) {\n el.addChild(point);\n delete point._is_new;\n } else {\n point.addChild(el);\n }\n }\n\n el.update();\n el.element2D.prepareUpdate().update().updateRenderer();\n return el;\n};\n\nJXG.registerElement('line3d', JXG.createLine3D);\n\n// -----------------------\n// Planes\n// -----------------------\n\n/**\n * Constructor for 3D planes.\n * @class Creates a new 3D plane object. Do not use this constructor to create a 3D plane. Use {@link JXG.Board#create} with type {@link Plane3D} instead.\n *\n * @augments JXG.GeometryElement3D\n * @augments JXG.GeometryElement\n * @param {View3D} view\n * @param {Point3D|Array} point\n * @param {Array} direction1\n * @param {Array} range_u\n * @param {Array} direction2\n * @param {Array} range_v\n * @param {Object} attributes\n * @see JXG.Board#generateName\n */\nJXG.Plane3D = function (view, point, dir1, range_u, dir2, range_v, attributes) {\n this.constructor(view.board, attributes, Const.OBJECT_TYPE_PLANE3D, Const.OBJECT_CLASS_3D);\n this.constructor3D(view, 'plane3d');\n\n this.board.finalizeAdding(this);\n\n /**\n * 3D point which - together with two direction vectors - defines the plane.\n *\n * @name point\n * @memberOf Plane3D\n * @type JXG.Point3D\n *\n * @see Plane3D#direction1\n * @see Plane3D#direction2\n */\n this.point = point;\n\n /**\n * Two linearly independent vectors - together with a point - define the plane. Each of these direction vectors is an\n * array of numbers or functions (either of length 3 or 4) or function returning array of length 3 or 4.\n * Homogeneous coordinates of directions have the form [0, x, y, z].\n *\n * @name Plane3D#direction1\n * @type Array|Function\n *\n * @see Plane3D.point\n * @see Plane3D#direction2\n */\n this.direction1 = dir1;\n\n /**\n * Two linearly independent vectors - together with a point - define the plane. Each of these direction vectors is an\n * array of numbers or functions (either of length 3 or 4) or function returning array of length 3 or 4.\n * Homogeneous coordinates of directions have the form [0, x, y, z].\n *\n * @type Array|Function\n * @name Plane3D#direction2\n * @see Plane3D.point\n * @see Plane3D#direction1\n */\n this.direction2 = dir2;\n\n /**\n * Range [r1, r2] of {@link direction1}. The 3D line goes from (point + r1 * direction1) to (point + r2 * direction1)\n * @name Plane3D#range_u\n * @type {Array}\n * @default [-Infinity, Infinity]\n * @default\n */\n this.range_u = range_u || [-Infinity, Infinity];\n\n /**\n * Range [r1, r2] of {@link direction2}. The 3D line goes from (point + r1 * direction2) to (point + r2 * direction2)\n * @name Plane3D#range_v\n * @type {Array}\n * @type {Array}\n * @default [-Infinity, Infinity]\n */\n this.range_v = range_v || [-Infinity, Infinity];\n\n /**\n * Spanning vector 1 of the 3D plane. Contains the evaluated coordinates from {@link direction1} and {@link range1}.\n * and is of length 4, the first entry being 0, i.e. homogenous coordinates.\n *\n * @name Plane3D#vec1\n * @type Array\n * @private\n *\n * @see Plane3D#updateCoords\n */\n this.vec1 = [0, 0, 0, 0];\n\n /**\n * Spanning vector 2 of the 3D plane. Contains the evaluated coordinates from {@link Plane3D#direction2} and {@link Plane3D#range2}\n * and is of length 4, the first entry being 0, i.e. homogenous coordinates.\n *\n * @name Plane3D#vec2\n * @type Array\n * @private\n *\n * @see Plane3D#updateCoords\n */\n this.vec2 = [0, 0, 0, 0];\n\n /**\n * Mesh (grid) element of the plane.\n *\n * @name Plane3D#mesh3d\n * @type Mesh3D\n * @private\n */\n this.mesh3d = null;\n\n /**\n * Normal vector of the plane. Left hand side of the Hesse normal form.\n * @name Plane3D#normal\n * @type Array\n * @private\n *\n * @see Plane3D.updateNormal\n *\n */\n this.normal = [0, 0, 0, 0];\n\n /**\n * Right hand side of the Hesse normal form.\n * @name Plane3D#d\n * @type Array\n * @private\n *\n * @see Plane3D.updateNormal\n *\n */\n this.d = 0;\n\n this.updateCoords();\n this.updateNormal();\n};\n\nJXG.Plane3D.prototype = new JXG.GeometryElement();\n\nType.copyPrototypeMethods(JXG.Plane3D, JXG.GeometryElement3D, 'constructor3D');\nType.copyMethodMap(JXG.Plane3D, {\n // TODO\n});\n\nJXG.extend(\n JXG.Plane3D.prototype,\n /** @lends JXG.Plane3D.prototype */ {\n\n /**\n * Get coordinate array [1, x, y, z] of a point on the plane for parameters (u, v).\n *\n * @name Plane3D#F\n * @function\n * @param {Number} u\n * @param {Number} v\n * @returns Array of length 3.\n */\n F: function (u, v) {\n var i, v1, v2, l1, l2;\n\n v1 = this.vec1.slice();\n v2 = this.vec2.slice();\n l1 = Mat.norm(v1, 4);\n l2 = Mat.norm(v2, 4);\n for (i = 1; i < 4; i++) {\n v1[i] /= l1;\n v2[i] /= l2;\n }\n\n return [\n 1,\n this.point.X() + u * v1[0] + v * v2[0],\n this.point.Y() + u * v1[1] + v * v2[1],\n this.point.Z() + u * v1[2] + v * v2[2]\n ];\n },\n\n /**\n * Get x-coordinate of a point on the plane for parameters (u, v).\n *\n * @name Plane3D#X\n * @function\n * @param {Number} u\n * @param {Number} v\n * @returns Number\n */\n X: function(u, v) {\n return this.F(u, v)[1];\n },\n\n /**\n * Get y-coordinate of a point on the plane for parameters (u, v).\n *\n * @name Plane3D#Y\n * @function\n * @param {Number} u\n * @param {Number} v\n * @returns Number\n */\n Y: function(u, v) {\n return this.F(u, v)[2];\n },\n\n /**\n * Get z-coordinate of a point on the plane for parameters (u, v).\n *\n * @name Plane3D#Z\n * @function\n * @param {Number} u\n * @param {Number} v\n * @returns Number\n */\n Z: function(u, v) {\n return this.F(u, v)[3];\n },\n\n /**\n * Update the arrays {@link JXG.Plane3D#vec1} and {@link JXG.Plane3D#vec1} containing the homogeneous coords of the spanning vectors.\n *\n * @name Plane3D#updateCoords\n * @function\n * @returns {Object} Reference to Plane3D object\n * @private\n */\n updateCoords: function() {\n var i, s;\n\n if (Type.exists(this.direction1.view) && this.direction1.type === Const.OBJECT_TYPE_LINE3D) {\n this.vec1 = this.direction1.vec.slice();\n } else if (Type.isFunction(this.direction1)) {\n this.vec1 = Type.evaluate(this.direction1);\n if (this.vec1.length === 3) {\n this.vec1.unshift(0);\n }\n } else {\n s = 0;\n if (this.direction1.length === 3) {\n this.vec1[0] = 0;\n s = 1;\n }\n for (i = 0; i < this.direction1.length; i++) {\n this.vec1[s + i] = Type.evaluate(this.direction1[i]);\n }\n }\n\n if (Type.exists(this.direction2.view) && this.direction2.type === Const.OBJECT_TYPE_LINE3D) {\n this.vec2 = this.direction2.vec.slice();\n } else if (Type.isFunction(this.direction2)) {\n this.vec2 = Type.evaluate(this.direction2);\n if (this.vec2.length === 3) {\n this.vec2.unshift(0);\n }\n } else {\n s = 0;\n if (this.direction2.length === 3) {\n this.vec2[0] = 0;\n s = 1;\n }\n for (i = 0; i < this.direction2.length; i++) {\n this.vec2[s + i] = Type.evaluate(this.direction2[i]);\n }\n }\n\n return this;\n },\n\n /**\n * Update the Hesse normal form of the plane, i.e. update normal vector and right hand side.\n * Updates also {@link vec1} and {@link vec2}.\n *\n * @name Plane3D#updateNormal\n * @function\n * @returns {Object} Reference to the Plane3D object\n * @private\n * @example\n * plane.updateNormal();\n *\n */\n updateNormal: function () {\n var i, len;\n\n if (!this.needsUpdate) {\n // Extraordinary update, conflicts with rotating of box and plane transformations\n // this.updateCoords();\n }\n\n this.normal = Mat.crossProduct(this.vec1.slice(1), this.vec2.slice(1));\n\n len = Mat.norm(this.normal);\n if (Math.abs(len) > Mat.eps * Mat.eps) {\n for (i = 0; i < 3; i++) {\n this.normal[i] /= len;\n }\n }\n this.normal.unshift(0);\n this.d = Mat.innerProduct(this.point.coords, this.normal, 4);\n\n return this;\n },\n\n // Already documented in element3d.js\n updateDataArray: function () {\n var s1, e1, s2, e2, c2d, l1, l2,\n planes = ['xPlaneRear', 'yPlaneRear', 'zPlaneRear'], // Must be ordered x, y, z\n points = [],\n v1 = [0, 0, 0],\n v2 = [0, 0, 0],\n q = [0, 0, 0],\n p = [0, 0, 0],\n eps = 1.e-12,\n d, i, j, a, b, first, pos, pos_akt,\n view = this.view;\n\n this.dataX = [];\n this.dataY = [];\n\n this.updateNormal();\n\n // Infinite plane\n if (\n this.elType !== 'axisplane3d' &&\n view.defaultAxes &&\n Type.evaluate(this.range_u[0]) === -Infinity &&\n Type.evaluate(this.range_u[1]) === Infinity &&\n Type.evaluate(this.range_v[0]) === -Infinity &&\n Type.evaluate(this.range_v[1]) === Infinity\n ) {\n // Determine the intersections of the plane with\n // the view bbox3d.\n //\n // Start with the rear plane.\n // For each face of the bbox3d we determine two points\n // which are the end points of the intersecting line\n // between the plane and a face of bbox3d.\n // We start with the three rear planes (set in planes[] above)\n for (j = 0; j < planes.length; j++) {\n p = view.intersectionPlanePlane(this, view.defaultAxes[planes[j]]);\n if (p[0] !== false && p[1] !== false) {\n // This test is necessary to filter out intersection lines which are\n // identical to intersections of axis planes (they would occur twice),\n // i.e. edges of bbox3d.\n for (i = 0; i < points.length; i++) {\n if (\n (Geometry.distance(p[0], points[i][0], 4) < eps &&\n Geometry.distance(p[1], points[i][1], 4) < eps) ||\n (Geometry.distance(p[0], points[i][1], 4) < eps &&\n Geometry.distance(p[1], points[i][0], 4) < eps)\n ) {\n break;\n }\n }\n if (i === points.length) {\n points.push(p.slice());\n }\n }\n\n // Take a point on the corresponding front plane of bbox3d.\n p = [1, 0, 0, 0];\n p[j + 1] = view.bbox3D[j][1];\n\n // Use the Hesse normal form of front plane to intersect it with the plane\n // d is the rhs of the Hesse normal form of the front plane.\n d = Mat.innerProduct(p, view.defaultAxes[planes[j]].normal, 4);\n p = view.intersectionPlanePlane(this, view.defaultAxes[planes[j]], d);\n\n if (p[0] !== false && p[1] !== false) {\n // Do the same test as above\n for (i = 0; i < points.length; i++) {\n // Same test for edges of bbox3d as above\n if (\n (Geometry.distance(p[0], points[i][0], 4) < eps &&\n Geometry.distance(p[1], points[i][1], 4) < eps) ||\n (Geometry.distance(p[0], points[i][1], 4) < eps &&\n Geometry.distance(p[1], points[i][0], 4) < eps)\n ) {\n break;\n }\n }\n if (i === points.length) {\n points.push(p.slice());\n }\n }\n }\n\n // Handle the case that the plane does not intersect bbox3d at all.\n if (points.length === 0) {\n return { X: this.dataX, Y: this.dataY };\n }\n\n // Concatenate the intersection points to a polygon.\n // If all went well, each intersection should appear\n // twice in the list.\n first = 0;\n pos = first;\n i = 0;\n do {\n p = points[pos][i];\n if (p.length === 4) {\n c2d = view.project3DTo2D(p);\n this.dataX.push(c2d[1]);\n this.dataY.push(c2d[2]);\n }\n i = (i + 1) % 2;\n p = points[pos][i];\n\n pos_akt = pos;\n for (j = 0; j < points.length; j++) {\n if (j !== pos && Geometry.distance(p, points[j][0]) < eps) {\n pos = j;\n i = 0;\n break;\n }\n if (j !== pos && Geometry.distance(p, points[j][1]) < eps) {\n pos = j;\n i = 1;\n break;\n }\n }\n if (pos === pos_akt) {\n console.log('Error plane3d update: did not find next', pos);\n break;\n }\n } while (pos !== first);\n\n c2d = view.project3DTo2D(points[first][0]);\n this.dataX.push(c2d[1]);\n this.dataY.push(c2d[2]);\n } else {\n // 3D bounded flat\n s1 = Type.evaluate(this.range_u[0]);\n e1 = Type.evaluate(this.range_u[1]);\n s2 = Type.evaluate(this.range_v[0]);\n e2 = Type.evaluate(this.range_v[1]);\n\n q = this.point.coords;\n v1 = this.vec1.slice();\n v2 = this.vec2.slice();\n l1 = Mat.norm(v1, 4);\n l2 = Mat.norm(v2, 4);\n for (i = 1; i < 4; i++) {\n v1[i] /= l1;\n v2[i] /= l2;\n }\n\n for (j = 0; j < 4; j++) {\n switch (j) {\n case 0:\n a = s1;\n b = s2;\n break;\n case 1:\n a = e1;\n b = s2;\n break;\n case 2:\n a = e1;\n b = e2;\n break;\n case 3:\n a = s1;\n b = e2;\n }\n for (i = 0; i < 4; i++) {\n p[i] = q[i] + a * v1[i] + b * v2[i];\n }\n c2d = view.project3DTo2D(p);\n this.dataX.push(c2d[1]);\n this.dataY.push(c2d[2]);\n }\n // Close the curve\n this.dataX.push(this.dataX[0]);\n this.dataY.push(this.dataY[0]);\n }\n return { X: this.dataX, Y: this.dataY };\n },\n\n // Already documented in element3d.js\n addTransform: function (el, transform) {\n this.addTransformGeneric(el, transform);\n this.point.addTransform(el.point, transform);\n return this;\n },\n\n removeTransform: function (transform) {\n this.removeTransformGeneric(transform);\n this.point.removeTransform(transform);\n\n return this;\n },\n\n clearTransforms: function () {\n this.clearTransformsGeneric();\n this.point.clearTransformsGeneric();\n\n return this;\n },\n\n // Already documented in element3d.js\n updateTransform: function () {\n var c1, c2, i;\n\n if (this.transformations.length === 0 || this.baseElement === null) {\n return this;\n }\n\n if (this === this.baseElement) {\n c1 = this.vec1;\n c2 = this.vec2;\n } else {\n c1 = this.baseElement.vec1;\n c2 = this.baseElement.vec2;\n }\n\n for (i = 0; i < this.transformations.length; i++) {\n this.transformations[i].update();\n c1 = Mat.matVecMult(this.transformations[i].matrix, c1);\n c2 = Mat.matVecMult(this.transformations[i].matrix, c2);\n }\n this.vec1 = c1;\n this.vec2 = c2;\n\n return this;\n },\n\n // Already documented in element3d.js\n update: function () {\n if (this.needsUpdate) {\n this.updateCoords()\n .updateTransform();\n }\n return this;\n },\n\n // Already documented in element3d.js\n updateRenderer: function () {\n this.needsUpdate = false;\n\n return this;\n },\n\n // Already documented in element3d.js\n // projectScreenCoords: function (pScr, params, cyclic) {\n // if (params.length === 0) {\n // params.unshift(\n // 0.5 * (this.range_u[0] + this.range_u[1]),\n // 0.5 * (this.range_v[0] + this.range_v[1])\n // );\n // }\n // return Geometry.projectScreenCoordsToParametric(pScr, this, params, cyclic);\n // },\n\n // Already documented in element3d.js\n projectCoords: function (p, params) {\n return Geometry.projectCoordsToParametric(p, this, 2, params);\n }\n }\n);\n\n/**\n * @class A 3D plane is defined either by a point and two linearly independent vectors, or by three points.\n *\n * @description\n * A 3D plane is defined either by a point and two linearly independent vectors, or by three points.\n * In the first case, the parameters are a 3D point (or a coordinate array) and two vectors (arrays).\n * In the second case, the parameters consist of three 3D points (given as points or coordinate arrays).\n * In order to distinguish the two cases, in the latter case (three points), the additional attribute {@link Plane3D#threePoints}\n * has to be supplied if both, the second point and the third point, are given as arrays or functions. Otherwise, it would not be\n * clear if the input arrays have to be interpreted as points or directions.\n * \n *
\n * @param {JXG.Point3D,array,function_JXG.Point3D,array,function_JXG.Point3D,array,function} point1,point2,point3 The plane is defined by three points.\n * @type JXG.Plane3D\n *\n * @example\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]],\n * {\n * depthOrder: {\n * enabled: true\n * },\n * projection: 'central',\n * xPlaneRear: {fillOpacity: 0.2},\n * yPlaneRear: {fillOpacity: 0.2},\n * zPlaneRear: {fillOpacity: 0.2}\n * }\n * );\n *\n * var A = view.create('point3d', [-2, 0, 1], {size: 2});\n *\n * // Infinite Plane by point and two directions\n * var plane = view.create('plane3d', [A, [1, 0, 0], [0, 1, 0], [-Infinity, Infinity], [-Infinity, Infinity]]);\n *\n * \n * \n *\n * @example\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]],\n * {\n * depthOrder: {\n * enabled: true\n * },\n * projection: 'central',\n * xPlaneRear: {fillOpacity: 0.2},\n * yPlaneRear: {fillOpacity: 0.2},\n * zPlaneRear: {fillOpacity: 0.2}\n * }\n * );\n *\n * var A = view.create('point3d', [-2, 0, 1], {size: 2});\n *\n * // Finite Plane by point and two directions\n * var plane1 = view.create('plane3d', [A, [1, 0, 0], [0, 1, 0], [-2, 2], [-2, 2]]);\n * var plane2 = view.create('plane3d', [[0, 0, -1], [1, 0, 0], [0, 1, 0], [-2, 2], [-2, 2]], {\n * mesh3d: { visible: true },\n * point: {visible: true, name: \"B\", fixed: false}\n * });\n *\n * \n * \n * @example\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]],\n * {\n * depthOrder: {\n * enabled: true\n * },\n * projection: 'central',\n * xPlaneRear: { visible: false, fillOpacity: 0.2 },\n * yPlaneRear: { visible: false, fillOpacity: 0.2 },\n * zPlaneRear: { fillOpacity: 0.2 }\n * }\n * );\n *\n * var A = view.create('point3d', [-2, 0, 1], { size: 2 });\n *\n * var line1 = view.create('line3d', [A, [0, 0, 1], [-Infinity, Infinity]], { strokeColor: 'blue' });\n * var line2 = view.create('line3d', [A, [1, 1, 0], [-Infinity, Infinity]], { strokeColor: 'blue' });\n *\n * // Plane by point and two lines\n * var plane2 = view.create('plane3d', [A, line1, line2], {\n * fillColor: 'blue'\n * });\n *\n * \n * \n *\n * @example\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]],\n * {\n * depthOrder: {\n * enabled: true\n * },\n * projection: 'central',\n * xPlaneRear: {fillOpacity: 0.2},\n * yPlaneRear: {fillOpacity: 0.2},\n * zPlaneRear: {fillOpacity: 0.2}\n * }\n * );\n *\n * var A = view.create('point3d', [0, 0, 1], {size: 2});\n * var B = view.create('point3d', [2, 2, 1], {size: 2});\n * var C = view.create('point3d', [-2, 0, 1], {size: 2});\n *\n * // Plane by three points\n * var plane = view.create('plane3d', [A, B, C], {\n * fillColor: 'blue'\n * });\n *\n * \n * \n *\n * @example\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]],\n * {\n * depthOrder: {\n * enabled: true\n * },\n * projection: 'central',\n * xPlaneRear: {fillOpacity: 0.2},\n * yPlaneRear: {fillOpacity: 0.2},\n * zPlaneRear: {fillOpacity: 0.2}\n * }\n * );\n *\n * var A = view.create('point3d', [-2, 0, 1], {size: 2});\n *\n * // Infinite Plane by two directions,\n * // range1 = range2 = [-Infinity, Infinity]\n * var plane1 = view.create('plane3d', [A, [1, 0, 0], [0, 1, 0]], {\n * fillColor: 'blue',\n * });\n *\n * // Infinite Plane by three points,\n * var plane2 = view.create('plane3d', [A, [1, 0, 0], [0, 1, 0]], {\n * threePoints: true,\n * fillColor: 'red',\n * point2: {visible: true},\n * point3: {visible: true}\n * });\n *\n * \n * \n *\n */\nJXG.createPlane3D = function (board, parents, attributes) {\n var view = parents[0],\n attr,\n point, point2, point3,\n dir1, dir2, range_u, range_v,\n el, mesh3d,\n surface,\n su, sv, type, tiling,\n m, ma, mi, ma_a, mi_a, s, v,\n e,\n staticColorMap = true,\n // bb, size,\n base = null,\n transform = null;\n\n attr = Type.copyAttributes(attributes, board.options, 'plane3d');\n if (//parents.length === 4 &&\n // ()\n attr.threepoints || Type.isPoint3D(parents[2]) || Type.isPoint3D(parents[3])\n ) {\n // Three points\n point = Type.providePoints3D(view, [parents[1]], attributes, 'plane3d', ['point1'])[0];\n point2 = Type.providePoints3D(view, [parents[2]], attributes, 'plane3d', ['point2'])[0];\n point3 = Type.providePoints3D(view, [parents[3]], attributes, 'plane3d', ['point3'])[0];\n dir1 = function() {\n return [point2.X() - point.X(), point2.Y() - point.Y(), point2.Z() - point.Z()];\n };\n dir2 = function() {\n return [point3.X() - point.X(), point3.Y() - point.Y(), point3.Z() - point.Z()];\n };\n range_u = parents[4] || [-Infinity, Infinity];\n range_v = parents[5] || [-Infinity, Infinity];\n } else {\n if (parents[1].type === Const.OBJECT_TYPE_PLANE3D &&\n Type.isTransformationOrArray(parents[2])\n ) {\n // Plane + transformation\n base = parents[1];\n transform = parents[2];\n\n point = Type.providePoints3D(view, [[0, 0, 0, 0]], attributes, 'plane3d', ['point'])[0];\n dir1 = [0, 0.0001, 0, 0];\n dir2 = [0, 0, 0.0001, 0];\n range_u = parents[3] || [-Infinity, Infinity];\n range_v = parents[4] || [-Infinity, Infinity];\n } else {\n // Point, direction and ranges\n point = Type.providePoints3D(view, [parents[1]], attributes, 'plane3d', ['point'])[0];\n dir1 = parents[2];\n dir2 = parents[3];\n range_u = parents[4] || [-Infinity, Infinity];\n range_v = parents[5] || [-Infinity, Infinity];\n }\n if (point === false) {\n throw new Error(\n \"JSXGraph: Can't create plane3d with first parent of type '\" + typeof parents[1] +\n \"'.\" +\n \"\\nPossible first parent types are: point3d, array of length 3, function returning an array of length 3.\"\n );\n }\n if ((base !== null && parents < 3) || (base === null && parents.length < 4)) {\n throw new Error(\n \"JSXGraph: Can't create plane3d with parents of type '\" +\n typeof parents[1] + \", \" +\n typeof parents[2] + \", \" +\n typeof parents[3] + \", \" +\n typeof parents[4] + \", \" +\n typeof parents[5] + \"'.\"\n );\n }\n }\n\n el = new JXG.Plane3D(view, point, dir1, range_u, dir2, range_v, attr);\n point.addChild(el);\n\n type = el.evalVisProp('type');\n tiling = el.evalVisProp('tiling');\n\n // Path filled with gradient color\n attr = el.setAttr2D(attr);\n el.element2D = view.create('curve', [[], []], attr);\n el.element2D.view = view;\n el.element2D.dump = false;\n\n if (base !== null && transform !== null) {\n el.addTransform(base, transform);\n el.addParents(base);\n }\n\n /**\n * @class\n * @ignore\n */\n el.element2D.updateDataArray = function () {\n var ret = el.updateDataArray();\n this.dataX = ret.X;\n this.dataY = ret.Y;\n };\n el.addChild(el.element2D);\n el.inherits.push(el.element2D);\n el.element2D.setParents(el);\n\n if (\n Math.abs(el.range_u[0]) !== Infinity &&\n Math.abs(el.range_u[1]) !== Infinity &&\n Math.abs(el.range_v[0]) !== Infinity &&\n Math.abs(el.range_v[1]) !== Infinity\n ) {\n\n if (type === 'wireframe') {\n // Uses mesh3d\n attr = Type.copyAttributes(attr.mesh3d, board.options, 'mesh3d');\n mesh3d = view.create('mesh3d', [\n function () {\n return point.coords;\n },\n // dir1, dir2, range_u, range_v\n function() { return el.vec1; },\n function() { return el.vec2; },\n el.range_u,\n el.range_v\n ], attr);\n el.mesh3d = mesh3d;\n el.addChild(mesh3d);\n // el.inherits.push(mesh3d); // TODO Does not work\n el.element2D.inherits.push(mesh3d); // Does work - instead\n mesh3d.setParents(el);\n el.mesh3d.view = view;\n } else {\n su = el.evalVisProp('stepsu');\n sv = el.evalVisProp('stepsv');\n\n // Eliminate the call to the expensive el.updateDataArray();\n el.element2D.updateDataArray = function() {};\n\n // // Attempt to handle infinite planes\n // bb = el.view.bbox3D;\n // size = 0.5 * Math.sqrt((bb[0][0] - bb[0][1])**2 + (bb[1][0] - bb[1][1])**2 + (bb[2][0] - bb[2][1])**2);\n // ru0 = (Math.abs(ru0) === Infinity) ? -size : ru0;\n // ru1 = (Math.abs(ru1) === Infinity) ? size : ru1;\n // rv0 = (Math.abs(rv0) === Infinity) ? -size : rv0;\n // rv1 = (Math.abs(rv1) === Infinity) ? size : rv1;\n\n el.F = function (u, v) {\n return [\n el.point.coords[0] + u * el.vec1[0] + v * el.vec2[0],\n el.point.coords[1] + u * el.vec1[1] + v * el.vec2[1],\n el.point.coords[2] + u * el.vec1[2] + v * el.vec2[2],\n el.point.coords[3] + u * el.vec1[3] + v * el.vec2[3]\n ];\n };\n\n if (tiling === 'triangle') {\n surface = Tiling.triangulation(\n el,\n el.range_u,\n el.range_v,\n su, sv\n );\n } else {\n surface = Tiling.rectangulation(\n el,\n el.range_u,\n el.range_v,\n su, sv\n );\n }\n\n // coords = Tiling.mapMeshTo3D(surface, el);\n // surface = [coords, surface[1]];\n\n if (type === 'colormap') {\n attr.polyhedron.shader.enabled = false;\n\n // Static\n m = el.evalVisProp('colormap.max');\n ma = m[0];\n ma_a = m[1];\n m = el.evalVisProp('colormap.min');\n mi = m[0];\n mi_a = m[1];\n s = el.evalVisProp('colormap.s');\n v = el.evalVisProp('colormap.v');\n for (e in el.visProp.colormap) {\n if (el.visProp.colormap.hasOwnProperty(e)) {\n if (Type.isFunction(el.visProp.colormap[e])) {\n staticColorMap = false;\n break;\n }\n }\n }\n\n attr.polyhedron.fillcolorarray = [];\n attr.polyhedron.fillcolor = (self) => {\n var j, hsl,\n z = 0,\n p = self.polyhedron,\n face = p.faces[self.faceNumber],\n le = face.length;\n\n // Dynamic version\n if (!staticColorMap) {\n m = el.evalVisProp('colormap.max');\n ma = m[0];\n ma_a = m[1];\n m = el.evalVisProp('colormap.min');\n mi = m[0];\n mi_a = m[1];\n }\n\n if (le !== 0) {\n for (j = 0; j < le; j++) {\n z += p.coords[face[j]][3];\n }\n z /= le;\n }\n z = mi_a + (z - mi) * (ma_a - mi_a) / (ma - mi);\n\n if (staticColorMap) {\n hsl = JXG.hsv2hsl(z, s, v);\n } else {\n // Dynamic version - slower\n hsl = JXG.hsv2hsl(z, el.evalVisProp('colormap.s'), el.evalVisProp('colormap.v'));\n }\n return `hsl(${z} ${hsl[1] * 100}% ${hsl[2] * 100}%)`;\n };\n } else if (type === 'shader') {\n attr.polyhedron.shader.enabled = true;\n } else {\n // colorarray\n attr.polyhedron.shader.enabled = false;\n }\n\n el.polyhedron = view.create('polyhedron3d', surface, attr.polyhedron);\n el.addChild(el.polyhedron);\n el.inherits.push(el.polyhedron);\n el.polyhedron.setParents(el);\n }\n }\n\n // Wireframe\n el.element2D.prepareUpdate().update();\n if (!board.isSuspendedUpdate) {\n el.element2D.updateVisibility().updateRenderer();\n }\n\n return el;\n};\n\nJXG.registerElement('plane3d', JXG.createPlane3D);\n\n/**\n * @class The line that is the intersection of two (infinite) plane elements in 3D.\n *\n * @pseudo\n * @name IntersectionLine3D\n * @augments JXG.Line3D\n * @constructor\n * @type JXG.Line3D\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Plane3D_JXG.Plane3D} el1,el2 The result will be the intersection of el1 and el2.\n * @example\n * // Create the intersection line of two planes\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[-1, 3], [-1, 3], [-1, 3]]],\n * {\n * xPlaneRear: {visible:false},\n * yPlaneRear: {visible:false},\n * zPlaneRear: {fillOpacity: 0.2, gradient: null}\n * }\n * );\n * var a = view.create('point3d', [2, 2, 0]);\n *\n * var p1 = view.create(\n * 'plane3d',\n * [a, [1, 0, 0], [0, 1, 0]],\n * {fillColor: '#00ff80'}\n * );\n * var p2 = view.create(\n * 'plane3d',\n * [a, [-2, 1, 1], [1, -2, 1]],\n * {fillColor: '#ff0000'}\n * );\n *\n * var i = view.create('intersectionline3d', [p1, p2]);\n *\n * \n * \n *\n */\nJXG.createIntersectionLine3D = function (board, parents, attributes) {\n var view = parents[0],\n el1 = parents[1],\n el2 = parents[2],\n ixnLine, i, func,\n attr = Type.copyAttributes(attributes, board.options, 'intersectionline3d'),\n pts = [];\n\n func = Geometry.intersectionFunction3D(view, el1, el2);\n for (i = 0; i < 2; i++) {\n pts[i] = view.create('point3d', func[i], attr['point' + (i + 1)]);\n }\n ixnLine = view.create('line3d', pts, attr);\n\n try {\n el1.addChild(ixnLine);\n el2.addChild(ixnLine);\n } catch (_e) {\n throw new Error(\n \"JSXGraph: Can't create 'intersection' with parent types '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\"\n );\n }\n\n ixnLine.type = Const.OBJECT_TYPE_INTERSECTION_LINE3D;\n ixnLine.elType = 'intersectionline3d';\n ixnLine.setParents([el1.id, el2.id]);\n\n return ixnLine;\n};\n\nJXG.registerElement('intersectionline3d', JXG.createIntersectionLine3D);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n */\nJXG.createText3D = function (board, parents, attributes) {\n var view = parents[0],\n attr, F, slide,\n text,\n c2d, el;\n\n // If the last element of parents is a 3D object,\n // the point is a glider on that element.\n if (parents.length > 2 && Type.exists(parents[parents.length - 1].is3D)) {\n slide = parents.pop();\n } else {\n slide = null;\n }\n\n if (parents.length === 3) {\n // [view, array|fun, text] (Array [x, y, z] | function) returning [x, y, z] and string | function\n F = parents[1];\n text = parents[2];\n } else if (parents.length === 5) {\n // [view, x, y, z, text], (3 numbers | functions) sand string | function\n F = parents.slice(1, 4);\n text = parents[4];\n } else {\n throw new Error(\n \"JSXGraph: Can't create text3d with parent types '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [[x,y,z], text], [x,y,z, text]\"\n );\n // \"\\nPossible parent types: [[x,y,z]], [x,y,z], [element,transformation]\"); // TODO\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'text3d');\n el = new JXG.Text3D(view, F, text, slide, attr);\n el.initCoords();\n\n c2d = view.project3DTo2D(el.coords);\n\n attr = el.setAttr2D(attr);\n el.element2D = view.create('text', [c2d[1], c2d[2], text], attr);\n el.element2D.view = view;\n el.element2D.dump = false;\n el.addChild(el.element2D);\n el.inherits.push(el.element2D);\n el.element2D.setParents(el);\n\n // If this point is a glider, record that in the update tree\n if (el.slide) {\n el.slide.addChild(el);\n el.setParents(el.slide);\n }\n\n el._c2d = el.element2D.coords.usrCoords.slice(); // Store a copy of the coordinates to detect dragging\n\n return el;\n};\n\nJXG.registerElement(\"text3d\", JXG.createText3D);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n *
\n * Each two consecutive points of the list define a line.\n * polyhedron = {\n * view: view,\n * vertices: {},\n * coords: {},\n * coords2D: {},\n * zIndex: {},\n * faces: []\n * };\n * @param {Array} faces List of face3d objects. These have been already generated in `createPolyhedron3D`.\n * @param {Object} attributes An object containing visual properties like in {@link JXG.Options#polyhedron3d} and {@link JXG.Options#elements},\n * and optionally a name and an id.\n */\nJXG.Polyhedron3D = function (view, polyhedron, faces, attributes) {\n var e,\n genericMethods,\n generateMethod,\n that = this;\n\n this.constructor(view.board, attributes, Const.OBJECT_TYPE_POLYHEDRON3D, Const.OBJECT_CLASS_3D);\n this.constructor3D(view, 'polyhedron3d');\n\n this.board.finalizeAdding(this);\n\n this.elType = 'polyhedron3d';\n\n /**\n * List of Face3D objects.\n * @name Polyhedron3D#faces\n * @type Array\n */\n this.faces = faces;\n\n /**\n * Number of faces\n * @name Polyhedron3D#numberFaces\n * @type Number\n */\n this.numberFaces = faces.length;\n\n /**\n * Contains the defining data of the polyhedron:\n * Definitions of vertices and a list of vertices for each face. This is pretty much the input given\n * in the construction of the polyhedron plus internal data.\n * @name Polyhedron3D#def\n * @type Object\n * @example\n * polyhedron = {\n * view: view,\n * vertices: {},\n * coords: {},\n * coords2D: {},\n * zIndex: {},\n * faces: []\n * };\n */\n this.def = polyhedron;\n\n // Simultaneous methods for all faces\n genericMethods = [\n \"setAttribute\",\n \"setParents\",\n \"prepareUpdate\",\n \"updateRenderer\",\n \"update\",\n \"fullUpdate\",\n \"highlight\",\n \"noHighlight\"\n ];\n\n /**\n * Generate methods like `updateRenderer` or `setAttribute` which call simultaneously\n * the method with the same name for each face3d element of the polyhedron.\n * @param {String} what Method name\n * @returns {Function} Function consisting of a loop that calls the method for each face.\n */\n generateMethod = function (what) {\n return function () {\n var i;\n\n for (i in that.faces) {\n if (that.faces.hasOwnProperty(i)) {\n if (Type.exists(that.faces[i][what])) {\n that.faces[i][what].apply(that.faces[i], arguments);\n }\n }\n }\n return that;\n };\n };\n\n for (e = 0; e < genericMethods.length; e++) {\n this[genericMethods[e]] = generateMethod(genericMethods[e]);\n }\n};\n\nJXG.Polyhedron3D.prototype = new JXG.GeometryElement();\n\nType.copyPrototypeMethods(JXG.Polyhedron3D, JXG.GeometryElement3D, 'constructor3D');\nType.copyMethodMap(JXG.Polyhedron3D, {\n setAttribute: \"setAttribute\",\n setParents: \"setParents\",\n addTransform: \"addTransform\",\n removeTransform: \"removeTransform\",\n clearTransforms: \"clearTransforms\"\n});\n\nJXG.extend(\n JXG.Polyhedron3D.prototype,\n /** @lends JXG.Polyhedron3D.prototype */ {\n\n // Already documented in element3d.js\n addTransform: function (el, transform) {\n if (this.faces.length > 0 && el.faces.length > 0) {\n this.faces[0].addTransform(el.faces[0], transform);\n } else {\n throw new Error(\"Adding transformation failed. At least one of the two polyhedra has no faces.\");\n }\n return this;\n },\n\n // Already documented in element3d.js\n removeTransform: function (transform) {\n if (this.faces.length > 0) {\n this.faces[0].removeTransform(transform);\n } else {\n throw new Error(\"Removing transformation failed. The polyhedron has no faces.\");\n }\n return this;\n },\n\n // Already documented in element3d.js\n clearTransforms: function () {\n if (this.faces.length > 0) {\n this.faces[0].clearTransforms();\n } else {\n throw new Error(\"Removing transformation failed. The polyhedron has no faces.\");\n }\n return this;\n },\n\n /**\n * Output polyhedron in ASCII STL format.\n * Normals are ignored and output as 0 0 0.\n *\n * @param {String} name Set name of the model, overwrites property name\n * @returns String\n */\n toSTL: function(name) {\n var i, j, v, f, c, le,\n txt = 'solid ';\n\n if (name === undefined) {\n name = this.name;\n }\n\n txt += name + '\\n';\n\n for (i = 0; i < this.def.faces.length; i++) {\n txt += ' facet normal 0 0 0\\n outer loop\\n';\n f = this.def.faces[i];\n le = f.length;\n v = this.def.coords;\n for (j = 0; j < le; j++) {\n c = v[f[j]];\n txt += ' vertex ' + c[1] + ' ' + c[2] + ' ' + c[3] + '\\n';\n }\n txt += ' endloop\\n endfacet\\n';\n }\n txt += 'endsolid ' + name + '\\n';\n\n return txt;\n }\n }\n);\n\n/**\n * @class A polyhedron in a 3D view consists of faces.\n * @pseudo\n * @description Create a polyhedron in a 3D view consisting of faces. Faces can\n * be 0-, 1- or 2-dimensional.\n *\n * @name Polyhedron3D\n * @augments JXG.GeometryElement3D\n * @constructor\n * @type Object\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {} TODO\n *\n * @example\n * var box = [-4, 4];\n * var view = board.create(\n * 'view3d',\n * [[-5, -3], [8, 8],\n * [box, box, box]],\n * {\n * projection: 'parallel',\n * trackball: { enabled: false },\n * depthOrder: {\n * enabled: true\n * },\n * xPlaneRear: { visible: false },\n * yPlaneRear: { visible: false },\n * zPlaneRear: { fillOpacity: 0.2 }\n * }\n * );\n * var cube = view.create('polyhedron3d', [\n * [\n * [-3, -3, -3],\n * [3, -3, -3],\n * [3, 3, -3],\n * [-3, 3, -3],\n *\n * [-3, -3, 3],\n * [3, -3, 3],\n * [3, 3, 3],\n * [-3, 3, 3]\n * ],\n * [\n * [0, 1, 2, 3],\n * [0, 1, 5, 4],\n * [[1, 2, 6, 5], { fillColor: 'black', fillOpacity: 0.5, strokeWidth: 5 }],\n * [2, 3, 7, 6],\n * [3, 0, 4, 7],\n * [4, 5, 6, 7]\n * ]\n * ], {\n * fillColorArray: ['blue', 'red', 'yellow']\n * });\n *\n * \n * \n *\n * @example\n * var box = [-4, 4];\n * var view = board.create(\n * 'view3d',\n * [[-5, -3], [8, 8],\n * [box, box, box]],\n * {\n * projection: 'parallel',\n * trackball: { enabled: false },\n * depthOrder: {\n * enabled: true\n * },\n * xPlaneRear: { visible: false },\n * yPlaneRear: { visible: false },\n * zPlaneRear: { fillOpacity: 0.2 }\n * }\n * );\n * var aa = view.create('point3d', [-3, -3, -3], { name: 'A', layer: 12});\n * var bb = view.create('point3d', [() => aa.X(), () => aa.Y(), 3], { name: 'B', fixed: true, layer: 12});\n * var cube = view.create('polyhedron3d', [\n * {\n * a: 'A',\n * b: [3, -3, -3],\n * c: [3, 3, -3],\n * d: [-3, 3, -3],\n *\n * e: bb,\n * f: [3, -3, 3],\n * g: [3, 3, 3],\n * h: [-3, 3, 3]\n * },\n * [\n * ['a', 'b', 'c', 'd'],\n * ['a', 'b', 'f', 'e'],\n * ['b', 'c', 'g', 'f'],\n * ['c', 'd', 'h', 'g'],\n * ['d', 'a', 'e', 'h'],\n * ['e', 'f', 'g', 'h'],\n *\n * ['a', 'g'], // Edge\n * ['f'] // Vertex\n * ]\n * ], {\n * fillColorArray: ['blue', 'red', 'yellow'],\n * fillOpacity: 0.4,\n * layer: 12\n * });\n * cube.faces[6].setAttribute({ strokeWidth: 5 });\n * cube.faces[7].setAttribute({ strokeWidth: 10 });\n *\n * \n * \n *\n * @example\n * var box = [-4, 4];\n * var view = board.create(\n * 'view3d',\n * [[-5, -3], [8, 8],\n * [box, box, box]],\n * {\n * projection: 'parallel',\n * trackball: { enabled: false },\n * depthOrder: {\n * enabled: true\n * },\n * xPlaneRear: { visible: false },\n * yPlaneRear: { visible: false },\n * zPlaneRear: { fillOpacity: 0.2 }\n * }\n * );\n * var s = board.create('slider', [[-4, -6], [4, -6], [0, 2, 4]], { name: 's' });\n * var cube = view.create('polyhedron3d', [\n * [\n * () => { let f = s.Value(); return [-f, -f, -f]; },\n * () => { let f = s.Value(); return [f, -f, -f]; },\n * () => { let f = s.Value(); return [f, f, -f]; },\n * () => { let f = s.Value(); return [-f, f, -f]; },\n *\n * () => { let f = s.Value(); return [-f, -f, f]; },\n * () => { let f = s.Value(); return [f, -f, f]; },\n * () => { let f = s.Value(); return [f, f, f]; },\n * // () => { let f = s.Value(); return [-f, f, f]; }\n * [ () => -s.Value(), () => s.Value(), () => s.Value() ]\n * ],\n * [\n * [0, 1, 2, 3],\n * [0, 1, 5, 4],\n * [1, 2, 6, 5],\n * [2, 3, 7, 6],\n * [3, 0, 4, 7],\n * [4, 5, 6, 7],\n * ]\n * ], {\n * strokeWidth: 3,\n * fillOpacity: 0.6,\n * fillColorArray: ['blue', 'red', 'yellow'],\n * shader: {\n * enabled:false\n * }\n * });\n *\n * \n * \n *\n * @example\n * var box = [-4, 4];\n * var view = board.create(\n * 'view3d',\n * [[-5, -3], [8, 8],\n * [box, box, box]],\n * {\n * projection: 'parallel',\n * trackball: { enabled: false },\n * depthOrder: {\n * enabled: true\n * },\n * xPlaneRear: { visible: false },\n * yPlaneRear: { visible: false },\n * zPlaneRear: { fillOpacity: 0.2 }\n * }\n * );\n * let rho = 1.6180339887;\n * let vertexList = [\n * [0, -1, -rho], [0, +1, -rho], [0, -1, rho], [0, +1, rho],\n * [1, rho, 0], [-1, rho, 0], [1, -rho, 0], [-1, -rho, 0],\n * [-rho, 0, 1], [-rho, 0, -1], [rho, 0, 1], [rho, 0, -1]\n * ];\n * let faceArray = [\n * [4, 1, 11],\n * [11, 1, 0],\n * [6, 11, 0],\n * [0, 1, 9],\n * [11, 10, 4],\n * [9, 1, 5],\n * [8, 9, 5],\n * [5, 3, 8],\n * [6, 10, 11],\n * [2, 3, 10],\n * [2, 10, 6],\n * [8, 3, 2],\n * [3, 4, 10],\n * [7, 8, 2],\n * [9, 8, 7],\n * [0, 9, 7],\n * [4, 3, 5],\n * [5, 1, 4],\n * [0, 7, 6],\n * [7, 2, 6]\n * ];\n * var ico = view.create('polyhedron3d', [vertexList, faceArray], {\n * fillColorArray: [],\n * fillOpacity: 1,\n * strokeWidth: 0.1,\n * layer: 12,\n * shader: {\n * enabled: true,\n * type: 'angle',\n * hue: 60,\n * saturation: 90,\n * minlightness: 60,\n * maxLightness: 80\n * }\n * });\n *\n * \n * \n *\n */\nJXG.createPolyhedron3D = function (board, parents, attributes) {\n var view = parents[0],\n i, le,\n face, f,\n el,\n attr, attr_polyhedron,\n faceList = [],\n base = null,\n transform = null,\n\n polyhedron = {\n view: view,\n vertices: {},\n coords: {},\n coords2D: {},\n zIndex: {},\n faces: []\n };\n\n if (Type.exists(parents[1].type) && parents[1].type === Const.OBJECT_TYPE_POLYHEDRON3D) {\n // Polyhedron from baseElement and transformations\n base = parents[1];\n transform = parents[2];\n polyhedron.vertices = base.def.vertices;\n polyhedron.faces = base.def.faces;\n } else {\n // Copy vertices into a dict\n if (Type.isArray(parents[1])) {\n le = parents[1].length;\n for (i = 0; i < le; i++) {\n polyhedron.vertices[i] = parents[1][i];\n }\n } else if (Type.isObject(parents[1])) {\n for (i in parents[1]) {\n if (parents[1].hasOwnProperty(i)) {\n polyhedron.vertices[i] = parents[1][i];\n }\n }\n }\n polyhedron.faces = parents[2];\n }\n\n attr_polyhedron = Type.copyAttributes(attributes, board.options, 'polyhedron3d');\n\n console.time('polyhedron');\n\n view.board.suspendUpdate();\n // Create face3d elements\n le = polyhedron.faces.length;\n for (i = 0; i < le; i++) {\n attr = Type.copyAttributes(attributes, board.options, 'face3d');\n if (attr_polyhedron.fillcolorarray.length > 0) {\n attr.fillcolor = attr_polyhedron.fillcolorarray[i % attr_polyhedron.fillcolorarray.length];\n }\n f = polyhedron.faces[i];\n\n if (Type.isArray(f) && f.length === 2 && Type.isObject(f[1]) && Type.isArray(f[0])) {\n // Handle case that face is of type [[points], {attr}]\n Type.mergeAttr(attr, f[1]);\n // Normalize face array, i.e. don't store attributes of that face in polyhedron\n polyhedron.faces[i] = f[0];\n }\n\n face = view.create('face3d', [polyhedron, i], attr);\n faceList.push(face);\n }\n el = new JXG.Polyhedron3D(view, polyhedron, faceList, attr_polyhedron);\n el.setParents(el); // Sets el as parent to all faces.\n for (i = 0; i < le; i++) {\n el.inherits.push(el.faces[i]);\n // el.addChild(el.faces[i]); // This takes very long time. We avoid it with\n // a special treatment in removeObject\n }\n if (base !== null) {\n el.addTransform(base, transform);\n el.addParents(base);\n }\n view.board.unsuspendUpdate();\n\n console.timeEnd('polyhedron');\n\n return el;\n};\n\nJXG.registerElement(\"polyhedron3d\", JXG.createPolyhedron3D);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Aaron Fenyes,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see
\n * The parameters 'twoPoints' – The sphere is defined by its center and a point on the sphere.'pointRadius' – The sphere is defined by its center and its radius in user units.p1, p2 and radius must be set according to this method parameter.\n * @param {JXG.Point3D} par1 The center of the sphere.\n * @param {JXG.Point3D} par2 Can be:\n * 'twoPoints')'pointRadius')
\n * @type String\n * @see JXG.Sphere3D#center\n * @see JXG.Sphere3D#point2\n */\n this.method = method;\n\n /**\n * The sphere's center. Do not set this parameter directly, as that will break JSXGraph's update system.\n * @type JXG.Point3D\n */\n this.center = this.board.select(par1);\n\n /**\n * A point on the sphere; only set if the construction method is 'twoPoints'. Do not set this parameter directly, as that will break JSXGraph's update system.\n * @type JXG.Point3D\n * @see JXG.Sphere3D#method\n */\n this.point2 = null;\n\n this.points = [];\n\n /**\n * The 2D representation of the element.\n * @type GeometryElement\n */\n this.element2D = null;\n\n /**\n * Elements supporting the 2D representation.\n * @type Array\n * @private\n */\n this.aux2D = [];\n\n /**\n * The type of projection ('twoPoints' – The sphere is defined by its center and a point on the sphere.'pointRadius' – The sphere is defined by its center and its radius in user units.'parallel' or 'central') that the sphere is currently drawn in.\n * @type String\n */\n this.projectionType = view.projectionType;\n\n if (method === 'twoPoints') {\n this.point2 = this.board.select(par2);\n this.radius = this.Radius();\n } else if (method === 'pointRadius') {\n // Converts JessieCode syntax into JavaScript syntax and generally ensures that the radius is a function\n this.updateRadius = Type.createFunction(par2, this.board);\n // First evaluation of the radius function\n this.updateRadius();\n this.addParentsFromJCFunctions([this.updateRadius]);\n }\n\n if (Type.exists(this.center._is_new)) {\n this.addChild(this.center);\n delete this.center._is_new;\n } else {\n this.center.addChild(this);\n }\n\n if (method === 'twoPoints') {\n if (Type.exists(this.point2._is_new)) {\n this.addChild(this.point2);\n delete this.point2._is_new;\n } else {\n this.point2.addChild(this);\n }\n }\n};\n\nJXG.Sphere3D.prototype = new JXG.GeometryElement();\n\nType.copyPrototypeMethods(JXG.Sphere3D, JXG.GeometryElement3D, 'constructor3D');\nType.copyMethodMap(JXG.Sphere3D, {\n center: \"center\",\n point2: \"point2\",\n Radius: \"Radius\"\n});\n\nJXG.extend(\n JXG.Sphere3D.prototype,\n /** @lends JXG.Sphere3D.prototype */ {\n\n X: function(u, v) {\n var r = this.Radius();\n return r * Math.sin(u) * Math.cos(v);\n },\n\n Y: function(u, v) {\n var r = this.Radius();\n return r * Math.sin(u) * Math.sin(v);\n },\n\n Z: function(u, v) {\n var r = this.Radius();\n return r * Math.cos(u);\n },\n\n range_u: [0, 2 * Math.PI],\n range_v: [0, Math.PI],\n\n update: function () {\n if (this.projectionType !== this.view.projectionType) {\n this.rebuildProjection();\n }\n return this;\n },\n\n updateRenderer: function () {\n this.needsUpdate = false;\n return this;\n },\n\n /**\n * Set a new radius, then update the board.\n * @param {String|Number|function} r A string, function or number describing the new radius\n * @returns {JXG.Sphere3D} Reference to this sphere\n */\n setRadius: function (r) {\n this.updateRadius = Type.createFunction(r, this.board);\n this.addParentsFromJCFunctions([this.updateRadius]);\n this.board.update();\n\n return this;\n },\n\n /**\n * Calculates the radius of the circle.\n * @param {String|Number|function} [value] Set new radius\n * @returns {Number} The radius of the circle\n */\n Radius: function (value) {\n if (Type.exists(value)) {\n this.setRadius(value);\n return this.Radius();\n }\n\n if (this.method === 'twoPoints') {\n if (!this.center.testIfFinite() || !this.point2.testIfFinite()) {\n return NaN;\n }\n\n return this.center.distance(this.point2);\n }\n\n if (this.method === 'pointRadius') {\n return Math.abs(this.updateRadius());\n }\n\n return NaN;\n },\n\n // The central projection of a sphere is an ellipse. The front and back\n // points of the sphere---that is, the points closest to and furthest\n // from the screen---project to the foci of the ellipse.\n //\n // To see this, look at the cone tangent to the sphere whose tip is at\n // the camera. The image of the sphere is the ellipse where this cone\n // intersects the screen. By acting on the sphere with scalings centered\n // on the camera, you can send it to either of the Dandelin spheres that\n // touch the screen at the foci of the image ellipse.\n //\n // This factory method produces two functions, `focusFn(-1)` and\n // `focusFn(1)`, that evaluate to the projections of the front and back\n // points of the sphere, respectively.\n focusFn: function (sgn) {\n var that = this;\n\n return function () {\n var camDir = that.view.boxToCam[3],\n r = that.Radius();\n\n return that.view.project3DTo2D([\n that.center.X() + sgn * r * camDir[1],\n that.center.Y() + sgn * r * camDir[2],\n that.center.Z() + sgn * r * camDir[3]\n ]).slice(1, 3);\n };\n },\n\n innerVertexFn: function () {\n var that = this;\n\n return function () {\n var view = that.view,\n p = view.worldToFocal(that.center.coords, false),\n distOffAxis = Mat.hypot(p[0], p[1]),\n cam = view.boxToCam,\n r = that.Radius(),\n angleOffAxis = Math.atan(-distOffAxis / p[2]),\n steepness = Math.acos(r / Mat.norm(p)),\n lean = angleOffAxis + steepness,\n cos_lean = Math.cos(lean),\n sin_lean = Math.sin(lean),\n inward;\n\n if (distOffAxis > 1e-8) {\n // if the center of the sphere isn't too close to the camera\n // axis, find the direction in plane of the screen that\n // points from the center of the sphere toward the camera\n // axis\n inward = [\n -(p[0] * cam[1][1] + p[1] * cam[2][1]) / distOffAxis,\n -(p[0] * cam[1][2] + p[1] * cam[2][2]) / distOffAxis,\n -(p[0] * cam[1][3] + p[1] * cam[2][3]) / distOffAxis\n ];\n } else {\n // if the center of the sphere is very close to the camera\n // axis, choose an arbitrary unit vector in the plane of the\n // screen\n inward = [cam[1][1], cam[1][2], cam[1][3]];\n }\n return view.project3DTo2D([\n that.center.X() + r * (sin_lean * inward[0] + cos_lean * cam[3][1]),\n that.center.Y() + r * (sin_lean * inward[1] + cos_lean * cam[3][2]),\n that.center.Z() + r * (sin_lean * inward[2] + cos_lean * cam[3][3])\n ]);\n };\n },\n\n buildCentralProjection: function (attr) {\n var view = this.view,\n auxStyle = { visible: false, withLabel: false },\n frontFocus = view.create('point', this.focusFn(-1), auxStyle),\n backFocus = view.create('point', this.focusFn(1), auxStyle),\n innerVertex = view.create('point', this.innerVertexFn(view), auxStyle);\n\n this.aux2D = [frontFocus, backFocus, innerVertex];\n this.element2D = view.create('ellipse', this.aux2D, attr === undefined ? this.visProp : attr);\n },\n\n buildParallelProjection: function (attr) {\n // The parallel projection of a sphere is a circle\n var that = this,\n // center2d = function () {\n // var c3d = [1, that.center.X(), that.center.Y(), that.center.Z()];\n // return that.view.project3DTo2D(c3d);\n // },\n radius2d = function () {\n var boxSize = that.view.bbox3D[0][1] - that.view.bbox3D[0][0];\n return that.Radius() * that.view.size[0] / boxSize;\n };\n\n this.aux2D = [];\n this.element2D = this.view.create(\n 'circle',\n // [center2d, radius2d],\n [that.center.element2D, radius2d],\n attr === undefined ? this.visProp : attr\n );\n },\n\n // replace our 2D representation with a new one that's consistent with\n // the view's current projection type\n rebuildProjection: function (attr) {\n var i;\n\n // remove the old 2D representation from the scene tree\n if (this.element2D) {\n this.view.board.removeObject(this.element2D);\n for (i in this.aux2D) {\n if (this.aux2D.hasOwnProperty(i)) {\n this.view.board.removeObject(this.aux2D[i]);\n }\n }\n }\n\n // build a new 2D representation. the representation is stored in\n // `this.element2D`, and any auxiliary elements are stored in\n // `this.aux2D`\n this.projectionType = this.view.projectionType;\n if (this.projectionType === 'central') {\n this.buildCentralProjection(attr);\n } else {\n this.buildParallelProjection(attr);\n }\n\n // attach the new 2D representation to the scene tree\n this.addChild(this.element2D);\n this.inherits.push(this.element2D);\n this.element2D.view = this.view;\n this.element2D.dump = false;\n },\n\n // Already documented in element3d.js\n projectCoords: function(p, params) {\n var r = this.Radius(),\n pp = [1].concat(p),\n c = this.center.coords,\n d = Geometry.distance(c, pp, 4),\n v = Stat.subtract(pp, c);\n\n if (d === 0) {\n // p is at the center, take an arbitrary point on sphere\n params[0] = 0;\n params[1] = 0;\n return [1, r, 0, 0];\n }\n if (r === 0) {\n params[0] = 0;\n params[1] = 0;\n return this.center.coords;\n }\n\n d = r / d;\n v[0] = 1;\n v[1] *= d;\n v[2] *= d;\n v[3] *= d;\n\n // Preimage of the new position\n params[1] = Math.atan2(v[2], v[1]);\n params[1] += (params[1] < 0) ? Math.PI : 0;\n if (params[1] !== 0) {\n params[0] = Math.atan2(v[2], v[3] * Math.sin(params[1]));\n } else {\n params[0] = Math.atan2(v[1], v[3] * Math.cos(params[1]));\n }\n params[0] += (params[0] < 0) ? 2 * Math.PI : 0;\n\n return v;\n }\n\n // projectScreenCoords: function (pScr, params, cyclic) {\n // if (params.length === 0) {\n // params.unshift(\n // 0.5 * (this.range_u[0] + this.range_u[1]),\n // 0.5 * (this.range_v[0] + this.range_v[1])\n // );\n // }\n // return Geometry.projectScreenCoordsToParametric(pScr, this, params, cyclic);\n // }\n }\n);\n\n/**\n * @class A sphere in a 3D view.\n * A sphere consists of all points with a given distance from a given point.\n * The given point is called the center, and the given distance is called the radius.\n * A sphere can be constructed by providing a center and a point on the sphere or a center and a radius (given as a number or function).\n * If the radius is a negative value, its absolute value is taken.\n *\n * @pseudo\n * @name Sphere3D\n * @augments JXG.Sphere3D\n * @constructor\n * @type JXG.Sphere3D\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {JXG.Point3D_number,JXG.Point3D} center,radius The center must be given as a {@link JXG.Point3D} (see {@link JXG.providePoints3D}),\n * but the radius can be given as a number (which will create a sphere with a fixed radius) or another {@link JXG.Point3D}.\n * \n *\n * @example\n * // Glider on sphere\n * var view = board.create(\n * 'view3d',\n * [[-6, -3], [8, 8],\n * [[-3, 3], [-3, 3], [-3, 3]]],\n * {\n * depthOrder: {\n * enabled: true\n * },\n * projection: 'central',\n * xPlaneRear: {fillOpacity: 0.2, gradient: null},\n * yPlaneRear: {fillOpacity: 0.2, gradient: null},\n * zPlaneRear: {fillOpacity: 0.2, gradient: null}\n * }\n * );\n *\n * // Two points\n * var center = view.create('point3d', [0, 0, 0], {withLabel: false, size: 2});\n * var point = view.create('point3d', [2, 0, 0], {withLabel: false, size: 2});\n *\n * // Sphere\n * var sphere = view.create('sphere3d', [center, point], {fillOpacity: 0.8});\n *\n * // Glider on sphere\n * var glide = view.create('point3d', [2, 2, 0, sphere], {withLabel: false, color: 'red', size: 4});\n * var l1 = view.create('line3d', [glide, center], { strokeWidth: 2, dash: 2 });\n *\n * \n * \n *\n */\nJXG.createSphere3D = function (board, parents, attributes) {\n // parents[0]: view\n // parents[1]: point,\n // parents[2]: point or radius\n\n var view = parents[0],\n attr, p, point_style, provided,\n el, i;\n\n attr = Type.copyAttributes(attributes, board.options, 'sphere3d');\n p = [];\n for (i = 1; i < parents.length; i++) {\n if (Type.isPointType3D(board, parents[i])) {\n if (p.length === 0) {\n point_style = 'center';\n } else {\n point_style = 'point';\n }\n provided = Type.providePoints3D(view, [parents[i]], attributes, 'sphere3d', [point_style])[0];\n if (provided === false) {\n throw new Error(\n \"JSXGraph: Can't create sphere3d from this type. Please provide a point type.\"\n );\n }\n p.push(provided);\n } else {\n p.push(parents[i]);\n }\n }\n\n if (Type.isPoint3D(p[0]) && Type.isPoint3D(p[1])) {\n // Point/Point\n el = new JXG.Sphere3D(view, \"twoPoints\", p[0], p[1], attr);\n\n /////////////// nothing in docs suggest you can use [number, pointType]\n // } else if (\n // (Type.isNumber(p[0]) || Type.isFunction(p[0]) || Type.isString(p[0])) &&\n // Type.isPoint3D(p[1])\n // ) {\n // // Number/Point\n // el = new JXG.Sphere3D(view, \"pointRadius\", p[1], p[0], attr);\n\n } else if (\n Type.isPoint3D(p[0]) &&\n (Type.isNumber(p[1]) || Type.isFunction(p[1]) || Type.isString(p[1]))\n ) {\n // Point/Number\n el = new JXG.Sphere3D(view, \"pointRadius\", p[0], p[1], attr);\n } else {\n throw new Error(\n \"JSXGraph: Can't create sphere3d with parent types '\" +\n typeof parents[1] +\n \"' and '\" +\n typeof parents[2] +\n \"'.\" +\n \"\\nPossible parent types: [point,point], [point,number], [point,function]\"\n );\n }\n\n // Build a 2D representation, and attach it to the scene tree, and update it\n // to the correct initial state\n // Here, element2D is created.\n attr = el.setAttr2D(attr);\n el.rebuildProjection(attr);\n\n el.element2D.prepareUpdate().update();\n if (!board.isSuspendedUpdate) {\n el.element2D.updateVisibility().updateRenderer();\n }\n\n return el;\n};\n\nJXG.registerElement(\"sphere3d\", JXG.createSphere3D);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n */\nJXG.createParametricSurface3D = function (board, parents, attributes) {\n var view = parents[0],\n F, X, Y, Z,\n range_u, range_v, attr, attr2d,\n base = null,\n transform = null,\n surface,\n tiling, type,\n // colormap:\n m, ma, mi, ma_a, mi_a, s, v,\n staticColorMap, e, el;\n\n if (parents.length === 3) {\n // [view, base_el, transform]\n base = parents[1];\n transform = parents[2];\n F = null;\n X = null;\n Y = null;\n Z = null;\n\n } else if (parents.length === 4) {\n // [view, F, range_u, range_v]\n F = parents[1];\n range_u = parents[2];\n range_v = parents[3];\n X = null;\n Y = null;\n Z = null;\n } else {\n // [view, X, Y, Z, range_u, range_v]\n X = parents[1];\n Y = parents[2];\n Z = parents[3];\n range_u = parents[4];\n range_v = parents[5];\n F = null;\n }\n\n attr = Type.copyAttributes(attributes, board.options, 'surface3d');\n el = new JXG.Surface3D(view, F, X, Y, Z, range_u, range_v, attr);\n\n tiling = el.evalVisProp('tiling');\n type = el.evalVisProp('type');\n\n // Wireframe\n attr2d = el.setAttr2D(attr);\n el.element2D = view.create(\"curve\", [[], []], attr2d);\n el.element2D.view = view;\n el.element2D.dump = false;\n if (base !== null) {\n el.addTransform(base, transform);\n el.addParents(base);\n }\n\n /**\n * @class\n * @ignore\n */\n el.element2D.updateDataArray = function () {\n var ret = el.updateDataArray2D();\n this.dataX = ret.X;\n this.dataY = ret.Y;\n };\n el.addChild(el.element2D);\n el.inherits.push(el.element2D);\n el.element2D.setParents(el);\n\n // Set style\n if (type !== 'wireframe') {\n // Create a polyhedron representing the surface3d\n if (tiling === 'triangle' || tiling === 'rectangle') {\n if (tiling === 'triangle') {\n surface = Tiling.triangulation(\n el,\n el.range_u,\n el.range_v,\n el.evalVisProp('stepsu'), el.evalVisProp('stepsv')\n );\n\n } else if (tiling === \"rectangle\") {\n surface = Tiling.rectangulation(\n el,\n el.range_u,\n el.range_v,\n el.evalVisProp('stepsu'), el.evalVisProp('stepsv')\n );\n\n }\n }\n\n // attr.polyhedron.shader.enabled = false;\n // attr.polyhedron.fillcolorarray = ['none'];\n el.element2D.setAttribute({ visible: false });\n // Eliminate the call to the expensive el.updateDataArray();\n el.element2D.updateDataArray = function() {};\n\n if (type === 'colormap') {\n attr.polyhedron.shader.enabled = false;\n\n m = el.evalVisProp('colormap.max');\n ma = m[0];\n ma_a = m[1];\n m = el.evalVisProp('colormap.min');\n mi = m[0];\n mi_a = m[1];\n s = el.evalVisProp('colormap.s');\n v = el.evalVisProp('colormap.v');\n\n // Check if the colormap is static, i.e.\n // no sub-property in colormap is a function\n staticColorMap = true;\n for (e in el.visProp.colormap) {\n if (el.visProp.colormap.hasOwnProperty(e)) {\n if (Type.isFunction(el.visProp.colormap[e])) {\n staticColorMap = false;\n break;\n }\n }\n }\n\n attr.polyhedron.fillcolorarray = [];\n attr.polyhedron.fillcolor = (self) => {\n var j, hsl,\n z = 0,\n p = self.polyhedron,\n face = p.faces[self.faceNumber],\n le = face.length;\n\n // Dynamic version\n if (!staticColorMap) {\n m = el.evalVisProp('colormap.max');\n ma = m[0];\n ma_a = m[1];\n m = el.evalVisProp('colormap.min');\n mi = m[0];\n mi_a = m[1];\n }\n\n // Determine the z-coordinate of the face's centroid\n if (le !== 0) {\n for (j = 0; j < le; j++) {\n z += p.coords[face[j]][3];\n }\n z /= le;\n }\n // Map z to the color interval\n z = mi_a + (z - mi) * (ma_a - mi_a) / (ma - mi);\n\n if (staticColorMap) {\n hsl = JXG.hsv2hsl(z, s, v);\n } else {\n // Dynamic version - slower\n hsl = JXG.hsv2hsl(z, el.evalVisProp('colormap.s'), el.evalVisProp('colormap.v'));\n }\n return `hsl(${z} ${hsl[1] * 100}% ${hsl[2] * 100}%)`;\n };\n } else if (type === 'shader') {\n attr.polyhedron.shader.enabled = true;\n } else {\n // colorarray\n attr.polyhedron.shader.enabled = false;\n }\n\n // Create the polyhedron representing the parametricsurface3d\n el.polyhedron = view.create('polyhedron3d', surface, attr.polyhedron);\n el.addChild(el.polyhedron);\n el.inherits.push(el.polyhedron);\n el.polyhedron.setParents(el);\n }\n // Wireframe\n el.element2D.prepareUpdate().update();\n if (!board.isSuspendedUpdate) {\n el.element2D.updateVisibility().updateRenderer();\n }\n\n return el;\n};\nJXG.registerElement(\"parametricsurface3d\", JXG.createParametricSurface3D);\n\n/**\n * @class A 3D functiongraph visualizes a map (x, y) → f(x, y).\n * The graph is a {@link Curve3D} element.\n * @pseudo\n * @description A 3D function graph is defined by a function\n * F: R2 → R.\n *\n * @name Functiongraph3D\n * @augments ParametricSurface3D\n * @constructor\n * @type Object\n * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.\n * @param {Function,String_Array_Array} F,rangeX,rangeY F(x,y) is a function returning a number (or a JessieCode string), rangeX is the array containing\n * lower and upper bound for the range of x, rangeY is the array containing\n * lower and upper bound for the range of y.\n * @example\n * var box = [-5, 5];\n * var view = board.create('view3d',\n * [\n * [-6, -3], [8, 8],\n * [box, box, box]\n * ],\n * {\n * xPlaneRear: {visible: false},\n * yPlaneRear: {visible: false},\n * });\n *\n * // Function F to be plotted\n * var F = (x, y) => Math.sin(x * y / 4);\n *\n * // 3D surface\n * var c = view.create('functiongraph3d', [\n * F,\n * box, // () => [-s.Value()*5, s.Value() * 5],\n * box, // () => [-s.Value()*5, s.Value() * 5],\n * ], {\n * strokeWidth: 0.5,\n * stepsU: 70,\n * stepsV: 70\n * });\n *\n * \n * \n *\n */\nJXG.createFunctiongraph3D = function (board, parents, attributes) {\n var view = parents[0],\n X = function (u, v) {\n return u;\n },\n Y = function (u, v) {\n return v;\n },\n Z = Type.createFunction(parents[1], board, 'x, y'),\n range_u = parents[2],\n range_v = parents[3],\n el;\n\n el = view.create(\"parametricsurface3d\", [X, Y, Z, range_u, range_v], attributes);\n el.elType = 'functiongraph3d';\n\n return el;\n};\nJXG.registerElement(\"functiongraph3d\", JXG.createFunctiongraph3D);\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Andreas Walter,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see \n * \n *\n */\n STL: function (str) {\n var i, j, pos, le,\n li,\n lines,\n coords,\n face_num, found,\n polyhedra = [],\n vertices = [],\n faces = [];\n\n lines = str.split('\\n');\n\n le = lines.length;\n for (i = 0; i < le; i++) {\n li = lines[i].trim();\n\n if (li.indexOf('solid') === 0) {\n // New model\n face_num = -1;\n vertices = [];\n faces = [];\n } else if (li.indexOf('endsolid') === 0) {\n polyhedra.push([vertices.slice(), faces.slice()]);\n // break;\n } else if (li.indexOf('facet') === 0) {\n face_num++;\n faces.push([]);\n } else if (li.indexOf('outer loop') === 0 || li.indexOf('endloop') === 0) {\n continue;\n } else if (li.indexOf('vertex') === 0) {\n coords = li.split(' ').slice(1).map((x) => parseFloat(x));\n found = false;\n for (j = 0; j < vertices.length; j++) {\n if (JXG.Math.Geometry.distance(vertices[j], coords, 3) < JXG.Math.eps) {\n // Debug:\n // console.log(\"Point already defined\")\n found = true;\n pos = j;\n break;\n }\n }\n if (found === false) {\n pos = vertices.length;\n vertices.push(coords);\n }\n faces[face_num].push(pos);\n }\n }\n // console.log('v:', vertices.length, 'f:', faces.length)\n\n // return [vertices, faces];\n return polyhedra;\n }\n\n};\n\n\nexport default JXG.Parse3D;\n","/*\n Copyright 2008-2026\n Matthias Ehmann,\n Carsten Miller,\n Alfred Wassermann\n\n This file is part of JSXGraph.\n\n JSXGraph is free software dual licensed under the GNU LGPL or MIT License.\n\n You can redistribute it and/or modify it under the terms of the\n\n * GNU Lesser General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version\n OR\n * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT\n\n JSXGraph is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU Lesser General Public License for more details.\n\n You should have received a copy of the GNU Lesser General Public License and\n the MIT License along with JSXGraph. If not, see