      1 /*
      2     Copyright 2008-2024
      3         Matthias Ehmann,
      4         Michael Gerhaeuser,
      5         Carsten Miller,
      6         Bianca Valentin,
      7         Alfred Wassermann,
      8         Peter Wilfahrt
      9
     10     This file is part of JSXGraph.
     11
     12     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
     13
     14     You can redistribute it and/or modify it under the terms of the
     15
     16       * GNU Lesser General Public License as published by
     17         the Free Software Foundation, either version 3 of the License, or
     18         (at your option) any later version
     19       OR
     20       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
     21
     22     JSXGraph is distributed in the hope that it will be useful,
     23     but WITHOUT ANY WARRANTY; without even the implied warranty of
     24     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     25     GNU Lesser General Public License for more details.
     26
     27     You should have received a copy of the GNU Lesser General Public License and
     28     the MIT License along with JSXGraph. If not, see <https://www.gnu.org/licenses/>
     29     and <https://opensource.org/licenses/MIT/>.
     30  */
     31
     32 /*global JXG: true, define: true, console: true, window: true*/
     33 /*jslint nomen: true, plusplus: true*/
     34
     35 /**
     36  * @fileoverview The geometry object Point is defined in this file. Point stores all
     37  * style and functional properties that are required to draw and move a point on
     38  * a board.
     39  */
     40
     41 import JXG from "../jxg.js";
     42 import Options from "../options.js";
     43 import Mat from "../math/math.js";
     44 import Geometry from "../math/geometry.js";
     45 import Const from "./constants.js";
     46 import GeometryElement from "./element.js";
     47 import Type from "../utils/type.js";
     48 import CoordsElement from "./coordselement.js";
     49
     50 /**
     51  * A point is the basic geometric element. Based on points lines and circles can be constructed which can be intersected
     52  * which in turn are points again which can be used to construct new lines, circles, polygons, etc. This class holds methods for
     53  * all kind of points like free points, gliders, and intersection points.
     54  * @class Creates a new point object. Do not use this constructor to create a point. Use {@link JXG.Board#create} with
     55  * type {@link Point}, {@link Glider}, or {@link Intersection} instead.
     56  * @augments JXG.GeometryElement
     57  * @augments JXG.CoordsElement
     58  * @param {string|JXG.Board} board The board the new point is drawn on.
     59  * @param {Array} coordinates An array with the user coordinates of the point.
     60  * @param {Object} attributes An object containing visual properties like in {@link JXG.Options#point} and
     61  * {@link JXG.Options#elements}, and optional a name and an id.
     62  * @see JXG.Board#generateName
     63  */
     64 JXG.Point = function (board, coordinates, attributes) {
     65     this.constructor(board, attributes, Const.OBJECT_TYPE_POINT, Const.OBJECT_CLASS_POINT);
     66     this.element = this.board.select(attributes.anchor);
     67     this.coordsConstructor(coordinates);
     68
     69     this.elType = "point";
     70
     71     /* Register point at board. */
     72     this.id = this.board.setId(this, "P");
     73     this.board.renderer.drawPoint(this);
     74     this.board.finalizeAdding(this);
     75
     76     this.createGradient();
     77     this.createLabel();
     78 };
     79
     80 /**
     81  * Inherits here from {@link JXG.GeometryElement}.
     82  */
     83 JXG.Point.prototype = new GeometryElement();
     84 Type.copyPrototypeMethods(JXG.Point, CoordsElement, "coordsConstructor");
     85
     86 JXG.extend(
     87     JXG.Point.prototype,
     88     /** @lends JXG.Point.prototype */ {
     89         /**
     90          * Checks whether (x,y) is near the point.
     91          * @param {Number} x Coordinate in x direction, screen coordinates.
     92          * @param {Number} y Coordinate in y direction, screen coordinates.
     93          * @returns {Boolean} True if (x,y) is near the point, False otherwise.
     94          * @private
     95          */
     96         hasPoint: function (x, y) {
     97             var coordsScr = this.coords.scrCoords,
     98                 r,
     99                 prec,
    100                 type,
    101                 unit = Type.evaluate(this.visProp.sizeunit);
    102
    103             if (Type.isObject(Type.evaluate(this.visProp.precision))) {
    104                 type = this.board._inputDevice;
    105                 prec = Type.evaluate(this.visProp.precision[type]);
    106             } else {
    107                 // 'inherit'
    108                 prec = this.board.options.precision.hasPoint;
    109             }
    110             r = parseFloat(Type.evaluate(this.visProp.size));
    111             if (unit === "user") {
    112                 r *= Math.sqrt(Math.abs(this.board.unitX * this.board.unitY));
    113             }
    114
    115             r += parseFloat(Type.evaluate(this.visProp.strokewidth)) * 0.5;
    116             if (r < prec) {
    117                 r = prec;
    118             }
    119
    120             return Math.abs(coordsScr[1] - x) < r + 2 && Math.abs(coordsScr[2] - y) < r + 2;
    121         },
    122
    123         /**
    124          * Updates the position of the point.
    125          */
    126         update: function (fromParent) {
    127             if (!this.needsUpdate) {
    128                 return this;
    129             }
    130
    131             this.updateCoords(fromParent);
    132
    133             if (Type.evaluate(this.visProp.trace)) {
    134                 this.cloneToBackground(true);
    135             }
    136
    137             return this;
    138         },
    139
    140         /**
    141          * Applies the transformations of the element to {@link JXG.Point#baseElement}.
    142          * Point transformations are relative to a base element.
    143          * @param {Boolean} fromParent True if the drag comes from a child element. This is the case if a line
    144          *    through two points is dragged. Otherwise, the element is the drag element and we apply the
    145          *    the inverse transformation to the baseElement if is different from the element.
    146          * @returns {JXG.CoordsElement} Reference to this object.
    147          */
    148         updateTransform: function (fromParent) {
    149             var c, i;
    150
    151             if (this.transformations.length === 0 || this.baseElement === null) {
    152                 return this;
    153             }
    154
    155             if (this === this.baseElement) {
    156                 // Case of bindTo
    157                 c = this.transformations[0].apply(this.baseElement, "self");
    158                 this.coords.setCoordinates(Const.COORDS_BY_USER, c);
    159             } else {
    160                 c = this.transformations[0].apply(this.baseElement);
    161             }
    162             this.coords.setCoordinates(Const.COORDS_BY_USER, c);
    163
    164             for (i = 1; i < this.transformations.length; i++) {
    165                 this.coords.setCoordinates(
    166                     Const.COORDS_BY_USER,
    167                     this.transformations[i].apply(this)
    168                 );
    169             }
    170             return this;
    171         },
    172
    173         /**
    174          * Calls the renderer to update the drawing.
    175          * @private
    176          */
    177         updateRenderer: function () {
    178             this.updateRendererGeneric("updatePoint");
    179             return this;
    180         },
    181
    182         // documented in JXG.GeometryElement
    183         bounds: function () {
    184             return this.coords.usrCoords.slice(1).concat(this.coords.usrCoords.slice(1));
    185         },
    186
    187         /**
    188          * Convert the point to intersection point and update the construction.
    189          * To move the point visual onto the intersection, a call of board update is necessary.
    190          *
    191          * @param {String|Object} el1, el2, i, j The intersecting objects and the numbers.
    192          **/
    193         makeIntersection: function (el1, el2, i, j) {
    194             var func;
    195
    196             el1 = this.board.select(el1);
    197             el2 = this.board.select(el2);
    198
    199             func = Geometry.intersectionFunction(
    200                 this.board,
    201                 el1,
    202                 el2,
    203                 i,
    204                 j,
    205                 this.visProp.alwaysintersect
    206             );
    207             this.addConstraint([func]);
    208
    209             try {
    210                 el1.addChild(this);
    211                 el2.addChild(this);
    212             } catch (e) {
    213                 throw new Error(
    214                     "JSXGraph: Can't create 'intersection' with parent types '" +
    215                         typeof el1 +
    216                         "' and '" +
    217                         typeof el2 +
    218                         "'."
    219                 );
    220             }
    221
    222             this.type = Const.OBJECT_TYPE_INTERSECTION;
    223             this.elType = "intersection";
    224             this.parents = [el1.id, el2.id, i, j];
    225
    226             this.generatePolynomial = function () {
    227                 var poly1 = el1.generatePolynomial(this),
    228                     poly2 = el2.generatePolynomial(this);
    229
    230                 if (poly1.length === 0 || poly2.length === 0) {
    231                     return [];
    232                 }
    233
    234                 return [poly1[0], poly2[0]];
    235             };
    236
    237             this.prepareUpdate().update();
    238         },
    239
    240         /**
    241          * Set the style of a point.
    242          * Used for GEONExT import and should not be used to set the point's face and size.
    243          * @param {Number} i Integer to determine the style.
    244          * @private
    245          */
    246         setStyle: function (i) {
    247             var facemap = [
    248                     // 0-2
    249                     "cross",
    250                     "cross",
    251                     "cross",
    252                     // 3-6
    253                     "circle",
    254                     "circle",
    255                     "circle",
    256                     "circle",
    257                     // 7-9
    258                     "square",
    259                     "square",
    260                     "square",
    261                     // 10-12
    262                     "plus",
    263                     "plus",
    264                     "plus"
    265                 ],
    266                 sizemap = [
    267                     // 0-2
    268                     2, 3, 4,
    269                     // 3-6
    270                     1, 2, 3, 4,
    271                     // 7-9
    272                     2, 3, 4,
    273                     // 10-12
    274                     2, 3, 4
    275                 ];
    276
    277             this.visProp.face = facemap[i];
    278             this.visProp.size = sizemap[i];
    279
    280             this.board.renderer.changePointStyle(this);
    281             return this;
    282         },
    283
    284         /**
    285          * @deprecated Use JXG#normalizePointFace instead
    286          * @param s
    287          * @returns {*}
    288          */
    289         normalizeFace: function (s) {
    290             JXG.deprecated("Point.normalizeFace()", "JXG.normalizePointFace()");
    291             return Options.normalizePointFace(s);
    292         },
    293
    294         /**
    295          * Set the face of a point element.
    296          * @param {String} f String which determines the face of the point. See {@link JXG.GeometryElement#face} for a list of available faces.
    297          * @see JXG.GeometryElement#face
    298          * @deprecated Use setAttribute()
    299          */
    300         face: function (f) {
    301             JXG.deprecated("Point.face()", "Point.setAttribute()");
    302             this.setAttribute({ face: f });
    303         },
    304
    305         /**
    306          * Set the size of a point element
    307          * @param {Number} s Integer which determines the size of the point.
    308          * @see JXG.GeometryElement#size
    309          * @deprecated Use setAttribute()
    310          */
    311         size: function (s) {
    312             JXG.deprecated("Point.size()", "Point.setAttribute()");
    313             this.setAttribute({ size: s });
    314         },
    315
    316         /**
    317          * Test if the point is on (is incident with) element "el".
    318          *
    319          * @param {JXG.GeometryElement} el
    320          * @param {Number} tol
    321          * @returns {Boolean}
    322          *
    323          * @example
    324          * var circ = board.create('circle', [[-2, -2], 1]);
    325          * var seg = board.create('segment', [[-1, -3], [0,0]]);
    326          * var line = board.create('line', [[1, 3], [2, -2]]);
    327          * var po = board.create('point', [-1, 0], {color: 'blue'});
    328          * var curve = board.create('functiongraph', ['sin(x)'], {strokeColor: 'blue'});
    329          * var pol = board.create('polygon', [[2,2], [4,2], [4,3]], {strokeColor: 'blue'});
    330          *
    331          * var point = board.create('point', [-1, 1], {
    332          *               attractors: [line, seg, circ, po, curve, pol],
    333          *               attractorDistance: 0.2
    334          *             });
    335          *
    336          * var txt = board.create('text', [-4, 3, function() {
    337          *              return 'point on line: ' + point.isOn(line) + '<br>' +
    338          *                 'point on seg: ' + point.isOn(seg) + '<br>' +
    339          *                 'point on circ = ' + point.isOn(circ) + '<br>' +
    340          *                 'point on point = ' + point.isOn(po) + '<br>' +
    341          *                 'point on curve = ' + point.isOn(curve) + '<br>' +
    342          *                 'point on polygon = ' + point.isOn(pol) + '<br>';
    343          * }]);
    344          *
    345          * </pre><div id="JXG6c7d7404-758a-44eb-802c-e9644b9fab71" class="jxgbox" style="width: 300px; height: 300px;"></div>
    346          * <script type="text/javascript">
    347          *     (function() {
    348          *         var board = JXG.JSXGraph.initBoard('JXG6c7d7404-758a-44eb-802c-e9644b9fab71',
    349          *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
    350          *     var circ = board.create('circle', [[-2, -2], 1]);
    351          *     var seg = board.create('segment', [[-1, -3], [0,0]]);
    352          *     var line = board.create('line', [[1, 3], [2, -2]]);
    353          *     var po = board.create('point', [-1, 0], {color: 'blue'});
    354          *     var curve = board.create('functiongraph', ['sin(x)'], {strokeColor: 'blue'});
    355          *     var pol = board.create('polygon', [[2,2], [4,2], [4,3]], {strokeColor: 'blue'});
    356          *
    357          *     var point = board.create('point', [-1, 1], {
    358          *                   attractors: [line, seg, circ, po, curve, pol],
    359          *                   attractorDistance: 0.2
    360          *                 });
    361          *
    362          *     var txt = board.create('text', [-4, 3, function() {
    363          *             return 'point on line: ' + point.isOn(line) + '<br>' +
    364          *                     'point on seg: ' + point.isOn(seg) + '<br>' +
    365          *                     'point on circ = ' + point.isOn(circ) + '<br>' +
    366          *                     'point on point = ' + point.isOn(po) + '<br>' +
    367          *                     'point on curve = ' + point.isOn(curve) + '<br>' +
    368          *                     'point on polygon = ' + point.isOn(pol) + '<br>';
    369          *     }]);
    370          *
    371          *     })();
    372          *
    373          * </script><pre>
    374          *
    375          */
    376         isOn: function (el, tol) {
    377             var arr, crds;
    378
    379             tol = tol || Mat.eps;
    380
    381             if (Type.isPoint(el)) {
    382                 return this.Dist(el) < tol;
    383             } else if (el.elementClass === Const.OBJECT_CLASS_LINE) {
    384                 if (el.elType === "segment" && !Type.evaluate(this.visProp.alwaysintersect)) {
    385                     arr = JXG.Math.Geometry.projectCoordsToSegment(
    386                         this.coords.usrCoords,
    387                         el.point1.coords.usrCoords,
    388                         el.point2.coords.usrCoords
    389                     );
    390                     if (
    391                         arr[1] >= 0 &&
    392                         arr[1] <= 1 &&
    393                         Geometry.distPointLine(this.coords.usrCoords, el.stdform) < tol
    394                     ) {
    395                         return true;
    396                     } else {
    397                         return false;
    398                     }
    399                 } else {
    400                     return Geometry.distPointLine(this.coords.usrCoords, el.stdform) < tol;
    401                 }
    402             } else if (el.elementClass === Const.OBJECT_CLASS_CIRCLE) {
    403                 if (Type.evaluate(el.visProp.hasinnerpoints)) {
    404                     return this.Dist(el.center) < el.Radius() + tol;
    405                 }
    406                 return Math.abs(this.Dist(el.center) - el.Radius()) < tol;
    407             } else if (el.elementClass === Const.OBJECT_CLASS_CURVE) {
    408                 crds = Geometry.projectPointToCurve(this, el, this.board)[0];
    409                 return Geometry.distance(this.coords.usrCoords, crds.usrCoords, 3) < tol;
    410             } else if (el.type === Const.OBJECT_TYPE_POLYGON) {
    411                 if (Type.evaluate(el.visProp.hasinnerpoints)) {
    412                     if (
    413                         el.pnpoly(
    414                             this.coords.usrCoords[1],
    415                             this.coords.usrCoords[2],
    416                             JXG.COORDS_BY_USER
    417                         )
    418                     ) {
    419                         return true;
    420                     }
    421                 }
    422                 arr = Geometry.projectCoordsToPolygon(this.coords.usrCoords, el);
    423                 return Geometry.distance(this.coords.usrCoords, arr, 3) < tol;
    424             } else if (el.type === Const.OBJECT_TYPE_TURTLE) {
    425                 crds = Geometry.projectPointToTurtle(this, el, this.board);
    426                 return Geometry.distance(this.coords.usrCoords, crds.usrCoords, 3) < tol;
    427             }
    428
    429             // TODO: Arc, Sector
    430             return false;
    431         },
    432
    433         // Already documented in GeometryElement
    434         cloneToBackground: function () {
    435             var copy = {};
    436
    437             copy.id = this.id + "T" + this.numTraces;
    438             this.numTraces += 1;
    439
    440             copy.coords = this.coords;
    441             copy.visProp = Type.deepCopy(this.visProp, this.visProp.traceattributes, true);
    442             copy.visProp.layer = this.board.options.layer.trace;
    443             copy.elementClass = Const.OBJECT_CLASS_POINT;
    444             copy.board = this.board;
    445             Type.clearVisPropOld(copy);
    446
    447             copy.visPropCalc = {
    448                 visible: Type.evaluate(copy.visProp.visible)
    449             };
    450
    451             this.board.renderer.drawPoint(copy);
    452             this.traces[copy.id] = copy.rendNode;
    453
    454             return this;
    455         }
    456     }
    457 );
    458
    459 /**
    460  * @class This element is used to provide a constructor for a general point. A free point is created if the given parent elements are all numbers
    461  * 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 GEONE<sub>x</sub>T
    462  * 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
    463  * position directly.
    464  * @see Glider for a non-free point that is attached to another geometric element.
    465  * @pseudo
    466  * @name Point
    467  * @augments JXG.Point
    468  * @constructor
    469  * @type JXG.Point
    470  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
    471  * @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 GEONE<sub>x</sub>T
    472  * constraint, or a function which takes no parameter and returns a number. Every parent element determines one coordinate. If a coordinate is
    473  * 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
    474  * 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
    475  * 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
    476  * parent elements are given they will be interpreted as homogeneous coordinates.
    477  * @param {JXG.Point_JXG.Transformation_Array} Point,Transformation A point can also be created providing a transformation or an array of transformations.
    478  * The resulting point is a clone of the base point transformed by the given Transformation. {@see JXG.Transformation}.
    479  *
    480  * @example
    481  * // Create a free point using affine Euclidean coordinates
    482  * var p1 = board.create('point', [3.5, 2.0]);
    483  * </pre><div class="jxgbox" id="JXG672f1764-7dfa-4abc-a2c6-81fbbf83e44b" style="width: 200px; height: 200px;"></div>
    484  * <script type="text/javascript">
    485  *   var board = JXG.JSXGraph.initBoard('JXG672f1764-7dfa-4abc-a2c6-81fbbf83e44b', {boundingbox: [-1, 5, 5, -1], axis: true, showcopyright: false, shownavigation: false});
    486  *   var p1 = board.create('point', [3.5, 2.0]);
    487  * </script><pre>
    488  * @example
    489  * // Create a constrained point using anonymous function
    490  * var p2 = board.create('point', [3.5, function () { return p1.X(); }]);
    491  * </pre><div class="jxgbox" id="JXG4fd4410c-3383-4e80-b1bb-961f5eeef224" style="width: 200px; height: 200px;"></div>
    492  * <script type="text/javascript">
    493  *   var fpex1_board = JXG.JSXGraph.initBoard('JXG4fd4410c-3383-4e80-b1bb-961f5eeef224', {boundingbox: [-1, 5, 5, -1], axis: true, showcopyright: false, shownavigation: false});
    494  *   var fpex1_p1 = fpex1_board.create('point', [3.5, 2.0]);
    495  *   var fpex1_p2 = fpex1_board.create('point', [3.5, function () { return fpex1_p1.X(); }]);
    496  * </script><pre>
    497  * @example
    498  * // Create a point using transformations
    499  * var trans = board.create('transform', [2, 0.5], {type:'scale'});
    500  * var p3 = board.create('point', [p2, trans]);
    501  * </pre><div class="jxgbox" id="JXG630afdf3-0a64-46e0-8a44-f51bd197bb8d" style="width: 400px; height: 400px;"></div>
    502  * <script type="text/javascript">
    503  *   var fpex2_board = JXG.JSXGraph.initBoard('JXG630afdf3-0a64-46e0-8a44-f51bd197bb8d', {boundingbox: [-1, 9, 9, -1], axis: true, showcopyright: false, shownavigation: false});
    504  *   var fpex2_trans = fpex2_board.create('transform', [2, 0.5], {type:'scale'});
    505  *   var fpex2_p2 = fpex2_board.create('point', [3.5, 2.0]);
    506  *   var fpex2_p3 = fpex2_board.create('point', [fpex2_p2, fpex2_trans]);
    507  * </script><pre>
    508  */
    509 JXG.createPoint = function (board, parents, attributes) {
    510     var el, attr;
    511
    512     attr = Type.copyAttributes(attributes, board.options, "point");
    513     el = CoordsElement.create(JXG.Point, board, parents, attr);
    514     if (!el) {
    515         throw new Error(
    516             "JSXGraph: Can't create point with parent types '" +
    517                 typeof parents[0] +
    518                 "' and '" +
    519                 typeof parents[1] +
    520                 "'." +
    521                 "\nPossible parent types: [x,y], [z,x,y], [element,transformation]"
    522         );
    523     }
    524
    525     return el;
    526 };
    527
    528 /**
    529  * @class This element is used to provide a constructor for a glider point.
    530  * @pseudo
    531  * @description A glider is a point which lives on another geometric element like a line, circle, curve, turtle.
    532  * @name Glider
    533  * @augments JXG.Point
    534  * @constructor
    535  * @type JXG.Point
    536  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
    537  * @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.
    538  * 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
    539  * coordinates, otherwise they will be interpreted as homogeneous coordinates. In any case the point will be projected on the glide object.
    540  * @example
    541  * // Create a glider with user defined coordinates. If the coordinates are not on
    542  * // the circle (like in this case) the point will be projected onto the circle.
    543  * var p1 = board.create('point', [2.0, 2.0]);
    544  * var c1 = board.create('circle', [p1, 2.0]);
    545  * var p2 = board.create('glider', [2.0, 1.5, c1]);
    546  * </pre><div class="jxgbox" id="JXG4f65f32f-e50a-4b50-9b7c-f6ec41652930" style="width: 300px; height: 300px;"></div>
    547  * <script type="text/javascript">
    548  *   var gpex1_board = JXG.JSXGraph.initBoard('JXG4f65f32f-e50a-4b50-9b7c-f6ec41652930', {boundingbox: [-1, 5, 5, -1], axis: true, showcopyright: false, shownavigation: false});
    549  *   var gpex1_p1 = gpex1_board.create('point', [2.0, 2.0]);
    550  *   var gpex1_c1 = gpex1_board.create('circle', [gpex1_p1, 2.0]);
    551  *   var gpex1_p2 = gpex1_board.create('glider', [2.0, 1.5, gpex1_c1]);
    552  * </script><pre>
    553  * @example
    554  * // Create a glider with default coordinates (1,0,0). Same premises as above.
    555  * var p1 = board.create('point', [2.0, 2.0]);
    556  * var c1 = board.create('circle', [p1, 2.0]);
    557  * var p2 = board.create('glider', [c1]);
    558  * </pre><div class="jxgbox" id="JXG4de7f181-631a-44b1-a12f-bc4d995609e8" style="width: 200px; height: 200px;"></div>
    559  * <script type="text/javascript">
    560  *   var gpex2_board = JXG.JSXGraph.initBoard('JXG4de7f181-631a-44b1-a12f-bc4d995609e8', {boundingbox: [-1, 5, 5, -1], axis: true, showcopyright: false, shownavigation: false});
    561  *   var gpex2_p1 = gpex2_board.create('point', [2.0, 2.0]);
    562  *   var gpex2_c1 = gpex2_board.create('circle', [gpex2_p1, 2.0]);
    563  *   var gpex2_p2 = gpex2_board.create('glider', [gpex2_c1]);
    564  * </script><pre>
    565  *@example
    566  * //animate example 2
    567  * var p1 = board.create('point', [2.0, 2.0]);
    568  * var c1 = board.create('circle', [p1, 2.0]);
    569  * var p2 = board.create('glider', [c1]);
    570  * var button1 = board.create('button', [1, 7, 'start animation',function(){p2.startAnimation(1,4)}]);
    571  * var button2 = board.create('button', [1, 5, 'stop animation',function(){p2.stopAnimation()}]);
    572  * </pre><div class="jxgbox" id="JXG4de7f181-631a-44b1-a12f-bc4d133709e8" style="width: 200px; height: 200px;"></div>
    573  * <script type="text/javascript">
    574  *   var gpex3_board = JXG.JSXGraph.initBoard('JXG4de7f181-631a-44b1-a12f-bc4d133709e8', {boundingbox: [-1, 10, 10, -1], axis: true, showcopyright: false, shownavigation: false});
    575  *   var gpex3_p1 = gpex3_board.create('point', [2.0, 2.0]);
    576  *   var gpex3_c1 = gpex3_board.create('circle', [gpex3_p1, 2.0]);
    577  *   var gpex3_p2 = gpex3_board.create('glider', [gpex3_c1]);
    578  *   gpex3_board.create('button', [1, 7, 'start animation',function(){gpex3_p2.startAnimation(1,4)}]);
    579  *   gpex3_board.create('button', [1, 5, 'stop animation',function(){gpex3_p2.stopAnimation()}]);
    580  * </script><pre>
    581  */
    582 JXG.createGlider = function (board, parents, attributes) {
    583     var el,
    584         coords,
    585         attr = Type.copyAttributes(attributes, board.options, "glider");
    586
    587     if (parents.length === 1) {
    588         coords = [0, 0];
    589     } else {
    590         coords = parents.slice(0, 2);
    591     }
    592     el = board.create("point", coords, attr);
    593
    594     // eltype is set in here
    595     el.makeGlider(parents[parents.length - 1]);
    596
    597     return el;
    598 };
    599
    600 /**
    601  * @class An intersection point is a point which lives on two JSXGraph elements, i.e. it is one point of the set
    602  * consisting of the intersection points of the two elements. The following element types can be (mutually) intersected: line, circle,
    603  * curve, polygon, polygonal chain.
    604  *
    605  * @pseudo
    606  * @name Intersection
    607  * @augments JXG.Point
    608  * @constructor
    609  * @type JXG.Point
    610  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
    611  * @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
    612  * intersection point if two points are available: <ul>
    613  *   <li>i==0: use the positive square root,</li>
    614  *   <li>i==1: use the negative square root.</li></ul>
    615  * @example
    616  * // Create an intersection point of circle and line
    617  * var p1 = board.create('point', [4.0, 4.0]);
    618  * var c1 = board.create('circle', [p1, 2.0]);
    619  *
    620  * var p2 = board.create('point', [1.0, 1.0]);
    621  * var p3 = board.create('point', [5.0, 3.0]);
    622  * var l1 = board.create('line', [p2, p3]);
    623  *
    624  * var i = board.create('intersection', [c1, l1, 0]);
    625  * </pre><div class="jxgbox" id="JXGe5b0e190-5200-4bc3-b995-b6cc53dc5dc0" style="width: 300px; height: 300px;"></div>
    626  * <script type="text/javascript">
    627  *   var ipex1_board = JXG.JSXGraph.initBoard('JXGe5b0e190-5200-4bc3-b995-b6cc53dc5dc0', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false});
    628  *   var ipex1_p1 = ipex1_board.create('point', [4.0, 4.0]);
    629  *   var ipex1_c1 = ipex1_board.create('circle', [ipex1_p1, 2.0]);
    630  *   var ipex1_p2 = ipex1_board.create('point', [1.0, 1.0]);
    631  *   var ipex1_p3 = ipex1_board.create('point', [5.0, 3.0]);
    632  *   var ipex1_l1 = ipex1_board.create('line', [ipex1_p2, ipex1_p3]);
    633  *   var ipex1_i = ipex1_board.create('intersection', [ipex1_c1, ipex1_l1, 0]);
    634  * </script><pre>
    635  */
    636 JXG.createIntersectionPoint = function (board, parents, attributes) {
    637     var el, el1, el2, func,
    638         i, j,
    639         attr = Type.copyAttributes(attributes, board.options, "intersection");
    640
    641     // make sure we definitely have the indices
    642     parents.push(0, 0);
    643
    644     el1 = board.select(parents[0]);
    645     el2 = board.select(parents[1]);
    646
    647     i = parents[2] || 0;
    648     j = parents[3] || 0;
    649
    650     el = board.create("point", [0, 0, 0], attr);
    651
    652     // el.visProp.alwaysintersect is evaluated as late as in the returned function
    653     func = Geometry.intersectionFunction(board, el1, el2, i, j, el.visProp.alwaysintersect);
    654     el.addConstraint([func]);
    655
    656     try {
    657         el1.addChild(el);
    658         el2.addChild(el);
    659     } catch (e) {
    660         throw new Error(
    661             "JSXGraph: Can't create 'intersection' with parent types '" +
    662                 typeof parents[0] +
    663                 "' and '" +
    664                 typeof parents[1] +
    665                 "'."
    666         );
    667     }
    668
    669     el.type = Const.OBJECT_TYPE_INTERSECTION;
    670     el.elType = "intersection";
    671     el.setParents([el1.id, el2.id]);
    672
    673     /**
    674      * Array of length 2 containing the numbers i and j.
    675      * The intersection point is i-th intersection point.
    676      * j is unused.
    677      * @type Array
    678      * @name intersectionNumbers
    679      * @memberOf Intersection
    680      * @private
    681      */
    682     el.intersectionNumbers = [i, j];
    683     el.getParents = function () {
    684         return this.parents.concat(this.intersectionNumbers);
    685     };
    686
    687     el.generatePolynomial = function () {
    688         var poly1 = el1.generatePolynomial(el),
    689             poly2 = el2.generatePolynomial(el);
    690
    691         if (poly1.length === 0 || poly2.length === 0) {
    692             return [];
    693         }
    694
    695         return [poly1[0], poly2[0]];
    696     };
    697
    698     return el;
    699 };
    700
    701 /**
    702  * @class This element is used to provide a constructor for the "other" intersection point.
    703  * @pseudo
    704  * @description If two elements of type curve, circle or line intersect in more than one point, with this element it is possible
    705  * to construct the "other" intersection. This is a an intersection which is different from a supplied point or different from any
    706  * point in an array of supplied points. This might be helpful in situtations where one intersection point is already part of the construction
    707  * or in situtation where the order of the intersection points changes while interacting with the construction.
    708  *
    709  * @name OtherIntersection
    710  * @augments JXG.Point
    711  * @constructor
    712  * @type JXG.Point
    713  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
    714  * @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
    715  * which have to be different from the new intersection point.
    716  *
    717  * @example
    718  * // Create an intersection point of circle and line
    719  * var p1 = board.create('point', [2.0, 2.0]);
    720  * var c1 = board.create('circle', [p1, 2.0]);
    721  *
    722  * var p2 = board.create('point', [2.0, 2.0]);
    723  * var p3 = board.create('point', [2.0, 2.0]);
    724  * var l1 = board.create('line', [p2, p3]);
    725  *
    726  * var p1 = board.create('intersection', [c1, l1, 0]);
    727  * var p2 = board.create('otherintersection', [c1, l1, p1]);
    728  * </pre><div class="jxgbox" id="JXG45e25f12-a1de-4257-a466-27a2ae73614c" style="width: 300px; height: 300px;"></div>
    729  * <script type="text/javascript">
    730  *   var ipex2_board = JXG.JSXGraph.initBoard('JXG45e25f12-a1de-4257-a466-27a2ae73614c', {boundingbox: [-1, 7, 7, -1], axis: false, showcopyright: false, shownavigation: false});
    731  *   var ipex2_p1 = ipex2_board.create('point', [4.0, 4.0]);
    732  *   var ipex2_c1 = ipex2_board.create('circle', [ipex2_p1, 2.0]);
    733  *   var ipex2_p2 = ipex2_board.create('point', [1.0, 1.0]);
    734  *   var ipex2_p3 = ipex2_board.create('point', [5.0, 3.0]);
    735  *   var ipex2_l1 = ipex2_board.create('line', [ipex2_p2, ipex2_p3]);
    736  *   var ipex2_i = ipex2_board.create('intersection', [ipex2_c1, ipex2_l1, 0], {name:'D'});
    737  *   var ipex2_j = ipex2_board.create('otherintersection', [ipex2_c1, ipex2_l1, ipex2_i], {name:'E'});
    738  * </script><pre>
    739  *
    740  * @example
    741  *  // circle / circle
    742  *  var c1 = board.create('circle', [[0, 0], 3]);
    743  *  var c2 = board.create('circle', [[2, 2], 3]);
    744  *
    745  *  var p1 = board.create('intersection', [c1, c2, 0]);
    746  *  var p2 = board.create('otherintersection', [c1, c2, p1]);
    747  *
    748  * </pre><div id="JXGdb5c974c-3092-4cdf-b5ef-d0af4a912581" class="jxgbox" style="width: 300px; height: 300px;"></div>
    749  * <script type="text/javascript">
    750  *     (function() {
    751  *         var board = JXG.JSXGraph.initBoard('JXGdb5c974c-3092-4cdf-b5ef-d0af4a912581',
    752  *             {boundingbox: [-8, 8, 8,-8], axis: false, showcopyright: false, shownavigation: false});
    753  *           var c1 = board.create('circle', [[0, 0], 3]);
    754  *           var c2 = board.create('circle', [[2, 2], 3]);
    755  *
    756  *           var p1 = board.create('intersection', [c1, c2, 0]);
    757  *           var p2 = board.create('otherintersection', [c1, c2, p1]);
    758  *     })();
    759  * </script><pre>
    760  *
    761  * @example
    762  *  // curve / line
    763  *  var curve = board.create('implicitcurve', ['-(y**2) + x**3 - 2 * x + 1'], { strokeWidth: 2 });
    764  *  var A = board.create('glider', [-1.5, 1, curve]);
    765  *  var B = board.create('glider', [0.5, 0.5, curve]);
    766  *  var line = board.create('line', [A, B], { color: 'black', strokeWidth: 1 });
    767  *  var C = board.create('otherintersection', [curve, line, [A, B]], {precision: 0.01});
    768  *  var D = board.create('point', [() => C.X(), () => -C.Y()], { name: '-C = A + B' });
    769  *
    770  * </pre><div id="JXG033f15b0-f5f1-4003-ab6a-b7e13e867fbd" class="jxgbox" style="width: 300px; height: 300px;"></div>
    771  * <script type="text/javascript">
    772  *     (function() {
    773  *         var board = JXG.JSXGraph.initBoard('JXG033f15b0-f5f1-4003-ab6a-b7e13e867fbd',
    774  *             {boundingbox: [-2, 2, 2, -2], axis: false, showcopyright: false, shownavigation: false});
    775  *           var curve = board.create('implicitcurve', ['-(y**2) + x**3 - 2 * x + 1'], { strokeWidth: 2 });
    776  *           var A = board.create('glider', [-1.5, 1, curve]);
    777  *           var B = board.create('glider', [0.5, 0.5, curve]);
    778  *           var line = board.create('line', [A, B], { color: 'black', strokeWidth: 1 });
    779  *           var C = board.create('otherintersection', [curve, line, [A, B]], {precision: 0.01});
    780  *           var D = board.create('point', [() => C.X(), () => -C.Y()], { name: '-C = A + B' });
    781  *     })();
    782  * </script><pre>
    783  *
    784  * @example
    785  *  // curve / curve
    786  *  var c1 = board.create('functiongraph', ['x**2 - 3'], { strokeWidth: 2 });
    787  *  var A = board.create('point', [0, 2]);
    788  *  var c2 = board.create('functiongraph', [(x) => -(x**2) + 2 * A.X() * x + A.Y() - A.X()**2], { strokeWidth: 2 });
    789  *  var p1 = board.create('intersection', [c1, c2]);
    790  *  var p2 = board.create('otherintersection', [c1, c2, [p1]]);
    791  *
    792  * </pre><div id="JXG29359aa9-3066-4f45-9e5d-d74201b991d3" class="jxgbox" style="width: 300px; height: 300px;"></div>
    793  * <script type="text/javascript">
    794  *     (function() {
    795  *         var board = JXG.JSXGraph.initBoard('JXG29359aa9-3066-4f45-9e5d-d74201b991d3',
    796  *             {boundingbox: [-5, 5, 5, -5], axis: true, showcopyright: false, shownavigation: false});
    797  *           var c1 = board.create('functiongraph', ['x**2 - 3'], { strokeWidth: 2 });
    798  *           var A = board.create('point', [0, 2]);
    799  *           var c2 = board.create('functiongraph', [(x) => -(x**2) + 2 * A.X() * x + A.Y() - A.X()**2], { strokeWidth: 2 });
    800  *           var p1 = board.create('intersection', [c1, c2]);
    801  *           var p2 = board.create('otherintersection', [c1, c2, [p1]]);
    802  *     })();
    803  * </script><pre>
    804  *
    805  */
    806 JXG.createOtherIntersectionPoint = function (board, parents, attributes) {
    807     var el, el1, el2, i,
    808     others, func, input,
    809     isGood = true,
    810     attr = Type.copyAttributes(attributes, board.options, 'otherintersection');
    811
    812     if (parents.length !== 3) {
    813         isGood = false;
    814     } else {
    815         el1 = board.select(parents[0]);
    816         el2 = board.select(parents[1]);
    817         if (Type.isArray(parents[2])) {
    818             others = parents[2];
    819         } else {
    820             others = [parents[2]];
    821         }
    822
    823         for (i = 0; i < others.length; i++) {
    824             others[i] = board.select(others[i]);
    825             if (!Type.isPoint(others[i])) {
    826                 isGood = false;
    827                 break;
    828             }
    829         }
    830         if (isGood) {
    831             input = [el1, el2];
    832             // Sort parent elements in order: curve, circle, line
    833             input.sort(function (a, b) { return b.elementClass - a.elementClass; });
    834
    835             // Two lines are forbidden:
    836             if ([Const.OBJECT_CLASS_CIRCLE, Const.OBJECT_CLASS_CURVE].indexOf(input[0].elementClass) < 0) {
    837                 isGood = false;
    838             } else if ([Const.OBJECT_CLASS_CIRCLE, Const.OBJECT_CLASS_CURVE, Const.OBJECT_CLASS_LINE].indexOf(input[1].elementClass) < 0) {
    839                 isGood = false;
    840             }
    841         }
    842     }
    843
    844     if (!isGood) {
    845         throw new Error(
    846             "JSXGraph: Can't create 'other intersection point' with parent types '" +
    847                 typeof parents[0] + "',  '" + typeof parents[1] + "'and  '" + typeof parents[2] + "'." +
    848                 "\nPossible parent types: [circle|curve|line,circle|curve|line, point], not two lines"
    849         );
    850     }
    851
    852     el = board.create('point', [0, 0, 0], attr);
    853     // el.visProp.alwaysintersect is evaluated as late as in the returned function
    854     func = Geometry.otherIntersectionFunction(input, others, el.visProp.alwaysintersect, el.visProp.precision);
    855     el.addConstraint([func]);
    856
    857     el.type = Const.OBJECT_TYPE_INTERSECTION;
    858     el.elType = "otherintersection";
    859     el.setParents([el1.id, el2.id]);
    860     el.addParents(others);
    861
    862     el1.addChild(el);
    863     el2.addChild(el);
    864
    865     if (el1.elementClass === Const.OBJECT_CLASS_CIRCLE) {
    866         // circle, circle|line
    867         el.generatePolynomial = function () {
    868             var poly1 = el1.generatePolynomial(el),
    869                 poly2 = el2.generatePolynomial(el);
    870
    871             if (poly1.length === 0 || poly2.length === 0) {
    872                 return [];
    873             }
    874
    875             return [poly1[0], poly2[0]];
    876         };
    877     }
    878
    879     return el;
    880 };
    881
    882 /**
    883  * @class This element is used to provide a constructor for the pole point of a line with respect to a conic or a circle.
    884  * @pseudo
    885  * @description The pole point is the unique reciprocal relationship of a line with respect to a conic.
    886  * 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.
    887  * A line tangent to a conic has the pole point of that line with respect to that conic as the tangent point.
    888  * See {@link https://en.wikipedia.org/wiki/Pole_and_polar} for more information on pole and polar.
    889  * @name PolePoint
    890  * @augments JXG.Point
    891  * @constructor
    892  * @type JXG.Point
    893  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
    894  * @param {JXG.Conic,JXG.Circle_JXG.Point} el1,el2 or
    895  * @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.
    896  * @example
    897  * // Create the pole point of a line with respect to a conic
    898  * var p1 = board.create('point', [-1, 2]);
    899  * var p2 = board.create('point', [ 1, 4]);
    900  * var p3 = board.create('point', [-1,-2]);
    901  * var p4 = board.create('point', [ 0, 0]);
    902  * var p5 = board.create('point', [ 4,-2]);
    903  * var c1 = board.create('conic',[p1,p2,p3,p4,p5]);
    904  * var p6 = board.create('point', [-1, 4]);
    905  * var p7 = board.create('point', [2, -2]);
    906  * var l1 = board.create('line', [p6, p7]);
    907  * var p8 = board.create('polepoint', [c1, l1]);
    908  * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-8018d0d17a98" class="jxgbox" style="width:400px; height:400px;"></div>
    909  * <script type='text/javascript'>
    910  * var ppex1_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-8018d0d17a98', {boundingbox: [-3, 5, 5, -3], axis: true, showcopyright: false, shownavigation: false});
    911  * var ppex1_p1 = ppex1_board.create('point', [-1, 2]);
    912  * var ppex1_p2 = ppex1_board.create('point', [ 1, 4]);
    913  * var ppex1_p3 = ppex1_board.create('point', [-1,-2]);
    914  * var ppex1_p4 = ppex1_board.create('point', [ 0, 0]);
    915  * var ppex1_p5 = ppex1_board.create('point', [ 4,-2]);
    916  * var ppex1_c1 = ppex1_board.create('conic',[ppex1_p1,ppex1_p2,ppex1_p3,ppex1_p4,ppex1_p5]);
    917  * var ppex1_p6 = ppex1_board.create('point', [-1, 4]);
    918  * var ppex1_p7 = ppex1_board.create('point', [2, -2]);
    919  * var ppex1_l1 = ppex1_board.create('line', [ppex1_p6, ppex1_p7]);
    920  * var ppex1_p8 = ppex1_board.create('polepoint', [ppex1_c1, ppex1_l1]);
    921  * </script><pre>
    922  * @example
    923  * // Create the pole point of a line with respect to a circle
    924  * var p1 = board.create('point', [1, 1]);
    925  * var p2 = board.create('point', [2, 3]);
    926  * var c1 = board.create('circle',[p1,p2]);
    927  * var p3 = board.create('point', [-1, 4]);
    928  * var p4 = board.create('point', [4, -1]);
    929  * var l1 = board.create('line', [p3, p4]);
    930  * var p5 = board.create('polepoint', [c1, l1]);
    931  * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-9018d0d17a98" class="jxgbox" style="width:400px; height:400px;"></div>
    932  * <script type='text/javascript'>
    933  * var ppex2_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-9018d0d17a98', {boundingbox: [-3, 7, 7, -3], axis: true, showcopyright: false, shownavigation: false});
    934  * var ppex2_p1 = ppex2_board.create('point', [1, 1]);
    935  * var ppex2_p2 = ppex2_board.create('point', [2, 3]);
    936  * var ppex2_c1 = ppex2_board.create('circle',[ppex2_p1,ppex2_p2]);
    937  * var ppex2_p3 = ppex2_board.create('point', [-1, 4]);
    938  * var ppex2_p4 = ppex2_board.create('point', [4, -1]);
    939  * var ppex2_l1 = ppex2_board.create('line', [ppex2_p3, ppex2_p4]);
    940  * var ppex2_p5 = ppex2_board.create('polepoint', [ppex2_c1, ppex2_l1]);
    941  * </script><pre>
    942  */
    943 JXG.createPolePoint = function (board, parents, attributes) {
    944     var el,
    945         el1,
    946         el2,
    947         firstParentIsConic,
    948         secondParentIsConic,
    949         firstParentIsLine,
    950         secondParentIsLine;
    951
    952     if (parents.length > 1) {
    953         firstParentIsConic =
    954             parents[0].type === Const.OBJECT_TYPE_CONIC ||
    955             parents[0].elementClass === Const.OBJECT_CLASS_CIRCLE;
    956         secondParentIsConic =
    957             parents[1].type === Const.OBJECT_TYPE_CONIC ||
    958             parents[1].elementClass === Const.OBJECT_CLASS_CIRCLE;
    959
    960         firstParentIsLine = parents[0].elementClass === Const.OBJECT_CLASS_LINE;
    961         secondParentIsLine = parents[1].elementClass === Const.OBJECT_CLASS_LINE;
    962     }
    963
    964     /*        if (parents.length !== 2 || !((
    965                 parents[0].type === Const.OBJECT_TYPE_CONIC ||
    966                 parents[0].elementClass === Const.OBJECT_CLASS_CIRCLE) &&
    967                 parents[1].elementClass === Const.OBJECT_CLASS_LINE ||
    968                 parents[0].elementClass === Const.OBJECT_CLASS_LINE && (
    969                 parents[1].type === Const.OBJECT_TYPE_CONIC ||
    970                 parents[1].elementClass === Const.OBJECT_CLASS_CIRCLE))) {*/
    971     if (
    972         parents.length !== 2 ||
    973         !(
    974             (firstParentIsConic && secondParentIsLine) ||
    975             (firstParentIsLine && secondParentIsConic)
    976         )
    977     ) {
    978         // Failure
    979         throw new Error(
    980             "JSXGraph: Can't create 'pole point' with parent types '" +
    981                 typeof parents[0] +
    982                 "' and '" +
    983                 typeof parents[1] +
    984                 "'." +
    985                 "\nPossible parent type: [conic|circle,line], [line,conic|circle]"
    986         );
    987     }
    988
    989     if (secondParentIsLine) {
    990         el1 = board.select(parents[0]);
    991         el2 = board.select(parents[1]);
    992     } else {
    993         el1 = board.select(parents[1]);
    994         el2 = board.select(parents[0]);
    995     }
    996
    997     el = board.create(
    998         "point",
    999         [
    1000             function () {
    1001                 var q = el1.quadraticform,
    1002                     s = el2.stdform.slice(0, 3);
    1003
    1004                 return [
    1005                     JXG.Math.Numerics.det([s, q[1], q[2]]),
    1006                     JXG.Math.Numerics.det([q[0], s, q[2]]),
    1007                     JXG.Math.Numerics.det([q[0], q[1], s])
    1008                 ];
    1009             }
    1010         ],
    1011         attributes
    1012     );
    1013
    1014     el.elType = "polepoint";
    1015     el.setParents([el1.id, el2.id]);
    1016
    1017     el1.addChild(el);
    1018     el2.addChild(el);
    1019
    1020     return el;
    1021 };
    1022
    1023 JXG.registerElement("point", JXG.createPoint);
    1024 JXG.registerElement("glider", JXG.createGlider);
    1025 JXG.registerElement("intersection", JXG.createIntersectionPoint);
    1026 JXG.registerElement("otherintersection", JXG.createOtherIntersectionPoint);
    1027 JXG.registerElement("polepoint", JXG.createPolePoint);
    1028
    1029 export default JXG.Point;
    1030 // export default {
    1031 //     Point: JXG.Point,
    1032 //     createPoint: JXG.createPoint,
    1033 //     createGlider: JXG.createGlider,
    1034 //     createIntersection: JXG.createIntersectionPoint,
    1035 //     createOtherIntersection: JXG.createOtherIntersectionPoint,
    1036 //     createPolePoint: JXG.createPolePoint
    1037 // };
    1038