1 /*
  2     Copyright 2008-2022
  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 <http://www.gnu.org/licenses/>
 29     and <http://opensource.org/licenses/MIT/>.
 30  */
 31 
 32 
 33 /*global JXG: true, define: true, console: true, window: true*/
 34 /*jslint nomen: true, plusplus: true*/
 35 
 36 /* depends:
 37  jxg
 38  options
 39  math/math
 40  math/geometry
 41  math/numerics
 42  base/coords
 43  base/constants
 44  base/element
 45  parser/geonext
 46  utils/type
 47   elements:
 48    transform
 49  */
 50 
 51 /**
 52  * @fileoverview The geometry object Point is defined in this file. Point stores all
 53  * style and functional properties that are required to draw and move a point on
 54  * a board.
 55  */
 56 
 57 define([
 58     'jxg', 'options', 'math/math', 'math/geometry', 'base/constants', 'base/element',
 59     'utils/type', 'base/coordselement'
 60 ], function (JXG, Options, Mat, Geometry, Const, GeometryElement, Type, CoordsElement) {
 61 
 62     "use strict";
 63 
 64     /**
 65      * A point is the basic geometric element. Based on points lines and circles can be constructed which can be intersected
 66      * which in turn are points again which can be used to construct new lines, circles, polygons, etc. This class holds methods for
 67      * all kind of points like free points, gliders, and intersection points.
 68      * @class Creates a new point object. Do not use this constructor to create a point. Use {@link JXG.Board#create} with
 69      * type {@link Point}, {@link Glider}, or {@link Intersection} instead.
 70      * @augments JXG.GeometryElement
 71      * @augments JXG.CoordsElement
 72      * @param {string|JXG.Board} board The board the new point is drawn on.
 73      * @param {Array} coordinates An array with the user coordinates of the point.
 74      * @param {Object} attributes An object containing visual properties like in {@link JXG.Options#point} and
 75      * {@link JXG.Options#elements}, and optional a name and an id.
 76      * @see JXG.Board#generateName
 77      */
 78     JXG.Point = function (board, coordinates, attributes) {
 79         this.constructor(board, attributes, Const.OBJECT_TYPE_POINT, Const.OBJECT_CLASS_POINT);
 80         this.element = this.board.select(attributes.anchor);
 81         this.coordsConstructor(coordinates);
 82 
 83         this.elType = 'point';
 84 
 85         /* Register point at board. */
 86         this.id = this.board.setId(this, 'P');
 87         this.board.renderer.drawPoint(this);
 88         this.board.finalizeAdding(this);
 89 
 90         this.createGradient();
 91         this.createLabel();
 92 
 93     };
 94 
 95     /**
 96      * Inherits here from {@link JXG.GeometryElement}.
 97      */
 98     JXG.Point.prototype = new GeometryElement();
 99     Type.copyPrototypeMethods(JXG.Point, CoordsElement, 'coordsConstructor');
100 
101     JXG.extend(JXG.Point.prototype, /** @lends JXG.Point.prototype */ {
102         /**
103          * Checks whether (x,y) is near the point.
104          * @param {Number} x Coordinate in x direction, screen coordinates.
105          * @param {Number} y Coordinate in y direction, screen coordinates.
106          * @returns {Boolean} True if (x,y) is near the point, False otherwise.
107          * @private
108          */
109         hasPoint: function (x, y) {
110             var coordsScr = this.coords.scrCoords, r,
111                 prec, type,
112                 unit = Type.evaluate(this.visProp.sizeunit);
113 
114             if (Type.isObject(Type.evaluate(this.visProp.precision))) {
115                 type = this.board._inputDevice;
116                 prec = Type.evaluate(this.visProp.precision[type]);
117             } else {
118                 // 'inherit'
119                 prec = this.board.options.precision.hasPoint;
120             }
121             r = parseFloat(Type.evaluate(this.visProp.size));
122             if (unit === 'user') {
123                 r *= Math.sqrt(this.board.unitX * this.board.unitY);
124             }
125 
126             r += parseFloat(Type.evaluate(this.visProp.strokewidth)) * 0.5;
127             if (r < prec) {
128                 r = prec;
129             }
130 
131             return ((Math.abs(coordsScr[1] - x) < r + 2) && (Math.abs(coordsScr[2] - y) < r + 2));
132         },
133 
134         /**
135          * Updates the position of the point.
136          */
137         update: function (fromParent) {
138             if (!this.needsUpdate) {
139                 return this;
140             }
141 
142             this.updateCoords(fromParent);
143 
144             if (Type.evaluate(this.visProp.trace)) {
145                 this.cloneToBackground(true);
146             }
147 
148             return this;
149         },
150 
151         /**
152          * Applies the transformations of the element to {@link JXG.Point#baseElement}.
153          * Point transformations are relative to a base element.
154          * @param {Boolean} fromParent True if the drag comes from a child element. This is the case if a line
155          *    through two points is dragged. Otherwise, the element is the drag element and we apply the
156          *    the inverse transformation to the baseElement if is different from the element.
157          * @returns {JXG.CoordsElement} Reference to this object.
158          */
159         updateTransform: function (fromParent) {
160             var c, i;
161 
162             if (this.transformations.length === 0 || this.baseElement === null) {
163                 return this;
164             }
165 
166             if (this === this.baseElement) {
167                 // Case of bindTo
168                 c = this.transformations[0].apply(this.baseElement, 'self');
169                 this.coords.setCoordinates(Const.COORDS_BY_USER, c);
170             } else {
171                 c = this.transformations[0].apply(this.baseElement);
172             }
173             this.coords.setCoordinates(Const.COORDS_BY_USER, c);
174 
175             for (i = 1; i < this.transformations.length; i++) {
176                 this.coords.setCoordinates(Const.COORDS_BY_USER, this.transformations[i].apply(this));
177             }
178             return this;
179         },
180 
181         /**
182          * Calls the renderer to update the drawing.
183          * @private
184          */
185         updateRenderer: function () {
186             this.updateRendererGeneric('updatePoint');
187             return this;
188         },
189 
190         // documented in JXG.GeometryElement
191         bounds: function () {
192             return this.coords.usrCoords.slice(1).concat(this.coords.usrCoords.slice(1));
193         },
194 
195         /**
196          * Convert the point to intersection point and update the construction.
197          * To move the point visual onto the intersection, a call of board update is necessary.
198          *
199          * @param {String|Object} el1, el2, i, j The intersecting objects and the numbers.
200          **/
201         makeIntersection: function (el1, el2, i, j) {
202             var func;
203 
204             el1 = this.board.select(el1);
205             el2 = this.board.select(el2);
206 
207             func = Geometry.intersectionFunction(this.board, el1, el2, i, j,
208                     Type.evaluate(this.visProp.alwaysintersect));
209             this.addConstraint([func]);
210 
211             try {
212                 el1.addChild(this);
213                 el2.addChild(this);
214             } catch (e) {
215                 throw new Error("JSXGraph: Can't create 'intersection' with parent types '" +
216                     (typeof el1) + "' and '" + (typeof el2) + "'.");
217             }
218 
219             this.type = Const.OBJECT_TYPE_INTERSECTION;
220             this.elType = 'intersection';
221             this.parents = [el1.id, el2.id, i, j];
222 
223             this.generatePolynomial = function () {
224                 var poly1 = el1.generatePolynomial(this),
225                     poly2 = el2.generatePolynomial(this);
226 
227                 if ((poly1.length === 0) || (poly2.length === 0)) {
228                     return [];
229                 }
230 
231                 return [poly1[0], poly2[0]];
232             };
233 
234             this.prepareUpdate().update();
235         },
236 
237         /**
238          * Set the style of a point.
239          * Used for GEONExT import and should not be used to set the point's face and size.
240          * @param {Number} i Integer to determine the style.
241          * @private
242          */
243         setStyle: function (i) {
244             var facemap = [
245                 // 0-2
246                 'cross', 'cross', 'cross',
247                 // 3-6
248                 'circle', 'circle', 'circle', 'circle',
249                 // 7-9
250                 'square', 'square', 'square',
251                 // 10-12
252                 'plus', 'plus', 'plus'
253             ], sizemap = [
254                 // 0-2
255                 2, 3, 4,
256                 // 3-6
257                 1, 2, 3, 4,
258                 // 7-9
259                 2, 3, 4,
260                 // 10-12
261                 2, 3, 4
262             ];
263 
264             this.visProp.face = facemap[i];
265             this.visProp.size = sizemap[i];
266 
267             this.board.renderer.changePointStyle(this);
268             return this;
269         },
270 
271         /**
272          * @deprecated Use JXG#normalizePointFace instead
273          * @param s
274          * @returns {*}
275          */
276         normalizeFace: function (s) {
277             JXG.deprecated('Point.normalizeFace()', 'JXG.normalizePointFace()');
278             return Options.normalizePointFace(s);
279         },
280 
281         /**
282          * Set the face of a point element.
283          * @param {String} f String which determines the face of the point. See {@link JXG.GeometryElement#face} for a list of available faces.
284          * @see JXG.GeometryElement#face
285          * @deprecated Use setAttribute()
286          */
287         face: function (f) {
288             JXG.deprecated('Point.face()', 'Point.setAttribute()');
289             this.setAttribute({face: f});
290         },
291 
292         /**
293          * Set the size of a point element
294          * @param {Number} s Integer which determines the size of the point.
295          * @see JXG.GeometryElement#size
296          * @deprecated Use setAttribute()
297          */
298         size: function (s) {
299             JXG.deprecated('Point.size()', 'Point.setAttribute()');
300             this.setAttribute({size: s});
301         },
302 
303         /**
304          * Test if the point is on (is incident with) element "el".
305          *
306          * @param {JXG.GeometryElement} el
307          * @param {Number} tol
308          * @returns {Boolean}
309          *
310          * @example
311          * var circ = board.create('circle', [[-2, -2], 1]);
312          * var seg = board.create('segment', [[-1, -3], [0,0]]);
313          * var line = board.create('line', [[1, 3], [2, -2]]);
314          * var po = board.create('point', [-1, 0], {color: 'blue'});
315          * var curve = board.create('functiongraph', ['sin(x)'], {strokeColor: 'blue'});
316          * var pol = board.create('polygon', [[2,2], [4,2], [4,3]], {strokeColor: 'blue'});
317          *
318          * var point = board.create('point', [-1, 1], {
319          *               attractors: [line, seg, circ, po, curve, pol],
320          *               attractorDistance: 0.2
321          *             });
322          *
323          * var txt = board.create('text', [-4, 3, function() {
324          *              return 'point on line: ' + point.isOn(line) + '<br>' +
325          *                 'point on seg: ' + point.isOn(seg) + '<br>' +
326          *                 'point on circ = ' + point.isOn(circ) + '<br>' +
327          *                 'point on point = ' + point.isOn(po) + '<br>' +
328          *                 'point on curve = ' + point.isOn(curve) + '<br>' +
329          *                 'point on polygon = ' + point.isOn(pol) + '<br>';
330          * }]);
331          *
332          * </pre><div id="JXG6c7d7404-758a-44eb-802c-e9644b9fab71" class="jxgbox" style="width: 300px; height: 300px;"></div>
333          * <script type="text/javascript">
334          *     (function() {
335          *         var board = JXG.JSXGraph.initBoard('JXG6c7d7404-758a-44eb-802c-e9644b9fab71',
336          *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
337          *     var circ = board.create('circle', [[-2, -2], 1]);
338          *     var seg = board.create('segment', [[-1, -3], [0,0]]);
339          *     var line = board.create('line', [[1, 3], [2, -2]]);
340          *     var po = board.create('point', [-1, 0], {color: 'blue'});
341          *     var curve = board.create('functiongraph', ['sin(x)'], {strokeColor: 'blue'});
342          *     var pol = board.create('polygon', [[2,2], [4,2], [4,3]], {strokeColor: 'blue'});
343          *
344          *     var point = board.create('point', [-1, 1], {
345          *                   attractors: [line, seg, circ, po, curve, pol],
346          *                   attractorDistance: 0.2
347          *                 });
348          *
349          *     var txt = board.create('text', [-4, 3, function() {
350          *             return 'point on line: ' + point.isOn(line) + '<br>' +
351          *                     'point on seg: ' + point.isOn(seg) + '<br>' +
352          *                     'point on circ = ' + point.isOn(circ) + '<br>' +
353          *                     'point on point = ' + point.isOn(po) + '<br>' +
354          *                     'point on curve = ' + point.isOn(curve) + '<br>' +
355          *                     'point on polygon = ' + point.isOn(pol) + '<br>';
356          *     }]);
357          *
358          *     })();
359          *
360          * </script><pre>
361          *
362          */
363         isOn: function(el, tol) {
364             var arr, crds;
365 
366             tol = tol || Mat.eps;
367 
368             if (Type.isPoint(el)) {
369                 return this.Dist(el) < tol;
370             } else if (el.elementClass === Const.OBJECT_CLASS_LINE) {
371                 if (el.elType === 'segment' && !Type.evaluate(this.visProp.alwaysintersect)) {
372                     arr = JXG.Math.Geometry.projectCoordsToSegment(
373                                 this.coords.usrCoords,
374                                 el.point1.coords.usrCoords,
375                                 el.point2.coords.usrCoords);
376                     if (arr[1] >= 0 && arr[1] <= 1 &&
377                         Geometry.distPointLine(this.coords.usrCoords, el.stdform) < tol) {
378                            return true;
379                     } else {
380                         return false;
381                     }
382                 } else {
383                     return Geometry.distPointLine(this.coords.usrCoords, el.stdform) < tol;
384                 }
385             } else if (el.elementClass === Const.OBJECT_CLASS_CIRCLE) {
386                 if (Type.evaluate(el.visProp.hasinnerpoints)) {
387                     return this.Dist(el.center) < el.Radius() + tol;
388                 }
389                 return Math.abs(this.Dist(el.center) - el.Radius()) < tol;
390             } else if (el.elementClass === Const.OBJECT_CLASS_CURVE) {
391                 crds = Geometry.projectPointToCurve(this, el, this.board)[0];
392                 return Geometry.distance(this.coords.usrCoords, crds.usrCoords, 3) < tol;
393             } else if (el.type === Const.OBJECT_TYPE_POLYGON) {
394                 if (Type.evaluate(el.visProp.hasinnerpoints)) {
395                     if (el.pnpoly(this.coords.usrCoords[1], this.coords.usrCoords[2], JXG.COORDS_BY_USER)) {
396                         return true;
397                     }
398                 }
399                 arr = Geometry.projectCoordsToPolygon(this.coords.usrCoords, el);
400                 return Geometry.distance(this.coords.usrCoords, arr, 3) < tol;
401             } else if (el.type === Const.OBJECT_TYPE_TURTLE) {
402                 crds = Geometry.projectPointToTurtle(this, el, this.board);
403                 return Geometry.distance(this.coords.usrCoords, crds.usrCoords, 3) < tol;
404             }
405 
406             // TODO: Arc, Sector
407             return false;
408         },
409 
410         // Already documented in GeometryElement
411         cloneToBackground: function () {
412             var copy = {};
413 
414             copy.id = this.id + 'T' + this.numTraces;
415             this.numTraces += 1;
416 
417             copy.coords = this.coords;
418             copy.visProp = Type.deepCopy(this.visProp, this.visProp.traceattributes, true);
419             copy.visProp.layer = this.board.options.layer.trace;
420             copy.elementClass = Const.OBJECT_CLASS_POINT;
421             copy.board = this.board;
422             Type.clearVisPropOld(copy);
423 
424             copy.visPropCalc = {
425                 visible: Type.evaluate(copy.visProp.visible)
426             };
427 
428             this.board.renderer.drawPoint(copy);
429             this.traces[copy.id] = copy.rendNode;
430 
431             return this;
432         }
433 
434     });
435 
436     /**
437      * @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
438      * 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
439      * 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
440      * position directly.
441      * @pseudo
442      * @description
443      * @name Point
444      * @augments JXG.Point
445      * @constructor
446      * @type JXG.Point
447      * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
448      * @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
449      * constraint, or a function which takes no parameter and returns a number. Every parent element determines one coordinate. If a coordinate is
450      * 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
451      * 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
452      * 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
453      * parent elements are given they will be interpreted as homogeneous coordinates.
454      * @param {JXG.Point_JXG.Transformation_Array} Point,Transformation A point can also be created providing a transformation or an array of transformations.
455      * The resulting point is a clone of the base point transformed by the given Transformation. {@see JXG.Transformation}.
456      *
457      * @example
458      * // Create a free point using affine Euclidean coordinates
459      * var p1 = board.create('point', [3.5, 2.0]);
460      * </pre><div class="jxgbox" id="JXG672f1764-7dfa-4abc-a2c6-81fbbf83e44b" style="width: 200px; height: 200px;"></div>
461      * <script type="text/javascript">
462      *   var board = JXG.JSXGraph.initBoard('JXG672f1764-7dfa-4abc-a2c6-81fbbf83e44b', {boundingbox: [-1, 5, 5, -1], axis: true, showcopyright: false, shownavigation: false});
463      *   var p1 = board.create('point', [3.5, 2.0]);
464      * </script><pre>
465      * @example
466      * // Create a constrained point using anonymous function
467      * var p2 = board.create('point', [3.5, function () { return p1.X(); }]);
468      * </pre><div class="jxgbox" id="JXG4fd4410c-3383-4e80-b1bb-961f5eeef224" style="width: 200px; height: 200px;"></div>
469      * <script type="text/javascript">
470      *   var fpex1_board = JXG.JSXGraph.initBoard('JXG4fd4410c-3383-4e80-b1bb-961f5eeef224', {boundingbox: [-1, 5, 5, -1], axis: true, showcopyright: false, shownavigation: false});
471      *   var fpex1_p1 = fpex1_board.create('point', [3.5, 2.0]);
472      *   var fpex1_p2 = fpex1_board.create('point', [3.5, function () { return fpex1_p1.X(); }]);
473      * </script><pre>
474      * @example
475      * // Create a point using transformations
476      * var trans = board.create('transform', [2, 0.5], {type:'scale'});
477      * var p3 = board.create('point', [p2, trans]);
478      * </pre><div class="jxgbox" id="JXG630afdf3-0a64-46e0-8a44-f51bd197bb8d" style="width: 400px; height: 400px;"></div>
479      * <script type="text/javascript">
480      *   var fpex2_board = JXG.JSXGraph.initBoard('JXG630afdf3-0a64-46e0-8a44-f51bd197bb8d', {boundingbox: [-1, 9, 9, -1], axis: true, showcopyright: false, shownavigation: false});
481      *   var fpex2_trans = fpex2_board.create('transform', [2, 0.5], {type:'scale'});
482      *   var fpex2_p2 = fpex2_board.create('point', [3.5, 2.0]);
483      *   var fpex2_p3 = fpex2_board.create('point', [fpex2_p2, fpex2_trans]);
484      * </script><pre>
485      */
486     JXG.createPoint = function (board, parents, attributes) {
487         var el, attr;
488 
489         attr = Type.copyAttributes(attributes, board.options, 'point');
490         el = CoordsElement.create(JXG.Point, board, parents, attr);
491         if (!el) {
492             throw new Error("JSXGraph: Can't create point with parent types '" +
493                     (typeof parents[0]) + "' and '" + (typeof parents[1]) + "'." +
494                     "\nPossible parent types: [x,y], [z,x,y], [element,transformation]");
495         }
496 
497         return el;
498     };
499 
500     /**
501      * @class This element is used to provide a constructor for a glider point.
502      * @pseudo
503      * @description A glider is a point which lives on another geometric element like a line, circle, curve, turtle.
504      * @name Glider
505      * @augments JXG.Point
506      * @constructor
507      * @type JXG.Point
508      * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
509      * @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.
510      * 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
511      * coordinates, otherwise they will be interpreted as homogeneous coordinates. In any case the point will be projected on the glide object.
512      * @example
513      * // Create a glider with user defined coordinates. If the coordinates are not on
514      * // the circle (like in this case) the point will be projected onto the circle.
515      * var p1 = board.create('point', [2.0, 2.0]);
516      * var c1 = board.create('circle', [p1, 2.0]);
517      * var p2 = board.create('glider', [2.0, 1.5, c1]);
518      * </pre><div class="jxgbox" id="JXG4f65f32f-e50a-4b50-9b7c-f6ec41652930" style="width: 300px; height: 300px;"></div>
519      * <script type="text/javascript">
520      *   var gpex1_board = JXG.JSXGraph.initBoard('JXG4f65f32f-e50a-4b50-9b7c-f6ec41652930', {boundingbox: [-1, 5, 5, -1], axis: true, showcopyright: false, shownavigation: false});
521      *   var gpex1_p1 = gpex1_board.create('point', [2.0, 2.0]);
522      *   var gpex1_c1 = gpex1_board.create('circle', [gpex1_p1, 2.0]);
523      *   var gpex1_p2 = gpex1_board.create('glider', [2.0, 1.5, gpex1_c1]);
524      * </script><pre>
525      * @example
526      * // Create a glider with default coordinates (1,0,0). Same premises as above.
527      * var p1 = board.create('point', [2.0, 2.0]);
528      * var c1 = board.create('circle', [p1, 2.0]);
529      * var p2 = board.create('glider', [c1]);
530      * </pre><div class="jxgbox" id="JXG4de7f181-631a-44b1-a12f-bc4d995609e8" style="width: 200px; height: 200px;"></div>
531      * <script type="text/javascript">
532      *   var gpex2_board = JXG.JSXGraph.initBoard('JXG4de7f181-631a-44b1-a12f-bc4d995609e8', {boundingbox: [-1, 5, 5, -1], axis: true, showcopyright: false, shownavigation: false});
533      *   var gpex2_p1 = gpex2_board.create('point', [2.0, 2.0]);
534      *   var gpex2_c1 = gpex2_board.create('circle', [gpex2_p1, 2.0]);
535      *   var gpex2_p2 = gpex2_board.create('glider', [gpex2_c1]);
536      * </script><pre>
537      *@example
538      * //animate example 2
539      * var p1 = board.create('point', [2.0, 2.0]);
540      * var c1 = board.create('circle', [p1, 2.0]);
541      * var p2 = board.create('glider', [c1]);
542      * var button1 = board.create('button', [1, 7, 'start animation',function(){p2.startAnimation(1,4)}]);
543      * var button2 = board.create('button', [1, 5, 'stop animation',function(){p2.stopAnimation()}]);
544      * </pre><div class="jxgbox" id="JXG4de7f181-631a-44b1-a12f-bc4d133709e8" style="width: 200px; height: 200px;"></div>
545      * <script type="text/javascript">
546      *   var gpex3_board = JXG.JSXGraph.initBoard('JXG4de7f181-631a-44b1-a12f-bc4d133709e8', {boundingbox: [-1, 10, 10, -1], axis: true, showcopyright: false, shownavigation: false});
547      *   var gpex3_p1 = gpex3_board.create('point', [2.0, 2.0]);
548      *   var gpex3_c1 = gpex3_board.create('circle', [gpex3_p1, 2.0]);
549      *   var gpex3_p2 = gpex3_board.create('glider', [gpex3_c1]);
550      *   gpex3_board.create('button', [1, 7, 'start animation',function(){gpex3_p2.startAnimation(1,4)}]);
551      *   gpex3_board.create('button', [1, 5, 'stop animation',function(){gpex3_p2.stopAnimation()}]);
552      * </script><pre>
553      */
554     JXG.createGlider = function (board, parents, attributes) {
555         var el, coords,
556             attr = Type.copyAttributes(attributes, board.options, 'glider');
557 
558         if (parents.length === 1) {
559             coords = [0, 0];
560         } else {
561             coords = parents.slice(0, 2);
562         }
563         el = board.create('point', coords, attr);
564 
565         // eltype is set in here
566         el.makeGlider(parents[parents.length - 1]);
567 
568         return el;
569     };
570 
571 
572     /**
573      * @class An intersection point is a point which lives on two JSXGraph elements, i.e. it is one point of the the set
574      * consisting of the intersection points of the two elements. The following element types can be (mutually) intersected: line, circle,
575      * curve, polygon, polygonal chain.
576      *
577      * @pseudo
578      * @name Intersection
579      * @augments JXG.Point
580      * @constructor
581      * @type JXG.Point
582      * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
583      * @param {JXG.Line,JXG.Circle_JXG.Line,JXG.Circle_Number} el1,el2,i The result will be a intersection point on el1 and el2. i determines the
584      * intersection point if two points are available: <ul>
585      *   <li>i==0: use the positive square root,</li>
586      *   <li>i==1: use the negative square root.</li></ul>
587      * @example
588      * // Create an intersection point of circle and line
589      * var p1 = board.create('point', [2.0, 2.0]);
590      * var c1 = board.create('circle', [p1, 2.0]);
591      *
592      * var p2 = board.create('point', [2.0, 2.0]);
593      * var p3 = board.create('point', [2.0, 2.0]);
594      * var l1 = board.create('line', [p2, p3]);
595      *
596      * var i = board.create('intersection', [c1, l1, 0]);
597      * </pre><div class="jxgbox" id="JXGe5b0e190-5200-4bc3-b995-b6cc53dc5dc0" style="width: 300px; height: 300px;"></div>
598      * <script type="text/javascript">
599      *   var ipex1_board = JXG.JSXGraph.initBoard('JXGe5b0e190-5200-4bc3-b995-b6cc53dc5dc0', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false});
600      *   var ipex1_p1 = ipex1_board.create('point', [4.0, 4.0]);
601      *   var ipex1_c1 = ipex1_board.create('circle', [ipex1_p1, 2.0]);
602      *   var ipex1_p2 = ipex1_board.create('point', [1.0, 1.0]);
603      *   var ipex1_p3 = ipex1_board.create('point', [5.0, 3.0]);
604      *   var ipex1_l1 = ipex1_board.create('line', [ipex1_p2, ipex1_p3]);
605      *   var ipex1_i = ipex1_board.create('intersection', [ipex1_c1, ipex1_l1, 0]);
606      * </script><pre>
607      */
608     JXG.createIntersectionPoint = function (board, parents, attributes) {
609         var el, el1, el2, func, i, j,
610             attr = Type.copyAttributes(attributes, board.options, 'intersection');
611 
612         // make sure we definitely have the indices
613         parents.push(0, 0);
614 
615         el1 = board.select(parents[0]);
616         el2 = board.select(parents[1]);
617 
618         i = parents[2] || 0;
619         j = parents[3] || 0;
620 
621         el = board.create('point', [0, 0, 0], attr);
622 
623         // el.visProp.alwaysintersect is evaluated as late as in the returned function
624         func = Geometry.intersectionFunction(board, el1, el2, i, j, el.visProp.alwaysintersect);
625         el.addConstraint([func]);
626 
627         try {
628             el1.addChild(el);
629             el2.addChild(el);
630         } catch (e) {
631             throw new Error("JSXGraph: Can't create 'intersection' with parent types '" +
632                 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "'.");
633         }
634 
635         el.type = Const.OBJECT_TYPE_INTERSECTION;
636         el.elType = 'intersection';
637         el.setParents([el1.id, el2.id]);
638 
639         /**
640          * Array of length 2 containing the numbers i and j.
641          * The intersection point is i-th intersection point.
642          * j is unused.
643          * @type Array
644          * @private
645          */
646         el.intersectionNumbers = [i, j];
647         el.getParents = function() {
648             return this.parents.concat(this.intersectionNumbers);
649         };
650 
651         el.generatePolynomial = function () {
652             var poly1 = el1.generatePolynomial(el),
653                 poly2 = el2.generatePolynomial(el);
654 
655             if ((poly1.length === 0) || (poly2.length === 0)) {
656                 return [];
657             }
658 
659             return [poly1[0], poly2[0]];
660         };
661 
662         return el;
663     };
664 
665     /**
666      * @class This element is used to provide a constructor for the "other" intersection point.
667      * @pseudo
668      * @description An intersection point is a point which lives on two Lines or Circles or one Line and one Circle at the same time, i.e.
669      * an intersection point of the two elements. Additionally, one intersection point is provided. The function returns the other intersection point.
670      * @name OtherIntersection
671      * @augments JXG.Point
672      * @constructor
673      * @type JXG.Point
674      * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
675      * @param {JXG.Line,JXG.Circle_JXG.Line,JXG.Circle_JXG.Point} el1,el2,p The result will be a intersection point on el1 and el2. i determines the
676      * intersection point different from p:
677      * @example
678      * // Create an intersection point of circle and line
679      * var p1 = board.create('point', [2.0, 2.0]);
680      * var c1 = board.create('circle', [p1, 2.0]);
681      *
682      * var p2 = board.create('point', [2.0, 2.0]);
683      * var p3 = board.create('point', [2.0, 2.0]);
684      * var l1 = board.create('line', [p2, p3]);
685      *
686      * var i = board.create('intersection', [c1, l1, 0]);
687      * var j = board.create('otherintersection', [c1, l1, i]);
688      * </pre><div class="jxgbox" id="JXG45e25f12-a1de-4257-a466-27a2ae73614c" style="width: 300px; height: 300px;"></div>
689      * <script type="text/javascript">
690      *   var ipex2_board = JXG.JSXGraph.initBoard('JXG45e25f12-a1de-4257-a466-27a2ae73614c', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false});
691      *   var ipex2_p1 = ipex2_board.create('point', [4.0, 4.0]);
692      *   var ipex2_c1 = ipex2_board.create('circle', [ipex2_p1, 2.0]);
693      *   var ipex2_p2 = ipex2_board.create('point', [1.0, 1.0]);
694      *   var ipex2_p3 = ipex2_board.create('point', [5.0, 3.0]);
695      *   var ipex2_l1 = ipex2_board.create('line', [ipex2_p2, ipex2_p3]);
696      *   var ipex2_i = ipex2_board.create('intersection', [ipex2_c1, ipex2_l1, 0], {name:'D'});
697      *   var ipex2_j = ipex2_board.create('otherintersection', [ipex2_c1, ipex2_l1, ipex2_i], {name:'E'});
698      * </script><pre>
699      */
700     JXG.createOtherIntersectionPoint = function (board, parents, attributes) {
701         var el, el1, el2, other;
702 
703         if (parents.length !== 3 ||
704                 !Type.isPoint(parents[2]) ||
705                 (parents[0].elementClass !== Const.OBJECT_CLASS_LINE && parents[0].elementClass !== Const.OBJECT_CLASS_CIRCLE) ||
706                 (parents[1].elementClass !== Const.OBJECT_CLASS_LINE && parents[1].elementClass !== Const.OBJECT_CLASS_CIRCLE)) {
707             // Failure
708             throw new Error("JSXGraph: Can't create 'other intersection point' with parent types '" +
709                 (typeof parents[0]) + "',  '" + (typeof parents[1]) + "'and  '" + (typeof parents[2]) + "'." +
710                 "\nPossible parent types: [circle|line,circle|line,point]");
711         }
712 
713         el1 = board.select(parents[0]);
714         el2 = board.select(parents[1]);
715         other = board.select(parents[2]);
716 
717         el = board.create('point', [function () {
718             var c = Geometry.meet(el1.stdform, el2.stdform, 0, el1.board);
719 
720             if (Math.abs(other.X() - c.usrCoords[1]) > Mat.eps ||
721                     Math.abs(other.Y() - c.usrCoords[2]) > Mat.eps ||
722                     Math.abs(other.Z() - c.usrCoords[0]) > Mat.eps) {
723                 return c;
724             }
725 
726             return Geometry.meet(el1.stdform, el2.stdform, 1, el1.board);
727         }], attributes);
728 
729         el.type = Const.OBJECT_TYPE_INTERSECTION;
730         el.elType = 'otherintersection';
731         el.setParents([el1.id, el2.id, other]);
732 
733         el1.addChild(el);
734         el2.addChild(el);
735 
736         el.generatePolynomial = function () {
737             var poly1 = el1.generatePolynomial(el),
738                 poly2 = el2.generatePolynomial(el);
739 
740             if ((poly1.length === 0) || (poly2.length === 0)) {
741                 return [];
742             }
743 
744             return [poly1[0], poly2[0]];
745         };
746 
747         return el;
748     };
749 
750     /**
751      * @class This element is used to provide a constructor for the pole point of a line with respect to a conic or a circle.
752      * @pseudo
753      * @description The pole point is the unique reciprocal relationship of a line with respect to a conic.
754      * 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.
755      * A line tangent to a conic has the pole point of that line with respect to that conic as the tangent point.
756      * See {@link http://en.wikipedia.org/wiki/Pole_and_polar} for more information on pole and polar.
757      * @name PolePoint
758      * @augments JXG.Point
759      * @constructor
760      * @type JXG.Point
761      * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
762      * @param {JXG.Conic,JXG.Circle_JXG.Point} el1,el2 or
763      * @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.
764      * @example
765      * // Create the pole point of a line with respect to a conic
766      * var p1 = board.create('point', [-1, 2]);
767      * var p2 = board.create('point', [ 1, 4]);
768      * var p3 = board.create('point', [-1,-2]);
769      * var p4 = board.create('point', [ 0, 0]);
770      * var p5 = board.create('point', [ 4,-2]);
771      * var c1 = board.create('conic',[p1,p2,p3,p4,p5]);
772      * var p6 = board.create('point', [-1, 4]);
773      * var p7 = board.create('point', [2, -2]);
774      * var l1 = board.create('line', [p6, p7]);
775      * var p8 = board.create('polepoint', [c1, l1]);
776      * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-8018d0d17a98" class="jxgbox" style="width:400px; height:400px;"></div>
777      * <script type='text/javascript'>
778      * var ppex1_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-8018d0d17a98', {boundingbox: [-3, 5, 5, -3], axis: true, showcopyright: false, shownavigation: false});
779      * var ppex1_p1 = ppex1_board.create('point', [-1, 2]);
780      * var ppex1_p2 = ppex1_board.create('point', [ 1, 4]);
781      * var ppex1_p3 = ppex1_board.create('point', [-1,-2]);
782      * var ppex1_p4 = ppex1_board.create('point', [ 0, 0]);
783      * var ppex1_p5 = ppex1_board.create('point', [ 4,-2]);
784      * var ppex1_c1 = ppex1_board.create('conic',[ppex1_p1,ppex1_p2,ppex1_p3,ppex1_p4,ppex1_p5]);
785      * var ppex1_p6 = ppex1_board.create('point', [-1, 4]);
786      * var ppex1_p7 = ppex1_board.create('point', [2, -2]);
787      * var ppex1_l1 = ppex1_board.create('line', [ppex1_p6, ppex1_p7]);
788      * var ppex1_p8 = ppex1_board.create('polepoint', [ppex1_c1, ppex1_l1]);
789      * </script><pre>
790      * @example
791      * // Create the pole point of a line with respect to a circle
792      * var p1 = board.create('point', [1, 1]);
793      * var p2 = board.create('point', [2, 3]);
794      * var c1 = board.create('circle',[p1,p2]);
795      * var p3 = board.create('point', [-1, 4]);
796      * var p4 = board.create('point', [4, -1]);
797      * var l1 = board.create('line', [p3, p4]);
798      * var p5 = board.create('polepoint', [c1, l1]);
799      * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-9018d0d17a98" class="jxgbox" style="width:400px; height:400px;"></div>
800      * <script type='text/javascript'>
801      * var ppex2_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-9018d0d17a98', {boundingbox: [-3, 7, 7, -3], axis: true, showcopyright: false, shownavigation: false});
802      * var ppex2_p1 = ppex2_board.create('point', [1, 1]);
803      * var ppex2_p2 = ppex2_board.create('point', [2, 3]);
804      * var ppex2_c1 = ppex2_board.create('circle',[ppex2_p1,ppex2_p2]);
805      * var ppex2_p3 = ppex2_board.create('point', [-1, 4]);
806      * var ppex2_p4 = ppex2_board.create('point', [4, -1]);
807      * var ppex2_l1 = ppex2_board.create('line', [ppex2_p3, ppex2_p4]);
808      * var ppex2_p5 = ppex2_board.create('polepoint', [ppex2_c1, ppex2_l1]);
809      * </script><pre>
810      */
811     JXG.createPolePoint = function (board, parents, attributes) {
812         var el, el1, el2,
813             firstParentIsConic, secondParentIsConic,
814             firstParentIsLine, secondParentIsLine;
815 
816         if (parents.length > 1) {
817             firstParentIsConic = (parents[0].type === Const.OBJECT_TYPE_CONIC ||
818                 parents[0].elementClass === Const.OBJECT_CLASS_CIRCLE);
819             secondParentIsConic = (parents[1].type === Const.OBJECT_TYPE_CONIC ||
820                 parents[1].elementClass === Const.OBJECT_CLASS_CIRCLE);
821 
822             firstParentIsLine = (parents[0].elementClass === Const.OBJECT_CLASS_LINE);
823             secondParentIsLine = (parents[1].elementClass === Const.OBJECT_CLASS_LINE);
824         }
825 
826 /*        if (parents.length !== 2 || !((
827                 parents[0].type === Const.OBJECT_TYPE_CONIC ||
828                 parents[0].elementClass === Const.OBJECT_CLASS_CIRCLE) &&
829                 parents[1].elementClass === Const.OBJECT_CLASS_LINE ||
830                 parents[0].elementClass === Const.OBJECT_CLASS_LINE && (
831                 parents[1].type === Const.OBJECT_TYPE_CONIC ||
832                 parents[1].elementClass === Const.OBJECT_CLASS_CIRCLE))) {*/
833         if (parents.length !== 2 ||
834                 !((firstParentIsConic && secondParentIsLine) ||
835                     (firstParentIsLine && secondParentIsConic))) {
836             // Failure
837             throw new Error("JSXGraph: Can't create 'pole point' with parent types '" +
838                 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "'." +
839                 "\nPossible parent type: [conic|circle,line], [line,conic|circle]");
840         }
841 
842         if (secondParentIsLine) {
843             el1 = board.select(parents[0]);
844             el2 = board.select(parents[1]);
845         } else {
846             el1 = board.select(parents[1]);
847             el2 = board.select(parents[0]);
848         }
849 
850         el = board.create('point',
851             [function () {
852                 var q = el1.quadraticform,
853                     s = el2.stdform.slice(0, 3);
854 
855                 return [JXG.Math.Numerics.det([s, q[1], q[2]]),
856                         JXG.Math.Numerics.det([q[0], s, q[2]]),
857                         JXG.Math.Numerics.det([q[0], q[1], s])];
858             }], attributes);
859 
860         el.elType = 'polepoint';
861         el.setParents([el1.id, el2.id]);
862 
863         el1.addChild(el);
864         el2.addChild(el);
865 
866         return el;
867     };
868 
869     JXG.registerElement('point', JXG.createPoint);
870     JXG.registerElement('glider', JXG.createGlider);
871     JXG.registerElement('intersection', JXG.createIntersectionPoint);
872     JXG.registerElement('otherintersection', JXG.createOtherIntersectionPoint);
873     JXG.registerElement('polepoint', JXG.createPolePoint);
874 
875     return {
876         Point: JXG.Point,
877         createPoint: JXG.createPoint,
878         createGlider: JXG.createGlider,
879         createIntersection: JXG.createIntersectionPoint,
880         createOtherIntersection: JXG.createOtherIntersectionPoint,
881         createPolePoint: JXG.createPolePoint
882     };
883 });
884