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*/
 33 /*jslint nomen: true, plusplus: true, unparam: true*/
 34 
 35 import JXG from "../jxg.js";
 36 import Const from "./constants.js";
 37 import Coords from "./coords.js";
 38 import Mat from "../math/math.js";
 39 import Statistics from "../math/statistics.js";
 40 import Options from "../options.js";
 41 import EventEmitter from "../utils/event.js";
 42 import Color from "../utils/color.js";
 43 import Type from "../utils/type.js";
 44 
 45 /**
 46  * Constructs a new GeometryElement object.
 47  * @class This is the parent class for all geometry elements like points, circles, lines, curves...
 48  * @constructor
 49  * @param {JXG.Board} board Reference to the board the element is constructed on.
 50  * @param {Object} attributes Hash of attributes and their values.
 51  * @param {Number} type Element type (a <tt>JXG.OBJECT_TYPE_</tt> value).
 52  * @param {Number} oclass The element's class (a <tt>JXG.OBJECT_CLASS_</tt> value).
 53  * @borrows JXG.EventEmitter#on as this.on
 54  * @borrows JXG.EventEmitter#off as this.off
 55  * @borrows JXG.EventEmitter#triggerEventHandlers as this.triggerEventHandlers
 56  * @borrows JXG.EventEmitter#eventHandlers as this.eventHandlers
 57  */
 58 JXG.GeometryElement = function (board, attributes, type, oclass) {
 59     var name, key, attr;
 60 
 61     /**
 62      * Controls if updates are necessary
 63      * @type Boolean
 64      * @default true
 65      */
 66     this.needsUpdate = true;
 67 
 68     /**
 69      * Controls if this element can be dragged. In GEONExT only
 70      * free points and gliders can be dragged.
 71      * @type Boolean
 72      * @default false
 73      */
 74     this.isDraggable = false;
 75 
 76     /**
 77      * If element is in two dimensional real space this is true, else false.
 78      * @type Boolean
 79      * @default true
 80      */
 81     this.isReal = true;
 82 
 83     /**
 84      * Stores all dependent objects to be updated when this point is moved.
 85      * @type Object
 86      */
 87     this.childElements = {};
 88 
 89     /**
 90      * If element has a label subelement then this property will be set to true.
 91      * @type Boolean
 92      * @default false
 93      */
 94     this.hasLabel = false;
 95 
 96     /**
 97      * True, if the element is currently highlighted.
 98      * @type Boolean
 99      * @default false
100      */
101     this.highlighted = false;
102 
103     /**
104      * Stores all Intersection Objects which in this moment are not real and
105      * so hide this element.
106      * @type Object
107      */
108     this.notExistingParents = {};
109 
110     /**
111      * Keeps track of all objects drawn as part of the trace of the element.
112      * @see JXG.GeometryElement#clearTrace
113      * @see JXG.GeometryElement#numTraces
114      * @type Object
115      */
116     this.traces = {};
117 
118     /**
119      * Counts the number of objects drawn as part of the trace of the element.
120      * @see JXG.GeometryElement#clearTrace
121      * @see JXG.GeometryElement#traces
122      * @type Number
123      */
124     this.numTraces = 0;
125 
126     /**
127      * Stores the  transformations which are applied during update in an array
128      * @type Array
129      * @see JXG.Transformation
130      */
131     this.transformations = [];
132 
133     /**
134      * @type JXG.GeometryElement
135      * @default null
136      * @private
137      */
138     this.baseElement = null;
139 
140     /**
141      * Elements depending on this element are stored here.
142      * @type Object
143      */
144     this.descendants = {};
145 
146     /**
147      * Elements on which this element depends on are stored here.
148      * @type Object
149      */
150     this.ancestors = {};
151 
152     /**
153      * Ids of elements on which this element depends directly are stored here.
154      * @type Object
155      */
156     this.parents = [];
157 
158     /**
159      * Stores variables for symbolic computations
160      * @type Object
161      */
162     this.symbolic = {};
163 
164     /**
165      * Stores the SVG (or VML) rendering node for the element. This enables low-level
166      * access to SVG nodes. The properties of such an SVG node can then be changed
167      * by calling setAttribute(). Note that there are a few elements which consist
168      * of more than one SVG nodes:
169      * <ul>
170      * <li> Elements with arrow tail or head: rendNodeTriangleStart, rendNodeTriangleEnd
171      * <li> SVG (or VML) texts: rendNodeText
172      * <li> Button: rendNodeForm, rendNodeButton, rendNodeTag
173      * <li> Checkbox: rendNodeForm, rendNodeCheckbox, rendNodeLabel, rendNodeTag
174      * <li> Input: rendNodeForm, rendNodeInput, rendNodeLabel, rendNodeTag
175      * </ul>
176      *
177      * Here is are two examples: The first example shows how to access the SVG node,
178      * the second example demonstrates how to change SVG attributes.
179      * @example
180      *     var p1 = board.create('point', [0, 0]);
181      *     console.log(p1.rendNode);
182      *     // returns the full SVG node details of the point p1, something like:
183      *     // <ellipse id='box_jxgBoard1P6' stroke='#ff0000' stroke-opacity='1' stroke-width='2px'
184      *     //   fill='#ff0000' fill-opacity='1' cx='250' cy='250' rx='4' ry='4'
185      *     //   style='position: absolute;'>
186      *     // </ellipse>
187      *
188      * @example
189      *     var s = board.create('segment', [p1, p2], {strokeWidth: 60});
190      *     s.rendNode.setAttribute('stroke-linecap', 'round');
191      *
192      * @type Object
193      */
194     this.rendNode = null;
195 
196     /**
197      * The string used with {@link JXG.Board#create}
198      * @type String
199      */
200     this.elType = "";
201 
202     /**
203      * The element is saved with an explicit entry in the file (<tt>true</tt>) or implicitly
204      * via a composition.
205      * @type Boolean
206      * @default true
207      */
208     this.dump = true;
209 
210     /**
211      * Subs contains the subelements, created during the create method.
212      * @type Object
213      */
214     this.subs = {};
215 
216     /**
217      * Inherits contains the subelements, which may have an attribute
218      * (in particular the attribute "visible") having value 'inherit'.
219      * @type Object
220      */
221     this.inherits = [];
222 
223     /**
224      * The position of this element inside the {@link JXG.Board#objectsList}.
225      * @type Number
226      * @default -1
227      * @private
228      */
229     this._pos = -1;
230 
231     /**
232      * [c, b0, b1, a, k, r, q0, q1]
233      *
234      * See
235      * A.E. Middleditch, T.W. Stacey, and S.B. Tor:
236      * "Intersection Algorithms for Lines and Circles",
237      * ACM Transactions on Graphics, Vol. 8, 1, 1989, pp 25-40.
238      *
239      * The meaning of the parameters is:
240      * Circle: points p=[p0, p1] on the circle fulfill
241      *  a<p, p> + <b, p> + c = 0
242      * For convenience we also store
243      *  r: radius
244      *  k: discriminant = sqrt(<b,b>-4ac)
245      *  q=[q0, q1] center
246      *
247      * Points have radius = 0.
248      * Lines have radius = infinity.
249      * b: normalized vector, representing the direction of the line.
250      *
251      * Should be put into Coords, when all elements possess Coords.
252      * @type Array
253      * @default [1, 0, 0, 0, 1, 1, 0, 0]
254      */
255     this.stdform = [1, 0, 0, 0, 1, 1, 0, 0];
256 
257     /**
258      * The methodMap determines which methods can be called from within JessieCode and under which name it
259      * can be used. The map is saved in an object, the name of a property is the name of the method used in JessieCode,
260      * the value of a property is the name of the method in JavaScript.
261      * @type Object
262      */
263     this.methodMap = {
264         setLabel: "setLabel",
265         label: "label",
266         setName: "setName",
267         getName: "getName",
268         Name: "getName",
269         addTransform: "addTransform",
270         setProperty: "setAttribute",
271         setAttribute: "setAttribute",
272         addChild: "addChild",
273         animate: "animate",
274         on: "on",
275         off: "off",
276         trigger: "trigger",
277         addTicks: "addTicks",
278         removeTicks: "removeTicks",
279         removeAllTicks: "removeAllTicks",
280         Bounds: "bounds"
281     };
282 
283     /**
284      * Quadratic form representation of circles (and conics)
285      * @type Array
286      * @default [[1,0,0],[0,1,0],[0,0,1]]
287      */
288     this.quadraticform = [
289         [1, 0, 0],
290         [0, 1, 0],
291         [0, 0, 1]
292     ];
293 
294     /**
295      * An associative array containing all visual properties.
296      * @type Object
297      * @default empty object
298      */
299     this.visProp = {};
300 
301     /**
302      * An associative array containing visual properties which are calculated from
303      * the attribute values (i.e. visProp) and from other constraints.
304      * An example: if an intersection point does not have real coordinates,
305      * visPropCalc.visible is set to false.
306      * Additionally, the user can control visibility with the attribute "visible",
307      * even by supplying a functions as value.
308      *
309      * @type Object
310      * @default empty object
311      */
312     this.visPropCalc = {
313         visible: false
314     };
315 
316     EventEmitter.eventify(this);
317 
318     /**
319      * Is the mouse over this element?
320      * @type Boolean
321      * @default false
322      */
323     this.mouseover = false;
324 
325     /**
326      * Time stamp containing the last time this element has been dragged.
327      * @type Date
328      * @default creation time
329      */
330     this.lastDragTime = new Date();
331 
332     this.view = null;
333 
334     if (arguments.length > 0) {
335         /**
336          * Reference to the board associated with the element.
337          * @type JXG.Board
338          */
339         this.board = board;
340 
341         /**
342          * Type of the element.
343          * @constant
344          * @type Number
345          */
346         this.type = type;
347 
348         /**
349          * Original type of the element at construction time. Used for removing glider property.
350          * @constant
351          * @type Number
352          */
353         this._org_type = type;
354 
355         /**
356          * The element's class.
357          * @constant
358          * @type Number
359          */
360         this.elementClass = oclass || Const.OBJECT_CLASS_OTHER;
361 
362         /**
363          * Unique identifier for the element. Equivalent to id-attribute of renderer element.
364          * @type String
365          */
366         this.id = attributes.id;
367 
368         name = attributes.name;
369         /* If name is not set or null or even undefined, generate an unique name for this object */
370         if (!Type.exists(name)) {
371             name = this.board.generateName(this);
372         }
373 
374         if (name !== "") {
375             this.board.elementsByName[name] = this;
376         }
377 
378         /**
379          * Not necessarily unique name for the element.
380          * @type String
381          * @default Name generated by {@link JXG.Board#generateName}.
382          * @see JXG.Board#generateName
383          */
384         this.name = name;
385 
386         this.needsRegularUpdate = attributes.needsregularupdate;
387 
388         // create this.visPropOld and set default values
389         Type.clearVisPropOld(this);
390 
391         attr = this.resolveShortcuts(attributes);
392         for (key in attr) {
393             if (attr.hasOwnProperty(key)) {
394                 this._set(key, attr[key]);
395             }
396         }
397 
398         this.visProp.draft = attr.draft && attr.draft.draft;
399         //this.visProp.gradientangle = '270';
400         // this.visProp.gradientsecondopacity = this.evalVisProp('fillopacity');
401         //this.visProp.gradientpositionx = 0.5;
402         //this.visProp.gradientpositiony = 0.5;
403     }
404 };
405 
406 JXG.extend(
407     JXG.GeometryElement.prototype,
408     /** @lends JXG.GeometryElement.prototype */ {
409         /**
410          * Add an element as a child to the current element. Can be used to model dependencies between geometry elements.
411          * @param {JXG.GeometryElement} obj The dependent object.
412          */
413         addChild: function (obj) {
414             var el, el2;
415 
416             this.childElements[obj.id] = obj;
417             this.addDescendants(obj);
418             obj.ancestors[this.id] = this;
419 
420             for (el in this.descendants) {
421                 if (this.descendants.hasOwnProperty(el)) {
422                     this.descendants[el].ancestors[this.id] = this;
423 
424                     for (el2 in this.ancestors) {
425                         if (this.ancestors.hasOwnProperty(el2)) {
426                             this.descendants[el].ancestors[this.ancestors[el2].id] =
427                                 this.ancestors[el2];
428                         }
429                     }
430                 }
431             }
432 
433             for (el in this.ancestors) {
434                 if (this.ancestors.hasOwnProperty(el)) {
435                     for (el2 in this.descendants) {
436                         if (this.descendants.hasOwnProperty(el2)) {
437                             this.ancestors[el].descendants[this.descendants[el2].id] =
438                                 this.descendants[el2];
439                         }
440                     }
441                 }
442             }
443             return this;
444         },
445 
446         /**
447          * @param {JXG.GeometryElement} obj The element that is to be added to the descendants list.
448          * @private
449          * @return this
450         */
451         // Adds the given object to the descendants list of this object and all its child objects.
452         addDescendants: function (obj) {
453             var el;
454 
455             this.descendants[obj.id] = obj;
456             for (el in obj.childElements) {
457                 if (obj.childElements.hasOwnProperty(el)) {
458                     this.addDescendants(obj.childElements[el]);
459                 }
460             }
461             return this;
462         },
463 
464         /**
465          * Adds ids of elements to the array this.parents. This method needs to be called if some dependencies
466          * can not be detected automatically by JSXGraph. For example if a function graph is given by a function
467          * which refers to coordinates of a point, calling addParents() is necessary.
468          *
469          * @param {Array} parents Array of elements or ids of elements.
470          * Alternatively, one can give a list of objects as parameters.
471          * @returns {JXG.Object} reference to the object itself.
472          *
473          * @example
474          * // Movable function graph
475          * var A = board.create('point', [1, 0], {name:'A'}),
476          *     B = board.create('point', [3, 1], {name:'B'}),
477          *     f = board.create('functiongraph', function(x) {
478          *          var ax = A.X(),
479          *              ay = A.Y(),
480          *              bx = B.X(),
481          *              by = B.Y(),
482          *              a = (by - ay) / ( (bx - ax) * (bx - ax) );
483          *           return a * (x - ax) * (x - ax) + ay;
484          *      }, {fixed: false});
485          * f.addParents([A, B]);
486          * </pre><div class="jxgbox" id="JXG7c91d4d2-986c-4378-8135-24505027f251" style="width: 400px; height: 400px;"></div>
487          * <script type="text/javascript">
488          * (function() {
489          *   var board = JXG.JSXGraph.initBoard('JXG7c91d4d2-986c-4378-8135-24505027f251', {boundingbox: [-1, 9, 9, -1], axis: true, showcopyright: false, shownavigation: false});
490          *   var A = board.create('point', [1, 0], {name:'A'}),
491          *       B = board.create('point', [3, 1], {name:'B'}),
492          *       f = board.create('functiongraph', function(x) {
493          *            var ax = A.X(),
494          *                ay = A.Y(),
495          *                bx = B.X(),
496          *                by = B.Y(),
497          *                a = (by - ay) / ( (bx - ax) * (bx - ax) );
498          *             return a * (x - ax) * (x - ax) + ay;
499          *        }, {fixed: false});
500          *   f.addParents([A, B]);
501          * })();
502          * </script><pre>
503          *
504          **/
505         addParents: function (parents) {
506             var i, len, par;
507 
508             if (Type.isArray(parents)) {
509                 par = parents;
510             } else {
511                 par = arguments;
512             }
513 
514             len = par.length;
515             for (i = 0; i < len; ++i) {
516                 if (!Type.exists(par[i])) {
517                     continue;
518                 }
519                 if (Type.isId(this.board, par[i])) {
520                     this.parents.push(par[i]);
521                 } else if (Type.exists(par[i].id)) {
522                     this.parents.push(par[i].id);
523                 }
524             }
525             this.parents = Type.uniqueArray(this.parents);
526         },
527 
528         /**
529          * Sets ids of elements to the array this.parents.
530          * First, this.parents is cleared. See {@link JXG.GeometryElement#addParents}.
531          * @param {Array} parents Array of elements or ids of elements.
532          * Alternatively, one can give a list of objects as parameters.
533          * @returns {JXG.Object} reference to the object itself.
534          **/
535         setParents: function (parents) {
536             this.parents = [];
537             this.addParents(parents);
538         },
539 
540         /**
541          * Add dependence on elements in JessieCode functions.
542          * @param {Array} function_array Array of functions containing potential properties "deps" with
543          * elements the function depends on.
544          * @returns {JXG.Object} reference to the object itself
545          * @private
546          */
547         addParentsFromJCFunctions: function (function_array) {
548             var i, e, obj;
549             for (i = 0; i < function_array.length; i++) {
550                 for (e in function_array[i].deps) {
551                     obj = function_array[i].deps[e];
552                     this.addParents(obj);
553                     obj.addChild(this);
554                 }
555             }
556             return this;
557         },
558 
559         /**
560          * Remove an element as a child from the current element.
561          * @param {JXG.GeometryElement} obj The dependent object.
562          * @returns {JXG.Object} reference to the object itself
563          */
564         removeChild: function (obj) {
565             //var el, el2;
566 
567             delete this.childElements[obj.id];
568             this.removeDescendants(obj);
569             delete obj.ancestors[this.id];
570 
571             /*
572              // I do not know if these addDescendants stuff has to be adapted to removeChild. A.W.
573             for (el in this.descendants) {
574                 if (this.descendants.hasOwnProperty(el)) {
575                     delete this.descendants[el].ancestors[this.id];
576 
577                     for (el2 in this.ancestors) {
578                         if (this.ancestors.hasOwnProperty(el2)) {
579                             this.descendants[el].ancestors[this.ancestors[el2].id] = this.ancestors[el2];
580                         }
581                     }
582                 }
583             }
584 
585             for (el in this.ancestors) {
586                 if (this.ancestors.hasOwnProperty(el)) {
587                     for (el2 in this.descendants) {
588                         if (this.descendants.hasOwnProperty(el2)) {
589                             this.ancestors[el].descendants[this.descendants[el2].id] = this.descendants[el2];
590                         }
591                     }
592                 }
593             }
594             */
595             return this;
596         },
597 
598         /**
599          * Removes the given object from the descendants list of this object and all its child objects.
600          * @param {JXG.GeometryElement} obj The element that is to be removed from the descendants list.
601          * @private
602          * @returns {JXG.Object} reference to the object itself
603          */
604         removeDescendants: function (obj) {
605             var el;
606 
607             delete this.descendants[obj.id];
608             for (el in obj.childElements) {
609                 if (obj.childElements.hasOwnProperty(el)) {
610                     this.removeDescendants(obj.childElements[el]);
611                 }
612             }
613             return this;
614         },
615 
616         /**
617          * Counts the direct children of an object without counting labels.
618          * @private
619          * @returns {number} Number of children
620          */
621         countChildren: function () {
622             var prop,
623                 d,
624                 s = 0;
625 
626             d = this.childElements;
627             for (prop in d) {
628                 if (d.hasOwnProperty(prop) && prop.indexOf("Label") < 0) {
629                     s++;
630                 }
631             }
632             return s;
633         },
634 
635         /**
636          * Returns the elements name. Used in JessieCode.
637          * @returns {String}
638          */
639         getName: function () {
640             return this.name;
641         },
642 
643         /**
644          * Add transformations to this element.
645          * @param {JXG.Transformation|Array} transform Either one {@link JXG.Transformation}
646          * or an array of {@link JXG.Transformation}s.
647          * @returns {JXG.GeometryElement} Reference to the element.
648          */
649         addTransform: function (transform) {
650             return this;
651         },
652 
653         /**
654          * Decides whether an element can be dragged. This is used in
655          * {@link JXG.GeometryElement#setPositionDirectly} methods
656          * where all parent elements are checked if they may be dragged, too.
657          * @private
658          * @returns {boolean}
659          */
660         draggable: function () {
661             return (
662                 this.isDraggable &&
663                 !this.evalVisProp('fixed') &&
664                 // !this.visProp.frozen &&
665                 this.type !== Const.OBJECT_TYPE_GLIDER
666             );
667         },
668 
669         /**
670          * Translates the object by <tt>(x, y)</tt>. In case the element is defined by points, the defining points are
671          * translated, e.g. a circle constructed by a center point and a point on the circle line.
672          * @param {Number} method The type of coordinates used here.
673          * Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
674          * @param {Array} coords array of translation vector.
675          * @returns {JXG.GeometryElement} Reference to the element object.
676          *
677          * @see JXG.GeometryElement3D#setPosition2D
678          */
679         setPosition: function (method, coords) {
680             var parents = [],
681                 el,
682                 i, len, t;
683 
684             if (!Type.exists(this.parents)) {
685                 return this;
686             }
687 
688             len = this.parents.length;
689             for (i = 0; i < len; ++i) {
690                 el = this.board.select(this.parents[i]);
691                 if (Type.isPoint(el)) {
692                     if (!el.draggable()) {
693                         return this;
694                     }
695                     parents.push(el);
696                 }
697             }
698 
699             if (coords.length === 3) {
700                 coords = coords.slice(1);
701             }
702 
703             t = this.board.create("transform", coords, { type: "translate" });
704 
705             // We distinguish two cases:
706             // 1) elements which depend on free elements, i.e. arcs and sectors
707             // 2) other elements
708             //
709             // In the first case we simply transform the parents elements
710             // In the second case we add a transform to the element.
711             //
712             len = parents.length;
713             if (len > 0) {
714                 t.applyOnce(parents);
715 
716                 // Handle dragging of a 3D element
717                 if (Type.exists(this.view) && this.view.elType === 'view3d') {
718                     for (i = 0; i < this.parents.length; ++i) {
719                         // Search for the parent 3D element
720                         el = this.view.select(this.parents[i]);
721                         if (Type.exists(el.setPosition2D)) {
722                             el.setPosition2D(t);
723                         }
724                     }
725                 }
726 
727             } else {
728                 if (
729                     this.transformations.length > 0 &&
730                     this.transformations[this.transformations.length - 1].isNumericMatrix
731                 ) {
732                     this.transformations[this.transformations.length - 1].melt(t);
733                 } else {
734                     this.addTransform(t);
735                 }
736             }
737 
738             /*
739              * If - against the default configuration - defining gliders are marked as
740              * draggable, then their position has to be updated now.
741              */
742             for (i = 0; i < len; ++i) {
743                 if (parents[i].type === Const.OBJECT_TYPE_GLIDER) {
744                     parents[i].updateGlider();
745                 }
746             }
747 
748             return this;
749         },
750 
751         /**
752          * Moves an element by the difference of two coordinates.
753          * @param {Number} method The type of coordinates used here.
754          * Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
755          * @param {Array} coords coordinates in screen/user units
756          * @param {Array} oldcoords previous coordinates in screen/user units
757          * @returns {JXG.GeometryElement} this element
758          */
759         setPositionDirectly: function (method, coords, oldcoords) {
760             var c = new Coords(method, coords, this.board, false),
761                 oldc = new Coords(method, oldcoords, this.board, false),
762                 dc = Statistics.subtract(c.usrCoords, oldc.usrCoords);
763 
764             this.setPosition(Const.COORDS_BY_USER, dc);
765 
766             return this;
767         },
768 
769         /**
770          * Array of strings containing the polynomials defining the element.
771          * Used for determining geometric loci the groebner way.
772          * @returns {Array} An array containing polynomials describing the locus of the current object.
773          * @public
774          */
775         generatePolynomial: function () {
776             return [];
777         },
778 
779         /**
780          * Animates properties for that object like stroke or fill color, opacity and maybe
781          * even more later.
782          * @param {Object} hash Object containing properties with target values for the animation.
783          * @param {number} time Number of milliseconds to complete the animation.
784          * @param {Object} [options] Optional settings for the animation:<ul><li>callback: A function that is called as soon as the animation is finished.</li></ul>
785          * @returns {JXG.GeometryElement} A reference to the object
786          */
787         animate: function (hash, time, options) {
788             options = options || {};
789             var r,
790                 p,
791                 i,
792                 delay = this.board.attr.animationdelay,
793                 steps = Math.ceil(time / delay),
794                 self = this,
795                 animateColor = function (startRGB, endRGB, property) {
796                     var hsv1, hsv2, sh, ss, sv;
797                     hsv1 = Color.rgb2hsv(startRGB);
798                     hsv2 = Color.rgb2hsv(endRGB);
799 
800                     sh = (hsv2[0] - hsv1[0]) / steps;
801                     ss = (hsv2[1] - hsv1[1]) / steps;
802                     sv = (hsv2[2] - hsv1[2]) / steps;
803                     self.animationData[property] = [];
804 
805                     for (i = 0; i < steps; i++) {
806                         self.animationData[property][steps - i - 1] = Color.hsv2rgb(
807                             hsv1[0] + (i + 1) * sh,
808                             hsv1[1] + (i + 1) * ss,
809                             hsv1[2] + (i + 1) * sv
810                         );
811                     }
812                 },
813                 animateFloat = function (start, end, property, round) {
814                     var tmp, s;
815 
816                     start = parseFloat(start);
817                     end = parseFloat(end);
818 
819                     // we can't animate without having valid numbers.
820                     // And parseFloat returns NaN if the given string doesn't contain
821                     // a valid float number.
822                     if (isNaN(start) || isNaN(end)) {
823                         return;
824                     }
825 
826                     s = (end - start) / steps;
827                     self.animationData[property] = [];
828 
829                     for (i = 0; i < steps; i++) {
830                         tmp = start + (i + 1) * s;
831                         self.animationData[property][steps - i - 1] = round
832                             ? Math.floor(tmp)
833                             : tmp;
834                     }
835                 };
836 
837             this.animationData = {};
838 
839             for (r in hash) {
840                 if (hash.hasOwnProperty(r)) {
841                     p = r.toLowerCase();
842 
843                     switch (p) {
844                         case "strokecolor":
845                         case "fillcolor":
846                             animateColor(this.visProp[p], hash[r], p);
847                             break;
848                         case "size":
849                             if (!Type.isPoint(this)) {
850                                 break;
851                             }
852                             animateFloat(this.visProp[p], hash[r], p, true);
853                             break;
854                         case "strokeopacity":
855                         case "strokewidth":
856                         case "fillopacity":
857                             animateFloat(this.visProp[p], hash[r], p, false);
858                             break;
859                     }
860                 }
861             }
862 
863             this.animationCallback = options.callback;
864             this.board.addAnimation(this);
865             return this;
866         },
867 
868         /**
869          * General update method. Should be overwritten by the element itself.
870          * Can be used sometimes to commit changes to the object.
871          * @return {JXG.GeometryElement} Reference to the element
872          */
873         update: function () {
874             if (this.evalVisProp('trace')) {
875                 this.cloneToBackground();
876             }
877             return this;
878         },
879 
880         /**
881          * Provide updateRenderer method.
882          * @return {JXG.GeometryElement} Reference to the element
883          * @private
884          */
885         updateRenderer: function () {
886             return this;
887         },
888 
889         /**
890          * Run through the full update chain of an element.
891          * @param  {Boolean} visible Set visibility in case the elements attribute value is 'inherit'. null is allowed.
892          * @return {JXG.GeometryElement} Reference to the element
893          * @private
894          */
895         fullUpdate: function (visible) {
896             return this.prepareUpdate().update().updateVisibility(visible).updateRenderer();
897         },
898 
899         /**
900          * Show the element or hide it. If hidden, it will still exist but not be
901          * visible on the board.
902          * <p>
903          * Sets also the display of the inherits elements. These can be
904          * JSXGraph elements or arrays of JSXGraph elements.
905          * However, deeper nesting than this is not supported.
906          *
907          * @param  {Boolean} val true: show the element, false: hide the element
908          * @return {JXG.GeometryElement} Reference to the element
909          * @private
910          */
911         setDisplayRendNode: function (val) {
912             var i, len, s, len_s, obj;
913 
914             if (val === undefined) {
915                 val = this.visPropCalc.visible;
916             }
917 
918             if (val === this.visPropOld.visible) {
919                 return this;
920             }
921 
922             // Set display of the element itself
923             this.board.renderer.display(this, val);
924 
925             // Set the visibility of elements which inherit the attribute 'visible'
926             len = this.inherits.length;
927             for (s = 0; s < len; s++) {
928                 obj = this.inherits[s];
929                 if (Type.isArray(obj)) {
930                     len_s = obj.length;
931                     for (i = 0; i < len_s; i++) {
932                         if (
933                             Type.exists(obj[i]) &&
934                             Type.exists(obj[i].rendNode) &&
935                             obj[i].evalVisProp('visible') === 'inherit'
936                         ) {
937                             obj[i].setDisplayRendNode(val);
938                         }
939                     }
940                 } else {
941                     if (
942                         Type.exists(obj) &&
943                         Type.exists(obj.rendNode) &&
944                         obj.evalVisProp('visible') === 'inherit'
945                     ) {
946                         obj.setDisplayRendNode(val);
947                     }
948                 }
949             }
950 
951             // Set the visibility of the label if it inherits the attribute 'visible'
952             if (this.hasLabel && Type.exists(this.label) && Type.exists(this.label.rendNode)) {
953                 if (this.label.evalVisProp('visible') === "inherit") {
954                     this.label.setDisplayRendNode(val);
955                 }
956             }
957 
958             return this;
959         },
960 
961         /**
962          * Hide the element. It will still exist but not be visible on the board.
963          * Alias for "element.setAttribute({visible: false});"
964          * @return {JXG.GeometryElement} Reference to the element
965          */
966         hide: function () {
967             this.setAttribute({ visible: false });
968             return this;
969         },
970 
971         /**
972          * Hide the element. It will still exist but not be visible on the board.
973          * Alias for {@link JXG.GeometryElement#hide}
974          * @returns {JXG.GeometryElement} Reference to the element
975          */
976         hideElement: function () {
977             this.hide();
978             return this;
979         },
980 
981         /**
982          * Make the element visible.
983          * Alias for "element.setAttribute({visible: true});"
984          * @return {JXG.GeometryElement} Reference to the element
985          */
986         show: function () {
987             this.setAttribute({ visible: true });
988             return this;
989         },
990 
991         /**
992          * Make the element visible.
993          * Alias for {@link JXG.GeometryElement#show}
994          * @returns {JXG.GeometryElement} Reference to the element
995          */
996         showElement: function () {
997             this.show();
998             return this;
999         },
1000 
1001         /**
1002          * Set the visibility of an element. The visibility is influenced by
1003          * (listed in ascending priority):
1004          * <ol>
1005          * <li> The value of the element's attribute 'visible'
1006          * <li> The visibility of a parent element. (Example: label)
1007          * This overrules the value of the element's attribute value only if
1008          * this attribute value of the element is 'inherit'.
1009          * <li> being inside of the canvas
1010          * </ol>
1011          * <p>
1012          * This method is called three times for most elements:
1013          * <ol>
1014          * <li> between {@link JXG.GeometryElement#update}
1015          * and {@link JXG.GeometryElement#updateRenderer}. In case the value is 'inherit', nothing is done.
1016          * <li> Recursively, called by itself for child elements. Here, 'inherit' is overruled by the parent's value.
1017          * <li> In {@link JXG.GeometryElement#updateRenderer}, if the element is outside of the canvas.
1018          * </ol>
1019          *
1020          * @param  {Boolean} parent_val Visibility of the parent element.
1021          * @return {JXG.GeometryElement} Reference to the element.
1022          * @private
1023          */
1024         updateVisibility: function (parent_val) {
1025             var i, len, s, len_s, obj, val;
1026 
1027             if (this.needsUpdate) {
1028                 if (Type.exists(this.view) && this.view.evalVisProp('visible') === false) {
1029                     // Handle hiding of view3d
1030                     this.visPropCalc.visible = false;
1031 
1032                 } else {
1033                     // Handle the element
1034                     if (parent_val !== undefined) {
1035                         this.visPropCalc.visible = parent_val;
1036                     } else {
1037                         val = this.evalVisProp('visible');
1038 
1039                         // infobox uses hiddenByParent
1040                         if (Type.exists(this.hiddenByParent) && this.hiddenByParent) {
1041                             val = false;
1042                         }
1043                         if (val !== "inherit") {
1044                             this.visPropCalc.visible = val;
1045                         }
1046                     }
1047 
1048                     // Handle elements which inherit the visibility
1049                     len = this.inherits.length;
1050                     for (s = 0; s < len; s++) {
1051                         obj = this.inherits[s];
1052                         if (Type.isArray(obj)) {
1053                             len_s = obj.length;
1054                             for (i = 0; i < len_s; i++) {
1055                                 if (
1056                                     Type.exists(obj[i]) /*&& Type.exists(obj[i].rendNode)*/ &&
1057                                     obj[i].evalVisProp('visible') === "inherit"
1058                                 ) {
1059                                     obj[i]
1060                                         .prepareUpdate()
1061                                         .updateVisibility(this.visPropCalc.visible);
1062                                 }
1063                             }
1064                         } else {
1065                             if (
1066                                 Type.exists(obj) /*&& Type.exists(obj.rendNode)*/ &&
1067                                 obj.evalVisProp('visible') === "inherit"
1068                             ) {
1069                                 obj.prepareUpdate().updateVisibility(this.visPropCalc.visible);
1070                             }
1071                         }
1072                     }
1073                 }
1074 
1075                 // Handle the label if it inherits the visibility
1076                 if (
1077                     Type.exists(this.label) &&
1078                     Type.exists(this.label.visProp) &&
1079                     this.label.evalVisProp('visible')
1080                 ) {
1081                     this.label.prepareUpdate().updateVisibility(this.visPropCalc.visible);
1082                 }
1083             }
1084             return this;
1085         },
1086 
1087         /**
1088          * Sets the value of attribute <tt>key</tt> to <tt>value</tt>.
1089          * Here, mainly hex strings for rga(a) colors are parsed and values of type object get a special treatment.
1090          * Other values are just set to the key.
1091          *
1092          * @param {String} key The attribute's name.
1093          * @param value The new value
1094          * @private
1095          */
1096         _set: function (key, value) {
1097             var el;
1098 
1099             key = key.toLocaleLowerCase();
1100 
1101             // Search for entries in visProp with "color" as part of the key name
1102             // and containing a RGBA string
1103             if (
1104                 this.visProp.hasOwnProperty(key) &&
1105                 key.indexOf("color") >= 0 &&
1106                 Type.isString(value) &&
1107                 value.length === 9 &&
1108                 value.charAt(0) === "#"
1109             ) {
1110                 value = Color.rgba2rgbo(value);
1111                 this.visProp[key] = value[0];
1112                 // Previously: *=. But then, we can only decrease opacity.
1113                 this.visProp[key.replace("color", "opacity")] = value[1];
1114             } else {
1115                 if (
1116                     value !== null &&
1117                     Type.isObject(value) &&
1118                     !Type.exists(value.id) &&
1119                     !Type.exists(value.name)
1120                 ) {
1121                     // value is of type {prop: val, prop: val,...}
1122                     // Convert these attributes to lowercase, too
1123                     this.visProp[key] = {};
1124                     for (el in value) {
1125                         if (value.hasOwnProperty(el)) {
1126                             this.visProp[key][el.toLocaleLowerCase()] = value[el];
1127                         }
1128                     }
1129                 } else {
1130                     this.visProp[key] = value;
1131                 }
1132             }
1133         },
1134 
1135         /**
1136          * Resolves attribute shortcuts like <tt>color</tt> and expands them, e.g. <tt>strokeColor</tt> and <tt>fillColor</tt>.
1137          * Writes the expanded attributes back to the given <tt>attributes</tt>.
1138          * @param {Object} attributes object
1139          * @returns {Object} The given attributes object with shortcuts expanded.
1140          * @private
1141          */
1142         resolveShortcuts: function (attributes) {
1143             var key, i, j,
1144                 subattr = ["traceattributes", "traceAttributes"];
1145 
1146             for (key in Options.shortcuts) {
1147                 if (Options.shortcuts.hasOwnProperty(key)) {
1148                     if (Type.exists(attributes[key])) {
1149                         for (i = 0; i < Options.shortcuts[key].length; i++) {
1150                             if (!Type.exists(attributes[Options.shortcuts[key][i]])) {
1151                                 attributes[Options.shortcuts[key][i]] = attributes[key];
1152                             }
1153                         }
1154                     }
1155                     for (j = 0; j < subattr.length; j++) {
1156                         if (Type.isObject(attributes[subattr[j]])) {
1157                             attributes[subattr[j]] = this.resolveShortcuts(
1158                                 attributes[subattr[j]]
1159                             );
1160                         }
1161                     }
1162                 }
1163             }
1164             return attributes;
1165         },
1166 
1167         /**
1168          * Sets a label and its text
1169          * If label doesn't exist, it creates one
1170          * @param {String} str
1171          */
1172         setLabel: function (str) {
1173             if (!this.hasLabel) {
1174                 this.setAttribute({ withlabel: true });
1175             }
1176             this.setLabelText(str);
1177         },
1178 
1179         /**
1180          * Updates the element's label text, strips all html.
1181          * @param {String} str
1182          */
1183         setLabelText: function (str) {
1184             if (Type.exists(this.label)) {
1185                 str = str.replace(/</g, "<").replace(/>/g, ">");
1186                 this.label.setText(str);
1187             }
1188 
1189             return this;
1190         },
1191 
1192         /**
1193          * Updates the element's label text and the element's attribute "name", strips all html.
1194          * @param {String} str
1195          */
1196         setName: function (str) {
1197             str = str.replace(/</g, "<").replace(/>/g, ">");
1198             if (this.elType !== "slider") {
1199                 this.setLabelText(str);
1200             }
1201             this.setAttribute({ name: str });
1202         },
1203 
1204         /**
1205          * Deprecated alias for {@link JXG.GeometryElement#setAttribute}.
1206          * @deprecated Use {@link JXG.GeometryElement#setAttribute}.
1207          */
1208         setProperty: function () {
1209             JXG.deprecated("setProperty()", "setAttribute()");
1210             this.setAttribute.apply(this, arguments);
1211         },
1212 
1213         /**
1214          * Sets an arbitrary number of attributes. This method has one or more
1215          * parameters of the following types:
1216          * <ul>
1217          * <li> object: {key1:value1,key2:value2,...}
1218          * <li> string: 'key:value'
1219          * <li> array: ['key', value]
1220          * </ul>
1221          * @param {Object} attributes An object with attributes.
1222          * @returns {JXG.GeometryElement} A reference to the element.
1223          *
1224          * @function
1225          * @example
1226          * // Set attribute directly on creation of an element using the attributes object parameter
1227          * var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 5, 5, 1]};
1228          * var p = board.create('point', [2, 2], {visible: false});
1229          *
1230          * // Now make this point visible and fixed:
1231          * p.setAttribute({
1232          *     fixed: true,
1233          *     visible: true
1234          * });
1235          */
1236         setAttribute: function (attr) {
1237             var i, j, le, key, value, arg,
1238                 opacity, pair, oldvalue,
1239                 attributes = {};
1240 
1241             // Normalize the user input
1242             for (i = 0; i < arguments.length; i++) {
1243                 arg = arguments[i];
1244                 if (Type.isString(arg)) {
1245                     // pairRaw is string of the form 'key:value'
1246                     pair = arg.split(":");
1247                     attributes[Type.trim(pair[0])] = Type.trim(pair[1]);
1248                 } else if (!Type.isArray(arg)) {
1249                     // pairRaw consists of objects of the form {key1:value1,key2:value2,...}
1250                     JXG.extend(attributes, arg);
1251                 } else {
1252                     // pairRaw consists of array [key,value]
1253                     attributes[arg[0]] = arg[1];
1254                 }
1255             }
1256 
1257             // Handle shortcuts
1258             attributes = this.resolveShortcuts(attributes);
1259 
1260             for (i in attributes) {
1261                 if (attributes.hasOwnProperty(i)) {
1262                     key = i.replace(/\s+/g, "").toLowerCase();
1263                     value = attributes[i];
1264 
1265                     // This handles the subobjects, if the key:value pairs are contained in an object.
1266                     // Example:
1267                     // ticks.setAttribute({
1268                     //      strokeColor: 'blue',
1269                     //      label: {
1270                     //          visible: false
1271                     //      }
1272                     // })
1273                     // Now, only the supplied label attributes are overwritten.
1274                     // Otherwise, the value of label would be {visible:false} only.
1275                     if (Type.isObject(value) && Type.exists(this.visProp[key])) {
1276                         // this.visProp[key] = Type.merge(this.visProp[key], value);
1277                         if (!Type.isObject(this.visProp[key]) && Type.isObject(value)) {
1278                             // Handle cases like key=firstarrow and
1279                             // firstarrow==false and value = { type:1 }.
1280                             // That is a primitive type is replaced by an object.
1281                             this.visProp[key] = {};
1282                         }
1283                         Type.mergeAttr(this.visProp[key], value);
1284 
1285                         // First, handle the special case
1286                         // ticks.setAttribute({label: {anchorX: "right", ..., visible: true});
1287                         if (this.type === Const.OBJECT_TYPE_TICKS && Type.exists(this.labels)) {
1288                             le = this.labels.length;
1289                             for (j = 0; j < le; j++) {
1290                                 this.labels[j].setAttribute(value);
1291                             }
1292                         } else if (Type.exists(this[key])) {
1293                             // Attribute looks like: point1: {...}
1294                             // Handle this in the sub-element: this.point1.setAttribute({...})
1295                             if (Type.isArray(this[key])) {
1296                                 for (j = 0; j < this[key].length; j++) {
1297                                     this[key][j].setAttribute(value);
1298                                 }
1299                             } else {
1300                                 this[key].setAttribute(value);
1301                             }
1302                         } else {
1303                             // Cases like firstarrow: {...}
1304                             oldvalue = null;
1305                             this.triggerEventHandlers(["attribute:" + key], [oldvalue, value, this]);
1306                         }
1307                         continue;
1308                     }
1309 
1310                     oldvalue = this.visProp[key];
1311                     switch (key) {
1312                         case "checked":
1313                             // checkbox Is not available on initial call.
1314                             if (Type.exists(this.rendNodeTag)) {
1315                                 this.rendNodeCheckbox.checked = !!value;
1316                             }
1317                             break;
1318                         case "disabled":
1319                             // button, checkbox, input. Is not available on initial call.
1320                             if (Type.exists(this.rendNodeTag)) {
1321                                 this.rendNodeTag.disabled = !!value;
1322                             }
1323                             break;
1324                         case "face":
1325                             if (Type.isPoint(this)) {
1326                                 this.visProp.face = value;
1327                                 this.board.renderer.changePointStyle(this);
1328                             }
1329                             break;
1330                         case "generatelabelvalue":
1331                             if (
1332                                 this.type === Const.OBJECT_TYPE_TICKS &&
1333                                 Type.isFunction(value)
1334                             ) {
1335                                 this.generateLabelValue = value;
1336                             }
1337                             break;
1338                         case "gradient":
1339                             this.visProp.gradient = value;
1340                             this.board.renderer.setGradient(this);
1341                             break;
1342                         case "gradientsecondcolor":
1343                             value = Color.rgba2rgbo(value);
1344                             this.visProp.gradientsecondcolor = value[0];
1345                             this.visProp.gradientsecondopacity = value[1];
1346                             this.board.renderer.updateGradient(this);
1347                             break;
1348                         case "gradientsecondopacity":
1349                             this.visProp.gradientsecondopacity = value;
1350                             this.board.renderer.updateGradient(this);
1351                             break;
1352                         case "infoboxtext":
1353                             if (Type.isString(value)) {
1354                                 this.infoboxText = value;
1355                             } else {
1356                                 this.infoboxText = false;
1357                             }
1358                             break;
1359                         case "labelcolor":
1360                             value = Color.rgba2rgbo(value);
1361                             opacity = value[1];
1362                             value = value[0];
1363                             if (opacity === 0) {
1364                                 if (Type.exists(this.label) && this.hasLabel) {
1365                                     this.label.hideElement();
1366                                 }
1367                             }
1368                             if (Type.exists(this.label) && this.hasLabel) {
1369                                 this.label.visProp.strokecolor = value;
1370                                 this.board.renderer.setObjectStrokeColor(
1371                                     this.label,
1372                                     value,
1373                                     opacity
1374                                 );
1375                             }
1376                             if (this.elementClass === Const.OBJECT_CLASS_TEXT) {
1377                                 this.visProp.strokecolor = value;
1378                                 this.visProp.strokeopacity = opacity;
1379                                 this.board.renderer.setObjectStrokeColor(this, value, opacity);
1380                             }
1381                             break;
1382                         case "layer":
1383                             this.board.renderer.setLayer(this, this.eval(value));
1384                             this._set(key, value);
1385                             break;
1386                         case "maxlength":
1387                             // input. Is not available on initial call.
1388                             if (Type.exists(this.rendNodeTag)) {
1389                                 this.rendNodeTag.maxlength = !!value;
1390                             }
1391                             break;
1392                         case "name":
1393                             oldvalue = this.name;
1394                             delete this.board.elementsByName[this.name];
1395                             this.name = value;
1396                             this.board.elementsByName[this.name] = this;
1397                             break;
1398                         case "needsregularupdate":
1399                             this.needsRegularUpdate = !(value === "false" || value === false);
1400                             this.board.renderer.setBuffering(
1401                                 this,
1402                                 this.needsRegularUpdate ? "auto" : "static"
1403                             );
1404                             break;
1405                         case "onpolygon":
1406                             if (this.type === Const.OBJECT_TYPE_GLIDER) {
1407                                 this.onPolygon = !!value;
1408                             }
1409                             break;
1410                         case "radius":
1411                             if (
1412                                 this.type === Const.OBJECT_TYPE_ANGLE ||
1413                                 this.type === Const.OBJECT_TYPE_SECTOR
1414                             ) {
1415                                 this.setRadius(value);
1416                             }
1417                             break;
1418                         case "rotate":
1419                             if (
1420                                 (this.elementClass === Const.OBJECT_CLASS_TEXT &&
1421                                     this.evalVisProp('display') === "internal") ||
1422                                 this.type === Const.OBJECT_TYPE_IMAGE
1423                             ) {
1424                                 this.addRotation(value);
1425                             }
1426                             break;
1427                         case "tabindex":
1428                             if (Type.exists(this.rendNode)) {
1429                                 this.rendNode.setAttribute("tabindex", value);
1430                                 this._set(key, value);
1431                             }
1432                             break;
1433                         // case "ticksdistance":
1434                         //     if (this.type === Const.OBJECT_TYPE_TICKS && Type.isNumber(value)) {
1435                         //         this.ticksFunction = this.makeTicksFunction(value);
1436                         //     }
1437                         //     break;
1438                         case "trace":
1439                             if (value === "false" || value === false) {
1440                                 this.clearTrace();
1441                                 this.visProp.trace = false;
1442                             } else if (value === "pause") {
1443                                 this.visProp.trace = false;
1444                             } else {
1445                                 this.visProp.trace = true;
1446                             }
1447                             break;
1448                         case "visible":
1449                             if (value === "false") {
1450                                 this.visProp.visible = false;
1451                             } else if (value === "true") {
1452                                 this.visProp.visible = true;
1453                             } else {
1454                                 this.visProp.visible = value;
1455                             }
1456 
1457                             this.setDisplayRendNode(this.evalVisProp('visible'));
1458                             if (
1459                                 this.evalVisProp('visible') &&
1460                                 Type.exists(this.updateSize)
1461                             ) {
1462                                 this.updateSize();
1463                             }
1464 
1465                             break;
1466                         case "withlabel":
1467                             this.visProp.withlabel = value;
1468                             if (!this.evalVisProp('withlabel')) {
1469                                 if (this.label && this.hasLabel) {
1470                                     //this.label.hideElement();
1471                                     this.label.setAttribute({ visible: false });
1472                                 }
1473                             } else {
1474                                 if (!this.label) {
1475                                     this.createLabel();
1476                                 }
1477                                 //this.label.showElement();
1478                                 this.label.setAttribute({ visible: "inherit" });
1479                                 //this.label.setDisplayRendNode(this.evalVisProp('visible'));
1480                             }
1481                             this.hasLabel = value;
1482                             break;
1483                         case "straightfirst":
1484                         case "straightlast":
1485                             this._set(key, value);
1486                             for (j in this.childElements) {
1487                                 if (this.childElements.hasOwnProperty(j) && this.childElements[j].elType === 'glider') {
1488                                     this.childElements[j].fullUpdate();
1489                                 }
1490                             }
1491                             break;
1492                         default:
1493                             if (Type.exists(this.visProp[key]) &&
1494                                 (!JXG.Validator[key] ||                                   // No validator for this key => OK
1495                                     (JXG.Validator[key] && JXG.Validator[key](value)) ||  // Value passes the validator => OK
1496                                     (JXG.Validator[key] &&                                // Value is function, function value passes the validator => OK
1497                                         Type.isFunction(value) && JXG.Validator[key](value(this))
1498                                     )
1499                                 )
1500                             ) {
1501                                 value = (value.toLowerCase && value.toLowerCase() === "false")
1502                                             ? false
1503                                             : value;
1504                                 this._set(key, value);
1505                             } else {
1506                                 JXG.warn("attribute '" + key + "' does not accept type '" + (typeof value) + "' of value " + value + ".");
1507                             }
1508                             break;
1509                     }
1510                     this.triggerEventHandlers(["attribute:" + key], [oldvalue, value, this]);
1511                 }
1512             }
1513 
1514             this.triggerEventHandlers(["attribute"], [attributes, this]);
1515 
1516             if (!this.evalVisProp('needsregularupdate')) {
1517                 this.board.fullUpdate();
1518             } else {
1519                 this.board.update(this);
1520             }
1521             if (this.elementClass === Const.OBJECT_CLASS_TEXT) {
1522                 this.updateSize();
1523             }
1524 
1525             return this;
1526         },
1527 
1528         /**
1529          * Deprecated alias for {@link JXG.GeometryElement#getAttribute}.
1530          * @deprecated Use {@link JXG.GeometryElement#getAttribute}.
1531          */
1532         getProperty: function () {
1533             JXG.deprecated("getProperty()", "getAttribute()");
1534             this.getProperty.apply(this, arguments);
1535         },
1536 
1537         /**
1538          * Get the value of the property <tt>key</tt>.
1539          * @param {String} key The name of the property you are looking for
1540          * @returns The value of the property
1541          */
1542         getAttribute: function (key) {
1543             var result;
1544             key = key.toLowerCase();
1545 
1546             switch (key) {
1547                 case "needsregularupdate":
1548                     result = this.needsRegularUpdate;
1549                     break;
1550                 case "labelcolor":
1551                     result = this.label.visProp.strokecolor;
1552                     break;
1553                 case "infoboxtext":
1554                     result = this.infoboxText;
1555                     break;
1556                 case "withlabel":
1557                     result = this.hasLabel;
1558                     break;
1559                 default:
1560                     result = this.visProp[key];
1561                     break;
1562             }
1563 
1564             return result;
1565         },
1566 
1567         /**
1568          * Get value of an attribute. If the value that attribute is a function, call the function and return its value.
1569          * In that case, the function is called with the GeometryElement as (only) parameter. For label elements (i.e.
1570          * if the attribute "islabel" is true), the anchor element is supplied. The label element can be accessed as
1571          * sub-object "label".
1572          * If the attribute does not exist, undefined will be returned.
1573          *
1574          * @param {String} key Attribute key
1575          * @returns {String|Number|Boolean} value of attribute "key" (evaluated in case of a function) or undefined
1576          *
1577          * @see GeometryElement#eval
1578          * @see JXG#evaluate
1579          */
1580         evalVisProp: function (key) {
1581             var val, arr, i, le;
1582 
1583             key = key.toLowerCase();
1584             if (key.indexOf('.') === -1) {
1585                 // e.g. 'visible'
1586                 val = this.visProp[key];
1587             } else {
1588                 // e.g. label.visible
1589                 arr = key.split('.');
1590                 le = arr.length;
1591                 val = this.visProp;
1592                 for (i = 0; i < le; i++) {
1593                     val = val[arr[i]];
1594                 }
1595             }
1596 
1597             if (JXG.isFunction(val)) {
1598                 // For labels supply the anchor element as parameter.
1599                 if (this.visProp.islabel === true && Type.exists(this.visProp.anchor)) {
1600                     // 3D: supply the 3D element
1601                     if (this.visProp.anchor.visProp.element3d !== null) {
1602                         return val(this.visProp.anchor.visProp.element3d);
1603                     }
1604                     // 2D: supply the 2D element
1605                     return val(this.visProp.anchor);
1606                 }
1607                 // For 2D elements representing 3D elements, return the 3D element.
1608                 if (JXG.exists(this.visProp.element3d)) {
1609                     return val(this.visProp.element3d);
1610                 }
1611                 // In all other cases, return the element itself
1612                 return val(this);
1613             }
1614             // val is not of type function
1615             return val;
1616         },
1617 
1618         /**
1619          * Get value of a parameter. If the parameter is a function, call the function and return its value.
1620          * In that case, the function is called with the GeometryElement as (only) parameter. For label elements (i.e.
1621          * if the attribute "islabel" is true), the anchor element is supplied. The label of an element can be accessed as
1622          * sub-object "label" then.
1623          *
1624          * @param {String|Number|Function|Object} val If not a function, it will be returned as is. If function it will be evaluated, where the GeometryElement is
1625          * supplied as the (only) parameter of that function.
1626          * @returns {String|Number|Object}
1627          *
1628          * @see GeometryElement#evalVisProp
1629          * @see JXG#evaluate
1630          */
1631         eval: function(val) {
1632             if (JXG.isFunction(val)) {
1633                 // For labels supply the anchor element as parameter.
1634                 if (this.visProp.islabel === true && Type.exists(this.visProp.anchor)) {
1635                     // 3D: supply the 3D element
1636                     if (this.visProp.anchor.visProp.element3d !== null) {
1637                         return val(this.visProp.anchor.visProp.element3d);
1638                     }
1639                     // 2D: supply the 2D element
1640                     return val(this.visProp.anchor);
1641                 }
1642                 // For 2D elements representing 3D elements, return the 3D element.
1643                 if (this.visProp.element3d !== null) {
1644                     return val(this.visProp.element3d);
1645                 }
1646                 // In all other cases, return the element itself
1647                 return val(this);
1648             }
1649             // val is not of type function
1650             return val;
1651         },
1652 
1653         /**
1654          * Set the dash style of an object. See {@link JXG.GeometryElement#dash}
1655          * for a list of available dash styles.
1656          * You should use {@link JXG.GeometryElement#setAttribute} instead of this method.
1657          *
1658          * @param {number} dash Indicates the new dash style
1659          * @private
1660          */
1661         setDash: function (dash) {
1662             this.setAttribute({ dash: dash });
1663             return this;
1664         },
1665 
1666         /**
1667          * Notify all child elements for updates.
1668          * @private
1669          */
1670         prepareUpdate: function () {
1671             this.needsUpdate = true;
1672             return this;
1673         },
1674 
1675         /**
1676          * Removes the element from the construction.  This only removes the SVG or VML node of the element and its label (if available) from
1677          * the renderer, to remove the element completely you should use {@link JXG.Board#removeObject}.
1678          */
1679         remove: function () {
1680             // this.board.renderer.remove(this.board.renderer.getElementById(this.id));
1681             this.board.renderer.remove(this.rendNode);
1682 
1683             if (this.hasLabel) {
1684                 this.board.renderer.remove(this.board.renderer.getElementById(this.label.id));
1685             }
1686             return this;
1687         },
1688 
1689         /**
1690          * Returns the coords object where a text that is bound to the element shall be drawn.
1691          * Differs in some cases from the values that getLabelAnchor returns.
1692          * @returns {JXG.Coords} JXG.Coords Place where the text shall be drawn.
1693          * @see JXG.GeometryElement#getLabelAnchor
1694          */
1695         getTextAnchor: function () {
1696             return new Coords(Const.COORDS_BY_USER, [0, 0], this.board);
1697         },
1698 
1699         /**
1700          * Returns the coords object where the label of the element shall be drawn.
1701          * Differs in some cases from the values that getTextAnchor returns.
1702          * @returns {JXG.Coords} JXG.Coords Place where the text shall be drawn.
1703          * @see JXG.GeometryElement#getTextAnchor
1704          */
1705         getLabelAnchor: function () {
1706             return new Coords(Const.COORDS_BY_USER, [0, 0], this.board);
1707         },
1708 
1709         /**
1710          * Determines whether the element has arrows at start or end of the arc.
1711          * If it is set to be a "typical" vector, ie lastArrow == true,
1712          * then the element.type is set to VECTOR.
1713          * @param {Boolean} firstArrow True if there is an arrow at the start of the arc, false otherwise.
1714          * @param {Boolean} lastArrow True if there is an arrow at the end of the arc, false otherwise.
1715          */
1716         setArrow: function (firstArrow, lastArrow) {
1717             this.visProp.firstarrow = firstArrow;
1718             this.visProp.lastarrow = lastArrow;
1719             if (lastArrow) {
1720                 this.type = Const.OBJECT_TYPE_VECTOR;
1721                 this.elType = "arrow";
1722             }
1723 
1724             this.prepareUpdate().update().updateVisibility().updateRenderer();
1725             return this;
1726         },
1727 
1728         /**
1729          * Creates a gradient nodes in the renderer.
1730          * @see JXG.SVGRenderer#setGradient
1731          * @private
1732          */
1733         createGradient: function () {
1734             var ev_g = this.evalVisProp('gradient');
1735             if (ev_g === "linear" || ev_g === "radial") {
1736                 this.board.renderer.setGradient(this);
1737             }
1738         },
1739 
1740         /**
1741          * Creates a label element for this geometry element.
1742          * @see JXG.GeometryElement#addLabelToElement
1743          */
1744         createLabel: function () {
1745             var attr,
1746                 that = this;
1747 
1748             // this is a dirty hack to resolve the text-dependency. If there is no text element available,
1749             // just don't create a label. This method is usually not called by a user, so we won't throw
1750             // an exception here and simply output a warning via JXG.debug.
1751             if (JXG.elements.text) {
1752                 attr = Type.deepCopy(this.visProp.label, null);
1753                 attr.id = this.id + "Label";
1754                 attr.isLabel = true;
1755                 attr.anchor = this;
1756                 attr.priv = this.visProp.priv;
1757 
1758                 if (this.visProp.withlabel) {
1759                     this.label = JXG.elements.text(
1760                         this.board,
1761                         [
1762                             0,
1763                             0,
1764                             function () {
1765                                 if (Type.isFunction(that.name)) {
1766                                     return that.name(that);
1767                                 }
1768                                 return that.name;
1769                             }
1770                         ],
1771                         attr
1772                     );
1773                     this.label.needsUpdate = true;
1774                     this.label.dump = false;
1775                     this.label.fullUpdate();
1776 
1777                     this.hasLabel = true;
1778                 }
1779             } else {
1780                 JXG.debug(
1781                     "JSXGraph: Can't create label: text element is not available. Make sure you include base/text"
1782                 );
1783             }
1784 
1785             return this;
1786         },
1787 
1788         /**
1789          * Highlights the element.
1790          * @private
1791          * @param {Boolean} [force=false] Force the highlighting
1792          * @returns {JXG.Board}
1793          */
1794         highlight: function (force) {
1795             force = Type.def(force, false);
1796             // I know, we have the JXG.Board.highlightedObjects AND JXG.GeometryElement.highlighted and YES we need both.
1797             // Board.highlightedObjects is for the internal highlighting and GeometryElement.highlighted is for user highlighting
1798             // initiated by the user, e.g. through custom DOM events. We can't just pick one because this would break user
1799             // defined highlighting in many ways:
1800             //  * if overriding the highlight() methods the user had to handle the highlightedObjects stuff, otherwise he'd break
1801             //    everything (e.g. the pie chart example https://jsxgraph.org/wiki/index.php/Pie_chart (not exactly
1802             //    user defined but for this type of chart the highlight method was overridden and not adjusted to the changes in here)
1803             //    where it just kept highlighting until the radius of the pie was far beyond infinity...
1804             //  * user defined highlighting would get pointless, everytime the user highlights something using .highlight(), it would get
1805             //    dehighlighted immediately, because highlight puts the element into highlightedObjects and from there it gets dehighlighted
1806             //    through dehighlightAll.
1807 
1808             // highlight only if not highlighted
1809             if (this.evalVisProp('highlight') && (!this.highlighted || force)) {
1810                 this.highlighted = true;
1811                 this.board.highlightedObjects[this.id] = this;
1812                 this.board.renderer.highlight(this);
1813             }
1814             return this;
1815         },
1816 
1817         /**
1818          * Uses the "normal" properties of the element.
1819          * @returns {JXG.Board}
1820          */
1821         noHighlight: function () {
1822             // see comment in JXG.GeometryElement.highlight()
1823 
1824             // dehighlight only if not highlighted
1825             if (this.highlighted) {
1826                 this.highlighted = false;
1827                 delete this.board.highlightedObjects[this.id];
1828                 this.board.renderer.noHighlight(this);
1829             }
1830             return this;
1831         },
1832 
1833         /**
1834          * Removes all objects generated by the trace function.
1835          */
1836         clearTrace: function () {
1837             var obj;
1838 
1839             for (obj in this.traces) {
1840                 if (this.traces.hasOwnProperty(obj)) {
1841                     this.board.renderer.remove(this.traces[obj]);
1842                 }
1843             }
1844 
1845             this.numTraces = 0;
1846             return this;
1847         },
1848 
1849         /**
1850          * Copy the element to background. This is used for tracing elements.
1851          * @returns {JXG.GeometryElement} A reference to the element
1852          */
1853         cloneToBackground: function () {
1854             return this;
1855         },
1856 
1857         /**
1858          * Dimensions of the smallest rectangle enclosing the element.
1859          * @returns {Array} The coordinates of the enclosing rectangle in a format
1860          * like the bounding box in {@link JXG.Board#setBoundingBox}.
1861          *
1862          * @returns {Array} similar to {@link JXG.Board#setBoundingBox}.
1863          */
1864         bounds: function () {
1865             return [0, 0, 0, 0];
1866         },
1867 
1868         /**
1869          * Normalize the element's standard form.
1870          * @private
1871          */
1872         normalize: function () {
1873             this.stdform = Mat.normalize(this.stdform);
1874             return this;
1875         },
1876 
1877         /**
1878          * EXPERIMENTAL. Generate JSON object code of visProp and other properties.
1879          * @type String
1880          * @private
1881          * @ignore
1882          * @deprecated
1883          * @returns JSON string containing element's properties.
1884          */
1885         toJSON: function () {
1886             var vis,
1887                 key,
1888                 json = ['{"name":', this.name];
1889 
1890             json.push(", " + '"id":' + this.id);
1891 
1892             vis = [];
1893             for (key in this.visProp) {
1894                 if (this.visProp.hasOwnProperty(key)) {
1895                     if (Type.exists(this.visProp[key])) {
1896                         vis.push('"' + key + '":' + this.visProp[key]);
1897                     }
1898                 }
1899             }
1900             json.push(', "visProp":{' + vis.toString() + "}");
1901             json.push("}");
1902 
1903             return json.join("");
1904         },
1905 
1906         /**
1907          * Rotate texts or images by a given degree.
1908          * @param {number} angle The degree of the rotation (90 means vertical text).
1909          * @see JXG.GeometryElement#rotate
1910          */
1911         addRotation: function (angle) {
1912             var tOffInv,
1913                 tOff,
1914                 tS,
1915                 tSInv,
1916                 tRot,
1917                 that = this;
1918 
1919             if (
1920                 (this.elementClass === Const.OBJECT_CLASS_TEXT ||
1921                     this.type === Const.OBJECT_TYPE_IMAGE) &&
1922                 angle !== 0
1923             ) {
1924                 tOffInv = this.board.create(
1925                     "transform",
1926                     [
1927                         function () {
1928                             return -that.X();
1929                         },
1930                         function () {
1931                             return -that.Y();
1932                         }
1933                     ],
1934                     { type: "translate" }
1935                 );
1936 
1937                 tOff = this.board.create(
1938                     "transform",
1939                     [
1940                         function () {
1941                             return that.X();
1942                         },
1943                         function () {
1944                             return that.Y();
1945                         }
1946                     ],
1947                     { type: "translate" }
1948                 );
1949 
1950                 tS = this.board.create(
1951                     "transform",
1952                     [
1953                         function () {
1954                             return that.board.unitX / that.board.unitY;
1955                         },
1956                         function () {
1957                             return 1;
1958                         }
1959                     ],
1960                     { type: "scale" }
1961                 );
1962 
1963                 tSInv = this.board.create(
1964                     "transform",
1965                     [
1966                         function () {
1967                             return that.board.unitY / that.board.unitX;
1968                         },
1969                         function () {
1970                             return 1;
1971                         }
1972                     ],
1973                     { type: "scale" }
1974                 );
1975 
1976                 tRot = this.board.create(
1977                     "transform",
1978                     [
1979                         function () {
1980                             return (that.eval(angle) * Math.PI) / 180;
1981                         }
1982                     ],
1983                     { type: "rotate" }
1984                 );
1985 
1986                 tOffInv.bindTo(this);
1987                 tS.bindTo(this);
1988                 tRot.bindTo(this);
1989                 tSInv.bindTo(this);
1990                 tOff.bindTo(this);
1991             }
1992 
1993             return this;
1994         },
1995 
1996         /**
1997          * Set the highlightStrokeColor of an element
1998          * @ignore
1999          * @name JXG.GeometryElement#highlightStrokeColorMethod
2000          * @param {String} sColor String which determines the stroke color of an object when its highlighted.
2001          * @see JXG.GeometryElement#highlightStrokeColor
2002          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2003          */
2004         highlightStrokeColor: function (sColor) {
2005             JXG.deprecated("highlightStrokeColor()", "setAttribute()");
2006             this.setAttribute({ highlightStrokeColor: sColor });
2007             return this;
2008         },
2009 
2010         /**
2011          * Set the strokeColor of an element
2012          * @ignore
2013          * @name JXG.GeometryElement#strokeColorMethod
2014          * @param {String} sColor String which determines the stroke color of an object.
2015          * @see JXG.GeometryElement#strokeColor
2016          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2017          */
2018         strokeColor: function (sColor) {
2019             JXG.deprecated("strokeColor()", "setAttribute()");
2020             this.setAttribute({ strokeColor: sColor });
2021             return this;
2022         },
2023 
2024         /**
2025          * Set the strokeWidth of an element
2026          * @ignore
2027          * @name JXG.GeometryElement#strokeWidthMethod
2028          * @param {Number} width Integer which determines the stroke width of an outline.
2029          * @see JXG.GeometryElement#strokeWidth
2030          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2031          */
2032         strokeWidth: function (width) {
2033             JXG.deprecated("strokeWidth()", "setAttribute()");
2034             this.setAttribute({ strokeWidth: width });
2035             return this;
2036         },
2037 
2038         /**
2039          * Set the fillColor of an element
2040          * @ignore
2041          * @name JXG.GeometryElement#fillColorMethod
2042          * @param {String} fColor String which determines the fill color of an object.
2043          * @see JXG.GeometryElement#fillColor
2044          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2045          */
2046         fillColor: function (fColor) {
2047             JXG.deprecated("fillColor()", "setAttribute()");
2048             this.setAttribute({ fillColor: fColor });
2049             return this;
2050         },
2051 
2052         /**
2053          * Set the highlightFillColor of an element
2054          * @ignore
2055          * @name JXG.GeometryElement#highlightFillColorMethod
2056          * @param {String} fColor String which determines the fill color of an object when its highlighted.
2057          * @see JXG.GeometryElement#highlightFillColor
2058          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2059          */
2060         highlightFillColor: function (fColor) {
2061             JXG.deprecated("highlightFillColor()", "setAttribute()");
2062             this.setAttribute({ highlightFillColor: fColor });
2063             return this;
2064         },
2065 
2066         /**
2067          * Set the labelColor of an element
2068          * @ignore
2069          * @param {String} lColor String which determines the text color of an object's label.
2070          * @see JXG.GeometryElement#labelColor
2071          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2072          */
2073         labelColor: function (lColor) {
2074             JXG.deprecated("labelColor()", "setAttribute()");
2075             this.setAttribute({ labelColor: lColor });
2076             return this;
2077         },
2078 
2079         /**
2080          * Set the dash type of an element
2081          * @ignore
2082          * @name JXG.GeometryElement#dashMethod
2083          * @param {Number} d Integer which determines the way of dashing an element's outline.
2084          * @see JXG.GeometryElement#dash
2085          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2086          */
2087         dash: function (d) {
2088             JXG.deprecated("dash()", "setAttribute()");
2089             this.setAttribute({ dash: d });
2090             return this;
2091         },
2092 
2093         /**
2094          * Set the visibility of an element
2095          * @ignore
2096          * @name JXG.GeometryElement#visibleMethod
2097          * @param {Boolean} v Boolean which determines whether the element is drawn.
2098          * @see JXG.GeometryElement#visible
2099          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2100          */
2101         visible: function (v) {
2102             JXG.deprecated("visible()", "setAttribute()");
2103             this.setAttribute({ visible: v });
2104             return this;
2105         },
2106 
2107         /**
2108          * Set the shadow of an element
2109          * @ignore
2110          * @name JXG.GeometryElement#shadowMethod
2111          * @param {Boolean} s Boolean which determines whether the element has a shadow or not.
2112          * @see JXG.GeometryElement#shadow
2113          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2114          */
2115         shadow: function (s) {
2116             JXG.deprecated("shadow()", "setAttribute()");
2117             this.setAttribute({ shadow: s });
2118             return this;
2119         },
2120 
2121         /**
2122          * The type of the element as used in {@link JXG.Board#create}.
2123          * @returns {String}
2124          */
2125         getType: function () {
2126             return this.elType;
2127         },
2128 
2129         /**
2130          * List of the element ids resp. values used as parents in {@link JXG.Board#create}.
2131          * @returns {Array}
2132          */
2133         getParents: function () {
2134             return Type.isArray(this.parents) ? this.parents : [];
2135         },
2136 
2137         /**
2138          * @ignore
2139          * @private
2140          * Snaps the element to the grid. Only works for points, lines and circles. Points will snap to the grid
2141          * as defined in their properties {@link JXG.Point#snapSizeX} and {@link JXG.Point#snapSizeY}. Lines and circles
2142          * will snap their parent points to the grid, if they have {@link JXG.Point#snapToGrid} set to true.
2143          * @returns {JXG.GeometryElement} Reference to the element.
2144          */
2145         snapToGrid: function () {
2146             return this;
2147         },
2148 
2149         /**
2150          * Snaps the element to points. Only works for points. Points will snap to the next point
2151          * as defined in their properties {@link JXG.Point#attractorDistance} and {@link JXG.Point#attractorUnit}.
2152          * Lines and circles
2153          * will snap their parent points to points.
2154          * @private
2155          * @returns {JXG.GeometryElement} Reference to the element.
2156          */
2157         snapToPoints: function () {
2158             return this;
2159         },
2160 
2161         /**
2162          * Retrieve a copy of the current visProp.
2163          * @returns {Object}
2164          */
2165         getAttributes: function () {
2166             var attributes = Type.deepCopy(this.visProp),
2167                 /*
2168                 cleanThis = ['attractors', 'snatchdistance', 'traceattributes', 'frozen',
2169                     'shadow', 'gradientangle', 'gradientsecondopacity', 'gradientpositionx', 'gradientpositiony',
2170                     'needsregularupdate', 'zoom', 'layer', 'offset'],
2171                 */
2172                 cleanThis = [],
2173                 i,
2174                 len = cleanThis.length;
2175 
2176             attributes.id = this.id;
2177             attributes.name = this.name;
2178 
2179             for (i = 0; i < len; i++) {
2180                 delete attributes[cleanThis[i]];
2181             }
2182 
2183             return attributes;
2184         },
2185 
2186         /**
2187          * Checks whether (x,y) is near the element.
2188          * @param {Number} x Coordinate in x direction, screen coordinates.
2189          * @param {Number} y Coordinate in y direction, screen coordinates.
2190          * @returns {Boolean} True if (x,y) is near the element, False otherwise.
2191          */
2192         hasPoint: function (x, y) {
2193             return false;
2194         },
2195 
2196         /**
2197          * Adds ticks to this line or curve. Ticks can be added to a curve or any kind of line: line, arrow, and axis.
2198          * @param {JXG.Ticks} ticks Reference to a ticks object which is describing the ticks (color, distance, how many, etc.).
2199          * @returns {String} Id of the ticks object.
2200          */
2201         addTicks: function (ticks) {
2202             if (ticks.id === "" || !Type.exists(ticks.id)) {
2203                 ticks.id = this.id + "_ticks_" + (this.ticks.length + 1);
2204             }
2205 
2206             this.board.renderer.drawTicks(ticks);
2207             this.ticks.push(ticks);
2208 
2209             return ticks.id;
2210         },
2211 
2212         /**
2213          * Removes all ticks from a line or curve.
2214          */
2215         removeAllTicks: function () {
2216             var t;
2217             if (Type.exists(this.ticks)) {
2218                 for (t = this.ticks.length - 1; t >= 0; t--) {
2219                     this.removeTicks(this.ticks[t]);
2220                 }
2221                 this.ticks = [];
2222                 this.board.update();
2223             }
2224         },
2225 
2226         /**
2227          * Removes ticks identified by parameter named tick from this line or curve.
2228          * @param {JXG.Ticks} tick Reference to tick object to remove.
2229          */
2230         removeTicks: function (tick) {
2231             var t, j;
2232 
2233             if (Type.exists(this.defaultTicks) && this.defaultTicks === tick) {
2234                 this.defaultTicks = null;
2235             }
2236 
2237             if (Type.exists(this.ticks)) {
2238                 for (t = this.ticks.length - 1; t >= 0; t--) {
2239                     if (this.ticks[t] === tick) {
2240                         this.board.removeObject(this.ticks[t]);
2241 
2242                         if (this.ticks[t].ticks) {
2243                             for (j = 0; j < this.ticks[t].ticks.length; j++) {
2244                                 if (Type.exists(this.ticks[t].labels[j])) {
2245                                     this.board.removeObject(this.ticks[t].labels[j]);
2246                                 }
2247                             }
2248                         }
2249 
2250                         delete this.ticks[t];
2251                         break;
2252                     }
2253                 }
2254             }
2255         },
2256 
2257         /**
2258          * Determine values of snapSizeX and snapSizeY. If the attributes
2259          * snapSizex and snapSizeY are greater than zero, these values are taken.
2260          * Otherwise, determine the distance between major ticks of the
2261          * default axes.
2262          * @returns {Array} containing the snap sizes for x and y direction.
2263          * @private
2264          */
2265         getSnapSizes: function () {
2266             var sX, sY, ticks;
2267 
2268             sX = this.evalVisProp('snapsizex');
2269             sY = this.evalVisProp('snapsizey');
2270 
2271             if (sX <= 0 && this.board.defaultAxes && this.board.defaultAxes.x.defaultTicks) {
2272                 ticks = this.board.defaultAxes.x.defaultTicks;
2273                 sX = ticks.ticksDelta * (ticks.evalVisProp('minorticks') + 1);
2274             }
2275 
2276             if (sY <= 0 && this.board.defaultAxes && this.board.defaultAxes.y.defaultTicks) {
2277                 ticks = this.board.defaultAxes.y.defaultTicks;
2278                 sY = ticks.ticksDelta * (ticks.evalVisProp('minorticks') + 1);
2279             }
2280 
2281             return [sX, sY];
2282         },
2283 
2284         /**
2285          * Move an element to its nearest grid point.
2286          * The function uses the coords object of the element as
2287          * its actual position. If there is no coords object or if the object is fixed, nothing is done.
2288          * @param {Boolean} force force snapping independent from what the snaptogrid attribute says
2289          * @param {Boolean} fromParent True if the drag comes from a child element. This is the case if a line
2290          *    through two points is dragged. In this case we do not try to force the points to stay inside of
2291          *    the visible board, but the distance between the two points stays constant.
2292          * @returns {JXG.GeometryElement} Reference to this element
2293          */
2294         handleSnapToGrid: function (force, fromParent) {
2295             var x, y, rx, ry, rcoords,
2296                 mi, ma,
2297                 boardBB, res, sX, sY,
2298                 needsSnapToGrid = false,
2299                 attractToGrid = this.evalVisProp('attracttogrid'),
2300                 ev_au = this.evalVisProp('attractorunit'),
2301                 ev_ad = this.evalVisProp('attractordistance');
2302 
2303             if (!Type.exists(this.coords) || this.evalVisProp('fixed')) {
2304                 return this;
2305             }
2306 
2307             needsSnapToGrid =
2308                 this.evalVisProp('snaptogrid') || attractToGrid || force === true;
2309 
2310             if (needsSnapToGrid) {
2311                 x = this.coords.usrCoords[1];
2312                 y = this.coords.usrCoords[2];
2313                 res = this.getSnapSizes();
2314                 sX = res[0];
2315                 sY = res[1];
2316 
2317                 // If no valid snap sizes are available, don't change the coords.
2318                 if (sX > 0 && sY > 0) {
2319                     boardBB = this.board.getBoundingBox();
2320                     rx = Math.round(x / sX) * sX;
2321                     ry = Math.round(y / sY) * sY;
2322 
2323                     rcoords = new JXG.Coords(Const.COORDS_BY_USER, [rx, ry], this.board);
2324                     if (
2325                         !attractToGrid ||
2326                         rcoords.distance(
2327                             ev_au === "screen" ? Const.COORDS_BY_SCREEN : Const.COORDS_BY_USER,
2328                             this.coords
2329                         ) < ev_ad
2330                     ) {
2331                         x = rx;
2332                         y = ry;
2333                         // Checking whether x and y are still within boundingBox.
2334                         // If not, adjust them to remain within the board.
2335                         // Otherwise a point may become invisible.
2336                         if (!fromParent) {
2337                             mi = Math.min(boardBB[0], boardBB[2]);
2338                             ma = Math.max(boardBB[0], boardBB[2]);
2339                             if (x < mi && x > mi - sX) {
2340                                 x += sX;
2341                             } else if (x > ma && x < ma + sX) {
2342                                 x -= sX;
2343                             }
2344 
2345                             mi = Math.min(boardBB[1], boardBB[3]);
2346                             ma = Math.max(boardBB[1], boardBB[3]);
2347                             if (y < mi && y > mi - sY) {
2348                                 y += sY;
2349                             } else if (y > ma && y < ma + sY) {
2350                                 y -= sY;
2351                             }
2352                         }
2353                         this.coords.setCoordinates(Const.COORDS_BY_USER, [x, y]);
2354                     }
2355                 }
2356             }
2357             return this;
2358         },
2359 
2360         getBoundingBox: function () {
2361             var i, le, v,
2362                 x, y, r,
2363                 bb = [Infinity, Infinity, -Infinity, -Infinity];
2364 
2365             if (this.type === Const.OBJECT_TYPE_POLYGON) {
2366                 le = this.vertices.length - 1;
2367                 if (le <= 0) {
2368                     return bb;
2369                 }
2370                 for (i = 0; i < le; i++) {
2371                     v = this.vertices[i].X();
2372                     bb[0] = v < bb[0] ? v : bb[0];
2373                     bb[2] = v > bb[2] ? v : bb[2];
2374                     v = this.vertices[i].Y();
2375                     bb[1] = v < bb[1] ? v : bb[1];
2376                     bb[3] = v > bb[3] ? v : bb[3];
2377                 }
2378             } else if (this.elementClass === Const.OBJECT_CLASS_CIRCLE) {
2379                 x = this.center.X();
2380                 y = this.center.Y();
2381                 bb = [x - this.radius, y + this.radius, x + this.radius, y - this.radius];
2382             } else if (this.elementClass === Const.OBJECT_CLASS_CURVE) {
2383                 le = this.points.length;
2384                 if (le === 0) {
2385                     return bb;
2386                 }
2387                 for (i = 0; i < le; i++) {
2388                     v = this.points[i].usrCoords[1];
2389                     bb[0] = v < bb[0] ? v : bb[0];
2390                     bb[2] = v > bb[2] ? v : bb[2];
2391                     v = this.points[i].usrCoords[1];
2392                     bb[1] = v < bb[1] ? v : bb[1];
2393                     bb[3] = v > bb[3] ? v : bb[3];
2394                 }
2395             } else if (this.elementClass === Const.OBJECT_CLASS_POINT) {
2396                 x = this.X();
2397                 y = this.Y();
2398                 r = this.evalVisProp('size');
2399                 bb = [x - r / this.board.unitX, y - r / this.board.unitY, x + r / this.board.unitX, y + r / this.board.unitY];
2400             }
2401 
2402             return bb;
2403         },
2404 
2405         /**
2406          * Alias of {@link JXG.EventEmitter.on}.
2407          *
2408          * @name addEvent
2409          * @memberof JXG.GeometryElement
2410          * @function
2411          */
2412         addEvent: JXG.shortcut(JXG.GeometryElement.prototype, 'on'),
2413 
2414         /**
2415          * Alias of {@link JXG.EventEmitter.off}.
2416          *
2417          * @name removeEvent
2418          * @memberof JXG.GeometryElement
2419          * @function
2420          */
2421         removeEvent: JXG.shortcut(JXG.GeometryElement.prototype, 'off'),
2422 
2423         /**
2424          * Format a number according to the locale set in the attribute "intl".
2425          * If in the options of the intl-attribute "maximumFractionDigits" is not set,
2426          * the optional parameter digits is used instead.
2427          * See <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Intl/NumberFormat/NumberFormat">https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Intl/NumberFormat/NumberFormat</a>
2428          * for more  information about internationalization.
2429          *
2430          * @param {Number} value Number to be formatted
2431          * @param {Number} [digits=undefined] Optional number of digits
2432          * @returns {String|Number} string containing the formatted number according to the locale
2433          * or the number itself of the formatting is not possible.
2434          */
2435         formatNumberLocale: function (value, digits) {
2436             var loc, opt, key,
2437                 optCalc = {},
2438                 // These options are case sensitive:
2439                 translate = {
2440                     maximumfractiondigits: 'maximumFractionDigits',
2441                     minimumfractiondigits: 'minimumFractionDigits',
2442                     compactdisplay: 'compactDisplay',
2443                     currencydisplay: 'currencyDisplay',
2444                     currencysign: 'currencySign',
2445                     localematcher: 'localeMatcher',
2446                     numberingsystem: 'numberingSystem',
2447                     signdisplay: 'signDisplay',
2448                     unitdisplay: 'unitDisplay',
2449                     usegrouping: 'useGrouping',
2450                     roundingmode: 'roundingMode',
2451                     roundingpriority: 'roundingPriority',
2452                     roundingincrement: 'roundingIncrement',
2453                     trailingzerodisplay: 'trailingZeroDisplay',
2454                     minimumintegerdigits: 'minimumIntegerDigits',
2455                     minimumsignificantdigits: 'minimumSignificantDigits',
2456                     maximumsignificantdigits: 'maximumSignificantDigits'
2457                 };
2458 
2459             if (Type.exists(Intl) &&
2460                 this.useLocale()) {
2461 
2462                 loc = this.evalVisProp('intl.locale') ||
2463                     this.eval(this.board.attr.intl.locale);
2464                 opt = this.evalVisProp('intl.options') || {};
2465 
2466                 // Transfer back to camel case if necessary and evaluate
2467                 for (key in opt) {
2468                     if (opt.hasOwnProperty(key)) {
2469                         if (translate.hasOwnProperty(key)) {
2470                             optCalc[translate[key]] = this.eval(opt[key]);
2471                         } else {
2472                             optCalc[key] = this.eval(opt[key]);
2473                         }
2474                     }
2475                 }
2476 
2477                 // If maximumfractiondigits is not set,
2478                 // the value of the attribute "digits" is taken instead.
2479                 key = 'maximumfractiondigits';
2480                 if (!Type.exists(opt[key])) {
2481                     optCalc[translate[key]] = digits;
2482 
2483                     // key = 'minimumfractiondigits';
2484                     // if (!this.eval(opt[key]) || this.eval(opt[key]) > digits) {
2485                     //     optCalc[translate[key]] = digits;
2486                     // }
2487                 }
2488 
2489                 return Intl.NumberFormat(loc, optCalc).format(value);
2490             }
2491 
2492             return value;
2493         },
2494 
2495         /**
2496          * Checks if locale is enabled in the attribute. This may be in the attributes of the board,
2497          * or in the attributes of the text. The latter has higher priority. The board attribute is taken if
2498          * attribute "intl.enabled" of the text element is set to 'inherit'.
2499          *
2500          * @returns {Boolean} if locale can be used for number formatting.
2501          */
2502         useLocale: function () {
2503             var val;
2504 
2505             // Check if element supports intl
2506             if (!Type.exists(this.visProp.intl) ||
2507                 !Type.exists(this.visProp.intl.enabled)) {
2508                 return false;
2509             }
2510 
2511             // Check if intl is supported explicitly enabled for this element
2512             val = this.evalVisProp('intl.enabled');
2513 
2514             if (val === true) {
2515                 return true;
2516             }
2517 
2518             // Check intl attribute of the board
2519             if (val === 'inherit') {
2520                 if (this.eval(this.board.attr.intl.enabled) === true) {
2521                     return true;
2522                 }
2523             }
2524 
2525             return false;
2526         },
2527 
2528         /* **************************
2529          *     EVENT DEFINITION
2530          * for documentation purposes
2531          * ************************** */
2532 
2533         //region Event handler documentation
2534         /**
2535          * @event
2536          * @description This event is fired whenever the user is hovering over an element.
2537          * @name JXG.GeometryElement#over
2538          * @param {Event} e The browser's event object.
2539          */
2540         __evt__over: function (e) { },
2541 
2542         /**
2543          * @event
2544          * @description This event is fired whenever the user puts the mouse over an element.
2545          * @name JXG.GeometryElement#mouseover
2546          * @param {Event} e The browser's event object.
2547          */
2548         __evt__mouseover: function (e) { },
2549 
2550         /**
2551          * @event
2552          * @description This event is fired whenever the user is leaving an element.
2553          * @name JXG.GeometryElement#out
2554          * @param {Event} e The browser's event object.
2555          */
2556         __evt__out: function (e) { },
2557 
2558         /**
2559          * @event
2560          * @description This event is fired whenever the user puts the mouse away from an element.
2561          * @name JXG.GeometryElement#mouseout
2562          * @param {Event} e The browser's event object.
2563          */
2564         __evt__mouseout: function (e) { },
2565 
2566         /**
2567          * @event
2568          * @description This event is fired whenever the user is moving over an element.
2569          * @name JXG.GeometryElement#move
2570          * @param {Event} e The browser's event object.
2571          */
2572         __evt__move: function (e) { },
2573 
2574         /**
2575          * @event
2576          * @description This event is fired whenever the user is moving the mouse over an element.
2577          * @name JXG.GeometryElement#mousemove
2578          * @param {Event} e The browser's event object.
2579          */
2580         __evt__mousemove: function (e) { },
2581 
2582         /**
2583          * @event
2584          * @description This event is fired whenever the user drags an element.
2585          * @name JXG.GeometryElement#drag
2586          * @param {Event} e The browser's event object.
2587          */
2588         __evt__drag: function (e) { },
2589 
2590         /**
2591          * @event
2592          * @description This event is fired whenever the user drags the element with a mouse.
2593          * @name JXG.GeometryElement#mousedrag
2594          * @param {Event} e The browser's event object.
2595          */
2596         __evt__mousedrag: function (e) { },
2597 
2598         /**
2599          * @event
2600          * @description This event is fired whenever the user drags the element with a pen.
2601          * @name JXG.GeometryElement#pendrag
2602          * @param {Event} e The browser's event object.
2603          */
2604         __evt__pendrag: function (e) { },
2605 
2606         /**
2607          * @event
2608          * @description This event is fired whenever the user drags the element on a touch device.
2609          * @name JXG.GeometryElement#touchdrag
2610          * @param {Event} e The browser's event object.
2611          */
2612         __evt__touchdrag: function (e) { },
2613 
2614         /**
2615          * @event
2616          * @description This event is fired whenever the user drags the element by pressing arrow keys
2617          * on the keyboard.
2618          * @name JXG.GeometryElement#keydrag
2619          * @param {Event} e The browser's event object.
2620          */
2621         __evt__keydrag: function (e) { },
2622 
2623         /**
2624          * @event
2625          * @description Whenever the user starts to touch or click an element.
2626          * @name JXG.GeometryElement#down
2627          * @param {Event} e The browser's event object.
2628          */
2629         __evt__down: function (e) { },
2630 
2631         /**
2632          * @event
2633          * @description Whenever the user starts to click an element.
2634          * @name JXG.GeometryElement#mousedown
2635          * @param {Event} e The browser's event object.
2636          */
2637         __evt__mousedown: function (e) { },
2638 
2639         /**
2640          * @event
2641          * @description Whenever the user taps an element with the pen.
2642          * @name JXG.GeometryElement#pendown
2643          * @param {Event} e The browser's event object.
2644          */
2645         __evt__pendown: function (e) { },
2646 
2647         /**
2648          * @event
2649          * @description Whenever the user starts to touch an element.
2650          * @name JXG.GeometryElement#touchdown
2651          * @param {Event} e The browser's event object.
2652          */
2653         __evt__touchdown: function (e) { },
2654 
2655         /**
2656          * @event
2657          * @description Whenever the user clicks on an element.
2658          * @name JXG.Board#click
2659          * @param {Event} e The browser's event object.
2660          */
2661         __evt__click: function (e) { },
2662 
2663         /**
2664          * @event
2665          * @description Whenever the user double clicks on an element.
2666          * This event works on desktop browser, but is undefined
2667          * on mobile browsers.
2668          * @name JXG.Board#dblclick
2669          * @param {Event} e The browser's event object.
2670          * @see JXG.Board#clickDelay
2671          * @see JXG.Board#dblClickSuppressClick
2672          */
2673         __evt__dblclick: function (e) { },
2674 
2675         /**
2676          * @event
2677          * @description Whenever the user clicks on an element with a mouse device.
2678          * @name JXG.Board#mouseclick
2679          * @param {Event} e The browser's event object.
2680          */
2681         __evt__mouseclick: function (e) { },
2682 
2683         /**
2684          * @event
2685          * @description Whenever the user double clicks on an element with a mouse device.
2686          * @name JXG.Board#mousedblclick
2687          * @param {Event} e The browser's event object.
2688          */
2689         __evt__mousedblclick: function (e) { },
2690 
2691         /**
2692          * @event
2693          * @description Whenever the user clicks on an element with a pointer device.
2694          * @name JXG.Board#pointerclick
2695          * @param {Event} e The browser's event object.
2696          */
2697         __evt__pointerclick: function (e) { },
2698 
2699         /**
2700          * @event
2701          * @description Whenever the user double clicks on an element with a pointer device.
2702          * This event works on desktop browser, but is undefined
2703          * on mobile browsers.
2704          * @name JXG.Board#pointerdblclick
2705          * @param {Event} e The browser's event object.
2706          */
2707         __evt__pointerdblclick: function (e) { },
2708 
2709         /**
2710          * @event
2711          * @description Whenever the user stops to touch or click an element.
2712          * @name JXG.GeometryElement#up
2713          * @param {Event} e The browser's event object.
2714          */
2715         __evt__up: function (e) { },
2716 
2717         /**
2718          * @event
2719          * @description Whenever the user releases the mousebutton over an element.
2720          * @name JXG.GeometryElement#mouseup
2721          * @param {Event} e The browser's event object.
2722          */
2723         __evt__mouseup: function (e) { },
2724 
2725         /**
2726          * @event
2727          * @description Whenever the user lifts the pen over an element.
2728          * @name JXG.GeometryElement#penup
2729          * @param {Event} e The browser's event object.
2730          */
2731         __evt__penup: function (e) { },
2732 
2733         /**
2734          * @event
2735          * @description Whenever the user stops touching an element.
2736          * @name JXG.GeometryElement#touchup
2737          * @param {Event} e The browser's event object.
2738          */
2739         __evt__touchup: function (e) { },
2740 
2741         /**
2742          * @event
2743          * @description Notify every time an attribute is changed.
2744          * @name JXG.GeometryElement#attribute
2745          * @param {Object} o A list of changed attributes and their new value.
2746          * @param {Object} el Reference to the element
2747          */
2748         __evt__attribute: function (o, el) { },
2749 
2750         /**
2751          * @event
2752          * @description This is a generic event handler. It exists for every possible attribute that can be set for
2753          * any element, e.g. if you want to be notified everytime an element's strokecolor is changed, is the event
2754          * <tt>attribute:strokecolor</tt>.
2755          * @name JXG.GeometryElement#attribute:key
2756          * @param val The old value.
2757          * @param nval The new value
2758          * @param {Object} el Reference to the element
2759          */
2760         __evt__attribute_: function (val, nval, el) { },
2761 
2762         /**
2763          * @ignore
2764          */
2765         __evt: function () { }
2766         //endregion
2767     }
2768 );
2769 
2770 export default JXG.GeometryElement;
2771 // const GeometryElement = JXG.GeometryElement;
2772 // export { GeometryElement as default,  GeometryElement };
2773