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          * @param {String} key The attribute's name.
1090          * @param value The new value
1091          * @private
1092          */
1093         _set: function (key, value) {
1094             var el;
1095 
1096             key = key.toLocaleLowerCase();
1097 
1098             // Search for entries in visProp with "color" as part of the key name
1099             // and containing a RGBA string
1100             if (
1101                 this.visProp.hasOwnProperty(key) &&
1102                 key.indexOf("color") >= 0 &&
1103                 Type.isString(value) &&
1104                 value.length === 9 &&
1105                 value.charAt(0) === "#"
1106             ) {
1107                 value = Color.rgba2rgbo(value);
1108                 this.visProp[key] = value[0];
1109                 // Previously: *=. But then, we can only decrease opacity.
1110                 this.visProp[key.replace("color", "opacity")] = value[1];
1111             } else {
1112                 if (
1113                     value !== null &&
1114                     Type.isObject(value) &&
1115                     !Type.exists(value.id) &&
1116                     !Type.exists(value.name)
1117                 ) {
1118                     // value is of type {prop: val, prop: val,...}
1119                     // Convert these attributes to lowercase, too
1120                     this.visProp[key] = {};
1121                     for (el in value) {
1122                         if (value.hasOwnProperty(el)) {
1123                             this.visProp[key][el.toLocaleLowerCase()] = value[el];
1124                         }
1125                     }
1126                 } else {
1127                     this.visProp[key] = value;
1128                 }
1129             }
1130         },
1131 
1132         /**
1133          * Resolves attribute shortcuts like <tt>color</tt> and expands them, e.g. <tt>strokeColor</tt> and <tt>fillColor</tt>.
1134          * Writes the expanded attributes back to the given <tt>attributes</tt>.
1135          * @param {Object} attributes object
1136          * @returns {Object} The given attributes object with shortcuts expanded.
1137          * @private
1138          */
1139         resolveShortcuts: function (attributes) {
1140             var key, i, j,
1141                 subattr = ["traceattributes", "traceAttributes"];
1142 
1143             for (key in Options.shortcuts) {
1144                 if (Options.shortcuts.hasOwnProperty(key)) {
1145                     if (Type.exists(attributes[key])) {
1146                         for (i = 0; i < Options.shortcuts[key].length; i++) {
1147                             if (!Type.exists(attributes[Options.shortcuts[key][i]])) {
1148                                 attributes[Options.shortcuts[key][i]] = attributes[key];
1149                             }
1150                         }
1151                     }
1152                     for (j = 0; j < subattr.length; j++) {
1153                         if (Type.isObject(attributes[subattr[j]])) {
1154                             attributes[subattr[j]] = this.resolveShortcuts(
1155                                 attributes[subattr[j]]
1156                             );
1157                         }
1158                     }
1159                 }
1160             }
1161             return attributes;
1162         },
1163 
1164         /**
1165          * Sets a label and its text
1166          * If label doesn't exist, it creates one
1167          * @param {String} str
1168          */
1169         setLabel: function (str) {
1170             if (!this.hasLabel) {
1171                 this.setAttribute({ withlabel: true });
1172             }
1173             this.setLabelText(str);
1174         },
1175 
1176         /**
1177          * Updates the element's label text, strips all html.
1178          * @param {String} str
1179          */
1180         setLabelText: function (str) {
1181             if (Type.exists(this.label)) {
1182                 str = str.replace(/</g, "<").replace(/>/g, ">");
1183                 this.label.setText(str);
1184             }
1185 
1186             return this;
1187         },
1188 
1189         /**
1190          * Updates the element's label text and the element's attribute "name", strips all html.
1191          * @param {String} str
1192          */
1193         setName: function (str) {
1194             str = str.replace(/</g, "<").replace(/>/g, ">");
1195             if (this.elType !== "slider") {
1196                 this.setLabelText(str);
1197             }
1198             this.setAttribute({ name: str });
1199         },
1200 
1201         /**
1202          * Deprecated alias for {@link JXG.GeometryElement#setAttribute}.
1203          * @deprecated Use {@link JXG.GeometryElement#setAttribute}.
1204          */
1205         setProperty: function () {
1206             JXG.deprecated("setProperty()", "setAttribute()");
1207             this.setAttribute.apply(this, arguments);
1208         },
1209 
1210         /**
1211          * Sets an arbitrary number of attributes. This method has one or more
1212          * parameters of the following types:
1213          * <ul>
1214          * <li> object: {key1:value1,key2:value2,...}
1215          * <li> string: 'key:value'
1216          * <li> array: ['key', value]
1217          * </ul>
1218          * @param {Object} attributes An object with attributes.
1219          * @returns {JXG.GeometryElement} A reference to the element.
1220          *
1221          * @function
1222          * @example
1223          * // Set attribute directly on creation of an element using the attributes object parameter
1224          * var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 5, 5, 1]};
1225          * var p = board.create('point', [2, 2], {visible: false});
1226          *
1227          * // Now make this point visible and fixed:
1228          * p.setAttribute({
1229          *     fixed: true,
1230          *     visible: true
1231          * });
1232          */
1233         setAttribute: function (attr) {
1234             var i, j, le, key, value, arg,
1235                 opacity, pair, oldvalue,
1236                 attributes = {};
1237 
1238             // Normalize the user input
1239             for (i = 0; i < arguments.length; i++) {
1240                 arg = arguments[i];
1241                 if (Type.isString(arg)) {
1242                     // pairRaw is string of the form 'key:value'
1243                     pair = arg.split(":");
1244                     attributes[Type.trim(pair[0])] = Type.trim(pair[1]);
1245                 } else if (!Type.isArray(arg)) {
1246                     // pairRaw consists of objects of the form {key1:value1,key2:value2,...}
1247                     JXG.extend(attributes, arg);
1248                 } else {
1249                     // pairRaw consists of array [key,value]
1250                     attributes[arg[0]] = arg[1];
1251                 }
1252             }
1253 
1254             // Handle shortcuts
1255             attributes = this.resolveShortcuts(attributes);
1256 
1257             for (i in attributes) {
1258                 if (attributes.hasOwnProperty(i)) {
1259                     key = i.replace(/\s+/g, "").toLowerCase();
1260                     value = attributes[i];
1261 
1262                     // This handles the subobjects, if the key:value pairs are contained in an object.
1263                     // Example:
1264                     // ticks.setAttribute({
1265                     //      strokeColor: 'blue',
1266                     //      label: {
1267                     //          visible: false
1268                     //      }
1269                     // })
1270                     // Now, only the supplied label attributes are overwritten.
1271                     // Otherwise, the value of label would be {visible:false} only.
1272                     if (Type.isObject(value) && Type.exists(this.visProp[key])) {
1273                         this.visProp[key] = Type.merge(this.visProp[key], value);
1274 
1275                         // First, handle the special case
1276                         // ticks.setAttribute({label: {anchorX: "right", ..., visible: true});
1277                         if (this.type === Const.OBJECT_TYPE_TICKS && Type.exists(this.labels)) {
1278                             le = this.labels.length;
1279                             for (j = 0; j < le; j++) {
1280                                 this.labels[j].setAttribute(value);
1281                             }
1282                         } else if (Type.exists(this[key])) {
1283                             if (Type.isArray(this[key])) {
1284                                 for (j = 0; j < this[key].length; j++) {
1285                                     this[key][j].setAttribute(value);
1286                                 }
1287                             } else {
1288                                 this[key].setAttribute(value);
1289                             }
1290                         }
1291                         continue;
1292                     }
1293 
1294                     oldvalue = this.visProp[key];
1295                     switch (key) {
1296                         case "checked":
1297                             // checkbox Is not available on initial call.
1298                             if (Type.exists(this.rendNodeTag)) {
1299                                 this.rendNodeCheckbox.checked = !!value;
1300                             }
1301                             break;
1302                         case "disabled":
1303                             // button, checkbox, input. Is not available on initial call.
1304                             if (Type.exists(this.rendNodeTag)) {
1305                                 this.rendNodeTag.disabled = !!value;
1306                             }
1307                             break;
1308                         case "face":
1309                             if (Type.isPoint(this)) {
1310                                 this.visProp.face = value;
1311                                 this.board.renderer.changePointStyle(this);
1312                             }
1313                             break;
1314                         case "generatelabelvalue":
1315                             if (
1316                                 this.type === Const.OBJECT_TYPE_TICKS &&
1317                                 Type.isFunction(value)
1318                             ) {
1319                                 this.generateLabelValue = value;
1320                             }
1321                             break;
1322                         case "gradient":
1323                             this.visProp.gradient = value;
1324                             this.board.renderer.setGradient(this);
1325                             break;
1326                         case "gradientsecondcolor":
1327                             value = Color.rgba2rgbo(value);
1328                             this.visProp.gradientsecondcolor = value[0];
1329                             this.visProp.gradientsecondopacity = value[1];
1330                             this.board.renderer.updateGradient(this);
1331                             break;
1332                         case "gradientsecondopacity":
1333                             this.visProp.gradientsecondopacity = value;
1334                             this.board.renderer.updateGradient(this);
1335                             break;
1336                         case "infoboxtext":
1337                             if (Type.isString(value)) {
1338                                 this.infoboxText = value;
1339                             } else {
1340                                 this.infoboxText = false;
1341                             }
1342                             break;
1343                         case "labelcolor":
1344                             value = Color.rgba2rgbo(value);
1345                             opacity = value[1];
1346                             value = value[0];
1347                             if (opacity === 0) {
1348                                 if (Type.exists(this.label) && this.hasLabel) {
1349                                     this.label.hideElement();
1350                                 }
1351                             }
1352                             if (Type.exists(this.label) && this.hasLabel) {
1353                                 this.label.visProp.strokecolor = value;
1354                                 this.board.renderer.setObjectStrokeColor(
1355                                     this.label,
1356                                     value,
1357                                     opacity
1358                                 );
1359                             }
1360                             if (this.elementClass === Const.OBJECT_CLASS_TEXT) {
1361                                 this.visProp.strokecolor = value;
1362                                 this.visProp.strokeopacity = opacity;
1363                                 this.board.renderer.setObjectStrokeColor(this, value, opacity);
1364                             }
1365                             break;
1366                         case "layer":
1367                             this.board.renderer.setLayer(this, this.eval(value));
1368                             this._set(key, value);
1369                             break;
1370                         case "maxlength":
1371                             // input. Is not available on initial call.
1372                             if (Type.exists(this.rendNodeTag)) {
1373                                 this.rendNodeTag.maxlength = !!value;
1374                             }
1375                             break;
1376                         case "name":
1377                             oldvalue = this.name;
1378                             delete this.board.elementsByName[this.name];
1379                             this.name = value;
1380                             this.board.elementsByName[this.name] = this;
1381                             break;
1382                         case "needsregularupdate":
1383                             this.needsRegularUpdate = !(value === "false" || value === false);
1384                             this.board.renderer.setBuffering(
1385                                 this,
1386                                 this.needsRegularUpdate ? "auto" : "static"
1387                             );
1388                             break;
1389                         case "onpolygon":
1390                             if (this.type === Const.OBJECT_TYPE_GLIDER) {
1391                                 this.onPolygon = !!value;
1392                             }
1393                             break;
1394                         case "radius":
1395                             if (
1396                                 this.type === Const.OBJECT_TYPE_ANGLE ||
1397                                 this.type === Const.OBJECT_TYPE_SECTOR
1398                             ) {
1399                                 this.setRadius(value);
1400                             }
1401                             break;
1402                         case "rotate":
1403                             if (
1404                                 (this.elementClass === Const.OBJECT_CLASS_TEXT &&
1405                                     this.evalVisProp('display') === "internal") ||
1406                                 this.type === Const.OBJECT_TYPE_IMAGE
1407                             ) {
1408                                 this.addRotation(value);
1409                             }
1410                             break;
1411                         case "tabindex":
1412                             if (Type.exists(this.rendNode)) {
1413                                 this.rendNode.setAttribute("tabindex", value);
1414                                 this._set(key, value);
1415                             }
1416                             break;
1417                         // case "ticksdistance":
1418                         //     if (this.type === Const.OBJECT_TYPE_TICKS && Type.isNumber(value)) {
1419                         //         this.ticksFunction = this.makeTicksFunction(value);
1420                         //     }
1421                         //     break;
1422                         case "trace":
1423                             if (value === "false" || value === false) {
1424                                 this.clearTrace();
1425                                 this.visProp.trace = false;
1426                             } else if (value === "pause") {
1427                                 this.visProp.trace = false;
1428                             } else {
1429                                 this.visProp.trace = true;
1430                             }
1431                             break;
1432                         case "visible":
1433                             if (value === "false") {
1434                                 this.visProp.visible = false;
1435                             } else if (value === "true") {
1436                                 this.visProp.visible = true;
1437                             } else {
1438                                 this.visProp.visible = value;
1439                             }
1440 
1441                             this.setDisplayRendNode(this.evalVisProp('visible'));
1442                             if (
1443                                 this.evalVisProp('visible') &&
1444                                 Type.exists(this.updateSize)
1445                             ) {
1446                                 this.updateSize();
1447                             }
1448 
1449                             break;
1450                         case "withlabel":
1451                             this.visProp.withlabel = value;
1452                             if (!this.evalVisProp('withlabel')) {
1453                                 if (this.label && this.hasLabel) {
1454                                     //this.label.hideElement();
1455                                     this.label.setAttribute({ visible: false });
1456                                 }
1457                             } else {
1458                                 if (!this.label) {
1459                                     this.createLabel();
1460                                 }
1461                                 //this.label.showElement();
1462                                 this.label.setAttribute({ visible: "inherit" });
1463                                 //this.label.setDisplayRendNode(this.evalVisProp('visible'));
1464                             }
1465                             this.hasLabel = value;
1466                             break;
1467                         case "straightfirst":
1468                         case "straightlast":
1469                             this._set(key, value);
1470                             for (j in this.childElements) {
1471                                 if (this.childElements.hasOwnProperty(j) && this.childElements[j].elType === 'glider') {
1472                                     this.childElements[j].fullUpdate();
1473                                 }
1474                             }
1475                             break;
1476                         default:
1477                             if (
1478                                 Type.exists(this.visProp[key]) &&
1479                                 (!JXG.Validator[key] ||
1480                                     (JXG.Validator[key] && JXG.Validator[key](value)) ||
1481                                     (JXG.Validator[key] &&
1482                                         Type.isFunction(value) &&
1483                                         JXG.Validator[key](value(this))))
1484                             ) {
1485                                 value =
1486                                     (value.toLowerCase && value.toLowerCase() === "false")
1487                                         ? false
1488                                         : value;
1489                                 this._set(key, value);
1490                             }
1491                             break;
1492                     }
1493                     this.triggerEventHandlers(["attribute:" + key], [oldvalue, value, this]);
1494                 }
1495             }
1496 
1497             this.triggerEventHandlers(["attribute"], [attributes, this]);
1498 
1499             if (!this.evalVisProp('needsregularupdate')) {
1500                 this.board.fullUpdate();
1501             } else {
1502                 this.board.update(this);
1503             }
1504             if (this.elementClass === Const.OBJECT_CLASS_TEXT) {
1505                 this.updateSize();
1506             }
1507 
1508             return this;
1509         },
1510 
1511         /**
1512          * Deprecated alias for {@link JXG.GeometryElement#getAttribute}.
1513          * @deprecated Use {@link JXG.GeometryElement#getAttribute}.
1514          */
1515         getProperty: function () {
1516             JXG.deprecated("getProperty()", "getAttribute()");
1517             this.getProperty.apply(this, arguments);
1518         },
1519 
1520         /**
1521          * Get the value of the property <tt>key</tt>.
1522          * @param {String} key The name of the property you are looking for
1523          * @returns The value of the property
1524          */
1525         getAttribute: function (key) {
1526             var result;
1527             key = key.toLowerCase();
1528 
1529             switch (key) {
1530                 case "needsregularupdate":
1531                     result = this.needsRegularUpdate;
1532                     break;
1533                 case "labelcolor":
1534                     result = this.label.visProp.strokecolor;
1535                     break;
1536                 case "infoboxtext":
1537                     result = this.infoboxText;
1538                     break;
1539                 case "withlabel":
1540                     result = this.hasLabel;
1541                     break;
1542                 default:
1543                     result = this.visProp[key];
1544                     break;
1545             }
1546 
1547             return result;
1548         },
1549 
1550         /**
1551          * Get value of an attribute. If the value that attribute is a function, call the function and return its value.
1552          * In that case, the function is called with the GeometryElement as (only) parameter. For label elements (i.e.
1553          * if the attribute "islabel" is true), the anchor element is supplied. The label element can be accessed as
1554          * sub-object "label".
1555          * If the attribute does not exist, undefined will be returned.
1556          *
1557          * @param {String} key Attribute key
1558          * @returns {String|Number|Boolean} value of attribute "key" (evaluated in case of a function) or undefined
1559          *
1560          * @see GeometryElement#eval
1561          * @see JXG#evaluate
1562          */
1563         evalVisProp: function (key) {
1564             var val, arr, i, le;
1565 
1566             if (key.indexOf('.') === -1) {
1567                 // e.g. 'visible'
1568                 val = this.visProp[key];
1569             } else {
1570                 // e.g. label.visible
1571                 arr = key.split('.');
1572                 le = arr.length;
1573                 val = this.visProp;
1574                 for (i = 0; i < le; i++) {
1575                     val = val[arr[i]];
1576                 }
1577             }
1578 
1579             if (JXG.isFunction(val)) {
1580                 // For labels supply the anchor element as parameter.
1581                 if (this.visProp.islabel === true && Type.exists(this.visProp.anchor)) {
1582                     // 3D: supply the 3D element
1583                     if (this.visProp.anchor.visProp.element3d !== null) {
1584                         return val(this.visProp.anchor.visProp.element3d);
1585                     }
1586                     // 2D: supply the 2D element
1587                     return val(this.visProp.anchor);
1588                 }
1589                 // For 2D elements representing 3D elements, return the 3D element.
1590                 if (this.visProp.element3d !== null) {
1591                     return val(this.visProp.element3d);
1592                 }
1593                 // In all other cases, return the element itself
1594                 return val(this);
1595             }
1596             // val is not of type function
1597             return val;
1598         },
1599 
1600         /**
1601          * Get value of a parameter. If the parameter is a function, call the function and return its value.
1602          * In that case, the function is called with the GeometryElement as (only) parameter. For label elements (i.e.
1603          * if the attribute "islabel" is true), the anchor element is supplied. The label of an element can be accessed as
1604          * sub-object "label" then.
1605          *
1606          * @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
1607          * supplied as the (only) parameter of that function.
1608          * @returns {String|Number|Object}
1609          *
1610          * @see GeometryElement#evalVisProp
1611          * @see JXG#evaluate
1612          */
1613         eval: function(val) {
1614             if (JXG.isFunction(val)) {
1615                 // For labels supply the anchor element as parameter.
1616                 if (this.visProp.islabel === true && Type.exists(this.visProp.anchor)) {
1617                     // 3D: supply the 3D element
1618                     if (this.visProp.anchor.visProp.element3d !== null) {
1619                         return val(this.visProp.anchor.visProp.element3d);
1620                     }
1621                     // 2D: supply the 2D element
1622                     return val(this.visProp.anchor);
1623                 }
1624                 // For 2D elements representing 3D elements, return the 3D element.
1625                 if (this.visProp.element3d !== null) {
1626                     return val(this.visProp.element3d);
1627                 }
1628                 // In all other cases, return the element itself
1629                 return val(this);
1630             }
1631             // val is not of type function
1632             return val;
1633         },
1634 
1635         /**
1636          * Set the dash style of an object. See {@link JXG.GeometryElement#dash}
1637          * for a list of available dash styles.
1638          * You should use {@link JXG.GeometryElement#setAttribute} instead of this method.
1639          *
1640          * @param {number} dash Indicates the new dash style
1641          * @private
1642          */
1643         setDash: function (dash) {
1644             this.setAttribute({ dash: dash });
1645             return this;
1646         },
1647 
1648         /**
1649          * Notify all child elements for updates.
1650          * @private
1651          */
1652         prepareUpdate: function () {
1653             this.needsUpdate = true;
1654             return this;
1655         },
1656 
1657         /**
1658          * Removes the element from the construction.  This only removes the SVG or VML node of the element and its label (if available) from
1659          * the renderer, to remove the element completely you should use {@link JXG.Board#removeObject}.
1660          */
1661         remove: function () {
1662             // this.board.renderer.remove(this.board.renderer.getElementById(this.id));
1663             this.board.renderer.remove(this.rendNode);
1664 
1665             if (this.hasLabel) {
1666                 this.board.renderer.remove(this.board.renderer.getElementById(this.label.id));
1667             }
1668             return this;
1669         },
1670 
1671         /**
1672          * Returns the coords object where a text that is bound to the element shall be drawn.
1673          * Differs in some cases from the values that getLabelAnchor returns.
1674          * @returns {JXG.Coords} JXG.Coords Place where the text shall be drawn.
1675          * @see JXG.GeometryElement#getLabelAnchor
1676          */
1677         getTextAnchor: function () {
1678             return new Coords(Const.COORDS_BY_USER, [0, 0], this.board);
1679         },
1680 
1681         /**
1682          * Returns the coords object where the label of the element shall be drawn.
1683          * Differs in some cases from the values that getTextAnchor returns.
1684          * @returns {JXG.Coords} JXG.Coords Place where the text shall be drawn.
1685          * @see JXG.GeometryElement#getTextAnchor
1686          */
1687         getLabelAnchor: function () {
1688             return new Coords(Const.COORDS_BY_USER, [0, 0], this.board);
1689         },
1690 
1691         /**
1692          * Determines whether the element has arrows at start or end of the arc.
1693          * If it is set to be a "typical" vector, ie lastArrow == true,
1694          * then the element.type is set to VECTOR.
1695          * @param {Boolean} firstArrow True if there is an arrow at the start of the arc, false otherwise.
1696          * @param {Boolean} lastArrow True if there is an arrow at the end of the arc, false otherwise.
1697          */
1698         setArrow: function (firstArrow, lastArrow) {
1699             this.visProp.firstarrow = firstArrow;
1700             this.visProp.lastarrow = lastArrow;
1701             if (lastArrow) {
1702                 this.type = Const.OBJECT_TYPE_VECTOR;
1703                 this.elType = "arrow";
1704             }
1705 
1706             this.prepareUpdate().update().updateVisibility().updateRenderer();
1707             return this;
1708         },
1709 
1710         /**
1711          * Creates a gradient nodes in the renderer.
1712          * @see JXG.SVGRenderer#setGradient
1713          * @private
1714          */
1715         createGradient: function () {
1716             var ev_g = this.evalVisProp('gradient');
1717             if (ev_g === "linear" || ev_g === "radial") {
1718                 this.board.renderer.setGradient(this);
1719             }
1720         },
1721 
1722         /**
1723          * Creates a label element for this geometry element.
1724          * @see JXG.GeometryElement#addLabelToElement
1725          */
1726         createLabel: function () {
1727             var attr,
1728                 that = this;
1729 
1730             // this is a dirty hack to resolve the text-dependency. If there is no text element available,
1731             // just don't create a label. This method is usually not called by a user, so we won't throw
1732             // an exception here and simply output a warning via JXG.debug.
1733             if (JXG.elements.text) {
1734                 attr = Type.deepCopy(this.visProp.label, null);
1735                 attr.id = this.id + "Label";
1736                 attr.isLabel = true;
1737                 attr.anchor = this;
1738                 attr.priv = this.visProp.priv;
1739 
1740                 if (this.visProp.withlabel) {
1741                     this.label = JXG.elements.text(
1742                         this.board,
1743                         [
1744                             0,
1745                             0,
1746                             function () {
1747                                 if (Type.isFunction(that.name)) {
1748                                     return that.name(that);
1749                                 }
1750                                 return that.name;
1751                             }
1752                         ],
1753                         attr
1754                     );
1755                     this.label.needsUpdate = true;
1756                     this.label.dump = false;
1757                     this.label.fullUpdate();
1758 
1759                     this.hasLabel = true;
1760                 }
1761             } else {
1762                 JXG.debug(
1763                     "JSXGraph: Can't create label: text element is not available. Make sure you include base/text"
1764                 );
1765             }
1766 
1767             return this;
1768         },
1769 
1770         /**
1771          * Highlights the element.
1772          * @private
1773          * @param {Boolean} [force=false] Force the highlighting
1774          * @returns {JXG.Board}
1775          */
1776         highlight: function (force) {
1777             force = Type.def(force, false);
1778             // I know, we have the JXG.Board.highlightedObjects AND JXG.GeometryElement.highlighted and YES we need both.
1779             // Board.highlightedObjects is for the internal highlighting and GeometryElement.highlighted is for user highlighting
1780             // initiated by the user, e.g. through custom DOM events. We can't just pick one because this would break user
1781             // defined highlighting in many ways:
1782             //  * if overriding the highlight() methods the user had to handle the highlightedObjects stuff, otherwise he'd break
1783             //    everything (e.g. the pie chart example https://jsxgraph.org/wiki/index.php/Pie_chart (not exactly
1784             //    user defined but for this type of chart the highlight method was overridden and not adjusted to the changes in here)
1785             //    where it just kept highlighting until the radius of the pie was far beyond infinity...
1786             //  * user defined highlighting would get pointless, everytime the user highlights something using .highlight(), it would get
1787             //    dehighlighted immediately, because highlight puts the element into highlightedObjects and from there it gets dehighlighted
1788             //    through dehighlightAll.
1789 
1790             // highlight only if not highlighted
1791             if (this.evalVisProp('highlight') && (!this.highlighted || force)) {
1792                 this.highlighted = true;
1793                 this.board.highlightedObjects[this.id] = this;
1794                 this.board.renderer.highlight(this);
1795             }
1796             return this;
1797         },
1798 
1799         /**
1800          * Uses the "normal" properties of the element.
1801          * @returns {JXG.Board}
1802          */
1803         noHighlight: function () {
1804             // see comment in JXG.GeometryElement.highlight()
1805 
1806             // dehighlight only if not highlighted
1807             if (this.highlighted) {
1808                 this.highlighted = false;
1809                 delete this.board.highlightedObjects[this.id];
1810                 this.board.renderer.noHighlight(this);
1811             }
1812             return this;
1813         },
1814 
1815         /**
1816          * Removes all objects generated by the trace function.
1817          */
1818         clearTrace: function () {
1819             var obj;
1820 
1821             for (obj in this.traces) {
1822                 if (this.traces.hasOwnProperty(obj)) {
1823                     this.board.renderer.remove(this.traces[obj]);
1824                 }
1825             }
1826 
1827             this.numTraces = 0;
1828             return this;
1829         },
1830 
1831         /**
1832          * Copy the element to background. This is used for tracing elements.
1833          * @returns {JXG.GeometryElement} A reference to the element
1834          */
1835         cloneToBackground: function () {
1836             return this;
1837         },
1838 
1839         /**
1840          * Dimensions of the smallest rectangle enclosing the element.
1841          * @returns {Array} The coordinates of the enclosing rectangle in a format
1842          * like the bounding box in {@link JXG.Board#setBoundingBox}.
1843          *
1844          * @returns {Array} similar to {@link JXG.Board#setBoundingBox}.
1845          */
1846         bounds: function () {
1847             return [0, 0, 0, 0];
1848         },
1849 
1850         /**
1851          * Normalize the element's standard form.
1852          * @private
1853          */
1854         normalize: function () {
1855             this.stdform = Mat.normalize(this.stdform);
1856             return this;
1857         },
1858 
1859         /**
1860          * EXPERIMENTAL. Generate JSON object code of visProp and other properties.
1861          * @type String
1862          * @private
1863          * @ignore
1864          * @deprecated
1865          * @returns JSON string containing element's properties.
1866          */
1867         toJSON: function () {
1868             var vis,
1869                 key,
1870                 json = ['{"name":', this.name];
1871 
1872             json.push(", " + '"id":' + this.id);
1873 
1874             vis = [];
1875             for (key in this.visProp) {
1876                 if (this.visProp.hasOwnProperty(key)) {
1877                     if (Type.exists(this.visProp[key])) {
1878                         vis.push('"' + key + '":' + this.visProp[key]);
1879                     }
1880                 }
1881             }
1882             json.push(', "visProp":{' + vis.toString() + "}");
1883             json.push("}");
1884 
1885             return json.join("");
1886         },
1887 
1888         /**
1889          * Rotate texts or images by a given degree.
1890          * @param {number} angle The degree of the rotation (90 means vertical text).
1891          * @see JXG.GeometryElement#rotate
1892          */
1893         addRotation: function (angle) {
1894             var tOffInv,
1895                 tOff,
1896                 tS,
1897                 tSInv,
1898                 tRot,
1899                 that = this;
1900 
1901             if (
1902                 (this.elementClass === Const.OBJECT_CLASS_TEXT ||
1903                     this.type === Const.OBJECT_TYPE_IMAGE) &&
1904                 angle !== 0
1905             ) {
1906                 tOffInv = this.board.create(
1907                     "transform",
1908                     [
1909                         function () {
1910                             return -that.X();
1911                         },
1912                         function () {
1913                             return -that.Y();
1914                         }
1915                     ],
1916                     { type: "translate" }
1917                 );
1918 
1919                 tOff = this.board.create(
1920                     "transform",
1921                     [
1922                         function () {
1923                             return that.X();
1924                         },
1925                         function () {
1926                             return that.Y();
1927                         }
1928                     ],
1929                     { type: "translate" }
1930                 );
1931 
1932                 tS = this.board.create(
1933                     "transform",
1934                     [
1935                         function () {
1936                             return that.board.unitX / that.board.unitY;
1937                         },
1938                         function () {
1939                             return 1;
1940                         }
1941                     ],
1942                     { type: "scale" }
1943                 );
1944 
1945                 tSInv = this.board.create(
1946                     "transform",
1947                     [
1948                         function () {
1949                             return that.board.unitY / that.board.unitX;
1950                         },
1951                         function () {
1952                             return 1;
1953                         }
1954                     ],
1955                     { type: "scale" }
1956                 );
1957 
1958                 tRot = this.board.create(
1959                     "transform",
1960                     [
1961                         function () {
1962                             return (that.eval(angle) * Math.PI) / 180;
1963                         }
1964                     ],
1965                     { type: "rotate" }
1966                 );
1967 
1968                 tOffInv.bindTo(this);
1969                 tS.bindTo(this);
1970                 tRot.bindTo(this);
1971                 tSInv.bindTo(this);
1972                 tOff.bindTo(this);
1973             }
1974 
1975             return this;
1976         },
1977 
1978         /**
1979          * Set the highlightStrokeColor of an element
1980          * @ignore
1981          * @name JXG.GeometryElement#highlightStrokeColorMethod
1982          * @param {String} sColor String which determines the stroke color of an object when its highlighted.
1983          * @see JXG.GeometryElement#highlightStrokeColor
1984          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
1985          */
1986         highlightStrokeColor: function (sColor) {
1987             JXG.deprecated("highlightStrokeColor()", "setAttribute()");
1988             this.setAttribute({ highlightStrokeColor: sColor });
1989             return this;
1990         },
1991 
1992         /**
1993          * Set the strokeColor of an element
1994          * @ignore
1995          * @name JXG.GeometryElement#strokeColorMethod
1996          * @param {String} sColor String which determines the stroke color of an object.
1997          * @see JXG.GeometryElement#strokeColor
1998          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
1999          */
2000         strokeColor: function (sColor) {
2001             JXG.deprecated("strokeColor()", "setAttribute()");
2002             this.setAttribute({ strokeColor: sColor });
2003             return this;
2004         },
2005 
2006         /**
2007          * Set the strokeWidth of an element
2008          * @ignore
2009          * @name JXG.GeometryElement#strokeWidthMethod
2010          * @param {Number} width Integer which determines the stroke width of an outline.
2011          * @see JXG.GeometryElement#strokeWidth
2012          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2013          */
2014         strokeWidth: function (width) {
2015             JXG.deprecated("strokeWidth()", "setAttribute()");
2016             this.setAttribute({ strokeWidth: width });
2017             return this;
2018         },
2019 
2020         /**
2021          * Set the fillColor of an element
2022          * @ignore
2023          * @name JXG.GeometryElement#fillColorMethod
2024          * @param {String} fColor String which determines the fill color of an object.
2025          * @see JXG.GeometryElement#fillColor
2026          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2027          */
2028         fillColor: function (fColor) {
2029             JXG.deprecated("fillColor()", "setAttribute()");
2030             this.setAttribute({ fillColor: fColor });
2031             return this;
2032         },
2033 
2034         /**
2035          * Set the highlightFillColor of an element
2036          * @ignore
2037          * @name JXG.GeometryElement#highlightFillColorMethod
2038          * @param {String} fColor String which determines the fill color of an object when its highlighted.
2039          * @see JXG.GeometryElement#highlightFillColor
2040          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2041          */
2042         highlightFillColor: function (fColor) {
2043             JXG.deprecated("highlightFillColor()", "setAttribute()");
2044             this.setAttribute({ highlightFillColor: fColor });
2045             return this;
2046         },
2047 
2048         /**
2049          * Set the labelColor of an element
2050          * @ignore
2051          * @param {String} lColor String which determines the text color of an object's label.
2052          * @see JXG.GeometryElement#labelColor
2053          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2054          */
2055         labelColor: function (lColor) {
2056             JXG.deprecated("labelColor()", "setAttribute()");
2057             this.setAttribute({ labelColor: lColor });
2058             return this;
2059         },
2060 
2061         /**
2062          * Set the dash type of an element
2063          * @ignore
2064          * @name JXG.GeometryElement#dashMethod
2065          * @param {Number} d Integer which determines the way of dashing an element's outline.
2066          * @see JXG.GeometryElement#dash
2067          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2068          */
2069         dash: function (d) {
2070             JXG.deprecated("dash()", "setAttribute()");
2071             this.setAttribute({ dash: d });
2072             return this;
2073         },
2074 
2075         /**
2076          * Set the visibility of an element
2077          * @ignore
2078          * @name JXG.GeometryElement#visibleMethod
2079          * @param {Boolean} v Boolean which determines whether the element is drawn.
2080          * @see JXG.GeometryElement#visible
2081          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2082          */
2083         visible: function (v) {
2084             JXG.deprecated("visible()", "setAttribute()");
2085             this.setAttribute({ visible: v });
2086             return this;
2087         },
2088 
2089         /**
2090          * Set the shadow of an element
2091          * @ignore
2092          * @name JXG.GeometryElement#shadowMethod
2093          * @param {Boolean} s Boolean which determines whether the element has a shadow or not.
2094          * @see JXG.GeometryElement#shadow
2095          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2096          */
2097         shadow: function (s) {
2098             JXG.deprecated("shadow()", "setAttribute()");
2099             this.setAttribute({ shadow: s });
2100             return this;
2101         },
2102 
2103         /**
2104          * The type of the element as used in {@link JXG.Board#create}.
2105          * @returns {String}
2106          */
2107         getType: function () {
2108             return this.elType;
2109         },
2110 
2111         /**
2112          * List of the element ids resp. values used as parents in {@link JXG.Board#create}.
2113          * @returns {Array}
2114          */
2115         getParents: function () {
2116             return Type.isArray(this.parents) ? this.parents : [];
2117         },
2118 
2119         /**
2120          * @ignore
2121          * @private
2122          * Snaps the element to the grid. Only works for points, lines and circles. Points will snap to the grid
2123          * as defined in their properties {@link JXG.Point#snapSizeX} and {@link JXG.Point#snapSizeY}. Lines and circles
2124          * will snap their parent points to the grid, if they have {@link JXG.Point#snapToGrid} set to true.
2125          * @returns {JXG.GeometryElement} Reference to the element.
2126          */
2127         snapToGrid: function () {
2128             return this;
2129         },
2130 
2131         /**
2132          * Snaps the element to points. Only works for points. Points will snap to the next point
2133          * as defined in their properties {@link JXG.Point#attractorDistance} and {@link JXG.Point#attractorUnit}.
2134          * Lines and circles
2135          * will snap their parent points to points.
2136          * @private
2137          * @returns {JXG.GeometryElement} Reference to the element.
2138          */
2139         snapToPoints: function () {
2140             return this;
2141         },
2142 
2143         /**
2144          * Retrieve a copy of the current visProp.
2145          * @returns {Object}
2146          */
2147         getAttributes: function () {
2148             var attributes = Type.deepCopy(this.visProp),
2149                 /*
2150                 cleanThis = ['attractors', 'snatchdistance', 'traceattributes', 'frozen',
2151                     'shadow', 'gradientangle', 'gradientsecondopacity', 'gradientpositionx', 'gradientpositiony',
2152                     'needsregularupdate', 'zoom', 'layer', 'offset'],
2153                 */
2154                 cleanThis = [],
2155                 i,
2156                 len = cleanThis.length;
2157 
2158             attributes.id = this.id;
2159             attributes.name = this.name;
2160 
2161             for (i = 0; i < len; i++) {
2162                 delete attributes[cleanThis[i]];
2163             }
2164 
2165             return attributes;
2166         },
2167 
2168         /**
2169          * Checks whether (x,y) is near the element.
2170          * @param {Number} x Coordinate in x direction, screen coordinates.
2171          * @param {Number} y Coordinate in y direction, screen coordinates.
2172          * @returns {Boolean} True if (x,y) is near the element, False otherwise.
2173          */
2174         hasPoint: function (x, y) {
2175             return false;
2176         },
2177 
2178         /**
2179          * Adds ticks to this line or curve. Ticks can be added to a curve or any kind of line: line, arrow, and axis.
2180          * @param {JXG.Ticks} ticks Reference to a ticks object which is describing the ticks (color, distance, how many, etc.).
2181          * @returns {String} Id of the ticks object.
2182          */
2183         addTicks: function (ticks) {
2184             if (ticks.id === "" || !Type.exists(ticks.id)) {
2185                 ticks.id = this.id + "_ticks_" + (this.ticks.length + 1);
2186             }
2187 
2188             this.board.renderer.drawTicks(ticks);
2189             this.ticks.push(ticks);
2190 
2191             return ticks.id;
2192         },
2193 
2194         /**
2195          * Removes all ticks from a line or curve.
2196          */
2197         removeAllTicks: function () {
2198             var t;
2199             if (Type.exists(this.ticks)) {
2200                 for (t = this.ticks.length - 1; t >= 0; t--) {
2201                     this.removeTicks(this.ticks[t]);
2202                 }
2203                 this.ticks = [];
2204                 this.board.update();
2205             }
2206         },
2207 
2208         /**
2209          * Removes ticks identified by parameter named tick from this line or curve.
2210          * @param {JXG.Ticks} tick Reference to tick object to remove.
2211          */
2212         removeTicks: function (tick) {
2213             var t, j;
2214 
2215             if (Type.exists(this.defaultTicks) && this.defaultTicks === tick) {
2216                 this.defaultTicks = null;
2217             }
2218 
2219             if (Type.exists(this.ticks)) {
2220                 for (t = this.ticks.length - 1; t >= 0; t--) {
2221                     if (this.ticks[t] === tick) {
2222                         this.board.removeObject(this.ticks[t]);
2223 
2224                         if (this.ticks[t].ticks) {
2225                             for (j = 0; j < this.ticks[t].ticks.length; j++) {
2226                                 if (Type.exists(this.ticks[t].labels[j])) {
2227                                     this.board.removeObject(this.ticks[t].labels[j]);
2228                                 }
2229                             }
2230                         }
2231 
2232                         delete this.ticks[t];
2233                         break;
2234                     }
2235                 }
2236             }
2237         },
2238 
2239         /**
2240          * Determine values of snapSizeX and snapSizeY. If the attributes
2241          * snapSizex and snapSizeY are greater than zero, these values are taken.
2242          * Otherwise, determine the distance between major ticks of the
2243          * default axes.
2244          * @returns {Array} containing the snap sizes for x and y direction.
2245          * @private
2246          */
2247         getSnapSizes: function () {
2248             var sX, sY, ticks;
2249 
2250             sX = this.evalVisProp('snapsizex');
2251             sY = this.evalVisProp('snapsizey');
2252 
2253             if (sX <= 0 && this.board.defaultAxes && this.board.defaultAxes.x.defaultTicks) {
2254                 ticks = this.board.defaultAxes.x.defaultTicks;
2255                 sX = ticks.ticksDelta * (ticks.evalVisProp('minorticks') + 1);
2256             }
2257 
2258             if (sY <= 0 && this.board.defaultAxes && this.board.defaultAxes.y.defaultTicks) {
2259                 ticks = this.board.defaultAxes.y.defaultTicks;
2260                 sY = ticks.ticksDelta * (ticks.evalVisProp('minorticks') + 1);
2261             }
2262 
2263             return [sX, sY];
2264         },
2265 
2266         /**
2267          * Move an element to its nearest grid point.
2268          * The function uses the coords object of the element as
2269          * its actual position. If there is no coords object or if the object is fixed, nothing is done.
2270          * @param {Boolean} force force snapping independent from what the snaptogrid attribute says
2271          * @param {Boolean} fromParent True if the drag comes from a child element. This is the case if a line
2272          *    through two points is dragged. In this case we do not try to force the points to stay inside of
2273          *    the visible board, but the distance between the two points stays constant.
2274          * @returns {JXG.GeometryElement} Reference to this element
2275          */
2276         handleSnapToGrid: function (force, fromParent) {
2277             var x, y, rx, ry, rcoords,
2278                 mi, ma,
2279                 boardBB, res, sX, sY,
2280                 needsSnapToGrid = false,
2281                 attractToGrid = this.evalVisProp('attracttogrid'),
2282                 ev_au = this.evalVisProp('attractorunit'),
2283                 ev_ad = this.evalVisProp('attractordistance');
2284 
2285             if (!Type.exists(this.coords) || this.evalVisProp('fixed')) {
2286                 return this;
2287             }
2288 
2289             needsSnapToGrid =
2290                 this.evalVisProp('snaptogrid') || attractToGrid || force === true;
2291 
2292             if (needsSnapToGrid) {
2293                 x = this.coords.usrCoords[1];
2294                 y = this.coords.usrCoords[2];
2295                 res = this.getSnapSizes();
2296                 sX = res[0];
2297                 sY = res[1];
2298 
2299                 // If no valid snap sizes are available, don't change the coords.
2300                 if (sX > 0 && sY > 0) {
2301                     boardBB = this.board.getBoundingBox();
2302                     rx = Math.round(x / sX) * sX;
2303                     ry = Math.round(y / sY) * sY;
2304 
2305                     rcoords = new JXG.Coords(Const.COORDS_BY_USER, [rx, ry], this.board);
2306                     if (
2307                         !attractToGrid ||
2308                         rcoords.distance(
2309                             ev_au === "screen" ? Const.COORDS_BY_SCREEN : Const.COORDS_BY_USER,
2310                             this.coords
2311                         ) < ev_ad
2312                     ) {
2313                         x = rx;
2314                         y = ry;
2315                         // Checking whether x and y are still within boundingBox.
2316                         // If not, adjust them to remain within the board.
2317                         // Otherwise a point may become invisible.
2318                         if (!fromParent) {
2319                             mi = Math.min(boardBB[0], boardBB[2]);
2320                             ma = Math.max(boardBB[0], boardBB[2]);
2321                             if (x < mi && x > mi - sX) {
2322                                 x += sX;
2323                             } else if (x > ma && x < ma + sX) {
2324                                 x -= sX;
2325                             }
2326 
2327                             mi = Math.min(boardBB[1], boardBB[3]);
2328                             ma = Math.max(boardBB[1], boardBB[3]);
2329                             if (y < mi && y > mi - sY) {
2330                                 y += sY;
2331                             } else if (y > ma && y < ma + sY) {
2332                                 y -= sY;
2333                             }
2334                         }
2335                         this.coords.setCoordinates(Const.COORDS_BY_USER, [x, y]);
2336                     }
2337                 }
2338             }
2339             return this;
2340         },
2341 
2342         getBoundingBox: function () {
2343             var i,
2344                 le,
2345                 v,
2346                 x,
2347                 y,
2348                 bb = [Infinity, Infinity, -Infinity, -Infinity];
2349 
2350             if (this.type === Const.OBJECT_TYPE_POLYGON) {
2351                 le = this.vertices.length - 1;
2352                 if (le <= 0) {
2353                     return bb;
2354                 }
2355                 for (i = 0; i < le; i++) {
2356                     v = this.vertices[i].X();
2357                     bb[0] = v < bb[0] ? v : bb[0];
2358                     bb[2] = v > bb[2] ? v : bb[2];
2359                     v = this.vertices[i].Y();
2360                     bb[1] = v < bb[1] ? v : bb[1];
2361                     bb[3] = v > bb[3] ? v : bb[3];
2362                 }
2363             } else if (this.elementClass === Const.OBJECT_CLASS_CIRCLE) {
2364                 x = this.center.X();
2365                 y = this.center.Y();
2366                 bb = [x - this.radius, y + this.radius, x + this.radius, y - this.radius];
2367             } else if (this.elementClass === Const.OBJECT_CLASS_CURVE) {
2368                 le = this.vertices.length;
2369                 if (le === 0) {
2370                     return bb;
2371                 }
2372                 for (i = 0; i < le; i++) {
2373                     v = this.points[i].coords.usrCoords[1];
2374                     bb[0] = v < bb[0] ? v : bb[0];
2375                     bb[2] = v > bb[2] ? v : bb[2];
2376                     v = this.points[i].coords.usrCoords[1];
2377                     bb[1] = v < bb[1] ? v : bb[1];
2378                     bb[3] = v > bb[3] ? v : bb[3];
2379                 }
2380             }
2381 
2382             return bb;
2383         },
2384 
2385         /**
2386          * Alias of {@link JXG.EventEmitter.on}.
2387          *
2388          * @name addEvent
2389          * @memberof JXG.GeometryElement
2390          * @function
2391          */
2392         addEvent: JXG.shortcut(JXG.GeometryElement.prototype, 'on'),
2393 
2394         /**
2395          * Alias of {@link JXG.EventEmitter.off}.
2396          *
2397          * @name removeEvent
2398          * @memberof JXG.GeometryElement
2399          * @function
2400          */
2401         removeEvent: JXG.shortcut(JXG.GeometryElement.prototype, 'off'),
2402 
2403         /**
2404          * Format a number according to the locale set in the attribute "intl".
2405          * If in the options of the intl-attribute "maximumFractionDigits" is not set,
2406          * the optional parameter digits is used instead.
2407          * 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>
2408          * for more  information about internationalization.
2409          *
2410          * @param {Number} value Number to be formatted
2411          * @param {Number} [digits=undefined] Optional number of digits
2412          * @returns {String|Number} string containing the formatted number according to the locale
2413          * or the number itself of the formatting is not possible.
2414          */
2415         formatNumberLocale: function (value, digits) {
2416             var loc, opt, key,
2417                 optCalc = {},
2418                 // These options are case sensitive:
2419                 translate = {
2420                     maximumfractiondigits: 'maximumFractionDigits',
2421                     minimumfractiondigits: 'minimumFractionDigits',
2422                     compactdisplay: 'compactDisplay',
2423                     currencydisplay: 'currencyDisplay',
2424                     currencysign: 'currencySign',
2425                     localematcher: 'localeMatcher',
2426                     numberingsystem: 'numberingSystem',
2427                     signdisplay: 'signDisplay',
2428                     unitdisplay: 'unitDisplay',
2429                     usegrouping: 'useGrouping',
2430                     roundingmode: 'roundingMode',
2431                     roundingpriority: 'roundingPriority',
2432                     roundingincrement: 'roundingIncrement',
2433                     trailingzerodisplay: 'trailingZeroDisplay',
2434                     minimumintegerdigits: 'minimumIntegerDigits',
2435                     minimumsignificantdigits: 'minimumSignificantDigits',
2436                     maximumsignificantdigits: 'maximumSignificantDigits'
2437                 };
2438 
2439             if (Type.exists(Intl) &&
2440                 this.useLocale()) {
2441 
2442                 loc = this.evalVisProp('intl.locale') ||
2443                     this.eval(this.board.attr.intl.locale);
2444                 opt = this.evalVisProp('intl.options') || {};
2445 
2446                 // Transfer back to camel case if necessary and evaluate
2447                 for (key in opt) {
2448                     if (opt.hasOwnProperty(key)) {
2449                         if (translate.hasOwnProperty(key)) {
2450                             optCalc[translate[key]] = this.eval(opt[key]);
2451                         } else {
2452                             optCalc[key] = this.eval(opt[key]);
2453                         }
2454                     }
2455                 }
2456 
2457                 // If maximumfractiondigits is not set,
2458                 // the value of the attribute "digits" is taken instead.
2459                 key = 'maximumfractiondigits';
2460                 if (!Type.exists(opt[key])) {
2461                     optCalc[translate[key]] = digits;
2462 
2463                     // key = 'minimumfractiondigits';
2464                     // if (!this.eval(opt[key]) || this.eval(opt[key]) > digits) {
2465                     //     optCalc[translate[key]] = digits;
2466                     // }
2467                 }
2468 
2469                 return Intl.NumberFormat(loc, optCalc).format(value);
2470             }
2471 
2472             return value;
2473         },
2474 
2475         /**
2476          * Checks if locale is enabled in the attribute. This may be in the attributes of the board,
2477          * or in the attributes of the text. The latter has higher priority. The board attribute is taken if
2478          * attribute "intl.enabled" of the text element is set to 'inherit'.
2479          *
2480          * @returns {Boolean} if locale can be used for number formatting.
2481          */
2482         useLocale: function () {
2483             var val;
2484 
2485             // Check if element supports intl
2486             if (!Type.exists(this.visProp.intl) ||
2487                 !Type.exists(this.visProp.intl.enabled)) {
2488                 return false;
2489             }
2490 
2491             // Check if intl is supported explicitly enabled for this element
2492             val = this.evalVisProp('intl.enabled');
2493 
2494             if (val === true) {
2495                 return true;
2496             }
2497 
2498             // Check intl attribute of the board
2499             if (val === 'inherit') {
2500                 if (this.eval(this.board.attr.intl.enabled) === true) {
2501                     return true;
2502                 }
2503             }
2504 
2505             return false;
2506         },
2507 
2508         /* **************************
2509          *     EVENT DEFINITION
2510          * for documentation purposes
2511          * ************************** */
2512 
2513         //region Event handler documentation
2514         /**
2515          * @event
2516          * @description This event is fired whenever the user is hovering over an element.
2517          * @name JXG.GeometryElement#over
2518          * @param {Event} e The browser's event object.
2519          */
2520         __evt__over: function (e) { },
2521 
2522         /**
2523          * @event
2524          * @description This event is fired whenever the user puts the mouse over an element.
2525          * @name JXG.GeometryElement#mouseover
2526          * @param {Event} e The browser's event object.
2527          */
2528         __evt__mouseover: function (e) { },
2529 
2530         /**
2531          * @event
2532          * @description This event is fired whenever the user is leaving an element.
2533          * @name JXG.GeometryElement#out
2534          * @param {Event} e The browser's event object.
2535          */
2536         __evt__out: function (e) { },
2537 
2538         /**
2539          * @event
2540          * @description This event is fired whenever the user puts the mouse away from an element.
2541          * @name JXG.GeometryElement#mouseout
2542          * @param {Event} e The browser's event object.
2543          */
2544         __evt__mouseout: function (e) { },
2545 
2546         /**
2547          * @event
2548          * @description This event is fired whenever the user is moving over an element.
2549          * @name JXG.GeometryElement#move
2550          * @param {Event} e The browser's event object.
2551          */
2552         __evt__move: function (e) { },
2553 
2554         /**
2555          * @event
2556          * @description This event is fired whenever the user is moving the mouse over an element.
2557          * @name JXG.GeometryElement#mousemove
2558          * @param {Event} e The browser's event object.
2559          */
2560         __evt__mousemove: function (e) { },
2561 
2562         /**
2563          * @event
2564          * @description This event is fired whenever the user drags an element.
2565          * @name JXG.GeometryElement#drag
2566          * @param {Event} e The browser's event object.
2567          */
2568         __evt__drag: function (e) { },
2569 
2570         /**
2571          * @event
2572          * @description This event is fired whenever the user drags the element with a mouse.
2573          * @name JXG.GeometryElement#mousedrag
2574          * @param {Event} e The browser's event object.
2575          */
2576         __evt__mousedrag: function (e) { },
2577 
2578         /**
2579          * @event
2580          * @description This event is fired whenever the user drags the element with a pen.
2581          * @name JXG.GeometryElement#pendrag
2582          * @param {Event} e The browser's event object.
2583          */
2584         __evt__pendrag: function (e) { },
2585 
2586         /**
2587          * @event
2588          * @description This event is fired whenever the user drags the element on a touch device.
2589          * @name JXG.GeometryElement#touchdrag
2590          * @param {Event} e The browser's event object.
2591          */
2592         __evt__touchdrag: function (e) { },
2593 
2594         /**
2595          * @event
2596          * @description This event is fired whenever the user drags the element by pressing arrow keys
2597          * on the keyboard.
2598          * @name JXG.GeometryElement#keydrag
2599          * @param {Event} e The browser's event object.
2600          */
2601         __evt__keydrag: function (e) { },
2602 
2603         /**
2604          * @event
2605          * @description Whenever the user starts to touch or click an element.
2606          * @name JXG.GeometryElement#down
2607          * @param {Event} e The browser's event object.
2608          */
2609         __evt__down: function (e) { },
2610 
2611         /**
2612          * @event
2613          * @description Whenever the user starts to click an element.
2614          * @name JXG.GeometryElement#mousedown
2615          * @param {Event} e The browser's event object.
2616          */
2617         __evt__mousedown: function (e) { },
2618 
2619         /**
2620          * @event
2621          * @description Whenever the user taps an element with the pen.
2622          * @name JXG.GeometryElement#pendown
2623          * @param {Event} e The browser's event object.
2624          */
2625         __evt__pendown: function (e) { },
2626 
2627         /**
2628          * @event
2629          * @description Whenever the user starts to touch an element.
2630          * @name JXG.GeometryElement#touchdown
2631          * @param {Event} e The browser's event object.
2632          */
2633         __evt__touchdown: function (e) { },
2634 
2635         /**
2636          * @event
2637          * @description Whenever the user clicks on an element.
2638          * @name JXG.Board#click
2639          * @param {Event} e The browser's event object.
2640          */
2641         __evt__click: function (e) { },
2642 
2643         /**
2644          * @event
2645          * @description Whenever the user double clicks on an element.
2646          * This event works on desktop browser, but is undefined
2647          * on mobile browsers.
2648          * @name JXG.Board#dblclick
2649          * @param {Event} e The browser's event object.
2650          * @see JXG.Board#clickDelay
2651          * @see JXG.Board#dblClickSuppressClick
2652          */
2653         __evt__dblclick: function (e) { },
2654 
2655         /**
2656          * @event
2657          * @description Whenever the user clicks on an element with a mouse device.
2658          * @name JXG.Board#mouseclick
2659          * @param {Event} e The browser's event object.
2660          */
2661         __evt__mouseclick: function (e) { },
2662 
2663         /**
2664          * @event
2665          * @description Whenever the user double clicks on an element with a mouse device.
2666          * @name JXG.Board#mousedblclick
2667          * @param {Event} e The browser's event object.
2668          */
2669         __evt__mousedblclick: function (e) { },
2670 
2671         /**
2672          * @event
2673          * @description Whenever the user clicks on an element with a pointer device.
2674          * @name JXG.Board#pointerclick
2675          * @param {Event} e The browser's event object.
2676          */
2677         __evt__pointerclick: function (e) { },
2678 
2679         /**
2680          * @event
2681          * @description Whenever the user double clicks on an element with a pointer device.
2682          * This event works on desktop browser, but is undefined
2683          * on mobile browsers.
2684          * @name JXG.Board#pointerdblclick
2685          * @param {Event} e The browser's event object.
2686          */
2687         __evt__pointerdblclick: function (e) { },
2688 
2689         /**
2690          * @event
2691          * @description Whenever the user stops to touch or click an element.
2692          * @name JXG.GeometryElement#up
2693          * @param {Event} e The browser's event object.
2694          */
2695         __evt__up: function (e) { },
2696 
2697         /**
2698          * @event
2699          * @description Whenever the user releases the mousebutton over an element.
2700          * @name JXG.GeometryElement#mouseup
2701          * @param {Event} e The browser's event object.
2702          */
2703         __evt__mouseup: function (e) { },
2704 
2705         /**
2706          * @event
2707          * @description Whenever the user lifts the pen over an element.
2708          * @name JXG.GeometryElement#penup
2709          * @param {Event} e The browser's event object.
2710          */
2711         __evt__penup: function (e) { },
2712 
2713         /**
2714          * @event
2715          * @description Whenever the user stops touching an element.
2716          * @name JXG.GeometryElement#touchup
2717          * @param {Event} e The browser's event object.
2718          */
2719         __evt__touchup: function (e) { },
2720 
2721         /**
2722          * @event
2723          * @description Notify every time an attribute is changed.
2724          * @name JXG.GeometryElement#attribute
2725          * @param {Object} o A list of changed attributes and their new value.
2726          * @param {Object} el Reference to the element
2727          */
2728         __evt__attribute: function (o, el) { },
2729 
2730         /**
2731          * @event
2732          * @description This is a generic event handler. It exists for every possible attribute that can be set for
2733          * any element, e.g. if you want to be notified everytime an element's strokecolor is changed, is the event
2734          * <tt>attribute:strokecolor</tt>.
2735          * @name JXG.GeometryElement#attribute:key
2736          * @param val The old value.
2737          * @param nval The new value
2738          * @param {Object} el Reference to the element
2739          */
2740         __evt__attribute_: function (val, nval, el) { },
2741 
2742         /**
2743          * @ignore
2744          */
2745         __evt: function () { }
2746         //endregion
2747     }
2748 );
2749 
2750 export default JXG.GeometryElement;
2751 // const GeometryElement = JXG.GeometryElement;
2752 // export { GeometryElement as default,  GeometryElement };
2753