1 /*
  2     Copyright 2008-2025
  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);  // TODO TomBerend removed this. Check if it is possible.
418             obj.ancestors[this.id] = this;
419 
420             for (el in this.descendants) {
421                 if (this.descendants.hasOwnProperty(el)) {
422                     this.descendants[el].ancestors[this.id] = this;
423 
424                     for (el2 in this.ancestors) {
425                         if (this.ancestors.hasOwnProperty(el2)) {
426                             this.descendants[el].ancestors[this.ancestors[el2].id] =
427                                 this.ancestors[el2];
428                         }
429                     }
430                 }
431             }
432 
433             for (el in this.ancestors) {
434                 if (this.ancestors.hasOwnProperty(el)) {
435                     for (el2 in this.descendants) {
436                         if (this.descendants.hasOwnProperty(el2)) {
437                             this.ancestors[el].descendants[this.descendants[el2].id] =
438                                 this.descendants[el2];
439                         }
440                     }
441                 }
442             }
443             return this;
444         },
445 
446         /**
447          * @param {JXG.GeometryElement} obj The element that is to be added to the descendants list.
448          * @private
449          * @return this
450         */
451         // Adds the given object to the descendants list of this object and all its child objects.
452         addDescendants: function (obj) {
453             var el;
454 
455             this.descendants[obj.id] = obj;
456             for (el in obj.childElements) {
457                 if (obj.childElements.hasOwnProperty(el)) {
458                     this.addDescendants(obj.childElements[el]);
459                 }
460             }
461             return this;
462         },
463 
464         /**
465          * Adds ids of elements to the array this.parents. This method needs to be called if some dependencies
466          * can not be detected automatically by JSXGraph. For example if a function graph is given by a function
467          * which refers to coordinates of a point, calling addParents() is necessary.
468          *
469          * @param {Array} parents Array of elements or ids of elements.
470          * Alternatively, one can give a list of objects as parameters.
471          * @returns {JXG.Object} reference to the object itself.
472          *
473          * @example
474          * // Movable function graph
475          * var A = board.create('point', [1, 0], {name:'A'}),
476          *     B = board.create('point', [3, 1], {name:'B'}),
477          *     f = board.create('functiongraph', function(x) {
478          *          var ax = A.X(),
479          *              ay = A.Y(),
480          *              bx = B.X(),
481          *              by = B.Y(),
482          *              a = (by - ay) / ( (bx - ax) * (bx - ax) );
483          *           return a * (x - ax) * (x - ax) + ay;
484          *      }, {fixed: false});
485          * f.addParents([A, B]);
486          * </pre><div class="jxgbox" id="JXG7c91d4d2-986c-4378-8135-24505027f251" style="width: 400px; height: 400px;"></div>
487          * <script type="text/javascript">
488          * (function() {
489          *   var board = JXG.JSXGraph.initBoard('JXG7c91d4d2-986c-4378-8135-24505027f251', {boundingbox: [-1, 9, 9, -1], axis: true, showcopyright: false, shownavigation: false});
490          *   var A = board.create('point', [1, 0], {name:'A'}),
491          *       B = board.create('point', [3, 1], {name:'B'}),
492          *       f = board.create('functiongraph', function(x) {
493          *            var ax = A.X(),
494          *                ay = A.Y(),
495          *                bx = B.X(),
496          *                by = B.Y(),
497          *                a = (by - ay) / ( (bx - ax) * (bx - ax) );
498          *             return a * (x - ax) * (x - ax) + ay;
499          *        }, {fixed: false});
500          *   f.addParents([A, B]);
501          * })();
502          * </script><pre>
503          *
504          **/
505         addParents: function (parents) {
506             var i, len, par;
507 
508             if (Type.isArray(parents)) {
509                 par = parents;
510             } else {
511                 par = arguments;
512             }
513 
514             len = par.length;
515             for (i = 0; i < len; ++i) {
516                 if (!Type.exists(par[i])) {
517                     continue;
518                 }
519                 if (Type.isId(this.board, par[i])) {
520                     this.parents.push(par[i]);
521                 } else if (Type.exists(par[i].id)) {
522                     this.parents.push(par[i].id);
523                 }
524             }
525             this.parents = Type.uniqueArray(this.parents);
526         },
527 
528         /**
529          * Sets ids of elements to the array this.parents.
530          * First, this.parents is cleared. See {@link JXG.GeometryElement#addParents}.
531          * @param {Array} parents Array of elements or ids of elements.
532          * Alternatively, one can give a list of objects as parameters.
533          * @returns {JXG.Object} reference to the object itself.
534          **/
535         setParents: function (parents) {
536             this.parents = [];
537             this.addParents(parents);
538         },
539 
540         /**
541          * Add dependence on elements in JessieCode functions.
542          * @param {Array} function_array Array of functions containing potential properties "deps" with
543          * elements the function depends on.
544          * @returns {JXG.Object} reference to the object itself
545          * @private
546          */
547         addParentsFromJCFunctions: function (function_array) {
548             var i, e, obj;
549             for (i = 0; i < function_array.length; i++) {
550                 for (e in function_array[i].deps) {
551                     obj = function_array[i].deps[e];
552                     this.addParents(obj);
553                     obj.addChild(this);
554                 }
555             }
556             return this;
557         },
558 
559         /**
560          * Remove an element as a child from the current element.
561          * @param {JXG.GeometryElement} obj The dependent object.
562          * @returns {JXG.Object} reference to the object itself
563          */
564         removeChild: function (obj) {
565             //var el, el2;
566 
567             delete this.childElements[obj.id];
568             this.removeDescendants(obj);
569             delete obj.ancestors[this.id];
570 
571             /*
572              // I do not know if these addDescendants stuff has to be adapted to removeChild. A.W.
573             for (el in this.descendants) {
574                 if (this.descendants.hasOwnProperty(el)) {
575                     delete this.descendants[el].ancestors[this.id];
576 
577                     for (el2 in this.ancestors) {
578                         if (this.ancestors.hasOwnProperty(el2)) {
579                             this.descendants[el].ancestors[this.ancestors[el2].id] = this.ancestors[el2];
580                         }
581                     }
582                 }
583             }
584 
585             for (el in this.ancestors) {
586                 if (this.ancestors.hasOwnProperty(el)) {
587                     for (el2 in this.descendants) {
588                         if (this.descendants.hasOwnProperty(el2)) {
589                             this.ancestors[el].descendants[this.descendants[el2].id] = this.descendants[el2];
590                         }
591                     }
592                 }
593             }
594             */
595             return this;
596         },
597 
598         /**
599          * Removes the given object from the descendants list of this object and all its child objects.
600          * @param {JXG.GeometryElement} obj The element that is to be removed from the descendants list.
601          * @private
602          * @returns {JXG.Object} reference to the object itself
603          */
604         removeDescendants: function (obj) {
605             var el;
606 
607             delete this.descendants[obj.id];
608             for (el in obj.childElements) {
609                 if (obj.childElements.hasOwnProperty(el)) {
610                     this.removeDescendants(obj.childElements[el]);
611                 }
612             }
613             return this;
614         },
615 
616         /**
617          * Counts the direct children of an object without counting labels.
618          * @private
619          * @returns {number} Number of children
620          */
621         countChildren: function () {
622             var prop,
623                 d,
624                 s = 0;
625 
626             d = this.childElements;
627             for (prop in d) {
628                 if (d.hasOwnProperty(prop) && prop.indexOf('Label') < 0) {
629                     s++;
630                 }
631             }
632             return s;
633         },
634 
635         /**
636          * Returns the elements name. Used in JessieCode.
637          * @returns {String}
638          */
639         getName: function () {
640             return this.name;
641         },
642 
643         /**
644          * Add transformations to this element.
645          * @param {JXG.Transformation|Array} transform Either one {@link JXG.Transformation}
646          * or an array of {@link JXG.Transformation}s.
647          * @returns {JXG.GeometryElement} Reference to the element.
648          */
649         addTransform: function (transform) {
650             return this;
651         },
652 
653         /**
654          * Decides whether an element can be dragged. This is used in
655          * {@link JXG.GeometryElement#setPositionDirectly} methods
656          * where all parent elements are checked if they may be dragged, too.
657          * @private
658          * @returns {boolean}
659          */
660         draggable: function () {
661             return (
662                 this.isDraggable &&
663                 !this.evalVisProp('fixed') &&
664                 // !this.visProp.frozen &&
665                 this.type !== Const.OBJECT_TYPE_GLIDER
666             );
667         },
668 
669         /**
670          * Translates the object by <tt>(x, y)</tt>. In case the element is defined by points, the defining points are
671          * translated, e.g. a circle constructed by a center point and a point on the circle line.
672          * @param {Number} method The type of coordinates used here.
673          * Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
674          * @param {Array} coords array of translation vector.
675          * @returns {JXG.GeometryElement} Reference to the element object.
676          *
677          * @see JXG.GeometryElement3D#setPosition2D
678          */
679         setPosition: function (method, coords) {
680             var parents = [],
681                 el,
682                 i, len, t;
683 
684             if (!Type.exists(this.parents)) {
685                 return this;
686             }
687 
688             len = this.parents.length;
689             for (i = 0; i < len; ++i) {
690                 el = this.board.select(this.parents[i]);
691                 if (Type.isPoint(el)) {
692                     if (!el.draggable()) {
693                         return this;
694                     }
695                     parents.push(el);
696                 }
697             }
698 
699             if (coords.length === 3) {
700                 coords = coords.slice(1);
701             }
702 
703             t = this.board.create("transform", coords, { type: "translate" });
704 
705             // We distinguish two cases:
706             // 1) elements which depend on free elements, i.e. arcs and sectors
707             // 2) other elements
708             //
709             // In the first case we simply transform the parents elements
710             // In the second case we add a transform to the element.
711             //
712             len = parents.length;
713             if (len > 0) {
714                 t.applyOnce(parents);
715 
716                 // Handle dragging of a 3D element
717                 if (Type.exists(this.view) && this.view.elType === 'view3d') {
718                     for (i = 0; i < this.parents.length; ++i) {
719                         // Search for the parent 3D element
720                         el = this.view.select(this.parents[i]);
721                         if (Type.exists(el.setPosition2D)) {
722                             el.setPosition2D(t);
723                         }
724                     }
725                 }
726 
727             } else {
728                 if (
729                     this.transformations.length > 0 &&
730                     this.transformations[this.transformations.length - 1].isNumericMatrix
731                 ) {
732                     this.transformations[this.transformations.length - 1].melt(t);
733                 } else {
734                     this.addTransform(t);
735                 }
736             }
737 
738             /*
739              * If - against the default configuration - defining gliders are marked as
740              * draggable, then their position has to be updated now.
741              */
742             for (i = 0; i < len; ++i) {
743                 if (parents[i].type === Const.OBJECT_TYPE_GLIDER) {
744                     parents[i].updateGlider();
745                 }
746             }
747 
748             return this;
749         },
750 
751         /**
752          * Moves an element by the difference of two coordinates.
753          * @param {Number} method The type of coordinates used here.
754          * Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
755          * @param {Array} coords coordinates in screen/user units
756          * @param {Array} oldcoords previous coordinates in screen/user units
757          * @returns {JXG.GeometryElement} this element
758          */
759         setPositionDirectly: function (method, coords, oldcoords) {
760             var c = new Coords(method, coords, this.board, false),
761                 oldc = new Coords(method, oldcoords, this.board, false),
762                 dc = Statistics.subtract(c.usrCoords, oldc.usrCoords);
763 
764             this.setPosition(Const.COORDS_BY_USER, dc);
765 
766             return this;
767         },
768 
769         /**
770          * Array of strings containing the polynomials defining the element.
771          * Used for determining geometric loci the groebner way.
772          * @returns {Array} An array containing polynomials describing the locus of the current object.
773          * @public
774          */
775         generatePolynomial: function () {
776             return [];
777         },
778 
779         /**
780          * Animates properties for that object like stroke or fill color, opacity and maybe
781          * even more later.
782          * @param {Object} hash Object containing properties with target values for the animation.
783          * @param {number} time Number of milliseconds to complete the animation.
784          * @param {Object} [options] Optional settings for the animation:<ul><li>callback: A function that is called as soon as the animation is finished.</li></ul>
785          * @returns {JXG.GeometryElement} A reference to the object
786          */
787         animate: function (hash, time, options) {
788             options = options || {};
789             var r,
790                 p,
791                 i,
792                 delay = this.board.attr.animationdelay,
793                 steps = Math.ceil(time / delay),
794                 self = this,
795                 animateColor = function (startRGB, endRGB, property) {
796                     var hsv1, hsv2, sh, ss, sv;
797                     hsv1 = Color.rgb2hsv(startRGB);
798                     hsv2 = Color.rgb2hsv(endRGB);
799 
800                     sh = (hsv2[0] - hsv1[0]) / steps;
801                     ss = (hsv2[1] - hsv1[1]) / steps;
802                     sv = (hsv2[2] - hsv1[2]) / steps;
803                     self.animationData[property] = [];
804 
805                     for (i = 0; i < steps; i++) {
806                         self.animationData[property][steps - i - 1] = Color.hsv2rgb(
807                             hsv1[0] + (i + 1) * sh,
808                             hsv1[1] + (i + 1) * ss,
809                             hsv1[2] + (i + 1) * sv
810                         );
811                     }
812                 },
813                 animateFloat = function (start, end, property, round) {
814                     var tmp, s;
815 
816                     start = parseFloat(start);
817                     end = parseFloat(end);
818 
819                     // we can't animate without having valid numbers.
820                     // And parseFloat returns NaN if the given string doesn't contain
821                     // a valid float number.
822                     if (isNaN(start) || isNaN(end)) {
823                         return;
824                     }
825 
826                     s = (end - start) / steps;
827                     self.animationData[property] = [];
828 
829                     for (i = 0; i < steps; i++) {
830                         tmp = start + (i + 1) * s;
831                         self.animationData[property][steps - i - 1] = round
832                             ? Math.floor(tmp)
833                             : tmp;
834                     }
835                 };
836 
837             this.animationData = {};
838 
839             for (r in hash) {
840                 if (hash.hasOwnProperty(r)) {
841                     p = r.toLowerCase();
842 
843                     switch (p) {
844                         case "strokecolor":
845                         case "fillcolor":
846                             animateColor(this.visProp[p], hash[r], p);
847                             break;
848                         case "size":
849                             if (!Type.isPoint(this)) {
850                                 break;
851                             }
852                             animateFloat(this.visProp[p], hash[r], p, true);
853                             break;
854                         case "strokeopacity":
855                         case "strokewidth":
856                         case "fillopacity":
857                             animateFloat(this.visProp[p], hash[r], p, false);
858                             break;
859                     }
860                 }
861             }
862 
863             this.animationCallback = options.callback;
864             this.board.addAnimation(this);
865             return this;
866         },
867 
868         /**
869          * General update method. Should be overwritten by the element itself.
870          * Can be used sometimes to commit changes to the object.
871          * @return {JXG.GeometryElement} Reference to the element
872          */
873         update: function () {
874             if (this.evalVisProp('trace')) {
875                 this.cloneToBackground();
876             }
877             return this;
878         },
879 
880         /**
881          * Provide updateRenderer method.
882          * @return {JXG.GeometryElement} Reference to the element
883          * @private
884          */
885         updateRenderer: function () {
886             return this;
887         },
888 
889         /**
890          * Run through the full update chain of an element.
891          * @param  {Boolean} visible Set visibility in case the elements attribute value is 'inherit'. null is allowed.
892          * @return {JXG.GeometryElement} Reference to the element
893          * @private
894          */
895         fullUpdate: function (visible) {
896             return this.prepareUpdate().update().updateVisibility(visible).updateRenderer();
897         },
898 
899         /**
900          * Show the element or hide it. If hidden, it will still exist but not be
901          * visible on the board.
902          * <p>
903          * Sets also the display of the inherits elements. These can be
904          * JSXGraph elements or arrays of JSXGraph elements.
905          * However, deeper nesting than this is not supported.
906          *
907          * @param  {Boolean} val true: show the element, false: hide the element
908          * @return {JXG.GeometryElement} Reference to the element
909          * @private
910          */
911         setDisplayRendNode: function (val) {
912             var i, len, s, len_s, obj;
913 
914             if (val === undefined) {
915                 val = this.visPropCalc.visible;
916             }
917 
918             if (val === this.visPropOld.visible) {
919                 return this;
920             }
921 
922             // Set display of the element itself
923             this.board.renderer.display(this, val);
924 
925             // Set the visibility of elements which inherit the attribute 'visible'
926             len = this.inherits.length;
927             for (s = 0; s < len; s++) {
928                 obj = this.inherits[s];
929                 if (Type.isArray(obj)) {
930                     len_s = obj.length;
931                     for (i = 0; i < len_s; i++) {
932                         if (
933                             Type.exists(obj[i]) &&
934                             Type.exists(obj[i].rendNode) &&
935                             obj[i].evalVisProp('visible') === 'inherit'
936                         ) {
937                             obj[i].setDisplayRendNode(val);
938                         }
939                     }
940                 } else {
941                     if (
942                         Type.exists(obj) &&
943                         Type.exists(obj.rendNode) &&
944                         obj.evalVisProp('visible') === 'inherit'
945                     ) {
946                         obj.setDisplayRendNode(val);
947                     }
948                 }
949             }
950 
951             // Set the visibility of the label if it inherits the attribute 'visible'
952             if (this.hasLabel && Type.exists(this.label) && Type.exists(this.label.rendNode)) {
953                 if (this.label.evalVisProp('visible') === 'inherit') {
954                     this.label.setDisplayRendNode(val);
955                 }
956             }
957 
958             return this;
959         },
960 
961         /**
962          * Hide the element. It will still exist but not be visible on the board.
963          * Alias for "element.setAttribute({visible: false});"
964          * @return {JXG.GeometryElement} Reference to the element
965          */
966         hide: function () {
967             this.setAttribute({ visible: false });
968             return this;
969         },
970 
971         /**
972          * Hide the element. It will still exist but not be visible on the board.
973          * Alias for {@link JXG.GeometryElement#hide}
974          * @returns {JXG.GeometryElement} Reference to the element
975          */
976         hideElement: function () {
977             this.hide();
978             return this;
979         },
980 
981         /**
982          * Make the element visible.
983          * Alias for "element.setAttribute({visible: true});"
984          * @return {JXG.GeometryElement} Reference to the element
985          */
986         show: function () {
987             this.setAttribute({ visible: true });
988             return this;
989         },
990 
991         /**
992          * Make the element visible.
993          * Alias for {@link JXG.GeometryElement#show}
994          * @returns {JXG.GeometryElement} Reference to the element
995          */
996         showElement: function () {
997             this.show();
998             return this;
999         },
1000 
1001         /**
1002          * Set the visibility of an element. The visibility is influenced by
1003          * (listed in ascending priority):
1004          * <ol>
1005          * <li> The value of the element's attribute 'visible'
1006          * <li> The visibility of a parent element. (Example: label)
1007          * This overrules the value of the element's attribute value only if
1008          * this attribute value of the element is 'inherit'.
1009          * <li> being inside of the canvas
1010          * </ol>
1011          * <p>
1012          * This method is called three times for most elements:
1013          * <ol>
1014          * <li> between {@link JXG.GeometryElement#update}
1015          * and {@link JXG.GeometryElement#updateRenderer}. In case the value is 'inherit', nothing is done.
1016          * <li> Recursively, called by itself for child elements. Here, 'inherit' is overruled by the parent's value.
1017          * <li> In {@link JXG.GeometryElement#updateRenderer}, if the element is outside of the canvas.
1018          * </ol>
1019          *
1020          * @param  {Boolean} parent_val Visibility of the parent element.
1021          * @return {JXG.GeometryElement} Reference to the element.
1022          * @private
1023          */
1024         updateVisibility: function (parent_val) {
1025             var i, len, s, len_s, obj, val;
1026 
1027             if (this.needsUpdate) {
1028                 if (Type.exists(this.view) && this.view.evalVisProp('visible') === false) {
1029                     // Handle hiding of view3d
1030                     this.visPropCalc.visible = false;
1031 
1032                 } else {
1033                     // Handle the element
1034                     if (parent_val !== undefined) {
1035                         this.visPropCalc.visible = parent_val;
1036                     } else {
1037                         val = this.evalVisProp('visible');
1038 
1039                         // infobox uses hiddenByParent
1040                         if (Type.exists(this.hiddenByParent) && this.hiddenByParent) {
1041                             val = false;
1042                         }
1043                         if (val !== 'inherit') {
1044                             this.visPropCalc.visible = val;
1045                         }
1046                     }
1047 
1048                     // Handle elements which inherit the visibility
1049                     len = this.inherits.length;
1050                     for (s = 0; s < len; s++) {
1051                         obj = this.inherits[s];
1052                         if (Type.isArray(obj)) {
1053                             len_s = obj.length;
1054                             for (i = 0; i < len_s; i++) {
1055                                 if (
1056                                     Type.exists(obj[i]) /*&& Type.exists(obj[i].rendNode)*/ &&
1057                                     obj[i].evalVisProp('visible') === 'inherit'
1058                                 ) {
1059                                     obj[i]
1060                                         .prepareUpdate()
1061                                         .updateVisibility(this.visPropCalc.visible);
1062                                 }
1063                             }
1064                         } else {
1065                             if (
1066                                 Type.exists(obj) /*&& Type.exists(obj.rendNode)*/ &&
1067                                 obj.evalVisProp('visible') === 'inherit'
1068                             ) {
1069                                 obj.prepareUpdate().updateVisibility(this.visPropCalc.visible);
1070                             }
1071                         }
1072                     }
1073                 }
1074 
1075                 // Handle the label if it inherits the visibility
1076                 if (
1077                     Type.exists(this.label) &&
1078                     Type.exists(this.label.visProp) &&
1079                     this.label.evalVisProp('visible')
1080                 ) {
1081                     this.label.prepareUpdate().updateVisibility(this.visPropCalc.visible);
1082                 }
1083             }
1084             return this;
1085         },
1086 
1087         /**
1088          * Sets the value of attribute <tt>key</tt> to <tt>value</tt>.
1089          * Here, mainly hex strings for rga(a) colors are parsed and values of type object get a special treatment.
1090          * Other values are just set to the key.
1091          *
1092          * @param {String} key The attribute's name.
1093          * @param value The new value
1094          * @private
1095          */
1096         _set: function (key, value) {
1097             var el;
1098 
1099             key = key.toLocaleLowerCase();
1100 
1101             // Search for entries in visProp with "color" as part of the key name
1102             // and containing a RGBA string
1103             if (
1104                 this.visProp.hasOwnProperty(key) &&
1105                 key.indexOf('color') >= 0 &&
1106                 Type.isString(value) &&
1107                 value.length === 9 &&
1108                 value.charAt(0) === "#"
1109             ) {
1110                 value = Color.rgba2rgbo(value);
1111                 this.visProp[key] = value[0];
1112                 // Previously: *=. But then, we can only decrease opacity.
1113                 this.visProp[key.replace("color", 'opacity')] = value[1];
1114             } else {
1115                 if (
1116                     value !== null &&
1117                     Type.isObject(value) &&
1118                     !Type.exists(value.id) &&
1119                     !Type.exists(value.name)
1120                 ) {
1121                     // value is of type {prop: val, prop: val,...}
1122                     // Convert these attributes to lowercase, too
1123                     this.visProp[key] = {};
1124                     for (el in value) {
1125                         if (value.hasOwnProperty(el)) {
1126                             this.visProp[key][el.toLocaleLowerCase()] = value[el];
1127                         }
1128                     }
1129                 } else {
1130                     this.visProp[key] = value;
1131                 }
1132             }
1133         },
1134 
1135         /**
1136          * Resolves attribute shortcuts like <tt>color</tt> and expands them, e.g. <tt>strokeColor</tt> and <tt>fillColor</tt>.
1137          * Writes the expanded attributes back to the given <tt>attributes</tt>.
1138          * @param {Object} attributes object
1139          * @returns {Object} The given attributes object with shortcuts expanded.
1140          * @private
1141          */
1142         resolveShortcuts: function (attributes) {
1143             var key, i, j,
1144                 subattr = ["traceattributes", "traceAttributes"];
1145 
1146             for (key in Options.shortcuts) {
1147                 if (Options.shortcuts.hasOwnProperty(key)) {
1148                     if (Type.exists(attributes[key])) {
1149                         for (i = 0; i < Options.shortcuts[key].length; i++) {
1150                             if (!Type.exists(attributes[Options.shortcuts[key][i]])) {
1151                                 attributes[Options.shortcuts[key][i]] = attributes[key];
1152                             }
1153                         }
1154                     }
1155                     for (j = 0; j < subattr.length; j++) {
1156                         if (Type.isObject(attributes[subattr[j]])) {
1157                             attributes[subattr[j]] = this.resolveShortcuts(attributes[subattr[j]]);
1158                         }
1159                     }
1160                 }
1161             }
1162             return attributes;
1163         },
1164 
1165         /**
1166          * Sets a label and its text
1167          * If label doesn't exist, it creates one
1168          * @param {String} str
1169          */
1170         setLabel: function (str) {
1171             if (!this.hasLabel) {
1172                 this.setAttribute({ withlabel: true });
1173             }
1174             this.setLabelText(str);
1175         },
1176 
1177         /**
1178          * Updates the element's label text, strips all html.
1179          * @param {String} str
1180          */
1181         setLabelText: function (str) {
1182             if (Type.exists(this.label)) {
1183                 str = str.replace(/</g, "<").replace(/>/g, ">");
1184                 this.label.setText(str);
1185             }
1186 
1187             return this;
1188         },
1189 
1190         /**
1191          * Updates the element's label text and the element's attribute "name", strips all html.
1192          * @param {String} str
1193          */
1194         setName: function (str) {
1195             str = str.replace(/</g, "<").replace(/>/g, ">");
1196             if (this.elType !== 'slider') {
1197                 this.setLabelText(str);
1198             }
1199             this.setAttribute({ name: str });
1200         },
1201 
1202         /**
1203          * Deprecated alias for {@link JXG.GeometryElement#setAttribute}.
1204          * @deprecated Use {@link JXG.GeometryElement#setAttribute}.
1205          */
1206         setProperty: function () {
1207             JXG.deprecated("setProperty()", "setAttribute()");
1208             this.setAttribute.apply(this, arguments);
1209         },
1210 
1211         /**
1212          * Sets an arbitrary number of attributes. This method has one or more
1213          * parameters of the following types:
1214          * <ul>
1215          * <li> object: {key1:value1,key2:value2,...}
1216          * <li> string: 'key:value'
1217          * <li> array: ['key', value]
1218          * </ul>
1219          * @param {Object} attributes An object with attributes.
1220          * @returns {JXG.GeometryElement} A reference to the element.
1221          *
1222          * @function
1223          * @example
1224          * // Set attribute directly on creation of an element using the attributes object parameter
1225          * var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1, 5, 5, 1]};
1226          * var p = board.create('point', [2, 2], {visible: false});
1227          *
1228          * // Now make this point visible and fixed:
1229          * p.setAttribute({
1230          *     fixed: true,
1231          *     visible: true
1232          * });
1233          */
1234         setAttribute: function (attr) {
1235             var i, j, le, key, value, arg,
1236                 opacity, pair, oldvalue,
1237                 attributes = {};
1238 
1239             // Normalize the user input
1240             for (i = 0; i < arguments.length; i++) {
1241                 arg = arguments[i];
1242                 if (Type.isString(arg)) {
1243                     // pairRaw is string of the form 'key:value'
1244                     pair = arg.split(":");
1245                     attributes[Type.trim(pair[0])] = Type.trim(pair[1]);
1246                 } else if (!Type.isArray(arg)) {
1247                     // pairRaw consists of objects of the form {key1:value1,key2:value2,...}
1248                     JXG.extend(attributes, arg);
1249                 } else {
1250                     // pairRaw consists of array [key,value]
1251                     attributes[arg[0]] = arg[1];
1252                 }
1253             }
1254 
1255             // Handle shortcuts
1256             attributes = this.resolveShortcuts(attributes);
1257 
1258             for (i in attributes) {
1259                 if (attributes.hasOwnProperty(i)) {
1260                     key = i.replace(/\s+/g, "").toLowerCase();
1261                     value = attributes[i];
1262 
1263                     // This handles the subobjects, if the key:value pairs are contained in an object.
1264                     // Example:
1265                     // ticks.setAttribute({
1266                     //      strokeColor: 'blue',
1267                     //      label: {
1268                     //          visible: false
1269                     //      }
1270                     // })
1271                     // Now, only the supplied label attributes are overwritten.
1272                     // Otherwise, the value of label would be {visible:false} only.
1273                     if (Type.isObject(value) && Type.exists(this.visProp[key])) {
1274                         // this.visProp[key] = Type.merge(this.visProp[key], value);
1275                         if (!Type.isObject(this.visProp[key]) && value !== null && Type.isObject(value)) {
1276                             // Handle cases like key=firstarrow and
1277                             // firstarrow==false and value = { type:1 }.
1278                             // That is a primitive type is replaced by an object.
1279                             this.visProp[key] = {};
1280                         }
1281                         Type.mergeAttr(this.visProp[key], value);
1282 
1283                         // First, handle the special case
1284                         // ticks.setAttribute({label: {anchorX: "right", ..., visible: true});
1285                         if (this.type === Const.OBJECT_TYPE_TICKS && Type.exists(this.labels)) {
1286                             le = this.labels.length;
1287                             for (j = 0; j < le; j++) {
1288                                 this.labels[j].setAttribute(value);
1289                             }
1290                         } else if (Type.exists(this[key])) {
1291                             // Attribute looks like: point1: {...}
1292                             // Handle this in the sub-element: this.point1.setAttribute({...})
1293                             if (Type.isArray(this[key])) {
1294                                 for (j = 0; j < this[key].length; j++) {
1295                                     this[key][j].setAttribute(value);
1296                                 }
1297                             } else {
1298                                 this[key].setAttribute(value);
1299                             }
1300                         } else {
1301                             // Cases like firstarrow: {...}
1302                             oldvalue = null;
1303                             this.triggerEventHandlers(["attribute:" + key], [oldvalue, value, this]);
1304                         }
1305                         continue;
1306                     }
1307 
1308                     oldvalue = this.visProp[key];
1309                     switch (key) {
1310                         case "checked":
1311                             // checkbox Is not available on initial call.
1312                             if (Type.exists(this.rendNodeTag)) {
1313                                 this.rendNodeCheckbox.checked = !!value;
1314                             }
1315                             break;
1316                         case "disabled":
1317                             // button, checkbox, input. Is not available on initial call.
1318                             if (Type.exists(this.rendNodeTag)) {
1319                                 this.rendNodeTag.disabled = !!value;
1320                             }
1321                             break;
1322                         case "face":
1323                             if (Type.isPoint(this)) {
1324                                 this.visProp.face = value;
1325                                 this.board.renderer.changePointStyle(this);
1326                             }
1327                             break;
1328                         case "generatelabelvalue":
1329                             if (
1330                                 this.type === Const.OBJECT_TYPE_TICKS &&
1331                                 Type.isFunction(value)
1332                             ) {
1333                                 this.generateLabelValue = value;
1334                             }
1335                             break;
1336                         case "gradient":
1337                             this.visProp.gradient = value;
1338                             this.board.renderer.setGradient(this);
1339                             break;
1340                         case "gradientsecondcolor":
1341                             value = Color.rgba2rgbo(value);
1342                             this.visProp.gradientsecondcolor = value[0];
1343                             this.visProp.gradientsecondopacity = value[1];
1344                             this.board.renderer.updateGradient(this);
1345                             break;
1346                         case "gradientsecondopacity":
1347                             this.visProp.gradientsecondopacity = value;
1348                             this.board.renderer.updateGradient(this);
1349                             break;
1350                         case "infoboxtext":
1351                             if (Type.isString(value)) {
1352                                 this.infoboxText = value;
1353                             } else {
1354                                 this.infoboxText = false;
1355                             }
1356                             break;
1357                         case "labelcolor":
1358                             value = Color.rgba2rgbo(value);
1359                             opacity = value[1];
1360                             value = value[0];
1361                             if (opacity === 0) {
1362                                 if (Type.exists(this.label) && this.hasLabel) {
1363                                     this.label.hideElement();
1364                                 }
1365                             }
1366                             if (Type.exists(this.label) && this.hasLabel) {
1367                                 this.label.visProp.strokecolor = value;
1368                                 this.board.renderer.setObjectStrokeColor(
1369                                     this.label,
1370                                     value,
1371                                     opacity
1372                                 );
1373                             }
1374                             if (this.elementClass === Const.OBJECT_CLASS_TEXT) {
1375                                 this.visProp.strokecolor = value;
1376                                 this.visProp.strokeopacity = opacity;
1377                                 this.board.renderer.setObjectStrokeColor(this, value, opacity);
1378                             }
1379                             break;
1380                         case "layer":
1381                             this.board.renderer.setLayer(this, this.eval(value));
1382                             this._set(key, value);
1383                             break;
1384                         case "maxlength":
1385                             // input. Is not available on initial call.
1386                             if (Type.exists(this.rendNodeTag)) {
1387                                 this.rendNodeTag.maxlength = !!value;
1388                             }
1389                             break;
1390                         case "name":
1391                             oldvalue = this.name;
1392                             delete this.board.elementsByName[this.name];
1393                             this.name = value;
1394                             this.board.elementsByName[this.name] = this;
1395                             break;
1396                         case "needsregularupdate":
1397                             this.needsRegularUpdate = !(value === "false" || value === false);
1398                             this.board.renderer.setBuffering(
1399                                 this,
1400                                 this.needsRegularUpdate ? "auto" : "static"
1401                             );
1402                             break;
1403                         case "onpolygon":
1404                             if (this.type === Const.OBJECT_TYPE_GLIDER) {
1405                                 this.onPolygon = !!value;
1406                             }
1407                             break;
1408                         case "radius":
1409                             if (
1410                                 this.type === Const.OBJECT_TYPE_ANGLE ||
1411                                 this.type === Const.OBJECT_TYPE_SECTOR
1412                             ) {
1413                                 this.setRadius(value);
1414                             }
1415                             break;
1416                         case "rotate":
1417                             if (
1418                                 (this.elementClass === Const.OBJECT_CLASS_TEXT &&
1419                                     this.evalVisProp('display') === 'internal') ||
1420                                 this.type === Const.OBJECT_TYPE_IMAGE
1421                             ) {
1422                                 this.addRotation(value);
1423                             }
1424                             break;
1425                         case "tabindex":
1426                             if (Type.exists(this.rendNode)) {
1427                                 this.rendNode.setAttribute("tabindex", value);
1428                                 this._set(key, value);
1429                             }
1430                             break;
1431                         // case "ticksdistance":
1432                         //     if (this.type === Const.OBJECT_TYPE_TICKS && Type.isNumber(value)) {
1433                         //         this.ticksFunction = this.makeTicksFunction(value);
1434                         //     }
1435                         //     break;
1436                         case "trace":
1437                             if (value === "false" || value === false) {
1438                                 this.clearTrace();
1439                                 this.visProp.trace = false;
1440                             } else if (value === 'pause') {
1441                                 this.visProp.trace = false;
1442                             } else {
1443                                 this.visProp.trace = true;
1444                             }
1445                             break;
1446                         case "visible":
1447                             if (value === 'false') {
1448                                 this.visProp.visible = false;
1449                             } else if (value === 'true') {
1450                                 this.visProp.visible = true;
1451                             } else {
1452                                 this.visProp.visible = value;
1453                             }
1454 
1455                             this.setDisplayRendNode(this.evalVisProp('visible'));
1456                             if (
1457                                 this.evalVisProp('visible') &&
1458                                 Type.exists(this.updateSize)
1459                             ) {
1460                                 this.updateSize();
1461                             }
1462 
1463                             break;
1464                         case "withlabel":
1465                             this.visProp.withlabel = value;
1466                             if (!this.evalVisProp('withlabel')) {
1467                                 if (this.label && this.hasLabel) {
1468                                     //this.label.hideElement();
1469                                     this.label.setAttribute({ visible: false });
1470                                 }
1471                             } else {
1472                                 if (!this.label) {
1473                                     this.createLabel();
1474                                 }
1475                                 //this.label.showElement();
1476                                 this.label.setAttribute({ visible: 'inherit' });
1477                                 //this.label.setDisplayRendNode(this.evalVisProp('visible'));
1478                             }
1479                             this.hasLabel = value;
1480                             break;
1481                         case "straightfirst":
1482                         case "straightlast":
1483                             this._set(key, value);
1484                             for (j in this.childElements) {
1485                                 if (this.childElements.hasOwnProperty(j) && this.childElements[j].elType === 'glider') {
1486                                     this.childElements[j].fullUpdate();
1487                                 }
1488                             }
1489                             break;
1490                         default:
1491                             if (Type.exists(this.visProp[key]) &&
1492                                 (!JXG.Validator[key] ||                                   // No validator for this key => OK
1493                                     (JXG.Validator[key] && JXG.Validator[key](value)) ||  // Value passes the validator => OK
1494                                     (JXG.Validator[key] &&                                // Value is function, function value passes the validator => OK
1495                                         Type.isFunction(value) && JXG.Validator[key](value(this))
1496                                     )
1497                                 )
1498                             ) {
1499                                 value = (value.toLowerCase && value.toLowerCase() === 'false')
1500                                             ? false
1501                                             : value;
1502                                 this._set(key, value);
1503                             } else {
1504                                 if (!(key in Options.shortcuts)) {
1505                                     JXG.warn("attribute '" + key + "' does not accept type '" + (typeof value) + "' of value " + value + '.');
1506                                 }
1507                             }
1508                             break;
1509                     }
1510                     this.triggerEventHandlers(["attribute:" + key], [oldvalue, value, this]);
1511                 }
1512             }
1513 
1514             this.triggerEventHandlers(["attribute"], [attributes, this]);
1515 
1516             if (!this.evalVisProp('needsregularupdate')) {
1517                 this.board.fullUpdate();
1518             } else {
1519                 this.board.update(this);
1520             }
1521             if (this.elementClass === Const.OBJECT_CLASS_TEXT) {
1522                 this.updateSize();
1523             }
1524 
1525             return this;
1526         },
1527 
1528         /**
1529          * Deprecated alias for {@link JXG.GeometryElement#getAttribute}.
1530          * @deprecated Use {@link JXG.GeometryElement#getAttribute}.
1531          */
1532         getProperty: function () {
1533             JXG.deprecated("getProperty()", "getAttribute()");
1534             this.getProperty.apply(this, arguments);
1535         },
1536 
1537         /**
1538          * Get the value of the property <tt>key</tt>.
1539          * @param {String} key The name of the property you are looking for
1540          * @returns The value of the property
1541          */
1542         getAttribute: function (key) {
1543             var result;
1544             key = key.toLowerCase();
1545 
1546             switch (key) {
1547                 case "needsregularupdate":
1548                     result = this.needsRegularUpdate;
1549                     break;
1550                 case "labelcolor":
1551                     result = this.label.visProp.strokecolor;
1552                     break;
1553                 case "infoboxtext":
1554                     result = this.infoboxText;
1555                     break;
1556                 case "withlabel":
1557                     result = this.hasLabel;
1558                     break;
1559                 default:
1560                     result = this.visProp[key];
1561                     break;
1562             }
1563 
1564             return result;
1565         },
1566 
1567         /**
1568          * Get value of an attribute. If the value that attribute is a function, call the function and return its value.
1569          * In that case, the function is called with the GeometryElement as (only) parameter. For label elements (i.e.
1570          * if the attribute "islabel" is true), the anchor element is supplied. The label element can be accessed as
1571          * sub-object "label".
1572          * If the attribute does not exist, undefined will be returned.
1573          *
1574          * @param {String} key Attribute key
1575          * @returns {String|Number|Boolean} value of attribute "key" (evaluated in case of a function) or undefined
1576          *
1577          * @see GeometryElement#eval
1578          * @see JXG#evaluate
1579          */
1580         evalVisProp: function (key) {
1581             var val, arr, i, le,
1582                 e, o, found;
1583 
1584             key = key.toLowerCase();
1585             if (key.indexOf('.') === -1) {
1586                 // e.g. 'visible'
1587                 val = this.visProp[key];
1588             } else {
1589                 // e.g. label.visible
1590                 arr = key.split('.');
1591                 le = arr.length;
1592                 val = this.visProp;
1593                 for (i = 0; i < le; i++) {
1594                     if (Type.exists(val)) {
1595                         val = val[arr[i]];
1596                     }
1597                 }
1598             }
1599 
1600             if (JXG.isFunction(val)) {
1601                 // For labels supply the anchor element as parameter.
1602                 if (this.visProp.islabel === true && Type.exists(this.visProp.anchor)) {
1603                     // 3D: supply the 3D element
1604                     if (this.visProp.anchor.visProp.element3d !== null) {
1605                         return val(this.visProp.anchor.visProp.element3d);
1606                     }
1607                     // 2D: supply the 2D element
1608                     return val(this.visProp.anchor);
1609                 }
1610                 // For 2D elements representing 3D elements, return the 3D element.
1611                 if (JXG.exists(this.visProp.element3d)) {
1612                     return val(this.visProp.element3d);
1613                 }
1614                 // In all other cases, return the element itself
1615                 return val(this);
1616             }
1617             // val is not of type function
1618 
1619             if (val === 'inherit') {
1620                 for (e in this.descendants) {
1621                     if (this.descendants.hasOwnProperty(e)) {
1622                         o = this.descendants[e];
1623                         // Check if this is in inherits of one of its descendant
1624                         found = false;
1625                         le = o.inherits.length;
1626                         for (i = 0; i < le; i++) {
1627                             if (this.id === o.inherits[i].id) {
1628                                 found = true;
1629                                 break;
1630                             }
1631                         }
1632                         if (found) {
1633                             val = o.evalVisProp(key);
1634                             break;
1635                         }
1636                     }
1637                 }
1638             }
1639 
1640             return val;
1641         },
1642 
1643         /**
1644          * Get value of a parameter. If the parameter is a function, call the function and return its value.
1645          * In that case, the function is called with the GeometryElement as (only) parameter. For label elements (i.e.
1646          * if the attribute "islabel" is true), the anchor element is supplied. The label of an element can be accessed as
1647          * sub-object "label" then.
1648          *
1649          * @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
1650          * supplied as the (only) parameter of that function.
1651          * @returns {String|Number|Object}
1652          *
1653          * @see GeometryElement#evalVisProp
1654          * @see JXG#evaluate
1655          */
1656         eval: function(val) {
1657             if (JXG.isFunction(val)) {
1658                 // For labels supply the anchor element as parameter.
1659                 if (this.visProp.islabel === true && Type.exists(this.visProp.anchor)) {
1660                     // 3D: supply the 3D element
1661                     if (this.visProp.anchor.visProp.element3d !== null) {
1662                         return val(this.visProp.anchor.visProp.element3d);
1663                     }
1664                     // 2D: supply the 2D element
1665                     return val(this.visProp.anchor);
1666                 }
1667                 // For 2D elements representing 3D elements, return the 3D element.
1668                 if (this.visProp.element3d !== null) {
1669                     return val(this.visProp.element3d);
1670                 }
1671                 // In all other cases, return the element itself
1672                 return val(this);
1673             }
1674             // val is not of type function
1675             return val;
1676         },
1677 
1678         /**
1679          * Set the dash style of an object. See {@link JXG.GeometryElement#dash}
1680          * for a list of available dash styles.
1681          * You should use {@link JXG.GeometryElement#setAttribute} instead of this method.
1682          *
1683          * @param {number} dash Indicates the new dash style
1684          * @private
1685          */
1686         setDash: function (dash) {
1687             this.setAttribute({ dash: dash });
1688             return this;
1689         },
1690 
1691         /**
1692          * Notify all child elements for updates.
1693          * @private
1694          */
1695         prepareUpdate: function () {
1696             this.needsUpdate = true;
1697             return this;
1698         },
1699 
1700         /**
1701          * Removes the element from the construction.  This only removes the SVG or VML node of the element and its label (if available) from
1702          * the renderer, to remove the element completely you should use {@link JXG.Board#removeObject}.
1703          */
1704         remove: function () {
1705             // this.board.renderer.remove(this.board.renderer.getElementById(this.id));
1706             this.board.renderer.remove(this.rendNode);
1707 
1708             if (this.hasLabel) {
1709                 this.board.renderer.remove(this.board.renderer.getElementById(this.label.id));
1710             }
1711             return this;
1712         },
1713 
1714         /**
1715          * Returns the coords object where a text that is bound to the element shall be drawn.
1716          * Differs in some cases from the values that getLabelAnchor returns.
1717          * @returns {JXG.Coords} JXG.Coords Place where the text shall be drawn.
1718          * @see JXG.GeometryElement#getLabelAnchor
1719          */
1720         getTextAnchor: function () {
1721             return new Coords(Const.COORDS_BY_USER, [0, 0], this.board);
1722         },
1723 
1724         /**
1725          * Returns the coords object where the label of the element shall be drawn.
1726          * Differs in some cases from the values that getTextAnchor returns.
1727          * @returns {JXG.Coords} JXG.Coords Place where the text shall be drawn.
1728          * @see JXG.GeometryElement#getTextAnchor
1729          */
1730         getLabelAnchor: function () {
1731             return new Coords(Const.COORDS_BY_USER, [0, 0], this.board);
1732         },
1733 
1734         /**
1735          * Determines whether the element has arrows at start or end of the arc.
1736          * If it is set to be a "typical" vector, ie lastArrow == true,
1737          * then the element.type is set to VECTOR.
1738          * @param {Boolean} firstArrow True if there is an arrow at the start of the arc, false otherwise.
1739          * @param {Boolean} lastArrow True if there is an arrow at the end of the arc, false otherwise.
1740          */
1741         setArrow: function (firstArrow, lastArrow) {
1742             this.visProp.firstarrow = firstArrow;
1743             this.visProp.lastarrow = lastArrow;
1744             if (lastArrow) {
1745                 this.type = Const.OBJECT_TYPE_VECTOR;
1746                 this.elType = 'arrow';
1747             }
1748 
1749             this.prepareUpdate().update().updateVisibility().updateRenderer();
1750             return this;
1751         },
1752 
1753         /**
1754          * Creates a gradient nodes in the renderer.
1755          * @see JXG.SVGRenderer#setGradient
1756          * @private
1757          */
1758         createGradient: function () {
1759             var ev_g = this.evalVisProp('gradient');
1760             if (ev_g === "linear" || ev_g === 'radial') {
1761                 this.board.renderer.setGradient(this);
1762             }
1763         },
1764 
1765         /**
1766          * Creates a label element for this geometry element.
1767          * @see JXG.GeometryElement#addLabelToElement
1768          */
1769         createLabel: function () {
1770             var attr,
1771                 that = this;
1772 
1773             // this is a dirty hack to resolve the text-dependency. If there is no text element available,
1774             // just don't create a label. This method is usually not called by a user, so we won't throw
1775             // an exception here and simply output a warning via JXG.debug.
1776             if (JXG.elements.text) {
1777                 attr = Type.deepCopy(this.visProp.label, null);
1778                 attr.id = this.id + 'Label';
1779                 attr.isLabel = true;
1780                 attr.anchor = this;
1781                 attr.priv = this.visProp.priv;
1782 
1783                 if (this.visProp.withlabel) {
1784                     this.label = JXG.elements.text(
1785                         this.board,
1786                         [
1787                             0,
1788                             0,
1789                             function () {
1790                                 if (Type.isFunction(that.name)) {
1791                                     return that.name(that);
1792                                 }
1793                                 return that.name;
1794                             }
1795                         ],
1796                         attr
1797                     );
1798                     this.label.needsUpdate = true;
1799                     this.label.dump = false;
1800                     this.label.fullUpdate();
1801 
1802                     this.hasLabel = true;
1803                 }
1804             } else {
1805                 JXG.debug(
1806                     "JSXGraph: Can't create label: text element is not available. Make sure you include base/text"
1807                 );
1808             }
1809 
1810             return this;
1811         },
1812 
1813         /**
1814          * Highlights the element.
1815          * @private
1816          * @param {Boolean} [force=false] Force the highlighting
1817          * @returns {JXG.Board}
1818          */
1819         highlight: function (force) {
1820             force = Type.def(force, false);
1821             // I know, we have the JXG.Board.highlightedObjects AND JXG.GeometryElement.highlighted and YES we need both.
1822             // Board.highlightedObjects is for the internal highlighting and GeometryElement.highlighted is for user highlighting
1823             // initiated by the user, e.g. through custom DOM events. We can't just pick one because this would break user
1824             // defined highlighting in many ways:
1825             //  * if overriding the highlight() methods the user had to handle the highlightedObjects stuff, otherwise he'd break
1826             //    everything (e.g. the pie chart example https://jsxgraph.org/wiki/index.php/Pie_chart (not exactly
1827             //    user defined but for this type of chart the highlight method was overridden and not adjusted to the changes in here)
1828             //    where it just kept highlighting until the radius of the pie was far beyond infinity...
1829             //  * user defined highlighting would get pointless, everytime the user highlights something using .highlight(), it would get
1830             //    dehighlighted immediately, because highlight puts the element into highlightedObjects and from there it gets dehighlighted
1831             //    through dehighlightAll.
1832 
1833             // highlight only if not highlighted
1834             if (this.evalVisProp('highlight') && (!this.highlighted || force)) {
1835                 this.highlighted = true;
1836                 this.board.highlightedObjects[this.id] = this;
1837                 this.board.renderer.highlight(this);
1838             }
1839             return this;
1840         },
1841 
1842         /**
1843          * Uses the "normal" properties of the element.
1844          * @returns {JXG.Board}
1845          */
1846         noHighlight: function () {
1847             // see comment in JXG.GeometryElement.highlight()
1848 
1849             // dehighlight only if not highlighted
1850             if (this.highlighted) {
1851                 this.highlighted = false;
1852                 delete this.board.highlightedObjects[this.id];
1853                 this.board.renderer.noHighlight(this);
1854             }
1855             return this;
1856         },
1857 
1858         /**
1859          * Removes all objects generated by the trace function.
1860          */
1861         clearTrace: function () {
1862             var obj;
1863 
1864             for (obj in this.traces) {
1865                 if (this.traces.hasOwnProperty(obj)) {
1866                     this.board.renderer.remove(this.traces[obj]);
1867                 }
1868             }
1869 
1870             this.numTraces = 0;
1871             return this;
1872         },
1873 
1874         /**
1875          * Copy the element to background. This is used for tracing elements.
1876          * @returns {JXG.GeometryElement} A reference to the element
1877          */
1878         cloneToBackground: function () {
1879             return this;
1880         },
1881 
1882         /**
1883          * Dimensions of the smallest rectangle enclosing the element.
1884          * @returns {Array} The coordinates of the enclosing rectangle in a format
1885          * like the bounding box in {@link JXG.Board#setBoundingBox}.
1886          *
1887          * @returns {Array} similar to {@link JXG.Board#setBoundingBox}.
1888          */
1889         bounds: function () {
1890             return [0, 0, 0, 0];
1891         },
1892 
1893         /**
1894          * Normalize the element's standard form.
1895          * @private
1896          */
1897         normalize: function () {
1898             this.stdform = Mat.normalize(this.stdform);
1899             return this;
1900         },
1901 
1902         /**
1903          * EXPERIMENTAL. Generate JSON object code of visProp and other properties.
1904          * @type String
1905          * @private
1906          * @ignore
1907          * @deprecated
1908          * @returns JSON string containing element's properties.
1909          */
1910         toJSON: function () {
1911             var vis,
1912                 key,
1913                 json = ['{"name":', this.name];
1914 
1915             json.push(", " + '"id":' + this.id);
1916 
1917             vis = [];
1918             for (key in this.visProp) {
1919                 if (this.visProp.hasOwnProperty(key)) {
1920                     if (Type.exists(this.visProp[key])) {
1921                         vis.push('"' + key + '":' + this.visProp[key]);
1922                     }
1923                 }
1924             }
1925             json.push(', "visProp":{' + vis.toString() + "}");
1926             json.push("}");
1927 
1928             return json.join("");
1929         },
1930 
1931         /**
1932          * Rotate texts or images by a given degree.
1933          * @param {number} angle The degree of the rotation (90 means vertical text).
1934          * @see JXG.GeometryElement#rotate
1935          */
1936         addRotation: function (angle) {
1937             var tOffInv,
1938                 tOff,
1939                 tS,
1940                 tSInv,
1941                 tRot,
1942                 that = this;
1943 
1944             if (
1945                 (this.elementClass === Const.OBJECT_CLASS_TEXT ||
1946                     this.type === Const.OBJECT_TYPE_IMAGE) &&
1947                 angle !== 0
1948             ) {
1949                 tOffInv = this.board.create(
1950                     "transform",
1951                     [
1952                         function () {
1953                             return -that.X();
1954                         },
1955                         function () {
1956                             return -that.Y();
1957                         }
1958                     ],
1959                     { type: "translate" }
1960                 );
1961 
1962                 tOff = this.board.create(
1963                     "transform",
1964                     [
1965                         function () {
1966                             return that.X();
1967                         },
1968                         function () {
1969                             return that.Y();
1970                         }
1971                     ],
1972                     { type: "translate" }
1973                 );
1974 
1975                 tS = this.board.create(
1976                     "transform",
1977                     [
1978                         function () {
1979                             return that.board.unitX / that.board.unitY;
1980                         },
1981                         function () {
1982                             return 1;
1983                         }
1984                     ],
1985                     { type: "scale" }
1986                 );
1987 
1988                 tSInv = this.board.create(
1989                     "transform",
1990                     [
1991                         function () {
1992                             return that.board.unitY / that.board.unitX;
1993                         },
1994                         function () {
1995                             return 1;
1996                         }
1997                     ],
1998                     { type: "scale" }
1999                 );
2000 
2001                 tRot = this.board.create(
2002                     "transform",
2003                     [
2004                         function () {
2005                             return (that.eval(angle) * Math.PI) / 180;
2006                         }
2007                     ],
2008                     { type: "rotate" }
2009                 );
2010 
2011                 tOffInv.bindTo(this);
2012                 tS.bindTo(this);
2013                 tRot.bindTo(this);
2014                 tSInv.bindTo(this);
2015                 tOff.bindTo(this);
2016             }
2017 
2018             return this;
2019         },
2020 
2021         /**
2022          * Set the highlightStrokeColor of an element
2023          * @ignore
2024          * @name JXG.GeometryElement#highlightStrokeColorMethod
2025          * @param {String} sColor String which determines the stroke color of an object when its highlighted.
2026          * @see JXG.GeometryElement#highlightStrokeColor
2027          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2028          */
2029         highlightStrokeColor: function (sColor) {
2030             JXG.deprecated("highlightStrokeColor()", "setAttribute()");
2031             this.setAttribute({ highlightStrokeColor: sColor });
2032             return this;
2033         },
2034 
2035         /**
2036          * Set the strokeColor of an element
2037          * @ignore
2038          * @name JXG.GeometryElement#strokeColorMethod
2039          * @param {String} sColor String which determines the stroke color of an object.
2040          * @see JXG.GeometryElement#strokeColor
2041          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2042          */
2043         strokeColor: function (sColor) {
2044             JXG.deprecated("strokeColor()", "setAttribute()");
2045             this.setAttribute({ strokeColor: sColor });
2046             return this;
2047         },
2048 
2049         /**
2050          * Set the strokeWidth of an element
2051          * @ignore
2052          * @name JXG.GeometryElement#strokeWidthMethod
2053          * @param {Number} width Integer which determines the stroke width of an outline.
2054          * @see JXG.GeometryElement#strokeWidth
2055          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2056          */
2057         strokeWidth: function (width) {
2058             JXG.deprecated("strokeWidth()", "setAttribute()");
2059             this.setAttribute({ strokeWidth: width });
2060             return this;
2061         },
2062 
2063         /**
2064          * Set the fillColor of an element
2065          * @ignore
2066          * @name JXG.GeometryElement#fillColorMethod
2067          * @param {String} fColor String which determines the fill color of an object.
2068          * @see JXG.GeometryElement#fillColor
2069          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2070          */
2071         fillColor: function (fColor) {
2072             JXG.deprecated("fillColor()", "setAttribute()");
2073             this.setAttribute({ fillColor: fColor });
2074             return this;
2075         },
2076 
2077         /**
2078          * Set the highlightFillColor of an element
2079          * @ignore
2080          * @name JXG.GeometryElement#highlightFillColorMethod
2081          * @param {String} fColor String which determines the fill color of an object when its highlighted.
2082          * @see JXG.GeometryElement#highlightFillColor
2083          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2084          */
2085         highlightFillColor: function (fColor) {
2086             JXG.deprecated("highlightFillColor()", "setAttribute()");
2087             this.setAttribute({ highlightFillColor: fColor });
2088             return this;
2089         },
2090 
2091         /**
2092          * Set the labelColor of an element
2093          * @ignore
2094          * @param {String} lColor String which determines the text color of an object's label.
2095          * @see JXG.GeometryElement#labelColor
2096          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2097          */
2098         labelColor: function (lColor) {
2099             JXG.deprecated("labelColor()", "setAttribute()");
2100             this.setAttribute({ labelColor: lColor });
2101             return this;
2102         },
2103 
2104         /**
2105          * Set the dash type of an element
2106          * @ignore
2107          * @name JXG.GeometryElement#dashMethod
2108          * @param {Number} d Integer which determines the way of dashing an element's outline.
2109          * @see JXG.GeometryElement#dash
2110          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2111          */
2112         dash: function (d) {
2113             JXG.deprecated("dash()", "setAttribute()");
2114             this.setAttribute({ dash: d });
2115             return this;
2116         },
2117 
2118         /**
2119          * Set the visibility of an element
2120          * @ignore
2121          * @name JXG.GeometryElement#visibleMethod
2122          * @param {Boolean} v Boolean which determines whether the element is drawn.
2123          * @see JXG.GeometryElement#visible
2124          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2125          */
2126         visible: function (v) {
2127             JXG.deprecated("visible()", "setAttribute()");
2128             this.setAttribute({ visible: v });
2129             return this;
2130         },
2131 
2132         /**
2133          * Set the shadow of an element
2134          * @ignore
2135          * @name JXG.GeometryElement#shadowMethod
2136          * @param {Boolean} s Boolean which determines whether the element has a shadow or not.
2137          * @see JXG.GeometryElement#shadow
2138          * @deprecated Use {@link JXG.GeometryElement#setAttribute}
2139          */
2140         shadow: function (s) {
2141             JXG.deprecated("shadow()", "setAttribute()");
2142             this.setAttribute({ shadow: s });
2143             return this;
2144         },
2145 
2146         /**
2147          * The type of the element as used in {@link JXG.Board#create}.
2148          * @returns {String}
2149          */
2150         getType: function () {
2151             return this.elType;
2152         },
2153 
2154         /**
2155          * List of the element ids resp. values used as parents in {@link JXG.Board#create}.
2156          * @returns {Array}
2157          */
2158         getParents: function () {
2159             return Type.isArray(this.parents) ? this.parents : [];
2160         },
2161 
2162         /**
2163          * @ignore
2164          * Snaps the element to the grid. Only works for points, lines and circles. Points will snap to the grid
2165          * as defined in their properties {@link JXG.Point#snapSizeX} and {@link JXG.Point#snapSizeY}. Lines and circles
2166          * will snap their parent points to the grid, if they have {@link JXG.Point#snapToGrid} set to true.
2167          * @private
2168          * @returns {JXG.GeometryElement} Reference to the element.
2169          */
2170         snapToGrid: function () {
2171             return this;
2172         },
2173 
2174         /**
2175          * Snaps the element to points. Only works for points. Points will snap to the next point
2176          * as defined in their properties {@link JXG.Point#attractorDistance} and {@link JXG.Point#attractorUnit}.
2177          * Lines and circles
2178          * will snap their parent points to points.
2179          * @private
2180          * @returns {JXG.GeometryElement} Reference to the element.
2181          */
2182         snapToPoints: function () {
2183             return this;
2184         },
2185 
2186         /**
2187          * Retrieve a copy of the current visProp.
2188          * @returns {Object}
2189          */
2190         getAttributes: function () {
2191             var attributes = Type.deepCopy(this.visProp),
2192                 /*
2193                 cleanThis = ['attractors', 'snatchdistance', 'traceattributes', 'frozen',
2194                     'shadow', 'gradientangle', 'gradientsecondopacity', 'gradientpositionx', 'gradientpositiony',
2195                     'needsregularupdate', 'zoom', 'layer', 'offset'],
2196                 */
2197                 cleanThis = [],
2198                 i,
2199                 len = cleanThis.length;
2200 
2201             attributes.id = this.id;
2202             attributes.name = this.name;
2203 
2204             for (i = 0; i < len; i++) {
2205                 delete attributes[cleanThis[i]];
2206             }
2207 
2208             return attributes;
2209         },
2210 
2211         /**
2212          * Checks whether (x,y) is near the element.
2213          * @param {Number} x Coordinate in x direction, screen coordinates.
2214          * @param {Number} y Coordinate in y direction, screen coordinates.
2215          * @returns {Boolean} True if (x,y) is near the element, False otherwise.
2216          */
2217         hasPoint: function (x, y) {
2218             return false;
2219         },
2220 
2221         /**
2222          * Adds ticks to this line or curve. Ticks can be added to a curve or any kind of line: line, arrow, and axis.
2223          * @param {JXG.Ticks} ticks Reference to a ticks object which is describing the ticks (color, distance, how many, etc.).
2224          * @returns {String} Id of the ticks object.
2225          */
2226         addTicks: function (ticks) {
2227             if (ticks.id === "" || !Type.exists(ticks.id)) {
2228                 ticks.id = this.id + "_ticks_" + (this.ticks.length + 1);
2229             }
2230 
2231             this.board.renderer.drawTicks(ticks);
2232             this.ticks.push(ticks);
2233 
2234             return ticks.id;
2235         },
2236 
2237         /**
2238          * Removes all ticks from a line or curve.
2239          */
2240         removeAllTicks: function () {
2241             var t;
2242             if (Type.exists(this.ticks)) {
2243                 for (t = this.ticks.length - 1; t >= 0; t--) {
2244                     this.removeTicks(this.ticks[t]);
2245                 }
2246                 this.ticks = [];
2247                 this.board.update();
2248             }
2249         },
2250 
2251         /**
2252          * Removes ticks identified by parameter named tick from this line or curve.
2253          * @param {JXG.Ticks} tick Reference to tick object to remove.
2254          */
2255         removeTicks: function (tick) {
2256             var t, j;
2257 
2258             if (Type.exists(this.defaultTicks) && this.defaultTicks === tick) {
2259                 this.defaultTicks = null;
2260             }
2261 
2262             if (Type.exists(this.ticks)) {
2263                 for (t = this.ticks.length - 1; t >= 0; t--) {
2264                     if (this.ticks[t] === tick) {
2265                         this.board.removeObject(this.ticks[t]);
2266 
2267                         if (this.ticks[t].ticks) {
2268                             for (j = 0; j < this.ticks[t].ticks.length; j++) {
2269                                 if (Type.exists(this.ticks[t].labels[j])) {
2270                                     this.board.removeObject(this.ticks[t].labels[j]);
2271                                 }
2272                             }
2273                         }
2274 
2275                         delete this.ticks[t];
2276                         break;
2277                     }
2278                 }
2279             }
2280         },
2281 
2282         /**
2283          * Determine values of snapSizeX and snapSizeY. If the attributes
2284          * snapSizex and snapSizeY are greater than zero, these values are taken.
2285          * Otherwise, determine the distance between major ticks of the
2286          * default axes.
2287          * @returns {Array} containing the snap sizes for x and y direction.
2288          * @private
2289          */
2290         getSnapSizes: function () {
2291             var sX, sY, ticks;
2292 
2293             sX = this.evalVisProp('snapsizex');
2294             sY = this.evalVisProp('snapsizey');
2295 
2296             if (sX <= 0 && this.board.defaultAxes && this.board.defaultAxes.x.defaultTicks) {
2297                 ticks = this.board.defaultAxes.x.defaultTicks;
2298                 sX = ticks.ticksDelta * (ticks.evalVisProp('minorticks') + 1);
2299             }
2300 
2301             if (sY <= 0 && this.board.defaultAxes && this.board.defaultAxes.y.defaultTicks) {
2302                 ticks = this.board.defaultAxes.y.defaultTicks;
2303                 sY = ticks.ticksDelta * (ticks.evalVisProp('minorticks') + 1);
2304             }
2305 
2306             return [sX, sY];
2307         },
2308 
2309         /**
2310          * Move an element to its nearest grid point.
2311          * The function uses the coords object of the element as
2312          * its actual position. If there is no coords object or if the object is fixed, nothing is done.
2313          * @param {Boolean} force force snapping independent from what the snaptogrid attribute says
2314          * @param {Boolean} fromParent True if the drag comes from a child element. This is the case if a line
2315          *    through two points is dragged. In this case we do not try to force the points to stay inside of
2316          *    the visible board, but the distance between the two points stays constant.
2317          * @returns {JXG.GeometryElement} Reference to this element
2318          */
2319         handleSnapToGrid: function (force, fromParent) {
2320             var x, y, rx, ry, rcoords,
2321                 mi, ma,
2322                 boardBB, res, sX, sY,
2323                 needsSnapToGrid = false,
2324                 attractToGrid = this.evalVisProp('attracttogrid'),
2325                 ev_au = this.evalVisProp('attractorunit'),
2326                 ev_ad = this.evalVisProp('attractordistance');
2327 
2328             if (!Type.exists(this.coords) || this.evalVisProp('fixed')) {
2329                 return this;
2330             }
2331 
2332             needsSnapToGrid =
2333                 this.evalVisProp('snaptogrid') || attractToGrid || force === true;
2334 
2335             if (needsSnapToGrid) {
2336                 x = this.coords.usrCoords[1];
2337                 y = this.coords.usrCoords[2];
2338                 res = this.getSnapSizes();
2339                 sX = res[0];
2340                 sY = res[1];
2341 
2342                 // If no valid snap sizes are available, don't change the coords.
2343                 if (sX > 0 && sY > 0) {
2344                     boardBB = this.board.getBoundingBox();
2345                     rx = Math.round(x / sX) * sX;
2346                     ry = Math.round(y / sY) * sY;
2347 
2348                     rcoords = new JXG.Coords(Const.COORDS_BY_USER, [rx, ry], this.board);
2349                     if (
2350                         !attractToGrid ||
2351                         rcoords.distance(
2352                             ev_au === "screen" ? Const.COORDS_BY_SCREEN : Const.COORDS_BY_USER,
2353                             this.coords
2354                         ) < ev_ad
2355                     ) {
2356                         x = rx;
2357                         y = ry;
2358                         // Checking whether x and y are still within boundingBox.
2359                         // If not, adjust them to remain within the board.
2360                         // Otherwise a point may become invisible.
2361                         if (!fromParent) {
2362                             mi = Math.min(boardBB[0], boardBB[2]);
2363                             ma = Math.max(boardBB[0], boardBB[2]);
2364                             if (x < mi && x > mi - sX) {
2365                                 x += sX;
2366                             } else if (x > ma && x < ma + sX) {
2367                                 x -= sX;
2368                             }
2369 
2370                             mi = Math.min(boardBB[1], boardBB[3]);
2371                             ma = Math.max(boardBB[1], boardBB[3]);
2372                             if (y < mi && y > mi - sY) {
2373                                 y += sY;
2374                             } else if (y > ma && y < ma + sY) {
2375                                 y -= sY;
2376                             }
2377                         }
2378                         this.coords.setCoordinates(Const.COORDS_BY_USER, [x, y]);
2379                     }
2380                 }
2381             }
2382             return this;
2383         },
2384 
2385         getBoundingBox: function () {
2386             var i, le, v,
2387                 x, y, r,
2388                 bb = [Infinity, Infinity, -Infinity, -Infinity];
2389 
2390             if (this.type === Const.OBJECT_TYPE_POLYGON) {
2391                 le = this.vertices.length - 1;
2392                 if (le <= 0) {
2393                     return bb;
2394                 }
2395                 for (i = 0; i < le; i++) {
2396                     v = this.vertices[i].X();
2397                     bb[0] = v < bb[0] ? v : bb[0];
2398                     bb[2] = v > bb[2] ? v : bb[2];
2399                     v = this.vertices[i].Y();
2400                     bb[1] = v < bb[1] ? v : bb[1];
2401                     bb[3] = v > bb[3] ? v : bb[3];
2402                 }
2403             } else if (this.elementClass === Const.OBJECT_CLASS_CIRCLE) {
2404                 x = this.center.X();
2405                 y = this.center.Y();
2406                 bb = [x - this.radius, y + this.radius, x + this.radius, y - this.radius];
2407             } else if (this.elementClass === Const.OBJECT_CLASS_CURVE) {
2408                 le = this.points.length;
2409                 if (le === 0) {
2410                     return bb;
2411                 }
2412                 for (i = 0; i < le; i++) {
2413                     v = this.points[i].usrCoords[1];
2414                     bb[0] = v < bb[0] ? v : bb[0];
2415                     bb[2] = v > bb[2] ? v : bb[2];
2416                     v = this.points[i].usrCoords[2];
2417                     bb[1] = v < bb[1] ? v : bb[1];
2418                     bb[3] = v > bb[3] ? v : bb[3];
2419                 }
2420             } else if (this.elementClass === Const.OBJECT_CLASS_POINT) {
2421                 x = this.X();
2422                 y = this.Y();
2423                 r = this.evalVisProp('size');
2424                 bb = [x - r / this.board.unitX, y - r / this.board.unitY, x + r / this.board.unitX, y + r / this.board.unitY];
2425             } else if (this.elementClass === Const.OBJECT_CLASS_LINE) {
2426                 v = this.point1.coords.usrCoords[1];
2427                 bb[0] = v < bb[0] ? v : bb[0];
2428                 bb[2] = v > bb[2] ? v : bb[2];
2429                 v = this.point1.coords.usrCoords[2];
2430                 bb[1] = v < bb[1] ? v : bb[1];
2431                 bb[3] = v > bb[3] ? v : bb[3];
2432 
2433                 v = this.point2.coords.usrCoords[1];
2434                 bb[0] = v < bb[0] ? v : bb[0];
2435                 bb[2] = v > bb[2] ? v : bb[2];
2436                 v = this.point2.coords.usrCoords[2];
2437                 bb[1] = v < bb[1] ? v : bb[1];
2438                 bb[3] = v > bb[3] ? v : bb[3];
2439             }
2440 
2441             return bb;
2442         },
2443 
2444         /**
2445          * Alias of {@link JXG.EventEmitter.on}.
2446          *
2447          * @name addEvent
2448          * @memberof JXG.GeometryElement
2449          * @function
2450          */
2451         addEvent: JXG.shortcut(JXG.GeometryElement.prototype, 'on'),
2452 
2453         /**
2454          * Alias of {@link JXG.EventEmitter.off}.
2455          *
2456          * @name removeEvent
2457          * @memberof JXG.GeometryElement
2458          * @function
2459          */
2460         removeEvent: JXG.shortcut(JXG.GeometryElement.prototype, 'off'),
2461 
2462         /**
2463          * Format a number according to the locale set in the attribute "intl".
2464          * If in the options of the intl-attribute "maximumFractionDigits" is not set,
2465          * the optional parameter digits is used instead.
2466          * 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>
2467          * for more  information about internationalization.
2468          *
2469          * @param {Number} value Number to be formatted
2470          * @param {Number} [digits=undefined] Optional number of digits
2471          * @returns {String|Number} string containing the formatted number according to the locale
2472          * or the number itself of the formatting is not possible.
2473          */
2474         formatNumberLocale: function (value, digits) {
2475             var loc, opt, key,
2476                 optCalc = {},
2477                 // These options are case sensitive:
2478                 translate = {
2479                     maximumfractiondigits: 'maximumFractionDigits',
2480                     minimumfractiondigits: 'minimumFractionDigits',
2481                     compactdisplay: 'compactDisplay',
2482                     currencydisplay: 'currencyDisplay',
2483                     currencysign: 'currencySign',
2484                     localematcher: 'localeMatcher',
2485                     numberingsystem: 'numberingSystem',
2486                     signdisplay: 'signDisplay',
2487                     unitdisplay: 'unitDisplay',
2488                     usegrouping: 'useGrouping',
2489                     roundingmode: 'roundingMode',
2490                     roundingpriority: 'roundingPriority',
2491                     roundingincrement: 'roundingIncrement',
2492                     trailingzerodisplay: 'trailingZeroDisplay',
2493                     minimumintegerdigits: 'minimumIntegerDigits',
2494                     minimumsignificantdigits: 'minimumSignificantDigits',
2495                     maximumsignificantdigits: 'maximumSignificantDigits'
2496                 };
2497 
2498             if (Type.exists(Intl) &&
2499                 this.useLocale()) {
2500 
2501                 loc = this.evalVisProp('intl.locale') ||
2502                     this.eval(this.board.attr.intl.locale);
2503                 opt = this.evalVisProp('intl.options') || {};
2504 
2505                 // Transfer back to camel case if necessary and evaluate
2506                 for (key in opt) {
2507                     if (opt.hasOwnProperty(key)) {
2508                         if (translate.hasOwnProperty(key)) {
2509                             optCalc[translate[key]] = this.eval(opt[key]);
2510                         } else {
2511                             optCalc[key] = this.eval(opt[key]);
2512                         }
2513                     }
2514                 }
2515 
2516                 // If maximumfractiondigits is not set,
2517                 // the value of the attribute "digits" is taken instead.
2518                 key = 'maximumfractiondigits';
2519                 if (!Type.exists(opt[key])) {
2520                     optCalc[translate[key]] = digits;
2521 
2522                     // key = 'minimumfractiondigits';
2523                     // if (!this.eval(opt[key]) || this.eval(opt[key]) > digits) {
2524                     //     optCalc[translate[key]] = digits;
2525                     // }
2526                 }
2527 
2528                 return Intl.NumberFormat(loc, optCalc).format(value);
2529             }
2530 
2531             return value;
2532         },
2533 
2534         /**
2535          * Checks if locale is enabled in the attribute. This may be in the attributes of the board,
2536          * or in the attributes of the text. The latter has higher priority. The board attribute is taken if
2537          * attribute "intl.enabled" of the text element is set to 'inherit'.
2538          *
2539          * @returns {Boolean} if locale can be used for number formatting.
2540          */
2541         useLocale: function () {
2542             var val;
2543 
2544             // Check if element supports intl
2545             if (!Type.exists(this.visProp.intl) ||
2546                 !Type.exists(this.visProp.intl.enabled)) {
2547                 return false;
2548             }
2549 
2550             // Check if intl is supported explicitly enabled for this element
2551             val = this.evalVisProp('intl.enabled');
2552 
2553             if (val === true) {
2554                 return true;
2555             }
2556 
2557             // Check intl attribute of the board
2558             if (val === 'inherit') {
2559                 if (this.eval(this.board.attr.intl.enabled) === true) {
2560                     return true;
2561                 }
2562             }
2563 
2564             return false;
2565         },
2566 
2567         /* **************************
2568          *     EVENT DEFINITION
2569          * for documentation purposes
2570          * ************************** */
2571 
2572         //region Event handler documentation
2573         /**
2574          * @event
2575          * @description This event is fired whenever the user is hovering over an element.
2576          * @name JXG.GeometryElement#over
2577          * @param {Event} e The browser's event object.
2578          */
2579         __evt__over: function (e) { },
2580 
2581         /**
2582          * @event
2583          * @description This event is fired whenever the user puts the mouse over an element.
2584          * @name JXG.GeometryElement#mouseover
2585          * @param {Event} e The browser's event object.
2586          */
2587         __evt__mouseover: function (e) { },
2588 
2589         /**
2590          * @event
2591          * @description This event is fired whenever the user is leaving an element.
2592          * @name JXG.GeometryElement#out
2593          * @param {Event} e The browser's event object.
2594          */
2595         __evt__out: function (e) { },
2596 
2597         /**
2598          * @event
2599          * @description This event is fired whenever the user puts the mouse away from an element.
2600          * @name JXG.GeometryElement#mouseout
2601          * @param {Event} e The browser's event object.
2602          */
2603         __evt__mouseout: function (e) { },
2604 
2605         /**
2606          * @event
2607          * @description This event is fired whenever the user is moving over an element.
2608          * @name JXG.GeometryElement#move
2609          * @param {Event} e The browser's event object.
2610          */
2611         __evt__move: function (e) { },
2612 
2613         /**
2614          * @event
2615          * @description This event is fired whenever the user is moving the mouse over an element.
2616          * @name JXG.GeometryElement#mousemove
2617          * @param {Event} e The browser's event object.
2618          */
2619         __evt__mousemove: function (e) { },
2620 
2621         /**
2622          * @event
2623          * @description This event is fired whenever the user drags an element.
2624          * @name JXG.GeometryElement#drag
2625          * @param {Event} e The browser's event object.
2626          */
2627         __evt__drag: function (e) { },
2628 
2629         /**
2630          * @event
2631          * @description This event is fired whenever the user drags the element with a mouse.
2632          * @name JXG.GeometryElement#mousedrag
2633          * @param {Event} e The browser's event object.
2634          */
2635         __evt__mousedrag: function (e) { },
2636 
2637         /**
2638          * @event
2639          * @description This event is fired whenever the user drags the element with a pen.
2640          * @name JXG.GeometryElement#pendrag
2641          * @param {Event} e The browser's event object.
2642          */
2643         __evt__pendrag: function (e) { },
2644 
2645         /**
2646          * @event
2647          * @description This event is fired whenever the user drags the element on a touch device.
2648          * @name JXG.GeometryElement#touchdrag
2649          * @param {Event} e The browser's event object.
2650          */
2651         __evt__touchdrag: function (e) { },
2652 
2653         /**
2654          * @event
2655          * @description This event is fired whenever the user drags the element by pressing arrow keys
2656          * on the keyboard.
2657          * @name JXG.GeometryElement#keydrag
2658          * @param {Event} e The browser's event object.
2659          */
2660         __evt__keydrag: function (e) { },
2661 
2662         /**
2663          * @event
2664          * @description Whenever the user starts to touch or click an element.
2665          * @name JXG.GeometryElement#down
2666          * @param {Event} e The browser's event object.
2667          */
2668         __evt__down: function (e) { },
2669 
2670         /**
2671          * @event
2672          * @description Whenever the user starts to click an element.
2673          * @name JXG.GeometryElement#mousedown
2674          * @param {Event} e The browser's event object.
2675          */
2676         __evt__mousedown: function (e) { },
2677 
2678         /**
2679          * @event
2680          * @description Whenever the user taps an element with the pen.
2681          * @name JXG.GeometryElement#pendown
2682          * @param {Event} e The browser's event object.
2683          */
2684         __evt__pendown: function (e) { },
2685 
2686         /**
2687          * @event
2688          * @description Whenever the user starts to touch an element.
2689          * @name JXG.GeometryElement#touchdown
2690          * @param {Event} e The browser's event object.
2691          */
2692         __evt__touchdown: function (e) { },
2693 
2694         /**
2695          * @event
2696          * @description Whenever the user clicks on an element.
2697          * @name JXG.Board#click
2698          * @param {Event} e The browser's event object.
2699          */
2700         __evt__click: function (e) { },
2701 
2702         /**
2703          * @event
2704          * @description Whenever the user double clicks on an element.
2705          * This event works on desktop browser, but is undefined
2706          * on mobile browsers.
2707          * @name JXG.Board#dblclick
2708          * @param {Event} e The browser's event object.
2709          * @see JXG.Board#clickDelay
2710          * @see JXG.Board#dblClickSuppressClick
2711          */
2712         __evt__dblclick: function (e) { },
2713 
2714         /**
2715          * @event
2716          * @description Whenever the user clicks on an element with a mouse device.
2717          * @name JXG.Board#mouseclick
2718          * @param {Event} e The browser's event object.
2719          */
2720         __evt__mouseclick: function (e) { },
2721 
2722         /**
2723          * @event
2724          * @description Whenever the user double clicks on an element with a mouse device.
2725          * @name JXG.Board#mousedblclick
2726          * @param {Event} e The browser's event object.
2727          */
2728         __evt__mousedblclick: function (e) { },
2729 
2730         /**
2731          * @event
2732          * @description Whenever the user clicks on an element with a pointer device.
2733          * @name JXG.Board#pointerclick
2734          * @param {Event} e The browser's event object.
2735          */
2736         __evt__pointerclick: function (e) { },
2737 
2738         /**
2739          * @event
2740          * @description Whenever the user double clicks on an element with a pointer device.
2741          * This event works on desktop browser, but is undefined
2742          * on mobile browsers.
2743          * @name JXG.Board#pointerdblclick
2744          * @param {Event} e The browser's event object.
2745          */
2746         __evt__pointerdblclick: function (e) { },
2747 
2748         /**
2749          * @event
2750          * @description Whenever the user stops to touch or click an element.
2751          * @name JXG.GeometryElement#up
2752          * @param {Event} e The browser's event object.
2753          */
2754         __evt__up: function (e) { },
2755 
2756         /**
2757          * @event
2758          * @description Whenever the user releases the mousebutton over an element.
2759          * @name JXG.GeometryElement#mouseup
2760          * @param {Event} e The browser's event object.
2761          */
2762         __evt__mouseup: function (e) { },
2763 
2764         /**
2765          * @event
2766          * @description Whenever the user lifts the pen over an element.
2767          * @name JXG.GeometryElement#penup
2768          * @param {Event} e The browser's event object.
2769          */
2770         __evt__penup: function (e) { },
2771 
2772         /**
2773          * @event
2774          * @description Whenever the user stops touching an element.
2775          * @name JXG.GeometryElement#touchup
2776          * @param {Event} e The browser's event object.
2777          */
2778         __evt__touchup: function (e) { },
2779 
2780         /**
2781          * @event
2782          * @description Notify every time an attribute is changed.
2783          * @name JXG.GeometryElement#attribute
2784          * @param {Object} o A list of changed attributes and their new value.
2785          * @param {Object} el Reference to the element
2786          */
2787         __evt__attribute: function (o, el) { },
2788 
2789         /**
2790          * @event
2791          * @description This is a generic event handler. It exists for every possible attribute that can be set for
2792          * any element, e.g. if you want to be notified everytime an element's strokecolor is changed, is the event
2793          * <tt>attribute:strokecolor</tt>.
2794          * @name JXG.GeometryElement#attribute:key
2795          * @param val The old value.
2796          * @param nval The new value
2797          * @param {Object} el Reference to the element
2798          */
2799         __evt__attribute_: function (val, nval, el) { },
2800 
2801         /**
2802          * @ignore
2803          */
2804         __evt: function () { }
2805         //endregion
2806     }
2807 );
2808 
2809 export default JXG.GeometryElement;
2810 // const GeometryElement = JXG.GeometryElement;
2811 // export { GeometryElement as default,  GeometryElement };
2812