1 /*
  2     Copyright 2008-2022
  3         Matthias Ehmann,
  4         Michael Gerhaeuser,
  5         Carsten Miller,
  6         Bianca Valentin,
  7         Alfred Wassermann,
  8         Peter Wilfahrt
  9 
 10     This file is part of JSXGraph.
 11 
 12     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
 13 
 14     You can redistribute it and/or modify it under the terms of the
 15 
 16       * GNU Lesser General Public License as published by
 17         the Free Software Foundation, either version 3 of the License, or
 18         (at your option) any later version
 19       OR
 20       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
 21 
 22     JSXGraph is distributed in the hope that it will be useful,
 23     but WITHOUT ANY WARRANTY; without even the implied warranty of
 24     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 25     GNU Lesser General Public License for more details.
 26 
 27     You should have received a copy of the GNU Lesser General Public License and
 28     the MIT License along with JSXGraph. If not, see <http://www.gnu.org/licenses/>
 29     and <http://opensource.org/licenses/MIT/>.
 30  */
 31 
 32 

 34 
 35 /*jslint nomen: true, plusplus: true*/
 36 
 37 /* depends:
 38  jxg
 39  base/constants
 40  base/coords
 41  options
 42  math/numerics
 43  math/math
 44  math/geometry
 45  math/complex
 46  parser/jessiecode
 47  parser/geonext
 48  utils/color
 49  utils/type
 50  utils/event
 51  utils/env
 52   elements:
 53    transform
 54    point
 55    line
 56    text
 57    grid
 58  */
 59 
 60 /**
 61  * @fileoverview The JXG.Board class is defined in this file. JXG.Board controls all properties and methods
 62  * used to manage a geonext board like managing geometric elements, managing mouse and touch events, etc.
 63  */
 64 
 65 define([
 66     'jxg', 'base/constants', 'base/coords', 'options', 'math/numerics', 'math/math', 'math/geometry', 'math/complex',
 67     'math/statistics',
 68     'parser/jessiecode', 'utils/color', 'utils/type', 'utils/event', 'utils/env',
 69     'base/composition'
 70 ], function (JXG, Const, Coords, Options, Numerics, Mat, Geometry, Complex, Statistics, JessieCode, Color, Type,
 71                 EventEmitter, Env, Composition) {
 72 
 73     'use strict';
 74 
 75     /**
 76      * Constructs a new Board object.
 77      * @class JXG.Board controls all properties and methods used to manage a geonext board like managing geometric
 78      * elements, managing mouse and touch events, etc. You probably don't want to use this constructor directly.
 79      * Please use {@link JXG.JSXGraph.initBoard} to initialize a board.
 80      * @constructor
 81      * @param {String} container The id or reference of the HTML DOM element the board is drawn in. This is usually a HTML div.
 82      * @param {JXG.AbstractRenderer} renderer The reference of a renderer.
 83      * @param {String} id Unique identifier for the board, may be an empty string or null or even undefined.
 84      * @param {JXG.Coords} origin The coordinates where the origin is placed, in user coordinates.
 85      * @param {Number} zoomX Zoom factor in x-axis direction
 86      * @param {Number} zoomY Zoom factor in y-axis direction
 87      * @param {Number} unitX Units in x-axis direction
 88      * @param {Number} unitY Units in y-axis direction
 89      * @param {Number} canvasWidth  The width of canvas
 90      * @param {Number} canvasHeight The height of canvas
 91      * @param {Object} attributes The attributes object given to {@link JXG.JSXGraph.initBoard}
 92      * @borrows JXG.EventEmitter#on as this.on
 93      * @borrows JXG.EventEmitter#off as this.off
 94      * @borrows JXG.EventEmitter#triggerEventHandlers as this.triggerEventHandlers
 95      * @borrows JXG.EventEmitter#eventHandlers as this.eventHandlers
 96      */
 97     JXG.Board = function (container, renderer, id, origin, zoomX, zoomY, unitX, unitY, canvasWidth, canvasHeight, attributes) {
 98         /**
 99          * Board is in no special mode, objects are highlighted on mouse over and objects may be
100          * clicked to start drag&drop.
101          * @type Number
102          * @constant
103          */
104         this.BOARD_MODE_NONE = 0x0000;
105 
106         /**
107          * Board is in drag mode, objects aren't highlighted on mouse over and the object referenced in
108          * {@link JXG.Board#mouse} is updated on mouse movement.
109          * @type Number
110          * @constant
111          * @see JXG.Board#drag_obj
112          */
113         this.BOARD_MODE_DRAG = 0x0001;
114 
115         /**
116          * In this mode a mouse move changes the origin's screen coordinates.
117          * @type Number
118          * @constant
119          */
120         this.BOARD_MODE_MOVE_ORIGIN = 0x0002;
121 
122         /**
123          * Update is made with high quality, e.g. graphs are evaluated at much more points.
124          * @type Number
125          * @constant
126          * @see JXG.Board#updateQuality
127          */
128         this.BOARD_MODE_ZOOM = 0x0011;
129 
130         /**
131          * Update is made with low quality, e.g. graphs are evaluated at a lesser amount of points.
132          * @type Number
133          * @constant
134          * @see JXG.Board#updateQuality
135          */
136         this.BOARD_QUALITY_LOW = 0x1;
137 
138         /**
139          * Update is made with high quality, e.g. graphs are evaluated at much more points.
140          * @type Number
141          * @constant
142          * @see JXG.Board#updateQuality
143          */
144         this.BOARD_QUALITY_HIGH = 0x2;
145 
146         /**
147          * Pointer to the document element containing the board.
148          * @type Object
149          */
150         // Former version:
151         // this.document = attributes.document || document;
152         if (Type.exists(attributes.document) && attributes.document !== false) {
153             this.document = attributes.document;
154         } else if (document !== undefined && Type.isObject(document)) {
155             this.document = document;
156         }
157 
158         /**
159          * The html-id of the html element containing the board.
160          * @type String
161          */
162         this.container = container;
163 
164         /**
165          * Pointer to the html element containing the board.
166          * @type Object
167          */
168         this.containerObj = (Env.isBrowser ? this.document.getElementById(this.container) : null);
169 
170         if (Env.isBrowser && renderer.type !== 'no' && this.containerObj === null) {
171             throw new Error("\nJSXGraph: HTML container element '" + container + "' not found.");
172         }
173 
174         /**
175          * A reference to this boards renderer.
176          * @type JXG.AbstractRenderer
177          * @name JXG.Board#renderer
178          * @private
179          * @ignore
180          */
181         this.renderer = renderer;
182 
183         /**
184          * Grids keeps track of all grids attached to this board.
185          * @type Array
186          * @private
187          */
188         this.grids = [];
189 
190         /**
191          * Some standard options
192          * @type JXG.Options
193          */
194         this.options = Type.deepCopy(Options);
195         this.attr = attributes;
196 
197         /**
198          * Dimension of the board.
199          * @default 2
200          * @type Number
201          */
202         this.dimension = 2;
203 
204         this.jc = new JessieCode();
205         this.jc.use(this);
206 
207         /**
208          * Coordinates of the boards origin. This a object with the two properties
209          * usrCoords and scrCoords. usrCoords always equals [1, 0, 0] and scrCoords
210          * stores the boards origin in homogeneous screen coordinates.
211          * @type Object
212          * @private
213          */
214         this.origin = {};
215         this.origin.usrCoords = [1, 0, 0];
216         this.origin.scrCoords = [1, origin[0], origin[1]];
217 
218         /**
219          * Zoom factor in X direction. It only stores the zoom factor to be able
220          * to get back to 100% in zoom100().
221          * @name JXG.Board.zoomX
222          * @type Number
223          * @private
224          * @ignore
225          */
226         this.zoomX = zoomX;
227 
228         /**
229          * Zoom factor in Y direction. It only stores the zoom factor to be able
230          * to get back to 100% in zoom100().
231          * @name JXG.Board.zoomY
232          * @type Number
233          * @private
234          * @ignore
235          */
236         this.zoomY = zoomY;
237 
238         /**
239          * The number of pixels which represent one unit in user-coordinates in x direction.
240          * @type Number
241          * @private
242          */
243         this.unitX = unitX * this.zoomX;
244 
245         /**
246          * The number of pixels which represent one unit in user-coordinates in y direction.
247          * @type Number
248          * @private
249          */
250         this.unitY = unitY * this.zoomY;
251 
252         /**
253          * Keep aspect ratio if bounding box is set and the width/height ratio differs from the
254          * width/height ratio of the canvas.
255          * @type Boolean
256          * @private
257          */
258         this.keepaspectratio = false;
259 
260         /**
261          * Canvas width.
262          * @type Number
263          * @private
264          */
265         this.canvasWidth = canvasWidth;
266 
267         /**
268          * Canvas Height
269          * @type Number
270          * @private
271          */
272         this.canvasHeight = canvasHeight;
273 
274         // If the given id is not valid, generate an unique id
275         if (Type.exists(id) && id !== '' && Env.isBrowser && !Type.exists(this.document.getElementById(id))) {
276             this.id = id;
277         } else {
278             this.id = this.generateId();
279         }
280 
281         EventEmitter.eventify(this);
282 
283         this.hooks = [];
284 
285         /**
286          * An array containing all other boards that are updated after this board has been updated.
287          * @type Array
288          * @see JXG.Board#addChild
289          * @see JXG.Board#removeChild
290          */
291         this.dependentBoards = [];
292 
293         /**
294          * During the update process this is set to false to prevent an endless loop.
295          * @default false
296          * @type Boolean
297          */
298         this.inUpdate = false;
299 
300         /**
301          * An associative array containing all geometric objects belonging to the board. Key is the id of the object and value is a reference to the object.
302          * @type Object
303          */
304         this.objects = {};
305 
306         /**
307          * An array containing all geometric objects on the board in the order of construction.
308          * @type Array
309          */
310         this.objectsList = [];
311 
312         /**
313          * An associative array containing all groups belonging to the board. Key is the id of the group and value is a reference to the object.
314          * @type Object
315          */
316         this.groups = {};
317 
318         /**
319          * Stores all the objects that are currently running an animation.
320          * @type Object
321          */
322         this.animationObjects = {};
323 
324         /**
325          * An associative array containing all highlighted elements belonging to the board.
326          * @type Object
327          */
328         this.highlightedObjects = {};
329 
330         /**
331          * Number of objects ever created on this board. This includes every object, even invisible and deleted ones.
332          * @type Number
333          */
334         this.numObjects = 0;
335 
336         /**
337          * An associative array to store the objects of the board by name. the name of the object is the key and value is a reference to the object.
338          * @type Object
339          */
340         this.elementsByName = {};
341 
342         /**
343          * The board mode the board is currently in. Possible values are
344          * <ul>
345          * <li>JXG.Board.BOARD_MODE_NONE</li>
346          * <li>JXG.Board.BOARD_MODE_DRAG</li>
347          * <li>JXG.Board.BOARD_MODE_MOVE_ORIGIN</li>
348          * </ul>
349          * @type Number
350          */
351         this.mode = this.BOARD_MODE_NONE;
352 
353         /**
354          * The update quality of the board. In most cases this is set to {@link JXG.Board#BOARD_QUALITY_HIGH}.
355          * If {@link JXG.Board#mode} equals {@link JXG.Board#BOARD_MODE_DRAG} this is set to
356          * {@link JXG.Board#BOARD_QUALITY_LOW} to speed up the update process by e.g. reducing the number of
357          * evaluation points when plotting functions. Possible values are
358          * <ul>
359          * <li>BOARD_QUALITY_LOW</li>
360          * <li>BOARD_QUALITY_HIGH</li>
361          * </ul>
362          * @type Number
363          * @see JXG.Board#mode
364          */
365         this.updateQuality = this.BOARD_QUALITY_HIGH;
366 
367         /**
368          * If true updates are skipped.
369          * @type Boolean
370          */
371         this.isSuspendedRedraw = false;
372 
373         this.calculateSnapSizes();
374 
375         /**
376          * The distance from the mouse to the dragged object in x direction when the user clicked the mouse button.
377          * @type Number
378          * @see JXG.Board#drag_dy
379          * @see JXG.Board#drag_obj
380          */
381         this.drag_dx = 0;
382 
383         /**
384          * The distance from the mouse to the dragged object in y direction when the user clicked the mouse button.
385          * @type Number
386          * @see JXG.Board#drag_dx
387          * @see JXG.Board#drag_obj
388          */
389         this.drag_dy = 0;
390 
391         /**
392          * The last position where a drag event has been fired.
393          * @type Array
394          * @see JXG.Board#moveObject
395          */
396         this.drag_position = [0, 0];
397 
398         /**
399          * References to the object that is dragged with the mouse on the board.
400          * @type JXG.GeometryElement
401          * @see JXG.Board#touches
402          */
403         this.mouse = {};
404 
405         /**
406          * Keeps track on touched elements, like {@link JXG.Board#mouse} does for mouse events.
407          * @type Array
408          * @see JXG.Board#mouse
409          */
410         this.touches = [];
411 
412         /**
413          * A string containing the XML text of the construction.
414          * This is set in {@link JXG.FileReader.parseString}.
415          * Only useful if a construction is read from a GEONExT-, Intergeo-, Geogebra-, or Cinderella-File.
416          * @type String
417          */
418         this.xmlString = '';
419 
420         /**
421          * Cached result of getCoordsTopLeftCorner for touch/mouseMove-Events to save some DOM operations.
422          * @type Array
423          */
424         this.cPos = [];
425 
426         /**
427          * Contains the last time (epoch, msec) since the last touchMove event which was not thrown away or since
428          * touchStart because Android's Webkit browser fires too much of them.
429          * @type Number
430          */
431         this.touchMoveLast = 0;
432 
433         /**
434          * Contains the pointerId of the last touchMove event which was not thrown away or since
435          * touchStart because Android's Webkit browser fires too much of them.
436          * @type Number
437          */
438          this.touchMoveLastId = Infinity;
439 
440         /**
441          * Contains the last time (epoch, msec) since the last getCoordsTopLeftCorner call which was not thrown away.
442          * @type Number
443          */
444         this.positionAccessLast = 0;
445 
446         /**
447          * Collects all elements that triggered a mouse down event.
448          * @type Array
449          */
450         this.downObjects = [];
451 
452         if (this.attr.showcopyright) {
453             this.renderer.displayCopyright(Const.licenseText, parseInt(this.options.text.fontSize, 10));
454         }
455 
456         /**
457          * Full updates are needed after zoom and axis translates. This saves some time during an update.
458          * @default false
459          * @type Boolean
460          */
461         this.needsFullUpdate = false;
462 
463         /**
464          * If reducedUpdate is set to true then only the dragged element and few (e.g. 2) following
465          * elements are updated during mouse move. On mouse up the whole construction is
466          * updated. This enables us to be fast even on very slow devices.
467          * @type Boolean
468          * @default false
469          */
470         this.reducedUpdate = false;
471 
472         /**
473          * The current color blindness deficiency is stored in this property. If color blindness is not emulated
474          * at the moment, it's value is 'none'.
475          */
476         this.currentCBDef = 'none';
477 
478         /**
479          * If GEONExT constructions are displayed, then this property should be set to true.
480          * At the moment there should be no difference. But this may change.
481          * This is set in {@link JXG.GeonextReader.readGeonext}.
482          * @type Boolean
483          * @default false
484          * @see JXG.GeonextReader.readGeonext
485          */
486         this.geonextCompatibilityMode = false;
487 
488         if (this.options.text.useASCIIMathML && translateASCIIMath) {
489             init();
490         } else {
491             this.options.text.useASCIIMathML = false;
492         }
493 
494         /**
495          * A flag which tells if the board registers mouse events.
496          * @type Boolean
497          * @default false
498          */
499         this.hasMouseHandlers = false;
500 
501         /**
502          * A flag which tells if the board registers touch events.
503          * @type Boolean
504          * @default false
505          */
506         this.hasTouchHandlers = false;
507 
508         /**
509          * A flag which stores if the board registered pointer events.
510          * @type Boolean
511          * @default false
512          */
513         this.hasPointerHandlers = false;
514 
515         /**
516          * A flag which tells if the board the JXG.Board#mouseUpListener is currently registered.
517          * @type Boolean
518          * @default false
519          */
520         this.hasMouseUp = false;
521 
522         /**
523          * A flag which tells if the board the JXG.Board#touchEndListener is currently registered.
524          * @type Boolean
525          * @default false
526          */
527         this.hasTouchEnd = false;
528 
529         /**
530          * A flag which tells us if the board has a pointerUp event registered at the moment.
531          * @type Boolean
532          * @default false
533          */
534         this.hasPointerUp = false;
535 
536         /**
537          * Offset for large coords elements like images
538          * @type Array
539          * @private
540          * @default [0, 0]
541          */
542         this._drag_offset = [0, 0];
543 
544         /**
545          * Stores the input device used in the last down or move event.
546          * @type String
547          * @private
548          * @default 'mouse'
549          */
550         this._inputDevice = 'mouse';
551 
552         /**
553          * Keeps a list of pointer devices which are currently touching the screen.
554          * @type Array
555          * @private
556          */
557         this._board_touches = [];
558 
559         /**
560          * A flag which tells us if the board is in the selecting mode
561          * @type Boolean
562          * @default false
563          */
564         this.selectingMode = false;
565 
566         /**
567          * A flag which tells us if the user is selecting
568          * @type Boolean
569          * @default false
570          */
571         this.isSelecting = false;
572 
573         /**
574          * A flag which tells us if the user is scrolling the viewport
575          * @type Boolean
576          * @private
577          * @default false
578          * @see JXG.Board#scrollListener
579          */
580         this._isScrolling = false;
581 
582         /**
583          * A flag which tells us if a resize is in process
584          * @type Boolean
585          * @private
586          * @default false
587          * @see JXG.Board#resizeListener
588          */
589         this._isResizing = false;
590 
591         /**
592          * A bounding box for the selection
593          * @type Array
594          * @default [ [0,0], [0,0] ]
595          */
596         this.selectingBox = [[0, 0], [0, 0]];
597 
598         this.mathLib = Math;        // Math or JXG.Math.IntervalArithmetic
599         this.mathLibJXG = JXG.Math; // JXG.Math or JXG.Math.IntervalArithmetic
600 
601         if (this.attr.registerevents) {
602             this.addEventHandlers();
603         }
604 
605         this.methodMap = {
606             update: 'update',
607             fullUpdate: 'fullUpdate',
608             on: 'on',
609             off: 'off',
610             trigger: 'trigger',
611             setView: 'setBoundingBox',
612             setBoundingBox: 'setBoundingBox',
613             migratePoint: 'migratePoint',
614             colorblind: 'emulateColorblindness',
615             suspendUpdate: 'suspendUpdate',
616             unsuspendUpdate: 'unsuspendUpdate',
617             clearTraces: 'clearTraces',
618             left: 'clickLeftArrow',
619             right: 'clickRightArrow',
620             up: 'clickUpArrow',
621             down: 'clickDownArrow',
622             zoomIn: 'zoomIn',
623             zoomOut: 'zoomOut',
624             zoom100: 'zoom100',
625             zoomElements: 'zoomElements',
626             remove: 'removeObject',
627             removeObject: 'removeObject'
628         };
629     };
630 
631     JXG.extend(JXG.Board.prototype, /** @lends JXG.Board.prototype */ {
632 
633         /**
634          * Generates an unique name for the given object. The result depends on the objects type, if the
635          * object is a {@link JXG.Point}, capital characters are used, if it is of type {@link JXG.Line}
636          * only lower case characters are used. If object is of type {@link JXG.Polygon}, a bunch of lower
637          * case characters prefixed with P_ are used. If object is of type {@link JXG.Circle} the name is
638          * generated using lower case characters. prefixed with k_ is used. In any other case, lower case
639          * chars prefixed with s_ is used.
640          * @param {Object} object Reference of an JXG.GeometryElement that is to be named.
641          * @returns {String} Unique name for the object.
642          */
643         generateName: function (object) {
644             var possibleNames, i,
645                 maxNameLength = this.attr.maxnamelength,
646                 pre = '',
647                 post = '',
648                 indices = [],
649                 name = '';
650 
651             if (object.type === Const.OBJECT_TYPE_TICKS) {
652                 return '';
653             }
654 
655             if (Type.isPoint(object)) {
656                 // points have capital letters
657                 possibleNames = ['', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O',
658                     'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'];
659             } else if (object.type === Const.OBJECT_TYPE_ANGLE) {
660                 possibleNames = ['', 'α', 'β', 'γ', 'δ', 'ε', 'ζ', 'η', 'θ',
661                     'ι', 'κ', 'λ', 'μ', 'ν', 'ξ', 'ο', 'π', 'ρ',
662                     'σ', 'τ', 'υ', 'φ', 'χ', 'ψ', 'ω'];
663             } else {
664                 // all other elements get lowercase labels
665                 possibleNames = ['', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o',
666                     'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'];
667             }
668 
669             if (!Type.isPoint(object) &&
670                     object.elementClass !== Const.OBJECT_CLASS_LINE &&
671                     object.type !== Const.OBJECT_TYPE_ANGLE) {
672                 if (object.type === Const.OBJECT_TYPE_POLYGON) {
673                     pre = 'P_{';
674                 } else if (object.elementClass === Const.OBJECT_CLASS_CIRCLE) {
675                     pre = 'k_{';
676                 } else if (object.elementClass === Const.OBJECT_CLASS_TEXT) {
677                     pre = 't_{';
678                 } else {
679                     pre = 's_{';
680                 }
681                 post = '}';
682             }
683 
684             for (i = 0; i < maxNameLength; i++) {
685                 indices[i] = 0;
686             }
687 
688             while (indices[maxNameLength - 1] < possibleNames.length) {
689                 for (indices[0] = 1; indices[0] < possibleNames.length; indices[0]++) {
690                     name = pre;
691 
692                     for (i = maxNameLength; i > 0; i--) {
693                         name += possibleNames[indices[i - 1]];
694                     }
695 
696                     if (!Type.exists(this.elementsByName[name + post])) {
697                         return name + post;
698                     }
699 
700                 }
701                 indices[0] = possibleNames.length;
702 
703                 for (i = 1; i < maxNameLength; i++) {
704                     if (indices[i - 1] === possibleNames.length) {
705                         indices[i - 1] = 1;
706                         indices[i] += 1;
707                     }
708                 }
709             }
710 
711             return '';
712         },
713 
714         /**
715          * Generates unique id for a board. The result is randomly generated and prefixed with 'jxgBoard'.
716          * @returns {String} Unique id for a board.
717          */
718         generateId: function () {
719             var r = 1;
720 
721             // as long as we don't have a unique id generate a new one
722             while (Type.exists(JXG.boards['jxgBoard' + r])) {
723                 r = Math.round(Math.random() * 65535);
724             }
725 
726             return ('jxgBoard' + r);
727         },
728 
729         /**
730          * Composes an id for an element. If the ID is empty ('' or null) a new ID is generated, depending on the
731          * object type. As a side effect {@link JXG.Board#numObjects}
732          * is updated.
733          * @param {Object} obj Reference of an geometry object that needs an id.
734          * @param {Number} type Type of the object.
735          * @returns {String} Unique id for an element.
736          */
737         setId: function (obj, type) {
738             var randomNumber,
739                 num = this.numObjects,
740                 elId = obj.id;
741 
742             this.numObjects += 1;
743 
744             // If no id is provided or id is empty string, a new one is chosen
745             if (elId === '' || !Type.exists(elId)) {
746                 elId = this.id + type + num;
747                 while (Type.exists(this.objects[elId])) {
748                     randomNumber = Math.round(Math.random() * 65535);
749                     elId = this.id + type + num + '-' + randomNumber;
750                 }
751             }
752 
753             obj.id = elId;
754             this.objects[elId] = obj;
755             obj._pos = this.objectsList.length;
756             this.objectsList[this.objectsList.length] = obj;
757 
758             return elId;
759         },
760 
761         /**
762          * After construction of the object the visibility is set
763          * and the label is constructed if necessary.
764          * @param {Object} obj The object to add.
765          */
766         finalizeAdding: function (obj) {
767             if (Type.evaluate(obj.visProp.visible) === false) {
768                 this.renderer.display(obj, false);
769             }
770         },
771 
772         finalizeLabel: function (obj) {
773             if (obj.hasLabel &&
774                 !Type.evaluate(obj.label.visProp.islabel) &&
775                 Type.evaluate(obj.label.visProp.visible) === false) {
776                 this.renderer.display(obj.label, false);
777             }
778         },
779 
780         /**********************************************************
781          *
782          * Event Handler helpers
783          *
784          **********************************************************/
785 
786         /**
787          * Returns false if the event has been triggered faster than the maximum frame rate.
788          *
789          * @param {Event} evt Event object given by the browser (unused)
790          * @returns {Boolean} If the event has been triggered faster than the maximum frame rate, false is returned.
791          * @private
792          * @see JXG.Board#pointerMoveListener
793          * @see JXG.Board#touchMoveListener
794          * @see JXG.Board#mouseMoveListener
795          */
796         checkFrameRate: function(evt) {
797             var handleEvt = false,
798                 time = new Date().getTime();
799 
800             if (Type.exists(evt.pointerId) && this.touchMoveLastId !== evt.pointerId) {
801                 handleEvt = true;
802                 this.touchMoveLastId = evt.pointerId;
803             }
804             if (!handleEvt && (time - this.touchMoveLast) * this.attr.maxframerate >= 1000) {
805                 handleEvt = true;
806             }
807             if (handleEvt) {
808                 this.touchMoveLast = time;
809             }
810             return handleEvt;
811         },
812 
813         /**
814          * Calculates mouse coordinates relative to the boards container.
815          * @returns {Array} Array of coordinates relative the boards container top left corner.
816          */
817         getCoordsTopLeftCorner: function () {
818             var cPos, doc, crect,
819                 docElement = this.document.documentElement || this.document.body.parentNode,
820                 docBody = this.document.body,
821                 container = this.containerObj,
822                 // viewport, content,
823                 zoom, o;
824 
825             /**
826              * During drags and origin moves the container element is usually not changed.
827              * Check the position of the upper left corner at most every 1000 msecs
828              */
829             if (this.cPos.length > 0 &&
830                     (this.mode === this.BOARD_MODE_DRAG || this.mode === this.BOARD_MODE_MOVE_ORIGIN ||
831                     (new Date()).getTime() - this.positionAccessLast < 1000)) {
832                 return this.cPos;
833             }
834             this.positionAccessLast = (new Date()).getTime();
835 
836             // Check if getBoundingClientRect exists. If so, use this as this covers *everything*
837             // even CSS3D transformations etc.
838             // Supported by all browsers but IE 6, 7.
839 
840             if (container.getBoundingClientRect) {
841                 crect = container.getBoundingClientRect();
842 
843 
844                 zoom = 1.0;
845                 // Recursively search for zoom style entries.
846                 // This is necessary for reveal.js on webkit.
847                 // It fails if the user does zooming
848                 o = container;
849                 while (o && Type.exists(o.parentNode)) {
850                     if (Type.exists(o.style) && Type.exists(o.style.zoom) && o.style.zoom !== '') {
851                         zoom *= parseFloat(o.style.zoom);
852                     }
853                     o = o.parentNode;
854                 }
855                 cPos = [crect.left * zoom, crect.top * zoom];
856 
857                 // add border width
858                 cPos[0] += Env.getProp(container, 'border-left-width');
859                 cPos[1] += Env.getProp(container, 'border-top-width');
860 
861                 // vml seems to ignore paddings
862                 if (this.renderer.type !== 'vml') {
863                     // add padding
864                     cPos[0] += Env.getProp(container, 'padding-left');
865                     cPos[1] += Env.getProp(container, 'padding-top');
866                 }
867 
868                 this.cPos = cPos.slice();
869                 return this.cPos;
870             }
871 
872             //
873             //  OLD CODE
874             //  IE 6-7 only:
875             //
876             cPos = Env.getOffset(container);
877             doc = this.document.documentElement.ownerDocument;
878 
879             if (!this.containerObj.currentStyle && doc.defaultView) {     // Non IE
880                 // this is for hacks like this one used in wordpress for the admin bar:
881                 // html { margin-top: 28px }
882                 // seems like it doesn't work in IE
883 
884                 cPos[0] += Env.getProp(docElement, 'margin-left');
885                 cPos[1] += Env.getProp(docElement, 'margin-top');
886 
887                 cPos[0] += Env.getProp(docElement, 'border-left-width');
888                 cPos[1] += Env.getProp(docElement, 'border-top-width');
889 
890                 cPos[0] += Env.getProp(docElement, 'padding-left');
891                 cPos[1] += Env.getProp(docElement, 'padding-top');
892             }
893 
894             if (docBody) {
895                 cPos[0] += Env.getProp(docBody, 'left');
896                 cPos[1] += Env.getProp(docBody, 'top');
897             }
898 
899             // Google Translate offers widgets for web authors. These widgets apparently tamper with the clientX
900             // and clientY coordinates of the mouse events. The minified sources seem to be the only publicly
901             // available version so we're doing it the hacky way: Add a fixed offset.


904                 cPos[0] += 10;
905                 cPos[1] += 25;
906             }
907 
908             // add border width
909             cPos[0] += Env.getProp(container, 'border-left-width');
910             cPos[1] += Env.getProp(container, 'border-top-width');
911 
912             // vml seems to ignore paddings
913             if (this.renderer.type !== 'vml') {
914                 // add padding
915                 cPos[0] += Env.getProp(container, 'padding-left');
916                 cPos[1] += Env.getProp(container, 'padding-top');
917             }
918 
919             cPos[0] += this.attr.offsetx;
920             cPos[1] += this.attr.offsety;
921 
922             this.cPos = cPos.slice();
923             return this.cPos;
924         },
925 
926         /**
927          * Get the position of the mouse in screen coordinates, relative to the upper left corner
928          * of the host tag.
929          * @param {Event} e Event object given by the browser.
930          * @param {Number} [i] Only use in case of touch events. This determines which finger to use and should not be set
931          * for mouseevents.
932          * @returns {Array} Contains the mouse coordinates in screen coordinates, ready for {@link JXG.Coords}
933          */
934         getMousePosition: function (e, i) {
935             var cPos = this.getCoordsTopLeftCorner(),
936                 absPos,
937                 v;
938 
939             // Position of cursor using clientX/Y
940             absPos = Env.getPosition(e, i, this.document);
941 
942             /**
943              * In case there has been no down event before.
944              */
945             if (!Type.exists(this.cssTransMat)) {
946                 this.updateCSSTransforms();
947             }
948             // Position relative to the top left corner
949             v = [1, absPos[0] - cPos[0], absPos[1] - cPos[1]];
950             v = Mat.matVecMult(this.cssTransMat, v);
951             v[1] /= v[0];
952             v[2] /= v[0];
953             return [v[1], v[2]];
954 
955             // Method without CSS transformation
956             /*
957              return [absPos[0] - cPos[0], absPos[1] - cPos[1]];
958              */
959         },
960 
961         /**
962          * Initiate moving the origin. This is used in mouseDown and touchStart listeners.
963          * @param {Number} x Current mouse/touch coordinates
964          * @param {Number} y Current mouse/touch coordinates
965          */
966         initMoveOrigin: function (x, y) {
967             this.drag_dx = x - this.origin.scrCoords[1];
968             this.drag_dy = y - this.origin.scrCoords[2];
969 
970             this.mode = this.BOARD_MODE_MOVE_ORIGIN;
971             this.updateQuality = this.BOARD_QUALITY_LOW;
972         },
973 
974         /**
975          * Collects all elements below the current mouse pointer and fulfilling the following constraints:
976          * <ul><li>isDraggable</li><li>visible</li><li>not fixed</li><li>not frozen</li></ul>
977          * @param {Number} x Current mouse/touch coordinates
978          * @param {Number} y current mouse/touch coordinates
979          * @param {Object} evt An event object
980          * @param {String} type What type of event? 'touch', 'mouse' or 'pen'.
981          * @returns {Array} A list of geometric elements.
982          */
983         initMoveObject: function (x, y, evt, type) {
984             var pEl,
985                 el,
986                 collect = [],
987                 offset = [],
988                 haspoint,
989                 len = this.objectsList.length,
990                 dragEl = {visProp: {layer: -10000}};
991 
992             //for (el in this.objects) {
993             for (el = 0; el < len; el++) {
994                 pEl = this.objectsList[el];
995                 haspoint = pEl.hasPoint && pEl.hasPoint(x, y);
996 
997                 if (pEl.visPropCalc.visible && haspoint) {
998                     pEl.triggerEventHandlers([type + 'down', 'down'], [evt]);
999                     this.downObjects.push(pEl);
1000                 }
1001 
1002                 if (haspoint &&
1003                     pEl.isDraggable &&
1004                     pEl.visPropCalc.visible &&
1005                     ((this.geonextCompatibilityMode &&
1006                         (Type.isPoint(pEl) ||
1007                          pEl.elementClass === Const.OBJECT_CLASS_TEXT)
1008                      ) ||
1009                      !this.geonextCompatibilityMode
1010                     ) &&
1011                     !Type.evaluate(pEl.visProp.fixed)
1012                     /*(!pEl.visProp.frozen) &&*/
1013                     ) {
1014 
1015                     // Elements in the highest layer get priority.
1016                     if (pEl.visProp.layer > dragEl.visProp.layer ||
1017                             (pEl.visProp.layer === dragEl.visProp.layer &&
1018                              pEl.lastDragTime.getTime() >= dragEl.lastDragTime.getTime()
1019                             )) {
1020                         // If an element and its label have the focus
1021                         // simultaneously, the element is taken.
1022                         // This only works if we assume that every browser runs
1023                         // through this.objects in the right order, i.e. an element A
1024                         // added before element B turns up here before B does.
1025                         if (!this.attr.ignorelabels ||
1026                             (!Type.exists(dragEl.label) || pEl !== dragEl.label)) {
1027                             dragEl = pEl;
1028                             collect.push(dragEl);
1029 
1030                             // Save offset for large coords elements.
1031                             if (Type.exists(dragEl.coords)) {
1032                                 offset.push(Statistics.subtract(dragEl.coords.scrCoords.slice(1), [x, y]));
1033                             } else {
1034                                 offset.push([0, 0]);
1035                             }
1036 
1037                             // we can't drop out of this loop because of the event handling system
1038                             //if (this.attr.takefirst) {
1039                             //    return collect;
1040                             //}
1041                         }
1042                     }
1043                 }
1044             }
1045 
1046             if (this.attr.drag.enabled && collect.length > 0) {
1047                 this.mode = this.BOARD_MODE_DRAG;
1048             }
1049 
1050             // A one-element array is returned.
1051             if (this.attr.takefirst) {
1052                 collect.length = 1;
1053                 this._drag_offset = offset[0];
1054             } else {
1055                 collect = collect.slice(-1);
1056                 this._drag_offset = offset[offset.length - 1];
1057             }
1058 
1059             if (!this._drag_offset) {
1060                 this._drag_offset = [0, 0];
1061             }
1062 
1063             // Move drag element to the top of the layer
1064             if (this.renderer.type === 'svg' &&
1065                 Type.exists(collect[0]) &&
1066                 Type.evaluate(collect[0].visProp.dragtotopoflayer) &&
1067                 collect.length === 1 &&
1068                 Type.exists(collect[0].rendNode)) {
1069 
1070                 collect[0].rendNode.parentNode.appendChild(collect[0].rendNode);
1071             }
1072 
1073             // Init rotation angle and scale factor for two finger movements
1074             this.previousRotation = 0.0;
1075             this.previousScale = 1.0;
1076 
1077             if (collect.length >= 1) {
1078                 collect[0].highlight(true);
1079                 this.triggerEventHandlers(['mousehit', 'hit'], [evt, collect[0]]);
1080             }
1081 
1082             return collect;
1083         },
1084 
1085         /**
1086          * Moves an object.
1087          * @param {Number} x Coordinate
1088          * @param {Number} y Coordinate
1089          * @param {Object} o The touch object that is dragged: {JXG.Board#mouse} or {JXG.Board#touches}.
1090          * @param {Object} evt The event object.
1091          * @param {String} type Mouse or touch event?
1092          */
1093         moveObject: function (x, y, o, evt, type) {
1094             var newPos = new Coords(Const.COORDS_BY_SCREEN, this.getScrCoordsOfMouse(x, y), this),
1095                 drag,
1096                 dragScrCoords, newDragScrCoords;
1097 
1098             if (!(o && o.obj)) {
1099                 return;
1100             }
1101             drag = o.obj;
1102 
1103             // Save updates for very small movements of coordsElements, see below
1104             if (drag.coords) {
1105                 dragScrCoords = drag.coords.scrCoords.slice();
1106             }
1107 
1108             /*
1109              * Save the position.
1110              */
1111             this.drag_position = [newPos.scrCoords[1], newPos.scrCoords[2]];
1112             this.drag_position = Statistics.add(this.drag_position, this._drag_offset);
1113             //
1114             // We have to distinguish between CoordsElements and other elements like lines.
1115             // The latter need the difference between two move events.
1116             if (Type.exists(drag.coords)) {
1117                 drag.setPositionDirectly(Const.COORDS_BY_SCREEN, this.drag_position);
1118             } else {
1119                 this.displayInfobox(false);
1120                                     // Hide infobox in case the user has touched an intersection point
1121                                     // and drags the underlying line now.
1122 
1123                 if (!isNaN(o.targets[0].Xprev + o.targets[0].Yprev)) {
1124                     drag.setPositionDirectly(Const.COORDS_BY_SCREEN,
1125                         [newPos.scrCoords[1], newPos.scrCoords[2]],
1126                         [o.targets[0].Xprev, o.targets[0].Yprev]
1127                         );
1128                 }
1129                 // Remember the actual position for the next move event. Then we are able to
1130                 // compute the difference vector.
1131                 o.targets[0].Xprev = newPos.scrCoords[1];
1132                 o.targets[0].Yprev = newPos.scrCoords[2];
1133             }
1134             // This may be necessary for some gliders and labels
1135             if (Type.exists(drag.coords)) {
1136                 drag.prepareUpdate().update(false).updateRenderer();
1137                 this.updateInfobox(drag);
1138                 drag.prepareUpdate().update(true).updateRenderer();
1139             }
1140 
1141             if (drag.coords) {
1142                 newDragScrCoords = drag.coords.scrCoords;
1143             }
1144             // No updates for very small movements of coordsElements
1145             if (!drag.coords ||
1146                 dragScrCoords[1] !== newDragScrCoords[1] ||
1147                 dragScrCoords[2] !== newDragScrCoords[2]) {
1148 
1149                 drag.triggerEventHandlers([type + 'drag', 'drag'], [evt]);
1150 
1151                 this.update();
1152             }
1153             drag.highlight(true);
1154             this.triggerEventHandlers(['mousehit', 'hit'], [evt, drag]);
1155 
1156             drag.lastDragTime = new Date();
1157         },
1158 
1159         /**
1160          * Moves elements in multitouch mode.
1161          * @param {Array} p1 x,y coordinates of first touch
1162          * @param {Array} p2 x,y coordinates of second touch
1163          * @param {Object} o The touch object that is dragged: {JXG.Board#touches}.
1164          * @param {Object} evt The event object that lead to this movement.
1165          */
1166         twoFingerMove: function (o, id, evt) {
1167             var drag;
1168 
1169             if (Type.exists(o) && Type.exists(o.obj)) {
1170                 drag = o.obj;
1171             } else {
1172                 return;
1173             }
1174 
1175             if (drag.elementClass === Const.OBJECT_CLASS_LINE ||
1176                 drag.type === Const.OBJECT_TYPE_POLYGON) {
1177                 this.twoFingerTouchObject(o.targets, drag, id);
1178             } else if (drag.elementClass === Const.OBJECT_CLASS_CIRCLE) {
1179                 this.twoFingerTouchCircle(o.targets, drag, id);
1180             }
1181 
1182             if (evt) {
1183                 drag.triggerEventHandlers(['touchdrag', 'drag'], [evt]);
1184             }
1185         },
1186 
1187         /**
1188          * Moves, rotates and scales a line or polygon with two fingers.
1189          * @param {Array} tar Array conatining touch event objects: {JXG.Board#touches.targets}.
1190          * @param {object} drag The object that is dragged:
1191          * @param {Number} id pointerId of the event. In case of old touch event this is emulated.
1192          */
1193         twoFingerTouchObject: function (tar, drag, id) {
1194             var np, op, nd, od,
1195                 d, alpha,
1196                 S, t1, t3, t4, t5,
1197                 ar, i, len,
1198                 fixEl, moveEl, fix;
1199 
1200             if (Type.exists(tar[0]) && Type.exists(tar[1]) &&
1201                 !isNaN(tar[0].Xprev + tar[0].Yprev + tar[1].Xprev + tar[1].Yprev)) {
1202 
1203                 if (id === tar[0].num) {
1204                     fixEl  = tar[1];
1205                     moveEl = tar[0];
1206                 } else {
1207                     fixEl  = tar[0];
1208                     moveEl = tar[1];
1209                 }
1210 
1211                 fix = (new Coords(Const.COORDS_BY_SCREEN, [fixEl.Xprev, fixEl.Yprev], this)).usrCoords;
1212                 // Previous finger position
1213                 op = (new Coords(Const.COORDS_BY_SCREEN, [moveEl.Xprev, moveEl.Yprev], this)).usrCoords;
1214                 // New finger position
1215                 np = (new Coords(Const.COORDS_BY_SCREEN, [moveEl.X, moveEl.Y], this)).usrCoords;
1216 
1217                 // Old and new directions
1218                 od = Mat.crossProduct(fix, op);
1219                 nd = Mat.crossProduct(fix, np);
1220 
1221                 // Intersection between the two directions
1222                 S = Mat.crossProduct(od, nd);
1223 
1224                 // If parallel translate, otherwise rotate
1225                 if (Math.abs(S[0]) < Mat.eps) {
1226                     return;
1227                 }
1228 
1229                 alpha = Geometry.rad(op.slice(1), fix.slice(1), np.slice(1));
1230 
1231                 t1 = this.create('transform', [alpha, [fix[1], fix[2]]], {type: 'rotate'});
1232                 t1.update();
1233 
1234                 if (Type.evaluate(drag.visProp.scalable)) {
1235                     // Scale
1236                     d = Geometry.distance(np, fix) / Geometry.distance(op, fix);
1237 
1238                     t3 = this.create('transform', [-fix[1], -fix[2]], {type: 'translate'});
1239                     t4 = this.create('transform', [d, d], {type: 'scale'});
1240                     t5 = this.create('transform', [fix[1], fix[2]], {type: 'translate'});
1241                     t1.melt(t3).melt(t4).melt(t5);
1242                 }
1243 
1244                 if (drag.elementClass === Const.OBJECT_CLASS_LINE) {
1245                     ar = [];
1246                     if (drag.point1.draggable()) {
1247                         ar.push(drag.point1);
1248                     }
1249                     if (drag.point2.draggable()) {
1250                         ar.push(drag.point2);
1251                     }
1252                     t1.applyOnce(ar);
1253                 } else if (drag.type === Const.OBJECT_TYPE_POLYGON) {
1254                     ar = [];
1255                     len = drag.vertices.length - 1;
1256                     for (i = 0; i < len; ++i) {
1257                         if (drag.vertices[i].draggable()) {
1258                             ar.push(drag.vertices[i]);
1259                         }
1260                     }
1261                     t1.applyOnce(ar);
1262                 }
1263 
1264                 this.update();
1265                 drag.highlight(true);
1266             }
1267         },
1268 
1269         /*
1270          * Moves, rotates and scales a circle with two fingers.
1271          * @param {Array} tar Array conatining touch event objects: {JXG.Board#touches.targets}.
1272          * @param {object} drag The object that is dragged:
1273          * @param {Number} id pointerId of the event. In case of old touch event this is emulated.
1274          */
1275         twoFingerTouchCircle: function (tar, drag, id) {
1276             var fixEl, moveEl, np, op, fix,
1277                 d, alpha, t1, t2, t3, t4;
1278 
1279             if (drag.method === 'pointCircle' || drag.method === 'pointLine') {
1280                 return;
1281             }
1282 
1283             if (Type.exists(tar[0]) && Type.exists(tar[1]) &&
1284                 !isNaN(tar[0].Xprev + tar[0].Yprev + tar[1].Xprev + tar[1].Yprev)) {
1285 
1286                 if (id === tar[0].num) {
1287                     fixEl  = tar[1];
1288                     moveEl = tar[0];
1289                 } else {
1290                     fixEl  = tar[0];
1291                     moveEl = tar[1];
1292                 }
1293 
1294                 fix = (new Coords(Const.COORDS_BY_SCREEN, [fixEl.Xprev, fixEl.Yprev], this)).usrCoords;
1295                 // Previous finger position
1296                 op = (new Coords(Const.COORDS_BY_SCREEN, [moveEl.Xprev, moveEl.Yprev], this)).usrCoords;
1297                 // New finger position
1298                 np = (new Coords(Const.COORDS_BY_SCREEN, [moveEl.X, moveEl.Y], this)).usrCoords;
1299 
1300                 alpha = Geometry.rad(op.slice(1), fix.slice(1), np.slice(1));
1301 
1302                 // Rotate and scale by the movement of the second finger
1303                 t1 = this.create('transform', [-fix[1], -fix[2]], {type: 'translate'});
1304                 t2 = this.create('transform', [alpha], {type: 'rotate'});
1305                 t1.melt(t2);
1306                 if (Type.evaluate(drag.visProp.scalable)) {
1307                     d = Geometry.distance(fix, np) / Geometry.distance(fix, op);
1308                     t3 = this.create('transform', [d, d], {type: 'scale'});
1309                     t1.melt(t3);
1310                 }
1311                 t4 = this.create('transform', [fix[1], fix[2]], {type: 'translate'});
1312                 t1.melt(t4);
1313 
1314                 if (drag.center.draggable()) {
1315                     t1.applyOnce([drag.center]);
1316                 }
1317 
1318                 if (drag.method === 'twoPoints') {
1319                     if (drag.point2.draggable()) {
1320                         t1.applyOnce([drag.point2]);
1321                     }
1322                 } else if (drag.method === 'pointRadius') {
1323                     if (Type.isNumber(drag.updateRadius.origin)) {
1324                         drag.setRadius(drag.radius * d);
1325                     }
1326                 }
1327 
1328                 this.update(drag.center);
1329                 drag.highlight(true);
1330             }
1331         },
1332 
1333         highlightElements: function (x, y, evt, target) {
1334             var el, pEl, pId,
1335                 overObjects = {},
1336                 len = this.objectsList.length;
1337 
1338             // Elements  below the mouse pointer which are not highlighted yet will be highlighted.
1339             for (el = 0; el < len; el++) {
1340                 pEl = this.objectsList[el];
1341                 pId = pEl.id;
1342                 if (Type.exists(pEl.hasPoint) && pEl.visPropCalc.visible && pEl.hasPoint(x, y)) {
1343                     // this is required in any case because otherwise the box won't be shown until the point is dragged
1344                     this.updateInfobox(pEl);
1345 
1346                     if (!Type.exists(this.highlightedObjects[pId])) { // highlight only if not highlighted
1347                         overObjects[pId] = pEl;
1348                         pEl.highlight();
1349                         // triggers board event.
1350                         this.triggerEventHandlers(['mousehit', 'hit'], [evt, pEl, target]);
1351                     }
1352 
1353                     if (pEl.mouseover) {
1354                         pEl.triggerEventHandlers(['mousemove', 'move'], [evt]);
1355                     } else {
1356                         pEl.triggerEventHandlers(['mouseover', 'over'], [evt]);
1357                         pEl.mouseover = true;
1358                     }
1359                 }
1360             }
1361 
1362             for (el = 0; el < len; el++) {
1363                 pEl = this.objectsList[el];
1364                 pId = pEl.id;
1365                 if (pEl.mouseover) {
1366                     if (!overObjects[pId]) {
1367                         pEl.triggerEventHandlers(['mouseout', 'out'], [evt]);
1368                         pEl.mouseover = false;
1369                     }
1370                 }
1371             }
1372         },
1373 
1374         /**
1375          * Helper function which returns a reasonable starting point for the object being dragged.
1376          * Formerly known as initXYstart().
1377          * @private
1378          * @param {JXG.GeometryElement} obj The object to be dragged
1379          * @param {Array} targets Array of targets. It is changed by this function.
1380          */
1381         saveStartPos: function (obj, targets) {
1382             var xy = [], i, len;
1383 
1384             if (obj.type === Const.OBJECT_TYPE_TICKS) {
1385                 xy.push([1, NaN, NaN]);
1386             } else if (obj.elementClass === Const.OBJECT_CLASS_LINE) {
1387                 xy.push(obj.point1.coords.usrCoords);
1388                 xy.push(obj.point2.coords.usrCoords);
1389             } else if (obj.elementClass === Const.OBJECT_CLASS_CIRCLE) {
1390                 xy.push(obj.center.coords.usrCoords);
1391                 if (obj.method === 'twoPoints') {
1392                     xy.push(obj.point2.coords.usrCoords);
1393                 }
1394             } else if (obj.type === Const.OBJECT_TYPE_POLYGON) {
1395                 len = obj.vertices.length - 1;
1396                 for (i = 0; i < len; i++) {
1397                     xy.push(obj.vertices[i].coords.usrCoords);
1398                 }
1399             } else if (obj.type === Const.OBJECT_TYPE_SECTOR) {
1400                 xy.push(obj.point1.coords.usrCoords);
1401                 xy.push(obj.point2.coords.usrCoords);
1402                 xy.push(obj.point3.coords.usrCoords);
1403             } else if (Type.isPoint(obj) || obj.type === Const.OBJECT_TYPE_GLIDER) {
1404                 xy.push(obj.coords.usrCoords);
1405             } else if (obj.elementClass === Const.OBJECT_CLASS_CURVE) {
1406                 // if (Type.exists(obj.parents)) {
1407                 //     len = obj.parents.length;
1408                 //     if (len > 0) {
1409                 //         for (i = 0; i < len; i++) {
1410                 //             xy.push(this.select(obj.parents[i]).coords.usrCoords);
1411                 //         }
1412                 //     } else
1413                 // }
1414                 if (obj.points.length > 0) {
1415                     xy.push(obj.points[0].usrCoords);
1416                 }
1417             } else {
1418                 try {
1419                     xy.push(obj.coords.usrCoords);
1420                 } catch (e) {
1421                     JXG.debug('JSXGraph+ saveStartPos: obj.coords.usrCoords not available: ' + e);
1422                 }
1423             }
1424 
1425             len = xy.length;
1426             for (i = 0; i < len; i++) {
1427                 targets.Zstart.push(xy[i][0]);
1428                 targets.Xstart.push(xy[i][1]);
1429                 targets.Ystart.push(xy[i][2]);
1430             }
1431         },
1432 
1433         mouseOriginMoveStart: function (evt) {
1434             var r, pos;
1435 
1436             r = this._isRequiredKeyPressed(evt, 'pan');
1437             if (r) {
1438                 pos = this.getMousePosition(evt);
1439                 this.initMoveOrigin(pos[0], pos[1]);
1440             }
1441 
1442             return r;
1443         },
1444 
1445         mouseOriginMove: function (evt) {
1446             var r = (this.mode === this.BOARD_MODE_MOVE_ORIGIN),
1447                 pos;
1448 
1449             if (r) {
1450                 pos = this.getMousePosition(evt);
1451                 this.moveOrigin(pos[0], pos[1], true);
1452             }
1453 
1454             return r;
1455         },
1456 
1457         /**
1458          * Start moving the origin with one finger.
1459          * @private
1460          * @param  {Object} evt Event from touchStartListener
1461          * @return {Boolean}   returns if the origin is moved.
1462          */
1463         touchStartMoveOriginOneFinger: function (evt) {
1464             var touches = evt[JXG.touchProperty],
1465                 conditions, pos;
1466 
1467             conditions = this.attr.pan.enabled &&
1468                 !this.attr.pan.needtwofingers &&
1469                 touches.length === 1;
1470 
1471             if (conditions) {
1472                 pos = this.getMousePosition(evt, 0);
1473                 this.initMoveOrigin(pos[0], pos[1]);
1474             }
1475 
1476             return conditions;
1477         },
1478 
1479         /**
1480          * Move the origin with one finger
1481          * @private
1482          * @param  {Object} evt Event from touchMoveListener
1483          * @return {Boolean}     returns if the origin is moved.
1484          */
1485         touchOriginMove: function (evt) {
1486             var r = (this.mode === this.BOARD_MODE_MOVE_ORIGIN),
1487                 pos;
1488 
1489             if (r) {
1490                 pos = this.getMousePosition(evt, 0);
1491                 this.moveOrigin(pos[0], pos[1], true);
1492             }
1493 
1494             return r;
1495         },
1496 
1497         /**
1498          * Stop moving the origin with one finger
1499          * @return {null} null
1500          * @private
1501          */
1502         originMoveEnd: function () {
1503             this.updateQuality = this.BOARD_QUALITY_HIGH;
1504             this.mode = this.BOARD_MODE_NONE;
1505         },
1506 
1507         /**********************************************************
1508          *
1509          * Event Handler
1510          *
1511          **********************************************************/
1512 
1513         /**
1514          *  Add all possible event handlers to the board object
1515          */
1516         addEventHandlers: function () {
1517             if (Env.supportsPointerEvents()) {
1518                 this.addPointerEventHandlers();
1519             } else {
1520                 this.addMouseEventHandlers();
1521                 this.addTouchEventHandlers();
1522             }
1523 
1524             // This one produces errors on IE
1525             //Env.addEvent(this.containerObj, 'contextmenu', function (e) { e.preventDefault(); return false;}, this);
1526             // This one works on IE, Firefox and Chromium with default configurations. On some Safari
1527             // or Opera versions the user must explicitly allow the deactivation of the context menu.
1528             if (this.containerObj !== null) {
1529                 this.containerObj.oncontextmenu = function (e) {
1530                     if (Type.exists(e)) {
1531                         e.preventDefault();
1532                     }
1533                     return false;
1534                 };
1535             }
1536 
1537             this.addFullscreenEventHandlers();
1538             this.addKeyboardEventHandlers();
1539 
1540             if (Env.isBrowser) {
1541                 try {
1542                     // resizeObserver: triggered if size of the JSXGraph div changes.
1543                     this.startResizeObserver();
1544                 } catch (err) {
1545                     // resize event: triggered if size of window changes
1546                     Env.addEvent(window, 'resize', this.resizeListener, this);
1547                     // intersectionObserver: triggered if JSXGraph becomes visible.
1548                     this.startIntersectionObserver();
1549                 }
1550                 // Scroll event: needs to be captured since on mobile devices
1551                 // sometimes a header bar is displayed / hidden, which triggers a
1552                 // resize event.
1553                 Env.addEvent(window, 'scroll', this.scrollListener, this);
1554             }
1555         },
1556 
1557         /**
1558          * Remove all event handlers from the board object
1559          */
1560         removeEventHandlers: function () {
1561             this.removeMouseEventHandlers();
1562             this.removeTouchEventHandlers();
1563             this.removePointerEventHandlers();
1564 
1565             this.removeFullscreenEventHandlers();
1566             this.removeKeyboardEventHandlers();
1567             if (Env.isBrowser) {
1568                 if (Type.exists(this.resizeObserver)) {
1569                     this.stopResizeObserver();
1570                 } else {
1571                     Env.removeEvent(window, 'resize', this.resizeListener, this);
1572                     this.stopIntersectionObserver();
1573                 }
1574                 Env.removeEvent(window, 'scroll', this.scrollListener, this);
1575             }
1576         },
1577 
1578         /**
1579          * Registers the MSPointer* event handlers.
1580          */
1581         addPointerEventHandlers: function () {
1582             if (!this.hasPointerHandlers && Env.isBrowser) {
1583                 var moveTarget = this.attr.movetarget || this.containerObj;
1584 
1585                 if (window.navigator.msPointerEnabled) {  // IE10-
1586                     Env.addEvent(this.containerObj, 'MSPointerDown', this.pointerDownListener, this);
1587                     Env.addEvent(moveTarget, 'MSPointerMove', this.pointerMoveListener, this);
1588                 } else {
1589                     Env.addEvent(this.containerObj, 'pointerdown', this.pointerDownListener, this);
1590                     Env.addEvent(moveTarget, 'pointermove', this.pointerMoveListener, this);
1591                 }
1592                 Env.addEvent(this.containerObj, 'mousewheel', this.mouseWheelListener, this);
1593                 Env.addEvent(this.containerObj, 'DOMMouseScroll', this.mouseWheelListener, this);
1594 
1595                 if (this.containerObj !== null) {
1596                     // This is needed for capturing touch events.
1597                     // It is also in jsxgraph.css, but one never knows...
1598                     this.containerObj.style.touchAction = 'none';
1599                 }
1600 
1601                 this.hasPointerHandlers = true;
1602             }
1603         },
1604 
1605         /**
1606          * Registers mouse move, down and wheel event handlers.
1607          */
1608         addMouseEventHandlers: function () {
1609             if (!this.hasMouseHandlers && Env.isBrowser) {
1610                 var moveTarget = this.attr.movetarget || this.containerObj;
1611 
1612                 Env.addEvent(this.containerObj, 'mousedown', this.mouseDownListener, this);
1613                 Env.addEvent(moveTarget, 'mousemove', this.mouseMoveListener, this);
1614 
1615                 Env.addEvent(this.containerObj, 'mousewheel', this.mouseWheelListener, this);
1616                 Env.addEvent(this.containerObj, 'DOMMouseScroll', this.mouseWheelListener, this);
1617 
1618                 this.hasMouseHandlers = true;
1619             }
1620         },
1621 
1622         /**
1623          * Register touch start and move and gesture start and change event handlers.
1624          * @param {Boolean} appleGestures If set to false the gesturestart and gesturechange event handlers
1625          * will not be registered.
1626          *
1627          * Since iOS 13, touch events were abandoned in favour of pointer events
1628          */
1629         addTouchEventHandlers: function (appleGestures) {
1630             if (!this.hasTouchHandlers && Env.isBrowser) {
1631                 var moveTarget = this.attr.movetarget || this.containerObj;
1632 
1633                 Env.addEvent(this.containerObj, 'touchstart', this.touchStartListener, this);
1634                 Env.addEvent(moveTarget, 'touchmove', this.touchMoveListener, this);
1635 
1636                 /*
1637                 if (!Type.exists(appleGestures) || appleGestures) {
1638                     // Gesture listener are called in touchStart and touchMove.
1639                     //Env.addEvent(this.containerObj, 'gesturestart', this.gestureStartListener, this);
1640                     //Env.addEvent(this.containerObj, 'gesturechange', this.gestureChangeListener, this);
1641                 }
1642                 */
1643 
1644                 this.hasTouchHandlers = true;
1645             }
1646         },
1647 
1648         /**
1649          * Add fullscreen events which update the CSS transformation matrix to correct
1650          * the mouse/touch/pointer positions in case of CSS transformations.
1651          */
1652         addFullscreenEventHandlers: function() {
1653             var i,
1654                 // standard/Edge, firefox, chrome/safari, IE11
1655                 events = ['fullscreenchange', 'mozfullscreenchange', 'webkitfullscreenchange', 'msfullscreenchange'],
1656                 le = events.length;
1657 
1658             if (!this.hasFullsceenEventHandlers && Env.isBrowser) {
1659                 for (i = 0; i < le; i++) {
1660                     Env.addEvent(this.document, events[i], this.fullscreenListener, this);
1661                 }
1662                 this.hasFullsceenEventHandlers = true;
1663             }
1664         },
1665 
1666         addKeyboardEventHandlers: function() {
1667             if (this.attr.keyboard.enabled && !this.hasKeyboardHandlers && Env.isBrowser) {
1668                 Env.addEvent(this.containerObj, 'keydown', this.keyDownListener, this);
1669                 Env.addEvent(this.containerObj, 'focusin', this.keyFocusInListener, this);
1670                 Env.addEvent(this.containerObj, 'focusout', this.keyFocusOutListener, this);
1671                 this.hasKeyboardHandlers = true;
1672             }
1673         },
1674 
1675         /**
1676          * Remove all registered touch event handlers.
1677          */
1678         removeKeyboardEventHandlers: function () {
1679             if (this.hasKeyboardHandlers && Env.isBrowser) {
1680                 Env.removeEvent(this.containerObj, 'keydown', this.keyDownListener, this);
1681                 Env.removeEvent(this.containerObj, 'focusin', this.keyFocusInListener, this);
1682                 Env.removeEvent(this.containerObj, 'focusout', this.keyFocusOutListener, this);
1683                 this.hasKeyboardHandlers = false;
1684             }
1685         },
1686 
1687         /**
1688          * Remove all registered event handlers regarding fullscreen mode.
1689          */
1690         removeFullscreenEventHandlers: function() {
1691             var i,
1692                 // standard/Edge, firefox, chrome/safari, IE11
1693                 events = ['fullscreenchange', 'mozfullscreenchange', 'webkitfullscreenchange', 'msfullscreenchange'],
1694                 le = events.length;
1695 
1696             if (this.hasFullsceenEventHandlers && Env.isBrowser) {
1697                 for (i = 0; i < le; i++) {
1698                     Env.removeEvent(this.document, events[i], this.fullscreenListener, this);
1699                 }
1700                 this.hasFullsceenEventHandlers = false;
1701             }
1702         },
1703 
1704         /**
1705          * Remove MSPointer* Event handlers.
1706          */
1707         removePointerEventHandlers: function () {
1708             if (this.hasPointerHandlers && Env.isBrowser) {
1709                 var moveTarget = this.attr.movetarget || this.containerObj;
1710 
1711                 if (window.navigator.msPointerEnabled) {  // IE10-
1712                     Env.removeEvent(this.containerObj, 'MSPointerDown', this.pointerDownListener, this);
1713                     Env.removeEvent(moveTarget, 'MSPointerMove', this.pointerMoveListener, this);
1714                 } else {
1715                     Env.removeEvent(this.containerObj, 'pointerdown', this.pointerDownListener, this);
1716                     Env.removeEvent(moveTarget, 'pointermove', this.pointerMoveListener, this);
1717                 }
1718 
1719                 Env.removeEvent(this.containerObj, 'mousewheel', this.mouseWheelListener, this);
1720                 Env.removeEvent(this.containerObj, 'DOMMouseScroll', this.mouseWheelListener, this);
1721 
1722                 if (this.hasPointerUp) {
1723                     if (window.navigator.msPointerEnabled) {  // IE10-
1724                         Env.removeEvent(this.document, 'MSPointerUp',   this.pointerUpListener, this);
1725                     } else {
1726                         Env.removeEvent(this.document, 'pointerup',     this.pointerUpListener, this);
1727                         Env.removeEvent(this.document, 'pointercancel', this.pointerUpListener, this);
1728                     }
1729                     this.hasPointerUp = false;
1730                 }
1731 
1732                 this.hasPointerHandlers = false;
1733             }
1734         },
1735 
1736         /**
1737          * De-register mouse event handlers.
1738          */
1739         removeMouseEventHandlers: function () {
1740             if (this.hasMouseHandlers && Env.isBrowser) {
1741                 var moveTarget = this.attr.movetarget || this.containerObj;
1742 
1743                 Env.removeEvent(this.containerObj, 'mousedown', this.mouseDownListener, this);
1744                 Env.removeEvent(moveTarget, 'mousemove', this.mouseMoveListener, this);
1745 
1746                 if (this.hasMouseUp) {
1747                     Env.removeEvent(this.document, 'mouseup', this.mouseUpListener, this);
1748                     this.hasMouseUp = false;
1749                 }
1750 
1751                 Env.removeEvent(this.containerObj, 'mousewheel', this.mouseWheelListener, this);
1752                 Env.removeEvent(this.containerObj, 'DOMMouseScroll', this.mouseWheelListener, this);
1753 
1754                 this.hasMouseHandlers = false;
1755             }
1756         },
1757 
1758         /**
1759          * Remove all registered touch event handlers.
1760          */
1761         removeTouchEventHandlers: function () {
1762             if (this.hasTouchHandlers && Env.isBrowser) {
1763                 var moveTarget = this.attr.movetarget || this.containerObj;
1764 
1765                 Env.removeEvent(this.containerObj, 'touchstart', this.touchStartListener, this);
1766                 Env.removeEvent(moveTarget, 'touchmove', this.touchMoveListener, this);
1767 
1768                 if (this.hasTouchEnd) {
1769                     Env.removeEvent(this.document, 'touchend', this.touchEndListener, this);
1770                     this.hasTouchEnd = false;
1771                 }
1772 
1773                 this.hasTouchHandlers = false;
1774             }
1775         },
1776 
1777         /**
1778          * Handler for click on left arrow in the navigation bar
1779          * @returns {JXG.Board} Reference to the board
1780          */
1781         clickLeftArrow: function () {
1782             this.moveOrigin(this.origin.scrCoords[1] + this.canvasWidth * 0.1, this.origin.scrCoords[2]);
1783             return this;
1784         },
1785 
1786         /**
1787          * Handler for click on right arrow in the navigation bar
1788          * @returns {JXG.Board} Reference to the board
1789          */
1790         clickRightArrow: function () {
1791             this.moveOrigin(this.origin.scrCoords[1] - this.canvasWidth * 0.1, this.origin.scrCoords[2]);
1792             return this;
1793         },
1794 
1795         /**
1796          * Handler for click on up arrow in the navigation bar
1797          * @returns {JXG.Board} Reference to the board
1798          */
1799         clickUpArrow: function () {
1800             this.moveOrigin(this.origin.scrCoords[1], this.origin.scrCoords[2] - this.canvasHeight * 0.1);
1801             return this;
1802         },
1803 
1804         /**
1805          * Handler for click on down arrow in the navigation bar
1806          * @returns {JXG.Board} Reference to the board
1807          */
1808         clickDownArrow: function () {
1809             this.moveOrigin(this.origin.scrCoords[1], this.origin.scrCoords[2] + this.canvasHeight * 0.1);
1810             return this;
1811         },
1812 
1813         /**
1814          * Triggered on iOS/Safari while the user inputs a gesture (e.g. pinch) and is used to zoom into the board.
1815          * Works on iOS/Safari and Android.
1816          * @param {Event} evt Browser event object
1817          * @returns {Boolean}
1818          */
1819         gestureChangeListener: function (evt) {
1820             var c,
1821                 dir1 = [],
1822                 dir2 = [],
1823                 angle,
1824                 mi = 10,
1825                 isPinch = false,
1826                 // Save zoomFactors
1827                 zx = this.attr.zoom.factorx,
1828                 zy = this.attr.zoom.factory,
1829                 factor,
1830                 dist,
1831                 dx, dy, theta, cx, cy, bound;
1832 
1833             if (this.mode !== this.BOARD_MODE_ZOOM) {
1834                 return true;
1835             }
1836             evt.preventDefault();
1837 
1838             dist = Geometry.distance([evt.touches[0].clientX, evt.touches[0].clientY],
1839                 [evt.touches[1].clientX, evt.touches[1].clientY], 2);
1840 
1841             // Android pinch to zoom
1842             // evt.scale was available in iOS touch events (pre iOS 13)
1843             // evt.scale is undefined in Android
1844             if (evt.scale === undefined) {
1845                 evt.scale = dist / this.prevDist;
1846             }
1847 
1848             if (!Type.exists(this.prevCoords)) {
1849                 return false;
1850             }
1851             // Compute the angle of the two finger directions
1852             dir1 = [evt.touches[0].clientX - this.prevCoords[0][0],
1853                     evt.touches[0].clientY - this.prevCoords[0][1]];
1854             dir2 = [evt.touches[1].clientX - this.prevCoords[1][0],
1855                     evt.touches[1].clientY - this.prevCoords[1][1]];
1856 
1857             if ((dir1[0] * dir1[0] + dir1[1] * dir1[1] < mi * mi) &&
1858                 (dir2[0] * dir2[0] + dir2[1] * dir2[1] < mi * mi)) {
1859                     return false;
1860             }
1861 
1862             angle = Geometry.rad(dir1, [0,0], dir2);
1863             if (this.isPreviousGesture !== 'pan' &&
1864                 Math.abs(angle) > Math.PI * 0.2 &&
1865                 Math.abs(angle) < Math.PI * 1.8) {
1866                 isPinch = true;
1867             }
1868 
1869             if (this.isPreviousGesture !== 'pan' && !isPinch) {
1870                 if (Math.abs(evt.scale) < 0.77 || Math.abs(evt.scale) > 1.3) {
1871                     isPinch = true;
1872                 }
1873             }
1874 
1875             factor = evt.scale / this.prevScale;
1876             this.prevScale = evt.scale;
1877             this.prevCoords = [[evt.touches[0].clientX, evt.touches[0].clientY],
1878                                [evt.touches[1].clientX, evt.touches[1].clientY]];
1879 
1880             c = new Coords(Const.COORDS_BY_SCREEN, this.getMousePosition(evt, 0), this);
1881 
1882             if (this.attr.pan.enabled &&
1883                 this.attr.pan.needtwofingers &&
1884                 !isPinch) {
1885                 // Pan detected
1886 
1887                 this.isPreviousGesture = 'pan';
1888 
1889                 this.moveOrigin(c.scrCoords[1], c.scrCoords[2], true);
1890             } else if (this.attr.zoom.enabled &&
1891                         Math.abs(factor - 1.0) < 0.5) {
1892                 // Pinch detected
1893 
1894                 if (this.attr.zoom.pinchhorizontal || this.attr.zoom.pinchvertical) {
1895                     dx = Math.abs(evt.touches[0].clientX - evt.touches[1].clientX);
1896                     dy = Math.abs(evt.touches[0].clientY - evt.touches[1].clientY);
1897                     theta = Math.abs(Math.atan2(dy, dx));
1898                     bound = Math.PI * this.attr.zoom.pinchsensitivity / 90.0;
1899                 }
1900 
1901                 if (this.attr.zoom.pinchhorizontal && theta < bound) {
1902                     this.attr.zoom.factorx = factor;
1903                     this.attr.zoom.factory = 1.0;
1904                     cx = 0;
1905                     cy = 0;
1906                 } else if (this.attr.zoom.pinchvertical && Math.abs(theta - Math.PI * 0.5) < bound) {
1907                     this.attr.zoom.factorx = 1.0;
1908                     this.attr.zoom.factory = factor;
1909                     cx = 0;
1910                     cy = 0;
1911                 } else {
1912                     this.attr.zoom.factorx = factor;
1913                     this.attr.zoom.factory = factor;
1914                     cx = c.usrCoords[1];
1915                     cy = c.usrCoords[2];
1916                 }
1917 
1918                 this.zoomIn(cx, cy);
1919 
1920                 // Restore zoomFactors
1921                 this.attr.zoom.factorx = zx;
1922                 this.attr.zoom.factory = zy;
1923             }
1924 
1925             return false;
1926         },
1927 
1928         /**
1929          * Called by iOS/Safari as soon as the user starts a gesture. Works natively on iOS/Safari,
1930          * on Android we emulate it.
1931          * @param {Event} evt
1932          * @returns {Boolean}
1933          */
1934         gestureStartListener: function (evt) {
1935             var pos;
1936 
1937             evt.preventDefault();
1938             this.prevScale = 1.0;
1939             // Android pinch to zoom
1940             this.prevDist = Geometry.distance([evt.touches[0].clientX, evt.touches[0].clientY],
1941                             [evt.touches[1].clientX, evt.touches[1].clientY], 2);
1942             this.prevCoords = [[evt.touches[0].clientX, evt.touches[0].clientY],
1943                                [evt.touches[1].clientX, evt.touches[1].clientY]];
1944             this.isPreviousGesture = 'none';
1945 
1946             // If pinch-to-zoom is interpreted as panning
1947             // we have to prepare move origin
1948             pos = this.getMousePosition(evt, 0);
1949             this.initMoveOrigin(pos[0], pos[1]);
1950 
1951             this.mode = this.BOARD_MODE_ZOOM;
1952             return false;
1953         },
1954 
1955         /**
1956          * Test if the required key combination is pressed for wheel zoom, move origin and
1957          * selection
1958          * @private
1959          * @param  {Object}  evt    Mouse or pen event
1960          * @param  {String}  action String containing the action: 'zoom', 'pan', 'selection'.
1961          * Corresponds to the attribute subobject.
1962          * @return {Boolean}        true or false.
1963          */
1964         _isRequiredKeyPressed: function (evt, action) {
1965             var obj = this.attr[action];
1966             if (!obj.enabled) {
1967                 return false;
1968             }
1969 
1970             if (((obj.needshift && evt.shiftKey) || (!obj.needshift && !evt.shiftKey)) &&
1971                 ((obj.needctrl && evt.ctrlKey) || (!obj.needctrl && !evt.ctrlKey))
1972             )  {
1973                 return true;
1974             }
1975 
1976             return false;
1977         },
1978 
1979         /*
1980          * Pointer events
1981          */
1982 
1983         /**
1984          *
1985          * Check if pointer event is already registered in {@link JXG.Board#_board_touches}.
1986          *
1987          * @param  {Object} evt Event object
1988          * @return {Boolean} true if down event has already been sent.
1989          * @private
1990          */
1991          _isPointerRegistered: function(evt) {
1992             var i, len = this._board_touches.length;
1993 
1994             for (i = 0; i < len; i++) {
1995                 if (this._board_touches[i].pointerId === evt.pointerId) {
1996                     return true;
1997                 }
1998             }
1999             return false;
2000         },
2001 
2002         /**
2003          *
2004          * Store the position of a pointer event.
2005          * If not yet done, registers a pointer event in {@link JXG.Board#_board_touches}.
2006          * Allows to follow the path of that finger on the screen.
2007          * Only two simultaneous touches are supported.
2008          *
2009          * @param {Object} evt Event object
2010          * @returns {JXG.Board} Reference to the board
2011          * @private
2012          */
2013          _pointerStorePosition: function (evt) {
2014             var i, found;
2015 
2016             for (i = 0, found = false; i < this._board_touches.length; i++) {
2017                 if (this._board_touches[i].pointerId === evt.pointerId) {
2018                     this._board_touches[i].clientX = evt.clientX;
2019                     this._board_touches[i].clientY = evt.clientY;
2020                     found = true;
2021                     break;
2022                 }
2023             }
2024 
2025             // Restrict the number of simultaneous touches to 2
2026             if (!found && this._board_touches.length < 2) {
2027                 this._board_touches.push({
2028                     pointerId: evt.pointerId,
2029                     clientX: evt.clientX,
2030                     clientY: evt.clientY
2031                 });
2032             }
2033 
2034             return this;
2035         },
2036 
2037         /**
2038          * Deregisters a pointer event in {@link JXG.Board#_board_touches}.
2039          * It happens if a finger has been lifted from the screen.
2040          *
2041          * @param {Object} evt Event object
2042          * @returns {JXG.Board} Reference to the board
2043          * @private
2044          */
2045         _pointerRemoveTouches: function (evt) {
2046             var i;
2047             for (i = 0; i < this._board_touches.length; i++) {
2048                 if (this._board_touches[i].pointerId === evt.pointerId) {
2049                     this._board_touches.splice(i, 1);
2050                     break;
2051                 }
2052             }
2053 
2054             return this;
2055         },
2056 
2057         /**
2058          * Remove all registered fingers from {@link JXG.Board#_board_touches}.
2059          * This might be necessary if too many fingers have been registered.
2060          * @returns {JXG.Board} Reference to the board
2061          * @private
2062          */
2063         _pointerClearTouches: function() {
2064             if (this._board_touches.length > 0) {
2065                 this.dehighlightAll();
2066             }
2067             this.updateQuality = this.BOARD_QUALITY_HIGH;
2068             this.mode = this.BOARD_MODE_NONE;
2069             this._board_touches = [];
2070             this.touches = [];
2071         },
2072 
2073         /**
2074          * Determine which input device is used for this action.
2075          * Possible devices are 'touch', 'pen' and 'mouse'.
2076          * This affects the precision and certain events.
2077          * In case of no browser, 'mouse' is used.
2078          *
2079          * @see JXG.Board#pointerDownListener
2080          * @see JXG.Board#pointerMoveListener
2081          * @see JXG.Board#initMoveObject
2082          * @see JXG.Board#moveObject
2083          *
2084          * @param {Event} evt The browsers event object.
2085          * @returns {String} 'mouse', 'pen', or 'touch'
2086          * @private
2087          */
2088         _getPointerInputDevice: function(evt) {
2089             if (Env.isBrowser) {
2090                 if (evt.pointerType === 'touch' ||        // New
2091                     (window.navigator.msMaxTouchPoints && // Old
2092                         window.navigator.msMaxTouchPoints > 1)) {
2093                     return 'touch';
2094                 }
2095                 if (evt.pointerType === 'mouse') {
2096                     return 'mouse';
2097                 }
2098                 if (evt.pointerType === 'pen') {
2099                     return 'pen';
2100                 }
2101             }
2102             return 'mouse';
2103         },
2104 
2105         /**
2106          * This method is called by the browser when a pointing device is pressed on the screen.
2107          * @param {Event} evt The browsers event object.
2108          * @param {Object} object If the object to be dragged is already known, it can be submitted via this parameter
2109          * @returns {Boolean} ...
2110          */
2111         pointerDownListener: function (evt, object) {
2112             var i, j, k, pos, elements, sel,
2113                 target_obj,
2114                 type = 'mouse', // Used in case of no browser
2115                 found, target;
2116 
2117             // Fix for Firefox browser: When using a second finger, the
2118             // touch event for the first finger is sent again.
2119             if (!object && this._isPointerRegistered(evt)) {
2120                 return false;
2121             }
2122 
2123             if (!object && evt.isPrimary) {
2124                 // First finger down. To be on the safe side this._board_touches is cleared.
2125                 this._pointerClearTouches();
2126             }
2127 
2128             if (!this.hasPointerUp) {
2129                 if (window.navigator.msPointerEnabled) {  // IE10-
2130                     Env.addEvent(this.document, 'MSPointerUp',   this.pointerUpListener, this);
2131                 } else {
2132                     // 'pointercancel' is fired e.g. if the finger leaves the browser and drags down the system menu on Android
2133                     Env.addEvent(this.document, 'pointerup',     this.pointerUpListener, this);
2134                     Env.addEvent(this.document, 'pointercancel', this.pointerUpListener, this);
2135                 }
2136                 this.hasPointerUp = true;
2137             }
2138 
2139             if (this.hasMouseHandlers) {
2140                 this.removeMouseEventHandlers();
2141             }
2142 
2143             if (this.hasTouchHandlers) {
2144                 this.removeTouchEventHandlers();
2145             }
2146 
2147             // Prevent accidental selection of text
2148             if (this.document.selection && Type.isFunction(this.document.selection.empty)) {
2149                 this.document.selection.empty();
2150             } else if (window.getSelection) {
2151                 sel = window.getSelection();
2152                 if (sel.removeAllRanges) {
2153                     try {
2154                         sel.removeAllRanges();
2155                     } catch (e) {}
2156                 }
2157             }
2158 
2159             // Mouse, touch or pen device
2160             this._inputDevice = this._getPointerInputDevice(evt);
2161             type = this._inputDevice;
2162             this.options.precision.hasPoint = this.options.precision[type];
2163 
2164             // Handling of multi touch with pointer events should be easier than the touch events.
2165             // Every pointer device has its own pointerId, e.g. the mouse
2166             // always has id 1 or 0, fingers and pens get unique ids every time a pointerDown event is fired and they will
2167             // keep this id until a pointerUp event is fired. What we have to do here is:
2168             //  1. collect all elements under the current pointer
2169             //  2. run through the touches control structure
2170             //    a. look for the object collected in step 1.
2171             //    b. if an object is found, check the number of pointers. If appropriate, add the pointer.
2172             pos = this.getMousePosition(evt);
2173 
2174             // selection
2175             this._testForSelection(evt);
2176             if (this.selectingMode) {
2177                 this._startSelecting(pos);
2178                 this.triggerEventHandlers(['touchstartselecting', 'pointerstartselecting', 'startselecting'], [evt]);
2179                 return;     // don't continue as a normal click
2180             }
2181 
2182             if (this.attr.drag.enabled && object) {
2183                 elements = [ object ];
2184                 this.mode = this.BOARD_MODE_DRAG;
2185             } else {
2186                 elements = this.initMoveObject(pos[0], pos[1], evt, type);
2187             }
2188 
2189             target_obj = {
2190                 num: evt.pointerId,
2191                 X: pos[0],
2192                 Y: pos[1],
2193                 Xprev: NaN,
2194                 Yprev: NaN,
2195                 Xstart: [],
2196                 Ystart: [],
2197                 Zstart: []
2198             };
2199 
2200             // If no draggable object can be found, get out here immediately
2201             if (elements.length > 0) {
2202                 // check touches structure
2203                 target = elements[elements.length - 1];
2204                 found = false;
2205 
2206                 // Reminder: this.touches is the list of elements which
2207                 // currently "possess" a pointer (mouse, pen, finger)
2208                 for (i = 0; i < this.touches.length; i++) {
2209                     // An element receives a further touch, i.e.
2210                     // the target is already in our touches array, add the pointer to the existing touch
2211                     if (this.touches[i].obj === target) {
2212                         j = i;
2213                         k = this.touches[i].targets.push(target_obj) - 1;
2214                         found = true;
2215                         break;
2216                     }
2217                 }
2218                 if (!found) {
2219                     // An new element hae been touched.
2220                     k = 0;
2221                     j = this.touches.push({
2222                         obj: target,
2223                         targets: [target_obj]
2224                     }) - 1;
2225                 }
2226 
2227                 this.dehighlightAll();
2228                 target.highlight(true);
2229 
2230                 this.saveStartPos(target, this.touches[j].targets[k]);
2231 
2232                 // Prevent accidental text selection
2233                 // this could get us new trouble: input fields, links and drop down boxes placed as text
2234                 // on the board don't work anymore.
2235                 if (evt && evt.preventDefault) {
2236                     evt.preventDefault();
2237                 } else if (window.event) {
2238                     window.event.returnValue = false;
2239                 }
2240             }
2241 
2242             if (this.touches.length > 0) {
2243                 evt.preventDefault();
2244                 evt.stopPropagation();
2245             }
2246 
2247             if (!Env.isBrowser) {
2248                 return false;
2249             }
2250             if (this._getPointerInputDevice(evt) !== 'touch') {
2251                 if (this.mode === this.BOARD_MODE_NONE) {
2252                     this.mouseOriginMoveStart(evt);
2253                 }
2254             } else {
2255                 this._pointerStorePosition(evt);
2256                 evt.touches = this._board_touches;
2257 
2258                 // Touch events on empty areas of the board are handled here, see also touchStartListener
2259                 // 1. case: one finger. If allowed, this triggers pan with one finger
2260                 if (evt.touches.length === 1 &&
2261                     this.mode === this.BOARD_MODE_NONE &&
2262                     this.touchStartMoveOriginOneFinger(evt)) {
2263                         // Empty by purpose
2264                 } else if (evt.touches.length === 2 &&
2265                             (this.mode === this.BOARD_MODE_NONE || this.mode === this.BOARD_MODE_MOVE_ORIGIN)
2266                         ) {
2267                     // 2. case: two fingers: pinch to zoom or pan with two fingers needed.
2268                     // This happens when the second finger hits the device. First, the
2269                     // "one finger pan mode" has to be cancelled.
2270                     if (this.mode === this.BOARD_MODE_MOVE_ORIGIN) {
2271                         this.originMoveEnd();
2272                     }
2273 
2274                     this.gestureStartListener(evt);
2275                 }
2276             }
2277 
2278             this.triggerEventHandlers(['touchstart', 'down', 'pointerdown', 'MSPointerDown'], [evt]);
2279             return false;
2280         },
2281 
2282         // /**
2283         //  * Called if pointer leaves an HTML tag. It is called by the inner-most tag.
2284         //  * That means, if a JSXGraph text, i.e. an HTML div, is placed close
2285         //  * to the border of the board, this pointerout event will be ignored.
2286         //  * @param  {Event} evt
2287         //  * @return {Boolean}
2288         //  */
2289         // pointerOutListener: function (evt) {
2290         //     if (evt.target === this.containerObj ||
2291         //         (this.renderer.type === 'svg' && evt.target === this.renderer.foreignObjLayer)) {
2292         //         this.pointerUpListener(evt);
2293         //     }
2294         //     return this.mode === this.BOARD_MODE_NONE;
2295         // },
2296 
2297         /**
2298          * Called periodically by the browser while the user moves a pointing device across the screen.
2299          * @param {Event} evt
2300          * @returns {Boolean}
2301          */
2302         pointerMoveListener: function (evt) {
2303             var i, j, pos, touchTargets,
2304                 type = 'mouse'; // in case of no browser
2305 
2306             if (this._getPointerInputDevice(evt) === 'touch' && !this._isPointerRegistered(evt)) {
2307                 // Test, if there was a previous down event of this _getPointerId
2308                 // (in case it is a touch event).
2309                 // Otherwise this move event is ignored. This is necessary e.g. for sketchometry.
2310                 return this.BOARD_MODE_NONE;
2311             }
2312 
2313             if (!this.checkFrameRate(evt)) {
2314                 return false;
2315             }
2316 
2317             if (this.mode !== this.BOARD_MODE_DRAG) {
2318                 this.dehighlightAll();
2319                 this.displayInfobox(false);
2320             }
2321 
2322             if (this.mode !== this.BOARD_MODE_NONE) {
2323                 evt.preventDefault();
2324                 evt.stopPropagation();
2325             }
2326 
2327             this.updateQuality = this.BOARD_QUALITY_LOW;
2328             // Mouse, touch or pen device
2329             this._inputDevice = this._getPointerInputDevice(evt);
2330             type = this._inputDevice;
2331             this.options.precision.hasPoint = this.options.precision[type];
2332 
2333             // selection
2334             if (this.selectingMode) {
2335                 pos = this.getMousePosition(evt);
2336                 this._moveSelecting(pos);
2337                 this.triggerEventHandlers(['touchmoveselecting', 'moveselecting', 'pointermoveselecting'], [evt, this.mode]);
2338             } else if (!this.mouseOriginMove(evt)) {
2339                 if (this.mode === this.BOARD_MODE_DRAG) {
2340                     // Run through all jsxgraph elements which are touched by at least one finger.
2341                     for (i = 0; i < this.touches.length; i++) {
2342                         touchTargets = this.touches[i].targets;
2343                         // Run through all touch events which have been started on this jsxgraph element.
2344                         for (j = 0; j < touchTargets.length; j++) {
2345                             if (touchTargets[j].num === evt.pointerId) {
2346 
2347                                 pos = this.getMousePosition(evt);
2348                                 touchTargets[j].X = pos[0];
2349                                 touchTargets[j].Y = pos[1];
2350 
2351                                 if (touchTargets.length === 1) {
2352                                     // Touch by one finger: this is possible for all elements that can be dragged
2353                                     this.moveObject(pos[0], pos[1], this.touches[i], evt, type);
2354                                 } else if (touchTargets.length === 2) {
2355                                     // Touch by two fingers: e.g. moving lines
2356                                     this.twoFingerMove(this.touches[i], evt.pointerId, evt);
2357 
2358                                     touchTargets[j].Xprev = pos[0];
2359                                     touchTargets[j].Yprev = pos[1];
2360                                 }
2361 
2362                                 // There is only one pointer in the evt object, so there's no point in looking further
2363                                 break;
2364                             }
2365                         }
2366                     }
2367                 } else {
2368                     if (this._getPointerInputDevice(evt) === 'touch') {
2369                         this._pointerStorePosition(evt);
2370 
2371                         if (this._board_touches.length === 2) {
2372                             evt.touches = this._board_touches;
2373                             this.gestureChangeListener(evt);
2374                         }
2375                     }
2376 
2377                     // Move event without dragging an element
2378                     pos = this.getMousePosition(evt);
2379                     this.highlightElements(pos[0], pos[1], evt, -1);
2380                 }
2381             }
2382 
2383             // Hiding the infobox is commented out, since it prevents showing the infobox
2384             // on IE 11+ on 'over'
2385             //if (this.mode !== this.BOARD_MODE_DRAG) {
2386                 //this.displayInfobox(false);
2387             //}
2388             this.triggerEventHandlers(['touchmove', 'move', 'pointermove', 'MSPointerMove'], [evt, this.mode]);
2389             this.updateQuality = this.BOARD_QUALITY_HIGH;
2390 
2391             return this.mode === this.BOARD_MODE_NONE;
2392         },
2393 
2394         /**
2395          * Triggered as soon as the user stops touching the device with at least one finger.
2396          * @param {Event} evt
2397          * @returns {Boolean}
2398          */
2399         pointerUpListener: function (evt) {
2400             var i, j, found, touchTargets;
2401 
2402             this.triggerEventHandlers(['touchend', 'up', 'pointerup', 'MSPointerUp'], [evt]);
2403             this.displayInfobox(false);
2404 
2405             if (evt) {
2406                 for (i = 0; i < this.touches.length; i++) {
2407                     touchTargets = this.touches[i].targets;
2408                     for (j = 0; j < touchTargets.length; j++) {
2409                         if (touchTargets[j].num === evt.pointerId) {
2410                             touchTargets.splice(j, 1);
2411                             if (touchTargets.length === 0) {
2412                                 this.touches.splice(i, 1);
2413                             }
2414                             break;
2415                         }
2416                     }
2417                 }
2418             }
2419 
2420             // selection
2421             if (this.selectingMode) {
2422                 this._stopSelecting(evt);
2423                 this.triggerEventHandlers(['touchstopselecting', 'pointerstopselecting', 'stopselecting'], [evt]);
2424             } else {
2425                 for (i = this.downObjects.length - 1; i > -1; i--) {
2426                     found = false;
2427                     for (j = 0; j < this.touches.length; j++) {
2428                         if (this.touches[j].obj.id === this.downObjects[i].id) {
2429                             found = true;
2430                         }
2431                     }
2432                     if (!found) {
2433                         this.downObjects[i].triggerEventHandlers(['touchend', 'up', 'pointerup', 'MSPointerUp'], [evt]);
2434                         this.downObjects[i].snapToGrid();
2435                         this.downObjects[i].snapToPoints();
2436                         this.downObjects.splice(i, 1);
2437                     }
2438                 }
2439             }
2440 
2441             // this._pointerRemoveTouches(evt);
2442             // if (this._board_touches.length === 0) {
2443                 if (this.hasPointerUp) {
2444                     if (window.navigator.msPointerEnabled) {  // IE10-
2445                         Env.removeEvent(this.document, 'MSPointerUp',   this.pointerUpListener, this);
2446                     } else {
2447                         Env.removeEvent(this.document, 'pointerup',     this.pointerUpListener, this);
2448                         Env.removeEvent(this.document, 'pointercancel', this.pointerUpListener, this);
2449                     }
2450                     this.hasPointerUp = false;
2451                 }
2452 
2453                 // this.dehighlightAll();
2454                 // this.updateQuality = this.BOARD_QUALITY_HIGH;
2455                 // this.mode = this.BOARD_MODE_NONE;
2456 
2457                 this.originMoveEnd();
2458                 this.update();
2459             // }
2460             // After one finger leaves the screen the gesture is stopped.
2461             this._pointerClearTouches();
2462             return true;
2463         },
2464 
2465         /**
2466          * Touch-Events
2467          */
2468 
2469         /**
2470          * This method is called by the browser when a finger touches the surface of the touch-device.
2471          * @param {Event} evt The browsers event object.
2472          * @returns {Boolean} ...
2473          */
2474         touchStartListener: function (evt) {
2475             var i, pos, elements, j, k,
2476                 eps = this.options.precision.touch,
2477                 obj, found, targets,
2478                 evtTouches = evt[JXG.touchProperty],
2479                 target, touchTargets;
2480 
2481             if (!this.hasTouchEnd) {
2482                 Env.addEvent(this.document, 'touchend', this.touchEndListener, this);
2483                 this.hasTouchEnd = true;
2484             }
2485 
2486             // Do not remove mouseHandlers, since Chrome on win tablets sends mouseevents if used with pen.
2487             //if (this.hasMouseHandlers) { this.removeMouseEventHandlers(); }
2488 
2489             // prevent accidental selection of text
2490             if (this.document.selection && Type.isFunction(this.document.selection.empty)) {
2491                 this.document.selection.empty();
2492             } else if (window.getSelection) {
2493                 window.getSelection().removeAllRanges();
2494             }
2495 
2496             // multitouch
2497             this._inputDevice = 'touch';
2498             this.options.precision.hasPoint = this.options.precision.touch;
2499 
2500             // This is the most critical part. first we should run through the existing touches and collect all targettouches that don't belong to our
2501             // previous touches. once this is done we run through the existing touches again and watch out for free touches that can be attached to our existing
2502             // touches, e.g. we translate (parallel translation) a line with one finger, now a second finger is over this line. this should change the operation to
2503             // a rotational translation. or one finger moves a circle, a second finger can be attached to the circle: this now changes the operation from translation to
2504             // stretching. as a last step we're going through the rest of the targettouches and initiate new move operations:
2505             //  * points have higher priority over other elements.
2506             //  * if we find a targettouch over an element that could be transformed with more than one finger, we search the rest of the targettouches, if they are over
2507             //    this element and add them.
2508             // ADDENDUM 11/10/11:
2509             //  (1) run through the touches control object,
2510             //  (2) try to find the targetTouches for every touch. on touchstart only new touches are added, hence we can find a targettouch
2511             //      for every target in our touches objects
2512             //  (3) if one of the targettouches was bound to a touches targets array, mark it
2513             //  (4) run through the targettouches. if the targettouch is marked, continue. otherwise check for elements below the targettouch:
2514             //      (a) if no element could be found: mark the target touches and continue
2515             //      --- in the following cases, "init" means:
2516             //           (i) check if the element is already used in another touches element, if so, mark the targettouch and continue
2517             //          (ii) if not, init a new touches element, add the targettouch to the touches property and mark it
2518             //      (b) if the element is a point, init
2519             //      (c) if the element is a line, init and try to find a second targettouch on that line. if a second one is found, add and mark it
2520             //      (d) if the element is a circle, init and try to find TWO other targettouches on that circle. if only one is found, mark it and continue. otherwise
2521             //          add both to the touches array and mark them.
2522             for (i = 0; i < evtTouches.length; i++) {
2523                 evtTouches[i].jxg_isused = false;
2524             }
2525 
2526             for (i = 0; i < this.touches.length; i++) {
2527                 touchTargets = this.touches[i].targets;
2528                 for (j = 0; j < touchTargets.length; j++) {
2529                     touchTargets[j].num = -1;
2530                     eps = this.options.precision.touch;
2531 
2532                     do {
2533                         for (k = 0; k < evtTouches.length; k++) {
2534                             // find the new targettouches
2535                             if (Math.abs(Math.pow(evtTouches[k].screenX - touchTargets[j].X, 2) +
2536                                     Math.pow(evtTouches[k].screenY - touchTargets[j].Y, 2)) < eps * eps) {
2537                                 touchTargets[j].num = k;
2538                                 touchTargets[j].X = evtTouches[k].screenX;
2539                                 touchTargets[j].Y = evtTouches[k].screenY;
2540                                 evtTouches[k].jxg_isused = true;
2541                                 break;
2542                             }
2543                         }
2544 
2545                         eps *= 2;
2546 
2547                     } while (touchTargets[j].num === -1 &&
2548                              eps < this.options.precision.touchMax);
2549 
2550                     if (touchTargets[j].num === -1) {
2551                         JXG.debug('i couldn\'t find a targettouches for target no ' + j + ' on ' + this.touches[i].obj.name + ' (' + this.touches[i].obj.id + '). Removed the target.');
2552                         JXG.debug('eps = ' + eps + ', touchMax = ' + Options.precision.touchMax);
2553                         touchTargets.splice(i, 1);
2554                     }
2555 
2556                 }
2557             }
2558 
2559             // we just re-mapped the targettouches to our existing touches list.
2560             // now we have to initialize some touches from additional targettouches
2561             for (i = 0; i < evtTouches.length; i++) {
2562                 if (!evtTouches[i].jxg_isused) {
2563 
2564                     pos = this.getMousePosition(evt, i);
2565                     // selection
2566                     // this._testForSelection(evt); // we do not have shift or ctrl keys yet.
2567                     if (this.selectingMode) {
2568                         this._startSelecting(pos);
2569                         this.triggerEventHandlers(['touchstartselecting', 'startselecting'], [evt]);
2570                         evt.preventDefault();
2571                         evt.stopPropagation();
2572                         this.options.precision.hasPoint = this.options.precision.mouse;
2573                         return this.touches.length > 0; // don't continue as a normal click
2574                     }
2575 
2576                     elements = this.initMoveObject(pos[0], pos[1], evt, 'touch');
2577                     if (elements.length !== 0) {
2578                         obj = elements[elements.length - 1];
2579                         target = {num: i,
2580                             X: evtTouches[i].screenX,
2581                             Y: evtTouches[i].screenY,
2582                             Xprev: NaN,
2583                             Yprev: NaN,
2584                             Xstart: [],
2585                             Ystart: [],
2586                             Zstart: []
2587                         };
2588 
2589                         if (Type.isPoint(obj) ||
2590                                 obj.elementClass === Const.OBJECT_CLASS_TEXT ||
2591                                 obj.type === Const.OBJECT_TYPE_TICKS ||
2592                                 obj.type === Const.OBJECT_TYPE_IMAGE) {
2593                             // It's a point, so it's single touch, so we just push it to our touches
2594                             targets = [target];
2595 
2596                             // For the UNDO/REDO of object moves
2597                             this.saveStartPos(obj, targets[0]);
2598 
2599                             this.touches.push({ obj: obj, targets: targets });
2600                             obj.highlight(true);
2601 
2602                         } else if (obj.elementClass === Const.OBJECT_CLASS_LINE ||
2603                                 obj.elementClass === Const.OBJECT_CLASS_CIRCLE ||
2604                                 obj.elementClass === Const.OBJECT_CLASS_CURVE ||
2605                                 obj.type === Const.OBJECT_TYPE_POLYGON) {
2606                             found = false;
2607 
2608                             // first check if this geometric object is already captured in this.touches
2609                             for (j = 0; j < this.touches.length; j++) {
2610                                 if (obj.id === this.touches[j].obj.id) {
2611                                     found = true;
2612                                     // only add it, if we don't have two targets in there already
2613                                     if (this.touches[j].targets.length === 1) {
2614                                         // For the UNDO/REDO of object moves
2615                                         this.saveStartPos(obj, target);
2616                                         this.touches[j].targets.push(target);
2617                                     }
2618 
2619                                     evtTouches[i].jxg_isused = true;
2620                                 }
2621                             }
2622 
2623                             // we couldn't find it in touches, so we just init a new touches
2624                             // IF there is a second touch targetting this line, we will find it later on, and then add it to
2625                             // the touches control object.
2626                             if (!found) {
2627                                 targets = [target];
2628 
2629                                 // For the UNDO/REDO of object moves
2630                                 this.saveStartPos(obj, targets[0]);
2631                                 this.touches.push({ obj: obj, targets: targets });
2632                                 obj.highlight(true);
2633                             }
2634                         }
2635                     }
2636 
2637                     evtTouches[i].jxg_isused = true;
2638                 }
2639             }
2640 
2641             if (this.touches.length > 0) {
2642                 evt.preventDefault();
2643                 evt.stopPropagation();
2644             }
2645 
2646             // Touch events on empty areas of the board are handled here:
2647             // 1. case: one finger. If allowed, this triggers pan with one finger
2648             if (evtTouches.length === 1 && this.mode === this.BOARD_MODE_NONE && this.touchStartMoveOriginOneFinger(evt)) {
2649             } else if (evtTouches.length === 2 &&
2650                         (this.mode === this.BOARD_MODE_NONE || this.mode === this.BOARD_MODE_MOVE_ORIGIN)
2651                     ) {
2652                 // 2. case: two fingers: pinch to zoom or pan with two fingers needed.
2653                 // This happens when the second finger hits the device. First, the
2654                 // "one finger pan mode" has to be cancelled.
2655                 if (this.mode === this.BOARD_MODE_MOVE_ORIGIN) {
2656                     this.originMoveEnd();
2657                 }
2658                 this.gestureStartListener(evt);
2659             }
2660 
2661             this.options.precision.hasPoint = this.options.precision.mouse;
2662             this.triggerEventHandlers(['touchstart', 'down'], [evt]);
2663 
2664             return false;
2665             //return this.touches.length > 0;
2666         },
2667 
2668         /**
2669          * Called periodically by the browser while the user moves his fingers across the device.
2670          * @param {Event} evt
2671          * @returns {Boolean}
2672          */
2673         touchMoveListener: function (evt) {
2674             var i, pos1, pos2,
2675                 touchTargets,
2676                 evtTouches = evt[JXG.touchProperty];
2677 
2678             if (!this.checkFrameRate(evt)) {
2679                 return false;
2680             }
2681 
2682             if (this.mode !== this.BOARD_MODE_NONE) {
2683                 evt.preventDefault();
2684                 evt.stopPropagation();
2685             }
2686 
2687             if (this.mode !== this.BOARD_MODE_DRAG) {
2688                 this.dehighlightAll();
2689                 this.displayInfobox(false);
2690             }
2691 
2692             this._inputDevice = 'touch';
2693             this.options.precision.hasPoint = this.options.precision.touch;
2694             this.updateQuality = this.BOARD_QUALITY_LOW;
2695 
2696             // selection
2697             if (this.selectingMode) {
2698                 for (i = 0; i < evtTouches.length; i++) {
2699                     if (!evtTouches[i].jxg_isused) {
2700                         pos1 = this.getMousePosition(evt, i);
2701                         this._moveSelecting(pos1);
2702                         this.triggerEventHandlers(['touchmoves', 'moveselecting'], [evt, this.mode]);
2703                         break;
2704                     }
2705                 }
2706             } else {
2707                 if (!this.touchOriginMove(evt)) {
2708                     if (this.mode === this.BOARD_MODE_DRAG) {
2709                         // Runs over through all elements which are touched
2710                         // by at least one finger.
2711                         for (i = 0; i < this.touches.length; i++) {
2712                             touchTargets = this.touches[i].targets;
2713                             if (touchTargets.length === 1) {
2714 
2715 
2716                                 // Touch by one finger:  this is possible for all elements that can be dragged
2717                                 if (evtTouches[touchTargets[0].num]) {
2718                                     pos1 = this.getMousePosition(evt, touchTargets[0].num);
2719                                     if (pos1[0] < 0 || pos1[0] > this.canvasWidth ||
2720                                         pos1[1] < 0 || pos1[1] > this.canvasHeight) {
2721                                         return;
2722                                     }
2723                                     touchTargets[0].X = pos1[0];
2724                                     touchTargets[0].Y = pos1[1];
2725                                     this.moveObject(pos1[0], pos1[1], this.touches[i], evt, 'touch');
2726                                 }
2727 
2728                             } else if (touchTargets.length === 2 &&
2729                                 touchTargets[0].num > -1 &&
2730                                 touchTargets[1].num > -1) {
2731 
2732                                 // Touch by two fingers: moving lines, ...
2733                                 if (evtTouches[touchTargets[0].num] &&
2734                                     evtTouches[touchTargets[1].num]) {
2735 
2736                                     // Get coordinates of the two touches
2737                                     pos1 = this.getMousePosition(evt, touchTargets[0].num);
2738                                     pos2 = this.getMousePosition(evt, touchTargets[1].num);
2739                                     if (pos1[0] < 0 || pos1[0] > this.canvasWidth ||
2740                                         pos1[1] < 0 || pos1[1] > this.canvasHeight ||
2741                                         pos2[0] < 0 || pos2[0] > this.canvasWidth ||
2742                                         pos2[1] < 0 || pos2[1] > this.canvasHeight) {
2743                                         return;
2744                                     }
2745 
2746                                     touchTargets[0].X = pos1[0];
2747                                     touchTargets[0].Y = pos1[1];
2748                                     touchTargets[1].X = pos2[0];
2749                                     touchTargets[1].Y = pos2[1];
2750 
2751                                     this.twoFingerMove(this.touches[i], touchTargets[0].num, evt);
2752                                     this.twoFingerMove(this.touches[i], touchTargets[1].num);
2753 
2754                                     touchTargets[0].Xprev = pos1[0];
2755                                     touchTargets[0].Yprev = pos1[1];
2756                                     touchTargets[1].Xprev = pos2[0];
2757                                     touchTargets[1].Yprev = pos2[1];
2758                                 }
2759                             }
2760                         }
2761                     } else {
2762                         if (evtTouches.length === 2) {
2763                             this.gestureChangeListener(evt);
2764                         }
2765                         // Move event without dragging an element
2766                         pos1 = this.getMousePosition(evt, 0);
2767                         this.highlightElements(pos1[0], pos1[1], evt, -1);
2768                     }
2769                 }
2770             }
2771 
2772             if (this.mode !== this.BOARD_MODE_DRAG) {
2773                 this.displayInfobox(false);
2774             }
2775 
2776             this.triggerEventHandlers(['touchmove', 'move'], [evt, this.mode]);
2777             this.options.precision.hasPoint = this.options.precision.mouse;
2778             this.updateQuality = this.BOARD_QUALITY_HIGH;
2779 
2780             return this.mode === this.BOARD_MODE_NONE;
2781         },
2782 
2783         /**
2784          * Triggered as soon as the user stops touching the device with at least one finger.
2785          * @param {Event} evt
2786          * @returns {Boolean}
2787          */
2788         touchEndListener: function (evt) {
2789             var i, j, k,
2790                 eps = this.options.precision.touch,
2791                 tmpTouches = [], found, foundNumber,
2792                 evtTouches = evt && evt[JXG.touchProperty],
2793                 touchTargets;
2794 
2795             this.triggerEventHandlers(['touchend', 'up'], [evt]);
2796             this.displayInfobox(false);
2797 
2798             // selection
2799             if (this.selectingMode) {
2800                 this._stopSelecting(evt);
2801                 this.triggerEventHandlers(['touchstopselecting', 'stopselecting'], [evt]);
2802             } else if (evtTouches && evtTouches.length > 0) {
2803                 for (i = 0; i < this.touches.length; i++) {
2804                     tmpTouches[i] = this.touches[i];
2805                 }
2806                 this.touches.length = 0;
2807 
2808                 // try to convert the operation, e.g. if a lines is rotated and translated with two fingers and one finger is lifted,
2809                 // convert the operation to a simple one-finger-translation.
2810                 // ADDENDUM 11/10/11:
2811                 // see addendum to touchStartListener from 11/10/11
2812                 // (1) run through the tmptouches
2813                 // (2) check the touches.obj, if it is a
2814                 //     (a) point, try to find the targettouch, if found keep it and mark the targettouch, else drop the touch.
2815                 //     (b) line with
2816                 //          (i) one target: try to find it, if found keep it mark the targettouch, else drop the touch.
2817                 //         (ii) two targets: if none can be found, drop the touch. if one can be found, remove the other target. mark all found targettouches
2818                 //     (c) circle with [proceed like in line]
2819 
2820                 // init the targettouches marker
2821                 for (i = 0; i < evtTouches.length; i++) {
2822                     evtTouches[i].jxg_isused = false;
2823                 }
2824 
2825                 for (i = 0; i < tmpTouches.length; i++) {
2826                     // could all targets of the current this.touches.obj be assigned to targettouches?
2827                     found = false;
2828                     foundNumber = 0;
2829                     touchTargets = tmpTouches[i].targets;
2830 
2831                     for (j = 0; j < touchTargets.length; j++) {
2832                         touchTargets[j].found = false;
2833                         for (k = 0; k < evtTouches.length; k++) {
2834                             if (Math.abs(Math.pow(evtTouches[k].screenX - touchTargets[j].X, 2) + Math.pow(evtTouches[k].screenY - touchTargets[j].Y, 2)) < eps * eps) {
2835                                 touchTargets[j].found = true;
2836                                 touchTargets[j].num = k;
2837                                 touchTargets[j].X = evtTouches[k].screenX;
2838                                 touchTargets[j].Y = evtTouches[k].screenY;
2839                                 foundNumber += 1;
2840                                 break;
2841                             }
2842                         }
2843                     }
2844 
2845                     if (Type.isPoint(tmpTouches[i].obj)) {
2846                         found = (touchTargets[0] && touchTargets[0].found);
2847                     } else if (tmpTouches[i].obj.elementClass === Const.OBJECT_CLASS_LINE) {
2848                         found = (touchTargets[0] && touchTargets[0].found) || (touchTargets[1] && touchTargets[1].found);
2849                     } else if (tmpTouches[i].obj.elementClass === Const.OBJECT_CLASS_CIRCLE) {
2850                         found = foundNumber === 1 || foundNumber === 3;
2851                     }
2852 
2853                     // if we found this object to be still dragged by the user, add it back to this.touches
2854                     if (found) {
2855                         this.touches.push({
2856                             obj: tmpTouches[i].obj,
2857                             targets: []
2858                         });
2859 
2860                         for (j = 0; j < touchTargets.length; j++) {
2861                             if (touchTargets[j].found) {
2862                                 this.touches[this.touches.length - 1].targets.push({
2863                                     num: touchTargets[j].num,
2864                                     X: touchTargets[j].screenX,
2865                                     Y: touchTargets[j].screenY,
2866                                     Xprev: NaN,
2867                                     Yprev: NaN,
2868                                     Xstart: touchTargets[j].Xstart,
2869                                     Ystart: touchTargets[j].Ystart,
2870                                     Zstart: touchTargets[j].Zstart
2871                                 });
2872                             }
2873                         }
2874 
2875                     } else {
2876                         tmpTouches[i].obj.noHighlight();
2877                     }
2878                 }
2879 
2880             } else {
2881                 this.touches.length = 0;
2882             }
2883 
2884             for (i = this.downObjects.length - 1; i > -1; i--) {
2885                 found = false;
2886                 for (j = 0; j < this.touches.length; j++) {
2887                     if (this.touches[j].obj.id === this.downObjects[i].id) {
2888                         found = true;
2889                     }
2890                 }
2891                 if (!found) {
2892                     this.downObjects[i].triggerEventHandlers(['touchup', 'up'], [evt]);
2893                     this.downObjects[i].snapToGrid();
2894                     this.downObjects[i].snapToPoints();
2895                     this.downObjects.splice(i, 1);
2896                 }
2897             }
2898 
2899             if (!evtTouches || evtTouches.length === 0) {
2900 
2901                 if (this.hasTouchEnd) {
2902                     Env.removeEvent(this.document, 'touchend', this.touchEndListener, this);
2903                     this.hasTouchEnd = false;
2904                 }
2905 
2906                 this.dehighlightAll();
2907                 this.updateQuality = this.BOARD_QUALITY_HIGH;
2908 
2909                 this.originMoveEnd();
2910                 this.update();
2911             }
2912 
2913             return true;
2914         },
2915 
2916         /**
2917          * This method is called by the browser when the mouse button is clicked.
2918          * @param {Event} evt The browsers event object.
2919          * @returns {Boolean} True if no element is found under the current mouse pointer, false otherwise.
2920          */
2921         mouseDownListener: function (evt) {
2922             var pos, elements, result;
2923 
2924             // prevent accidental selection of text
2925             if (this.document.selection && Type.isFunction(this.document.selection.empty)) {
2926                 this.document.selection.empty();
2927             } else if (window.getSelection) {
2928                 window.getSelection().removeAllRanges();
2929             }
2930 
2931             if (!this.hasMouseUp) {
2932                 Env.addEvent(this.document, 'mouseup', this.mouseUpListener, this);
2933                 this.hasMouseUp = true;
2934             } else {
2935                 // In case this.hasMouseUp==true, it may be that there was a
2936                 // mousedown event before which was not followed by an mouseup event.
2937                 // This seems to happen with interactive whiteboard pens sometimes.
2938                 return;
2939             }
2940 
2941             this._inputDevice = 'mouse';
2942             this.options.precision.hasPoint = this.options.precision.mouse;
2943             pos = this.getMousePosition(evt);
2944 
2945             // selection
2946             this._testForSelection(evt);
2947             if (this.selectingMode) {
2948                 this._startSelecting(pos);
2949                 this.triggerEventHandlers(['mousestartselecting', 'startselecting'], [evt]);
2950                 return;     // don't continue as a normal click
2951             }
2952 
2953             elements = this.initMoveObject(pos[0], pos[1], evt, 'mouse');
2954 
2955             // if no draggable object can be found, get out here immediately
2956             if (elements.length === 0) {
2957                 this.mode = this.BOARD_MODE_NONE;
2958                 result = true;
2959             } else {
2960                 /** @ignore */
2961                 this.mouse = {
2962                     obj: null,
2963                     targets: [{
2964                         X: pos[0],
2965                         Y: pos[1],
2966                         Xprev: NaN,
2967                         Yprev: NaN
2968                     }]
2969                 };
2970                 this.mouse.obj = elements[elements.length - 1];
2971 
2972                 this.dehighlightAll();
2973                 this.mouse.obj.highlight(true);
2974 
2975                 this.mouse.targets[0].Xstart = [];
2976                 this.mouse.targets[0].Ystart = [];
2977                 this.mouse.targets[0].Zstart = [];
2978 
2979                 this.saveStartPos(this.mouse.obj, this.mouse.targets[0]);
2980 
2981                 // prevent accidental text selection
2982                 // this could get us new trouble: input fields, links and drop down boxes placed as text
2983                 // on the board don't work anymore.
2984                 if (evt && evt.preventDefault) {
2985                     evt.preventDefault();
2986                 } else if (window.event) {
2987                     window.event.returnValue = false;
2988                 }
2989             }
2990 
2991             if (this.mode === this.BOARD_MODE_NONE) {
2992                 result = this.mouseOriginMoveStart(evt);
2993             }
2994 
2995             this.triggerEventHandlers(['mousedown', 'down'], [evt]);
2996 
2997             return result;
2998         },
2999 
3000         /**
3001          * This method is called by the browser when the mouse is moved.
3002          * @param {Event} evt The browsers event object.
3003          */
3004         mouseMoveListener: function (evt) {
3005             var pos;
3006 
3007             if (!this.checkFrameRate(evt)) {
3008                 return false;
3009             }
3010 
3011             pos = this.getMousePosition(evt);
3012 
3013             this.updateQuality = this.BOARD_QUALITY_LOW;
3014 
3015             if (this.mode !== this.BOARD_MODE_DRAG) {
3016                 this.dehighlightAll();
3017                 this.displayInfobox(false);
3018             }
3019 
3020             // we have to check for four cases:
3021             //   * user moves origin
3022             //   * user drags an object
3023             //   * user just moves the mouse, here highlight all elements at
3024             //     the current mouse position
3025             //   * the user is selecting
3026 
3027             // selection
3028             if (this.selectingMode) {
3029                 this._moveSelecting(pos);
3030                 this.triggerEventHandlers(['mousemoveselecting', 'moveselecting'], [evt, this.mode]);
3031             } else if (!this.mouseOriginMove(evt)) {
3032                 if (this.mode === this.BOARD_MODE_DRAG) {
3033                     this.moveObject(pos[0], pos[1], this.mouse, evt, 'mouse');
3034                 } else { // BOARD_MODE_NONE
3035                     // Move event without dragging an element
3036                     this.highlightElements(pos[0], pos[1], evt, -1);
3037                 }
3038                 this.triggerEventHandlers(['mousemove', 'move'], [evt, this.mode]);
3039             }
3040             this.updateQuality = this.BOARD_QUALITY_HIGH;
3041         },
3042 
3043         /**
3044          * This method is called by the browser when the mouse button is released.
3045          * @param {Event} evt
3046          */
3047         mouseUpListener: function (evt) {
3048             var i;
3049 
3050             if (this.selectingMode === false) {
3051                 this.triggerEventHandlers(['mouseup', 'up'], [evt]);
3052             }
3053 
3054             // redraw with high precision
3055             this.updateQuality = this.BOARD_QUALITY_HIGH;
3056 
3057             if (this.mouse && this.mouse.obj) {
3058                 // The parameter is needed for lines with snapToGrid enabled
3059                 this.mouse.obj.snapToGrid(this.mouse.targets[0]);
3060                 this.mouse.obj.snapToPoints();
3061             }
3062 
3063             this.originMoveEnd();
3064             this.dehighlightAll();
3065             this.update();
3066 
3067             // selection
3068             if (this.selectingMode) {
3069                 this._stopSelecting(evt);
3070                 this.triggerEventHandlers(['mousestopselecting', 'stopselecting'], [evt]);
3071             } else {
3072                 for (i = 0; i < this.downObjects.length; i++) {
3073                     this.downObjects[i].triggerEventHandlers(['mouseup', 'up'], [evt]);
3074                 }
3075             }
3076 
3077             this.downObjects.length = 0;
3078 
3079             if (this.hasMouseUp) {
3080                 Env.removeEvent(this.document, 'mouseup', this.mouseUpListener, this);
3081                 this.hasMouseUp = false;
3082             }
3083 
3084             // release dragged mouse object
3085             /** @ignore */
3086             this.mouse = null;
3087         },
3088 
3089         /**
3090          * Handler for mouse wheel events. Used to zoom in and out of the board.
3091          * @param {Event} evt
3092          * @returns {Boolean}
3093          */
3094         mouseWheelListener: function (evt) {
3095             if (!this.attr.zoom.wheel || !this._isRequiredKeyPressed(evt, 'zoom')) {
3096                 return true;
3097             }
3098 
3099             evt = evt || window.event;
3100             var wd = evt.detail ? -evt.detail : evt.wheelDelta / 40,
3101                 pos = new Coords(Const.COORDS_BY_SCREEN, this.getMousePosition(evt), this);
3102 
3103             if (wd > 0) {
3104                 this.zoomIn(pos.usrCoords[1], pos.usrCoords[2]);
3105             } else {
3106                 this.zoomOut(pos.usrCoords[1], pos.usrCoords[2]);
3107             }
3108 
3109             this.triggerEventHandlers(['mousewheel'], [evt]);
3110 
3111             evt.preventDefault();
3112             return false;
3113         },
3114 
3115         /**
3116          * Allow moving of JSXGraph elements with arrow keys
3117          * and zooming of the construction with + / -.
3118          * Panning of the construction is done with arrow keys
3119          * if the pan key (shift or ctrl) is pressed.
3120          * The selection of the element is done with the tab key.
3121          *
3122          * @param  {Event} evt The browser's event object
3123          *
3124          * @see JXG.Board#keyboard
3125          * @see JXG.Board#keyFocusInListener
3126          * @see JXG.Board#keyFocusOutListener
3127          *
3128          */
3129         keyDownListener: function (evt) {
3130             var id_node = evt.target.id,
3131                 id, el, res,
3132                 sX = 0,
3133                 sY = 0,
3134                 // dx, dy are provided in screen units and
3135                 // are converted to user coordinates
3136                 dx = Type.evaluate(this.attr.keyboard.dx) / this.unitX,
3137                 dy = Type.evaluate(this.attr.keyboard.dy) / this.unitY,
3138                 doZoom = false,
3139                 done = true,
3140                 dir, actPos;
3141 
3142             if (!this.attr.keyboard.enabled || id_node === '') {
3143                 return false;
3144             }
3145 
3146             // Get the JSXGraph id from the id of the SVG node.
3147             id = id_node.replace(this.containerObj.id + '_', '');
3148             el = this.select(id);
3149 
3150             if (Type.exists(el.coords)) {
3151                 actPos = el.coords.usrCoords.slice(1);
3152             }
3153 
3154             if (Type.evaluate(this.attr.keyboard.panshift) || Type.evaluate(this.attr.keyboard.panctrl)) {
3155                 doZoom = true;
3156             }
3157 
3158             if ((Type.evaluate(this.attr.keyboard.panshift) && evt.shiftKey) ||
3159                 (Type.evaluate(this.attr.keyboard.panctrl) && evt.ctrlKey)) {
3160                 if (evt.keyCode === 38) {           // up
3161                     this.clickUpArrow();
3162                 } else if (evt.keyCode === 40) {    // down
3163                     this.clickDownArrow();
3164                 } else if (evt.keyCode === 37) {    // left
3165                     this.clickLeftArrow();
3166                 } else if (evt.keyCode === 39) {    // right
3167                     this.clickRightArrow();
3168                 } else {
3169                     done = false;
3170                 }
3171             } else {
3172                 // Adapt dx, dy to snapToGrid and attractToGrid
3173                 // snapToGrid has priority.
3174                 if (Type.exists(el.visProp)) {
3175                     if (Type.exists(el.visProp.snaptogrid) &&
3176                         el.visProp.snaptogrid &&
3177                         Type.evaluate(el.visProp.snapsizex) &&
3178                         Type.evaluate(el.visProp.snapsizey)) {
3179 
3180                         // Adapt dx, dy such that snapToGrid is possible
3181                         res = el.getSnapSizes();
3182                         sX = res[0];
3183                         sY = res[1];
3184                         dx = Math.max(sX, dx);
3185                         dy = Math.max(sY, dy);
3186 
3187                     } else if (Type.exists(el.visProp.attracttogrid) &&
3188                         el.visProp.attracttogrid &&
3189                         Type.evaluate(el.visProp.attractordistance) &&
3190                         Type.evaluate(el.visProp.attractorunit)) {
3191 
3192                         // Adapt dx, dy such that attractToGrid is possible
3193                         sX = 1.1 * Type.evaluate(el.visProp.attractordistance);
3194                         sY = sX;
3195 
3196                         if (Type.evaluate(el.visProp.attractorunit) === 'screen') {
3197                             sX /= this.unitX;
3198                             sY /= this.unitX;
3199                         }
3200                         dx = Math.max(sX, dx);
3201                         dy = Math.max(sY, dy);
3202                     }
3203 
3204                 }
3205 
3206                 if (evt.keyCode === 38) {           // up
3207                     dir = [0, dy];
3208                 } else if (evt.keyCode === 40) {    // down
3209                     dir = [0, -dy];
3210                 } else if (evt.keyCode === 37) {    // left
3211                     dir = [-dx, 0];
3212                 } else if (evt.keyCode === 39) {    // right
3213                     dir = [dx, 0];
3214                 // } else if (evt.keyCode === 9) {  // tab
3215 
3216                 } else if (doZoom && evt.key === '+') {   // +
3217                     this.zoomIn();
3218                 } else if (doZoom && evt.key === '-') {   // -
3219                     this.zoomOut();
3220                 } else if (doZoom && evt.key === 'o') {   // o
3221                     this.zoom100();
3222                 } else {
3223                     done = false;
3224                 }
3225 
3226                 if (dir && el.isDraggable &&
3227                         el.visPropCalc.visible &&
3228                         ((this.geonextCompatibilityMode &&
3229                             (Type.isPoint(el) ||
3230                             el.elementClass === Const.OBJECT_CLASS_TEXT)
3231                         ) || !this.geonextCompatibilityMode) &&
3232                         !Type.evaluate(el.visProp.fixed)
3233                     ) {
3234 
3235                     if (Type.exists(el.coords)) {
3236                         dir[0] += actPos[0];
3237                         dir[1] += actPos[1];
3238                     }
3239                     // For coordsElement setPosition has to call setPositionDirectly.
3240                     // Otherwise the position is set by a translation.
3241                     el.setPosition(JXG.COORDS_BY_USER, dir);
3242                     if (Type.exists(el.coords)) {
3243                         this.updateInfobox(el);
3244                     }
3245                     this.triggerEventHandlers(['hit'], [evt, el]);
3246                 }
3247             }
3248 
3249             this.update();
3250 
3251             if (done) {
3252                 evt.preventDefault();
3253             }
3254             return true;
3255         },
3256 
3257         /**
3258          * Event listener for SVG elements getting focus.
3259          * This is needed for highlighting when using keyboard control.
3260          *
3261          * @see JXG.Board#keyFocusOutListener
3262          * @see JXG.Board#keyDownListener
3263          * @see JXG.Board#keyboard
3264          *
3265          * @param  {Event} evt The browser's event object
3266          */
3267         keyFocusInListener: function (evt) {
3268             var id_node = evt.target.id,
3269                 id, el;
3270 
3271             if (!this.attr.keyboard.enabled || id_node === '') {
3272                 return false;
3273             }
3274 
3275             id = id_node.replace(this.containerObj.id + '_', '');
3276             el = this.select(id);
3277             if (Type.exists(el.highlight)) {
3278                 el.highlight(true);
3279             }
3280             if (Type.exists(el.coords)) {
3281                 this.updateInfobox(el);
3282             }
3283             this.triggerEventHandlers(['hit'], [evt, el]);
3284         },
3285 
3286         /**
3287          * Event listener for SVG elements losing focus.
3288          * This is needed for dehighlighting when using keyboard control.
3289          *
3290          * @see JXG.Board#keyFocusInListener
3291          * @see JXG.Board#keyDownListener
3292          * @see JXG.Board#keyboard
3293          *
3294          * @param  {Event} evt The browser's event object
3295          */
3296         keyFocusOutListener: function (evt) {
3297             if (!this.attr.keyboard.enabled) {
3298                 return false;
3299             }
3300             // var id_node = evt.target.id,
3301             //     id, el;
3302 
3303             // id = id_node.replace(this.containerObj.id + '_', '');
3304             // el = this.select(id);
3305             this.dehighlightAll();
3306             this.displayInfobox(false);
3307         },
3308 
3309         /**
3310          * Update the width and height of the JSXGraph container div element.
3311          * Read actual values with getBoundingClientRect(),
3312          * and call board.resizeContainer() with this values.
3313          * <p>
3314          * If necessary, also call setBoundingBox().
3315          *
3316          * @see JXG.Board#startResizeObserver
3317          * @see JXG.Board#resizeListener
3318          * @see JXG.Board#resizeContainer
3319          * @see JXG.Board#setBoundingBox
3320          *
3321          */
3322         updateContainerDims: function() {
3323             var w, h,
3324                 bb, css;
3325 
3326             // Get size of the board's container div
3327             bb = this.containerObj.getBoundingClientRect();
3328             w = bb.width;
3329             h = bb.height;
3330 
3331             // Subtract the border size
3332             if (window && window.getComputedStyle) {
3333                 css = window.getComputedStyle(this.containerObj, null);
3334                 w -= parseFloat(css.getPropertyValue('border-left-width')) + parseFloat(css.getPropertyValue('border-right-width'));
3335                 h -= parseFloat(css.getPropertyValue('border-top-width'))  + parseFloat(css.getPropertyValue('border-bottom-width'));
3336             }
3337 
3338             // If div is invisible - do nothing
3339             if (w <= 0 || h <= 0) {
3340                 return;
3341             }
3342 
3343             // If bounding box is not yet initialized, do it now.
3344             if (isNaN(this.getBoundingBox()[0])) {
3345                 this.setBoundingBox(this.attr.boundingbox, this.keepaspectratio, 'keep');
3346             }
3347 
3348             // Do nothing if the dimension did not change since being visible
3349             // the last time. Note that if the div had display:none in the mean time,
3350             // we did not store this._prevDim.
3351             if (Type.exists(this._prevDim) &&
3352                 this._prevDim.w === w && this._prevDim.h === h) {
3353                     return;
3354             }
3355 
3356             // Set the size of the SVG or canvas element
3357             this.resizeContainer(w, h, true);
3358             this._prevDim = {
3359                 w: w,
3360                 h: h
3361             };
3362         },
3363 
3364         /**
3365          * Start observer which reacts to size changes of the JSXGraph
3366          * container div element. Calls updateContainerDims().
3367          * If not available, an event listener for the window-resize event is started.
3368          * On mobile devices also scrolling might trigger resizes.
3369          * However, resize events triggered by scrolling events should be ignored.
3370          * Therefore, also a scrollListener is started.
3371          * Resize can be controlled with the board attribute resize.
3372          *
3373          * @see JXG.Board#updateContainerDims
3374          * @see JXG.Board#resizeListener
3375          * @see JXG.Board#scrollListener
3376          * @see JXG.Board#resize
3377          *
3378          */
3379         startResizeObserver: function() {
3380             var that = this;
3381 
3382             if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {
3383                 return;
3384             }
3385 
3386             this.resizeObserver = new ResizeObserver(function(entries) {
3387                 if (!that._isResizing) {
3388                     that._isResizing = true;
3389                     window.setTimeout(function() {
3390                         try {
3391                             that.updateContainerDims();
3392                         } catch (err) {
3393                             that.stopResizeObserver();
3394                         } finally {
3395                             that._isResizing = false;
3396                         }
3397                     }, that.attr.resize.throttle);
3398                 }
3399             });
3400             this.resizeObserver.observe(this.containerObj);
3401         },
3402 
3403         /**
3404          * Stops the resize observer.
3405          * @see JXG.Board#startResizeObserver
3406          *
3407          */
3408         stopResizeObserver: function() {
3409             if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {
3410                 return;
3411             }
3412 
3413             if (Type.exists(this.resizeObserver)) {
3414                 this.resizeObserver.unobserve(this.containerObj);
3415             }
3416         },
3417 
3418         /**
3419          * Fallback solutions if there is no resizeObserver available in the browser.
3420          * Reacts to resize events of the window (only). Otherwise similar to
3421          * startResizeObserver(). To handle changes of the visibility
3422          * of the JSXGraph container element, additionally an intersection observer is used.
3423          * which watches changes in the visibility of the JSXGraph container element.
3424          * This is necessary e.g. for register tabs or dia shows.
3425          *
3426          * @see JXG.Board#startResizeObserver
3427          * @see JXG.Board#startIntersectionObserver
3428          */
3429         resizeListener: function() {
3430             var that = this;
3431 
3432             if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {
3433                 return;
3434             }
3435             if (!this._isScrolling && !this._isResizing) {
3436                 this._isResizing = true;
3437                 window.setTimeout(function() {
3438                     that.updateContainerDims();
3439                     that._isResizing = false;
3440                 }, this.attr.resize.throttle);
3441             }
3442         },
3443 
3444         /**
3445          * Listener to watch for scroll events. Sets board._isScrolling = true
3446          * @param  {Event} evt The browser's event object
3447          *
3448          * @see JXG.Board#startResizeObserver
3449          * @see JXG.Board#resizeListener
3450          *
3451          */
3452         scrollListener: function(evt) {
3453             var that = this;
3454 
3455             if (!Env.isBrowser) {
3456                 return;
3457             }
3458             if (!this._isScrolling) {
3459                 this._isScrolling = true;
3460                 window.setTimeout(function() {
3461                     that._isScrolling = false;
3462                 }, 66);
3463             }
3464         },
3465 
3466         /**
3467          * Watch for changes of the visibility of the JSXGraph container element.
3468          *
3469          * @see JXG.Board#startResizeObserver
3470          * @see JXG.Board#resizeListener
3471          *
3472          */
3473         startIntersectionObserver: function() {
3474             var that = this,
3475                 options = {
3476                     root: null,
3477                     rootMargin: '0px',
3478                     threshold: 0.8
3479                 };
3480 
3481             try {
3482                 this.intersectionObserver = new IntersectionObserver(function(entries) {
3483                     // If bounding box is not yet initialized, do it now.
3484                     if (isNaN(that.getBoundingBox()[0])) {
3485                         that.updateContainerDims();
3486                     }
3487                 }, options);
3488                 this.intersectionObserver.observe(that.containerObj);
3489             } catch (err) {
3490                 console.log('JSXGraph: IntersectionObserver not available in this browser.');
3491             }
3492         },
3493 
3494         /**
3495          * Stop the intersection observer
3496          *
3497          * @see JXG.Board#startIntersectionObserver
3498          *
3499          */
3500         stopIntersectionObserver: function() {
3501             if (Type.exists(this.intersectionObserver)) {
3502                 this.intersectionObserver.unobserve(this.containerObj);
3503             }
3504         },
3505 
3506         /**********************************************************
3507          *
3508          * End of Event Handlers
3509          *
3510          **********************************************************/
3511 
3512         /**
3513          * Initialize the info box object which is used to display
3514          * the coordinates of points near the mouse pointer,
3515          * @returns {JXG.Board} Reference to the board
3516         */
3517         initInfobox: function () {
3518             var  attr = Type.copyAttributes({}, this.options, 'infobox');
3519 
3520             attr.id = this.id + '_infobox';
3521             /**
3522              * Infobox close to points in which the points' coordinates are displayed.
3523              * This is simply a JXG.Text element. Access through board.infobox.
3524              * Uses CSS class .JXGinfobox.
3525              * @type JXG.Text
3526              *
3527              */
3528             this.infobox = this.create('text', [0, 0, '0,0'], attr);
3529 
3530             this.infobox.distanceX = -20;
3531             this.infobox.distanceY = 25;
3532             // this.infobox.needsUpdateSize = false;  // That is not true, but it speeds drawing up.
3533 
3534             this.infobox.dump = false;
3535 
3536             this.displayInfobox(false);
3537             return this;
3538         },
3539 
3540         /**
3541          * Updates and displays a little info box to show coordinates of current selected points.
3542          * @param {JXG.GeometryElement} el A GeometryElement
3543          * @returns {JXG.Board} Reference to the board
3544          * @see JXG.Board#displayInfobox
3545          * @see JXG.Board#showInfobox
3546          * @see Point#showInfobox
3547          *
3548          */
3549         updateInfobox: function (el) {
3550             var x, y, xc, yc,
3551             vpinfoboxdigits,
3552             vpsi = Type.evaluate(el.visProp.showinfobox);
3553 
3554             if ((!Type.evaluate(this.attr.showinfobox) &&  vpsi === 'inherit') ||
3555                 !vpsi) {
3556                 return this;
3557             }
3558 
3559             if (Type.isPoint(el)) {
3560                 xc = el.coords.usrCoords[1];
3561                 yc = el.coords.usrCoords[2];
3562 
3563                 vpinfoboxdigits = Type.evaluate(el.visProp.infoboxdigits);
3564                 this.infobox.setCoords(xc + this.infobox.distanceX / this.unitX,
3565                                        yc + this.infobox.distanceY / this.unitY);
3566 
3567                 if (typeof el.infoboxText !== 'string') {
3568                     if (vpinfoboxdigits === 'auto') {
3569                         x = Type.autoDigits(xc);
3570                         y = Type.autoDigits(yc);
3571                     } else if (Type.isNumber(vpinfoboxdigits)) {
3572                         x = Type.toFixed(xc, vpinfoboxdigits);
3573                         y = Type.toFixed(yc, vpinfoboxdigits);
3574                     } else {
3575                         x = xc;
3576                         y = yc;
3577                     }
3578 
3579                     this.highlightInfobox(x, y, el);
3580                 } else {
3581                     this.highlightCustomInfobox(el.infoboxText, el);
3582                 }
3583 
3584                 this.displayInfobox(true);
3585             }
3586             return this;
3587         },
3588 
3589         /**
3590          * Set infobox visible / invisible.
3591          *
3592          * It uses its property hiddenByParent to memorize its status.
3593          * In this way, many DOM access can be avoided.
3594          *
3595          * @param  {Boolean} val true for visible, false for invisible
3596          * @returns {JXG.Board} Reference to the board.
3597          * @see JXG.Board#updateInfobox
3598          *
3599          */
3600         displayInfobox: function(val) {
3601             if (this.infobox.hiddenByParent === val) {
3602                 this.infobox.hiddenByParent = !val;
3603                 this.infobox.prepareUpdate().updateVisibility(val).updateRenderer();
3604             }
3605             return this;
3606         },
3607 
3608         // Alias for displayInfobox to be backwards compatible.
3609         // The method showInfobox clashes with the board attribute showInfobox
3610         showInfobox: function(val) {
3611             return this.displayInfobox(val);
3612         },
3613 
3614         /**
3615          * Changes the text of the info box to show the given coordinates.
3616          * @param {Number} x
3617          * @param {Number} y
3618          * @param {JXG.GeometryElement} [el] The element the mouse is pointing at
3619          * @returns {JXG.Board} Reference to the board.
3620          */
3621         highlightInfobox: function (x, y, el) {
3622             this.highlightCustomInfobox('(' + x + ', ' + y + ')', el);
3623             return this;
3624         },
3625 
3626         /**
3627          * Changes the text of the info box to what is provided via text.
3628          * @param {String} text
3629          * @param {JXG.GeometryElement} [el]
3630          * @returns {JXG.Board} Reference to the board.
3631          */
3632         highlightCustomInfobox: function (text, el) {
3633             this.infobox.setText(text);
3634             return this;
3635         },
3636 
3637         /**
3638          * Remove highlighting of all elements.
3639          * @returns {JXG.Board} Reference to the board.
3640          */
3641         dehighlightAll: function () {
3642             var el, pEl, needsDehighlight = false;
3643 
3644             for (el in this.highlightedObjects) {
3645                 if (this.highlightedObjects.hasOwnProperty(el)) {
3646                     pEl = this.highlightedObjects[el];
3647 
3648                     if (this.hasMouseHandlers || this.hasPointerHandlers) {
3649                         pEl.noHighlight();
3650                     }
3651 
3652                     needsDehighlight = true;
3653 
3654                     // In highlightedObjects should only be objects which fulfill all these conditions
3655                     // And in case of complex elements, like a turtle based fractal, it should be faster to
3656                     // just de-highlight the element instead of checking hasPoint...
3657                     // if ((!Type.exists(pEl.hasPoint)) || !pEl.hasPoint(x, y) || !pEl.visPropCalc.visible)
3658                 }
3659             }
3660 
3661             this.highlightedObjects = {};
3662 
3663             // We do not need to redraw during dehighlighting in CanvasRenderer
3664             // because we are redrawing anyhow
3665             //  -- We do need to redraw during dehighlighting. Otherwise objects won't be dehighlighted until
3666             // another object is highlighted.
3667             if (this.renderer.type === 'canvas' && needsDehighlight) {
3668                 this.prepareUpdate();
3669                 this.renderer.suspendRedraw(this);
3670                 this.updateRenderer();
3671                 this.renderer.unsuspendRedraw();
3672             }
3673 
3674             return this;
3675         },
3676 
3677         /**
3678          * Returns the input parameters in an array. This method looks pointless and it really is, but it had a purpose
3679          * once.
3680          * @private
3681          * @param {Number} x X coordinate in screen coordinates
3682          * @param {Number} y Y coordinate in screen coordinates
3683          * @returns {Array} Coordinates [x, y] of the mouse in screen coordinates.
3684          * @see JXG.Board#getUsrCoordsOfMouse
3685          */
3686         getScrCoordsOfMouse: function (x, y) {
3687             return [x, y];
3688         },
3689 
3690         /**
3691          * This method calculates the user coords of the current mouse coordinates.
3692          * @param {Event} evt Event object containing the mouse coordinates.
3693          * @returns {Array} Coordinates [x, y] of the mouse in user coordinates.
3694          * @example
3695          * board.on('up', function (evt) {
3696          *         var a = board.getUsrCoordsOfMouse(evt),
3697          *             x = a[0],
3698          *             y = a[1],
3699          *             somePoint = board.create('point', [x,y], {name:'SomePoint',size:4});
3700          *             // Shorter version:
3701          *             //somePoint = board.create('point', a, {name:'SomePoint',size:4});
3702          *         });
3703          *
3704          * </pre><div id="JXG48d5066b-16ba-4920-b8ea-a4f8eff6b746" class="jxgbox" style="width: 300px; height: 300px;"></div>
3705          * <script type="text/javascript">
3706          *     (function() {
3707          *         var board = JXG.JSXGraph.initBoard('JXG48d5066b-16ba-4920-b8ea-a4f8eff6b746',
3708          *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
3709          *     board.on('up', function (evt) {
3710          *             var a = board.getUsrCoordsOfMouse(evt),
3711          *                 x = a[0],
3712          *                 y = a[1],
3713          *                 somePoint = board.create('point', [x,y], {name:'SomePoint',size:4});
3714          *                 // Shorter version:
3715          *                 //somePoint = board.create('point', a, {name:'SomePoint',size:4});
3716          *             });
3717          *
3718          *     })();
3719          *
3720          * </script><pre>
3721          *
3722          * @see JXG.Board#getScrCoordsOfMouse
3723          * @see JXG.Board#getAllUnderMouse
3724          */
3725         getUsrCoordsOfMouse: function (evt) {
3726             var cPos = this.getCoordsTopLeftCorner(),
3727                 absPos = Env.getPosition(evt, null, this.document),
3728                 x = absPos[0] - cPos[0],
3729                 y = absPos[1] - cPos[1],
3730                 newCoords = new Coords(Const.COORDS_BY_SCREEN, [x, y], this);
3731 
3732             return newCoords.usrCoords.slice(1);
3733         },
3734 
3735         /**
3736          * Collects all elements under current mouse position plus current user coordinates of mouse cursor.
3737          * @param {Event} evt Event object containing the mouse coordinates.
3738          * @returns {Array} Array of elements at the current mouse position plus current user coordinates of mouse.
3739          * @see JXG.Board#getUsrCoordsOfMouse
3740          * @see JXG.Board#getAllObjectsUnderMouse
3741          */
3742         getAllUnderMouse: function (evt) {
3743             var elList = this.getAllObjectsUnderMouse(evt);
3744             elList.push(this.getUsrCoordsOfMouse(evt));
3745 
3746             return elList;
3747         },
3748 
3749         /**
3750          * Collects all elements under current mouse position.
3751          * @param {Event} evt Event object containing the mouse coordinates.
3752          * @returns {Array} Array of elements at the current mouse position.
3753          * @see JXG.Board#getAllUnderMouse
3754          */
3755         getAllObjectsUnderMouse: function (evt) {
3756             var cPos = this.getCoordsTopLeftCorner(),
3757                 absPos = Env.getPosition(evt, null, this.document),
3758                 dx = absPos[0] - cPos[0],
3759                 dy = absPos[1] - cPos[1],
3760                 elList = [],
3761                 el,
3762                 pEl,
3763                 len = this.objectsList.length;
3764 
3765             for (el = 0; el < len; el++) {
3766                 pEl = this.objectsList[el];
3767                 if (pEl.visPropCalc.visible && pEl.hasPoint && pEl.hasPoint(dx, dy)) {
3768                     elList[elList.length] = pEl;
3769                 }
3770             }
3771 
3772             return elList;
3773         },
3774 
3775         /**
3776          * Update the coords object of all elements which possess this
3777          * property. This is necessary after changing the viewport.
3778          * @returns {JXG.Board} Reference to this board.
3779          **/
3780         updateCoords: function () {
3781             var el, ob, len = this.objectsList.length;
3782 
3783             for (ob = 0; ob < len; ob++) {
3784                 el = this.objectsList[ob];
3785 
3786                 if (Type.exists(el.coords)) {
3787                     if (Type.evaluate(el.visProp.frozen)) {
3788                         el.coords.screen2usr();
3789                     } else {
3790                         el.coords.usr2screen();
3791                     }
3792                 }
3793             }
3794             return this;
3795         },
3796 
3797         /**
3798          * Moves the origin and initializes an update of all elements.
3799          * @param {Number} x
3800          * @param {Number} y
3801          * @param {Boolean} [diff=false]
3802          * @returns {JXG.Board} Reference to this board.
3803          */
3804         moveOrigin: function (x, y, diff) {
3805             var ox, oy, ul, lr;
3806             if (Type.exists(x) && Type.exists(y)) {
3807                 ox = this.origin.scrCoords[1];
3808                 oy = this.origin.scrCoords[2];
3809 
3810                 this.origin.scrCoords[1] = x;
3811                 this.origin.scrCoords[2] = y;
3812 
3813                 if (diff) {
3814                     this.origin.scrCoords[1] -= this.drag_dx;
3815                     this.origin.scrCoords[2] -= this.drag_dy;
3816                 }
3817 
3818                 ul = (new Coords(Const.COORDS_BY_SCREEN, [0, 0], this)).usrCoords;
3819                 lr = (new Coords(Const.COORDS_BY_SCREEN, [this.canvasWidth, this.canvasHeight], this)).usrCoords;
3820                 if (ul[1] < this.maxboundingbox[0] ||
3821                     ul[2] > this.maxboundingbox[1] ||
3822                     lr[1] > this.maxboundingbox[2] ||
3823                     lr[2] < this.maxboundingbox[3]) {
3824 
3825                     this.origin.scrCoords[1] = ox;
3826                     this.origin.scrCoords[2] = oy;
3827                 }
3828             }
3829 
3830             this.updateCoords().clearTraces().fullUpdate();
3831             this.triggerEventHandlers(['boundingbox']);
3832 
3833             return this;
3834         },
3835 
3836         /**
3837          * Add conditional updates to the elements.
3838          * @param {String} str String containing coniditional update in geonext syntax
3839          */
3840         addConditions: function (str) {
3841             var term, m, left, right, name, el, property,
3842                 functions = [],
3843                 // plaintext = 'var el, x, y, c, rgbo;\n',
3844                 i = str.indexOf('<data>'),
3845                 j = str.indexOf('<' + '/data>'),
3846 
3847                 xyFun = function (board, el, f, what) {
3848                     return function () {
3849                         var e, t;
3850 
3851                         e = board.select(el.id);
3852                         t = e.coords.usrCoords[what];
3853 
3854                         if (what === 2) {
3855                             e.setPositionDirectly(Const.COORDS_BY_USER, [f(), t]);
3856                         } else {
3857                             e.setPositionDirectly(Const.COORDS_BY_USER, [t, f()]);
3858                         }
3859                         e.prepareUpdate().update();
3860                     };
3861                 },
3862 
3863                 visFun = function (board, el, f) {
3864                     return function () {
3865                         var e, v;
3866 
3867                         e = board.select(el.id);
3868                         v = f();
3869 
3870                         e.setAttribute({visible: v});
3871                     };
3872                 },
3873 
3874                 colFun = function (board, el, f, what) {
3875                     return function () {
3876                         var e, v;
3877 
3878                         e = board.select(el.id);
3879                         v = f();
3880 
3881                         if (what === 'strokewidth') {
3882                             e.visProp.strokewidth = v;
3883                         } else {
3884                             v = Color.rgba2rgbo(v);
3885                             e.visProp[what + 'color'] = v[0];
3886                             e.visProp[what + 'opacity'] = v[1];
3887                         }
3888                     };
3889                 },
3890 
3891                 posFun = function (board, el, f) {
3892                     return function () {
3893                         var e = board.select(el.id);
3894 
3895                         e.position = f();
3896                     };
3897                 },
3898 
3899                 styleFun = function (board, el, f) {
3900                     return function () {
3901                         var e = board.select(el.id);
3902 
3903                         e.setStyle(f());
3904                     };
3905                 };
3906 
3907             if (i < 0) {
3908                 return;
3909             }
3910 
3911             while (i >= 0) {
3912                 term = str.slice(i + 6, j);   // throw away <data>
3913                 m = term.indexOf('=');
3914                 left = term.slice(0, m);
3915                 right = term.slice(m + 1);
3916                 m = left.indexOf('.');     // Dies erzeugt Probleme bei Variablennamen der Form " Steuern akt."
3917                 name = left.slice(0, m);    //.replace(/\s+$/,''); // do NOT cut out name (with whitespace)
3918                 el = this.elementsByName[Type.unescapeHTML(name)];
3919 
3920                 property = left.slice(m + 1).replace(/\s+/g, '').toLowerCase(); // remove whitespace in property
3921                 right = Type.createFunction (right, this, '', true);
3922 
3923                 // Debug
3924                 if (!Type.exists(this.elementsByName[name])) {
3925                     JXG.debug("debug conditions: |" + name + "| undefined");
3926                 } else {
3927                     // plaintext += "el = this.objects[\"" + el.id + "\"];\n";
3928 
3929                     switch (property) {
3930                     case 'x':
3931                         functions.push(xyFun(this, el, right, 2));
3932                         break;
3933                     case 'y':
3934                         functions.push(xyFun(this, el, right, 1));
3935                         break;
3936                     case 'visible':
3937                         functions.push(visFun(this, el, right));
3938                         break;
3939                     case 'position':
3940                         functions.push(posFun(this, el, right));
3941                         break;
3942                     case 'stroke':
3943                         functions.push(colFun(this, el, right, 'stroke'));
3944                         break;
3945                     case 'style':
3946                         functions.push(styleFun(this, el, right));
3947                         break;
3948                     case 'strokewidth':
3949                         functions.push(colFun(this, el, right, 'strokewidth'));
3950                         break;
3951                     case 'fill':
3952                         functions.push(colFun(this, el, right, 'fill'));
3953                         break;
3954                     case 'label':
3955                         break;
3956                     default:
3957                         JXG.debug("property '" + property + "' in conditions not yet implemented:" + right);
3958                         break;
3959                     }
3960                 }
3961                 str = str.slice(j + 7); // cut off "</data>"
3962                 i = str.indexOf('<data>');
3963                 j = str.indexOf('<' + '/data>');
3964             }
3965 
3966             this.updateConditions = function () {
3967                 var i;
3968 
3969                 for (i = 0; i < functions.length; i++) {
3970                     functions[i]();
3971                 }
3972 
3973                 this.prepareUpdate().updateElements();
3974                 return true;
3975             };
3976             this.updateConditions();
3977         },
3978 
3979         /**
3980          * Computes the commands in the conditions-section of the gxt file.
3981          * It is evaluated after an update, before the unsuspendRedraw.
3982          * The function is generated in
3983          * @see JXG.Board#addConditions
3984          * @private
3985          */
3986         updateConditions: function () {
3987             return false;
3988         },
3989 
3990         /**
3991          * Calculates adequate snap sizes.
3992          * @returns {JXG.Board} Reference to the board.
3993          */
3994         calculateSnapSizes: function () {
3995             var p1 = new Coords(Const.COORDS_BY_USER, [0, 0], this),
3996                 p2 = new Coords(Const.COORDS_BY_USER, [this.options.grid.gridX, this.options.grid.gridY], this),
3997                 x = p1.scrCoords[1] - p2.scrCoords[1],
3998                 y = p1.scrCoords[2] - p2.scrCoords[2];
3999 
4000             this.options.grid.snapSizeX = this.options.grid.gridX;
4001             while (Math.abs(x) > 25) {
4002                 this.options.grid.snapSizeX *= 2;
4003                 x /= 2;
4004             }
4005 
4006             this.options.grid.snapSizeY = this.options.grid.gridY;
4007             while (Math.abs(y) > 25) {
4008                 this.options.grid.snapSizeY *= 2;
4009                 y /= 2;
4010             }
4011 
4012             return this;
4013         },
4014 
4015         /**
4016          * Apply update on all objects with the new zoom-factors. Clears all traces.
4017          * @returns {JXG.Board} Reference to the board.
4018          */
4019         applyZoom: function () {
4020             this.updateCoords().calculateSnapSizes().clearTraces().fullUpdate();
4021 
4022             return this;
4023         },
4024 
4025         /**
4026          * Zooms into the board by the factors board.attr.zoom.factorX and board.attr.zoom.factorY and applies the zoom.
4027          * The zoom operation is centered at x, y.
4028          * @param {Number} [x]
4029          * @param {Number} [y]
4030          * @returns {JXG.Board} Reference to the board
4031          */
4032         zoomIn: function (x, y) {
4033             var bb = this.getBoundingBox(),
4034                 zX = this.attr.zoom.factorx,
4035                 zY = this.attr.zoom.factory,
4036                 dX = (bb[2] - bb[0]) * (1.0 - 1.0 / zX),
4037                 dY = (bb[1] - bb[3]) * (1.0 - 1.0 / zY),
4038                 lr = 0.5,
4039                 tr = 0.5,
4040                 mi = this.attr.zoom.eps || this.attr.zoom.min || 0.001;  // this.attr.zoom.eps is deprecated
4041 
4042             if ((this.zoomX > this.attr.zoom.max && zX > 1.0) ||
4043                 (this.zoomY > this.attr.zoom.max && zY > 1.0) ||
4044                 (this.zoomX < mi && zX < 1.0) ||  // zoomIn is used for all zooms on touch devices
4045                 (this.zoomY < mi && zY < 1.0)) {
4046                 return this;
4047             }
4048 
4049             if (Type.isNumber(x) && Type.isNumber(y)) {
4050                 lr = (x - bb[0]) / (bb[2] - bb[0]);
4051                 tr = (bb[1] - y) / (bb[1] - bb[3]);
4052             }
4053 
4054             this.setBoundingBox([bb[0] + dX * lr, bb[1] - dY * tr, bb[2] - dX * (1 - lr), bb[3] + dY * (1 - tr)], this.keepaspectratio, 'update');
4055             return this.applyZoom();
4056         },
4057 
4058         /**
4059          * Zooms out of the board by the factors board.attr.zoom.factorX and board.attr.zoom.factorY and applies the zoom.
4060          * The zoom operation is centered at x, y.
4061          *
4062          * @param {Number} [x]
4063          * @param {Number} [y]
4064          * @returns {JXG.Board} Reference to the board
4065          */
4066         zoomOut: function (x, y) {
4067             var bb = this.getBoundingBox(),
4068                 zX = this.attr.zoom.factorx,
4069                 zY = this.attr.zoom.factory,
4070                 dX = (bb[2] - bb[0]) * (1.0 - zX),
4071                 dY = (bb[1] - bb[3]) * (1.0 - zY),
4072                 lr = 0.5,
4073                 tr = 0.5,
4074                 mi = this.attr.zoom.eps || this.attr.zoom.min || 0.001;  // this.attr.zoom.eps is deprecated
4075 
4076             if (this.zoomX < mi || this.zoomY < mi) {
4077                 return this;
4078             }
4079 
4080             if (Type.isNumber(x) && Type.isNumber(y)) {
4081                 lr = (x - bb[0]) / (bb[2] - bb[0]);
4082                 tr = (bb[1] - y) / (bb[1] - bb[3]);
4083             }
4084 
4085             this.setBoundingBox([bb[0] + dX * lr, bb[1] - dY * tr, bb[2] - dX * (1 - lr), bb[3] + dY * (1 - tr)], this.keepaspectratio, 'update');
4086 
4087             return this.applyZoom();
4088         },
4089 
4090         /**
4091          * Reset the zoom level to the original zoom level from initBoard();
4092          * Additionally, if the board as been initialized with a boundingBox (which is the default),
4093          * restore the viewport to the original viewport during initialization. Otherwise,
4094          * (i.e. if the board as been initialized with unitX/Y and originX/Y),
4095          * just set the zoom level to 100%.
4096          *
4097          * @returns {JXG.Board} Reference to the board
4098          */
4099         zoom100: function () {
4100             var bb, dX, dY;
4101 
4102             if (Type.exists(this.attr.boundingbox)) {
4103                 this.setBoundingBox(this.attr.boundingbox, this.keepaspectratio, 'reset');
4104             } else {
4105                 // Board has been set up with unitX/Y and originX/Y
4106                 bb = this.getBoundingBox();
4107                 dX = (bb[2] - bb[0]) * (1.0 - this.zoomX) * 0.5;
4108                 dY = (bb[1] - bb[3]) * (1.0 - this.zoomY) * 0.5;
4109                 this.setBoundingBox([bb[0] + dX, bb[1] - dY, bb[2] - dX, bb[3] + dY], this.keepaspectratio, 'reset');
4110             }
4111             return this.applyZoom();
4112         },
4113 
4114         /**
4115          * Zooms the board so every visible point is shown. Keeps aspect ratio.
4116          * @returns {JXG.Board} Reference to the board
4117          */
4118         zoomAllPoints: function () {
4119             var el, border, borderX, borderY, pEl,
4120                 minX = 0,
4121                 maxX = 0,
4122                 minY = 0,
4123                 maxY = 0,
4124                 len = this.objectsList.length;
4125 
4126             for (el = 0; el < len; el++) {
4127                 pEl = this.objectsList[el];
4128 
4129                 if (Type.isPoint(pEl) && pEl.visPropCalc.visible) {
4130                     if (pEl.coords.usrCoords[1] < minX) {
4131                         minX = pEl.coords.usrCoords[1];
4132                     } else if (pEl.coords.usrCoords[1] > maxX) {
4133                         maxX = pEl.coords.usrCoords[1];
4134                     }
4135                     if (pEl.coords.usrCoords[2] > maxY) {
4136                         maxY = pEl.coords.usrCoords[2];
4137                     } else if (pEl.coords.usrCoords[2] < minY) {
4138                         minY = pEl.coords.usrCoords[2];
4139                     }
4140                 }
4141             }
4142 
4143             border = 50;
4144             borderX = border / this.unitX;
4145             borderY = border / this.unitY;
4146 
4147             this.setBoundingBox([minX - borderX, maxY + borderY, maxX + borderX, minY - borderY], this.keepaspectratio, 'update');
4148 
4149             return this.applyZoom();
4150         },
4151 
4152         /**
4153          * Reset the bounding box and the zoom level to 100% such that a given set of elements is
4154          * within the board's viewport.
4155          * @param {Array} elements A set of elements given by id, reference, or name.
4156          * @returns {JXG.Board} Reference to the board.
4157          */
4158         zoomElements: function (elements) {
4159             var i, e, box,
4160                 newBBox = [Infinity, -Infinity, -Infinity, Infinity],
4161                 cx, cy, dx, dy, d;
4162 
4163             if (!Type.isArray(elements) || elements.length === 0) {
4164                 return this;
4165             }
4166 
4167             for (i = 0; i < elements.length; i++) {
4168                 e = this.select(elements[i]);
4169 
4170                 box = e.bounds();
4171                 if (Type.isArray(box)) {
4172                     if (box[0] < newBBox[0]) { newBBox[0] = box[0]; }
4173                     if (box[1] > newBBox[1]) { newBBox[1] = box[1]; }
4174                     if (box[2] > newBBox[2]) { newBBox[2] = box[2]; }
4175                     if (box[3] < newBBox[3]) { newBBox[3] = box[3]; }
4176                 }
4177             }
4178 
4179             if (Type.isArray(newBBox)) {
4180                 cx = 0.5 * (newBBox[0] + newBBox[2]);
4181                 cy = 0.5 * (newBBox[1] + newBBox[3]);
4182                 dx = 1.5 * (newBBox[2] - newBBox[0]) * 0.5;
4183                 dy = 1.5 * (newBBox[1] - newBBox[3]) * 0.5;
4184                 d = Math.max(dx, dy);
4185                 this.setBoundingBox([cx - d, cy + d, cx + d, cy - d], this.keepaspectratio, 'update');
4186             }
4187 
4188             return this;
4189         },
4190 
4191         /**
4192          * Sets the zoom level to <tt>fX</tt> resp <tt>fY</tt>.
4193          * @param {Number} fX
4194          * @param {Number} fY
4195          * @returns {JXG.Board} Reference to the board.
4196          */
4197         setZoom: function (fX, fY) {
4198             var oX = this.attr.zoom.factorx,
4199                 oY = this.attr.zoom.factory;
4200 
4201             this.attr.zoom.factorx = fX / this.zoomX;
4202             this.attr.zoom.factory = fY / this.zoomY;
4203 
4204             this.zoomIn();
4205 
4206             this.attr.zoom.factorx = oX;
4207             this.attr.zoom.factory = oY;
4208 
4209             return this;
4210         },
4211 
4212         /**
4213          * Removes object from board and renderer.
4214          * <p>
4215          * <b>Performance hints:</b> It is recommended to use the object's id.
4216          * If many elements are removed, it is best to call <tt>board.suspendUpdate()</tt>
4217          * before looping through the elements to be removed and call
4218          * <tt>board.unsuspendUpdate()</tt> after the loop. Further, it is advisable to loop
4219          * in reverse order, i.e. remove the object in reverse order of their creation time.
4220          *
4221          * @param {JXG.GeometryElement|Array} object The object to remove or array of objects to be removed.
4222          * The element(s) is/are given by name, id or a reference.
4223          * @param {Boolean} saveMethod If true, the algorithm runs through all elements
4224          * and tests if the element to be deleted is a child element. If yes, it will be
4225          * removed from the list of child elements. If false (default), the element
4226          * is removed from the lists of child elements of all its ancestors.
4227          * This should be much faster.
4228          * @returns {JXG.Board} Reference to the board
4229          */
4230         removeObject: function (object, saveMethod) {
4231             var el, i;
4232 
4233             if (Type.isArray(object)) {
4234                 for (i = 0; i < object.length; i++) {
4235                     this.removeObject(object[i]);
4236                 }
4237 
4238                 return this;
4239             }
4240 
4241             object = this.select(object);
4242 
4243             // If the object which is about to be removed unknown or a string, do nothing.
4244             // it is a string if a string was given and could not be resolved to an element.
4245             if (!Type.exists(object) || Type.isString(object)) {
4246                 return this;
4247             }
4248 
4249             try {
4250                 // remove all children.
4251                 for (el in object.childElements) {
4252                     if (object.childElements.hasOwnProperty(el)) {
4253                         object.childElements[el].board.removeObject(object.childElements[el]);
4254                     }
4255                 }
4256 
4257                 // Remove all children in elements like turtle
4258                 for (el in object.objects) {
4259                     if (object.objects.hasOwnProperty(el)) {
4260                         object.objects[el].board.removeObject(object.objects[el]);
4261                     }
4262                 }
4263 
4264                 // Remove the element from the childElement list and the descendant list of all elements.
4265                 if (saveMethod) {
4266                     // Running through all objects has quadratic complexity if many objects are deleted.
4267                     for (el in this.objects) {
4268                         if (this.objects.hasOwnProperty(el)) {
4269                             if (Type.exists(this.objects[el].childElements) &&
4270                                 Type.exists(this.objects[el].childElements.hasOwnProperty(object.id))
4271                             ) {
4272                                 delete this.objects[el].childElements[object.id];
4273                                 delete this.objects[el].descendants[object.id];
4274                             }
4275                         }
4276                     }
4277                 } else if (Type.exists(object.ancestors)) {
4278                     // Running through the ancestors should be much more efficient.
4279                     for (el in object.ancestors) {
4280                         if (object.ancestors.hasOwnProperty(el)) {
4281                             if (Type.exists(object.ancestors[el].childElements) &&
4282                                 Type.exists(object.ancestors[el].childElements.hasOwnProperty(object.id))
4283                             ) {
4284                                 delete object.ancestors[el].childElements[object.id];
4285                                 delete object.ancestors[el].descendants[object.id];
4286                             }
4287                         }
4288                     }
4289                 }
4290 
4291                 // remove the object itself from our control structures
4292                 if (object._pos > -1) {
4293                     this.objectsList.splice(object._pos, 1);
4294                     for (el = object._pos; el < this.objectsList.length; el++) {
4295                         this.objectsList[el]._pos--;
4296                     }
4297                 } else if (object.type !== Const.OBJECT_TYPE_TURTLE) {
4298                     JXG.debug('Board.removeObject: object ' + object.id + ' not found in list.');
4299                 }
4300 
4301                 delete this.objects[object.id];
4302                 delete this.elementsByName[object.name];
4303 
4304                 if (object.visProp && Type.evaluate(object.visProp.trace)) {
4305                     object.clearTrace();
4306                 }
4307 
4308                 // the object deletion itself is handled by the object.
4309                 if (Type.exists(object.remove)) {
4310                     object.remove();
4311                 }
4312             } catch (e) {
4313                 JXG.debug(object.id + ': Could not be removed: ' + e);
4314             }
4315 
4316             this.update();
4317 
4318             return this;
4319         },
4320 
4321         /**
4322          * Removes the ancestors of an object an the object itself from board and renderer.
4323          * @param {JXG.GeometryElement} object The object to remove.
4324          * @returns {JXG.Board} Reference to the board
4325          */
4326         removeAncestors: function (object) {
4327             var anc;
4328 
4329             for (anc in object.ancestors) {
4330                 if (object.ancestors.hasOwnProperty(anc)) {
4331                     this.removeAncestors(object.ancestors[anc]);
4332                 }
4333             }
4334 
4335             this.removeObject(object);
4336 
4337             return this;
4338         },
4339 
4340         /**
4341          * Initialize some objects which are contained in every GEONExT construction by default,
4342          * but are not contained in the gxt files.
4343          * @returns {JXG.Board} Reference to the board
4344          */
4345         initGeonextBoard: function () {
4346             var p1, p2, p3;
4347 
4348             p1 = this.create('point', [0, 0], {
4349                 id: this.id + 'g00e0',
4350                 name: 'Ursprung',
4351                 withLabel: false,
4352                 visible: false,
4353                 fixed: true
4354             });
4355 
4356             p2 = this.create('point', [1, 0], {
4357                 id: this.id + 'gX0e0',
4358                 name: 'Punkt_1_0',
4359                 withLabel: false,
4360                 visible: false,
4361                 fixed: true
4362             });
4363 
4364             p3 = this.create('point', [0, 1], {
4365                 id: this.id + 'gY0e0',
4366                 name: 'Punkt_0_1',
4367                 withLabel: false,
4368                 visible: false,
4369                 fixed: true
4370             });
4371 
4372             this.create('line', [p1, p2], {
4373                 id: this.id + 'gXLe0',
4374                 name: 'X-Achse',
4375                 withLabel: false,
4376                 visible: false
4377             });
4378 
4379             this.create('line', [p1, p3], {
4380                 id: this.id + 'gYLe0',
4381                 name: 'Y-Achse',
4382                 withLabel: false,
4383                 visible: false
4384             });
4385 
4386             return this;
4387         },
4388 
4389         /**
4390          * Change the height and width of the board's container.
4391          * After doing so, {@link JXG.JSXGraph.setBoundingBox} is called using
4392          * the actual size of the bounding box and the actual value of keepaspectratio.
4393          * If setBoundingbox() should not be called automatically,
4394          * call resizeContainer with dontSetBoundingBox == true.
4395          * @param {Number} canvasWidth New width of the container.
4396          * @param {Number} canvasHeight New height of the container.
4397          * @param {Boolean} [dontset=false] If true do not set the CSS width and height of the DOM element.
4398          * @param {Boolean} [dontSetBoundingBox=false] If true do not call setBoundingBox().
4399          * @returns {JXG.Board} Reference to the board
4400          */
4401         resizeContainer: function (canvasWidth, canvasHeight, dontset, dontSetBoundingBox) {
4402             var box;
4403                 // w, h, cx, cy;
4404                 // box_act,
4405                 // shift_x = 0,
4406                 // shift_y = 0;
4407 
4408             if (!dontSetBoundingBox) {
4409                 // box_act = this.getBoundingBox();    // This is the actual bounding box.
4410                 box = this.getBoundingBox();    // This is the actual bounding box.
4411             }
4412 
4413             this.canvasWidth = parseFloat(canvasWidth);
4414             this.canvasHeight = parseFloat(canvasHeight);
4415 
4416             // if (!dontSetBoundingBox) {
4417             //     box     = this.attr.boundingbox;    // This is the intended bounding box.
4418 
4419             //     // The shift values compensate the follow-up correction
4420             //     // in setBoundingBox in case of "this.keepaspectratio==true"
4421             //     // Otherwise, shift_x and shift_y will be zero.
4422             //     // Obsolet since setBoundingBox centers in case of "this.keepaspectratio==true".
4423             //     // shift_x = box_act[0] - box[0] / this.zoomX;
4424             //     // shift_y = box_act[1] - box[1] / this.zoomY;
4425 
4426             //     cx = (box[2] + box[0]) * 0.5; // + shift_x;
4427             //     cy = (box[3] + box[1]) * 0.5; // + shift_y;
4428 
4429             //     w = (box[2] - box[0]) * 0.5 / this.zoomX;
4430             //     h = (box[1] - box[3]) * 0.5 / this.zoomY;
4431 
4432             //     box = [cx - w, cy + h, cx + w, cy - h];
4433             // }
4434 
4435             if (!dontset) {
4436                 this.containerObj.style.width = (this.canvasWidth) + 'px';
4437                 this.containerObj.style.height = (this.canvasHeight) + 'px';
4438             }
4439             this.renderer.resize(this.canvasWidth, this.canvasHeight);
4440 
4441             if (!dontSetBoundingBox) {
4442                 this.setBoundingBox(box, this.keepaspectratio, 'keep');
4443             }
4444 
4445             return this;
4446         },
4447 
4448         /**
4449          * Lists the dependencies graph in a new HTML-window.
4450          * @returns {JXG.Board} Reference to the board
4451          */
4452         showDependencies: function () {
4453             var el, t, c, f, i;
4454 
4455             t = '<p>\n';
4456             for (el in this.objects) {
4457                 if (this.objects.hasOwnProperty(el)) {
4458                     i = 0;
4459                     for (c in this.objects[el].childElements) {
4460                         if (this.objects[el].childElements.hasOwnProperty(c)) {
4461                             i += 1;
4462                         }
4463                     }
4464                     if (i >= 0) {
4465                         t += '<strong>' + this.objects[el].id + ':<' + '/strong> ';
4466                     }
4467 
4468                     for (c in this.objects[el].childElements) {
4469                         if (this.objects[el].childElements.hasOwnProperty(c)) {
4470                             t += this.objects[el].childElements[c].id + '(' + this.objects[el].childElements[c].name + ')' + ', ';
4471                         }
4472                     }
4473                     t += '<p>\n';
4474                 }
4475             }
4476             t += '<' + '/p>\n';
4477             f = window.open();
4478             f.document.open();
4479             f.document.write(t);
4480             f.document.close();
4481             return this;
4482         },
4483 
4484         /**
4485          * Lists the XML code of the construction in a new HTML-window.
4486          * @returns {JXG.Board} Reference to the board
4487          */
4488         showXML: function () {
4489             var f = window.open('');
4490             f.document.open();
4491             f.document.write('<pre>' + Type.escapeHTML(this.xmlString) + '<' + '/pre>');
4492             f.document.close();
4493             return this;
4494         },
4495 
4496         /**
4497          * Sets for all objects the needsUpdate flag to "true".
4498          * @returns {JXG.Board} Reference to the board
4499          */
4500         prepareUpdate: function () {
4501             var el, pEl, len = this.objectsList.length;
4502 
4503             /*
4504             if (this.attr.updatetype === 'hierarchical') {
4505                 return this;
4506             }
4507             */
4508 
4509             for (el = 0; el < len; el++) {
4510                 pEl = this.objectsList[el];
4511                 pEl.needsUpdate = pEl.needsRegularUpdate || this.needsFullUpdate;
4512             }
4513 
4514             for (el in this.groups) {
4515                 if (this.groups.hasOwnProperty(el)) {
4516                     pEl = this.groups[el];
4517                     pEl.needsUpdate = pEl.needsRegularUpdate || this.needsFullUpdate;
4518                 }
4519             }
4520 
4521             return this;
4522         },
4523 
4524         /**
4525          * Runs through all elements and calls their update() method.
4526          * @param {JXG.GeometryElement} drag Element that caused the update.
4527          * @returns {JXG.Board} Reference to the board
4528          */
4529         updateElements: function (drag) {
4530             var el, pEl;
4531             //var childId, i = 0;
4532 
4533             drag = this.select(drag);
4534 
4535             /*
4536             if (Type.exists(drag)) {
4537                 for (el = 0; el < this.objectsList.length; el++) {
4538                     pEl = this.objectsList[el];
4539                     if (pEl.id === drag.id) {
4540                         i = el;
4541                         break;
4542                     }
4543                 }
4544             }
4545             */
4546 
4547             for (el = 0; el < this.objectsList.length; el++) {
4548                 pEl = this.objectsList[el];
4549                 if (this.needsFullUpdate && pEl.elementClass === Const.OBJECT_CLASS_TEXT) {
4550                     pEl.updateSize();
4551                 }
4552 
4553                 // For updates of an element we distinguish if the dragged element is updated or
4554                 // other elements are updated.
4555                 // The difference lies in the treatment of gliders and points based on transformations.
4556                 pEl.update(!Type.exists(drag) || pEl.id !== drag.id)
4557                    .updateVisibility();
4558             }
4559 
4560             // update groups last
4561             for (el in this.groups) {
4562                 if (this.groups.hasOwnProperty(el)) {
4563                     this.groups[el].update(drag);
4564                 }
4565             }
4566 
4567             return this;
4568         },
4569 
4570         /**
4571          * Runs through all elements and calls their update() method.
4572          * @returns {JXG.Board} Reference to the board
4573          */
4574         updateRenderer: function () {
4575             var el,
4576                 len = this.objectsList.length;
4577 
4578             /*
4579             objs = this.objectsList.slice(0);
4580             objs.sort(function (a, b) {
4581                 if (a.visProp.layer < b.visProp.layer) {
4582                     return -1;
4583                 } else if (a.visProp.layer === b.visProp.layer) {
4584                     return b.lastDragTime.getTime() - a.lastDragTime.getTime();
4585                 } else {
4586                     return 1;
4587                 }
4588             });
4589             */
4590 
4591             if (this.renderer.type === 'canvas') {
4592                 this.updateRendererCanvas();
4593             } else {
4594                 for (el = 0; el < len; el++) {
4595                     this.objectsList[el].updateRenderer();
4596                 }
4597             }
4598             return this;
4599         },
4600 
4601         /**
4602          * Runs through all elements and calls their update() method.
4603          * This is a special version for the CanvasRenderer.
4604          * Here, we have to do our own layer handling.
4605          * @returns {JXG.Board} Reference to the board
4606          */
4607         updateRendererCanvas: function () {
4608             var el, pEl, i, mini, la,
4609                 olen = this.objectsList.length,
4610                 layers = this.options.layer,
4611                 len = this.options.layer.numlayers,
4612                 last = Number.NEGATIVE_INFINITY;
4613 
4614             for (i = 0; i < len; i++) {
4615                 mini = Number.POSITIVE_INFINITY;
4616 
4617                 for (la in layers) {
4618                     if (layers.hasOwnProperty(la)) {
4619                         if (layers[la] > last && layers[la] < mini) {
4620                             mini = layers[la];
4621                         }
4622                     }
4623                 }
4624 
4625                 last = mini;
4626 
4627                 for (el = 0; el < olen; el++) {
4628                     pEl = this.objectsList[el];
4629 
4630                     if (pEl.visProp.layer === mini) {
4631                         pEl.prepareUpdate().updateRenderer();
4632                     }
4633                 }
4634             }
4635             return this;
4636         },
4637 
4638         /**
4639          * Please use {@link JXG.Board.on} instead.
4640          * @param {Function} hook A function to be called by the board after an update occurred.
4641          * @param {String} [m='update'] When the hook is to be called. Possible values are <i>mouseup</i>, <i>mousedown</i> and <i>update</i>.
4642          * @param {Object} [context=board] Determines the execution context the hook is called. This parameter is optional, default is the
4643          * board object the hook is attached to.
4644          * @returns {Number} Id of the hook, required to remove the hook from the board.
4645          * @deprecated
4646          */
4647         addHook: function (hook, m, context) {
4648             JXG.deprecated('Board.addHook()', 'Board.on()');
4649             m = Type.def(m, 'update');
4650 
4651             context = Type.def(context, this);
4652 
4653             this.hooks.push([m, hook]);
4654             this.on(m, hook, context);
4655 
4656             return this.hooks.length - 1;
4657         },
4658 
4659         /**
4660          * Alias of {@link JXG.Board.on}.
4661          */
4662         addEvent: JXG.shortcut(JXG.Board.prototype, 'on'),
4663 
4664         /**
4665          * Please use {@link JXG.Board.off} instead.
4666          * @param {Number|function} id The number you got when you added the hook or a reference to the event handler.
4667          * @returns {JXG.Board} Reference to the board
4668          * @deprecated
4669          */
4670         removeHook: function (id) {
4671             JXG.deprecated('Board.removeHook()', 'Board.off()');
4672             if (this.hooks[id]) {
4673                 this.off(this.hooks[id][0], this.hooks[id][1]);
4674                 this.hooks[id] = null;
4675             }
4676 
4677             return this;
4678         },
4679 
4680         /**
4681          * Alias of {@link JXG.Board.off}.
4682          */
4683         removeEvent: JXG.shortcut(JXG.Board.prototype, 'off'),
4684 
4685         /**
4686          * Runs through all hooked functions and calls them.
4687          * @returns {JXG.Board} Reference to the board
4688          * @deprecated
4689          */
4690         updateHooks: function (m) {
4691             var arg = Array.prototype.slice.call(arguments, 0);
4692 
4693             JXG.deprecated('Board.updateHooks()', 'Board.triggerEventHandlers()');
4694 
4695             arg[0] = Type.def(arg[0], 'update');
4696             this.triggerEventHandlers([arg[0]], arguments);
4697 
4698             return this;
4699         },
4700 
4701         /**
4702          * Adds a dependent board to this board.
4703          * @param {JXG.Board} board A reference to board which will be updated after an update of this board occurred.
4704          * @returns {JXG.Board} Reference to the board
4705          */
4706         addChild: function (board) {
4707             if (Type.exists(board) && Type.exists(board.containerObj)) {
4708                 this.dependentBoards.push(board);
4709                 this.update();
4710             }
4711             return this;
4712         },
4713 
4714         /**
4715          * Deletes a board from the list of dependent boards.
4716          * @param {JXG.Board} board Reference to the board which will be removed.
4717          * @returns {JXG.Board} Reference to the board
4718          */
4719         removeChild: function (board) {
4720             var i;
4721 
4722             for (i = this.dependentBoards.length - 1; i >= 0; i--) {
4723                 if (this.dependentBoards[i] === board) {
4724                     this.dependentBoards.splice(i, 1);
4725                 }
4726             }
4727             return this;
4728         },
4729 
4730         /**
4731          * Runs through most elements and calls their update() method and update the conditions.
4732          * @param {JXG.GeometryElement} [drag] Element that caused the update.
4733          * @returns {JXG.Board} Reference to the board
4734          */
4735         update: function (drag) {
4736             var i, len, b, insert,
4737                 storeActiveEl;
4738 
4739             if (this.inUpdate || this.isSuspendedUpdate) {
4740                 return this;
4741             }
4742             this.inUpdate = true;
4743 
4744             if (this.attr.minimizereflow === 'all' && this.containerObj && this.renderer.type !== 'vml') {
4745                 storeActiveEl = document.activeElement; // Store focus element
4746                 insert = this.renderer.removeToInsertLater(this.containerObj);
4747             }
4748 
4749             if (this.attr.minimizereflow === 'svg' && this.renderer.type === 'svg') {
4750                 storeActiveEl = document.activeElement;
4751                 insert = this.renderer.removeToInsertLater(this.renderer.svgRoot);
4752             }
4753 
4754             this.prepareUpdate().updateElements(drag).updateConditions();
4755             this.renderer.suspendRedraw(this);
4756             this.updateRenderer();
4757             this.renderer.unsuspendRedraw();
4758             this.triggerEventHandlers(['update'], []);
4759 
4760             if (insert) {
4761                 insert();
4762                 storeActiveEl.focus();     // Restore focus element
4763             }
4764 
4765             // To resolve dependencies between boards
4766             // for (var board in JXG.boards) {
4767             len = this.dependentBoards.length;
4768             for (i = 0; i < len; i++) {
4769                 b = this.dependentBoards[i];
4770                 if (Type.exists(b) && b !== this) {
4771                     b.updateQuality = this.updateQuality;
4772                     b.prepareUpdate().updateElements().updateConditions();
4773                     b.renderer.suspendRedraw();
4774                     b.updateRenderer();
4775                     b.renderer.unsuspendRedraw();
4776                     b.triggerEventHandlers(['update'], []);
4777                 }
4778 
4779             }
4780 
4781             this.inUpdate = false;
4782             return this;
4783         },
4784 
4785         /**
4786          * Runs through all elements and calls their update() method and update the conditions.
4787          * This is necessary after zooming and changing the bounding box.
4788          * @returns {JXG.Board} Reference to the board
4789          */
4790         fullUpdate: function () {
4791             this.needsFullUpdate = true;
4792             this.update();
4793             this.needsFullUpdate = false;
4794             return this;
4795         },
4796 
4797         /**
4798          * Adds a grid to the board according to the settings given in board.options.
4799          * @returns {JXG.Board} Reference to the board.
4800          */
4801         addGrid: function () {
4802             this.create('grid', []);
4803 
4804             return this;
4805         },
4806 
4807         /**
4808          * Removes all grids assigned to this board. Warning: This method also removes all objects depending on one or
4809          * more of the grids.
4810          * @returns {JXG.Board} Reference to the board object.
4811          */
4812         removeGrids: function () {
4813             var i;
4814 
4815             for (i = 0; i < this.grids.length; i++) {
4816                 this.removeObject(this.grids[i]);
4817             }
4818 
4819             this.grids.length = 0;
4820             this.update(); // required for canvas renderer
4821 
4822             return this;
4823         },
4824 
4825         /**
4826          * Creates a new geometric element of type elementType.
4827          * @param {String} elementType Type of the element to be constructed given as a string e.g. 'point' or 'circle'.
4828          * @param {Array} parents Array of parent elements needed to construct the element e.g. coordinates for a point or two
4829          * points to construct a line. This highly depends on the elementType that is constructed. See the corresponding JXG.create*
4830          * methods for a list of possible parameters.
4831          * @param {Object} [attributes] An object containing the attributes to be set. This also depends on the elementType.
4832          * Common attributes are name, visible, strokeColor.
4833          * @returns {Object} Reference to the created element. This is usually a GeometryElement, but can be an array containing
4834          * two or more elements.
4835          */
4836         create: function (elementType, parents, attributes) {
4837             var el, i;
4838 
4839             elementType = elementType.toLowerCase();
4840 
4841             if (!Type.exists(parents)) {
4842                 parents = [];
4843             }
4844 
4845             if (!Type.exists(attributes)) {
4846                 attributes = {};
4847             }
4848 
4849             for (i = 0; i < parents.length; i++) {
4850                 if (Type.isString(parents[i]) &&
4851                     !(elementType === 'text' && i === 2) &&
4852                     !(elementType === 'solidofrevolution3d' && i === 2) &&
4853                     !((elementType === 'input' || elementType === 'checkbox' || elementType === 'button') &&
4854                       (i === 2 || i === 3)) &&
4855                     !(elementType === 'curve' && i > 0) // Allow curve plots with jessiecode
4856                 ) {
4857                     parents[i] = this.select(parents[i]);
4858                 }
4859             }
4860 
4861             if (Type.isFunction(JXG.elements[elementType])) {
4862                 el = JXG.elements[elementType](this, parents, attributes);
4863             } else {
4864                 throw new Error("JSXGraph: create: Unknown element type given: " + elementType);
4865             }
4866 
4867             if (!Type.exists(el)) {
4868                 JXG.debug("JSXGraph: create: failure creating " + elementType);
4869                 return el;
4870             }
4871 
4872             if (el.prepareUpdate && el.update && el.updateRenderer) {
4873                 el.fullUpdate();
4874             }
4875             return el;
4876         },
4877 
4878         /**
4879          * Deprecated name for {@link JXG.Board.create}.
4880          * @deprecated
4881          */
4882         createElement: function () {
4883             JXG.deprecated('Board.createElement()', 'Board.create()');
4884             return this.create.apply(this, arguments);
4885         },
4886 
4887         /**
4888          * Delete the elements drawn as part of a trace of an element.
4889          * @returns {JXG.Board} Reference to the board
4890          */
4891         clearTraces: function () {
4892             var el;
4893 
4894             for (el = 0; el < this.objectsList.length; el++) {
4895                 this.objectsList[el].clearTrace();
4896             }
4897 
4898             this.numTraces = 0;
4899             return this;
4900         },
4901 
4902         /**
4903          * Stop updates of the board.
4904          * @returns {JXG.Board} Reference to the board
4905          */
4906         suspendUpdate: function () {
4907             if (!this.inUpdate) {
4908                 this.isSuspendedUpdate = true;
4909             }
4910             return this;
4911         },
4912 
4913         /**
4914          * Enable updates of the board.
4915          * @returns {JXG.Board} Reference to the board
4916          */
4917         unsuspendUpdate: function () {
4918             if (this.isSuspendedUpdate) {
4919                 this.isSuspendedUpdate = false;
4920                 this.fullUpdate();
4921             }
4922             return this;
4923         },
4924 
4925         /**
4926          * Set the bounding box of the board.
4927          * @param {Array} bbox New bounding box [x1,y1,x2,y2]
4928          * @param {Boolean} [keepaspectratio=false] If set to true, the aspect ratio will be 1:1, but
4929          * the resulting viewport may be larger.
4930          * @param {String} [setZoom='reset'] Reset, keep or update the zoom level of the board. 'reset'
4931          * sets {@link JXG.Board#zoomX} and {@link JXG.Board#zoomY} to the start values (or 1.0).
4932          * 'update' adapts these values accoring to the new bounding box and 'keep' does nothing.
4933          * @returns {JXG.Board} Reference to the board
4934          */
4935         setBoundingBox: function (bbox, keepaspectratio, setZoom) {
4936             var h, w, ux, uy,
4937                 offX = 0,
4938                 offY = 0,
4939                 dim = Env.getDimensions(this.container, this.document);
4940 
4941             if (!Type.isArray(bbox)) {
4942                 return this;
4943             }
4944 
4945             if (bbox[0] < this.maxboundingbox[0] ||
4946                 bbox[1] > this.maxboundingbox[1] ||
4947                 bbox[2] > this.maxboundingbox[2] ||
4948                 bbox[3] < this.maxboundingbox[3]) {
4949                 return this;
4950             }
4951 
4952             if (!Type.exists(setZoom)) {
4953                 setZoom = 'reset';
4954             }
4955 
4956             ux = this.unitX;
4957             uy = this.unitY;
4958 
4959             this.canvasWidth = parseInt(dim.width, 10);
4960             this.canvasHeight = parseInt(dim.height, 10);
4961             w = this.canvasWidth;
4962             h = this.canvasHeight;
4963             if (keepaspectratio) {
4964                 this.unitX = w / (bbox[2] - bbox[0]);
4965                 this.unitY = h / (bbox[1] - bbox[3]);
4966                 if (Math.abs(this.unitX) < Math.abs(this.unitY)) {
4967                     this.unitY = Math.abs(this.unitX) * this.unitY / Math.abs(this.unitY);
4968                     // Add the additional units in equal portions above and below
4969                     offY = (h / this.unitY - (bbox[1] - bbox[3])) * 0.5;
4970                 } else {
4971                     this.unitX = Math.abs(this.unitY) * this.unitX / Math.abs(this.unitX);
4972                     // Add the additional units in equal portions left and right
4973                     offX = (w / this.unitX - (bbox[2] - bbox[0])) * 0.5;
4974                 }
4975                 this.keepaspectratio = true;
4976             } else {
4977                 this.unitX = w / (bbox[2] - bbox[0]);
4978                 this.unitY = h / (bbox[1] - bbox[3]);
4979                 this.keepaspectratio = false;
4980             }
4981 
4982             this.moveOrigin(-this.unitX * (bbox[0] - offX), this.unitY * (bbox[1] + offY));
4983 
4984             if (setZoom === 'update') {
4985                 this.zoomX *= this.unitX / ux;
4986                 this.zoomY *= this.unitY / uy;
4987             } else if (setZoom === 'reset') {
4988                 this.zoomX = Type.exists(this.attr.zoomx) ? this.attr.zoomx : 1.0;
4989                 this.zoomY = Type.exists(this.attr.zoomy) ? this.attr.zoomy : 1.0;
4990             }
4991 
4992             return this;
4993         },
4994 
4995         /**
4996          * Get the bounding box of the board.
4997          * @returns {Array} bounding box [x1,y1,x2,y2] upper left corner, lower right corner
4998          */
4999         getBoundingBox: function () {
5000             var ul = (new Coords(Const.COORDS_BY_SCREEN, [0, 0], this)).usrCoords,
5001                 lr = (new Coords(Const.COORDS_BY_SCREEN, [this.canvasWidth, this.canvasHeight], this)).usrCoords;
5002 
5003             return [ul[1], ul[2], lr[1], lr[2]];
5004         },
5005 
5006         /**
5007          * Adds an animation. Animations are controlled by the boards, so the boards need to be aware of the
5008          * animated elements. This function tells the board about new elements to animate.
5009          * @param {JXG.GeometryElement} element The element which is to be animated.
5010          * @returns {JXG.Board} Reference to the board
5011          */
5012         addAnimation: function (element) {
5013             var that = this;
5014 
5015             this.animationObjects[element.id] = element;
5016 
5017             if (!this.animationIntervalCode) {
5018                 this.animationIntervalCode = window.setInterval(function () {
5019                     that.animate();
5020                 }, element.board.attr.animationdelay);
5021             }
5022 
5023             return this;
5024         },
5025 
5026         /**
5027          * Cancels all running animations.
5028          * @returns {JXG.Board} Reference to the board
5029          */
5030         stopAllAnimation: function () {
5031             var el;
5032 
5033             for (el in this.animationObjects) {
5034                 if (this.animationObjects.hasOwnProperty(el) && Type.exists(this.animationObjects[el])) {
5035                     this.animationObjects[el] = null;
5036                     delete this.animationObjects[el];
5037                 }
5038             }
5039 
5040             window.clearInterval(this.animationIntervalCode);
5041             delete this.animationIntervalCode;
5042 
5043             return this;
5044         },
5045 
5046         /**
5047          * General purpose animation function. This currently only supports moving points from one place to another. This
5048          * is faster than managing the animation per point, especially if there is more than one animated point at the same time.
5049          * @returns {JXG.Board} Reference to the board
5050          */
5051         animate: function () {
5052             var props, el, o, newCoords, r, p, c, cbtmp,
5053                 count = 0,
5054                 obj = null;
5055 
5056             for (el in this.animationObjects) {
5057                 if (this.animationObjects.hasOwnProperty(el) && Type.exists(this.animationObjects[el])) {
5058                     count += 1;
5059                     o = this.animationObjects[el];
5060 
5061                     if (o.animationPath) {
5062                         if (Type.isFunction(o.animationPath)) {
5063                             newCoords = o.animationPath(new Date().getTime() - o.animationStart);
5064                         } else {
5065                             newCoords = o.animationPath.pop();
5066                         }
5067 
5068                         if ((!Type.exists(newCoords)) || (!Type.isArray(newCoords) && isNaN(newCoords))) {
5069                             delete o.animationPath;
5070                         } else {
5071                             o.setPositionDirectly(Const.COORDS_BY_USER, newCoords);
5072                             o.fullUpdate();
5073                             obj = o;
5074                         }
5075                     }
5076                     if (o.animationData) {
5077                         c = 0;
5078 
5079                         for (r in o.animationData) {
5080                             if (o.animationData.hasOwnProperty(r)) {
5081                                 p = o.animationData[r].pop();
5082 
5083                                 if (!Type.exists(p)) {
5084                                     delete o.animationData[p];
5085                                 } else {
5086                                     c += 1;
5087                                     props = {};
5088                                     props[r] = p;
5089                                     o.setAttribute(props);
5090                                 }
5091                             }
5092                         }
5093 
5094                         if (c === 0) {
5095                             delete o.animationData;
5096                         }
5097                     }
5098 
5099                     if (!Type.exists(o.animationData) && !Type.exists(o.animationPath)) {
5100                         this.animationObjects[el] = null;
5101                         delete this.animationObjects[el];
5102 
5103                         if (Type.exists(o.animationCallback)) {
5104                             cbtmp = o.animationCallback;
5105                             o.animationCallback = null;
5106                             cbtmp();
5107                         }
5108                     }
5109                 }
5110             }
5111 
5112             if (count === 0) {
5113                 window.clearInterval(this.animationIntervalCode);
5114                 delete this.animationIntervalCode;
5115             } else {
5116                 this.update(obj);
5117             }
5118 
5119             return this;
5120         },
5121 
5122         /**
5123          * Migrate the dependency properties of the point src
5124          * to the point dest and  delete the point src.
5125          * For example, a circle around the point src
5126          * receives the new center dest. The old center src
5127          * will be deleted.
5128          * @param {JXG.Point} src Original point which will be deleted
5129          * @param {JXG.Point} dest New point with the dependencies of src.
5130          * @param {Boolean} copyName Flag which decides if the name of the src element is copied to the
5131          *  dest element.
5132          * @returns {JXG.Board} Reference to the board
5133          */
5134         migratePoint: function (src, dest, copyName) {
5135             var child, childId, prop, found, i, srcLabelId, srcHasLabel = false;
5136 
5137             src = this.select(src);
5138             dest = this.select(dest);
5139 
5140             if (Type.exists(src.label)) {
5141                 srcLabelId = src.label.id;
5142                 srcHasLabel = true;
5143                 this.removeObject(src.label);
5144             }
5145 
5146             for (childId in src.childElements) {
5147                 if (src.childElements.hasOwnProperty(childId)) {
5148                     child = src.childElements[childId];
5149                     found = false;
5150 
5151                     for (prop in child) {
5152                         if (child.hasOwnProperty(prop)) {
5153                             if (child[prop] ===  src) {
5154                                 child[prop] = dest;
5155                                 found = true;
5156                             }
5157                         }
5158                     }
5159 
5160                     if (found) {
5161                         delete src.childElements[childId];
5162                     }
5163 
5164                     for (i = 0; i < child.parents.length; i++) {
5165                         if (child.parents[i] === src.id) {
5166                             child.parents[i] = dest.id;
5167                         }
5168                     }
5169 
5170                     dest.addChild(child);
5171                 }
5172             }
5173 
5174             // The destination object should receive the name
5175             // and the label of the originating (src) object
5176             if (copyName) {
5177                 if (srcHasLabel) {
5178                     delete dest.childElements[srcLabelId];
5179                     delete dest.descendants[srcLabelId];
5180                 }
5181 
5182                 if (dest.label) {
5183                     this.removeObject(dest.label);
5184                 }
5185 
5186                 delete this.elementsByName[dest.name];
5187                 dest.name = src.name;
5188                 if (srcHasLabel) {
5189                     dest.createLabel();
5190                 }
5191             }
5192 
5193             this.removeObject(src);
5194 
5195             if (Type.exists(dest.name) && dest.name !== '') {
5196                 this.elementsByName[dest.name] = dest;
5197             }
5198 
5199             this.fullUpdate();
5200 
5201             return this;
5202         },
5203 
5204         /**
5205          * Initializes color blindness simulation.
5206          * @param {String} deficiency Describes the color blindness deficiency which is simulated. Accepted values are 'protanopia', 'deuteranopia', and 'tritanopia'.
5207          * @returns {JXG.Board} Reference to the board
5208          */
5209         emulateColorblindness: function (deficiency) {
5210             var e, o;
5211 
5212             if (!Type.exists(deficiency)) {
5213                 deficiency = 'none';
5214             }
5215 
5216             if (this.currentCBDef === deficiency) {
5217                 return this;
5218             }
5219 
5220             for (e in this.objects) {
5221                 if (this.objects.hasOwnProperty(e)) {
5222                     o = this.objects[e];
5223 
5224                     if (deficiency !== 'none') {
5225                         if (this.currentCBDef === 'none') {
5226                             // this could be accomplished by JXG.extend, too. But do not use
5227                             // JXG.deepCopy as this could result in an infinite loop because in
5228                             // visProp there could be geometry elements which contain the board which
5229                             // contains all objects which contain board etc.
5230                             o.visPropOriginal = {
5231                                 strokecolor: o.visProp.strokecolor,
5232                                 fillcolor: o.visProp.fillcolor,
5233                                 highlightstrokecolor: o.visProp.highlightstrokecolor,
5234                                 highlightfillcolor: o.visProp.highlightfillcolor
5235                             };
5236                         }
5237                         o.setAttribute({
5238                             strokecolor: Color.rgb2cb(Type.evaluate(o.visPropOriginal.strokecolor), deficiency),
5239                             fillcolor: Color.rgb2cb(Type.evaluate(o.visPropOriginal.fillcolor), deficiency),
5240                             highlightstrokecolor: Color.rgb2cb(Type.evaluate(o.visPropOriginal.highlightstrokecolor), deficiency),
5241                             highlightfillcolor: Color.rgb2cb(Type.evaluate(o.visPropOriginal.highlightfillcolor), deficiency)
5242                         });
5243                     } else if (Type.exists(o.visPropOriginal)) {
5244                         JXG.extend(o.visProp, o.visPropOriginal);
5245                     }
5246                 }
5247             }
5248             this.currentCBDef = deficiency;
5249             this.update();
5250 
5251             return this;
5252         },
5253 
5254         /**
5255          * Select a single or multiple elements at once.
5256          * @param {String|Object|function} str The name, id or a reference to a JSXGraph element on this board. An object will
5257          * be used as a filter to return multiple elements at once filtered by the properties of the object.
5258          * @param {Boolean} onlyByIdOrName If true (default:false) elements are only filtered by their id, name or groupId.
5259          * The advanced filters consisting of objects or functions are ignored.
5260          * @returns {JXG.GeometryElement|JXG.Composition}
5261          * @example
5262          * // select the element with name A
5263          * board.select('A');
5264          *
5265          * // select all elements with strokecolor set to 'red' (but not '#ff0000')
5266          * board.select({
5267          *   strokeColor: 'red'
5268          * });
5269          *
5270          * // select all points on or below the x axis and make them black.
5271          * board.select({
5272          *   elementClass: JXG.OBJECT_CLASS_POINT,
5273          *   Y: function (v) {
5274          *     return v <= 0;
5275          *   }
5276          * }).setAttribute({color: 'black'});
5277          *
5278          * // select all elements
5279          * board.select(function (el) {
5280          *   return true;
5281          * });
5282          */
5283         select: function (str, onlyByIdOrName) {
5284             var flist, olist, i, l,
5285                 s = str;
5286 
5287             if (s === null) {
5288                 return s;
5289             }
5290 
5291             // it's a string, most likely an id or a name.
5292             if (Type.isString(s) && s !== '') {
5293                 // Search by ID
5294                 if (Type.exists(this.objects[s])) {
5295                     s = this.objects[s];
5296                 // Search by name
5297                 } else if (Type.exists(this.elementsByName[s])) {
5298                     s = this.elementsByName[s];
5299                 // Search by group ID
5300                 } else if (Type.exists(this.groups[s])) {
5301                     s = this.groups[s];
5302                 }
5303             // it's a function or an object, but not an element
5304             } else if (!onlyByIdOrName &&
5305                 (Type.isFunction(s) ||
5306                  (Type.isObject(s) && !Type.isFunction(s.setAttribute))
5307                 )) {
5308                 flist = Type.filterElements(this.objectsList, s);
5309 
5310                 olist = {};
5311                 l = flist.length;
5312                 for (i = 0; i < l; i++) {
5313                     olist[flist[i].id] = flist[i];
5314                 }
5315                 s = new Composition(olist);
5316             // it's an element which has been deleted (and still hangs around, e.g. in an attractor list
5317             } else if (Type.isObject(s) && Type.exists(s.id) && !Type.exists(this.objects[s.id])) {
5318                 s = null;
5319             }
5320 
5321             return s;
5322         },
5323 
5324         /**
5325          * Checks if the given point is inside the boundingbox.
5326          * @param {Number|JXG.Coords} x User coordinate or {@link JXG.Coords} object.
5327          * @param {Number} [y] User coordinate. May be omitted in case <tt>x</tt> is a {@link JXG.Coords} object.
5328          * @returns {Boolean}
5329          */
5330         hasPoint: function (x, y) {
5331             var px = x,
5332                 py = y,
5333                 bbox = this.getBoundingBox();
5334 
5335             if (Type.exists(x) && Type.isArray(x.usrCoords)) {
5336                 px = x.usrCoords[1];
5337                 py = x.usrCoords[2];
5338             }
5339 
5340             return !!(Type.isNumber(px) && Type.isNumber(py) &&
5341                 bbox[0] < px && px < bbox[2] && bbox[1] > py && py > bbox[3]);
5342         },
5343 
5344         /**
5345          * Update CSS transformations of type scaling. It is used to correct the mouse position
5346          * in {@link JXG.Board.getMousePosition}.
5347          * The inverse transformation matrix is updated on each mouseDown and touchStart event.
5348          *
5349          * It is up to the user to call this method after an update of the CSS transformation
5350          * in the DOM.
5351          */
5352         updateCSSTransforms: function () {
5353             var obj = this.containerObj,
5354                 o = obj,
5355                 o2 = obj;
5356 
5357             this.cssTransMat = Env.getCSSTransformMatrix(o);
5358 
5359             /*
5360              * In Mozilla and Webkit: offsetParent seems to jump at least to the next iframe,
5361              * if not to the body. In IE and if we are in an position:absolute environment
5362              * offsetParent walks up the DOM hierarchy.
5363              * In order to walk up the DOM hierarchy also in Mozilla and Webkit
5364              * we need the parentNode steps.
5365              */
5366             o = o.offsetParent;
5367             while (o) {
5368                 this.cssTransMat = Mat.matMatMult(Env.getCSSTransformMatrix(o), this.cssTransMat);
5369 
5370                 o2 = o2.parentNode;
5371                 while (o2 !== o) {
5372                     this.cssTransMat = Mat.matMatMult(Env.getCSSTransformMatrix(o), this.cssTransMat);
5373                     o2 = o2.parentNode;
5374                 }
5375 
5376                 o = o.offsetParent;
5377             }
5378             this.cssTransMat = Mat.inverse(this.cssTransMat);
5379 
5380             return this;
5381         },
5382 
5383         /**
5384          * Start selection mode. This function can either be triggered from outside or by
5385          * a down event together with correct key pressing. The default keys are
5386          * shift+ctrl. But this can be changed in the options.
5387          *
5388          * Starting from out side can be realized for example with a button like this:
5389          * <pre>
5390          * 	<button onclick="board.startSelectionMode()">Start</button>
5391          * </pre>
5392          * @example
5393          * //
5394          * // Set a new bounding box from the selection rectangle
5395          * //
5396          * var board = JXG.JSXGraph.initBoard('jxgbox', {
5397          *         boundingBox:[-3,2,3,-2],
5398          *         keepAspectRatio: false,
5399          *         axis:true,
5400          *         selection: {
5401          *             enabled: true,
5402          *             needShift: false,
5403          *             needCtrl: true,
5404          *             withLines: false,
5405          *             vertices: {
5406          *                 visible: false
5407          *             },
5408          *             fillColor: '#ffff00',
5409          *         }
5410          *      });
5411          *
5412          * var f = function f(x) { return Math.cos(x); },
5413          *     curve = board.create('functiongraph', [f]);
5414          *
5415          * board.on('stopselecting', function(){
5416          *     var box = board.stopSelectionMode(),
5417          *
5418          *         // bbox has the coordinates of the selection rectangle.
5419          *         // Attention: box[i].usrCoords have the form [1, x, y], i.e.
5420          *         // are homogeneous coordinates.
5421          *         bbox = box[0].usrCoords.slice(1).concat(box[1].usrCoords.slice(1));
5422          *
5423          *         // Set a new bounding box
5424          *         board.setBoundingBox(bbox, false);
5425          *  });
5426          *
5427          *
5428          * </pre><div class="jxgbox" id="JXG11eff3a6-8c50-11e5-b01d-901b0e1b8723" style="width: 300px; height: 300px;"></div>
5429          * <script type="text/javascript">
5430          *     (function() {
5431          *     //
5432          *     // Set a new bounding box from the selection rectangle
5433          *     //
5434          *     var board = JXG.JSXGraph.initBoard('JXG11eff3a6-8c50-11e5-b01d-901b0e1b8723', {
5435          *             boundingBox:[-3,2,3,-2],
5436          *             keepAspectRatio: false,
5437          *             axis:true,
5438          *             selection: {
5439          *                 enabled: true,
5440          *                 needShift: false,
5441          *                 needCtrl: true,
5442          *                 withLines: false,
5443          *                 vertices: {
5444          *                     visible: false
5445          *                 },
5446          *                 fillColor: '#ffff00',
5447          *             }
5448          *        });
5449          *
5450          *     var f = function f(x) { return Math.cos(x); },
5451          *         curve = board.create('functiongraph', [f]);
5452          *
5453          *     board.on('stopselecting', function(){
5454          *         var box = board.stopSelectionMode(),
5455          *
5456          *             // bbox has the coordinates of the selection rectangle.
5457          *             // Attention: box[i].usrCoords have the form [1, x, y], i.e.
5458          *             // are homogeneous coordinates.
5459          *             bbox = box[0].usrCoords.slice(1).concat(box[1].usrCoords.slice(1));
5460          *
5461          *             // Set a new bounding box
5462          *             board.setBoundingBox(bbox, false);
5463          *      });
5464          *     })();
5465          *
5466          * </script><pre>
5467          *
5468          */
5469         startSelectionMode: function () {
5470             this.selectingMode = true;
5471             this.selectionPolygon.setAttribute({visible: true});
5472             this.selectingBox = [[0, 0], [0, 0]];
5473             this._setSelectionPolygonFromBox();
5474             this.selectionPolygon.fullUpdate();
5475         },
5476 
5477         /**
5478          * Finalize the selection: disable selection mode and return the coordinates
5479          * of the selection rectangle.
5480          * @returns {Array} Coordinates of the selection rectangle. The array
5481          * contains two {@link JXG.Coords} objects. One the upper left corner and
5482          * the second for the lower right corner.
5483          */
5484         stopSelectionMode: function () {
5485             this.selectingMode = false;
5486             this.selectionPolygon.setAttribute({visible: false});
5487             return [this.selectionPolygon.vertices[0].coords, this.selectionPolygon.vertices[2].coords];
5488         },
5489 
5490         /**
5491          * Start the selection of a region.
5492          * @private
5493          * @param  {Array} pos Screen coordiates of the upper left corner of the
5494          * selection rectangle.
5495          */
5496         _startSelecting: function (pos) {
5497             this.isSelecting = true;
5498             this.selectingBox = [ [pos[0], pos[1]], [pos[0], pos[1]] ];
5499             this._setSelectionPolygonFromBox();
5500         },
5501 
5502         /**
5503          * Update the selection rectangle during a move event.
5504          * @private
5505          * @param  {Array} pos Screen coordiates of the move event
5506          */
5507         _moveSelecting: function (pos) {
5508             if (this.isSelecting) {
5509                 this.selectingBox[1] = [pos[0], pos[1]];
5510                 this._setSelectionPolygonFromBox();
5511                 this.selectionPolygon.fullUpdate();
5512             }
5513         },
5514 
5515         /**
5516          * Update the selection rectangle during an up event. Stop selection.
5517          * @private
5518          * @param  {Object} evt Event object
5519          */
5520         _stopSelecting:  function (evt) {
5521             var pos = this.getMousePosition(evt);
5522 
5523             this.isSelecting = false;
5524             this.selectingBox[1] = [pos[0], pos[1]];
5525             this._setSelectionPolygonFromBox();
5526         },
5527 
5528         /**
5529          * Update the Selection rectangle.
5530          * @private
5531          */
5532         _setSelectionPolygonFromBox: function () {
5533                var A = this.selectingBox[0],
5534                 B = this.selectingBox[1];
5535 
5536                this.selectionPolygon.vertices[0].setPositionDirectly(JXG.COORDS_BY_SCREEN, [A[0], A[1]]);
5537                this.selectionPolygon.vertices[1].setPositionDirectly(JXG.COORDS_BY_SCREEN, [A[0], B[1]]);
5538                this.selectionPolygon.vertices[2].setPositionDirectly(JXG.COORDS_BY_SCREEN, [B[0], B[1]]);
5539                this.selectionPolygon.vertices[3].setPositionDirectly(JXG.COORDS_BY_SCREEN, [B[0], A[1]]);
5540         },
5541 
5542         /**
5543          * Test if a down event should start a selection. Test if the
5544          * required keys are pressed. If yes, {@link JXG.Board.startSelectionMode} is called.
5545          * @param  {Object} evt Event object
5546          */
5547         _testForSelection: function (evt) {
5548             if (this._isRequiredKeyPressed(evt, 'selection')) {
5549                 if (!Type.exists(this.selectionPolygon)) {
5550                     this._createSelectionPolygon(this.attr);
5551                 }
5552                 this.startSelectionMode();
5553             }
5554         },
5555 
5556         /**
5557          * Create the internal selection polygon, which will be available as board.selectionPolygon.
5558          * @private
5559          * @param  {Object} attr board attributes, e.g. the subobject board.attr.
5560          * @returns {Object} pointer to the board to enable chaining.
5561          */
5562         _createSelectionPolygon: function(attr) {
5563             var selectionattr;
5564 
5565             if (!Type.exists(this.selectionPolygon)) {
5566                 selectionattr = Type.copyAttributes(attr, Options, 'board', 'selection');
5567                 if (selectionattr.enabled === true) {
5568                     this.selectionPolygon = this.create('polygon', [[0, 0], [0, 0], [0, 0], [0, 0]], selectionattr);
5569                 }
5570             }
5571 
5572             return this;
5573         },
5574 
5575         /* **************************
5576          *     EVENT DEFINITION
5577          * for documentation purposes
5578          * ************************** */
5579 
5580         //region Event handler documentation
5581 
5582         /**
5583          * @event
5584          * @description Whenever the user starts to touch or click the board.
5585          * @name JXG.Board#down
5586          * @param {Event} e The browser's event object.
5587          */
5588         __evt__down: function (e) { },
5589 
5590         /**
5591          * @event
5592          * @description Whenever the user starts to click on the board.
5593          * @name JXG.Board#mousedown
5594          * @param {Event} e The browser's event object.
5595          */
5596         __evt__mousedown: function (e) { },
5597 
5598         /**
5599          * @event
5600          * @description Whenever the user taps the pen on the board.
5601          * @name JXG.Board#pendown
5602          * @param {Event} e The browser's event object.
5603          */
5604         __evt__pendown: function (e) { },
5605 
5606         /**
5607          * @event
5608          * @description Whenever the user starts to click on the board with a
5609          * device sending pointer events.
5610          * @name JXG.Board#pointerdown
5611          * @param {Event} e The browser's event object.
5612          */
5613         __evt__pointerdown: function (e) { },
5614 
5615         /**
5616          * @event
5617          * @description Whenever the user starts to touch the board.
5618          * @name JXG.Board#touchstart
5619          * @param {Event} e The browser's event object.
5620          */
5621         __evt__touchstart: function (e) { },
5622 
5623         /**
5624          * @event
5625          * @description Whenever the user stops to touch or click the board.
5626          * @name JXG.Board#up
5627          * @param {Event} e The browser's event object.
5628          */
5629         __evt__up: function (e) { },
5630 
5631         /**
5632          * @event
5633          * @description Whenever the user releases the mousebutton over the board.
5634          * @name JXG.Board#mouseup
5635          * @param {Event} e The browser's event object.
5636          */
5637         __evt__mouseup: function (e) { },
5638 
5639         /**
5640          * @event
5641          * @description Whenever the user releases the mousebutton over the board with a
5642          * device sending pointer events.
5643          * @name JXG.Board#pointerup
5644          * @param {Event} e The browser's event object.
5645          */
5646         __evt__pointerup: function (e) { },
5647 
5648         /**
5649          * @event
5650          * @description Whenever the user stops touching the board.
5651          * @name JXG.Board#touchend
5652          * @param {Event} e The browser's event object.
5653          */
5654         __evt__touchend: function (e) { },
5655 
5656         /**
5657          * @event
5658          * @description This event is fired whenever the user is moving the finger or mouse pointer over the board.
5659          * @name JXG.Board#move
5660          * @param {Event} e The browser's event object.
5661          * @param {Number} mode The mode the board currently is in
5662          * @see JXG.Board#mode
5663          */
5664         __evt__move: function (e, mode) { },
5665 
5666         /**
5667          * @event
5668          * @description This event is fired whenever the user is moving the mouse over the board.
5669          * @name JXG.Board#mousemove
5670          * @param {Event} e The browser's event object.
5671          * @param {Number} mode The mode the board currently is in
5672          * @see JXG.Board#mode
5673          */
5674         __evt__mousemove: function (e, mode) { },
5675 
5676         /**
5677          * @event
5678          * @description This event is fired whenever the user is moving the pen over the board.
5679          * @name JXG.Board#penmove
5680          * @param {Event} e The browser's event object.
5681          * @param {Number} mode The mode the board currently is in
5682          * @see JXG.Board#mode
5683          */
5684         __evt__penmove: function (e, mode) { },
5685 
5686         /**
5687          * @event
5688          * @description This event is fired whenever the user is moving the mouse over the board  with a
5689          * device sending pointer events.
5690          * @name JXG.Board#pointermove
5691          * @param {Event} e The browser's event object.
5692          * @param {Number} mode The mode the board currently is in
5693          * @see JXG.Board#mode
5694          */
5695         __evt__pointermove: function (e, mode) { },
5696 
5697         /**
5698          * @event
5699          * @description This event is fired whenever the user is moving the finger over the board.
5700          * @name JXG.Board#touchmove
5701          * @param {Event} e The browser's event object.
5702          * @param {Number} mode The mode the board currently is in
5703          * @see JXG.Board#mode
5704          */
5705         __evt__touchmove: function (e, mode) { },
5706 
5707         /**
5708          * @event
5709          * @description Whenever an element is highlighted this event is fired.
5710          * @name JXG.Board#hit
5711          * @param {Event} e The browser's event object.
5712          * @param {JXG.GeometryElement} el The hit element.
5713          * @param target
5714          *
5715          * @example
5716          * var c = board.create('circle', [[1, 1], 2]);
5717          * board.on('hit', function(evt, el) {
5718          *     console.log("Hit element", el);
5719          * });
5720          *
5721          * </pre><div id="JXG19eb31ac-88e6-11e8-bcb5-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
5722          * <script type="text/javascript">
5723          *     (function() {
5724          *         var board = JXG.JSXGraph.initBoard('JXG19eb31ac-88e6-11e8-bcb5-901b0e1b8723',
5725          *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
5726          *     var c = board.create('circle', [[1, 1], 2]);
5727          *     board.on('hit', function(evt, el) {
5728          *         console.log("Hit element", el);
5729          *     });
5730          *
5731          *     })();
5732          *
5733          * </script><pre>
5734          */
5735         __evt__hit: function (e, el, target) { },
5736 
5737         /**
5738          * @event
5739          * @description Whenever an element is highlighted this event is fired.
5740          * @name JXG.Board#mousehit
5741          * @see JXG.Board#hit
5742          * @param {Event} e The browser's event object.
5743          * @param {JXG.GeometryElement} el The hit element.
5744          * @param target
5745          */
5746         __evt__mousehit: function (e, el, target) { },
5747 
5748         /**
5749          * @event
5750          * @description This board is updated.
5751          * @name JXG.Board#update
5752          */
5753         __evt__update: function () { },
5754 
5755         /**
5756          * @event
5757          * @description The bounding box of the board has changed.
5758          * @name JXG.Board#boundingbox
5759          */
5760         __evt__boundingbox: function () { },
5761 
5762         /**
5763          * @event
5764          * @description Select a region is started during a down event or by calling
5765          * {@link JXG.Board.startSelectionMode}
5766          * @name JXG.Board#startselecting
5767          */
5768          __evt__startselecting: function () { },
5769 
5770          /**
5771          * @event
5772          * @description Select a region is started during a down event
5773          * from a device sending mouse events or by calling
5774          * {@link JXG.Board.startSelectionMode}.
5775          * @name JXG.Board#mousestartselecting
5776          */
5777          __evt__mousestartselecting: function () { },
5778 
5779          /**
5780          * @event
5781          * @description Select a region is started during a down event
5782          * from a device sending pointer events or by calling
5783          * {@link JXG.Board.startSelectionMode}.
5784          * @name JXG.Board#pointerstartselecting
5785          */
5786          __evt__pointerstartselecting: function () { },
5787 
5788          /**
5789          * @event
5790          * @description Select a region is started during a down event
5791          * from a device sending touch events or by calling
5792          * {@link JXG.Board.startSelectionMode}.
5793          * @name JXG.Board#touchstartselecting
5794          */
5795          __evt__touchstartselecting: function () { },
5796 
5797          /**
5798           * @event
5799           * @description Selection of a region is stopped during an up event.
5800           * @name JXG.Board#stopselecting
5801           */
5802          __evt__stopselecting: function () { },
5803 
5804          /**
5805          * @event
5806          * @description Selection of a region is stopped during an up event
5807          * from a device sending mouse events.
5808          * @name JXG.Board#mousestopselecting
5809          */
5810          __evt__mousestopselecting: function () { },
5811 
5812          /**
5813          * @event
5814          * @description Selection of a region is stopped during an up event
5815          * from a device sending pointer events.
5816          * @name JXG.Board#pointerstopselecting
5817          */
5818          __evt__pointerstopselecting: function () { },
5819 
5820          /**
5821          * @event
5822          * @description Selection of a region is stopped during an up event
5823          * from a device sending touch events.
5824          * @name JXG.Board#touchstopselecting
5825          */
5826          __evt__touchstopselecting: function () { },
5827 
5828          /**
5829          * @event
5830          * @description A move event while selecting of a region is active.
5831          * @name JXG.Board#moveselecting
5832          */
5833          __evt__moveselecting: function () { },
5834 
5835          /**
5836          * @event
5837          * @description A move event while selecting of a region is active
5838          * from a device sending mouse events.
5839          * @name JXG.Board#mousemoveselecting
5840          */
5841          __evt__mousemoveselecting: function () { },
5842 
5843          /**
5844          * @event
5845          * @description Select a region is started during a down event
5846          * from a device sending mouse events.
5847          * @name JXG.Board#pointermoveselecting
5848          */
5849          __evt__pointermoveselecting: function () { },
5850 
5851          /**
5852          * @event
5853          * @description Select a region is started during a down event
5854          * from a device sending touch events.
5855          * @name JXG.Board#touchmoveselecting
5856          */
5857          __evt__touchmoveselecting: function () { },
5858 
5859         /**
5860          * @ignore
5861          */
5862         __evt: function () {},
5863 
5864         //endregion
5865 
5866         /**
5867          * Expand the JSXGraph construction to fullscreen.
5868          * In order to preserve the proportions of the JSXGraph element,
5869          * a wrapper div is created which is set to fullscreen.
5870          * <p>
5871          * The wrapping div has the CSS class 'jxgbox_wrap_private' which is
5872          * defined in the file 'jsxgraph.css'
5873          * <p>
5874          * This feature is not available on iPhones (as of December 2021).
5875          *
5876          * @param {String} id (Optional) id of the div element which is brought to fullscreen.
5877          * If not provided, this defaults to the JSXGraph div. However, it may be necessary for the aspect ratio trick
5878          * which using padding-bottom/top and an out div element. Then, the id of the outer div has to be supplied.
5879          *
5880          * @return {JXG.Board} Reference to the board
5881          *
5882          * @example
5883          * <div id='jxgbox' class='jxgbox' style='width:500px; height:200px;'></div>
5884          * <button onClick="board.toFullscreen()">Fullscreen</button>
5885          *
5886          * <script language="Javascript" type='text/javascript'>
5887          * var board = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-5,5,5,-5]});
5888          * var p = board.create('point', [0, 1]);
5889          * </script>
5890          *
5891          * </pre><div id="JXGd5bab8b6-fd40-11e8-ab14-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
5892          * <script type="text/javascript">
5893          *      var board_d5bab8b6;
5894          *     (function() {
5895          *         var board = JXG.JSXGraph.initBoard('JXGd5bab8b6-fd40-11e8-ab14-901b0e1b8723',
5896          *             {boundingbox:[-5,5,5,-5], axis: true, showcopyright: false, shownavigation: false});
5897          *         var p = board.create('point', [0, 1]);
5898          *         board_d5bab8b6 = board;
5899          *     })();
5900          * </script>
5901          * <button onClick="board_d5bab8b6.toFullscreen()">Fullscreen</button>
5902          * <pre>
5903          *
5904          * @example
5905          * <div id='outer' style='max-width: 500px; margin: 0 auto;'>
5906          * <div id='jxgbox' class='jxgbox' style='height: 0; padding-bottom: 100%'></div>
5907          * </div>
5908          * <button onClick="board.toFullscreen('outer')">Fullscreen</button>
5909          *
5910          * <script language="Javascript" type='text/javascript'>
5911          * var board = JXG.JSXGraph.initBoard('jxgbox', {
5912          *     axis:true,
5913          *     boundingbox:[-5,5,5,-5],
5914          *     fullscreen: { id: 'outer' },
5915          *     showFullscreen: true
5916          * });
5917          * var p = board.create('point', [-2, 3], {});
5918          * </script>
5919          *
5920          * </pre><div id="JXG7103f6b_outer" style='max-width: 500px; margin: 0 auto;'>
5921          * <div id="JXG7103f6be-6993-4ff8-8133-c78e50a8afac" class="jxgbox" style="height: 0; padding-bottom: 100%;"></div>
5922          * </div>
5923          * <button onClick="board_JXG7103f6be.toFullscreen('JXG7103f6b_outer')">Fullscreen</button>
5924          * <script type="text/javascript">
5925          *     var board_JXG7103f6be;
5926          *     (function() {
5927          *         var board = JXG.JSXGraph.initBoard('JXG7103f6be-6993-4ff8-8133-c78e50a8afac',
5928          *             {boundingbox: [-8, 8, 8,-8], axis: true, fullscreen: { id: 'JXG7103f6b_outer' }, showFullscreen: true,
5929          *              showcopyright: false, shownavigation: false});
5930          *     var p = board.create('point', [-2, 3], {});
5931          *     board_JXG7103f6be = board;
5932          *     })();
5933          *
5934          * </script><pre>
5935          *
5936          *
5937          */
5938         toFullscreen: function (id) {
5939             var wrap_id, wrap_node, inner_node;
5940 
5941             id = id || this.container;
5942             this._fullscreen_inner_id = id;
5943             inner_node = document.getElementById(id);
5944             wrap_id = 'fullscreenwrap_' + id;
5945 
5946             // Wrap a div around the JSXGraph div.
5947             if (this.document.getElementById(wrap_id)) {
5948                 wrap_node = this.document.getElementById(wrap_id);
5949             } else {
5950                 wrap_node = document.createElement('div');
5951                 wrap_node.classList.add('JXG_wrap_private');
5952                 wrap_node.setAttribute('id', wrap_id);
5953                 inner_node.parentNode.insertBefore(wrap_node, inner_node);
5954                 wrap_node.appendChild(inner_node);
5955             }
5956 
5957             // Get the real width and height of the JSXGraph div
5958             // and determine the scaling and vertical shift amount
5959             this._fullscreen_res = Env._getScaleFactors(inner_node);
5960 
5961             // Trigger fullscreen mode
5962             wrap_node.requestFullscreen = wrap_node.requestFullscreen ||
5963                 wrap_node.webkitRequestFullscreen ||
5964                 wrap_node.mozRequestFullScreen ||
5965                 wrap_node.msRequestFullscreen;
5966 
5967             if (wrap_node.requestFullscreen) {
5968                 wrap_node.requestFullscreen();
5969             }
5970 
5971             return this;
5972         },
5973 
5974         /**
5975          * If fullscreen mode is toggled, the possible CSS transformations
5976          * which are applied to the JSXGraph canvas have to be reread.
5977          * Otherwise the position of upper left corner is wrongly interpreted.
5978          *
5979          * @param  {Object} evt fullscreen event object (unused)
5980          */
5981         fullscreenListener: function (evt) {
5982             var res, inner_id, inner_node;
5983 
5984             inner_id = this._fullscreen_inner_id;
5985             if (!Type.exists(inner_id)) {
5986                 return;
5987             }
5988 
5989             document.fullscreenElement = document.fullscreenElement ||
5990                     document.webkitFullscreenElement ||
5991                     document.mozFullscreenElement ||
5992                     document.msFullscreenElement;
5993 
5994             inner_node = document.getElementById(inner_id);
5995             // If full screen mode is started we have to remove CSS margin around the JSXGraph div.
5996             // Otherwise, the positioning of the fullscreen div will be false.
5997             // When leaving the fullscreen mode, the margin is put back in.
5998             if (document.fullscreenElement) {
5999                 // Just entered fullscreen mode
6000 
6001                 // Get the data computed in board.toFullscreen()
6002                 res = this._fullscreen_res;
6003 
6004                 // Store the scaling data.
6005                 // It is used in AbstractRenderer.updateText to restore the scaling matrix
6006                 // which is removed by MathJax.
6007                 // Further, the CSS margin has to be removed when in fullscreen mode,
6008                 // and must be restored later.
6009                 inner_node._cssFullscreenStore = {
6010                     id: document.fullscreenElement.id,
6011                     isFullscreen: true,
6012                     margin: inner_node.style.margin,
6013                     width: inner_node.style.width,
6014                     scale: res.scale,
6015                     vshift: res.vshift
6016                 };
6017 
6018                 inner_node.style.margin = '';
6019                 inner_node.style.width = res.width + 'px';
6020 
6021                 // Do the shifting and scaling via CSS pseudo rules
6022                 // We do this after fullscreen mode has been established to get the correct size
6023                 // of the JSXGraph div.
6024                 Env.scaleJSXGraphDiv(document.fullscreenElement.id, inner_id, res.scale, res.vshift);
6025 
6026                 // Clear document.fullscreenElement, because Safari doesn't to it and
6027                 // when leaving full screen mode it is still set.
6028                 document.fullscreenElement = null;
6029 
6030             } else if (Type.exists(inner_node._cssFullscreenStore)) {
6031                 // Just left the fullscreen mode
6032 
6033                 // Remove the CSS rules added in Env.scaleJSXGraphDiv
6034                 try {
6035                     document.styleSheets[document.styleSheets.length - 1].deleteRule(0);
6036                 } catch (err) {
6037                     console.log('JSXGraph: Could not remove CSS rules for full screen mode');
6038                 }
6039 
6040                 inner_node._cssFullscreenStore.isFullscreen = false;
6041                 inner_node.style.margin = inner_node._cssFullscreenStore.margin;
6042                 inner_node.style.width = inner_node._cssFullscreenStore.width;
6043 
6044             }
6045 
6046             this.updateCSSTransforms();
6047         },
6048 
6049         /**
6050          * Function to animate a curve rolling on another curve.
6051          * @param {Curve} c1 JSXGraph curve building the floor where c2 rolls
6052          * @param {Curve} c2 JSXGraph curve which rolls on c1.
6053          * @param {number} start_c1 The parameter t such that c1(t) touches c2. This is the start position of the
6054          *                          rolling process
6055          * @param {Number} stepsize Increase in t in each step for the curve c1
6056          * @param {Number} direction
6057          * @param {Number} time Delay time for setInterval()
6058          * @param {Array} pointlist Array of points which are rolled in each step. This list should contain
6059          *      all points which define c2 and gliders on c2.
6060          *
6061          * @example
6062          *
6063          * // Line which will be the floor to roll upon.
6064          * var line = brd.create('curve', [function (t) { return t;}, function (t){ return 1;}], {strokeWidth:6});
6065          * // Center of the rolling circle
6066          * var C = brd.create('point',[0,2],{name:'C'});
6067          * // Starting point of the rolling circle
6068          * var P = brd.create('point',[0,1],{name:'P', trace:true});
6069          * // Circle defined as a curve. The circle "starts" at P, i.e. circle(0) = P
6070          * var circle = brd.create('curve',[
6071          *           function (t){var d = P.Dist(C),
6072          *                           beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);
6073          *                       t += beta;
6074          *                       return C.X()+d*Math.cos(t);
6075          *           },
6076          *           function (t){var d = P.Dist(C),
6077          *                           beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);
6078          *                       t += beta;
6079          *                       return C.Y()+d*Math.sin(t);
6080          *           },
6081          *           0,2*Math.PI],
6082          *           {strokeWidth:6, strokeColor:'green'});
6083          *
6084          * // Point on circle
6085          * var B = brd.create('glider',[0,2,circle],{name:'B', color:'blue',trace:false});
6086          * var roll = brd.createRoulette(line, circle, 0, Math.PI/20, 1, 100, [C,P,B]);
6087          * roll.start() // Start the rolling, to be stopped by roll.stop()
6088          *
6089          * </pre><div class="jxgbox" id="JXGe5e1b53c-a036-4a46-9e35-190d196beca5" style="width: 300px; height: 300px;"></div>
6090          * <script type="text/javascript">
6091          * var brd = JXG.JSXGraph.initBoard('JXGe5e1b53c-a036-4a46-9e35-190d196beca5', {boundingbox: [-5, 5, 5, -5], axis: true, showcopyright:false, shownavigation: false});
6092          * // Line which will be the floor to roll upon.
6093          * var line = brd.create('curve', [function (t) { return t;}, function (t){ return 1;}], {strokeWidth:6});
6094          * // Center of the rolling circle
6095          * var C = brd.create('point',[0,2],{name:'C'});
6096          * // Starting point of the rolling circle
6097          * var P = brd.create('point',[0,1],{name:'P', trace:true});
6098          * // Circle defined as a curve. The circle "starts" at P, i.e. circle(0) = P
6099          * var circle = brd.create('curve',[
6100          *           function (t){var d = P.Dist(C),
6101          *                           beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);
6102          *                       t += beta;
6103          *                       return C.X()+d*Math.cos(t);
6104          *           },
6105          *           function (t){var d = P.Dist(C),
6106          *                           beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);
6107          *                       t += beta;
6108          *                       return C.Y()+d*Math.sin(t);
6109          *           },
6110          *           0,2*Math.PI],
6111          *           {strokeWidth:6, strokeColor:'green'});
6112          *
6113          * // Point on circle
6114          * var B = brd.create('glider',[0,2,circle],{name:'B', color:'blue',trace:false});
6115          * var roll = brd.createRoulette(line, circle, 0, Math.PI/20, 1, 100, [C,P,B]);
6116          * roll.start() // Start the rolling, to be stopped by roll.stop()
6117          * </script><pre>
6118          */
6119         createRoulette: function (c1, c2, start_c1, stepsize, direction, time, pointlist) {
6120             var brd = this,
6121                 Roulette = function () {
6122                     var alpha = 0, Tx = 0, Ty = 0,
6123                         t1 = start_c1,
6124                         t2 = Numerics.root(
6125                             function (t) {
6126                                 var c1x = c1.X(t1),
6127                                     c1y = c1.Y(t1),
6128                                     c2x = c2.X(t),
6129                                     c2y = c2.Y(t);
6130 
6131                                 return (c1x - c2x) * (c1x - c2x) + (c1y - c2y) * (c1y - c2y);
6132                             },
6133                             [0, Math.PI * 2]
6134                         ),
6135                         t1_new = 0.0, t2_new = 0.0,
6136                         c1dist,
6137 
6138                         rotation = brd.create('transform', [
6139                             function () {
6140                                 return alpha;
6141                             }
6142                         ], {type: 'rotate'}),
6143 
6144                         rotationLocal = brd.create('transform', [
6145                             function () {
6146                                 return alpha;
6147                             },
6148                             function () {
6149                                 return c1.X(t1);
6150                             },
6151                             function () {
6152                                 return c1.Y(t1);
6153                             }
6154                         ], {type: 'rotate'}),
6155 
6156                         translate = brd.create('transform', [
6157                             function () {
6158                                 return Tx;
6159                             },
6160                             function () {
6161                                 return Ty;
6162                             }
6163                         ], {type: 'translate'}),
6164 
6165                         // arc length via Simpson's rule.
6166                         arclen = function (c, a, b) {
6167                             var cpxa = Numerics.D(c.X)(a),
6168                                 cpya = Numerics.D(c.Y)(a),
6169                                 cpxb = Numerics.D(c.X)(b),
6170                                 cpyb = Numerics.D(c.Y)(b),
6171                                 cpxab = Numerics.D(c.X)((a + b) * 0.5),
6172                                 cpyab = Numerics.D(c.Y)((a + b) * 0.5),
6173 
6174                                 fa = Math.sqrt(cpxa * cpxa + cpya * cpya),
6175                                 fb = Math.sqrt(cpxb * cpxb + cpyb * cpyb),
6176                                 fab = Math.sqrt(cpxab * cpxab + cpyab * cpyab);
6177 
6178                             return (fa + 4 * fab + fb) * (b - a) / 6;
6179                         },
6180 
6181                         exactDist = function (t) {
6182                             return c1dist - arclen(c2, t2, t);
6183                         },
6184 
6185                         beta = Math.PI / 18,
6186                         beta9 = beta * 9,
6187                         interval = null;
6188 
6189                     this.rolling = function () {
6190                         var h, g, hp, gp, z;
6191 
6192                         t1_new = t1 + direction * stepsize;
6193 
6194                         // arc length between c1(t1) and c1(t1_new)
6195                         c1dist = arclen(c1, t1, t1_new);
6196 
6197                         // find t2_new such that arc length between c2(t2) and c1(t2_new) equals c1dist.
6198                         t2_new = Numerics.root(exactDist, t2);
6199 
6200                         // c1(t) as complex number
6201                         h = new Complex(c1.X(t1_new), c1.Y(t1_new));
6202 
6203                         // c2(t) as complex number
6204                         g = new Complex(c2.X(t2_new), c2.Y(t2_new));
6205 
6206                         hp = new Complex(Numerics.D(c1.X)(t1_new), Numerics.D(c1.Y)(t1_new));
6207                         gp = new Complex(Numerics.D(c2.X)(t2_new), Numerics.D(c2.Y)(t2_new));
6208 
6209                         // z is angle between the tangents of c1 at t1_new, and c2 at t2_new
6210                         z = Complex.C.div(hp, gp);
6211 
6212                         alpha = Math.atan2(z.imaginary, z.real);
6213                         // Normalizing the quotient
6214                         z.div(Complex.C.abs(z));
6215                         z.mult(g);
6216                         Tx = h.real - z.real;
6217 
6218                         // T = h(t1_new)-g(t2_new)*h'(t1_new)/g'(t2_new);
6219                         Ty = h.imaginary - z.imaginary;
6220 
6221                         // -(10-90) degrees: make corners roll smoothly
6222                         if (alpha < -beta && alpha > -beta9) {
6223                             alpha = -beta;
6224                             rotationLocal.applyOnce(pointlist);
6225                         } else if (alpha > beta && alpha < beta9) {
6226                             alpha = beta;
6227                             rotationLocal.applyOnce(pointlist);
6228                         } else {
6229                             rotation.applyOnce(pointlist);
6230                             translate.applyOnce(pointlist);
6231                             t1 = t1_new;
6232                             t2 = t2_new;
6233                         }
6234                         brd.update();
6235                     };
6236 
6237                     this.start = function () {
6238                         if (time > 0) {
6239                             interval = window.setInterval(this.rolling, time);
6240                         }
6241                         return this;
6242                     };
6243 
6244                     this.stop = function () {
6245                         window.clearInterval(interval);
6246                         return this;
6247                     };
6248                     return this;
6249                 };
6250             return new Roulette();
6251         }
6252     });
6253 
6254     return JXG.Board;
6255 });
6256