1 /*
  2     Copyright 2008-2021
  3         Matthias Ehmann,
  4         Michael Gerhaeuser,
  5         Carsten Miller,
  6         Bianca Valentin,
  7         Alfred Wassermann,
  8         Peter Wilfahrt
  9 
 10     This file is part of JSXGraph.
 11 
 12     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
 13 
 14     You can redistribute it and/or modify it under the terms of the
 15 
 16       * GNU Lesser General Public License as published by
 17         the Free Software Foundation, either version 3 of the License, or
 18         (at your option) any later version
 19       OR
 20       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
 21 
 22     JSXGraph is distributed in the hope that it will be useful,
 23     but WITHOUT ANY WARRANTY; without even the implied warranty of
 24     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 25     GNU Lesser General Public License for more details.
 26 
 27     You should have received a copy of the GNU Lesser General Public License and
 28     the MIT License along with JSXGraph. If not, see <http://www.gnu.org/licenses/>
 29     and <http://opensource.org/licenses/MIT/>.
 30  */
 31 
 32 
 33 /*global JXG: true, define: true, AMprocessNode: true, MathJax: true, window: true, document: true, init: true, translateASCIIMath: true, google: true*/
 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.
902             // see https://groups.google.com/d/msg/google-translate-general/H2zj0TNjjpY/jw6irtPlCw8J
903             if (typeof google === 'object' && google.translate) {
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.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                 } else if (evt.touches.length == 2 &&
2264                             (this.mode === this.BOARD_MODE_NONE || this.mode === this.BOARD_MODE_MOVE_ORIGIN)
2265                         ) {
2266                     // 2. case: two fingers: pinch to zoom or pan with two fingers needed.
2267                     // This happens when the second finger hits the device. First, the
2268                     // "one finger pan mode" has to be cancelled.
2269                     if (this.mode === this.BOARD_MODE_MOVE_ORIGIN) {
2270                         this.originMoveEnd();
2271                     }
2272 
2273                     this.gestureStartListener(evt);
2274                 }
2275             }
2276 
2277             this.triggerEventHandlers(['touchstart', 'down', 'pointerdown', 'MSPointerDown'], [evt]);
2278             return false;
2279         },
2280 
2281         // /**
2282         //  * Called if pointer leaves an HTML tag. It is called by the inner-most tag.
2283         //  * That means, if a JSXGraph text, i.e. an HTML div, is placed close
2284         //  * to the border of the board, this pointerout event will be ignored.
2285         //  * @param  {Event} evt
2286         //  * @return {Boolean}
2287         //  */
2288         // pointerOutListener: function (evt) {
2289         //     if (evt.target === this.containerObj ||
2290         //         (this.renderer.type === 'svg' && evt.target === this.renderer.foreignObjLayer)) {
2291         //         this.pointerUpListener(evt);
2292         //     }
2293         //     return this.mode === this.BOARD_MODE_NONE;
2294         // },
2295 
2296         /**
2297          * Called periodically by the browser while the user moves a pointing device across the screen.
2298          * @param {Event} evt
2299          * @returns {Boolean}
2300          */
2301         pointerMoveListener: function (evt) {
2302             var i, j, pos, touchTargets,
2303                 type = 'mouse'; // in case of no browser
2304 
2305             if (this._getPointerInputDevice(evt) === 'touch' && !this._isPointerRegistered(evt)) {
2306                 // Test, if there was a previous down event of this _getPointerId
2307                 // (in case it is a touch event).
2308                 // Otherwise this move event is ignored. This is necessary e.g. for sketchometry.
2309                 return this.BOARD_MODE_NONE;
2310             }
2311 
2312             if (!this.checkFrameRate(evt)) {
2313                 return false;
2314             }
2315 
2316             if (this.mode !== this.BOARD_MODE_DRAG) {
2317                 this.dehighlightAll();
2318                 this.displayInfobox(false);
2319             }
2320 
2321             if (this.mode !== this.BOARD_MODE_NONE) {
2322                 evt.preventDefault();
2323                 evt.stopPropagation();
2324             }
2325 
2326             this.updateQuality = this.BOARD_QUALITY_LOW;
2327             // Mouse, touch or pen device
2328             this._inputDevice = this._getPointerInputDevice(evt);
2329             type = this._inputDevice;
2330             this.options.precision.hasPoint = this.options.precision[type];
2331 
2332             // selection
2333             if (this.selectingMode) {
2334                 pos = this.getMousePosition(evt);
2335                 this._moveSelecting(pos);
2336                 this.triggerEventHandlers(['touchmoveselecting', 'moveselecting', 'pointermoveselecting'], [evt, this.mode]);
2337             } else if (!this.mouseOriginMove(evt)) {
2338                 if (this.mode === this.BOARD_MODE_DRAG) {
2339                     // Run through all jsxgraph elements which are touched by at least one finger.
2340                     for (i = 0; i < this.touches.length; i++) {
2341                         touchTargets = this.touches[i].targets;
2342                         // Run through all touch events which have been started on this jsxgraph element.
2343                         for (j = 0; j < touchTargets.length; j++) {
2344                             if (touchTargets[j].num === evt.pointerId) {
2345                                 
2346                                 pos = this.getMousePosition(evt);
2347                                 touchTargets[j].X = pos[0];
2348                                 touchTargets[j].Y = pos[1];
2349 
2350                                 if (touchTargets.length === 1) {
2351                                     // Touch by one finger: this is possible for all elements that can be dragged
2352                                     this.moveObject(pos[0], pos[1], this.touches[i], evt, type);
2353                                 } else if (touchTargets.length === 2) {
2354                                     // Touch by two fingers: e.g. moving lines
2355                                     this.twoFingerMove(this.touches[i], evt.pointerId, evt);
2356 
2357                                     touchTargets[j].Xprev = pos[0];
2358                                     touchTargets[j].Yprev = pos[1];
2359                                 }
2360 
2361                                 // There is only one pointer in the evt object, so there's no point in looking further
2362                                 break;
2363                             }
2364                         }
2365                     }
2366                 } else {
2367                     if (this._getPointerInputDevice(evt) === 'touch') {
2368                         this._pointerStorePosition(evt);
2369 
2370                         if (this._board_touches.length === 2) {
2371                             evt.touches = this._board_touches;
2372                             this.gestureChangeListener(evt);
2373                         }
2374                     }
2375 
2376                     // Move event without dragging an element
2377                     pos = this.getMousePosition(evt);
2378                     this.highlightElements(pos[0], pos[1], evt, -1);
2379                 }
2380             }
2381 
2382             // Hiding the infobox is commented out, since it prevents showing the infobox
2383             // on IE 11+ on 'over'
2384             //if (this.mode !== this.BOARD_MODE_DRAG) {
2385                 //this.displayInfobox(false);
2386             //}
2387             this.triggerEventHandlers(['touchmove', 'move', 'pointermove', 'MSPointerMove'], [evt, this.mode]);
2388             this.updateQuality = this.BOARD_QUALITY_HIGH;
2389 
2390             return this.mode === this.BOARD_MODE_NONE;
2391         },
2392 
2393         /**
2394          * Triggered as soon as the user stops touching the device with at least one finger.
2395          * @param {Event} evt
2396          * @returns {Boolean}
2397          */
2398         pointerUpListener: function (evt) {
2399             var i, j, found, touchTargets;
2400 
2401             this.triggerEventHandlers(['touchend', 'up', 'pointerup', 'MSPointerUp'], [evt]);
2402             this.displayInfobox(false);
2403 
2404             if (evt) {
2405                 for (i = 0; i < this.touches.length; i++) {
2406                     touchTargets = this.touches[i].targets;
2407                     for (j = 0; j < touchTargets.length; j++) {
2408                         if (touchTargets[j].num === evt.pointerId) {
2409                             touchTargets.splice(j, 1);
2410                             if (touchTargets.length === 0) {
2411                                 this.touches.splice(i, 1);
2412                             }
2413                             break;
2414                         }
2415                     }
2416                 }
2417             }
2418 
2419             // selection
2420             if (this.selectingMode) {
2421                 this._stopSelecting(evt);
2422                 this.triggerEventHandlers(['touchstopselecting', 'pointerstopselecting', 'stopselecting'], [evt]);
2423             } else {
2424                 for (i = this.downObjects.length - 1; i > -1; i--) {
2425                     found = false;
2426                     for (j = 0; j < this.touches.length; j++) {
2427                         if (this.touches[j].obj.id === this.downObjects[i].id) {
2428                             found = true;
2429                         }
2430                     }
2431                     if (!found) {
2432                         this.downObjects[i].triggerEventHandlers(['touchend', 'up', 'pointerup', 'MSPointerUp'], [evt]);
2433                         this.downObjects[i].snapToGrid();
2434                         this.downObjects[i].snapToPoints();
2435                         this.downObjects.splice(i, 1);
2436                     }
2437                 }
2438             }
2439 
2440             // this._pointerRemoveTouches(evt);
2441             // if (this._board_touches.length === 0) {
2442                 if (this.hasPointerUp) {
2443                     if (window.navigator.msPointerEnabled) {  // IE10-
2444                         Env.removeEvent(this.document, 'MSPointerUp',   this.pointerUpListener, this);
2445                     } else {
2446                         Env.removeEvent(this.document, 'pointerup',     this.pointerUpListener, this);
2447                         Env.removeEvent(this.document, 'pointercancel', this.pointerUpListener, this);
2448                     }
2449                     this.hasPointerUp = false;
2450                 }
2451 
2452                 // this.dehighlightAll();
2453                 // this.updateQuality = this.BOARD_QUALITY_HIGH;
2454                 // this.mode = this.BOARD_MODE_NONE;
2455 
2456                 this.originMoveEnd();
2457                 this.update();
2458             // }
2459             // After one finger leaves the screen the gesture is stopped.
2460             this._pointerClearTouches();
2461             return true;
2462         },
2463 
2464         /**
2465          * Touch-Events
2466          */
2467 
2468         /**
2469          * This method is called by the browser when a finger touches the surface of the touch-device.
2470          * @param {Event} evt The browsers event object.
2471          * @returns {Boolean} ...
2472          */
2473         touchStartListener: function (evt) {
2474             var i, pos, elements, j, k,
2475                 eps = this.options.precision.touch,
2476                 obj, found, targets,
2477                 evtTouches = evt[JXG.touchProperty],
2478                 target, touchTargets;
2479 
2480             if (!this.hasTouchEnd) {
2481                 Env.addEvent(this.document, 'touchend', this.touchEndListener, this);
2482                 this.hasTouchEnd = true;
2483             }
2484 
2485             // Do not remove mouseHandlers, since Chrome on win tablets sends mouseevents if used with pen.
2486             //if (this.hasMouseHandlers) { this.removeMouseEventHandlers(); }
2487 
2488             // prevent accidental selection of text
2489             if (this.document.selection && Type.isFunction(this.document.selection.empty)) {
2490                 this.document.selection.empty();
2491             } else if (window.getSelection) {
2492                 window.getSelection().removeAllRanges();
2493             }
2494 
2495             // multitouch
2496             this._inputDevice = 'touch';
2497             this.options.precision.hasPoint = this.options.precision.touch;
2498 
2499             // This is the most critical part. first we should run through the existing touches and collect all targettouches that don't belong to our
2500             // 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
2501             // 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
2502             // 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
2503             // stretching. as a last step we're going through the rest of the targettouches and initiate new move operations:
2504             //  * points have higher priority over other elements.
2505             //  * 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
2506             //    this element and add them.
2507             // ADDENDUM 11/10/11:
2508             //  (1) run through the touches control object,
2509             //  (2) try to find the targetTouches for every touch. on touchstart only new touches are added, hence we can find a targettouch
2510             //      for every target in our touches objects
2511             //  (3) if one of the targettouches was bound to a touches targets array, mark it
2512             //  (4) run through the targettouches. if the targettouch is marked, continue. otherwise check for elements below the targettouch:
2513             //      (a) if no element could be found: mark the target touches and continue
2514             //      --- in the following cases, "init" means:
2515             //           (i) check if the element is already used in another touches element, if so, mark the targettouch and continue
2516             //          (ii) if not, init a new touches element, add the targettouch to the touches property and mark it
2517             //      (b) if the element is a point, init
2518             //      (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
2519             //      (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
2520             //          add both to the touches array and mark them.
2521             for (i = 0; i < evtTouches.length; i++) {
2522                 evtTouches[i].jxg_isused = false;
2523             }
2524 
2525             for (i = 0; i < this.touches.length; i++) {
2526                 touchTargets = this.touches[i].targets;
2527                 for (j = 0; j < touchTargets.length; j++) {
2528                     touchTargets[j].num = -1;
2529                     eps = this.options.precision.touch;
2530 
2531                     do {
2532                         for (k = 0; k < evtTouches.length; k++) {
2533                             // find the new targettouches
2534                             if (Math.abs(Math.pow(evtTouches[k].screenX - touchTargets[j].X, 2) +
2535                                     Math.pow(evtTouches[k].screenY - touchTargets[j].Y, 2)) < eps * eps) {
2536                                 touchTargets[j].num = k;
2537                                 touchTargets[j].X = evtTouches[k].screenX;
2538                                 touchTargets[j].Y = evtTouches[k].screenY;
2539                                 evtTouches[k].jxg_isused = true;
2540                                 break;
2541                             }
2542                         }
2543 
2544                         eps *= 2;
2545 
2546                     } while (touchTargets[j].num === -1 &&
2547                              eps < this.options.precision.touchMax);
2548 
2549                     if (touchTargets[j].num === -1) {
2550                         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.');
2551                         JXG.debug('eps = ' + eps + ', touchMax = ' + Options.precision.touchMax);
2552                         touchTargets.splice(i, 1);
2553                     }
2554 
2555                 }
2556             }
2557 
2558             // we just re-mapped the targettouches to our existing touches list.
2559             // now we have to initialize some touches from additional targettouches
2560             for (i = 0; i < evtTouches.length; i++) {
2561                 if (!evtTouches[i].jxg_isused) {
2562 
2563                     pos = this.getMousePosition(evt, i);
2564                     // selection
2565                     // this._testForSelection(evt); // we do not have shift or ctrl keys yet.
2566                     if (this.selectingMode) {
2567                         this._startSelecting(pos);
2568                         this.triggerEventHandlers(['touchstartselecting', 'startselecting'], [evt]);
2569                         evt.preventDefault();
2570                         evt.stopPropagation();
2571                         this.options.precision.hasPoint = this.options.precision.mouse;
2572                         return this.touches.length > 0; // don't continue as a normal click
2573                     }
2574 
2575                     elements = this.initMoveObject(pos[0], pos[1], evt, 'touch');
2576                     if (elements.length !== 0) {
2577                         obj = elements[elements.length - 1];
2578                         target = {num: i,
2579                             X: evtTouches[i].screenX,
2580                             Y: evtTouches[i].screenY,
2581                             Xprev: NaN,
2582                             Yprev: NaN,
2583                             Xstart: [],
2584                             Ystart: [],
2585                             Zstart: [] 
2586                         };
2587 
2588                         if (Type.isPoint(obj) ||
2589                                 obj.elementClass === Const.OBJECT_CLASS_TEXT ||
2590                                 obj.type === Const.OBJECT_TYPE_TICKS ||
2591                                 obj.type === Const.OBJECT_TYPE_IMAGE) {
2592                             // It's a point, so it's single touch, so we just push it to our touches
2593                             targets = [target_obj];
2594 
2595                             // For the UNDO/REDO of object moves
2596                             this.saveStartPos(obj, targets[0]);
2597 
2598                             this.touches.push({ obj: obj, targets: targets });
2599                             obj.highlight(true);
2600 
2601                         } else if (obj.elementClass === Const.OBJECT_CLASS_LINE ||
2602                                 obj.elementClass === Const.OBJECT_CLASS_CIRCLE ||
2603                                 obj.elementClass === Const.OBJECT_CLASS_CURVE ||
2604                                 obj.type === Const.OBJECT_TYPE_POLYGON) {
2605                             found = false;
2606 
2607                             // first check if this geometric object is already captured in this.touches
2608                             for (j = 0; j < this.touches.length; j++) {
2609                                 if (obj.id === this.touches[j].obj.id) {
2610                                     found = true;
2611                                     // only add it, if we don't have two targets in there already
2612                                     if (this.touches[j].targets.length === 1) {
2613                                         // For the UNDO/REDO of object moves
2614                                         this.saveStartPos(obj, target);
2615                                         this.touches[j].targets.push(target);
2616                                     }
2617 
2618                                     evtTouches[i].jxg_isused = true;
2619                                 }
2620                             }
2621 
2622                             // we couldn't find it in touches, so we just init a new touches
2623                             // IF there is a second touch targetting this line, we will find it later on, and then add it to
2624                             // the touches control object.
2625                             if (!found) {
2626                                 targets = [target];
2627 
2628                                 // For the UNDO/REDO of object moves
2629                                 this.saveStartPos(obj, targets[0]);
2630                                 this.touches.push({ obj: obj, targets: targets });
2631                                 obj.highlight(true);
2632                             }
2633                         }
2634                     }
2635 
2636                     evtTouches[i].jxg_isused = true;
2637                 }
2638             }
2639 
2640             if (this.touches.length > 0) {
2641                 evt.preventDefault();
2642                 evt.stopPropagation();
2643             }
2644 
2645             // Touch events on empty areas of the board are handled here:
2646             // 1. case: one finger. If allowed, this triggers pan with one finger
2647             if (evtTouches.length === 1 && this.mode === this.BOARD_MODE_NONE && this.touchStartMoveOriginOneFinger(evt)) {
2648             } else if (evtTouches.length === 2 &&
2649                         (this.mode === this.BOARD_MODE_NONE || this.mode === this.BOARD_MODE_MOVE_ORIGIN)
2650                     ) {
2651                 // 2. case: two fingers: pinch to zoom or pan with two fingers needed.
2652                 // This happens when the second finger hits the device. First, the
2653                 // "one finger pan mode" has to be cancelled.
2654                 if (this.mode === this.BOARD_MODE_MOVE_ORIGIN) {
2655                     this.originMoveEnd();
2656                 }
2657                 this.gestureStartListener(evt);
2658             }
2659 
2660             this.options.precision.hasPoint = this.options.precision.mouse;
2661             this.triggerEventHandlers(['touchstart', 'down'], [evt]);
2662 
2663             return false;
2664             //return this.touches.length > 0;
2665         },
2666 
2667         /**
2668          * Called periodically by the browser while the user moves his fingers across the device.
2669          * @param {Event} evt
2670          * @returns {Boolean}
2671          */
2672         touchMoveListener: function (evt) {
2673             var i, pos1, pos2, 
2674                 time, touchTargets,
2675                 evtTouches = evt[JXG.touchProperty];
2676 
2677             if (!this.checkFrameRate(evt)) {
2678                 return false;
2679             }
2680 
2681             if (this.mode !== this.BOARD_MODE_NONE) {
2682                 evt.preventDefault();
2683                 evt.stopPropagation();
2684             }
2685 
2686             if (this.mode !== this.BOARD_MODE_DRAG) {
2687                 this.dehighlightAll();
2688                 this.displayInfobox(false);
2689             }
2690 
2691             this._inputDevice = 'touch';
2692             this.options.precision.hasPoint = this.options.precision.touch;
2693             this.updateQuality = this.BOARD_QUALITY_LOW;
2694 
2695             // selection
2696             if (this.selectingMode) {
2697                 for (i = 0; i < evtTouches.length; i++) {
2698                     if (!evtTouches[i].jxg_isused) {
2699                         pos1 = this.getMousePosition(evt, i);
2700                         this._moveSelecting(pos1);
2701                         this.triggerEventHandlers(['touchmoves', 'moveselecting'], [evt, this.mode]);
2702                         break;
2703                     }
2704                 }
2705             } else {
2706                 if (!this.touchOriginMove(evt)) {
2707                     if (this.mode === this.BOARD_MODE_DRAG) {
2708                         // Runs over through all elements which are touched
2709                         // by at least one finger.
2710                         for (i = 0; i < this.touches.length; i++) {
2711                             touchTargets = this.touches[i].targets;
2712                             if (touchTargets.length === 1) {
2713 
2714 
2715                                 // Touch by one finger:  this is possible for all elements that can be dragged
2716                                 if (evtTouches[touchTargets[0].num]) {
2717                                     pos1 = this.getMousePosition(evt, touchTargets[0].num);
2718                                     if (pos1[0] < 0 || pos1[0] > this.canvasWidth ||
2719                                         pos1[1] < 0 || pos1[1] > this.canvasHeight) {
2720                                         return;
2721                                     }
2722                                     touchTargets[0].X = pos1[0];
2723                                     touchTargets[0].Y = pos1[1];
2724                                     this.moveObject(pos1[0], pos1[1], this.touches[i], evt, 'touch');
2725                                 }
2726 
2727                             } else if (touchTargets.length === 2 &&
2728                                 touchTargets[0].num > -1 &&
2729                                 touchTargets[1].num > -1) {
2730 
2731                                 // Touch by two fingers: moving lines, ...
2732                                 if (evtTouches[touchTargets[0].num] &&
2733                                     evtTouches[touchTargets[1].num]) {
2734 
2735                                     // Get coordinates of the two touches
2736                                     pos1 = this.getMousePosition(evt, touchTargets[0].num);
2737                                     pos2 = this.getMousePosition(evt, touchTargets[1].num);
2738                                     if (pos1[0] < 0 || pos1[0] > this.canvasWidth ||
2739                                         pos1[1] < 0 || pos1[1] > this.canvasHeight ||
2740                                         pos2[0] < 0 || pos2[0] > this.canvasWidth ||
2741                                         pos2[1] < 0 || pos2[1] > this.canvasHeight) {
2742                                         return;
2743                                     }
2744 
2745                                     touchTargets[0].X = pos1[0];
2746                                     touchTargets[0].Y = pos1[1];
2747                                     touchTargets[1].X = pos2[0];
2748                                     touchTargets[1].Y = pos2[1];
2749 
2750                                     this.twoFingerMove(this.touches[i], touchTargets[0].num, evt);
2751                                     this.twoFingerMove(this.touches[i], touchTargets[1].num);
2752 
2753                                     touchTargets[0].Xprev = pos1[0];
2754                                     touchTargets[0].Yprev = pos1[1];
2755                                     touchTargets[1].Xprev = pos2[0];
2756                                     touchTargets[1].Yprev = pos2[1];
2757                                 }
2758                             }
2759                         }
2760                     } else {
2761                         if (evtTouches.length === 2) {
2762                             this.gestureChangeListener(evt);
2763                         }
2764                         // Move event without dragging an element
2765                         pos1 = this.getMousePosition(evt, 0);
2766                         this.highlightElements(pos1[0], pos1[1], evt, -1);
2767                     }
2768                 }
2769             }
2770 
2771             if (this.mode !== this.BOARD_MODE_DRAG) {
2772                 this.displayInfobox(false);
2773             }
2774 
2775             this.triggerEventHandlers(['touchmove', 'move'], [evt, this.mode]);
2776             this.options.precision.hasPoint = this.options.precision.mouse;
2777             this.updateQuality = this.BOARD_QUALITY_HIGH;
2778 
2779             return this.mode === this.BOARD_MODE_NONE;
2780         },
2781 
2782         /**
2783          * Triggered as soon as the user stops touching the device with at least one finger.
2784          * @param {Event} evt
2785          * @returns {Boolean}
2786          */
2787         touchEndListener: function (evt) {
2788             var i, j, k,
2789                 eps = this.options.precision.touch,
2790                 tmpTouches = [], found, foundNumber,
2791                 evtTouches = evt && evt[JXG.touchProperty],
2792                 touchTargets;
2793 
2794             this.triggerEventHandlers(['touchend', 'up'], [evt]);
2795             this.displayInfobox(false);
2796 
2797             // selection
2798             if (this.selectingMode) {
2799                 this._stopSelecting(evt);
2800                 this.triggerEventHandlers(['touchstopselecting', 'stopselecting'], [evt]);
2801             } else if (evtTouches && evtTouches.length > 0) {
2802                 for (i = 0; i < this.touches.length; i++) {
2803                     tmpTouches[i] = this.touches[i];
2804                 }
2805                 this.touches.length = 0;
2806 
2807                 // try to convert the operation, e.g. if a lines is rotated and translated with two fingers and one finger is lifted,
2808                 // convert the operation to a simple one-finger-translation.
2809                 // ADDENDUM 11/10/11:
2810                 // see addendum to touchStartListener from 11/10/11
2811                 // (1) run through the tmptouches
2812                 // (2) check the touches.obj, if it is a
2813                 //     (a) point, try to find the targettouch, if found keep it and mark the targettouch, else drop the touch.
2814                 //     (b) line with
2815                 //          (i) one target: try to find it, if found keep it mark the targettouch, else drop the touch.
2816                 //         (ii) two targets: if none can be found, drop the touch. if one can be found, remove the other target. mark all found targettouches
2817                 //     (c) circle with [proceed like in line]
2818 
2819                 // init the targettouches marker
2820                 for (i = 0; i < evtTouches.length; i++) {
2821                     evtTouches[i].jxg_isused = false;
2822                 }
2823 
2824                 for (i = 0; i < tmpTouches.length; i++) {
2825                     // could all targets of the current this.touches.obj be assigned to targettouches?
2826                     found = false;
2827                     foundNumber = 0;
2828                     touchTargets = tmpTouches[i].targets;
2829 
2830                     for (j = 0; j < touchTargets.length; j++) {
2831                         touchTargets[j].found = false;
2832                         for (k = 0; k < evtTouches.length; k++) {
2833                             if (Math.abs(Math.pow(evtTouches[k].screenX - touchTargets[j].X, 2) + Math.pow(evtTouches[k].screenY - touchTargets[j].Y, 2)) < eps * eps) {
2834                                 touchTargets[j].found = true;
2835                                 touchTargets[j].num = k;
2836                                 touchTargets[j].X = evtTouches[k].screenX;
2837                                 touchTargets[j].Y = evtTouches[k].screenY;
2838                                 foundNumber += 1;
2839                                 break;
2840                             }
2841                         }
2842                     }
2843 
2844                     if (Type.isPoint(tmpTouches[i].obj)) {
2845                         found = (touchTargets[0] && touchTargets[0].found);
2846                     } else if (tmpTouches[i].obj.elementClass === Const.OBJECT_CLASS_LINE) {
2847                         found = (touchTargets[0] && touchTargets[0].found) || (touchTargets[1] && touchTargets[1].found);
2848                     } else if (tmpTouches[i].obj.elementClass === Const.OBJECT_CLASS_CIRCLE) {
2849                         found = foundNumber === 1 || foundNumber === 3;
2850                     }
2851 
2852                     // if we found this object to be still dragged by the user, add it back to this.touches
2853                     if (found) {
2854                         this.touches.push({
2855                             obj: tmpTouches[i].obj,
2856                             targets: []
2857                         });
2858 
2859                         for (j = 0; j < touchTargets.length; j++) {
2860                             if (touchTargets[j].found) {
2861                                 this.touches[this.touches.length - 1].targets.push({
2862                                     num: touchTargets[j].num,
2863                                     X: touchTargets[j].screenX,
2864                                     Y: touchTargets[j].screenY,
2865                                     Xprev: NaN,
2866                                     Yprev: NaN,
2867                                     Xstart: touchTargets[j].Xstart,
2868                                     Ystart: touchTargets[j].Ystart,
2869                                     Zstart: touchTargets[j].Zstart
2870                                 });
2871                             }
2872                         }
2873 
2874                     } else {
2875                         tmpTouches[i].obj.noHighlight();
2876                     }
2877                 }
2878 
2879             } else {
2880                 this.touches.length = 0;
2881             }
2882 
2883             for (i = this.downObjects.length - 1; i > -1; i--) {
2884                 found = false;
2885                 for (j = 0; j < this.touches.length; j++) {
2886                     if (this.touches[j].obj.id === this.downObjects[i].id) {
2887                         found = true;
2888                     }
2889                 }
2890                 if (!found) {
2891                     this.downObjects[i].triggerEventHandlers(['touchup', 'up'], [evt]);
2892                     this.downObjects[i].snapToGrid();
2893                     this.downObjects[i].snapToPoints();
2894                     this.downObjects.splice(i, 1);
2895                 }
2896             }
2897 
2898             if (!evtTouches || evtTouches.length === 0) {
2899 
2900                 if (this.hasTouchEnd) {
2901                     Env.removeEvent(this.document, 'touchend', this.touchEndListener, this);
2902                     this.hasTouchEnd = false;
2903                 }
2904 
2905                 this.dehighlightAll();
2906                 this.updateQuality = this.BOARD_QUALITY_HIGH;
2907 
2908                 this.originMoveEnd();
2909                 this.update();
2910             }
2911 
2912             return true;
2913         },
2914 
2915         /**
2916          * This method is called by the browser when the mouse button is clicked.
2917          * @param {Event} evt The browsers event object.
2918          * @returns {Boolean} True if no element is found under the current mouse pointer, false otherwise.
2919          */
2920         mouseDownListener: function (evt) {
2921             var pos, elements, result;
2922 
2923             // prevent accidental selection of text
2924             if (this.document.selection && Type.isFunction(this.document.selection.empty)) {
2925                 this.document.selection.empty();
2926             } else if (window.getSelection) {
2927                 window.getSelection().removeAllRanges();
2928             }
2929 
2930             if (!this.hasMouseUp) {
2931                 Env.addEvent(this.document, 'mouseup', this.mouseUpListener, this);
2932                 this.hasMouseUp = true;
2933             } else {
2934                 // In case this.hasMouseUp==true, it may be that there was a
2935                 // mousedown event before which was not followed by an mouseup event.
2936                 // This seems to happen with interactive whiteboard pens sometimes.
2937                 return;
2938             }
2939 
2940             this._inputDevice = 'mouse';
2941             this.options.precision.hasPoint = this.options.precision.mouse;
2942             pos = this.getMousePosition(evt);
2943 
2944             // selection
2945             this._testForSelection(evt);
2946             if (this.selectingMode) {
2947                 this._startSelecting(pos);
2948                 this.triggerEventHandlers(['mousestartselecting', 'startselecting'], [evt]);
2949                 return;     // don't continue as a normal click
2950             }
2951 
2952             elements = this.initMoveObject(pos[0], pos[1], evt, 'mouse');
2953 
2954             // if no draggable object can be found, get out here immediately
2955             if (elements.length === 0) {
2956                 this.mode = this.BOARD_MODE_NONE;
2957                 result = true;
2958             } else {
2959                 /** @ignore */
2960                 this.mouse = {
2961                     obj: null,
2962                     targets: [{
2963                         X: pos[0],
2964                         Y: pos[1],
2965                         Xprev: NaN,
2966                         Yprev: NaN
2967                     }]
2968                 };
2969                 this.mouse.obj = elements[elements.length - 1];
2970 
2971                 this.dehighlightAll();
2972                 this.mouse.obj.highlight(true);
2973 
2974                 this.mouse.targets[0].Xstart = [];
2975                 this.mouse.targets[0].Ystart = [];
2976                 this.mouse.targets[0].Zstart = [];
2977 
2978                 this.saveStartPos(this.mouse.obj, this.mouse.targets[0]);
2979 
2980                 // prevent accidental text selection
2981                 // this could get us new trouble: input fields, links and drop down boxes placed as text
2982                 // on the board don't work anymore.
2983                 if (evt && evt.preventDefault) {
2984                     evt.preventDefault();
2985                 } else if (window.event) {
2986                     window.event.returnValue = false;
2987                 }
2988             }
2989 
2990             if (this.mode === this.BOARD_MODE_NONE) {
2991                 result = this.mouseOriginMoveStart(evt);
2992             }
2993 
2994             this.triggerEventHandlers(['mousedown', 'down'], [evt]);
2995 
2996             return result;
2997         },
2998 
2999         /**
3000          * This method is called by the browser when the mouse is moved.
3001          * @param {Event} evt The browsers event object.
3002          */
3003         mouseMoveListener: function (evt) {
3004             var pos;
3005 
3006             if (!this.checkFrameRate(evt)) {
3007                 return false;
3008             }
3009 
3010             pos = this.getMousePosition(evt);
3011 
3012             this.updateQuality = this.BOARD_QUALITY_LOW;
3013 
3014             if (this.mode !== this.BOARD_MODE_DRAG) {
3015                 this.dehighlightAll();
3016                 this.displayInfobox(false);
3017             }
3018 
3019             // we have to check for four cases:
3020             //   * user moves origin
3021             //   * user drags an object
3022             //   * user just moves the mouse, here highlight all elements at
3023             //     the current mouse position
3024             //   * the user is selecting
3025 
3026             // selection
3027             if (this.selectingMode) {
3028                 this._moveSelecting(pos);
3029                 this.triggerEventHandlers(['mousemoveselecting', 'moveselecting'], [evt, this.mode]);
3030             } else if (!this.mouseOriginMove(evt)) {
3031                 if (this.mode === this.BOARD_MODE_DRAG) {
3032                     this.moveObject(pos[0], pos[1], this.mouse, evt, 'mouse');
3033                 } else { // BOARD_MODE_NONE
3034                     // Move event without dragging an element
3035                     this.highlightElements(pos[0], pos[1], evt, -1);
3036                 }
3037                 this.triggerEventHandlers(['mousemove', 'move'], [evt, this.mode]);
3038             }
3039             this.updateQuality = this.BOARD_QUALITY_HIGH;
3040         },
3041 
3042         /**
3043          * This method is called by the browser when the mouse button is released.
3044          * @param {Event} evt
3045          */
3046         mouseUpListener: function (evt) {
3047             var i;
3048 
3049             if (this.selectingMode === false) {
3050                 this.triggerEventHandlers(['mouseup', 'up'], [evt]);
3051             }
3052 
3053             // redraw with high precision
3054             this.updateQuality = this.BOARD_QUALITY_HIGH;
3055 
3056             if (this.mouse && this.mouse.obj) {
3057                 // The parameter is needed for lines with snapToGrid enabled
3058                 this.mouse.obj.snapToGrid(this.mouse.targets[0]);
3059                 this.mouse.obj.snapToPoints();
3060             }
3061 
3062             this.originMoveEnd();
3063             this.dehighlightAll();
3064             this.update();
3065 
3066             // selection
3067             if (this.selectingMode) {
3068                 this._stopSelecting(evt);
3069                 this.triggerEventHandlers(['mousestopselecting', 'stopselecting'], [evt]);
3070             } else {
3071                 for (i = 0; i < this.downObjects.length; i++) {
3072                     this.downObjects[i].triggerEventHandlers(['mouseup', 'up'], [evt]);
3073                 }
3074             }
3075 
3076             this.downObjects.length = 0;
3077 
3078             if (this.hasMouseUp) {
3079                 Env.removeEvent(this.document, 'mouseup', this.mouseUpListener, this);
3080                 this.hasMouseUp = false;
3081             }
3082 
3083             // release dragged mouse object
3084             /** @ignore */
3085             this.mouse = null;
3086         },
3087 
3088         /**
3089          * Handler for mouse wheel events. Used to zoom in and out of the board.
3090          * @param {Event} evt
3091          * @returns {Boolean}
3092          */
3093         mouseWheelListener: function (evt) {
3094             if (!this.attr.zoom.wheel || !this._isRequiredKeyPressed(evt, 'zoom')) {
3095                 return true;
3096             }
3097 
3098             evt = evt || window.event;
3099             var wd = evt.detail ? -evt.detail : evt.wheelDelta / 40,
3100                 pos = new Coords(Const.COORDS_BY_SCREEN, this.getMousePosition(evt), this);
3101 
3102             if (wd > 0) {
3103                 this.zoomIn(pos.usrCoords[1], pos.usrCoords[2]);
3104             } else {
3105                 this.zoomOut(pos.usrCoords[1], pos.usrCoords[2]);
3106             }
3107 
3108             this.triggerEventHandlers(['mousewheel'], [evt]);
3109 
3110             evt.preventDefault();
3111             return false;
3112         },
3113 
3114         /**
3115          * Allow moving of JSXGraph elements with arrow keys
3116          * and zooming of the construction with + / -.
3117          * Panning of the construction is done with arrow keys
3118          * if the pan key (shift or ctrl) is pressed.
3119          * The selection of the element is done with the tab key.
3120          *
3121          * @param  {Event} evt The browser's event object
3122          *
3123          * @see JXG.Board#keyboard
3124          * @see JXG.Board#keyFocusInListener
3125          * @see JXG.Board#keyFocusOutListener
3126          *
3127          */
3128         keyDownListener: function (evt) {
3129             var id_node = evt.target.id,
3130                 id, el, res,
3131                 sX = 0,
3132                 sY = 0,
3133                 // dx, dy are provided in screen units and
3134                 // are converted to user coordinates
3135                 dx = Type.evaluate(this.attr.keyboard.dx) / this.unitX,
3136                 dy = Type.evaluate(this.attr.keyboard.dy) / this.unitY,
3137                 doZoom = false,
3138                 dir, actPos;
3139 
3140             if (!this.attr.keyboard.enabled || id_node === '') {
3141                 return false;
3142             }
3143 
3144             // Get the JSXGraph id from the id of the SVG node.
3145             id = id_node.replace(this.containerObj.id + '_', '');
3146             el = this.select(id);
3147 
3148             if (Type.exists(el.coords)) {
3149                 actPos = el.coords.usrCoords.slice(1);
3150             }
3151 
3152             if (Type.evaluate(this.attr.keyboard.panshift) || Type.evaluate(this.attr.keyboard.panctrl)) {
3153                 doZoom = true;
3154             }
3155 
3156             if ((Type.evaluate(this.attr.keyboard.panshift) && evt.shiftKey) ||
3157                 (Type.evaluate(this.attr.keyboard.panctrl) && evt.ctrlKey)) {
3158                 if (evt.keyCode === 38) {           // up
3159                     this.clickUpArrow();
3160                 } else if (evt.keyCode === 40) {    // down
3161                     this.clickDownArrow();
3162                 } else if (evt.keyCode === 37) {    // left
3163                     this.clickLeftArrow();
3164                 } else if (evt.keyCode === 39) {    // right
3165                     this.clickRightArrow();
3166                 }
3167             } else {
3168                 // Adapt dx, dy to snapToGrid and attractToGrid
3169                 // snapToGrid has priority.
3170                 if (Type.exists(el.visProp)) {
3171                     if (Type.exists(el.visProp.snaptogrid) &&
3172                         el.visProp.snaptogrid &&
3173                         Type.evaluate(el.visProp.snapsizex) &&
3174                         Type.evaluate(el.visProp.snapsizey)) {
3175 
3176                         // Adapt dx, dy such that snapToGrid is possible
3177                         res = el.getSnapSizes();
3178                         sX = res[0];
3179                         sY = res[1];
3180                         dx = Math.max(sX, dx);
3181                         dy = Math.max(sY, dy);
3182 
3183                     } else if (Type.exists(el.visProp.attracttogrid) &&
3184                         el.visProp.attracttogrid &&
3185                         Type.evaluate(el.visProp.attractordistance) &&
3186                         Type.evaluate(el.visProp.attractorunit)) {
3187 
3188                         // Adapt dx, dy such that attractToGrid is possible
3189                         sX = 1.1 * Type.evaluate(el.visProp.attractordistance);
3190                         sY = sX;
3191 
3192                         if (Type.evaluate(el.visProp.attractorunit) == 'screen') {
3193                             sX /= this.unitX;
3194                             sY /= this.unitX;
3195                         }
3196                         dx = Math.max(sX, dx);
3197                         dy = Math.max(sY, dy);
3198                     }
3199 
3200                 }
3201 
3202                 if (evt.keyCode === 38) {           // up
3203                     dir = [0, dy];
3204                 } else if (evt.keyCode === 40) {    // down
3205                     dir = [0, -dy];
3206                 } else if (evt.keyCode === 37) {    // left
3207                     dir = [-dx, 0];
3208                 } else if (evt.keyCode === 39) {    // right
3209                     dir = [dx, 0];
3210                 // } else if (evt.keyCode === 9) {  // tab
3211 
3212                 } else if (doZoom && evt.key === '+') {   // +
3213                     this.zoomIn();
3214                 } else if (doZoom && evt.key === '-') {   // -
3215                     this.zoomOut();
3216                 } else if (doZoom && evt.key === 'o') {   // o
3217                     this.zoom100();
3218                 }
3219                 if (dir && el.isDraggable &&
3220                         el.visPropCalc.visible &&
3221                         ((this.geonextCompatibilityMode &&
3222                             (Type.isPoint(el) ||
3223                             el.elementClass === Const.OBJECT_CLASS_TEXT)
3224                         ) || !this.geonextCompatibilityMode) &&
3225                         !Type.evaluate(el.visProp.fixed)
3226                     ) {
3227 
3228                     if (Type.exists(el.coords)) {
3229                         dir[0] += actPos[0];
3230                         dir[1] += actPos[1];
3231                     }
3232                     // For coordsElement setPosition has to call setPositionDirectly.
3233                     // Otherwise the position is set by a translation.
3234                     el.setPosition(JXG.COORDS_BY_USER, dir);
3235                     if (Type.exists(el.coords)) {
3236                         this.updateInfobox(el);
3237                     }
3238                     this.triggerEventHandlers(['hit'], [evt, el]);
3239                 }
3240             }
3241 
3242             this.update();
3243 
3244             return true;
3245         },
3246 
3247         /**
3248          * Event listener for SVG elements getting focus.
3249          * This is needed for highlighting when using keyboard control.
3250          *
3251          * @see JXG.Board#keyFocusOutListener
3252          * @see JXG.Board#keyDownListener
3253          * @see JXG.Board#keyboard
3254          *
3255          * @param  {Event} evt The browser's event object
3256          */
3257         keyFocusInListener: function (evt) {
3258             var id_node = evt.target.id,
3259                 id, el;
3260 
3261             if (!this.attr.keyboard.enabled || id_node === '') {
3262                 return false;
3263             }
3264 
3265             id = id_node.replace(this.containerObj.id + '_', '');
3266             el = this.select(id);
3267             if (Type.exists(el.highlight)) {
3268                 el.highlight(true);
3269             }
3270             if (Type.exists(el.coords)) {
3271                 this.updateInfobox(el);
3272             }
3273             this.triggerEventHandlers(['hit'], [evt, el]);
3274         },
3275 
3276         /**
3277          * Event listener for SVG elements losing focus.
3278          * This is needed for dehighlighting when using keyboard control.
3279          *
3280          * @see JXG.Board#keyFocusInListener
3281          * @see JXG.Board#keyDownListener
3282          * @see JXG.Board#keyboard
3283          *
3284          * @param  {Event} evt The browser's event object
3285          */
3286         keyFocusOutListener: function (evt) {
3287             if (!this.attr.keyboard.enabled) {
3288                 return false;
3289             }
3290             // var id_node = evt.target.id,
3291             //     id, el;
3292 
3293             // id = id_node.replace(this.containerObj.id + '_', '');
3294             // el = this.select(id);
3295             this.dehighlightAll();
3296             this.displayInfobox(false);
3297         },
3298 
3299         /**
3300          * Update the width and height of the JSXGraph container div element.
3301          * Read actual values with getBoundingClientRect(),
3302          * and call board.resizeContainer() with this values.
3303          * <p>
3304          * If necessary, also call setBoundingBox().
3305          *
3306          * @see JXG.Board#startResizeObserver
3307          * @see JXG.Board#resizeListener
3308          * @see JXG.Board#resizeContainer
3309          * @see JXG.Board#setBoundingBox
3310          *
3311          */
3312         updateContainerDims: function() {
3313             var w, h,
3314                 bb, css;
3315 
3316             // Get size of the board's container div
3317             bb = this.containerObj.getBoundingClientRect();
3318             w = bb.width;
3319             h = bb.height;
3320 
3321             // Subtract the border size
3322             if (window && window.getComputedStyle) {
3323                 css = window.getComputedStyle(this.containerObj, null);
3324                 w -= parseFloat(css.getPropertyValue('border-left-width')) + parseFloat(css.getPropertyValue('border-right-width'));
3325                 h -= parseFloat(css.getPropertyValue('border-top-width'))  + parseFloat(css.getPropertyValue('border-bottom-width'));
3326             }
3327 
3328             // If div is invisible - do nothing
3329             if (w <= 0 || h <= 0) {
3330                 return;
3331             }
3332 
3333             // If bounding box is not yet initialized, do it now.
3334             if (isNaN(this.getBoundingBox()[0])) {
3335                 this.setBoundingBox(this.attr.boundingbox, this.keepaspectratio, 'keep');
3336             }
3337 
3338             // Do nothing if the dimension did not change since being visible
3339             // the last time. Note that if the div had display:none in the mean time,
3340             // we did not store this._prevDim.
3341             if (Type.exists(this._prevDim) &&
3342                 this._prevDim.w === w && this._prevDim.h === h) {
3343                     return;
3344             }
3345 
3346             // Set the size of the SVG or canvas element
3347             this.resizeContainer(w, h, true);
3348             this._prevDim = {
3349                 w: w,
3350                 h: h
3351             };
3352         },
3353 
3354         /**
3355          * Start observer which reacts to size changes of the JSXGraph
3356          * container div element. Calls updateContainerDims().
3357          * If not available, an event listener for the window-resize event is started.
3358          * On mobile devices also scrolling might trigger resizes.
3359          * However, resize events triggered by scrolling events should be ignored.
3360          * Therefore, also a scrollListener is started.
3361          * Resize can be controlled with the board attribute resize.
3362          *
3363          * @see JXG.Board#updateContainerDims
3364          * @see JXG.Board#resizeListener
3365          * @see JXG.Board#scrollListener
3366          * @see JXG.Board#resize
3367          *
3368          */
3369         startResizeObserver: function() {
3370             var that = this;
3371 
3372             if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {
3373                 return;
3374             }
3375 
3376             this.resizeObserver = new ResizeObserver(function(entries) {
3377                 if (!that._isResizing) {
3378                     that._isResizing = true;
3379                     window.setTimeout(function() {
3380                         try {
3381                             that.updateContainerDims();
3382                         } catch (err) {
3383                             that.stopResizeObserver();
3384                         } finally {
3385                             that._isResizing = false;
3386                         }
3387                     }, that.attr.resize.throttle);
3388                 }
3389             });
3390             this.resizeObserver.observe(this.containerObj);
3391         },
3392 
3393         /**
3394          * Stops the resize observer.
3395          * @see JXG.Board#startResizeObserver
3396          *
3397          */
3398         stopResizeObserver: function() {
3399             if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {
3400                 return;
3401             }
3402 
3403             if (Type.exists(this.resizeObserver)) {
3404                 this.resizeObserver.unobserve(this.containerObj);
3405             }
3406         },
3407 
3408         /**
3409          * Fallback solutions if there is no resizeObserver available in the browser.
3410          * Reacts to resize events of the window (only). Otherwise similar to
3411          * startResizeObserver(). To handle changes of the visibility
3412          * of the JSXGraph container element, additionally an intersection observer is used.
3413          * which watches changes in the visibility of the JSXGraph container element.
3414          * This is necessary e.g. for register tabs or dia shows.
3415          *
3416          * @see JXG.Board#startResizeObserver
3417          * @see JXG.Board#startIntersectionObserver
3418          */
3419         resizeListener: function() {
3420             var that = this;
3421 
3422             if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {
3423                 return;
3424             }
3425             if (!this._isScrolling && !this._isResizing) {
3426                 this._isResizing = true;
3427                 window.setTimeout(function() {
3428                     that.updateContainerDims();
3429                     that._isResizing = false;
3430                 }, this.attr.resize.throttle);
3431             }
3432         },
3433 
3434         /**
3435          * Listener to watch for scroll events. Sets board._isScrolling = true
3436          * @param  {Event} evt The browser's event object
3437          *
3438          * @see JXG.Board#startResizeObserver
3439          * @see JXG.Board#resizeListener
3440          *
3441          */
3442         scrollListener: function(evt) {
3443             var that = this;
3444 
3445             if (!Env.isBrowser) {
3446                 return;
3447             }
3448             if (!this._isScrolling) {
3449                 this._isScrolling = true;
3450                 window.setTimeout(function() {
3451                     that._isScrolling = false;
3452                 }, 66);
3453             }
3454         },
3455 
3456         /**
3457          * Watch for changes of the visibility of the JSXGraph container element.
3458          *
3459          * @see JXG.Board#startResizeObserver
3460          * @see JXG.Board#resizeListener
3461          *
3462          */
3463         startIntersectionObserver: function() {
3464             var that = this,
3465                 options = {
3466                     root: null,
3467                     rootMargin: '0px',
3468                     threshold: 0.8
3469                 };
3470 
3471             try {
3472                 this.intersectionObserver = new IntersectionObserver(function(entries) {
3473                     // If bounding box is not yet initialized, do it now.
3474                     if (isNaN(that.getBoundingBox()[0])) {
3475                         that.updateContainerDims();
3476                     }
3477                 }, options);
3478                 this.intersectionObserver.observe(that.containerObj);
3479             } catch (err) {
3480                 console.log('JSXGraph: IntersectionObserver not available in this browser.');
3481             }
3482         },
3483 
3484         /**
3485          * Stop the intersection observer
3486          *
3487          * @see JXG.Board#startIntersectionObserver
3488          *
3489          */
3490         stopIntersectionObserver: function() {
3491             if (Type.exists(this.intersectionObserver)) {
3492                 this.intersectionObserver.unobserve(this.containerObj);
3493             }
3494         },
3495 
3496         /**********************************************************
3497          *
3498          * End of Event Handlers
3499          *
3500          **********************************************************/
3501 
3502         /**
3503          * Initialize the info box object which is used to display
3504          * the coordinates of points near the mouse pointer,
3505          * @returns {JXG.Board} Reference to the board
3506         */
3507         initInfobox: function () {
3508             var  attr = Type.copyAttributes({}, this.options, 'infobox');
3509 
3510             attr.id = this.id + '_infobox';
3511             /**
3512              * Infobox close to points in which the points' coordinates are displayed.
3513              * This is simply a JXG.Text element. Access through board.infobox.
3514              * Uses CSS class .JXGinfobox.
3515              * @type JXG.Text
3516              *
3517              */
3518             this.infobox = this.create('text', [0, 0, '0,0'], attr);
3519 
3520             this.infobox.distanceX = -20;
3521             this.infobox.distanceY = 25;
3522             // this.infobox.needsUpdateSize = false;  // That is not true, but it speeds drawing up.
3523 
3524             this.infobox.dump = false;
3525 
3526             this.displayInfobox(false);
3527             return this;
3528         },
3529 
3530         /**
3531          * Updates and displays a little info box to show coordinates of current selected points.
3532          * @param {JXG.GeometryElement} el A GeometryElement
3533          * @returns {JXG.Board} Reference to the board
3534          * @see JXG.Board#displayInfobox
3535          * @see JXG.Board#showInfobox
3536          * @see Point#showInfobox
3537          *
3538          */
3539         updateInfobox: function (el) {
3540             var x, y, xc, yc,
3541             vpinfoboxdigits,
3542             vpsi = Type.evaluate(el.visProp.showinfobox);
3543 
3544             if ((!Type.evaluate(this.attr.showinfobox) &&  vpsi === 'inherit') ||
3545                 !vpsi) {
3546                 return this;
3547             }
3548 
3549             if (Type.isPoint(el)) {
3550                 xc = el.coords.usrCoords[1];
3551                 yc = el.coords.usrCoords[2];
3552 
3553                 vpinfoboxdigits = Type.evaluate(el.visProp.infoboxdigits);
3554                 this.infobox.setCoords(xc + this.infobox.distanceX / this.unitX,
3555                                        yc + this.infobox.distanceY / this.unitY);
3556 
3557                 if (typeof el.infoboxText !== 'string') {
3558                     if (vpinfoboxdigits === 'auto') {
3559                         x = Type.autoDigits(xc);
3560                         y = Type.autoDigits(yc);
3561                     } else if (Type.isNumber(vpinfoboxdigits)) {
3562                         x = Type.toFixed(xc, vpinfoboxdigits);
3563                         y = Type.toFixed(yc, vpinfoboxdigits);
3564                     } else {
3565                         x = xc;
3566                         y = yc;
3567                     }
3568 
3569                     this.highlightInfobox(x, y, el);
3570                 } else {
3571                     this.highlightCustomInfobox(el.infoboxText, el);
3572                 }
3573 
3574                 this.displayInfobox(true);
3575             }
3576             return this;
3577         },
3578 
3579         /**
3580          * Set infobox visible / invisible.
3581          *
3582          * It uses its property hiddenByParent to memorize its status.
3583          * In this way, many DOM access can be avoided.
3584          *
3585          * @param  {Boolean} val true for visible, false for invisible
3586          * @returns {JXG.Board} Reference to the board.
3587          * @see JXG.Board#updateInfobox
3588          *
3589          */
3590         displayInfobox: function(val) {
3591             if (this.infobox.hiddenByParent === val) {
3592                 this.infobox.hiddenByParent = !val;
3593                 this.infobox.prepareUpdate().updateVisibility(val).updateRenderer();
3594             }
3595             return this;
3596         },
3597 
3598         // Alias for displayInfobox to be backwards compatible.
3599         // The method showInfobox clashes with the board attribute showInfobox
3600         showInfobox: function(val) {
3601             return this.displayInfobox(val);
3602         },
3603 
3604         /**
3605          * Changes the text of the info box to show the given coordinates.
3606          * @param {Number} x
3607          * @param {Number} y
3608          * @param {JXG.GeometryElement} [el] The element the mouse is pointing at
3609          * @returns {JXG.Board} Reference to the board.
3610          */
3611         highlightInfobox: function (x, y, el) {
3612             this.highlightCustomInfobox('(' + x + ', ' + y + ')', el);
3613             return this;
3614         },
3615 
3616         /**
3617          * Changes the text of the info box to what is provided via text.
3618          * @param {String} text
3619          * @param {JXG.GeometryElement} [el]
3620          * @returns {JXG.Board} Reference to the board.
3621          */
3622         highlightCustomInfobox: function (text, el) {
3623             this.infobox.setText(text);
3624             return this;
3625         },
3626 
3627         /**
3628          * Remove highlighting of all elements.
3629          * @returns {JXG.Board} Reference to the board.
3630          */
3631         dehighlightAll: function () {
3632             var el, pEl, needsDehighlight = false;
3633 
3634             for (el in this.highlightedObjects) {
3635                 if (this.highlightedObjects.hasOwnProperty(el)) {
3636                     pEl = this.highlightedObjects[el];
3637 
3638                     if (this.hasMouseHandlers || this.hasPointerHandlers) {
3639                         pEl.noHighlight();
3640                     }
3641 
3642                     needsDehighlight = true;
3643 
3644                     // In highlightedObjects should only be objects which fulfill all these conditions
3645                     // And in case of complex elements, like a turtle based fractal, it should be faster to
3646                     // just de-highlight the element instead of checking hasPoint...
3647                     // if ((!Type.exists(pEl.hasPoint)) || !pEl.hasPoint(x, y) || !pEl.visPropCalc.visible)
3648                 }
3649             }
3650 
3651             this.highlightedObjects = {};
3652 
3653             // We do not need to redraw during dehighlighting in CanvasRenderer
3654             // because we are redrawing anyhow
3655             //  -- We do need to redraw during dehighlighting. Otherwise objects won't be dehighlighted until
3656             // another object is highlighted.
3657             if (this.renderer.type === 'canvas' && needsDehighlight) {
3658                 this.prepareUpdate();
3659                 this.renderer.suspendRedraw(this);
3660                 this.updateRenderer();
3661                 this.renderer.unsuspendRedraw();
3662             }
3663 
3664             return this;
3665         },
3666 
3667         /**
3668          * Returns the input parameters in an array. This method looks pointless and it really is, but it had a purpose
3669          * once.
3670          * @private
3671          * @param {Number} x X coordinate in screen coordinates
3672          * @param {Number} y Y coordinate in screen coordinates
3673          * @returns {Array} Coordinates [x, y] of the mouse in screen coordinates.
3674          * @see JXG.Board#getUsrCoordsOfMouse
3675          */
3676         getScrCoordsOfMouse: function (x, y) {
3677             return [x, y];
3678         },
3679 
3680         /**
3681          * This method calculates the user coords of the current mouse coordinates.
3682          * @param {Event} evt Event object containing the mouse coordinates.
3683          * @returns {Array} Coordinates [x, y] of the mouse in user coordinates.
3684          * @example
3685          * board.on('up', function (evt) {
3686          *         var a = board.getUsrCoordsOfMouse(evt),
3687          *             x = a[0],
3688          *             y = a[1],
3689          *             somePoint = board.create('point', [x,y], {name:'SomePoint',size:4});
3690          *             // Shorter version:
3691          *             //somePoint = board.create('point', a, {name:'SomePoint',size:4});
3692          *         });
3693          *
3694          * </pre><div id="JXG48d5066b-16ba-4920-b8ea-a4f8eff6b746" class="jxgbox" style="width: 300px; height: 300px;"></div>
3695          * <script type="text/javascript">
3696          *     (function() {
3697          *         var board = JXG.JSXGraph.initBoard('JXG48d5066b-16ba-4920-b8ea-a4f8eff6b746',
3698          *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
3699          *     board.on('up', function (evt) {
3700          *             var a = board.getUsrCoordsOfMouse(evt),
3701          *                 x = a[0],
3702          *                 y = a[1],
3703          *                 somePoint = board.create('point', [x,y], {name:'SomePoint',size:4});
3704          *                 // Shorter version:
3705          *                 //somePoint = board.create('point', a, {name:'SomePoint',size:4});
3706          *             });
3707          * 
3708          *     })();
3709          *
3710          * </script><pre>
3711          * 
3712          * @see JXG.Board#getScrCoordsOfMouse
3713          * @see JXG.Board#getAllUnderMouse
3714          */
3715         getUsrCoordsOfMouse: function (evt) {
3716             var cPos = this.getCoordsTopLeftCorner(),
3717                 absPos = Env.getPosition(evt, null, this.document),
3718                 x = absPos[0] - cPos[0],
3719                 y = absPos[1] - cPos[1],
3720                 newCoords = new Coords(Const.COORDS_BY_SCREEN, [x, y], this);
3721 
3722             return newCoords.usrCoords.slice(1);
3723         },
3724 
3725         /**
3726          * Collects all elements under current mouse position plus current user coordinates of mouse cursor.
3727          * @param {Event} evt Event object containing the mouse coordinates.
3728          * @returns {Array} Array of elements at the current mouse position plus current user coordinates of mouse.
3729          * @see JXG.Board#getUsrCoordsOfMouse
3730          * @see JXG.Board#getAllObjectsUnderMouse
3731          */
3732         getAllUnderMouse: function (evt) {
3733             var elList = this.getAllObjectsUnderMouse(evt);
3734             elList.push(this.getUsrCoordsOfMouse(evt));
3735 
3736             return elList;
3737         },
3738 
3739         /**
3740          * Collects all elements under current mouse position.
3741          * @param {Event} evt Event object containing the mouse coordinates.
3742          * @returns {Array} Array of elements at the current mouse position.
3743          * @see JXG.Board#getAllUnderMouse
3744          */
3745         getAllObjectsUnderMouse: function (evt) {
3746             var cPos = this.getCoordsTopLeftCorner(),
3747                 absPos = Env.getPosition(evt, null, this.document),
3748                 dx = absPos[0] - cPos[0],
3749                 dy = absPos[1] - cPos[1],
3750                 elList = [],
3751                 el,
3752                 pEl,
3753                 len = this.objectsList.length;
3754 
3755             for (el = 0; el < len; el++) {
3756                 pEl = this.objectsList[el];
3757                 if (pEl.visPropCalc.visible && pEl.hasPoint && pEl.hasPoint(dx, dy)) {
3758                     elList[elList.length] = pEl;
3759                 }
3760             }
3761 
3762             return elList;
3763         },
3764 
3765         /**
3766          * Update the coords object of all elements which possess this
3767          * property. This is necessary after changing the viewport.
3768          * @returns {JXG.Board} Reference to this board.
3769          **/
3770         updateCoords: function () {
3771             var el, ob, len = this.objectsList.length;
3772 
3773             for (ob = 0; ob < len; ob++) {
3774                 el = this.objectsList[ob];
3775 
3776                 if (Type.exists(el.coords)) {
3777                     if (Type.evaluate(el.visProp.frozen)) {
3778                         el.coords.screen2usr();
3779                     } else {
3780                         el.coords.usr2screen();
3781                     }
3782                 }
3783             }
3784             return this;
3785         },
3786 
3787         /**
3788          * Moves the origin and initializes an update of all elements.
3789          * @param {Number} x
3790          * @param {Number} y
3791          * @param {Boolean} [diff=false]
3792          * @returns {JXG.Board} Reference to this board.
3793          */
3794         moveOrigin: function (x, y, diff) {
3795             var ox, oy, ul, lr;
3796             if (Type.exists(x) && Type.exists(y)) {
3797                 ox = this.origin.scrCoords[1];
3798                 oy = this.origin.scrCoords[2];
3799 
3800                 this.origin.scrCoords[1] = x;
3801                 this.origin.scrCoords[2] = y;
3802 
3803                 if (diff) {
3804                     this.origin.scrCoords[1] -= this.drag_dx;
3805                     this.origin.scrCoords[2] -= this.drag_dy;
3806                 }
3807 
3808                 ul = (new Coords(Const.COORDS_BY_SCREEN, [0, 0], this)).usrCoords;
3809                 lr = (new Coords(Const.COORDS_BY_SCREEN, [this.canvasWidth, this.canvasHeight], this)).usrCoords;
3810                 if (ul[1] < this.maxboundingbox[0] ||
3811                     ul[2] > this.maxboundingbox[1] ||
3812                     lr[1] > this.maxboundingbox[2] ||
3813                     lr[2] < this.maxboundingbox[3]) {
3814 
3815                     this.origin.scrCoords[1] = ox;
3816                     this.origin.scrCoords[2] = oy;
3817                 }
3818             }
3819 
3820             this.updateCoords().clearTraces().fullUpdate();
3821             this.triggerEventHandlers(['boundingbox']);
3822 
3823             return this;
3824         },
3825 
3826         /**
3827          * Add conditional updates to the elements.
3828          * @param {String} str String containing coniditional update in geonext syntax
3829          */
3830         addConditions: function (str) {
3831             var term, m, left, right, name, el, property,
3832                 functions = [],
3833                 plaintext = 'var el, x, y, c, rgbo;\n',
3834                 i = str.indexOf('<data>'),
3835                 j = str.indexOf('<' + '/data>'),
3836 
3837                 xyFun = function (board, el, f, what) {
3838                     return function () {
3839                         var e, t;
3840 
3841                         e = board.select(el.id);
3842                         t = e.coords.usrCoords[what];
3843 
3844                         if (what === 2) {
3845                             e.setPositionDirectly(Const.COORDS_BY_USER, [f(), t]);
3846                         } else {
3847                             e.setPositionDirectly(Const.COORDS_BY_USER, [t, f()]);
3848                         }
3849                         e.prepareUpdate().update();
3850                     };
3851                 },
3852 
3853                 visFun = function (board, el, f) {
3854                     return function () {
3855                         var e, v;
3856 
3857                         e = board.select(el.id);
3858                         v = f();
3859 
3860                         e.setAttribute({visible: v});
3861                     };
3862                 },
3863 
3864                 colFun = function (board, el, f, what) {
3865                     return function () {
3866                         var e, v;
3867 
3868                         e = board.select(el.id);
3869                         v = f();
3870 
3871                         if (what === 'strokewidth') {
3872                             e.visProp.strokewidth = v;
3873                         } else {
3874                             v = Color.rgba2rgbo(v);
3875                             e.visProp[what + 'color'] = v[0];
3876                             e.visProp[what + 'opacity'] = v[1];
3877                         }
3878                     };
3879                 },
3880 
3881                 posFun = function (board, el, f) {
3882                     return function () {
3883                         var e = board.select(el.id);
3884 
3885                         e.position = f();
3886                     };
3887                 },
3888 
3889                 styleFun = function (board, el, f) {
3890                     return function () {
3891                         var e = board.select(el.id);
3892 
3893                         e.setStyle(f());
3894                     };
3895                 };
3896 
3897             if (i < 0) {
3898                 return;
3899             }
3900 
3901             while (i >= 0) {
3902                 term = str.slice(i + 6, j);   // throw away <data>
3903                 m = term.indexOf('=');
3904                 left = term.slice(0, m);
3905                 right = term.slice(m + 1);
3906                 m = left.indexOf('.');     // Dies erzeugt Probleme bei Variablennamen der Form " Steuern akt."
3907                 name = left.slice(0, m);    //.replace(/\s+$/,''); // do NOT cut out name (with whitespace)
3908                 el = this.elementsByName[Type.unescapeHTML(name)];
3909 
3910                 property = left.slice(m + 1).replace(/\s+/g, '').toLowerCase(); // remove whitespace in property
3911                 right = Type.createFunction (right, this, '', true);
3912 
3913                 // Debug
3914                 if (!Type.exists(this.elementsByName[name])) {
3915                     JXG.debug("debug conditions: |" + name + "| undefined");
3916                 } else {
3917                     plaintext += "el = this.objects[\"" + el.id + "\"];\n";
3918 
3919                     switch (property) {
3920                     case 'x':
3921                         functions.push(xyFun(this, el, right, 2));
3922                         break;
3923                     case 'y':
3924                         functions.push(xyFun(this, el, right, 1));
3925                         break;
3926                     case 'visible':
3927                         functions.push(visFun(this, el, right));
3928                         break;
3929                     case 'position':
3930                         functions.push(posFun(this, el, right));
3931                         break;
3932                     case 'stroke':
3933                         functions.push(colFun(this, el, right, 'stroke'));
3934                         break;
3935                     case 'style':
3936                         functions.push(styleFun(this, el, right));
3937                         break;
3938                     case 'strokewidth':
3939                         functions.push(colFun(this, el, right, 'strokewidth'));
3940                         break;
3941                     case 'fill':
3942                         functions.push(colFun(this, el, right, 'fill'));
3943                         break;
3944                     case 'label':
3945                         break;
3946                     default:
3947                         JXG.debug("property '" + property + "' in conditions not yet implemented:" + right);
3948                         break;
3949                     }
3950                 }
3951                 str = str.slice(j + 7); // cut off "</data>"
3952                 i = str.indexOf('<data>');
3953                 j = str.indexOf('<' + '/data>');
3954             }
3955 
3956             this.updateConditions = function () {
3957                 var i;
3958 
3959                 for (i = 0; i < functions.length; i++) {
3960                     functions[i]();
3961                 }
3962 
3963                 this.prepareUpdate().updateElements();
3964                 return true;
3965             };
3966             this.updateConditions();
3967         },
3968 
3969         /**
3970          * Computes the commands in the conditions-section of the gxt file.
3971          * It is evaluated after an update, before the unsuspendRedraw.
3972          * The function is generated in
3973          * @see JXG.Board#addConditions
3974          * @private
3975          */
3976         updateConditions: function () {
3977             return false;
3978         },
3979 
3980         /**
3981          * Calculates adequate snap sizes.
3982          * @returns {JXG.Board} Reference to the board.
3983          */
3984         calculateSnapSizes: function () {
3985             var p1 = new Coords(Const.COORDS_BY_USER, [0, 0], this),
3986                 p2 = new Coords(Const.COORDS_BY_USER, [this.options.grid.gridX, this.options.grid.gridY], this),
3987                 x = p1.scrCoords[1] - p2.scrCoords[1],
3988                 y = p1.scrCoords[2] - p2.scrCoords[2];
3989 
3990             this.options.grid.snapSizeX = this.options.grid.gridX;
3991             while (Math.abs(x) > 25) {
3992                 this.options.grid.snapSizeX *= 2;
3993                 x /= 2;
3994             }
3995 
3996             this.options.grid.snapSizeY = this.options.grid.gridY;
3997             while (Math.abs(y) > 25) {
3998                 this.options.grid.snapSizeY *= 2;
3999                 y /= 2;
4000             }
4001 
4002             return this;
4003         },
4004 
4005         /**
4006          * Apply update on all objects with the new zoom-factors. Clears all traces.
4007          * @returns {JXG.Board} Reference to the board.
4008          */
4009         applyZoom: function () {
4010             this.updateCoords().calculateSnapSizes().clearTraces().fullUpdate();
4011 
4012             return this;
4013         },
4014 
4015         /**
4016          * Zooms into the board by the factors board.attr.zoom.factorX and board.attr.zoom.factorY and applies the zoom.
4017          * The zoom operation is centered at x, y.
4018          * @param {Number} [x]
4019          * @param {Number} [y]
4020          * @returns {JXG.Board} Reference to the board
4021          */
4022         zoomIn: function (x, y) {
4023             var bb = this.getBoundingBox(),
4024                 zX = this.attr.zoom.factorx,
4025                 zY = this.attr.zoom.factory,
4026                 dX = (bb[2] - bb[0]) * (1.0 - 1.0 / zX),
4027                 dY = (bb[1] - bb[3]) * (1.0 - 1.0 / zY),
4028                 lr = 0.5,
4029                 tr = 0.5,
4030                 mi = this.attr.zoom.eps || this.attr.zoom.min || 0.001;  // this.attr.zoom.eps is deprecated
4031 
4032             if ((this.zoomX > this.attr.zoom.max && zX > 1.0) ||
4033                 (this.zoomY > this.attr.zoom.max && zY > 1.0) ||
4034                 (this.zoomX < mi && zX < 1.0) ||  // zoomIn is used for all zooms on touch devices
4035                 (this.zoomY < mi && zY < 1.0)) {
4036                 return this;
4037             }
4038 
4039             if (Type.isNumber(x) && Type.isNumber(y)) {
4040                 lr = (x - bb[0]) / (bb[2] - bb[0]);
4041                 tr = (bb[1] - y) / (bb[1] - bb[3]);
4042             }
4043 
4044             this.setBoundingBox([bb[0] + dX * lr, bb[1] - dY * tr, bb[2] - dX * (1 - lr), bb[3] + dY * (1 - tr)], this.keepaspectratio, 'update');
4045             return this.applyZoom();
4046         },
4047 
4048         /**
4049          * Zooms out of the board by the factors board.attr.zoom.factorX and board.attr.zoom.factorY and applies the zoom.
4050          * The zoom operation is centered at x, y.
4051          *
4052          * @param {Number} [x]
4053          * @param {Number} [y]
4054          * @returns {JXG.Board} Reference to the board
4055          */
4056         zoomOut: function (x, y) {
4057             var bb = this.getBoundingBox(),
4058                 zX = this.attr.zoom.factorx,
4059                 zY = this.attr.zoom.factory,
4060                 dX = (bb[2] - bb[0]) * (1.0 - zX),
4061                 dY = (bb[1] - bb[3]) * (1.0 - zY),
4062                 lr = 0.5,
4063                 tr = 0.5,
4064                 mi = this.attr.zoom.eps || this.attr.zoom.min || 0.001;  // this.attr.zoom.eps is deprecated
4065 
4066             if (this.zoomX < mi || this.zoomY < mi) {
4067                 return this;
4068             }
4069 
4070             if (Type.isNumber(x) && Type.isNumber(y)) {
4071                 lr = (x - bb[0]) / (bb[2] - bb[0]);
4072                 tr = (bb[1] - y) / (bb[1] - bb[3]);
4073             }
4074 
4075             this.setBoundingBox([bb[0] + dX * lr, bb[1] - dY * tr, bb[2] - dX * (1 - lr), bb[3] + dY * (1 - tr)], this.keepaspectratio, 'update');
4076 
4077             return this.applyZoom();
4078         },
4079 
4080         /**
4081          * Reset the zoom level to the original zoom level from initBoard();
4082          * Additionally, if the board as been initialized with a boundingBox (which is the default),
4083          * restore the viewport to the original viewport during initialization. Otherwise,
4084          * (i.e. if the board as been initialized with unitX/Y and originX/Y),
4085          * just set the zoom level to 100%.
4086          *
4087          * @returns {JXG.Board} Reference to the board
4088          */
4089         zoom100: function () {
4090             var bb, dX, dY;
4091 
4092             if (Type.exists(this.attr.boundingbox)) {
4093                 this.setBoundingBox(this.attr.boundingbox, this.keepaspectratio, 'reset');
4094             } else {
4095                 // Board has been set up with unitX/Y and originX/Y
4096                 bb = this.getBoundingBox();
4097                 dX = (bb[2] - bb[0]) * (1.0 - this.zoomX) * 0.5;
4098                 dY = (bb[1] - bb[3]) * (1.0 - this.zoomY) * 0.5;
4099                 this.setBoundingBox([bb[0] + dX, bb[1] - dY, bb[2] - dX, bb[3] + dY], this.keepaspectratio, 'reset');
4100             }
4101             return this.applyZoom();
4102         },
4103 
4104         /**
4105          * Zooms the board so every visible point is shown. Keeps aspect ratio.
4106          * @returns {JXG.Board} Reference to the board
4107          */
4108         zoomAllPoints: function () {
4109             var el, border, borderX, borderY, pEl,
4110                 minX = 0,
4111                 maxX = 0,
4112                 minY = 0,
4113                 maxY = 0,
4114                 len = this.objectsList.length;
4115 
4116             for (el = 0; el < len; el++) {
4117                 pEl = this.objectsList[el];
4118 
4119                 if (Type.isPoint(pEl) && pEl.visPropCalc.visible) {
4120                     if (pEl.coords.usrCoords[1] < minX) {
4121                         minX = pEl.coords.usrCoords[1];
4122                     } else if (pEl.coords.usrCoords[1] > maxX) {
4123                         maxX = pEl.coords.usrCoords[1];
4124                     }
4125                     if (pEl.coords.usrCoords[2] > maxY) {
4126                         maxY = pEl.coords.usrCoords[2];
4127                     } else if (pEl.coords.usrCoords[2] < minY) {
4128                         minY = pEl.coords.usrCoords[2];
4129                     }
4130                 }
4131             }
4132 
4133             border = 50;
4134             borderX = border / this.unitX;
4135             borderY = border / this.unitY;
4136 
4137             this.setBoundingBox([minX - borderX, maxY + borderY, maxX + borderX, minY - borderY], this.keepaspectratio, 'update');
4138 
4139             return this.applyZoom();
4140         },
4141 
4142         /**
4143          * Reset the bounding box and the zoom level to 100% such that a given set of elements is
4144          * within the board's viewport.
4145          * @param {Array} elements A set of elements given by id, reference, or name.
4146          * @returns {JXG.Board} Reference to the board.
4147          */
4148         zoomElements: function (elements) {
4149             var i, e, box,
4150                 newBBox = [Infinity, -Infinity, -Infinity, Infinity],
4151                 cx, cy, dx, dy, d;
4152 
4153             if (!Type.isArray(elements) || elements.length === 0) {
4154                 return this;
4155             }
4156 
4157             for (i = 0; i < elements.length; i++) {
4158                 e = this.select(elements[i]);
4159 
4160                 box = e.bounds();
4161                 if (Type.isArray(box)) {
4162                     if (box[0] < newBBox[0]) { newBBox[0] = box[0]; }
4163                     if (box[1] > newBBox[1]) { newBBox[1] = box[1]; }
4164                     if (box[2] > newBBox[2]) { newBBox[2] = box[2]; }
4165                     if (box[3] < newBBox[3]) { newBBox[3] = box[3]; }
4166                 }
4167             }
4168 
4169             if (Type.isArray(newBBox)) {
4170                 cx = 0.5 * (newBBox[0] + newBBox[2]);
4171                 cy = 0.5 * (newBBox[1] + newBBox[3]);
4172                 dx = 1.5 * (newBBox[2] - newBBox[0]) * 0.5;
4173                 dy = 1.5 * (newBBox[1] - newBBox[3]) * 0.5;
4174                 d = Math.max(dx, dy);
4175                 this.setBoundingBox([cx - d, cy + d, cx + d, cy - d], this.keepaspectratio, 'update');
4176             }
4177 
4178             return this;
4179         },
4180 
4181         /**
4182          * Sets the zoom level to <tt>fX</tt> resp <tt>fY</tt>.
4183          * @param {Number} fX
4184          * @param {Number} fY
4185          * @returns {JXG.Board} Reference to the board.
4186          */
4187         setZoom: function (fX, fY) {
4188             var oX = this.attr.zoom.factorx,
4189                 oY = this.attr.zoom.factory;
4190 
4191             this.attr.zoom.factorx = fX / this.zoomX;
4192             this.attr.zoom.factory = fY / this.zoomY;
4193 
4194             this.zoomIn();
4195 
4196             this.attr.zoom.factorx = oX;
4197             this.attr.zoom.factory = oY;
4198 
4199             return this;
4200         },
4201 
4202         /**
4203          * Removes object from board and renderer.
4204          * <p>
4205          * <b>Performance hints:</b> It is recommended to use the object's id.
4206          * If many elements are removed, it is best to call <tt>board.suspendUpdate()</tt>
4207          * before looping through the elements to be removed and call
4208          * <tt>board.unsuspendUpdate()</tt> after the loop. Further, it is advisable to loop
4209          * in reverse order, i.e. remove the object in reverse order of their creation time.
4210          *
4211          * @param {JXG.GeometryElement|Array} object The object to remove or array of objects to be removed.
4212          * The element(s) is/are given by name, id or a reference.
4213          * @param {Boolean} saveMethod If true, the algorithm runs through all elements
4214          * and tests if the element to be deleted is a child element. If yes, it will be
4215          * removed from the list of child elements. If false (default), the element
4216          * is removed from the lists of child elements of all its ancestors.
4217          * This should be much faster.
4218          * @returns {JXG.Board} Reference to the board
4219          */
4220         removeObject: function (object, saveMethod) {
4221             var el, i;
4222 
4223             if (Type.isArray(object)) {
4224                 for (i = 0; i < object.length; i++) {
4225                     this.removeObject(object[i]);
4226                 }
4227 
4228                 return this;
4229             }
4230 
4231             object = this.select(object);
4232 
4233             // If the object which is about to be removed unknown or a string, do nothing.
4234             // it is a string if a string was given and could not be resolved to an element.
4235             if (!Type.exists(object) || Type.isString(object)) {
4236                 return this;
4237             }
4238 
4239             try {
4240                 // remove all children.
4241                 for (el in object.childElements) {
4242                     if (object.childElements.hasOwnProperty(el)) {
4243                         object.childElements[el].board.removeObject(object.childElements[el]);
4244                     }
4245                 }
4246 
4247                 // Remove all children in elements like turtle
4248                 for (el in object.objects) {
4249                     if (object.objects.hasOwnProperty(el)) {
4250                         object.objects[el].board.removeObject(object.objects[el]);
4251                     }
4252                 }
4253 
4254                 // Remove the element from the childElement list and the descendant list of all elements.
4255                 if (saveMethod) {
4256                     // Running through all objects has quadratic complexity if many objects are deleted.
4257                     for (el in this.objects) {
4258                         if (this.objects.hasOwnProperty(el)) {
4259                             if (Type.exists(this.objects[el].childElements) &&
4260                                 Type.exists(this.objects[el].childElements.hasOwnProperty(object.id))
4261                             ) {
4262                                 delete this.objects[el].childElements[object.id];
4263                                 delete this.objects[el].descendants[object.id];
4264                             }
4265                         }
4266                     }
4267                 } else if (Type.exists(object.ancestors)) {
4268                     // Running through the ancestors should be much more efficient.
4269                     for (el in object.ancestors) {
4270                         if (object.ancestors.hasOwnProperty(el)) {
4271                             if (Type.exists(object.ancestors[el].childElements) &&
4272                                 Type.exists(object.ancestors[el].childElements.hasOwnProperty(object.id))
4273                             ) {
4274                                 delete object.ancestors[el].childElements[object.id];
4275                                 delete object.ancestors[el].descendants[object.id];
4276                             }
4277                         }
4278                     }
4279                 }
4280 
4281                 // remove the object itself from our control structures
4282                 if (object._pos > -1) {
4283                     this.objectsList.splice(object._pos, 1);
4284                     for (el = object._pos; el < this.objectsList.length; el++) {
4285                         this.objectsList[el]._pos--;
4286                     }
4287                 } else if (object.type !== Const.OBJECT_TYPE_TURTLE) {
4288                     JXG.debug('Board.removeObject: object ' + object.id + ' not found in list.');
4289                 }
4290 
4291                 delete this.objects[object.id];
4292                 delete this.elementsByName[object.name];
4293 
4294                 if (object.visProp && Type.evaluate(object.visProp.trace)) {
4295                     object.clearTrace();
4296                 }
4297 
4298                 // the object deletion itself is handled by the object.
4299                 if (Type.exists(object.remove)) {
4300                     object.remove();
4301                 }
4302             } catch (e) {
4303                 JXG.debug(object.id + ': Could not be removed: ' + e);
4304             }
4305 
4306             this.update();
4307 
4308             return this;
4309         },
4310 
4311         /**
4312          * Removes the ancestors of an object an the object itself from board and renderer.
4313          * @param {JXG.GeometryElement} object The object to remove.
4314          * @returns {JXG.Board} Reference to the board
4315          */
4316         removeAncestors: function (object) {
4317             var anc;
4318 
4319             for (anc in object.ancestors) {
4320                 if (object.ancestors.hasOwnProperty(anc)) {
4321                     this.removeAncestors(object.ancestors[anc]);
4322                 }
4323             }
4324 
4325             this.removeObject(object);
4326 
4327             return this;
4328         },
4329 
4330         /**
4331          * Initialize some objects which are contained in every GEONExT construction by default,
4332          * but are not contained in the gxt files.
4333          * @returns {JXG.Board} Reference to the board
4334          */
4335         initGeonextBoard: function () {
4336             var p1, p2, p3;
4337 
4338             p1 = this.create('point', [0, 0], {
4339                 id: this.id + 'g00e0',
4340                 name: 'Ursprung',
4341                 withLabel: false,
4342                 visible: false,
4343                 fixed: true
4344             });
4345 
4346             p2 = this.create('point', [1, 0], {
4347                 id: this.id + 'gX0e0',
4348                 name: 'Punkt_1_0',
4349                 withLabel: false,
4350                 visible: false,
4351                 fixed: true
4352             });
4353 
4354             p3 = this.create('point', [0, 1], {
4355                 id: this.id + 'gY0e0',
4356                 name: 'Punkt_0_1',
4357                 withLabel: false,
4358                 visible: false,
4359                 fixed: true
4360             });
4361 
4362             this.create('line', [p1, p2], {
4363                 id: this.id + 'gXLe0',
4364                 name: 'X-Achse',
4365                 withLabel: false,
4366                 visible: false
4367             });
4368 
4369             this.create('line', [p1, p3], {
4370                 id: this.id + 'gYLe0',
4371                 name: 'Y-Achse',
4372                 withLabel: false,
4373                 visible: false
4374             });
4375 
4376             return this;
4377         },
4378 
4379         /**
4380          * Change the height and width of the board's container.
4381          * After doing so, {@link JXG.JSXGraph.setBoundingBox} is called using
4382          * the actual size of the bounding box and the actual value of keepaspectratio.
4383          * If setBoundingbox() should not be called automatically,
4384          * call resizeContainer with dontSetBoundingBox == true.
4385          * @param {Number} canvasWidth New width of the container.
4386          * @param {Number} canvasHeight New height of the container.
4387          * @param {Boolean} [dontset=false] If true do not set the CSS width and height of the DOM element.
4388          * @param {Boolean} [dontSetBoundingBox=false] If true do not call setBoundingBox().
4389          * @returns {JXG.Board} Reference to the board
4390          */
4391         resizeContainer: function (canvasWidth, canvasHeight, dontset, dontSetBoundingBox) {
4392             var box_act, box, w, h, cx, cy,
4393                 shift_x = 0,
4394                 shift_y = 0;
4395 
4396             if (!dontSetBoundingBox) {
4397                 box_act = this.getBoundingBox();    // This is the actual bounding box.
4398             }
4399 
4400             this.canvasWidth = parseFloat(canvasWidth);
4401             this.canvasHeight = parseFloat(canvasHeight);
4402 
4403             if (!dontSetBoundingBox) {
4404                 box     = this.attr.boundingbox;    // This is the intended bounding box.
4405                 
4406                 // The shift values compensate the follow-up correction
4407                 // in setBoundingBox in case of "this.keepaspectratio==true"
4408                 // Otherwise, shift_x and shift_y will be zero.
4409                 shift_x = box_act[0] - box[0] / this.zoomX;
4410                 shift_y = box_act[1] - box[1] / this.zoomY;
4411 
4412                 cx = (box[2] + box[0]) * 0.5 + shift_x;
4413                 cy = (box[3] + box[1]) * 0.5 + shift_y;
4414 
4415                 w = (box[2] - box[0]) * 0.5 / this.zoomX;
4416                 h = (box[1] - box[3]) * 0.5 / this.zoomY;
4417 
4418                 box = [cx - w, cy + h, cx + w, cy - h];
4419             }
4420 
4421             if (!dontset) {
4422                 this.containerObj.style.width = (this.canvasWidth) + 'px';
4423                 this.containerObj.style.height = (this.canvasHeight) + 'px';
4424             }
4425             this.renderer.resize(this.canvasWidth, this.canvasHeight);
4426 
4427             if (!dontSetBoundingBox) {
4428                 this.setBoundingBox(box, this.keepaspectratio, 'keep');
4429             }
4430 
4431             return this;
4432         },
4433 
4434         /**
4435          * Lists the dependencies graph in a new HTML-window.
4436          * @returns {JXG.Board} Reference to the board
4437          */
4438         showDependencies: function () {
4439             var el, t, c, f, i;
4440 
4441             t = '<p>\n';
4442             for (el in this.objects) {
4443                 if (this.objects.hasOwnProperty(el)) {
4444                     i = 0;
4445                     for (c in this.objects[el].childElements) {
4446                         if (this.objects[el].childElements.hasOwnProperty(c)) {
4447                             i += 1;
4448                         }
4449                     }
4450                     if (i >= 0) {
4451                         t += '<strong>' + this.objects[el].id + ':<' + '/strong> ';
4452                     }
4453 
4454                     for (c in this.objects[el].childElements) {
4455                         if (this.objects[el].childElements.hasOwnProperty(c)) {
4456                             t += this.objects[el].childElements[c].id + '(' + this.objects[el].childElements[c].name + ')' + ', ';
4457                         }
4458                     }
4459                     t += '<p>\n';
4460                 }
4461             }
4462             t += '<' + '/p>\n';
4463             f = window.open();<