1 /*
  2     Copyright 2008-2024
  3         Matthias Ehmann,
  4         Michael Gerhaeuser,
  5         Carsten Miller,
  6         Bianca Valentin,
  7         Alfred Wassermann,
  8         Peter Wilfahrt
  9 
 10     This file is part of JSXGraph.
 11 
 12     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
 13 
 14     You can redistribute it and/or modify it under the terms of the
 15 
 16       * GNU Lesser General Public License as published by
 17         the Free Software Foundation, either version 3 of the License, or
 18         (at your option) any later version
 19       OR
 20       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
 21 
 22     JSXGraph is distributed in the hope that it will be useful,
 23     but WITHOUT ANY WARRANTY; without even the implied warranty of
 24     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 25     GNU Lesser General Public License for more details.
 26 
 27     You should have received a copy of the GNU Lesser General Public License and
 28     the MIT License along with JSXGraph. If not, see <https://www.gnu.org/licenses/>
 29     and <https://opensource.org/licenses/MIT/>.
 30  */
 31 
 32 /*global JXG: true, define: true, AMprocessNode: true, MathJax: true, window: true, document: true, init: true, translateASCIIMath: true, google: true*/
 33 
 34 /*jslint nomen: true, plusplus: true*/
 35 
 36 /**
 37  * @fileoverview The JXG.Board class is defined in this file. JXG.Board controls all properties and methods
 38  * used to manage a geonext board like managing geometric elements, managing mouse and touch events, etc.
 39  */
 40 
 41 import JXG from '../jxg.js';
 42 import Const from './constants.js';
 43 import Coords from './coords.js';
 44 import Options from '../options.js';
 45 import Numerics from '../math/numerics.js';
 46 import Mat from '../math/math.js';
 47 import Geometry from '../math/geometry.js';
 48 import Complex from '../math/complex.js';
 49 import Statistics from '../math/statistics.js';
 50 import JessieCode from '../parser/jessiecode.js';
 51 import Color from '../utils/color.js';
 52 import Type from '../utils/type.js';
 53 import EventEmitter from '../utils/event.js';
 54 import Env from '../utils/env.js';
 55 import Composition from './composition.js';
 56 
 57 /**
 58  * Constructs a new Board object.
 59  * @class JXG.Board controls all properties and methods used to manage a geonext board like managing geometric
 60  * elements, managing mouse and touch events, etc. You probably don't want to use this constructor directly.
 61  * Please use {@link JXG.JSXGraph.initBoard} to initialize a board.
 62  * @constructor
 63  * @param {String|Object} container The id of or reference to the HTML DOM element
 64  * the board is drawn in. This is usually a HTML div. If it is the reference to an HTML element and this element does not have an attribute "id",
 65  * this attribute "id" is set to a random value.
 66  * @param {JXG.AbstractRenderer} renderer The reference of a renderer.
 67  * @param {String} id Unique identifier for the board, may be an empty string or null or even undefined.
 68  * @param {JXG.Coords} origin The coordinates where the origin is placed, in user coordinates.
 69  * @param {Number} zoomX Zoom factor in x-axis direction
 70  * @param {Number} zoomY Zoom factor in y-axis direction
 71  * @param {Number} unitX Units in x-axis direction
 72  * @param {Number} unitY Units in y-axis direction
 73  * @param {Number} canvasWidth  The width of canvas
 74  * @param {Number} canvasHeight The height of canvas
 75  * @param {Object} attributes The attributes object given to {@link JXG.JSXGraph.initBoard}
 76  * @borrows JXG.EventEmitter#on as this.on
 77  * @borrows JXG.EventEmitter#off as this.off
 78  * @borrows JXG.EventEmitter#triggerEventHandlers as this.triggerEventHandlers
 79  * @borrows JXG.EventEmitter#eventHandlers as this.eventHandlers
 80  */
 81 JXG.Board = function (container, renderer, id,
 82     origin, zoomX, zoomY, unitX, unitY,
 83     canvasWidth, canvasHeight, attributes) {
 84     /**
 85      * Board is in no special mode, objects are highlighted on mouse over and objects may be
 86      * clicked to start drag&drop.
 87      * @type Number
 88      * @constant
 89      */
 90     this.BOARD_MODE_NONE = 0x0000;
 91 
 92     /**
 93      * Board is in drag mode, objects aren't highlighted on mouse over and the object referenced in
 94      * {@link JXG.Board#mouse} is updated on mouse movement.
 95      * @type Number
 96      * @constant
 97      */
 98     this.BOARD_MODE_DRAG = 0x0001;
 99 
100     /**
101      * In this mode a mouse move changes the origin's screen coordinates.
102      * @type Number
103      * @constant
104      */
105     this.BOARD_MODE_MOVE_ORIGIN = 0x0002;
106 
107     /**
108      * Update is made with high quality, e.g. graphs are evaluated at much more points.
109      * @type Number
110      * @constant
111      * @see JXG.Board#updateQuality
112      */
113     this.BOARD_MODE_ZOOM = 0x0011;
114 
115     /**
116      * Update is made with low quality, e.g. graphs are evaluated at a lesser amount of points.
117      * @type Number
118      * @constant
119      * @see JXG.Board#updateQuality
120      */
121     this.BOARD_QUALITY_LOW = 0x1;
122 
123     /**
124      * Update is made with high quality, e.g. graphs are evaluated at much more points.
125      * @type Number
126      * @constant
127      * @see JXG.Board#updateQuality
128      */
129     this.BOARD_QUALITY_HIGH = 0x2;
130 
131     /**
132      * Pointer to the document element containing the board.
133      * @type Object
134      */
135     if (Type.exists(attributes.document) && attributes.document !== false) {
136         this.document = attributes.document;
137     } else if (Env.isBrowser) {
138         this.document = document;
139     }
140 
141     /**
142      * The html-id of the html element containing the board.
143      * @type String
144      */
145     this.container = ''; // container
146 
147     /**
148      * ID of the board
149      * @type String
150      */
151     this.id = '';
152 
153     /**
154      * Pointer to the html element containing the board.
155      * @type Object
156      */
157     this.containerObj = null; // (Env.isBrowser ? this.document.getElementById(this.container) : null);
158 
159     // Set this.container and this.containerObj
160     if (Type.isString(container)) {
161         // Hosting div is given as string
162         this.container = container; // container
163         this.containerObj = (Env.isBrowser ? this.document.getElementById(this.container) : null);
164 
165     } else if (Env.isBrowser) {
166 
167         // Hosting div is given as object pointer
168         this.containerObj = container;
169         this.container = this.containerObj.getAttribute('id');
170         if (this.container === null) {
171             // Set random ID to this.container, but not to the DOM element
172 
173             this.container = 'null' + parseInt(Math.random() * 16777216).toString();
174         }
175     }
176 
177     if (Env.isBrowser && renderer.type !== 'no' && this.containerObj === null) {
178         throw new Error('\nJSXGraph: HTML container element "' + container + '" not found.');
179     }
180 
181     // TODO
182     // Why do we need this.id AND this.container?
183     // There was never a board attribute "id".
184     // The origin seems to be that in the geonext renderer we use a separate id, extracted from the GEONExT file.
185     if (Type.exists(id) && id !== '' && Env.isBrowser && !Type.exists(this.document.getElementById(id))) {
186         // If the given id is not valid, generate an unique id
187         this.id = id;
188     } else {
189         this.id = this.generateId();
190     }
191 
192     /**
193      * A reference to this boards renderer.
194      * @type JXG.AbstractRenderer
195      * @name JXG.Board#renderer
196      * @private
197      * @ignore
198      */
199     this.renderer = renderer;
200 
201     /**
202      * Grids keeps track of all grids attached to this board.
203      * @type Array
204      * @private
205      */
206     this.grids = [];
207 
208     /**
209      * Copy of the default options
210      * @type JXG.Options
211      */
212     this.options = Type.deepCopy(Options);  // A possible theme is not yet merged in
213 
214     /**
215      * Board attributes
216      * @type Object
217      */
218     this.attr = attributes;
219 
220     if (this.attr.theme !== 'default' && Type.exists(JXG.themes[this.attr.theme])) {
221         Type.mergeAttr(this.options, JXG.themes[this.attr.theme], true);
222     }
223 
224     /**
225      * Dimension of the board.
226      * @default 2
227      * @type Number
228      */
229     this.dimension = 2;
230     this.jc = new JessieCode();
231     this.jc.use(this);
232 
233     /**
234      * Coordinates of the boards origin. This a object with the two properties
235      * usrCoords and scrCoords. usrCoords always equals [1, 0, 0] and scrCoords
236      * stores the boards origin in homogeneous screen coordinates.
237      * @type Object
238      * @private
239      */
240     this.origin = {};
241     this.origin.usrCoords = [1, 0, 0];
242     this.origin.scrCoords = [1, origin[0], origin[1]];
243 
244     /**
245      * Zoom factor in X direction. It only stores the zoom factor to be able
246      * to get back to 100% in zoom100().
247      * @name JXG.Board.zoomX
248      * @type Number
249      * @private
250      * @ignore
251      */
252     this.zoomX = zoomX;
253 
254     /**
255      * Zoom factor in Y direction. It only stores the zoom factor to be able
256      * to get back to 100% in zoom100().
257      * @name JXG.Board.zoomY
258      * @type Number
259      * @private
260      * @ignore
261      */
262     this.zoomY = zoomY;
263 
264     /**
265      * The number of pixels which represent one unit in user-coordinates in x direction.
266      * @type Number
267      * @private
268      */
269     this.unitX = unitX * this.zoomX;
270 
271     /**
272      * The number of pixels which represent one unit in user-coordinates in y direction.
273      * @type Number
274      * @private
275      */
276     this.unitY = unitY * this.zoomY;
277 
278     /**
279      * Keep aspect ratio if bounding box is set and the width/height ratio differs from the
280      * width/height ratio of the canvas.
281      * @type Boolean
282      * @private
283      */
284     this.keepaspectratio = false;
285 
286     /**
287      * Canvas width.
288      * @type Number
289      * @private
290      */
291     this.canvasWidth = canvasWidth;
292 
293     /**
294      * Canvas Height
295      * @type Number
296      * @private
297      */
298     this.canvasHeight = canvasHeight;
299 
300     EventEmitter.eventify(this);
301 
302     this.hooks = [];
303 
304     /**
305      * An array containing all other boards that are updated after this board has been updated.
306      * @type Array
307      * @see JXG.Board#addChild
308      * @see JXG.Board#removeChild
309      */
310     this.dependentBoards = [];
311 
312     /**
313      * During the update process this is set to false to prevent an endless loop.
314      * @default false
315      * @type Boolean
316      */
317     this.inUpdate = false;
318 
319     /**
320      * 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.
321      * @type Object
322      */
323     this.objects = {};
324 
325     /**
326      * An array containing all geometric objects on the board in the order of construction.
327      * @type Array
328      */
329     this.objectsList = [];
330 
331     /**
332      * 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.
333      * @type Object
334      */
335     this.groups = {};
336 
337     /**
338      * Stores all the objects that are currently running an animation.
339      * @type Object
340      */
341     this.animationObjects = {};
342 
343     /**
344      * An associative array containing all highlighted elements belonging to the board.
345      * @type Object
346      */
347     this.highlightedObjects = {};
348 
349     /**
350      * Number of objects ever created on this board. This includes every object, even invisible and deleted ones.
351      * @type Number
352      */
353     this.numObjects = 0;
354 
355     /**
356      * An associative array / dictionary 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.
357      * @type Object
358      */
359     this.elementsByName = {};
360 
361     /**
362      * The board mode the board is currently in. Possible values are
363      * <ul>
364      * <li>JXG.Board.BOARD_MODE_NONE</li>
365      * <li>JXG.Board.BOARD_MODE_DRAG</li>
366      * <li>JXG.Board.BOARD_MODE_MOVE_ORIGIN</li>
367      * </ul>
368      * @type Number
369      */
370     this.mode = this.BOARD_MODE_NONE;
371 
372     /**
373      * The update quality of the board. In most cases this is set to {@link JXG.Board#BOARD_QUALITY_HIGH}.
374      * If {@link JXG.Board#mode} equals {@link JXG.Board#BOARD_MODE_DRAG} this is set to
375      * {@link JXG.Board#BOARD_QUALITY_LOW} to speed up the update process by e.g. reducing the number of
376      * evaluation points when plotting functions. Possible values are
377      * <ul>
378      * <li>BOARD_QUALITY_LOW</li>
379      * <li>BOARD_QUALITY_HIGH</li>
380      * </ul>
381      * @type Number
382      * @see JXG.Board#mode
383      */
384     this.updateQuality = this.BOARD_QUALITY_HIGH;
385 
386     /**
387      * If true updates are skipped.
388      * @type Boolean
389      */
390     this.isSuspendedRedraw = false;
391 
392     this.calculateSnapSizes();
393 
394     /**
395      * The distance from the mouse to the dragged object in x direction when the user clicked the mouse button.
396      * @type Number
397      * @see JXG.Board#drag_dy
398      */
399     this.drag_dx = 0;
400 
401     /**
402      * The distance from the mouse to the dragged object in y direction when the user clicked the mouse button.
403      * @type Number
404      * @see JXG.Board#drag_dx
405      */
406     this.drag_dy = 0;
407 
408     /**
409      * The last position where a drag event has been fired.
410      * @type Array
411      * @see JXG.Board#moveObject
412      */
413     this.drag_position = [0, 0];
414 
415     /**
416      * References to the object that is dragged with the mouse on the board.
417      * @type JXG.GeometryElement
418      * @see JXG.Board#touches
419      */
420     this.mouse = {};
421 
422     /**
423      * Keeps track on touched elements, like {@link JXG.Board#mouse} does for mouse events.
424      * @type Array
425      * @see JXG.Board#mouse
426      */
427     this.touches = [];
428 
429     /**
430      * A string containing the XML text of the construction.
431      * This is set in {@link JXG.FileReader.parseString}.
432      * Only useful if a construction is read from a GEONExT-, Intergeo-, Geogebra-, or Cinderella-File.
433      * @type String
434      */
435     this.xmlString = '';
436 
437     /**
438      * Cached result of getCoordsTopLeftCorner for touch/mouseMove-Events to save some DOM operations.
439      * @type Array
440      */
441     this.cPos = [];
442 
443     /**
444      * Contains the last time (epoch, msec) since the last touchMove event which was not thrown away or since
445      * touchStart because Android's Webkit browser fires too much of them.
446      * @type Number
447      */
448     this.touchMoveLast = 0;
449 
450     /**
451      * Contains the pointerId of the last touchMove event which was not thrown away or since
452      * touchStart because Android's Webkit browser fires too much of them.
453      * @type Number
454      */
455     this.touchMoveLastId = Infinity;
456 
457     /**
458      * Contains the last time (epoch, msec) since the last getCoordsTopLeftCorner call which was not thrown away.
459      * @type Number
460      */
461     this.positionAccessLast = 0;
462 
463     /**
464      * Collects all elements that triggered a mouse down event.
465      * @type Array
466      */
467     this.downObjects = [];
468     this.clickObjects = {};
469 
470     /**
471      * Collects all elements that have keyboard focus. Should be either one or no element.
472      * Elements are stored with their id.
473      * @type Array
474      */
475     this.focusObjects = [];
476 
477     if (this.attr.showcopyright) {
478         this.renderer.displayCopyright(Const.licenseText, parseInt(this.options.text.fontSize, 10));
479     }
480 
481     /**
482      * Full updates are needed after zoom and axis translates. This saves some time during an update.
483      * @default false
484      * @type Boolean
485      */
486     this.needsFullUpdate = false;
487 
488     /**
489      * If reducedUpdate is set to true then only the dragged element and few (e.g. 2) following
490      * elements are updated during mouse move. On mouse up the whole construction is
491      * updated. This enables us to be fast even on very slow devices.
492      * @type Boolean
493      * @default false
494      */
495     this.reducedUpdate = false;
496 
497     /**
498      * The current color blindness deficiency is stored in this property. If color blindness is not emulated
499      * at the moment, it's value is 'none'.
500      */
501     this.currentCBDef = 'none';
502 
503     /**
504      * If GEONExT constructions are displayed, then this property should be set to true.
505      * At the moment there should be no difference. But this may change.
506      * This is set in {@link JXG.GeonextReader.readGeonext}.
507      * @type Boolean
508      * @default false
509      * @see JXG.GeonextReader.readGeonext
510      */
511     this.geonextCompatibilityMode = false;
512 
513     if (this.options.text.useASCIIMathML && translateASCIIMath) {
514         init();
515     } else {
516         this.options.text.useASCIIMathML = false;
517     }
518 
519     /**
520      * A flag which tells if the board registers mouse events.
521      * @type Boolean
522      * @default false
523      */
524     this.hasMouseHandlers = false;
525 
526     /**
527      * A flag which tells if the board registers touch events.
528      * @type Boolean
529      * @default false
530      */
531     this.hasTouchHandlers = false;
532 
533     /**
534      * A flag which stores if the board registered pointer events.
535      * @type Boolean
536      * @default false
537      */
538     this.hasPointerHandlers = false;
539 
540     /**
541      * A flag which stores if the board registered zoom events, i.e. mouse wheel scroll events.
542      * @type Boolean
543      * @default false
544      */
545     this.hasWheelHandlers = false;
546 
547     /**
548      * A flag which tells if the board the JXG.Board#mouseUpListener is currently registered.
549      * @type Boolean
550      * @default false
551      */
552     this.hasMouseUp = false;
553 
554     /**
555      * A flag which tells if the board the JXG.Board#touchEndListener is currently registered.
556      * @type Boolean
557      * @default false
558      */
559     this.hasTouchEnd = false;
560 
561     /**
562      * A flag which tells us if the board has a pointerUp event registered at the moment.
563      * @type Boolean
564      * @default false
565      */
566     this.hasPointerUp = false;
567 
568     /**
569      * Array containing the events related to resizing that have event listeners.
570      * @type Array
571      * @default []
572      */
573     this.resizeHandlers = [];
574 
575     /**
576      * Offset for large coords elements like images
577      * @type Array
578      * @private
579      * @default [0, 0]
580      */
581     this._drag_offset = [0, 0];
582 
583     /**
584      * Stores the input device used in the last down or move event.
585      * @type String
586      * @private
587      * @default 'mouse'
588      */
589     this._inputDevice = 'mouse';
590 
591     /**
592      * Keeps a list of pointer devices which are currently touching the screen.
593      * @type Array
594      * @private
595      */
596     this._board_touches = [];
597 
598     /**
599      * A flag which tells us if the board is in the selecting mode
600      * @type Boolean
601      * @default false
602      */
603     this.selectingMode = false;
604 
605     /**
606      * A flag which tells us if the user is selecting
607      * @type Boolean
608      * @default false
609      */
610     this.isSelecting = false;
611 
612     /**
613      * A flag which tells us if the user is scrolling the viewport
614      * @type Boolean
615      * @private
616      * @default false
617      * @see JXG.Board#scrollListener
618      */
619     this._isScrolling = false;
620 
621     /**
622      * A flag which tells us if a resize is in process
623      * @type Boolean
624      * @private
625      * @default false
626      * @see JXG.Board#resizeListener
627      */
628     this._isResizing = false;
629 
630     /**
631      * A flag which tells us if the update is triggered by a change of the
632      * 3D view. In that case we only have to update the projection of
633      * the 3D elements and can avoid a full board update.
634      *
635      * @type Boolean
636      * @private
637      * @default false
638      */
639     this._change3DView = false;
640 
641     /**
642      * A bounding box for the selection
643      * @type Array
644      * @default [ [0,0], [0,0] ]
645      */
646     this.selectingBox = [[0, 0], [0, 0]];
647 
648     /**
649      * Array to log user activity.
650      * Entries are objects of the form '{type, id, start, end}' notifying
651      * the start time as well as the last time of a single event of type 'type'
652      * on a JSXGraph element of id 'id'.
653      * <p> 'start' and 'end' contain the amount of milliseconds elapsed between 1 January 1970 00:00:00 UTC
654      * and the time the event happened.
655      * <p>
656      * For the time being (i.e. v1.5.0) the only supported type is 'drag'.
657      * @type Array
658      */
659     this.userLog = [];
660 
661     this.mathLib = Math;        // Math or JXG.Math.IntervalArithmetic
662     this.mathLibJXG = JXG.Math; // JXG.Math or JXG.Math.IntervalArithmetic
663 
664     if (this.attr.registerevents === true) {
665         this.attr.registerevents = {
666             fullscreen: true,
667             keyboard: true,
668             pointer: true,
669             resize: true,
670             wheel: true
671         };
672     } else if (typeof this.attr.registerevents === 'object') {
673         if (!Type.exists(this.attr.registerevents.fullscreen)) {
674             this.attr.registerevents.fullscreen = true;
675         }
676         if (!Type.exists(this.attr.registerevents.keyboard)) {
677             this.attr.registerevents.keyboard = true;
678         }
679         if (!Type.exists(this.attr.registerevents.pointer)) {
680             this.attr.registerevents.pointer = true;
681         }
682         if (!Type.exists(this.attr.registerevents.resize)) {
683             this.attr.registerevents.resize = true;
684         }
685         if (!Type.exists(this.attr.registerevents.wheel)) {
686             this.attr.registerevents.wheel = true;
687         }
688     }
689     if (this.attr.registerevents !== false) {
690         if (this.attr.registerevents.fullscreen) {
691             this.addFullscreenEventHandlers();
692         }
693         if (this.attr.registerevents.keyboard) {
694             this.addKeyboardEventHandlers();
695         }
696         if (this.attr.registerevents.pointer) {
697             this.addEventHandlers();
698         }
699         if (this.attr.registerevents.resize) {
700             this.addResizeEventHandlers();
701         }
702         if (this.attr.registerevents.wheel) {
703             this.addWheelEventHandlers();
704         }
705     }
706 
707     this.methodMap = {
708         update: 'update',
709         fullUpdate: 'fullUpdate',
710         on: 'on',
711         off: 'off',
712         trigger: 'trigger',
713         setAttribute: 'setAttribute',
714         setBoundingBox: 'setBoundingBox',
715         setView: 'setBoundingBox',
716         getBoundingBox: 'getBoundingBox',
717         BoundingBox: 'getBoundingBox',
718         getView: 'getBoundingBox',
719         View: 'getBoundingBox',
720         migratePoint: 'migratePoint',
721         colorblind: 'emulateColorblindness',
722         suspendUpdate: 'suspendUpdate',
723         unsuspendUpdate: 'unsuspendUpdate',
724         clearTraces: 'clearTraces',
725         left: 'clickLeftArrow',
726         right: 'clickRightArrow',
727         up: 'clickUpArrow',
728         down: 'clickDownArrow',
729         zoomIn: 'zoomIn',
730         zoomOut: 'zoomOut',
731         zoom100: 'zoom100',
732         zoomElements: 'zoomElements',
733         remove: 'removeObject',
734         removeObject: 'removeObject'
735     };
736 };
737 
738 JXG.extend(
739     JXG.Board.prototype,
740     /** @lends JXG.Board.prototype */ {
741         /**
742          * Generates an unique name for the given object. The result depends on the objects type, if the
743          * object is a {@link JXG.Point}, capital characters are used, if it is of type {@link JXG.Line}
744          * only lower case characters are used. If object is of type {@link JXG.Polygon}, a bunch of lower
745          * case characters prefixed with P_ are used. If object is of type {@link JXG.Circle} the name is
746          * generated using lower case characters. prefixed with k_ is used. In any other case, lower case
747          * chars prefixed with s_ is used.
748          * @param {Object} object Reference of an JXG.GeometryElement that is to be named.
749          * @returns {String} Unique name for the object.
750          */
751         generateName: function (object) {
752             var possibleNames, i,
753                 maxNameLength = this.attr.maxnamelength,
754                 pre = '',
755                 post = '',
756                 indices = [],
757                 name = '';
758 
759             if (object.type === Const.OBJECT_TYPE_TICKS) {
760                 return '';
761             }
762 
763             if (Type.isPoint(object) || Type.isPoint3D(object)) {
764                 // points have capital letters
765                 possibleNames = [
766                     '', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'
767                 ];
768             } else if (object.type === Const.OBJECT_TYPE_ANGLE) {
769                 possibleNames = [
770                     '', 'α', 'β', 'γ', 'δ', 'ε', 'ζ', 'η', 'θ', 'ι', 'κ', 'λ',
771                     'μ', 'ν', 'ξ', 'ο', 'π', 'ρ', 'σ', 'τ', 'υ', 'φ', 'χ', 'ψ', 'ω'
772                 ];
773             } else {
774                 // all other elements get lowercase labels
775                 possibleNames = [
776                     '', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'
777                 ];
778             }
779 
780             if (
781                 !Type.isPoint(object) &&
782                 !Type.isPoint3D(object) &&
783                 object.elementClass !== Const.OBJECT_CLASS_LINE &&
784                 object.type !== Const.OBJECT_TYPE_ANGLE
785             ) {
786                 if (object.type === Const.OBJECT_TYPE_POLYGON) {
787                     pre = 'P_{';
788                 } else if (object.elementClass === Const.OBJECT_CLASS_CIRCLE) {
789                     pre = 'k_{';
790                 } else if (object.elementClass === Const.OBJECT_CLASS_TEXT) {
791                     pre = 't_{';
792                 } else {
793                     pre = 's_{';
794                 }
795                 post = '}';
796             }
797 
798             for (i = 0; i < maxNameLength; i++) {
799                 indices[i] = 0;
800             }
801 
802             while (indices[maxNameLength - 1] < possibleNames.length) {
803                 for (indices[0] = 1; indices[0] < possibleNames.length; indices[0]++) {
804                     name = pre;
805 
806                     for (i = maxNameLength; i > 0; i--) {
807                         name += possibleNames[indices[i - 1]];
808                     }
809 
810                     if (!Type.exists(this.elementsByName[name + post])) {
811                         return name + post;
812                     }
813                 }
814                 indices[0] = possibleNames.length;
815 
816                 for (i = 1; i < maxNameLength; i++) {
817                     if (indices[i - 1] === possibleNames.length) {
818                         indices[i - 1] = 1;
819                         indices[i] += 1;
820                     }
821                 }
822             }
823 
824             return '';
825         },
826 
827         /**
828          * Generates unique id for a board. The result is randomly generated and prefixed with 'jxgBoard'.
829          * @returns {String} Unique id for a board.
830          */
831         generateId: function () {
832             var r = 1;
833 
834             // as long as we don't have a unique id generate a new one
835             while (Type.exists(JXG.boards['jxgBoard' + r])) {
836                 r = Math.round(Math.random() * 16777216);
837             }
838 
839             return 'jxgBoard' + r;
840         },
841 
842         /**
843          * Composes an id for an element. If the ID is empty ('' or null) a new ID is generated, depending on the
844          * object type. As a side effect {@link JXG.Board#numObjects}
845          * is updated.
846          * @param {Object} obj Reference of an geometry object that needs an id.
847          * @param {Number} type Type of the object.
848          * @returns {String} Unique id for an element.
849          */
850         setId: function (obj, type) {
851             var randomNumber,
852                 num = this.numObjects,
853                 elId = obj.id;
854 
855             this.numObjects += 1;
856 
857             // If no id is provided or id is empty string, a new one is chosen
858             if (elId === '' || !Type.exists(elId)) {
859                 elId = this.id + type + num;
860                 while (Type.exists(this.objects[elId])) {
861                     randomNumber = Math.round(Math.random() * 65535);
862                     elId = this.id + type + num + '-' + randomNumber;
863                 }
864             }
865 
866             obj.id = elId;
867             this.objects[elId] = obj;
868             obj._pos = this.objectsList.length;
869             this.objectsList[this.objectsList.length] = obj;
870 
871             return elId;
872         },
873 
874         /**
875          * After construction of the object the visibility is set
876          * and the label is constructed if necessary.
877          * @param {Object} obj The object to add.
878          */
879         finalizeAdding: function (obj) {
880             if (obj.evalVisProp('visible') === false) {
881                 this.renderer.display(obj, false);
882             }
883         },
884 
885         finalizeLabel: function (obj) {
886             if (
887                 obj.hasLabel &&
888                 !obj.label.evalVisProp('islabel') &&
889                 obj.label.evalVisProp('visible') === false
890             ) {
891                 this.renderer.display(obj.label, false);
892             }
893         },
894 
895         /**********************************************************
896          *
897          * Event Handler helpers
898          *
899          **********************************************************/
900 
901         /**
902          * Returns false if the event has been triggered faster than the maximum frame rate.
903          *
904          * @param {Event} evt Event object given by the browser (unused)
905          * @returns {Boolean} If the event has been triggered faster than the maximum frame rate, false is returned.
906          * @private
907          * @see JXG.Board#pointerMoveListener
908          * @see JXG.Board#touchMoveListener
909          * @see JXG.Board#mouseMoveListener
910          */
911         checkFrameRate: function (evt) {
912             var handleEvt = false,
913                 time = new Date().getTime();
914 
915             if (Type.exists(evt.pointerId) && this.touchMoveLastId !== evt.pointerId) {
916                 handleEvt = true;
917                 this.touchMoveLastId = evt.pointerId;
918             }
919             if (!handleEvt && (time - this.touchMoveLast) * this.attr.maxframerate >= 1000) {
920                 handleEvt = true;
921             }
922             if (handleEvt) {
923                 this.touchMoveLast = time;
924             }
925             return handleEvt;
926         },
927 
928         /**
929          * Calculates mouse coordinates relative to the boards container.
930          * @returns {Array} Array of coordinates relative the boards container top left corner.
931          */
932         getCoordsTopLeftCorner: function () {
933             var cPos,
934                 doc,
935                 crect,
936                 // In ownerDoc we need the 'real' document object.
937                 // The first version is used in the case of shadowDom,
938                 // the second case in the 'normal' case.
939                 ownerDoc = this.document.ownerDocument || this.document,
940                 docElement = ownerDoc.documentElement || this.document.body.parentNode,
941                 docBody = ownerDoc.body,
942                 container = this.containerObj,
943                 zoom,
944                 o;
945 
946             /**
947              * During drags and origin moves the container element is usually not changed.
948              * Check the position of the upper left corner at most every 1000 msecs
949              */
950             if (
951                 this.cPos.length > 0 &&
952                 (this.mode === this.BOARD_MODE_DRAG ||
953                     this.mode === this.BOARD_MODE_MOVE_ORIGIN ||
954                     new Date().getTime() - this.positionAccessLast < 1000)
955             ) {
956                 return this.cPos;
957             }
958             this.positionAccessLast = new Date().getTime();
959 
960             // Check if getBoundingClientRect exists. If so, use this as this covers *everything*
961             // even CSS3D transformations etc.
962             // Supported by all browsers but IE 6, 7.
963             if (container.getBoundingClientRect) {
964                 crect = container.getBoundingClientRect();
965 
966                 zoom = 1.0;
967                 // Recursively search for zoom style entries.
968                 // This is necessary for reveal.js on webkit.
969                 // It fails if the user does zooming
970                 o = container;
971                 while (o && Type.exists(o.parentNode)) {
972                     if (
973                         Type.exists(o.style) &&
974                         Type.exists(o.style.zoom) &&
975                         o.style.zoom !== ''
976                     ) {
977                         zoom *= parseFloat(o.style.zoom);
978                     }
979                     o = o.parentNode;
980                 }
981                 cPos = [crect.left * zoom, crect.top * zoom];
982 
983                 // add border width
984                 cPos[0] += Env.getProp(container, 'border-left-width');
985                 cPos[1] += Env.getProp(container, 'border-top-width');
986 
987                 // vml seems to ignore paddings
988                 if (this.renderer.type !== 'vml') {
989                     // add padding
990                     cPos[0] += Env.getProp(container, 'padding-left');
991                     cPos[1] += Env.getProp(container, 'padding-top');
992                 }
993 
994                 this.cPos = cPos.slice();
995                 return this.cPos;
996             }
997 
998             //
999             //  OLD CODE
1000             //  IE 6-7 only:
1001             //
1002             cPos = Env.getOffset(container);
1003             doc = this.document.documentElement.ownerDocument;
1004 
1005             if (!this.containerObj.currentStyle && doc.defaultView) {
1006                 // Non IE
1007                 // this is for hacks like this one used in wordpress for the admin bar:
1008                 // html { margin-top: 28px }
1009                 // seems like it doesn't work in IE
1010 
1011                 cPos[0] += Env.getProp(docElement, 'margin-left');
1012                 cPos[1] += Env.getProp(docElement, 'margin-top');
1013 
1014                 cPos[0] += Env.getProp(docElement, 'border-left-width');
1015                 cPos[1] += Env.getProp(docElement, 'border-top-width');
1016 
1017                 cPos[0] += Env.getProp(docElement, 'padding-left');
1018                 cPos[1] += Env.getProp(docElement, 'padding-top');
1019             }
1020 
1021             if (docBody) {
1022                 cPos[0] += Env.getProp(docBody, 'left');
1023                 cPos[1] += Env.getProp(docBody, 'top');
1024             }
1025 
1026             // Google Translate offers widgets for web authors. These widgets apparently tamper with the clientX
1027             // and clientY coordinates of the mouse events. The minified sources seem to be the only publicly
1028             // available version so we're doing it the hacky way: Add a fixed offset.
1029             // see https://groups.google.com/d/msg/google-translate-general/H2zj0TNjjpY/jw6irtPlCw8J
1030             if (typeof google === 'object' && google.translate) {
1031                 cPos[0] += 10;
1032                 cPos[1] += 25;
1033             }
1034 
1035             // add border width
1036             cPos[0] += Env.getProp(container, 'border-left-width');
1037             cPos[1] += Env.getProp(container, 'border-top-width');
1038 
1039             // vml seems to ignore paddings
1040             if (this.renderer.type !== 'vml') {
1041                 // add padding
1042                 cPos[0] += Env.getProp(container, 'padding-left');
1043                 cPos[1] += Env.getProp(container, 'padding-top');
1044             }
1045 
1046             cPos[0] += this.attr.offsetx;
1047             cPos[1] += this.attr.offsety;
1048 
1049             this.cPos = cPos.slice();
1050             return this.cPos;
1051         },
1052 
1053         /**
1054          * This function divides the board into 9 sections and returns an array <tt>[u,v]</tt> which symbolizes the location of <tt>position</tt>.
1055          * Optional a <tt>margin</tt> to the inner of the board is respected.<br>
1056          *
1057          * @name Board#getPointLoc
1058          * @param {Array} position Array of requested position <tt>[x, y]</tt> or <tt>[w, x, y]</tt>.
1059          * @param {Array|Number} [margin] Optional margin for the inner of the board: <tt>[top, right, bottom, left]</tt>. A single number <tt>m</tt> is interpreted as <tt>[m, m, m, m]</tt>.
1060          * @returns {Array} [u,v] with the following meanings:
1061          * <pre>
1062          *     v    u > |   -1    |    0   |    1   |
1063          * ------------------------------------------
1064          *     1        | [-1,1]  |  [0,1] |  [1,1] |
1065          * ------------------------------------------
1066          *     0        | [-1,0]  |  Board |  [1,0] |
1067          * ------------------------------------------
1068          *    -1        | [-1,-1] | [0,-1] | [1,-1] |
1069          * </pre>
1070          * Positions inside the board (minus margin) return the value <tt>[0,0]</tt>.
1071          *
1072          * @example
1073          *      var point1, point2, point3, point4, margin,
1074          *             p1Location, p2Location, p3Location, p4Location,
1075          *             helppoint1, helppoint2, helppoint3, helppoint4;
1076          *
1077          *      // margin to make the boundingBox virtually smaller
1078          *      margin = [2,2,2,2];
1079          *
1080          *      // Points which are seen on screen
1081          *      point1 = board.create('point', [0,0]);
1082          *      point2 = board.create('point', [0,7]);
1083          *      point3 = board.create('point', [7,7]);
1084          *      point4 = board.create('point', [-7,-5]);
1085          *
1086          *      p1Location = board.getPointLoc(point1.coords.usrCoords, margin);
1087          *      p2Location = board.getPointLoc(point2.coords.usrCoords, margin);
1088          *      p3Location = board.getPointLoc(point3.coords.usrCoords, margin);
1089          *      p4Location = board.getPointLoc(point4.coords.usrCoords, margin);
1090          *
1091          *      // Text seen on screen
1092          *      board.create('text', [1,-1, "getPointLoc(A): " + "[" + p1Location + "]"])
1093          *      board.create('text', [1,-2, "getPointLoc(B): " + "[" + p2Location + "]"])
1094          *      board.create('text', [1,-3, "getPointLoc(C): " + "[" + p3Location + "]"])
1095          *      board.create('text', [1,-4, "getPointLoc(D): " + "[" + p4Location + "]"])
1096          *
1097          *
1098          *      // Helping points that are used to create the helping lines
1099          *      helppoint1 = board.create('point', [(function (){
1100          *          var bbx = board.getBoundingBox();
1101          *          return [bbx[2] - 2, bbx[1] -2];
1102          *      })], {
1103          *          visible: false,
1104          *      })
1105          *
1106          *      helppoint2 = board.create('point', [(function (){
1107          *          var bbx = board.getBoundingBox();
1108          *          return [bbx[0] + 2, bbx[1] -2];
1109          *      })], {
1110          *          visible: false,
1111          *      })
1112          *
1113          *      helppoint3 = board.create('point', [(function (){
1114          *          var bbx = board.getBoundingBox();
1115          *          return [bbx[0]+ 2, bbx[3] + 2];
1116          *      })],{
1117          *          visible: false,
1118          *      })
1119          *
1120          *      helppoint4 = board.create('point', [(function (){
1121          *          var bbx = board.getBoundingBox();
1122          *          return [bbx[2] -2, bbx[3] + 2];
1123          *      })], {
1124          *          visible: false,
1125          *      })
1126          *
1127          *      // Helping lines to visualize the 9 sectors and the margin
1128          *      board.create('line', [helppoint1, helppoint2]);
1129          *      board.create('line', [helppoint2, helppoint3]);
1130          *      board.create('line', [helppoint3, helppoint4]);
1131          *      board.create('line', [helppoint4, helppoint1]);
1132          *
1133          * </pre><div id="JXG4b3efef5-839d-4fac-bad1-7a14c0a89c70" class="jxgbox" style="width: 500px; height: 500px;"></div>
1134          * <script type="text/javascript">
1135          *     (function() {
1136          *         var board = JXG.JSXGraph.initBoard('JXG4b3efef5-839d-4fac-bad1-7a14c0a89c70',
1137          *             {boundingbox: [-8, 8, 8,-8], maxboundingbox: [-7.5,7.5,7.5,-7.5], axis: true, showcopyright: false, shownavigation: false, showZoom: false});
1138          *     var point1, point2, point3, point4, margin,
1139          *             p1Location, p2Location, p3Location, p4Location,
1140          *             helppoint1, helppoint2, helppoint3, helppoint4;
1141          *
1142          *      // margin to make the boundingBox virtually smaller
1143          *      margin = [2,2,2,2];
1144          *
1145          *      // Points which are seen on screen
1146          *      point1 = board.create('point', [0,0]);
1147          *      point2 = board.create('point', [0,7]);
1148          *      point3 = board.create('point', [7,7]);
1149          *      point4 = board.create('point', [-7,-5]);
1150          *
1151          *      p1Location = board.getPointLoc(point1.coords.usrCoords, margin);
1152          *      p2Location = board.getPointLoc(point2.coords.usrCoords, margin);
1153          *      p3Location = board.getPointLoc(point3.coords.usrCoords, margin);
1154          *      p4Location = board.getPointLoc(point4.coords.usrCoords, margin);
1155          *
1156          *      // Text seen on screen
1157          *      board.create('text', [1,-1, "getPointLoc(A): " + "[" + p1Location + "]"])
1158          *      board.create('text', [1,-2, "getPointLoc(B): " + "[" + p2Location + "]"])
1159          *      board.create('text', [1,-3, "getPointLoc(C): " + "[" + p3Location + "]"])
1160          *      board.create('text', [1,-4, "getPointLoc(D): " + "[" + p4Location + "]"])
1161          *
1162          *
1163          *      // Helping points that are used to create the helping lines
1164          *      helppoint1 = board.create('point', [(function (){
1165          *          var bbx = board.getBoundingBox();
1166          *          return [bbx[2] - 2, bbx[1] -2];
1167          *      })], {
1168          *          visible: false,
1169          *      })
1170          *
1171          *      helppoint2 = board.create('point', [(function (){
1172          *          var bbx = board.getBoundingBox();
1173          *          return [bbx[0] + 2, bbx[1] -2];
1174          *      })], {
1175          *          visible: false,
1176          *      })
1177          *
1178          *      helppoint3 = board.create('point', [(function (){
1179          *          var bbx = board.getBoundingBox();
1180          *          return [bbx[0]+ 2, bbx[3] + 2];
1181          *      })],{
1182          *          visible: false,
1183          *      })
1184          *
1185          *      helppoint4 = board.create('point', [(function (){
1186          *          var bbx = board.getBoundingBox();
1187          *          return [bbx[2] -2, bbx[3] + 2];
1188          *      })], {
1189          *          visible: false,
1190          *      })
1191          *
1192          *      // Helping lines to visualize the 9 sectors and the margin
1193          *      board.create('line', [helppoint1, helppoint2]);
1194          *      board.create('line', [helppoint2, helppoint3]);
1195          *      board.create('line', [helppoint3, helppoint4]);
1196          *      board.create('line', [helppoint4, helppoint1]);
1197          *  })();
1198          *
1199          * </script><pre>
1200          *
1201          */
1202         getPointLoc: function (position, margin) {
1203             var bbox, pos, res, marg;
1204 
1205             bbox = this.getBoundingBox();
1206             pos = position;
1207             if (pos.length === 2) {
1208                 pos.unshift(undefined);
1209             }
1210             res = [0, 0];
1211             marg = margin || 0;
1212             if (Type.isNumber(marg)) {
1213                 marg = [marg, marg, marg, marg];
1214             }
1215 
1216             if (pos[1] > (bbox[2] - marg[1])) {
1217                 res[0] = 1;
1218             }
1219             if (pos[1] < (bbox[0] + marg[3])) {
1220                 res[0] = -1;
1221             }
1222 
1223             if (pos[2] > (bbox[1] - marg[0])) {
1224                 res[1] = 1;
1225             }
1226             if (pos[2] < (bbox[3] + marg[2])) {
1227                 res[1] = -1;
1228             }
1229 
1230             return res;
1231         },
1232 
1233         /**
1234          * This function calculates where the origin is located (@link Board#getPointLoc).
1235          * Optional a <tt>margin</tt> to the inner of the board is respected.<br>
1236          *
1237          * @name Board#getLocationOrigin
1238          * @param {Array|Number} [margin] Optional margin for the inner of the board: <tt>[top, right, bottom, left]</tt>. A single number <tt>m</tt> is interpreted as <tt>[m, m, m, m]</tt>.
1239          * @returns {Array} [u,v] which shows where the origin is located (@link Board#getPointLoc).
1240          */
1241         getLocationOrigin: function (margin) {
1242             return this.getPointLoc([0, 0], margin);
1243         },
1244 
1245         /**
1246          * Get the position of the pointing device in screen coordinates, relative to the upper left corner
1247          * of the host tag.
1248          * @param {Event} e Event object given by the browser.
1249          * @param {Number} [i] Only use in case of touch events. This determines which finger to use and should not be set
1250          * for mouseevents.
1251          * @returns {Array} Contains the mouse coordinates in screen coordinates, ready for {@link JXG.Coords}
1252          */
1253         getMousePosition: function (e, i) {
1254             var cPos = this.getCoordsTopLeftCorner(),
1255                 absPos,
1256                 v;
1257 
1258             // Position of cursor using clientX/Y
1259             absPos = Env.getPosition(e, i, this.document);
1260 
1261             // Old:
1262             // This seems to be obsolete anyhow:
1263             // "In case there has been no down event before."
1264             // if (!Type.exists(this.cssTransMat)) {
1265             // this.updateCSSTransforms();
1266             // }
1267             // New:
1268             // We have to update the CSS transform matrix all the time,
1269             // since libraries like ZIMJS do not notify JSXGraph about a change.
1270             // In particular, sending a resize event event to JSXGraph
1271             // would be necessary.
1272             this.updateCSSTransforms();
1273 
1274             // Position relative to the top left corner
1275             v = [1, absPos[0] - cPos[0], absPos[1] - cPos[1]];
1276             v = Mat.matVecMult(this.cssTransMat, v);
1277             v[1] /= v[0];
1278             v[2] /= v[0];
1279             return [v[1], v[2]];
1280 
1281             // Method without CSS transformation
1282             /*
1283              return [absPos[0] - cPos[0], absPos[1] - cPos[1]];
1284              */
1285         },
1286 
1287         /**
1288          * Initiate moving the origin. This is used in mouseDown and touchStart listeners.
1289          * @param {Number} x Current mouse/touch coordinates
1290          * @param {Number} y Current mouse/touch coordinates
1291          */
1292         initMoveOrigin: function (x, y) {
1293             this.drag_dx = x - this.origin.scrCoords[1];
1294             this.drag_dy = y - this.origin.scrCoords[2];
1295 
1296             this.mode = this.BOARD_MODE_MOVE_ORIGIN;
1297             this.updateQuality = this.BOARD_QUALITY_LOW;
1298         },
1299 
1300         /**
1301          * Collects all elements below the current mouse pointer and fulfilling the following constraints:
1302          * <ul><li>isDraggable</li><li>visible</li><li>not fixed</li><li>not frozen</li></ul>
1303          * @param {Number} x Current mouse/touch coordinates
1304          * @param {Number} y current mouse/touch coordinates
1305          * @param {Object} evt An event object
1306          * @param {String} type What type of event? 'touch', 'mouse' or 'pen'.
1307          * @returns {Array} A list of geometric elements.
1308          */
1309         initMoveObject: function (x, y, evt, type) {
1310             var pEl,
1311                 el,
1312                 collect = [],
1313                 offset = [],
1314                 haspoint,
1315                 len = this.objectsList.length,
1316                 dragEl = { visProp: { layer: -10000 } };
1317 
1318             // Store status of key presses for 3D movement
1319             this._shiftKey = evt.shiftKey;
1320             this._ctrlKey = evt.ctrlKey;
1321 
1322             //for (el in this.objects) {
1323             for (el = 0; el < len; el++) {
1324                 pEl = this.objectsList[el];
1325                 haspoint = pEl.hasPoint && pEl.hasPoint(x, y);
1326 
1327                 if (pEl.visPropCalc.visible && haspoint) {
1328                     pEl.triggerEventHandlers([type + 'down', 'down'], [evt]);
1329                     this.downObjects.push(pEl);
1330                 }
1331 
1332                 if (haspoint &&
1333                     pEl.isDraggable &&
1334                     pEl.visPropCalc.visible &&
1335                     ((this.geonextCompatibilityMode &&
1336                         (Type.isPoint(pEl) || pEl.elementClass === Const.OBJECT_CLASS_TEXT)) ||
1337                         !this.geonextCompatibilityMode) &&
1338                     !pEl.evalVisProp('fixed')
1339                     /*(!pEl.visProp.frozen) &&*/
1340                 ) {
1341                     // Elements in the highest layer get priority.
1342                     if (
1343                         pEl.visProp.layer > dragEl.visProp.layer ||
1344                         (pEl.visProp.layer === dragEl.visProp.layer &&
1345                             pEl.lastDragTime.getTime() >= dragEl.lastDragTime.getTime())
1346                     ) {
1347                         // If an element and its label have the focus
1348                         // simultaneously, the element is taken.
1349                         // This only works if we assume that every browser runs
1350                         // through this.objects in the right order, i.e. an element A
1351                         // added before element B turns up here before B does.
1352                         if (
1353                             !this.attr.ignorelabels ||
1354                             !Type.exists(dragEl.label) ||
1355                             pEl !== dragEl.label
1356                         ) {
1357                             dragEl = pEl;
1358                             collect.push(dragEl);
1359 
1360                             // Save offset for large coords elements.
1361                             if (Type.exists(dragEl.coords)) {
1362                                 if (dragEl.elementClass === Const.OBJECT_CLASS_POINT ||
1363                                     dragEl.relativeCoords    // Relative texts like labels
1364                                 ) {
1365                                     offset.push(Statistics.subtract(dragEl.coords.scrCoords.slice(1), [x, y]));
1366                                 } else {
1367                                    // Images and texts
1368                                     offset.push(Statistics.subtract(dragEl.actualCoords.scrCoords.slice(1), [x, y]));
1369                                 }
1370                             } else {
1371                                 offset.push([0, 0]);
1372                             }
1373 
1374                             // We can't drop out of this loop because of the event handling system
1375                             //if (this.attr.takefirst) {
1376                             //    return collect;
1377                             //}
1378                         }
1379                     }
1380                 }
1381             }
1382 
1383             if (this.attr.drag.enabled && collect.length > 0) {
1384                 this.mode = this.BOARD_MODE_DRAG;
1385             }
1386 
1387             // A one-element array is returned.
1388             if (this.attr.takefirst) {
1389                 collect.length = 1;
1390                 this._drag_offset = offset[0];
1391             } else {
1392                 collect = collect.slice(-1);
1393                 this._drag_offset = offset[offset.length - 1];
1394             }
1395 
1396             if (!this._drag_offset) {
1397                 this._drag_offset = [0, 0];
1398             }
1399 
1400             // Move drag element to the top of the layer
1401             if (this.renderer.type === 'svg' &&
1402                 Type.exists(collect[0]) &&
1403                 collect[0].evalVisProp('dragtotopoflayer') &&
1404                 collect.length === 1 &&
1405                 Type.exists(collect[0].rendNode)
1406             ) {
1407                 collect[0].rendNode.parentNode.appendChild(collect[0].rendNode);
1408             }
1409 
1410             // // Init rotation angle and scale factor for two finger movements
1411             // this.previousRotation = 0.0;
1412             // this.previousScale = 1.0;
1413 
1414             if (collect.length >= 1) {
1415                 collect[0].highlight(true);
1416                 this.triggerEventHandlers(['mousehit', 'hit'], [evt, collect[0]]);
1417             }
1418 
1419             return collect;
1420         },
1421 
1422         /**
1423          * Moves an object.
1424          * @param {Number} x Coordinate
1425          * @param {Number} y Coordinate
1426          * @param {Object} o The touch object that is dragged: {JXG.Board#mouse} or {JXG.Board#touches}.
1427          * @param {Object} evt The event object.
1428          * @param {String} type Mouse or touch event?
1429          */
1430         moveObject: function (x, y, o, evt, type) {
1431             var newPos = new Coords(
1432                 Const.COORDS_BY_SCREEN,
1433                 this.getScrCoordsOfMouse(x, y),
1434                 this
1435             ),
1436                 drag,
1437                 dragScrCoords,
1438                 newDragScrCoords;
1439 
1440             if (!(o && o.obj)) {
1441                 return;
1442             }
1443             drag = o.obj;
1444 
1445             // Avoid updates for very small movements of coordsElements, see below
1446             if (drag.coords) {
1447                 dragScrCoords = drag.coords.scrCoords.slice();
1448             }
1449 
1450             this.addLogEntry('drag', drag, newPos.usrCoords.slice(1));
1451 
1452             // Store the position and add the correctionvector from the mouse
1453             // position to the object's coords.
1454             this.drag_position = [newPos.scrCoords[1], newPos.scrCoords[2]];
1455             this.drag_position = Statistics.add(this.drag_position, this._drag_offset);
1456 
1457             // Store status of key presses for 3D movement
1458             this._shiftKey = evt.shiftKey;
1459             this._ctrlKey = evt.ctrlKey;
1460 
1461             //
1462             // We have to distinguish between CoordsElements and other elements like lines.
1463             // The latter need the difference between two move events.
1464             if (Type.exists(drag.coords)) {
1465                 drag.setPositionDirectly(Const.COORDS_BY_SCREEN, this.drag_position, [x, y]);
1466             } else {
1467                 this.displayInfobox(false);
1468                 // Hide infobox in case the user has touched an intersection point
1469                 // and drags the underlying line now.
1470 
1471                 if (!isNaN(o.targets[0].Xprev + o.targets[0].Yprev)) {
1472                     drag.setPositionDirectly(
1473                         Const.COORDS_BY_SCREEN,
1474                         [newPos.scrCoords[1], newPos.scrCoords[2]],
1475                         [o.targets[0].Xprev, o.targets[0].Yprev]
1476                     );
1477                 }
1478                 // Remember the actual position for the next move event. Then we are able to
1479                 // compute the difference vector.
1480                 o.targets[0].Xprev = newPos.scrCoords[1];
1481                 o.targets[0].Yprev = newPos.scrCoords[2];
1482             }
1483             // This may be necessary for some gliders and labels
1484             if (Type.exists(drag.coords)) {
1485                 drag.prepareUpdate().update(false).updateRenderer();
1486                 this.updateInfobox(drag);
1487                 drag.prepareUpdate().update(true).updateRenderer();
1488             }
1489 
1490             if (drag.coords) {
1491                 newDragScrCoords = drag.coords.scrCoords;
1492             }
1493             // No updates for very small movements of coordsElements
1494             if (
1495                 !drag.coords ||
1496                 dragScrCoords[1] !== newDragScrCoords[1] ||
1497                 dragScrCoords[2] !== newDragScrCoords[2]
1498             ) {
1499                 drag.triggerEventHandlers([type + 'drag', 'drag'], [evt]);
1500                 // Update all elements of the board
1501                 this.update(drag);
1502             }
1503             drag.highlight(true);
1504             this.triggerEventHandlers(['mousehit', 'hit'], [evt, drag]);
1505 
1506             drag.lastDragTime = new Date();
1507         },
1508 
1509         /**
1510          * Moves elements in multitouch mode.
1511          * @param {Array} p1 x,y coordinates of first touch
1512          * @param {Array} p2 x,y coordinates of second touch
1513          * @param {Object} o The touch object that is dragged: {JXG.Board#touches}.
1514          * @param {Object} evt The event object that lead to this movement.
1515          */
1516         twoFingerMove: function (o, id, evt) {
1517             var drag;
1518 
1519             if (Type.exists(o) && Type.exists(o.obj)) {
1520                 drag = o.obj;
1521             } else {
1522                 return;
1523             }
1524 
1525             if (
1526                 drag.elementClass === Const.OBJECT_CLASS_LINE ||
1527                 drag.type === Const.OBJECT_TYPE_POLYGON
1528             ) {
1529                 this.twoFingerTouchObject(o.targets, drag, id);
1530             } else if (drag.elementClass === Const.OBJECT_CLASS_CIRCLE) {
1531                 this.twoFingerTouchCircle(o.targets, drag, id);
1532             }
1533 
1534             if (evt) {
1535                 drag.triggerEventHandlers(['touchdrag', 'drag'], [evt]);
1536             }
1537         },
1538 
1539         /**
1540          * Compute the transformation matrix to move an element according to the
1541          * previous and actual positions of finger 1 and finger 2.
1542          * See also https://math.stackexchange.com/questions/4010538/solve-for-2d-translation-rotation-and-scale-given-two-touch-point-movements
1543          *
1544          * @param {Object} finger1 Actual and previous position of finger 1
1545          * @param {Object} finger1 Actual and previous position of finger 1
1546          * @param {Boolean} scalable Flag if element may be scaled
1547          * @param {Boolean} rotatable Flag if element may be rotated
1548          * @returns {Array}
1549          */
1550         getTwoFingerTransform(finger1, finger2, scalable, rotatable) {
1551             var crd,
1552                 x1, y1, x2, y2,
1553                 dx, dy,
1554                 xx1, yy1, xx2, yy2,
1555                 dxx, dyy,
1556                 C, S, LL, tx, ty, lbda;
1557 
1558             crd = new Coords(Const.COORDS_BY_SCREEN, [finger1.Xprev, finger1.Yprev], this).usrCoords;
1559             x1 = crd[1];
1560             y1 = crd[2];
1561             crd = new Coords(Const.COORDS_BY_SCREEN, [finger2.Xprev, finger2.Yprev], this).usrCoords;
1562             x2 = crd[1];
1563             y2 = crd[2];
1564 
1565             crd = new Coords(Const.COORDS_BY_SCREEN, [finger1.X, finger1.Y], this).usrCoords;
1566             xx1 = crd[1];
1567             yy1 = crd[2];
1568             crd = new Coords(Const.COORDS_BY_SCREEN, [finger2.X, finger2.Y], this).usrCoords;
1569             xx2 = crd[1];
1570             yy2 = crd[2];
1571 
1572             dx = x2 - x1;
1573             dy = y2 - y1;
1574             dxx = xx2 - xx1;
1575             dyy = yy2 - yy1;
1576 
1577             LL = dx * dx + dy * dy;
1578             C = (dxx * dx + dyy * dy) / LL;
1579             S = (dyy * dx - dxx * dy) / LL;
1580             if (!scalable) {
1581                 lbda = Mat.hypot(C, S);
1582                 C /= lbda;
1583                 S /= lbda;
1584             }
1585             if (!rotatable) {
1586                 S = 0;
1587             }
1588             tx = 0.5 * (xx1 + xx2 - C * (x1 + x2) + S * (y1 + y2));
1589             ty = 0.5 * (yy1 + yy2 - S * (x1 + x2) - C * (y1 + y2));
1590 
1591             return [1, 0, 0,
1592                 tx, C, -S,
1593                 ty, S, C];
1594         },
1595 
1596         /**
1597          * Moves, rotates and scales a line or polygon with two fingers.
1598          * <p>
1599          * If one vertex of the polygon snaps to the grid or to points or is not draggable,
1600          * two-finger-movement is cancelled.
1601          *
1602          * @param {Array} tar Array containing touch event objects: {JXG.Board#touches.targets}.
1603          * @param {object} drag The object that is dragged:
1604          * @param {Number} id pointerId of the event. In case of old touch event this is emulated.
1605          */
1606         twoFingerTouchObject: function (tar, drag, id) {
1607             var t, T,
1608                 ar, i, len,
1609                 snap = false;
1610 
1611             if (
1612                 Type.exists(tar[0]) &&
1613                 Type.exists(tar[1]) &&
1614                 !isNaN(tar[0].Xprev + tar[0].Yprev + tar[1].Xprev + tar[1].Yprev)
1615             ) {
1616 
1617                 T = this.getTwoFingerTransform(
1618                     tar[0], tar[1],
1619                     drag.evalVisProp('scalable'),
1620                     drag.evalVisProp('rotatable'));
1621                 t = this.create('transform', T, { type: 'generic' });
1622                 t.update();
1623 
1624                 if (drag.elementClass === Const.OBJECT_CLASS_LINE) {
1625                     ar = [];
1626                     if (drag.point1.draggable()) {
1627                         ar.push(drag.point1);
1628                     }
1629                     if (drag.point2.draggable()) {
1630                         ar.push(drag.point2);
1631                     }
1632                     t.applyOnce(ar);
1633                 } else if (drag.type === Const.OBJECT_TYPE_POLYGON) {
1634                     len = drag.vertices.length - 1;
1635                     snap = drag.evalVisProp('snaptogrid') || drag.evalVisProp('snaptopoints');
1636                     for (i = 0; i < len && !snap; ++i) {
1637                         snap = snap || drag.vertices[i].evalVisProp('snaptogrid') || drag.vertices[i].evalVisProp('snaptopoints');
1638                         snap = snap || (!drag.vertices[i].draggable());
1639                     }
1640                     if (!snap) {
1641                         ar = [];
1642                         for (i = 0; i < len; ++i) {
1643                             if (drag.vertices[i].draggable()) {
1644                                 ar.push(drag.vertices[i]);
1645                             }
1646                         }
1647                         t.applyOnce(ar);
1648                     }
1649                 }
1650 
1651                 this.update();
1652                 drag.highlight(true);
1653             }
1654         },
1655 
1656         /*
1657          * Moves, rotates and scales a circle with two fingers.
1658          * @param {Array} tar Array containing touch event objects: {JXG.Board#touches.targets}.
1659          * @param {object} drag The object that is dragged:
1660          * @param {Number} id pointerId of the event. In case of old touch event this is emulated.
1661          */
1662         twoFingerTouchCircle: function (tar, drag, id) {
1663             var fixEl, moveEl, np, op, fix, d, alpha, t1, t2, t3, t4;
1664 
1665             if (drag.method === 'pointCircle' || drag.method === 'pointLine') {
1666                 return;
1667             }
1668 
1669             if (
1670                 Type.exists(tar[0]) &&
1671                 Type.exists(tar[1]) &&
1672                 !isNaN(tar[0].Xprev + tar[0].Yprev + tar[1].Xprev + tar[1].Yprev)
1673             ) {
1674                 if (id === tar[0].num) {
1675                     fixEl = tar[1];
1676                     moveEl = tar[0];
1677                 } else {
1678                     fixEl = tar[0];
1679                     moveEl = tar[1];
1680                 }
1681 
1682                 fix = new Coords(Const.COORDS_BY_SCREEN, [fixEl.Xprev, fixEl.Yprev], this)
1683                     .usrCoords;
1684                 // Previous finger position
1685                 op = new Coords(Const.COORDS_BY_SCREEN, [moveEl.Xprev, moveEl.Yprev], this)
1686                     .usrCoords;
1687                 // New finger position
1688                 np = new Coords(Const.COORDS_BY_SCREEN, [moveEl.X, moveEl.Y], this).usrCoords;
1689 
1690                 alpha = Geometry.rad(op.slice(1), fix.slice(1), np.slice(1));
1691 
1692                 // Rotate and scale by the movement of the second finger
1693                 t1 = this.create('transform', [-fix[1], -fix[2]], {
1694                     type: 'translate'
1695                 });
1696                 t2 = this.create('transform', [alpha], { type: 'rotate' });
1697                 t1.melt(t2);
1698                 if (drag.evalVisProp('scalable')) {
1699                     d = Geometry.distance(fix, np) / Geometry.distance(fix, op);
1700                     t3 = this.create('transform', [d, d], { type: 'scale' });
1701                     t1.melt(t3);
1702                 }
1703                 t4 = this.create('transform', [fix[1], fix[2]], {
1704                     type: 'translate'
1705                 });
1706                 t1.melt(t4);
1707 
1708                 if (drag.center.draggable()) {
1709                     t1.applyOnce([drag.center]);
1710                 }
1711 
1712                 if (drag.method === 'twoPoints') {
1713                     if (drag.point2.draggable()) {
1714                         t1.applyOnce([drag.point2]);
1715                     }
1716                 } else if (drag.method === 'pointRadius') {
1717                     if (Type.isNumber(drag.updateRadius.origin)) {
1718                         drag.setRadius(drag.radius * d);
1719                     }
1720                 }
1721 
1722                 this.update(drag.center);
1723                 drag.highlight(true);
1724             }
1725         },
1726 
1727         highlightElements: function (x, y, evt, target) {
1728             var el,
1729                 pEl,
1730                 pId,
1731                 overObjects = {},
1732                 len = this.objectsList.length;
1733 
1734             // Elements  below the mouse pointer which are not highlighted yet will be highlighted.
1735             for (el = 0; el < len; el++) {
1736                 pEl = this.objectsList[el];
1737                 pId = pEl.id;
1738                 if (
1739                     Type.exists(pEl.hasPoint) &&
1740                     pEl.visPropCalc.visible &&
1741                     pEl.hasPoint(x, y)
1742                 ) {
1743                     // this is required in any case because otherwise the box won't be shown until the point is dragged
1744                     this.updateInfobox(pEl);
1745 
1746                     if (!Type.exists(this.highlightedObjects[pId])) {
1747                         // highlight only if not highlighted
1748                         overObjects[pId] = pEl;
1749                         pEl.highlight();
1750                         // triggers board event.
1751                         this.triggerEventHandlers(['mousehit', 'hit'], [evt, pEl, target]);
1752                     }
1753 
1754                     if (pEl.mouseover) {
1755                         pEl.triggerEventHandlers(['mousemove', 'move'], [evt]);
1756                     } else {
1757                         pEl.triggerEventHandlers(['mouseover', 'over'], [evt]);
1758                         pEl.mouseover = true;
1759                     }
1760                 }
1761             }
1762 
1763             for (el = 0; el < len; el++) {
1764                 pEl = this.objectsList[el];
1765                 pId = pEl.id;
1766                 if (pEl.mouseover) {
1767                     if (!overObjects[pId]) {
1768                         pEl.triggerEventHandlers(['mouseout', 'out'], [evt]);
1769                         pEl.mouseover = false;
1770                     }
1771                 }
1772             }
1773         },
1774 
1775         /**
1776          * Helper function which returns a reasonable starting point for the object being dragged.
1777          * Formerly known as initXYstart().
1778          * @private
1779          * @param {JXG.GeometryElement} obj The object to be dragged
1780          * @param {Array} targets Array of targets. It is changed by this function.
1781          */
1782         saveStartPos: function (obj, targets) {
1783             var xy = [],
1784                 i,
1785                 len;
1786 
1787             if (obj.type === Const.OBJECT_TYPE_TICKS) {
1788                 xy.push([1, NaN, NaN]);
1789             } else if (obj.elementClass === Const.OBJECT_CLASS_LINE) {
1790                 xy.push(obj.point1.coords.usrCoords);
1791                 xy.push(obj.point2.coords.usrCoords);
1792             } else if (obj.elementClass === Const.OBJECT_CLASS_CIRCLE) {
1793                 xy.push(obj.center.coords.usrCoords);
1794                 if (obj.method === 'twoPoints') {
1795                     xy.push(obj.point2.coords.usrCoords);
1796                 }
1797             } else if (obj.type === Const.OBJECT_TYPE_POLYGON) {
1798                 len = obj.vertices.length - 1;
1799                 for (i = 0; i < len; i++) {
1800                     xy.push(obj.vertices[i].coords.usrCoords);
1801                 }
1802             } else if (obj.type === Const.OBJECT_TYPE_SECTOR) {
1803                 xy.push(obj.point1.coords.usrCoords);
1804                 xy.push(obj.point2.coords.usrCoords);
1805                 xy.push(obj.point3.coords.usrCoords);
1806             } else if (Type.isPoint(obj) || obj.type === Const.OBJECT_TYPE_GLIDER) {
1807                 xy.push(obj.coords.usrCoords);
1808             } else if (obj.elementClass === Const.OBJECT_CLASS_CURVE) {
1809                 // if (Type.exists(obj.parents)) {
1810                 //     len = obj.parents.length;
1811                 //     if (len > 0) {
1812                 //         for (i = 0; i < len; i++) {
1813                 //             xy.push(this.select(obj.parents[i]).coords.usrCoords);
1814                 //         }
1815                 //     } else
1816                 // }
1817                 if (obj.points.length > 0) {
1818                     xy.push(obj.points[0].usrCoords);
1819                 }
1820             } else {
1821                 try {
1822                     xy.push(obj.coords.usrCoords);
1823                 } catch (e) {
1824                     JXG.debug(
1825                         'JSXGraph+ saveStartPos: obj.coords.usrCoords not available: ' + e
1826                     );
1827                 }
1828             }
1829 
1830             len = xy.length;
1831             for (i = 0; i < len; i++) {
1832                 targets.Zstart.push(xy[i][0]);
1833                 targets.Xstart.push(xy[i][1]);
1834                 targets.Ystart.push(xy[i][2]);
1835             }
1836         },
1837 
1838         mouseOriginMoveStart: function (evt) {
1839             var r, pos;
1840 
1841             r = this._isRequiredKeyPressed(evt, 'pan');
1842             if (r) {
1843                 pos = this.getMousePosition(evt);
1844                 this.initMoveOrigin(pos[0], pos[1]);
1845             }
1846 
1847             return r;
1848         },
1849 
1850         mouseOriginMove: function (evt) {
1851             var r = this.mode === this.BOARD_MODE_MOVE_ORIGIN,
1852                 pos;
1853 
1854             if (r) {
1855                 pos = this.getMousePosition(evt);
1856                 this.moveOrigin(pos[0], pos[1], true);
1857             }
1858 
1859             return r;
1860         },
1861 
1862         /**
1863          * Start moving the origin with one finger.
1864          * @private
1865          * @param  {Object} evt Event from touchStartListener
1866          * @return {Boolean}   returns if the origin is moved.
1867          */
1868         touchStartMoveOriginOneFinger: function (evt) {
1869             var touches = evt['touches'],
1870                 conditions,
1871                 pos;
1872 
1873             conditions =
1874                 this.attr.pan.enabled && !this.attr.pan.needtwofingers && touches.length === 1;
1875 
1876             if (conditions) {
1877                 pos = this.getMousePosition(evt, 0);
1878                 this.initMoveOrigin(pos[0], pos[1]);
1879             }
1880 
1881             return conditions;
1882         },
1883 
1884         /**
1885          * Move the origin with one finger
1886          * @private
1887          * @param  {Object} evt Event from touchMoveListener
1888          * @return {Boolean}     returns if the origin is moved.
1889          */
1890         touchOriginMove: function (evt) {
1891             var r = this.mode === this.BOARD_MODE_MOVE_ORIGIN,
1892                 pos;
1893 
1894             if (r) {
1895                 pos = this.getMousePosition(evt, 0);
1896                 this.moveOrigin(pos[0], pos[1], true);
1897             }
1898 
1899             return r;
1900         },
1901 
1902         /**
1903          * Stop moving the origin with one finger
1904          * @return {null} null
1905          * @private
1906          */
1907         originMoveEnd: function () {
1908             this.updateQuality = this.BOARD_QUALITY_HIGH;
1909             this.mode = this.BOARD_MODE_NONE;
1910         },
1911 
1912         /**********************************************************
1913          *
1914          * Event Handler
1915          *
1916          **********************************************************/
1917 
1918         /**
1919          * Suppresses the default event handling.
1920          * Used for context menu.
1921          *
1922          * @param {Event} e
1923          * @returns {Boolean} false
1924          */
1925         suppressDefault: function (e) {
1926             if (Type.exists(e)) {
1927                 e.preventDefault();
1928             }
1929             return false;
1930         },
1931 
1932         /**
1933          * Add all possible event handlers to the board object
1934          * that move objects, i.e. mouse, pointer and touch events.
1935          */
1936         addEventHandlers: function () {
1937             if (Env.supportsPointerEvents()) {
1938                 this.addPointerEventHandlers();
1939             } else {
1940                 this.addMouseEventHandlers();
1941                 this.addTouchEventHandlers();
1942             }
1943 
1944             if (this.containerObj !== null) {
1945                 // this.containerObj.oncontextmenu = this.suppressDefault;
1946                 Env.addEvent(this.containerObj, 'contextmenu', this.suppressDefault, this);
1947             }
1948 
1949             // This one produces errors on IE
1950             // // Env.addEvent(this.containerObj, 'contextmenu', function (e) { e.preventDefault(); return false;}, this);
1951             // This one works on IE, Firefox and Chromium with default configurations. On some Safari
1952             // or Opera versions the user must explicitly allow the deactivation of the context menu.
1953         },
1954 
1955         /**
1956          * Remove all event handlers from the board object
1957          */
1958         removeEventHandlers: function () {
1959             if ((this.hasPointerHandlers || this.hasMouseHandlers || this.hasTouchHandlers) &&
1960                 this.containerObj !== null
1961             ) {
1962                 Env.removeEvent(this.containerObj, 'contextmenu', this.suppressDefault, this);
1963             }
1964 
1965             this.removeMouseEventHandlers();
1966             this.removeTouchEventHandlers();
1967             this.removePointerEventHandlers();
1968 
1969             this.removeFullscreenEventHandlers();
1970             this.removeKeyboardEventHandlers();
1971             this.removeResizeEventHandlers();
1972 
1973             // if (Env.isBrowser) {
1974             //     if (Type.exists(this.resizeObserver)) {
1975             //         this.stopResizeObserver();
1976             //     } else {
1977             //         Env.removeEvent(window, 'resize', this.resizeListener, this);
1978             //         this.stopIntersectionObserver();
1979             //     }
1980             //     Env.removeEvent(window, 'scroll', this.scrollListener, this);
1981             // }
1982         },
1983 
1984         /**
1985          * Add resize related event handlers
1986          *
1987          */
1988         addResizeEventHandlers: function () {
1989             // var that = this;
1990 
1991             this.resizeHandlers = [];
1992             if (Env.isBrowser) {
1993                 try {
1994                     // Supported by all new browsers
1995                     // resizeObserver: triggered if size of the JSXGraph div changes.
1996                     this.startResizeObserver();
1997                     this.resizeHandlers.push('resizeobserver');
1998                 } catch (err) {
1999                     // Certain Safari and edge version do not support
2000                     // resizeObserver, but intersectionObserver.
2001                     // resize event: triggered if size of window changes
2002                     Env.addEvent(window, 'resize', this.resizeListener, this);
2003                     // intersectionObserver: triggered if JSXGraph becomes visible.
2004                     this.startIntersectionObserver();
2005                     this.resizeHandlers.push('resize');
2006                 }
2007                 // Scroll event: needs to be captured since on mobile devices
2008                 // sometimes a header bar is displayed / hidden, which triggers a
2009                 // resize event.
2010                 Env.addEvent(window, 'scroll', this.scrollListener, this);
2011                 this.resizeHandlers.push('scroll');
2012 
2013                 // On browser print:
2014                 // we need to call the listener when having @media: print.
2015                 try {
2016                     // window.matchMedia("print").addEventListener('change', this.printListenerMatch.apply(this, arguments));
2017                     window.matchMedia("print").addEventListener('change', this.printListenerMatch.bind(this));
2018                     window.matchMedia("screen").addEventListener('change', this.printListenerMatch.bind(this));
2019                     this.resizeHandlers.push('print');
2020                 } catch (err) {
2021                     JXG.debug("Error adding printListener", err);
2022                 }
2023                 // if (Type.isFunction(MediaQueryList.prototype.addEventListener)) {
2024                 //     window.matchMedia("print").addEventListener('change', function (mql) {
2025                 //         if (mql.matches) {
2026                 //             that.printListener();
2027                 //         }
2028                 //     });
2029                 // } else if (Type.isFunction(MediaQueryList.prototype.addListener)) { // addListener might be deprecated
2030                 //     window.matchMedia("print").addListener(function (mql, ev) {
2031                 //         if (mql.matches) {
2032                 //             that.printListener(ev);
2033                 //         }
2034                 //     });
2035                 // }
2036 
2037                 // When closing the print dialog we again have to resize.
2038                 // Env.addEvent(window, 'afterprint', this.printListener, this);
2039                 // this.resizeHandlers.push('afterprint');
2040             }
2041         },
2042 
2043         /**
2044          * Remove resize related event handlers
2045          *
2046          */
2047         removeResizeEventHandlers: function () {
2048             var i, e;
2049             if (this.resizeHandlers.length > 0 && Env.isBrowser) {
2050                 for (i = 0; i < this.resizeHandlers.length; i++) {
2051                     e = this.resizeHandlers[i];
2052                     switch (e) {
2053                         case 'resizeobserver':
2054                             if (Type.exists(this.resizeObserver)) {
2055                                 this.stopResizeObserver();
2056                             }
2057                             break;
2058                         case 'resize':
2059                             Env.removeEvent(window, 'resize', this.resizeListener, this);
2060                             if (Type.exists(this.intersectionObserver)) {
2061                                 this.stopIntersectionObserver();
2062                             }
2063                             break;
2064                         case 'scroll':
2065                             Env.removeEvent(window, 'scroll', this.scrollListener, this);
2066                             break;
2067                         case 'print':
2068                             window.matchMedia("print").removeEventListener('change', this.printListenerMatch.bind(this), false);
2069                             window.matchMedia("screen").removeEventListener('change', this.printListenerMatch.bind(this), false);
2070                             break;
2071                         // case 'afterprint':
2072                         //     Env.removeEvent(window, 'afterprint', this.printListener, this);
2073                         //     break;
2074                     }
2075                 }
2076                 this.resizeHandlers = [];
2077             }
2078         },
2079 
2080 
2081         /**
2082          * Registers pointer event handlers.
2083          */
2084         addPointerEventHandlers: function () {
2085             if (!this.hasPointerHandlers && Env.isBrowser) {
2086                 var moveTarget = this.attr.movetarget || this.containerObj;
2087 
2088                 if (window.navigator.msPointerEnabled) {
2089                     // IE10-
2090                     Env.addEvent(this.containerObj, 'MSPointerDown', this.pointerDownListener, this);
2091                     Env.addEvent(moveTarget, 'MSPointerMove', this.pointerMoveListener, this);
2092                 } else {
2093                     Env.addEvent(this.containerObj, 'pointerdown', this.pointerDownListener, this);
2094                     Env.addEvent(moveTarget, 'pointermove', this.pointerMoveListener, this);
2095                     Env.addEvent(moveTarget, 'pointerleave', this.pointerLeaveListener, this);
2096                     Env.addEvent(moveTarget, 'click', this.pointerClickListener, this);
2097                     Env.addEvent(moveTarget, 'dblclick', this.pointerDblClickListener, this);
2098                 }
2099 
2100                 if (this.containerObj !== null) {
2101                     // This is needed for capturing touch events.
2102                     // It is in jsxgraph.css, for ms-touch-action...
2103                     this.containerObj.style.touchAction = 'none';
2104                     // this.containerObj.style.touchAction = 'auto';
2105                 }
2106 
2107                 this.hasPointerHandlers = true;
2108             }
2109         },
2110 
2111         /**
2112          * Registers mouse move, down and wheel event handlers.
2113          */
2114         addMouseEventHandlers: function () {
2115             if (!this.hasMouseHandlers && Env.isBrowser) {
2116                 var moveTarget = this.attr.movetarget || this.containerObj;
2117 
2118                 Env.addEvent(this.containerObj, 'mousedown', this.mouseDownListener, this);
2119                 Env.addEvent(moveTarget, 'mousemove', this.mouseMoveListener, this);
2120                 Env.addEvent(moveTarget, 'click', this.mouseClickListener, this);
2121                 Env.addEvent(moveTarget, 'dblclick', this.mouseDblClickListener, this);
2122 
2123                 this.hasMouseHandlers = true;
2124             }
2125         },
2126 
2127         /**
2128          * Register touch start and move and gesture start and change event handlers.
2129          * @param {Boolean} appleGestures If set to false the gesturestart and gesturechange event handlers
2130          * will not be registered.
2131          *
2132          * Since iOS 13, touch events were abandoned in favour of pointer events
2133          */
2134         addTouchEventHandlers: function (appleGestures) {
2135             if (!this.hasTouchHandlers && Env.isBrowser) {
2136                 var moveTarget = this.attr.movetarget || this.containerObj;
2137 
2138                 Env.addEvent(this.containerObj, 'touchstart', this.touchStartListener, this);
2139                 Env.addEvent(moveTarget, 'touchmove', this.touchMoveListener, this);
2140 
2141                 /*
2142                 if (!Type.exists(appleGestures) || appleGestures) {
2143                     // Gesture listener are called in touchStart and touchMove.
2144                     //Env.addEvent(this.containerObj, 'gesturestart', this.gestureStartListener, this);
2145                     //Env.addEvent(this.containerObj, 'gesturechange', this.gestureChangeListener, this);
2146                 }
2147                 */
2148 
2149                 this.hasTouchHandlers = true;
2150             }
2151         },
2152 
2153         /**
2154          * Registers pointer event handlers.
2155          */
2156         addWheelEventHandlers: function () {
2157             if (!this.hasWheelHandlers && Env.isBrowser) {
2158                 Env.addEvent(this.containerObj, 'mousewheel', this.mouseWheelListener, this);
2159                 Env.addEvent(this.containerObj, 'DOMMouseScroll', this.mouseWheelListener, this);
2160                 this.hasWheelHandlers = true;
2161             }
2162         },
2163 
2164         /**
2165          * Add fullscreen events which update the CSS transformation matrix to correct
2166          * the mouse/touch/pointer positions in case of CSS transformations.
2167          */
2168         addFullscreenEventHandlers: function () {
2169             var i,
2170                 // standard/Edge, firefox, chrome/safari, IE11
2171                 events = [
2172                     'fullscreenchange',
2173                     'mozfullscreenchange',
2174                     'webkitfullscreenchange',
2175                     'msfullscreenchange'
2176                 ],
2177                 le = events.length;
2178 
2179             if (!this.hasFullscreenEventHandlers && Env.isBrowser) {
2180                 for (i = 0; i < le; i++) {
2181                     Env.addEvent(this.document, events[i], this.fullscreenListener, this);
2182                 }
2183                 this.hasFullscreenEventHandlers = true;
2184             }
2185         },
2186 
2187         /**
2188          * Register keyboard event handlers.
2189          */
2190         addKeyboardEventHandlers: function () {
2191             if (this.attr.keyboard.enabled && !this.hasKeyboardHandlers && Env.isBrowser) {
2192                 Env.addEvent(this.containerObj, 'keydown', this.keyDownListener, this);
2193                 Env.addEvent(this.containerObj, 'focusin', this.keyFocusInListener, this);
2194                 Env.addEvent(this.containerObj, 'focusout', this.keyFocusOutListener, this);
2195                 this.hasKeyboardHandlers = true;
2196             }
2197         },
2198 
2199         /**
2200          * Remove all registered touch event handlers.
2201          */
2202         removeKeyboardEventHandlers: function () {
2203             if (this.hasKeyboardHandlers && Env.isBrowser) {
2204                 Env.removeEvent(this.containerObj, 'keydown', this.keyDownListener, this);
2205                 Env.removeEvent(this.containerObj, 'focusin', this.keyFocusInListener, this);
2206                 Env.removeEvent(this.containerObj, 'focusout', this.keyFocusOutListener, this);
2207                 this.hasKeyboardHandlers = false;
2208             }
2209         },
2210 
2211         /**
2212          * Remove all registered event handlers regarding fullscreen mode.
2213          */
2214         removeFullscreenEventHandlers: function () {
2215             var i,
2216                 // standard/Edge, firefox, chrome/safari, IE11
2217                 events = [
2218                     'fullscreenchange',
2219                     'mozfullscreenchange',
2220                     'webkitfullscreenchange',
2221                     'msfullscreenchange'
2222                 ],
2223                 le = events.length;
2224 
2225             if (this.hasFullscreenEventHandlers && Env.isBrowser) {
2226                 for (i = 0; i < le; i++) {
2227                     Env.removeEvent(this.document, events[i], this.fullscreenListener, this);
2228                 }
2229                 this.hasFullscreenEventHandlers = false;
2230             }
2231         },
2232 
2233         /**
2234          * Remove MSPointer* Event handlers.
2235          */
2236         removePointerEventHandlers: function () {
2237             if (this.hasPointerHandlers && Env.isBrowser) {
2238                 var moveTarget = this.attr.movetarget || this.containerObj;
2239 
2240                 if (window.navigator.msPointerEnabled) {
2241                     // IE10-
2242                     Env.removeEvent(this.containerObj, 'MSPointerDown', this.pointerDownListener, this);
2243                     Env.removeEvent(moveTarget, 'MSPointerMove', this.pointerMoveListener, this);
2244                 } else {
2245                     Env.removeEvent(this.containerObj, 'pointerdown', this.pointerDownListener, this);
2246                     Env.removeEvent(moveTarget, 'pointermove', this.pointerMoveListener, this);
2247                     Env.removeEvent(moveTarget, 'pointerleave', this.pointerLeaveListener, this);
2248                     Env.removeEvent(moveTarget, 'click', this.pointerClickListener, this);
2249                     Env.removeEvent(moveTarget, 'dblclick', this.pointerDblClickListener, this);
2250                 }
2251 
2252                 if (this.hasWheelHandlers) {
2253                     Env.removeEvent(this.containerObj, 'mousewheel', this.mouseWheelListener, this);
2254                     Env.removeEvent(this.containerObj, 'DOMMouseScroll', this.mouseWheelListener, this);
2255                 }
2256 
2257                 if (this.hasPointerUp) {
2258                     if (window.navigator.msPointerEnabled) {
2259                         // IE10-
2260                         Env.removeEvent(this.document, 'MSPointerUp', this.pointerUpListener, this);
2261                     } else {
2262                         Env.removeEvent(this.document, 'pointerup', this.pointerUpListener, this);
2263                         Env.removeEvent(this.document, 'pointercancel', this.pointerUpListener, this);
2264                     }
2265                     this.hasPointerUp = false;
2266                 }
2267 
2268                 this.hasPointerHandlers = false;
2269             }
2270         },
2271 
2272         /**
2273          * De-register mouse event handlers.
2274          */
2275         removeMouseEventHandlers: function () {
2276             if (this.hasMouseHandlers && Env.isBrowser) {
2277                 var moveTarget = this.attr.movetarget || this.containerObj;
2278 
2279                 Env.removeEvent(this.containerObj, 'mousedown', this.mouseDownListener, this);
2280                 Env.removeEvent(moveTarget, 'mousemove', this.mouseMoveListener, this);
2281                 Env.removeEvent(moveTarget, 'click', this.mouseClickListener, this);
2282                 Env.removeEvent(moveTarget, 'dblclick', this.mouseDblClickListener, this);
2283 
2284                 if (this.hasMouseUp) {
2285                     Env.removeEvent(this.document, 'mouseup', this.mouseUpListener, this);
2286                     this.hasMouseUp = false;
2287                 }
2288 
2289                 if (this.hasWheelHandlers) {
2290                     Env.removeEvent(this.containerObj, 'mousewheel', this.mouseWheelListener, this);
2291                     Env.removeEvent(
2292                         this.containerObj,
2293                         'DOMMouseScroll',
2294                         this.mouseWheelListener,
2295                         this
2296                     );
2297                 }
2298 
2299                 this.hasMouseHandlers = false;
2300             }
2301         },
2302 
2303         /**
2304          * Remove all registered touch event handlers.
2305          */
2306         removeTouchEventHandlers: function () {
2307             if (this.hasTouchHandlers && Env.isBrowser) {
2308                 var moveTarget = this.attr.movetarget || this.containerObj;
2309 
2310                 Env.removeEvent(this.containerObj, 'touchstart', this.touchStartListener, this);
2311                 Env.removeEvent(moveTarget, 'touchmove', this.touchMoveListener, this);
2312 
2313                 if (this.hasTouchEnd) {
2314                     Env.removeEvent(this.document, 'touchend', this.touchEndListener, this);
2315                     this.hasTouchEnd = false;
2316                 }
2317 
2318                 this.hasTouchHandlers = false;
2319             }
2320         },
2321 
2322         /**
2323          * Handler for click on left arrow in the navigation bar
2324          * @returns {JXG.Board} Reference to the board
2325          */
2326         clickLeftArrow: function () {
2327             this.moveOrigin(
2328                 this.origin.scrCoords[1] + this.canvasWidth * 0.1,
2329                 this.origin.scrCoords[2]
2330             );
2331             return this;
2332         },
2333 
2334         /**
2335          * Handler for click on right arrow in the navigation bar
2336          * @returns {JXG.Board} Reference to the board
2337          */
2338         clickRightArrow: function () {
2339             this.moveOrigin(
2340                 this.origin.scrCoords[1] - this.canvasWidth * 0.1,
2341                 this.origin.scrCoords[2]
2342             );
2343             return this;
2344         },
2345 
2346         /**
2347          * Handler for click on up arrow in the navigation bar
2348          * @returns {JXG.Board} Reference to the board
2349          */
2350         clickUpArrow: function () {
2351             this.moveOrigin(
2352                 this.origin.scrCoords[1],
2353                 this.origin.scrCoords[2] - this.canvasHeight * 0.1
2354             );
2355             return this;
2356         },
2357 
2358         /**
2359          * Handler for click on down arrow in the navigation bar
2360          * @returns {JXG.Board} Reference to the board
2361          */
2362         clickDownArrow: function () {
2363             this.moveOrigin(
2364                 this.origin.scrCoords[1],
2365                 this.origin.scrCoords[2] + this.canvasHeight * 0.1
2366             );
2367             return this;
2368         },
2369 
2370         /**
2371          * Triggered on iOS/Safari while the user inputs a gesture (e.g. pinch) and is used to zoom into the board.
2372          * Works on iOS/Safari and Android.
2373          * @param {Event} evt Browser event object
2374          * @returns {Boolean}
2375          */
2376         gestureChangeListener: function (evt) {
2377             var c,
2378                 dir1 = [],
2379                 dir2 = [],
2380                 angle,
2381                 mi = 10,
2382                 isPinch = false,
2383                 // Save zoomFactors
2384                 zx = this.attr.zoom.factorx,
2385                 zy = this.attr.zoom.factory,
2386                 factor, dist, theta, bound,
2387                 zoomCenter,
2388                 doZoom = false,
2389                 dx, dy, cx, cy;
2390 
2391             if (this.mode !== this.BOARD_MODE_ZOOM) {
2392                 return true;
2393             }
2394             evt.preventDefault();
2395 
2396             dist = Geometry.distance(
2397                 [evt.touches[0].clientX, evt.touches[0].clientY],
2398                 [evt.touches[1].clientX, evt.touches[1].clientY],
2399                 2
2400             );
2401 
2402             // Android pinch to zoom
2403             // evt.scale was available in iOS touch events (pre iOS 13)
2404             // evt.scale is undefined in Android
2405             if (evt.scale === undefined) {
2406                 evt.scale = dist / this.prevDist;
2407             }
2408 
2409             if (!Type.exists(this.prevCoords)) {
2410                 return false;
2411             }
2412             // Compute the angle of the two finger directions
2413             dir1 = [
2414                 evt.touches[0].clientX - this.prevCoords[0][0],
2415                 evt.touches[0].clientY - this.prevCoords[0][1]
2416             ];
2417             dir2 = [
2418                 evt.touches[1].clientX - this.prevCoords[1][0],
2419                 evt.touches[1].clientY - this.prevCoords[1][1]
2420             ];
2421 
2422             if (
2423                 dir1[0] * dir1[0] + dir1[1] * dir1[1] < mi * mi &&
2424                 dir2[0] * dir2[0] + dir2[1] * dir2[1] < mi * mi
2425             ) {
2426                 return false;
2427             }
2428 
2429             angle = Geometry.rad(dir1, [0, 0], dir2);
2430             if (
2431                 this.isPreviousGesture !== 'pan' &&
2432                 Math.abs(angle) > Math.PI * 0.2 &&
2433                 Math.abs(angle) < Math.PI * 1.8
2434             ) {
2435                 isPinch = true;
2436             }
2437 
2438             if (this.isPreviousGesture !== 'pan' && !isPinch) {
2439                 if (Math.abs(evt.scale) < 0.77 || Math.abs(evt.scale) > 1.3) {
2440                     isPinch = true;
2441                 }
2442             }
2443 
2444             factor = evt.scale / this.prevScale;
2445             this.prevScale = evt.scale;
2446             this.prevCoords = [
2447                 [evt.touches[0].clientX, evt.touches[0].clientY],
2448                 [evt.touches[1].clientX, evt.touches[1].clientY]
2449             ];
2450 
2451             c = new Coords(Const.COORDS_BY_SCREEN, this.getMousePosition(evt, 0), this);
2452 
2453             if (this.attr.pan.enabled && this.attr.pan.needtwofingers && !isPinch) {
2454                 // Pan detected
2455                 this.isPreviousGesture = 'pan';
2456                 this.moveOrigin(c.scrCoords[1], c.scrCoords[2], true);
2457 
2458             } else if (this.attr.zoom.enabled && Math.abs(factor - 1.0) < 0.5) {
2459                 doZoom = false;
2460                 zoomCenter = this.attr.zoom.center;
2461                 // Pinch detected
2462                 if (this.attr.zoom.pinchhorizontal || this.attr.zoom.pinchvertical) {
2463                     dx = Math.abs(evt.touches[0].clientX - evt.touches[1].clientX);
2464                     dy = Math.abs(evt.touches[0].clientY - evt.touches[1].clientY);
2465                     theta = Math.abs(Math.atan2(dy, dx));
2466                     bound = (Math.PI * this.attr.zoom.pinchsensitivity) / 90.0;
2467                 }
2468 
2469                 if (!this.keepaspectratio &&
2470                     this.attr.zoom.pinchhorizontal &&
2471                     theta < bound) {
2472                     this.attr.zoom.factorx = factor;
2473                     this.attr.zoom.factory = 1.0;
2474                     cx = 0;
2475                     cy = 0;
2476                     doZoom = true;
2477                 } else if (!this.keepaspectratio &&
2478                     this.attr.zoom.pinchvertical &&
2479                     Math.abs(theta - Math.PI * 0.5) < bound
2480                 ) {
2481                     this.attr.zoom.factorx = 1.0;
2482                     this.attr.zoom.factory = factor;
2483                     cx = 0;
2484                     cy = 0;
2485                     doZoom = true;
2486                 } else if (this.attr.zoom.pinch) {
2487                     this.attr.zoom.factorx = factor;
2488                     this.attr.zoom.factory = factor;
2489                     cx = c.usrCoords[1];
2490                     cy = c.usrCoords[2];
2491                     doZoom = true;
2492                 }
2493 
2494                 if (doZoom) {
2495                     if (zoomCenter === 'board') {
2496                         this.zoomIn();
2497                     } else { // including zoomCenter === 'auto'
2498                         this.zoomIn(cx, cy);
2499                     }
2500 
2501                     // Restore zoomFactors
2502                     this.attr.zoom.factorx = zx;
2503                     this.attr.zoom.factory = zy;
2504                 }
2505             }
2506 
2507             return false;
2508         },
2509 
2510         /**
2511          * Called by iOS/Safari as soon as the user starts a gesture. Works natively on iOS/Safari,
2512          * on Android we emulate it.
2513          * @param {Event} evt
2514          * @returns {Boolean}
2515          */
2516         gestureStartListener: function (evt) {
2517             var pos;
2518 
2519             evt.preventDefault();
2520             this.prevScale = 1.0;
2521             // Android pinch to zoom
2522             this.prevDist = Geometry.distance(
2523                 [evt.touches[0].clientX, evt.touches[0].clientY],
2524                 [evt.touches[1].clientX, evt.touches[1].clientY],
2525                 2
2526             );
2527             this.prevCoords = [
2528                 [evt.touches[0].clientX, evt.touches[0].clientY],
2529                 [evt.touches[1].clientX, evt.touches[1].clientY]
2530             ];
2531             this.isPreviousGesture = 'none';
2532 
2533             // If pinch-to-zoom is interpreted as panning
2534             // we have to prepare move origin
2535             pos = this.getMousePosition(evt, 0);
2536             this.initMoveOrigin(pos[0], pos[1]);
2537 
2538             this.mode = this.BOARD_MODE_ZOOM;
2539             return false;
2540         },
2541 
2542         /**
2543          * Test if the required key combination is pressed for wheel zoom, move origin and
2544          * selection
2545          * @private
2546          * @param  {Object}  evt    Mouse or pen event
2547          * @param  {String}  action String containing the action: 'zoom', 'pan', 'selection'.
2548          * Corresponds to the attribute subobject.
2549          * @return {Boolean}        true or false.
2550          */
2551         _isRequiredKeyPressed: function (evt, action) {
2552             var obj = this.attr[action];
2553             if (!obj.enabled) {
2554                 return false;
2555             }
2556 
2557             if (
2558                 ((obj.needshift && evt.shiftKey) || (!obj.needshift && !evt.shiftKey)) &&
2559                 ((obj.needctrl && evt.ctrlKey) || (!obj.needctrl && !evt.ctrlKey))
2560             ) {
2561                 return true;
2562             }
2563 
2564             return false;
2565         },
2566 
2567         /*
2568          * Pointer events
2569          */
2570 
2571         /**
2572          *
2573          * Check if pointer event is already registered in {@link JXG.Board#_board_touches}.
2574          *
2575          * @param  {Object} evt Event object
2576          * @return {Boolean} true if down event has already been sent.
2577          * @private
2578          */
2579         _isPointerRegistered: function (evt) {
2580             var i,
2581                 len = this._board_touches.length;
2582 
2583             for (i = 0; i < len; i++) {
2584                 if (this._board_touches[i].pointerId === evt.pointerId) {
2585                     return true;
2586                 }
2587             }
2588             return false;
2589         },
2590 
2591         /**
2592          *
2593          * Store the position of a pointer event.
2594          * If not yet done, registers a pointer event in {@link JXG.Board#_board_touches}.
2595          * Allows to follow the path of that finger on the screen.
2596          * Only two simultaneous touches are supported.
2597          *
2598          * @param {Object} evt Event object
2599          * @returns {JXG.Board} Reference to the board
2600          * @private
2601          */
2602         _pointerStorePosition: function (evt) {
2603             var i, found;
2604 
2605             for (i = 0, found = false; i < this._board_touches.length; i++) {
2606                 if (this._board_touches[i].pointerId === evt.pointerId) {
2607                     this._board_touches[i].clientX = evt.clientX;
2608                     this._board_touches[i].clientY = evt.clientY;
2609                     found = true;
2610                     break;
2611                 }
2612             }
2613 
2614             // Restrict the number of simultaneous touches to 2
2615             if (!found && this._board_touches.length < 2) {
2616                 this._board_touches.push({
2617                     pointerId: evt.pointerId,
2618                     clientX: evt.clientX,
2619                     clientY: evt.clientY
2620                 });
2621             }
2622 
2623             return this;
2624         },
2625 
2626         /**
2627          * Deregisters a pointer event in {@link JXG.Board#_board_touches}.
2628          * It happens if a finger has been lifted from the screen.
2629          *
2630          * @param {Object} evt Event object
2631          * @returns {JXG.Board} Reference to the board
2632          * @private
2633          */
2634         _pointerRemoveTouches: function (evt) {
2635             var i;
2636             for (i = 0; i < this._board_touches.length; i++) {
2637                 if (this._board_touches[i].pointerId === evt.pointerId) {
2638                     this._board_touches.splice(i, 1);
2639                     break;
2640                 }
2641             }
2642 
2643             return this;
2644         },
2645 
2646         /**
2647          * Remove all registered fingers from {@link JXG.Board#_board_touches}.
2648          * This might be necessary if too many fingers have been registered.
2649          * @returns {JXG.Board} Reference to the board
2650          * @private
2651          */
2652         _pointerClearTouches: function (pId) {
2653             // var i;
2654             // if (pId) {
2655             //     for (i = 0; i < this._board_touches.length; i++) {
2656             //         if (pId === this._board_touches[i].pointerId) {
2657             //             this._board_touches.splice(i, i);
2658             //             break;
2659             //         }
2660             //     }
2661             // } else {
2662             // }
2663             if (this._board_touches.length > 0) {
2664                 this.dehighlightAll();
2665             }
2666             this.updateQuality = this.BOARD_QUALITY_HIGH;
2667             this.mode = this.BOARD_MODE_NONE;
2668             this._board_touches = [];
2669             this.touches = [];
2670         },
2671 
2672         /**
2673          * Determine which input device is used for this action.
2674          * Possible devices are 'touch', 'pen' and 'mouse'.
2675          * This affects the precision and certain events.
2676          * In case of no browser, 'mouse' is used.
2677          *
2678          * @see JXG.Board#pointerDownListener
2679          * @see JXG.Board#pointerMoveListener
2680          * @see JXG.Board#initMoveObject
2681          * @see JXG.Board#moveObject
2682          *
2683          * @param {Event} evt The browsers event object.
2684          * @returns {String} 'mouse', 'pen', or 'touch'
2685          * @private
2686          */
2687         _getPointerInputDevice: function (evt) {
2688             if (Env.isBrowser) {
2689                 if (
2690                     evt.pointerType === 'touch' || // New
2691                     (window.navigator.msMaxTouchPoints && // Old
2692                         window.navigator.msMaxTouchPoints > 1)
2693                 ) {
2694                     return 'touch';
2695                 }
2696                 if (evt.pointerType === 'mouse') {
2697                     return 'mouse';
2698                 }
2699                 if (evt.pointerType === 'pen') {
2700                     return 'pen';
2701                 }
2702             }
2703             return 'mouse';
2704         },
2705 
2706         /**
2707          * This method is called by the browser when a pointing device is pressed on the screen.
2708          * @param {Event} evt The browsers event object.
2709          * @param {Object} object If the object to be dragged is already known, it can be submitted via this parameter
2710          * @param {Boolean} [allowDefaultEventHandling=false] If true event is not canceled, i.e. prevent call of evt.preventDefault()
2711          * @returns {Boolean} false if the first finger event is sent twice, or not a browser, or in selection mode. Otherwise returns true.
2712          */
2713         pointerDownListener: function (evt, object, allowDefaultEventHandling) {
2714             var i, j, k, pos,
2715                 elements, sel, target_obj,
2716                 type = 'mouse', // Used in case of no browser
2717                 found, target, ta;
2718 
2719             // Fix for Firefox browser: When using a second finger, the
2720             // touch event for the first finger is sent again.
2721             if (!object && this._isPointerRegistered(evt)) {
2722                 return false;
2723             }
2724 
2725             if (Type.evaluate(this.attr.movetarget) === null &&
2726                 Type.exists(evt.target) && Type.exists(evt.target.releasePointerCapture)) {
2727                 evt.target.releasePointerCapture(evt.pointerId);
2728             }
2729 
2730             if (!object && evt.isPrimary) {
2731                 // First finger down. To be on the safe side this._board_touches is cleared.
2732                 // this._pointerClearTouches();
2733             }
2734 
2735             if (!this.hasPointerUp) {
2736                 if (window.navigator.msPointerEnabled) {
2737                     // IE10-
2738                     Env.addEvent(this.document, 'MSPointerUp', this.pointerUpListener, this);
2739                 } else {
2740                     // 'pointercancel' is fired e.g. if the finger leaves the browser and drags down the system menu on Android
2741                     Env.addEvent(this.document, 'pointerup', this.pointerUpListener, this);
2742                     Env.addEvent(this.document, 'pointercancel', this.pointerUpListener, this);
2743                 }
2744                 this.hasPointerUp = true;
2745             }
2746 
2747             if (this.hasMouseHandlers) {
2748                 this.removeMouseEventHandlers();
2749             }
2750 
2751             if (this.hasTouchHandlers) {
2752                 this.removeTouchEventHandlers();
2753             }
2754 
2755             // Prevent accidental selection of text
2756             if (this.document.selection && Type.isFunction(this.document.selection.empty)) {
2757                 this.document.selection.empty();
2758             } else if (window.getSelection) {
2759                 sel = window.getSelection();
2760                 if (sel.removeAllRanges) {
2761                     try {
2762                         sel.removeAllRanges();
2763                     } catch (e) { }
2764                 }
2765             }
2766 
2767             // Mouse, touch or pen device
2768             this._inputDevice = this._getPointerInputDevice(evt);
2769             type = this._inputDevice;
2770             this.options.precision.hasPoint = this.options.precision[type];
2771 
2772             // Handling of multi touch with pointer events should be easier than with touch events.
2773             // Every pointer device has its own pointerId, e.g. the mouse
2774             // always has id 1 or 0, fingers and pens get unique ids every time a pointerDown event is fired and they will
2775             // keep this id until a pointerUp event is fired. What we have to do here is:
2776             //  1. collect all elements under the current pointer
2777             //  2. run through the touches control structure
2778             //    a. look for the object collected in step 1.
2779             //    b. if an object is found, check the number of pointers. If appropriate, add the pointer.
2780             pos = this.getMousePosition(evt);
2781 
2782             // Handle selection rectangle
2783             this._testForSelection(evt);
2784             if (this.selectingMode) {
2785                 this._startSelecting(pos);
2786                 this.triggerEventHandlers(
2787                     ['touchstartselecting', 'pointerstartselecting', 'startselecting'],
2788                     [evt]
2789                 );
2790                 return; // don't continue as a normal click
2791             }
2792 
2793             if (this.attr.drag.enabled && object) {
2794                 elements = [object];
2795                 this.mode = this.BOARD_MODE_DRAG;
2796             } else {
2797                 elements = this.initMoveObject(pos[0], pos[1], evt, type);
2798             }
2799 
2800             target_obj = {
2801                 num: evt.pointerId,
2802                 X: pos[0],
2803                 Y: pos[1],
2804                 Xprev: NaN,
2805                 Yprev: NaN,
2806                 Xstart: [],
2807                 Ystart: [],
2808                 Zstart: []
2809             };
2810 
2811             // If no draggable object can be found, get out here immediately
2812             if (elements.length > 0) {
2813                 // check touches structure
2814                 target = elements[elements.length - 1];
2815                 found = false;
2816 
2817                 // Reminder: this.touches is the list of elements which
2818                 // currently 'possess' a pointer (mouse, pen, finger)
2819                 for (i = 0; i < this.touches.length; i++) {
2820                     // An element receives a further touch, i.e.
2821                     // the target is already in our touches array, add the pointer to the existing touch
2822                     if (this.touches[i].obj === target) {
2823                         j = i;
2824                         k = this.touches[i].targets.push(target_obj) - 1;
2825                         found = true;
2826                         break;
2827                     }
2828                 }
2829                 if (!found) {
2830                     // A new element has been touched.
2831                     k = 0;
2832                     j =
2833                         this.touches.push({
2834                             obj: target,
2835                             targets: [target_obj]
2836                         }) - 1;
2837                 }
2838 
2839                 this.dehighlightAll();
2840                 target.highlight(true);
2841 
2842                 this.saveStartPos(target, this.touches[j].targets[k]);
2843 
2844                 // Prevent accidental text selection
2845                 // this could get us new trouble: input fields, links and drop down boxes placed as text
2846                 // on the board don't work anymore.
2847                 if (evt && evt.preventDefault && !allowDefaultEventHandling) {
2848                     // All browser supporting pointer events know preventDefault()
2849                     evt.preventDefault();
2850                 }
2851             }
2852 
2853             if (this.touches.length > 0 && !allowDefaultEventHandling) {
2854                 evt.preventDefault();
2855                 evt.stopPropagation();
2856             }
2857 
2858             if (!Env.isBrowser) {
2859                 return false;
2860             }
2861             if (this._getPointerInputDevice(evt) !== 'touch') {
2862                 if (this.mode === this.BOARD_MODE_NONE) {
2863                     this.mouseOriginMoveStart(evt);
2864                 }
2865             } else {
2866                 this._pointerStorePosition(evt);
2867                 evt.touches = this._board_touches;
2868 
2869                 // Touch events on empty areas of the board are handled here, see also touchStartListener
2870                 // 1. case: one finger. If allowed, this triggers pan with one finger
2871                 if (
2872                     evt.touches.length === 1 &&
2873                     this.mode === this.BOARD_MODE_NONE &&
2874                     this.touchStartMoveOriginOneFinger(evt)
2875                 ) {
2876                     // Empty by purpose
2877                 } else if (
2878                     evt.touches.length === 2 &&
2879                     (this.mode === this.BOARD_MODE_NONE ||
2880                         this.mode === this.BOARD_MODE_MOVE_ORIGIN)
2881                 ) {
2882                     // 2. case: two fingers: pinch to zoom or pan with two fingers needed.
2883                     // This happens when the second finger hits the device. First, the
2884                     // 'one finger pan mode' has to be cancelled.
2885                     if (this.mode === this.BOARD_MODE_MOVE_ORIGIN) {
2886                         this.originMoveEnd();
2887                     }
2888 
2889                     this.gestureStartListener(evt);
2890                 }
2891             }
2892 
2893             // Allow browser scrolling
2894             // For this: pan by one finger has to be disabled
2895 
2896             ta = 'none';   // JSXGraph catches all user touch events
2897             if (this.mode === this.BOARD_MODE_NONE &&
2898                 Type.evaluate(this.attr.browserpan) &&
2899                 !(Type.evaluate(this.attr.pan.enabled) && !Type.evaluate(this.attr.pan.needtwofingers))
2900             ) {
2901                 // ta = 'pan-x pan-y';  // JSXGraph allows browser scrolling
2902                 ta = 'auto';  // JSXGraph allows browser scrolling
2903             }
2904             this.containerObj.style.touchAction = ta;
2905 
2906             this.triggerEventHandlers(['touchstart', 'down', 'pointerdown', 'MSPointerDown'], [evt]);
2907 
2908             return true;
2909         },
2910 
2911         /**
2912          * Internal handling of click events for pointers and mouse.
2913          *
2914          * @param {Event} evt The browsers event object.
2915          * @param {Array} evtArray list of event names
2916          * @private
2917          */
2918         _handleClicks: function(evt, evtArray) {
2919             var that = this,
2920                 el, delay, suppress;
2921 
2922             if (this.selectingMode) {
2923                 evt.stopPropagation();
2924                 return;
2925             }
2926 
2927             delay = Type.evaluate(this.attr.clickdelay);
2928             suppress = Type.evaluate(this.attr.dblclicksuppressclick);
2929 
2930             if (suppress) {
2931                 // dblclick suppresses previous click events
2932                 this._preventSingleClick = false;
2933 
2934                 // Wait if there is a dblclick event.
2935                 // If not fire a click event
2936                 this._singleClickTimer = setTimeout(function() {
2937                     if (!that._preventSingleClick) {
2938                         // Fire click event and remove element from click list
2939                         that.triggerEventHandlers(evtArray, [evt]);
2940                         for (el in that.clickObjects) {
2941                             if (that.clickObjects.hasOwnProperty(el)) {
2942                                 that.clickObjects[el].triggerEventHandlers(evtArray, [evt]);
2943                                 delete that.clickObjects[el];
2944                             }
2945                         }
2946                     }
2947                 }, delay);
2948             } else {
2949                 // dblclick is preceded by two click events
2950 
2951                 // Fire click events
2952                 that.triggerEventHandlers(evtArray, [evt]);
2953                 for (el in that.clickObjects) {
2954                     if (that.clickObjects.hasOwnProperty(el)) {
2955                         that.clickObjects[el].triggerEventHandlers(evtArray, [evt]);
2956                     }
2957                 }
2958 
2959                 // Clear list of clicked elements with a delay
2960                 setTimeout(function() {
2961                     for (el in that.clickObjects) {
2962                         if (that.clickObjects.hasOwnProperty(el)) {
2963                             delete that.clickObjects[el];
2964                         }
2965                     }
2966                 }, delay);
2967             }
2968             evt.stopPropagation();
2969         },
2970 
2971         /**
2972          * Internal handling of dblclick events for pointers and mouse.
2973          *
2974          * @param {Event} evt The browsers event object.
2975          * @param {Array} evtArray list of event names
2976          * @private
2977          */
2978         _handleDblClicks: function(evt, evtArray) {
2979             var el;
2980 
2981             if (this.selectingMode) {
2982                 evt.stopPropagation();
2983                 return;
2984             }
2985 
2986             // Notify that a dblclick has happened
2987             this._preventSingleClick = true;
2988             clearTimeout(this._singleClickTimer);
2989 
2990             // Fire dblclick event
2991             this.triggerEventHandlers(evtArray, [evt]);
2992             for (el in this.clickObjects) {
2993                 if (this.clickObjects.hasOwnProperty(el)) {
2994                     this.clickObjects[el].triggerEventHandlers(evtArray, [evt]);
2995                     delete this.clickObjects[el];
2996                 }
2997             }
2998 
2999             evt.stopPropagation();
3000         },
3001 
3002         /**
3003          * This method is called by the browser when a pointer device clicks on the screen.
3004          * @param {Event} evt The browsers event object.
3005          */
3006         pointerClickListener: function (evt) {
3007             this._handleClicks(evt, ['click', 'pointerclick']);
3008         },
3009 
3010         /**
3011          * This method is called by the browser when a pointer device double clicks on the screen.
3012          * @param {Event} evt The browsers event object.
3013          */
3014         pointerDblClickListener: function (evt) {
3015             this._handleDblClicks(evt, ['dblclick', 'pointerdblclick']);
3016         },
3017 
3018         /**
3019          * This method is called by the browser when the mouse device clicks on the screen.
3020          * @param {Event} evt The browsers event object.
3021          */
3022         mouseClickListener: function (evt) {
3023             this._handleClicks(evt, ['click', 'mouseclick']);
3024         },
3025 
3026         /**
3027          * This method is called by the browser when the mouse device double clicks on the screen.
3028          * @param {Event} evt The browsers event object.
3029          */
3030         mouseDblClickListener: function (evt) {
3031             this._handleDblClicks(evt, ['dblclick', 'mousedblclick']);
3032         },
3033 
3034         // /**
3035         //  * Called if pointer leaves an HTML tag. It is called by the inner-most tag.
3036         //  * That means, if a JSXGraph text, i.e. an HTML div, is placed close
3037         //  * to the border of the board, this pointerout event will be ignored.
3038         //  * @param  {Event} evt
3039         //  * @return {Boolean}
3040         //  */
3041         // pointerOutListener: function (evt) {
3042         //     if (evt.target === this.containerObj ||
3043         //         (this.renderer.type === 'svg' && evt.target === this.renderer.foreignObjLayer)) {
3044         //         this.pointerUpListener(evt);
3045         //     }
3046         //     return this.mode === this.BOARD_MODE_NONE;
3047         // },
3048 
3049         /**
3050          * Called periodically by the browser while the user moves a pointing device across the screen.
3051          * @param {Event} evt
3052          * @returns {Boolean}
3053          */
3054         pointerMoveListener: function (evt) {
3055             var i, j, pos, eps,
3056                 touchTargets,
3057                 type = 'mouse'; // in case of no browser
3058 
3059             if (
3060                 this._getPointerInputDevice(evt) === 'touch' &&
3061                 !this._isPointerRegistered(evt)
3062             ) {
3063                 // Test, if there was a previous down event of this _getPointerId
3064                 // (in case it is a touch event).
3065                 // Otherwise this move event is ignored. This is necessary e.g. for sketchometry.
3066                 return this.BOARD_MODE_NONE;
3067             }
3068 
3069             if (!this.checkFrameRate(evt)) {
3070                 return false;
3071             }
3072 
3073             if (this.mode !== this.BOARD_MODE_DRAG) {
3074                 this.dehighlightAll();
3075                 this.displayInfobox(false);
3076             }
3077 
3078             if (this.mode !== this.BOARD_MODE_NONE) {
3079                 evt.preventDefault();
3080                 evt.stopPropagation();
3081             }
3082 
3083             this.updateQuality = this.BOARD_QUALITY_LOW;
3084             // Mouse, touch or pen device
3085             this._inputDevice = this._getPointerInputDevice(evt);
3086             type = this._inputDevice;
3087             this.options.precision.hasPoint = this.options.precision[type];
3088             eps = this.options.precision.hasPoint * 0.3333;
3089 
3090             pos = this.getMousePosition(evt);
3091             // Ignore pointer move event if too close at the border
3092             // and setPointerCapture is off
3093             if (Type.evaluate(this.attr.movetarget) === null &&
3094                 pos[0] <= eps || pos[1] <= eps ||
3095                 pos[0] >= this.canvasWidth - eps ||
3096                 pos[1] >= this.canvasHeight - eps
3097             ) {
3098                 return this.mode === this.BOARD_MODE_NONE;
3099             }
3100 
3101             // selection
3102             if (this.selectingMode) {
3103                 this._moveSelecting(pos);
3104                 this.triggerEventHandlers(
3105                     ['touchmoveselecting', 'moveselecting', 'pointermoveselecting'],
3106                     [evt, this.mode]
3107                 );
3108             } else if (!this.mouseOriginMove(evt)) {
3109                 if (this.mode === this.BOARD_MODE_DRAG) {
3110                     // Run through all jsxgraph elements which are touched by at least one finger.
3111                     for (i = 0; i < this.touches.length; i++) {
3112                         touchTargets = this.touches[i].targets;
3113                         // Run through all touch events which have been started on this jsxgraph element.
3114                         for (j = 0; j < touchTargets.length; j++) {
3115                             if (touchTargets[j].num === evt.pointerId) {
3116                                 touchTargets[j].X = pos[0];
3117                                 touchTargets[j].Y = pos[1];
3118 
3119                                 if (touchTargets.length === 1) {
3120                                     // Touch by one finger: this is possible for all elements that can be dragged
3121                                     this.moveObject(pos[0], pos[1], this.touches[i], evt, type);
3122                                 } else if (touchTargets.length === 2) {
3123                                     // Touch by two fingers: e.g. moving lines
3124                                     this.twoFingerMove(this.touches[i], evt.pointerId, evt);
3125 
3126                                     touchTargets[j].Xprev = pos[0];
3127                                     touchTargets[j].Yprev = pos[1];
3128                                 }
3129 
3130                                 // There is only one pointer in the evt object, so there's no point in looking further
3131                                 break;
3132                             }
3133                         }
3134                     }
3135                 } else {
3136                     if (this._getPointerInputDevice(evt) === 'touch') {
3137                         this._pointerStorePosition(evt);
3138 
3139                         if (this._board_touches.length === 2) {
3140                             evt.touches = this._board_touches;
3141                             this.gestureChangeListener(evt);
3142                         }
3143                     }
3144 
3145                     // Move event without dragging an element
3146                     this.highlightElements(pos[0], pos[1], evt, -1);
3147                 }
3148             }
3149 
3150             // Hiding the infobox is commented out, since it prevents showing the infobox
3151             // on IE 11+ on 'over'
3152             //if (this.mode !== this.BOARD_MODE_DRAG) {
3153             //this.displayInfobox(false);
3154             //}
3155             this.triggerEventHandlers(['pointermove', 'MSPointerMove', 'move'], [evt, this.mode]);
3156             this.updateQuality = this.BOARD_QUALITY_HIGH;
3157 
3158             return this.mode === this.BOARD_MODE_NONE;
3159         },
3160 
3161         /**
3162          * Triggered as soon as the user stops touching the device with at least one finger.
3163          *
3164          * @param {Event} evt
3165          * @returns {Boolean}
3166          */
3167         pointerUpListener: function (evt) {
3168             var i, j, found, eh,
3169                 touchTargets,
3170                 updateNeeded = false;
3171 
3172             this.triggerEventHandlers(['touchend', 'up', 'pointerup', 'MSPointerUp'], [evt]);
3173             this.displayInfobox(false);
3174 
3175             if (evt) {
3176                 for (i = 0; i < this.touches.length; i++) {
3177                     touchTargets = this.touches[i].targets;
3178                     for (j = 0; j < touchTargets.length; j++) {
3179                         if (touchTargets[j].num === evt.pointerId) {
3180                             touchTargets.splice(j, 1);
3181                             if (touchTargets.length === 0) {
3182                                 this.touches.splice(i, 1);
3183                             }
3184                             break;
3185                         }
3186                     }
3187                 }
3188             }
3189 
3190             this.originMoveEnd();
3191             this.update();
3192 
3193             // selection
3194             if (this.selectingMode) {
3195                 this._stopSelecting(evt);
3196                 this.triggerEventHandlers(
3197                     ['touchstopselecting', 'pointerstopselecting', 'stopselecting'],
3198                     [evt]
3199                 );
3200                 this.stopSelectionMode();
3201             } else {
3202                 for (i = this.downObjects.length - 1; i > -1; i--) {
3203                     found = false;
3204                     for (j = 0; j < this.touches.length; j++) {
3205                         if (this.touches[j].obj.id === this.downObjects[i].id) {
3206                             found = true;
3207                         }
3208                     }
3209                     if (!found) {
3210                         this.downObjects[i].triggerEventHandlers(
3211                             ['touchend', 'up', 'pointerup', 'MSPointerUp'],
3212                             [evt]
3213                         );
3214                         if (!Type.exists(this.downObjects[i].coords)) {
3215                             // snapTo methods have to be called e.g. for line elements here.
3216                             // For coordsElements there might be a conflict with
3217                             // attractors, see commit from 2022.04.08, 11:12:18.
3218                             this.downObjects[i].snapToGrid();
3219                             this.downObjects[i].snapToPoints();
3220                             updateNeeded = true;
3221                         }
3222 
3223                         // Check if we have to keep the element for a click or dblclick event
3224                         // Otherwise remove it from downObjects
3225                         eh = this.downObjects[i].eventHandlers;
3226                         if ((Type.exists(eh.click) && eh.click.length > 0) ||
3227                             (Type.exists(eh.pointerclick) && eh.pointerclick.length > 0) ||
3228                             (Type.exists(eh.dblclick) && eh.dblclick.length > 0) ||
3229                             (Type.exists(eh.pointerdblclick) && eh.pointerdblclick.length > 0)
3230                         ) {
3231                             this.clickObjects[this.downObjects[i].id] = this.downObjects[i];
3232                         }
3233                         this.downObjects.splice(i, 1);
3234                     }
3235                 }
3236             }
3237 
3238             if (this.hasPointerUp) {
3239                 if (window.navigator.msPointerEnabled) {
3240                     // IE10-
3241                     Env.removeEvent(this.document, 'MSPointerUp', this.pointerUpListener, this);
3242                 } else {
3243                     Env.removeEvent(this.document, 'pointerup', this.pointerUpListener, this);
3244                     Env.removeEvent(
3245                         this.document,
3246                         'pointercancel',
3247                         this.pointerUpListener,
3248                         this
3249                     );
3250                 }
3251                 this.hasPointerUp = false;
3252             }
3253 
3254             // After one finger leaves the screen the gesture is stopped.
3255             this._pointerClearTouches(evt.pointerId);
3256             if (this._getPointerInputDevice(evt) !== 'touch') {
3257                 this.dehighlightAll();
3258             }
3259 
3260             if (updateNeeded) {
3261                 this.update();
3262             }
3263 
3264             return true;
3265         },
3266 
3267         /**
3268          * Triggered by the pointerleave event. This is needed in addition to
3269          * {@link JXG.Board#pointerUpListener} in the situation that a pen is used
3270          * and after an up event the pen leaves the hover range vertically. Here, it happens that
3271          * after the pointerup event further pointermove events are fired and elements get highlighted.
3272          * This highlighting has to be cancelled.
3273          *
3274          * @param {Event} evt
3275          * @returns {Boolean}
3276          */
3277         pointerLeaveListener: function (evt) {
3278             this.displayInfobox(false);
3279             this.dehighlightAll();
3280 
3281             return true;
3282         },
3283 
3284         /**
3285          * Touch-Events
3286          */
3287 
3288         /**
3289          * This method is called by the browser when a finger touches the surface of the touch-device.
3290          * @param {Event} evt The browsers event object.
3291          * @returns {Boolean} ...
3292          */
3293         touchStartListener: function (evt) {
3294             var i, j, k,
3295                 pos, elements, obj,
3296                 eps = this.options.precision.touch,
3297                 evtTouches = evt['touches'],
3298                 found,
3299                 targets, target,
3300                 touchTargets;
3301 
3302             if (!this.hasTouchEnd) {
3303                 Env.addEvent(this.document, 'touchend', this.touchEndListener, this);
3304                 this.hasTouchEnd = true;
3305             }
3306 
3307             // Do not remove mouseHandlers, since Chrome on win tablets sends mouseevents if used with pen.
3308             //if (this.hasMouseHandlers) { this.removeMouseEventHandlers(); }
3309 
3310             // prevent accidental selection of text
3311             if (this.document.selection && Type.isFunction(this.document.selection.empty)) {
3312                 this.document.selection.empty();
3313             } else if (window.getSelection) {
3314                 window.getSelection().removeAllRanges();
3315             }
3316 
3317             // multitouch
3318             this._inputDevice = 'touch';
3319             this.options.precision.hasPoint = this.options.precision.touch;
3320 
3321             // This is the most critical part. first we should run through the existing touches and collect all targettouches that don't belong to our
3322             // 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
3323             // 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
3324             // 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
3325             // stretching. as a last step we're going through the rest of the targettouches and initiate new move operations:
3326             //  * points have higher priority over other elements.
3327             //  * 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
3328             //    this element and add them.
3329             // ADDENDUM 11/10/11:
3330             //  (1) run through the touches control object,
3331             //  (2) try to find the targetTouches for every touch. on touchstart only new touches are added, hence we can find a targettouch
3332             //      for every target in our touches objects
3333             //  (3) if one of the targettouches was bound to a touches targets array, mark it
3334             //  (4) run through the targettouches. if the targettouch is marked, continue. otherwise check for elements below the targettouch:
3335             //      (a) if no element could be found: mark the target touches and continue
3336             //      --- in the following cases, 'init' means:
3337             //           (i) check if the element is already used in another touches element, if so, mark the targettouch and continue
3338             //          (ii) if not, init a new touches element, add the targettouch to the touches property and mark it
3339             //      (b) if the element is a point, init
3340             //      (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
3341             //      (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
3342             //          add both to the touches array and mark them.
3343             for (i = 0; i < evtTouches.length; i++) {
3344                 evtTouches[i].jxg_isused = false;
3345             }
3346 
3347             for (i = 0; i < this.touches.length; i++) {
3348                 touchTargets = this.touches[i].targets;
3349                 for (j = 0; j < touchTargets.length; j++) {
3350                     touchTargets[j].num = -1;
3351                     eps = this.options.precision.touch;
3352 
3353                     do {
3354                         for (k = 0; k < evtTouches.length; k++) {
3355                             // find the new targettouches
3356                             if (
3357                                 Math.abs(
3358                                     Math.pow(evtTouches[k].screenX - touchTargets[j].X, 2) +
3359                                     Math.pow(evtTouches[k].screenY - touchTargets[j].Y, 2)
3360                                 ) <
3361                                 eps * eps
3362                             ) {
3363                                 touchTargets[j].num = k;
3364                                 touchTargets[j].X = evtTouches[k].screenX;
3365                                 touchTargets[j].Y = evtTouches[k].screenY;
3366                                 evtTouches[k].jxg_isused = true;
3367                                 break;
3368                             }
3369                         }
3370 
3371                         eps *= 2;
3372                     } while (
3373                         touchTargets[j].num === -1 &&
3374                         eps < this.options.precision.touchMax
3375                     );
3376 
3377                     if (touchTargets[j].num === -1) {
3378                         JXG.debug(
3379                             "i couldn't find a targettouches for target no " +
3380                             j +
3381                             ' on ' +
3382                             this.touches[i].obj.name +
3383                             ' (' +
3384                             this.touches[i].obj.id +
3385                             '). Removed the target.'
3386                         );
3387                         JXG.debug(
3388                             'eps = ' + eps + ', touchMax = ' + Options.precision.touchMax
3389                         );
3390                         touchTargets.splice(i, 1);
3391                     }
3392                 }
3393             }
3394 
3395             // we just re-mapped the targettouches to our existing touches list.
3396             // now we have to initialize some touches from additional targettouches
3397             for (i = 0; i < evtTouches.length; i++) {
3398                 if (!evtTouches[i].jxg_isused) {
3399                     pos = this.getMousePosition(evt, i);
3400                     // selection
3401                     // this._testForSelection(evt); // we do not have shift or ctrl keys yet.
3402                     if (this.selectingMode) {
3403                         this._startSelecting(pos);
3404                         this.triggerEventHandlers(
3405                             ['touchstartselecting', 'startselecting'],
3406                             [evt]
3407                         );
3408                         evt.preventDefault();
3409                         evt.stopPropagation();
3410                         this.options.precision.hasPoint = this.options.precision.mouse;
3411                         return this.touches.length > 0; // don't continue as a normal click
3412                     }
3413 
3414                     elements = this.initMoveObject(pos[0], pos[1], evt, 'touch');
3415                     if (elements.length !== 0) {
3416                         obj = elements[elements.length - 1];
3417                         target = {
3418                             num: i,
3419                             X: evtTouches[i].screenX,
3420                             Y: evtTouches[i].screenY,
3421                             Xprev: NaN,
3422                             Yprev: NaN,
3423                             Xstart: [],
3424                             Ystart: [],
3425                             Zstart: []
3426                         };
3427 
3428                         if (
3429                             Type.isPoint(obj) ||
3430                             obj.elementClass === Const.OBJECT_CLASS_TEXT ||
3431                             obj.type === Const.OBJECT_TYPE_TICKS ||
3432                             obj.type === Const.OBJECT_TYPE_IMAGE
3433                         ) {
3434                             // It's a point, so it's single touch, so we just push it to our touches
3435                             targets = [target];
3436 
3437                             // For the UNDO/REDO of object moves
3438                             this.saveStartPos(obj, targets[0]);
3439 
3440                             this.touches.push({ obj: obj, targets: targets });
3441                             obj.highlight(true);
3442                         } else if (
3443                             obj.elementClass === Const.OBJECT_CLASS_LINE ||
3444                             obj.elementClass === Const.OBJECT_CLASS_CIRCLE ||
3445                             obj.elementClass === Const.OBJECT_CLASS_CURVE ||
3446                             obj.type === Const.OBJECT_TYPE_POLYGON
3447                         ) {
3448                             found = false;
3449 
3450                             // first check if this geometric object is already captured in this.touches
3451                             for (j = 0; j < this.touches.length; j++) {
3452                                 if (obj.id === this.touches[j].obj.id) {
3453                                     found = true;
3454                                     // only add it, if we don't have two targets in there already
3455                                     if (this.touches[j].targets.length === 1) {
3456                                         // For the UNDO/REDO of object moves
3457                                         this.saveStartPos(obj, target);
3458                                         this.touches[j].targets.push(target);
3459                                     }
3460 
3461                                     evtTouches[i].jxg_isused = true;
3462                                 }
3463                             }
3464 
3465                             // we couldn't find it in touches, so we just init a new touches
3466                             // IF there is a second touch targetting this line, we will find it later on, and then add it to
3467                             // the touches control object.
3468                             if (!found) {
3469                                 targets = [target];
3470 
3471                                 // For the UNDO/REDO of object moves
3472                                 this.saveStartPos(obj, targets[0]);
3473                                 this.touches.push({ obj: obj, targets: targets });
3474                                 obj.highlight(true);
3475                             }
3476                         }
3477                     }
3478 
3479                     evtTouches[i].jxg_isused = true;
3480                 }
3481             }
3482 
3483             if (this.touches.length > 0) {
3484                 evt.preventDefault();
3485                 evt.stopPropagation();
3486             }
3487 
3488             // Touch events on empty areas of the board are handled here:
3489             // 1. case: one finger. If allowed, this triggers pan with one finger
3490             if (
3491                 evtTouches.length === 1 &&
3492                 this.mode === this.BOARD_MODE_NONE &&
3493                 this.touchStartMoveOriginOneFinger(evt)
3494             ) {
3495             } else if (
3496                 evtTouches.length === 2 &&
3497                 (this.mode === this.BOARD_MODE_NONE ||
3498                     this.mode === this.BOARD_MODE_MOVE_ORIGIN)
3499             ) {
3500                 // 2. case: two fingers: pinch to zoom or pan with two fingers needed.
3501                 // This happens when the second finger hits the device. First, the
3502                 // 'one finger pan mode' has to be cancelled.
3503                 if (this.mode === this.BOARD_MODE_MOVE_ORIGIN) {
3504                     this.originMoveEnd();
3505                 }
3506                 this.gestureStartListener(evt);
3507             }
3508 
3509             this.options.precision.hasPoint = this.options.precision.mouse;
3510             this.triggerEventHandlers(['touchstart', 'down'], [evt]);
3511 
3512             return false;
3513             //return this.touches.length > 0;
3514         },
3515 
3516         /**
3517          * Called periodically by the browser while the user moves his fingers across the device.
3518          * @param {Event} evt
3519          * @returns {Boolean}
3520          */
3521         touchMoveListener: function (evt) {
3522             var i,
3523                 pos1,
3524                 pos2,
3525                 touchTargets,
3526                 evtTouches = evt['touches'];
3527 
3528             if (!this.checkFrameRate(evt)) {
3529                 return false;
3530             }
3531 
3532             if (this.mode !== this.BOARD_MODE_NONE) {
3533                 evt.preventDefault();
3534                 evt.stopPropagation();
3535             }
3536 
3537             if (this.mode !== this.BOARD_MODE_DRAG) {
3538                 this.dehighlightAll();
3539                 this.displayInfobox(false);
3540             }
3541 
3542             this._inputDevice = 'touch';
3543             this.options.precision.hasPoint = this.options.precision.touch;
3544             this.updateQuality = this.BOARD_QUALITY_LOW;
3545 
3546             // selection
3547             if (this.selectingMode) {
3548                 for (i = 0; i < evtTouches.length; i++) {
3549                     if (!evtTouches[i].jxg_isused) {
3550                         pos1 = this.getMousePosition(evt, i);
3551                         this._moveSelecting(pos1);
3552                         this.triggerEventHandlers(
3553                             ['touchmoves', 'moveselecting'],
3554                             [evt, this.mode]
3555                         );
3556                         break;
3557                     }
3558                 }
3559             } else {
3560                 if (!this.touchOriginMove(evt)) {
3561                     if (this.mode === this.BOARD_MODE_DRAG) {
3562                         // Runs over through all elements which are touched
3563                         // by at least one finger.
3564                         for (i = 0; i < this.touches.length; i++) {
3565                             touchTargets = this.touches[i].targets;
3566                             if (touchTargets.length === 1) {
3567                                 // Touch by one finger:  this is possible for all elements that can be dragged
3568                                 if (evtTouches[touchTargets[0].num]) {
3569                                     pos1 = this.getMousePosition(evt, touchTargets[0].num);
3570                                     if (
3571                                         pos1[0] < 0 ||
3572                                         pos1[0] > this.canvasWidth ||
3573                                         pos1[1] < 0 ||
3574                                         pos1[1] > this.canvasHeight
3575                                     ) {
3576                                         return;
3577                                     }
3578                                     touchTargets[0].X = pos1[0];
3579                                     touchTargets[0].Y = pos1[1];
3580                                     this.moveObject(
3581                                         pos1[0],
3582                                         pos1[1],
3583                                         this.touches[i],
3584                                         evt,
3585                                         'touch'
3586                                     );
3587                                 }
3588                             } else if (
3589                                 touchTargets.length === 2 &&
3590                                 touchTargets[0].num > -1 &&
3591                                 touchTargets[1].num > -1
3592                             ) {
3593                                 // Touch by two fingers: moving lines, ...
3594                                 if (
3595                                     evtTouches[touchTargets[0].num] &&
3596                                     evtTouches[touchTargets[1].num]
3597                                 ) {
3598                                     // Get coordinates of the two touches
3599                                     pos1 = this.getMousePosition(evt, touchTargets[0].num);
3600                                     pos2 = this.getMousePosition(evt, touchTargets[1].num);
3601                                     if (
3602                                         pos1[0] < 0 ||
3603                                         pos1[0] > this.canvasWidth ||
3604                                         pos1[1] < 0 ||
3605                                         pos1[1] > this.canvasHeight ||
3606                                         pos2[0] < 0 ||
3607                                         pos2[0] > this.canvasWidth ||
3608                                         pos2[1] < 0 ||
3609                                         pos2[1] > this.canvasHeight
3610                                     ) {
3611                                         return;
3612                                     }
3613 
3614                                     touchTargets[0].X = pos1[0];
3615                                     touchTargets[0].Y = pos1[1];
3616                                     touchTargets[1].X = pos2[0];
3617                                     touchTargets[1].Y = pos2[1];
3618 
3619                                     this.twoFingerMove(
3620                                         this.touches[i],
3621                                         touchTargets[0].num,
3622                                         evt
3623                                     );
3624 
3625                                     touchTargets[0].Xprev = pos1[0];
3626                                     touchTargets[0].Yprev = pos1[1];
3627                                     touchTargets[1].Xprev = pos2[0];
3628                                     touchTargets[1].Yprev = pos2[1];
3629                                 }
3630                             }
3631                         }
3632                     } else {
3633                         if (evtTouches.length === 2) {
3634                             this.gestureChangeListener(evt);
3635                         }
3636                         // Move event without dragging an element
3637                         pos1 = this.getMousePosition(evt, 0);
3638                         this.highlightElements(pos1[0], pos1[1], evt, -1);
3639                     }
3640                 }
3641             }
3642 
3643             if (this.mode !== this.BOARD_MODE_DRAG) {
3644                 this.displayInfobox(false);
3645             }
3646 
3647             this.triggerEventHandlers(['touchmove', 'move'], [evt, this.mode]);
3648             this.options.precision.hasPoint = this.options.precision.mouse;
3649             this.updateQuality = this.BOARD_QUALITY_HIGH;
3650 
3651             return this.mode === this.BOARD_MODE_NONE;
3652         },
3653 
3654         /**
3655          * Triggered as soon as the user stops touching the device with at least one finger.
3656          * @param {Event} evt
3657          * @returns {Boolean}
3658          */
3659         touchEndListener: function (evt) {
3660             var i,
3661                 j,
3662                 k,
3663                 eps = this.options.precision.touch,
3664                 tmpTouches = [],
3665                 found,
3666                 foundNumber,
3667                 evtTouches = evt && evt['touches'],
3668                 touchTargets,
3669                 updateNeeded = false;
3670 
3671             this.triggerEventHandlers(['touchend', 'up'], [evt]);
3672             this.displayInfobox(false);
3673 
3674             // selection
3675             if (this.selectingMode) {
3676                 this._stopSelecting(evt);
3677                 this.triggerEventHandlers(['touchstopselecting', 'stopselecting'], [evt]);
3678                 this.stopSelectionMode();
3679             } else if (evtTouches && evtTouches.length > 0) {
3680                 for (i = 0; i < this.touches.length; i++) {
3681                     tmpTouches[i] = this.touches[i];
3682                 }
3683                 this.touches.length = 0;
3684 
3685                 // try to convert the operation, e.g. if a lines is rotated and translated with two fingers and one finger is lifted,
3686                 // convert the operation to a simple one-finger-translation.
3687                 // ADDENDUM 11/10/11:
3688                 // see addendum to touchStartListener from 11/10/11
3689                 // (1) run through the tmptouches
3690                 // (2) check the touches.obj, if it is a
3691                 //     (a) point, try to find the targettouch, if found keep it and mark the targettouch, else drop the touch.
3692                 //     (b) line with
3693                 //          (i) one target: try to find it, if found keep it mark the targettouch, else drop the touch.
3694                 //         (ii) two targets: if none can be found, drop the touch. if one can be found, remove the other target. mark all found targettouches
3695                 //     (c) circle with [proceed like in line]
3696 
3697                 // init the targettouches marker
3698                 for (i = 0; i < evtTouches.length; i++) {
3699                     evtTouches[i].jxg_isused = false;
3700                 }
3701 
3702                 for (i = 0; i < tmpTouches.length; i++) {
3703                     // could all targets of the current this.touches.obj be assigned to targettouches?
3704                     found = false;
3705                     foundNumber = 0;
3706                     touchTargets = tmpTouches[i].targets;
3707 
3708                     for (j = 0; j < touchTargets.length; j++) {
3709                         touchTargets[j].found = false;
3710                         for (k = 0; k < evtTouches.length; k++) {
3711                             if (
3712                                 Math.abs(
3713                                     Math.pow(evtTouches[k].screenX - touchTargets[j].X, 2) +
3714                                     Math.pow(evtTouches[k].screenY - touchTargets[j].Y, 2)
3715                                 ) <
3716                                 eps * eps
3717                             ) {
3718                                 touchTargets[j].found = true;
3719                                 touchTargets[j].num = k;
3720                                 touchTargets[j].X = evtTouches[k].screenX;
3721                                 touchTargets[j].Y = evtTouches[k].screenY;
3722                                 foundNumber += 1;
3723                                 break;
3724                             }
3725                         }
3726                     }
3727 
3728                     if (Type.isPoint(tmpTouches[i].obj)) {
3729                         found = touchTargets[0] && touchTargets[0].found;
3730                     } else if (tmpTouches[i].obj.elementClass === Const.OBJECT_CLASS_LINE) {
3731                         found =
3732                             (touchTargets[0] && touchTargets[0].found) ||
3733                             (touchTargets[1] && touchTargets[1].found);
3734                     } else if (tmpTouches[i].obj.elementClass === Const.OBJECT_CLASS_CIRCLE) {
3735                         found = foundNumber === 1 || foundNumber === 3;
3736                     }
3737 
3738                     // if we found this object to be still dragged by the user, add it back to this.touches
3739                     if (found) {
3740                         this.touches.push({
3741                             obj: tmpTouches[i].obj,
3742                             targets: []
3743                         });
3744 
3745                         for (j = 0; j < touchTargets.length; j++) {
3746                             if (touchTargets[j].found) {
3747                                 this.touches[this.touches.length - 1].targets.push({
3748                                     num: touchTargets[j].num,
3749                                     X: touchTargets[j].screenX,
3750                                     Y: touchTargets[j].screenY,
3751                                     Xprev: NaN,
3752                                     Yprev: NaN,
3753                                     Xstart: touchTargets[j].Xstart,
3754                                     Ystart: touchTargets[j].Ystart,
3755                                     Zstart: touchTargets[j].Zstart
3756                                 });
3757                             }
3758                         }
3759                     } else {
3760                         tmpTouches[i].obj.noHighlight();
3761                     }
3762                 }
3763             } else {
3764                 this.touches.length = 0;
3765             }
3766 
3767             for (i = this.downObjects.length - 1; i > -1; i--) {
3768                 found = false;
3769                 for (j = 0; j < this.touches.length; j++) {
3770                     if (this.touches[j].obj.id === this.downObjects[i].id) {
3771                         found = true;
3772                     }
3773                 }
3774                 if (!found) {
3775                     this.downObjects[i].triggerEventHandlers(['touchup', 'up'], [evt]);
3776                     if (!Type.exists(this.downObjects[i].coords)) {
3777                         // snapTo methods have to be called e.g. for line elements here.
3778                         // For coordsElements there might be a conflict with
3779                         // attractors, see commit from 2022.04.08, 11:12:18.
3780                         this.downObjects[i].snapToGrid();
3781                         this.downObjects[i].snapToPoints();
3782                         updateNeeded = true;
3783                     }
3784                     this.downObjects.splice(i, 1);
3785                 }
3786             }
3787 
3788             if (!evtTouches || evtTouches.length === 0) {
3789                 if (this.hasTouchEnd) {
3790                     Env.removeEvent(this.document, 'touchend', this.touchEndListener, this);
3791                     this.hasTouchEnd = false;
3792                 }
3793 
3794                 this.dehighlightAll();
3795                 this.updateQuality = this.BOARD_QUALITY_HIGH;
3796 
3797                 this.originMoveEnd();
3798                 if (updateNeeded) {
3799                     this.update();
3800                 }
3801             }
3802 
3803             return true;
3804         },
3805 
3806         /**
3807          * This method is called by the browser when the mouse button is clicked.
3808          * @param {Event} evt The browsers event object.
3809          * @returns {Boolean} True if no element is found under the current mouse pointer, false otherwise.
3810          */
3811         mouseDownListener: function (evt) {
3812             var pos, elements, result;
3813 
3814             // prevent accidental selection of text
3815             if (this.document.selection && Type.isFunction(this.document.selection.empty)) {
3816                 this.document.selection.empty();
3817             } else if (window.getSelection) {
3818                 window.getSelection().removeAllRanges();
3819             }
3820 
3821             if (!this.hasMouseUp) {
3822                 Env.addEvent(this.document, 'mouseup', this.mouseUpListener, this);
3823                 this.hasMouseUp = true;
3824             } else {
3825                 // In case this.hasMouseUp==true, it may be that there was a
3826                 // mousedown event before which was not followed by an mouseup event.
3827                 // This seems to happen with interactive whiteboard pens sometimes.
3828                 return;
3829             }
3830 
3831             this._inputDevice = 'mouse';
3832             this.options.precision.hasPoint = this.options.precision.mouse;
3833             pos = this.getMousePosition(evt);
3834 
3835             // selection
3836             this._testForSelection(evt);
3837             if (this.selectingMode) {
3838                 this._startSelecting(pos);
3839                 this.triggerEventHandlers(['mousestartselecting', 'startselecting'], [evt]);
3840                 return; // don't continue as a normal click
3841             }
3842 
3843             elements = this.initMoveObject(pos[0], pos[1], evt, 'mouse');
3844 
3845             // if no draggable object can be found, get out here immediately
3846             if (elements.length === 0) {
3847                 this.mode = this.BOARD_MODE_NONE;
3848                 result = true;
3849             } else {
3850                 this.mouse = {
3851                     obj: null,
3852                     targets: [
3853                         {
3854                             X: pos[0],
3855                             Y: pos[1],
3856                             Xprev: NaN,
3857                             Yprev: NaN
3858                         }
3859                     ]
3860                 };
3861                 this.mouse.obj = elements[elements.length - 1];
3862 
3863                 this.dehighlightAll();
3864                 this.mouse.obj.highlight(true);
3865 
3866                 this.mouse.targets[0].Xstart = [];
3867                 this.mouse.targets[0].Ystart = [];
3868                 this.mouse.targets[0].Zstart = [];
3869 
3870                 this.saveStartPos(this.mouse.obj, this.mouse.targets[0]);
3871 
3872                 // prevent accidental text selection
3873                 // this could get us new trouble: input fields, links and drop down boxes placed as text
3874                 // on the board don't work anymore.
3875                 if (evt && evt.preventDefault) {
3876                     evt.preventDefault();
3877                 } else if (window.event) {
3878                     window.event.returnValue = false;
3879                 }
3880             }
3881 
3882             if (this.mode === this.BOARD_MODE_NONE) {
3883                 result = this.mouseOriginMoveStart(evt);
3884             }
3885 
3886             this.triggerEventHandlers(['mousedown', 'down'], [evt]);
3887 
3888             return result;
3889         },
3890 
3891         /**
3892          * This method is called by the browser when the mouse is moved.
3893          * @param {Event} evt The browsers event object.
3894          */
3895         mouseMoveListener: function (evt) {
3896             var pos;
3897 
3898             if (!this.checkFrameRate(evt)) {
3899                 return false;
3900             }
3901 
3902             pos = this.getMousePosition(evt);
3903 
3904             this.updateQuality = this.BOARD_QUALITY_LOW;
3905 
3906             if (this.mode !== this.BOARD_MODE_DRAG) {
3907                 this.dehighlightAll();
3908                 this.displayInfobox(false);
3909             }
3910 
3911             // we have to check for four cases:
3912             //   * user moves origin
3913             //   * user drags an object
3914             //   * user just moves the mouse, here highlight all elements at
3915             //     the current mouse position
3916             //   * the user is selecting
3917 
3918             // selection
3919             if (this.selectingMode) {
3920                 this._moveSelecting(pos);
3921                 this.triggerEventHandlers(
3922                     ['mousemoveselecting', 'moveselecting'],
3923                     [evt, this.mode]
3924                 );
3925             } else if (!this.mouseOriginMove(evt)) {
3926                 if (this.mode === this.BOARD_MODE_DRAG) {
3927                     this.moveObject(pos[0], pos[1], this.mouse, evt, 'mouse');
3928                 } else {
3929                     // BOARD_MODE_NONE
3930                     // Move event without dragging an element
3931                     this.highlightElements(pos[0], pos[1], evt, -1);
3932                 }
3933                 this.triggerEventHandlers(['mousemove', 'move'], [evt, this.mode]);
3934             }
3935             this.updateQuality = this.BOARD_QUALITY_HIGH;
3936         },
3937 
3938         /**
3939          * This method is called by the browser when the mouse button is released.
3940          * @param {Event} evt
3941          */
3942         mouseUpListener: function (evt) {
3943             var i;
3944 
3945             if (this.selectingMode === false) {
3946                 this.triggerEventHandlers(['mouseup', 'up'], [evt]);
3947             }
3948 
3949             // redraw with high precision
3950             this.updateQuality = this.BOARD_QUALITY_HIGH;
3951 
3952             if (this.mouse && this.mouse.obj) {
3953                 if (!Type.exists(this.mouse.obj.coords)) {
3954                     // snapTo methods have to be called e.g. for line elements here.
3955                     // For coordsElements there might be a conflict with
3956                     // attractors, see commit from 2022.04.08, 11:12:18.
3957                     // The parameter is needed for lines with snapToGrid enabled
3958                     this.mouse.obj.snapToGrid(this.mouse.targets[0]);
3959                     this.mouse.obj.snapToPoints();
3960                 }
3961             }
3962 
3963             this.originMoveEnd();
3964             this.dehighlightAll();
3965             this.update();
3966 
3967             // selection
3968             if (this.selectingMode) {
3969                 this._stopSelecting(evt);
3970                 this.triggerEventHandlers(['mousestopselecting', 'stopselecting'], [evt]);
3971                 this.stopSelectionMode();
3972             } else {
3973                 for (i = 0; i < this.downObjects.length; i++) {
3974                     this.downObjects[i].triggerEventHandlers(['mouseup', 'up'], [evt]);
3975                 }
3976             }
3977 
3978             this.downObjects.length = 0;
3979 
3980             if (this.hasMouseUp) {
3981                 Env.removeEvent(this.document, 'mouseup', this.mouseUpListener, this);
3982                 this.hasMouseUp = false;
3983             }
3984 
3985             // release dragged mouse object
3986             this.mouse = null;
3987         },
3988 
3989         /**
3990          * Handler for mouse wheel events. Used to zoom in and out of the board.
3991          * @param {Event} evt
3992          * @returns {Boolean}
3993          */
3994         mouseWheelListener: function (evt) {
3995             var wd, zoomCenter, pos;
3996 
3997             if (!this.attr.zoom.enabled ||
3998                 !this.attr.zoom.wheel ||
3999                 !this._isRequiredKeyPressed(evt, 'zoom')) {
4000 
4001                 return true;
4002             }
4003 
4004             evt = evt || window.event;
4005             wd = evt.detail ? -evt.detail : evt.wheelDelta / 40;
4006             zoomCenter = this.attr.zoom.center;
4007 
4008             if (zoomCenter === 'board') {
4009                 pos = [];
4010             } else { // including zoomCenter === 'auto'
4011                 pos = new Coords(Const.COORDS_BY_SCREEN, this.getMousePosition(evt), this).usrCoords;
4012             }
4013 
4014             // pos == [] does not throw an error
4015             if (wd > 0) {
4016                 this.zoomIn(pos[1], pos[2]);
4017             } else {
4018                 this.zoomOut(pos[1], pos[2]);
4019             }
4020 
4021             this.triggerEventHandlers(['mousewheel'], [evt]);
4022 
4023             evt.preventDefault();
4024             return false;
4025         },
4026 
4027         /**
4028          * Allow moving of JSXGraph elements with arrow keys.
4029          * The selection of the element is done with the tab key. For this,
4030          * the attribute 'tabindex' of the element has to be set to some number (default=0).
4031          * tabindex corresponds to the HTML and SVG attribute of the same name.
4032          * <p>
4033          * Panning of the construction is done with arrow keys
4034          * if the pan key (shift or ctrl - depending on the board attributes) is pressed.
4035          * <p>
4036          * Zooming is triggered with the keys +, o, -, if
4037          * the pan key (shift or ctrl - depending on the board attributes) is pressed.
4038          * <p>
4039          * Keyboard control (move, pan, and zoom) is disabled if an HTML element of type input or textarea has received focus.
4040          *
4041          * @param  {Event} evt The browser's event object
4042          *
4043          * @see JXG.Board#keyboard
4044          * @see JXG.Board#keyFocusInListener
4045          * @see JXG.Board#keyFocusOutListener
4046          *
4047          */
4048         keyDownListener: function (evt) {
4049             var id_node = evt.target.id,
4050                 id, el, res, doc,
4051                 sX = 0,
4052                 sY = 0,
4053                 // dx, dy are provided in screen units and
4054                 // are converted to user coordinates
4055                 dx = Type.evaluate(this.attr.keyboard.dx) / this.unitX,
4056                 dy = Type.evaluate(this.attr.keyboard.dy) / this.unitY,
4057                 // u = 100,
4058                 doZoom = false,
4059                 done = true,
4060                 dir,
4061                 actPos;
4062 
4063             if (!this.attr.keyboard.enabled || id_node === '') {
4064                 return false;
4065             }
4066 
4067             // dx = Math.round(dx * u) / u;
4068             // dy = Math.round(dy * u) / u;
4069 
4070             // An element of type input or textarea has focus, get out of here.
4071             doc = this.containerObj.shadowRoot || document;
4072             if (doc.activeElement) {
4073                 el = doc.activeElement;
4074                 if (el.tagName === 'INPUT' || el.tagName === 'textarea') {
4075                     return false;
4076                 }
4077             }
4078 
4079             // Get the JSXGraph id from the id of the SVG node.
4080             id = id_node.replace(this.containerObj.id + '_', '');
4081             el = this.select(id);
4082 
4083             if (Type.exists(el.coords)) {
4084                 actPos = el.coords.usrCoords.slice(1);
4085             }
4086 
4087             if (
4088                 (Type.evaluate(this.attr.keyboard.panshift) && evt.shiftKey) ||
4089                 (Type.evaluate(this.attr.keyboard.panctrl) && evt.ctrlKey)
4090             ) {
4091                 // Pan key has been pressed
4092 
4093                 if (Type.evaluate(this.attr.zoom.enabled) === true) {
4094                     doZoom = true;
4095                 }
4096 
4097                 // Arrow keys
4098                 if (evt.keyCode === 38) {
4099                     // up
4100                     this.clickUpArrow();
4101                 } else if (evt.keyCode === 40) {
4102                     // down
4103                     this.clickDownArrow();
4104                 } else if (evt.keyCode === 37) {
4105                     // left
4106                     this.clickLeftArrow();
4107                 } else if (evt.keyCode === 39) {
4108                     // right
4109                     this.clickRightArrow();
4110 
4111                     // Zoom keys
4112                 } else if (doZoom && evt.keyCode === 171) {
4113                     // +
4114                     this.zoomIn();
4115                 } else if (doZoom && evt.keyCode === 173) {
4116                     // -
4117                     this.zoomOut();
4118                 } else if (doZoom && evt.keyCode === 79) {
4119                     // o
4120                     this.zoom100();
4121                 } else {
4122                     done = false;
4123                 }
4124             } else if (!evt.shiftKey && !evt.ctrlKey) {         // Move an element if neither shift or ctrl are pressed
4125                 // Adapt dx, dy to snapToGrid and attractToGrid.
4126                 // snapToGrid has priority.
4127                 if (Type.exists(el.visProp)) {
4128                     if (
4129                         Type.exists(el.visProp.snaptogrid) &&
4130                         el.visProp.snaptogrid &&
4131                         el.evalVisProp('snapsizex') &&
4132                         el.evalVisProp('snapsizey')
4133                     ) {
4134                         // Adapt dx, dy such that snapToGrid is possible
4135                         res = el.getSnapSizes();
4136                         sX = res[0];
4137                         sY = res[1];
4138                         // If snaptogrid is true,
4139                         // we can only jump from grid point to grid point.
4140                         dx = sX;
4141                         dy = sY;
4142                     } else if (
4143                         Type.exists(el.visProp.attracttogrid) &&
4144                         el.visProp.attracttogrid &&
4145                         el.evalVisProp('attractordistance') &&
4146                         el.evalVisProp('attractorunit')
4147                     ) {
4148                         // Adapt dx, dy such that attractToGrid is possible
4149                         sX = 1.1 * el.evalVisProp('attractordistance');
4150                         sY = sX;
4151 
4152                         if (el.evalVisProp('attractorunit') === 'screen') {
4153                             sX /= this.unitX;
4154                             sY /= this.unitX;
4155                         }
4156                         dx = Math.max(sX, dx);
4157                         dy = Math.max(sY, dy);
4158                     }
4159                 }
4160 
4161                 if (evt.keyCode === 38) {
4162                     // up
4163                     dir = [0, dy];
4164                 } else if (evt.keyCode === 40) {
4165                     // down
4166                     dir = [0, -dy];
4167                 } else if (evt.keyCode === 37) {
4168                     // left
4169                     dir = [-dx, 0];
4170                 } else if (evt.keyCode === 39) {
4171                     // right
4172                     dir = [dx, 0];
4173                 } else {
4174                     done = false;
4175                 }
4176 
4177                 if (dir && el.isDraggable &&
4178                     el.visPropCalc.visible &&
4179                     ((this.geonextCompatibilityMode &&
4180                         (Type.isPoint(el) ||
4181                             el.elementClass === Const.OBJECT_CLASS_TEXT)
4182                     ) || !this.geonextCompatibilityMode) &&
4183                     !el.evalVisProp('fixed')
4184                 ) {
4185                     this.mode = this.BOARD_MODE_DRAG;
4186                     if (Type.exists(el.coords)) {
4187                         dir[0] += actPos[0];
4188                         dir[1] += actPos[1];
4189                     }
4190                     // For coordsElement setPosition has to call setPositionDirectly.
4191                     // Otherwise the position is set by a translation.
4192                     if (Type.exists(el.coords)) {
4193                         el.setPosition(JXG.COORDS_BY_USER, dir);
4194                         this.updateInfobox(el);
4195                     } else {
4196                         this.displayInfobox(false);
4197                         el.setPositionDirectly(
4198                             Const.COORDS_BY_USER,
4199                             dir,
4200                             [0, 0]
4201                         );
4202                     }
4203 
4204                     this.triggerEventHandlers(['keymove', 'move'], [evt, this.mode]);
4205                     el.triggerEventHandlers(['keydrag', 'drag'], [evt]);
4206                     this.mode = this.BOARD_MODE_NONE;
4207                 }
4208             }
4209 
4210             this.update();
4211 
4212             if (done && Type.exists(evt.preventDefault)) {
4213                 evt.preventDefault();
4214             }
4215             return done;
4216         },
4217 
4218         /**
4219          * Event listener for SVG elements getting focus.
4220          * This is needed for highlighting when using keyboard control.
4221          * Only elements having the attribute 'tabindex' can receive focus.
4222          *
4223          * @see JXG.Board#keyFocusOutListener
4224          * @see JXG.Board#keyDownListener
4225          * @see JXG.Board#keyboard
4226          *
4227          * @param  {Event} evt The browser's event object
4228          */
4229         keyFocusInListener: function (evt) {
4230             var id_node = evt.target.id,
4231                 id,
4232                 el;
4233 
4234             if (!this.attr.keyboard.enabled || id_node === '') {
4235                 return false;
4236             }
4237 
4238             // Get JSXGraph id from node id
4239             id = id_node.replace(this.containerObj.id + '_', '');
4240             el = this.select(id);
4241             if (Type.exists(el.highlight)) {
4242                 el.highlight(true);
4243                 this.focusObjects = [id];
4244                 el.triggerEventHandlers(['hit'], [evt]);
4245             }
4246             if (Type.exists(el.coords)) {
4247                 this.updateInfobox(el);
4248             }
4249         },
4250 
4251         /**
4252          * Event listener for SVG elements losing focus.
4253          * This is needed for dehighlighting when using keyboard control.
4254          * Only elements having the attribute 'tabindex' can receive focus.
4255          *
4256          * @see JXG.Board#keyFocusInListener
4257          * @see JXG.Board#keyDownListener
4258          * @see JXG.Board#keyboard
4259          *
4260          * @param  {Event} evt The browser's event object
4261          */
4262         keyFocusOutListener: function (evt) {
4263             if (!this.attr.keyboard.enabled) {
4264                 return false;
4265             }
4266             this.focusObjects = []; // This has to be before displayInfobox(false)
4267             this.dehighlightAll();
4268             this.displayInfobox(false);
4269         },
4270 
4271         /**
4272          * Update the width and height of the JSXGraph container div element.
4273          * If width and height are not supplied, read actual values with offsetWidth/Height,
4274          * and call board.resizeContainer() with this values.
4275          * <p>
4276          * If necessary, also call setBoundingBox().
4277          * @param {Number} [width=this.containerObj.offsetWidth] Width of the container element
4278          * @param {Number} [height=this.containerObj.offsetHeight] Height of the container element
4279          * @returns
4280          *
4281          * @see JXG.Board#startResizeObserver
4282          * @see JXG.Board#resizeListener
4283          * @see JXG.Board#resizeContainer
4284          * @see JXG.Board#setBoundingBox
4285          *
4286          */
4287         updateContainerDims: function (width, height) {
4288             var w = width,
4289                 h = height,
4290                 // bb,
4291                 css,
4292                 width_adjustment, height_adjustment;
4293 
4294             if (width === undefined) {
4295                 // Get size of the board's container div
4296                 //
4297                 // offsetWidth/Height ignores CSS transforms,
4298                 // getBoundingClientRect includes CSS transforms
4299                 //
4300                 // bb = this.containerObj.getBoundingClientRect();
4301                 // w = bb.width;
4302                 // h = bb.height;
4303                 w = this.containerObj.offsetWidth;
4304                 h = this.containerObj.offsetHeight;
4305             }
4306 
4307             if (width === undefined && window && window.getComputedStyle) {
4308                 // Subtract the border size
4309                 css = window.getComputedStyle(this.containerObj, null);
4310                 width_adjustment = parseFloat(css.getPropertyValue('border-left-width')) + parseFloat(css.getPropertyValue('border-right-width'));
4311                 if (!isNaN(width_adjustment)) {
4312                     w -= width_adjustment;
4313                 }
4314                 height_adjustment = parseFloat(css.getPropertyValue('border-top-width')) + parseFloat(css.getPropertyValue('border-bottom-width'));
4315                 if (!isNaN(height_adjustment)) {
4316                     h -= height_adjustment;
4317                 }
4318             }
4319 
4320             // If div is invisible - do nothing
4321             if (w <= 0 || h <= 0 || isNaN(w) || isNaN(h)) {
4322                 return;
4323             }
4324 
4325             // If bounding box is not yet initialized, do it now.
4326             if (isNaN(this.getBoundingBox()[0])) {
4327                 this.setBoundingBox(this.attr.boundingbox, this.keepaspectratio, 'keep');
4328             }
4329 
4330             // Do nothing if the dimension did not change since being visible
4331             // the last time. Note that if the div had display:none in the mean time,
4332             // we did not store this._prevDim.
4333             if (Type.exists(this._prevDim) && this._prevDim.w === w && this._prevDim.h === h) {
4334                 return;
4335             }
4336             // Set the size of the SVG or canvas element
4337             this.resizeContainer(w, h, true);
4338             this._prevDim = {
4339                 w: w,
4340                 h: h
4341             };
4342         },
4343 
4344         /**
4345          * Start observer which reacts to size changes of the JSXGraph
4346          * container div element. Calls updateContainerDims().
4347          * If not available, an event listener for the window-resize event is started.
4348          * On mobile devices also scrolling might trigger resizes.
4349          * However, resize events triggered by scrolling events should be ignored.
4350          * Therefore, also a scrollListener is started.
4351          * Resize can be controlled with the board attribute resize.
4352          *
4353          * @see JXG.Board#updateContainerDims
4354          * @see JXG.Board#resizeListener
4355          * @see JXG.Board#scrollListener
4356          * @see JXG.Board#resize
4357          *
4358          */
4359         startResizeObserver: function () {
4360             var that = this;
4361 
4362             if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {
4363                 return;
4364             }
4365 
4366             this.resizeObserver = new ResizeObserver(function (entries) {
4367                 var bb;
4368                 if (!that._isResizing) {
4369                     that._isResizing = true;
4370                     bb = entries[0].contentRect;
4371                     window.setTimeout(function () {
4372                         try {
4373                             that.updateContainerDims(bb.width, bb.height);
4374                         } catch (e) {
4375                             JXG.debug(e);   // Used to log errors during board.update()
4376                             that.stopResizeObserver();
4377                         } finally {
4378                             that._isResizing = false;
4379                         }
4380                     }, that.attr.resize.throttle);
4381                 }
4382             });
4383             this.resizeObserver.observe(this.containerObj);
4384         },
4385 
4386         /**
4387          * Stops the resize observer.
4388          * @see JXG.Board#startResizeObserver
4389          *
4390          */
4391         stopResizeObserver: function () {
4392             if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {
4393                 return;
4394             }
4395 
4396             if (Type.exists(this.resizeObserver)) {
4397                 this.resizeObserver.unobserve(this.containerObj);
4398             }
4399         },
4400 
4401         /**
4402          * Fallback solutions if there is no resizeObserver available in the browser.
4403          * Reacts to resize events of the window (only). Otherwise similar to
4404          * startResizeObserver(). To handle changes of the visibility
4405          * of the JSXGraph container element, additionally an intersection observer is used.
4406          * which watches changes in the visibility of the JSXGraph container element.
4407          * This is necessary e.g. for register tabs or dia shows.
4408          *
4409          * @see JXG.Board#startResizeObserver
4410          * @see JXG.Board#startIntersectionObserver
4411          */
4412         resizeListener: function () {
4413             var that = this;
4414 
4415             if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {
4416                 return;
4417             }
4418             if (!this._isScrolling && !this._isResizing) {
4419                 this._isResizing = true;
4420                 window.setTimeout(function () {
4421                     that.updateContainerDims();
4422                     that._isResizing = false;
4423                 }, this.attr.resize.throttle);
4424             }
4425         },
4426 
4427         /**
4428          * Listener to watch for scroll events. Sets board._isScrolling = true
4429          * @param  {Event} evt The browser's event object
4430          *
4431          * @see JXG.Board#startResizeObserver
4432          * @see JXG.Board#resizeListener
4433          *
4434          */
4435         scrollListener: function (evt) {
4436             var that = this;
4437 
4438             if (!Env.isBrowser) {
4439                 return;
4440             }
4441             if (!this._isScrolling) {
4442                 this._isScrolling = true;
4443                 window.setTimeout(function () {
4444                     that._isScrolling = false;
4445                 }, 66);
4446             }
4447         },
4448 
4449         /**
4450          * Watch for changes of the visibility of the JSXGraph container element.
4451          *
4452          * @see JXG.Board#startResizeObserver
4453          * @see JXG.Board#resizeListener
4454          *
4455          */
4456         startIntersectionObserver: function () {
4457             var that = this,
4458                 options = {
4459                     root: null,
4460                     rootMargin: '0px',
4461                     threshold: 0.8
4462                 };
4463 
4464             try {
4465                 this.intersectionObserver = new IntersectionObserver(function (entries) {
4466                     // If bounding box is not yet initialized, do it now.
4467                     if (isNaN(that.getBoundingBox()[0])) {
4468                         that.updateContainerDims();
4469                     }
4470                 }, options);
4471                 this.intersectionObserver.observe(that.containerObj);
4472             } catch (err) {
4473                 JXG.debug('JSXGraph: IntersectionObserver not available in this browser.');
4474             }
4475         },
4476 
4477         /**
4478          * Stop the intersection observer
4479          *
4480          * @see JXG.Board#startIntersectionObserver
4481          *
4482          */
4483         stopIntersectionObserver: function () {
4484             if (Type.exists(this.intersectionObserver)) {
4485                 this.intersectionObserver.unobserve(this.containerObj);
4486             }
4487         },
4488 
4489         /**
4490          * Update the container before and after printing.
4491          * @param {Event} [evt]
4492          */
4493         printListener: function(evt) {
4494             this.updateContainerDims();
4495         },
4496 
4497         /**
4498          * Wrapper for printListener to be used in mediaQuery matches.
4499          * @param {MediaQueryList} mql
4500          */
4501         printListenerMatch: function (mql) {
4502             if (mql.matches) {
4503                 this.printListener();
4504             }
4505         },
4506 
4507         /**********************************************************
4508          *
4509          * End of Event Handlers
4510          *
4511          **********************************************************/
4512 
4513         /**
4514          * Initialize the info box object which is used to display
4515          * the coordinates of points near the mouse pointer,
4516          * @returns {JXG.Board} Reference to the board
4517          */
4518         initInfobox: function (attributes) {
4519             var attr = Type.copyAttributes(attributes, this.options, 'infobox');
4520 
4521             attr.id = this.id + '_infobox';
4522 
4523             /**
4524              * Infobox close to points in which the points' coordinates are displayed.
4525              * This is simply a JXG.Text element. Access through board.infobox.
4526              * Uses CSS class .JXGinfobox.
4527              *
4528              * @namespace
4529              * @name JXG.Board.infobox
4530              * @type JXG.Text
4531              *
4532              * @example
4533              * const board = JXG.JSXGraph.initBoard(BOARDID, {
4534              *     boundingbox: [-0.5, 0.5, 0.5, -0.5],
4535              *     intl: {
4536              *         enabled: false,
4537              *         locale: 'de-DE'
4538              *     },
4539              *     keepaspectratio: true,
4540              *     axis: true,
4541              *     infobox: {
4542              *         distanceY: 40,
4543              *         intl: {
4544              *             enabled: true,
4545              *             options: {
4546              *                 minimumFractionDigits: 1,
4547              *                 maximumFractionDigits: 2
4548              *             }
4549              *         }
4550              *     }
4551              * });
4552              * var p = board.create('point', [0.1, 0.1], {});
4553              *
4554              * </pre><div id="JXG822161af-fe77-4769-850f-cdf69935eab0" class="jxgbox" style="width: 300px; height: 300px;"></div>
4555              * <script type="text/javascript">
4556              *     (function() {
4557              *     const board = JXG.JSXGraph.initBoard('JXG822161af-fe77-4769-850f-cdf69935eab0', {
4558              *         boundingbox: [-0.5, 0.5, 0.5, -0.5], showcopyright: false, shownavigation: false,
4559              *         intl: {
4560              *             enabled: false,
4561              *             locale: 'de-DE'
4562              *         },
4563              *         keepaspectratio: true,
4564              *         axis: true,
4565              *         infobox: {
4566              *             distanceY: 40,
4567              *             intl: {
4568              *                 enabled: true,
4569              *                 options: {
4570              *                     minimumFractionDigits: 1,
4571              *                     maximumFractionDigits: 2
4572              *                 }
4573              *             }
4574              *         }
4575              *     });
4576              *     var p = board.create('point', [0.1, 0.1], {});
4577              *     })();
4578              *
4579              * </script><pre>
4580              *
4581              */
4582             this.infobox = this.create('text', [0, 0, '0,0'], attr);
4583             // this.infobox.needsUpdateSize = false;  // That is not true, but it speeds drawing up.
4584             this.infobox.dump = false;
4585 
4586             this.displayInfobox(false);
4587             return this;
4588         },
4589 
4590         /**
4591          * Updates and displays a little info box to show coordinates of current selected points.
4592          * @param {JXG.GeometryElement} el A GeometryElement
4593          * @returns {JXG.Board} Reference to the board
4594          * @see JXG.Board#displayInfobox
4595          * @see JXG.Board#showInfobox
4596          * @see Point#showInfobox
4597          *
4598          */
4599         updateInfobox: function (el) {
4600             var x, y, xc, yc,
4601                 vpinfoboxdigits,
4602                 distX, distY,
4603                 vpsi = el.evalVisProp('showinfobox');
4604 
4605             if ((!Type.evaluate(this.attr.showinfobox) && vpsi === 'inherit') || !vpsi) {
4606                 return this;
4607             }
4608 
4609             if (Type.isPoint(el)) {
4610                 xc = el.coords.usrCoords[1];
4611                 yc = el.coords.usrCoords[2];
4612                 distX = this.infobox.evalVisProp('distancex');
4613                 distY = this.infobox.evalVisProp('distancey');
4614 
4615                 this.infobox.setCoords(
4616                     xc + distX / this.unitX,
4617                     yc + distY / this.unitY
4618                 );
4619 
4620                 vpinfoboxdigits = el.evalVisProp('infoboxdigits');
4621                 if (typeof el.infoboxText !== 'string') {
4622                     if (vpinfoboxdigits === 'auto') {
4623                         if (this.infobox.useLocale()) {
4624                             x = this.infobox.formatNumberLocale(xc);
4625                             y = this.infobox.formatNumberLocale(yc);
4626                         } else {
4627                             x = Type.autoDigits(xc);
4628                             y = Type.autoDigits(yc);
4629                         }
4630                     } else if (Type.isNumber(vpinfoboxdigits)) {
4631                         if (this.infobox.useLocale()) {
4632                             x = this.infobox.formatNumberLocale(xc, vpinfoboxdigits);
4633                             y = this.infobox.formatNumberLocale(yc, vpinfoboxdigits);
4634                         } else {
4635                             x = Type.toFixed(xc, vpinfoboxdigits);
4636                             y = Type.toFixed(yc, vpinfoboxdigits);
4637                         }
4638 
4639                     } else {
4640                         x = xc;
4641                         y = yc;
4642                     }
4643 
4644                     this.highlightInfobox(x, y, el);
4645                 } else {
4646                     this.highlightCustomInfobox(el.infoboxText, el);
4647                 }
4648 
4649                 this.displayInfobox(true);
4650             }
4651             return this;
4652         },
4653 
4654         /**
4655          * Set infobox visible / invisible.
4656          *
4657          * It uses its property hiddenByParent to memorize its status.
4658          * In this way, many DOM access can be avoided.
4659          *
4660          * @param  {Boolean} val true for visible, false for invisible
4661          * @returns {JXG.Board} Reference to the board.
4662          * @see JXG.Board#updateInfobox
4663          *
4664          */
4665         displayInfobox: function (val) {
4666             if (!val && this.focusObjects.length > 0 &&
4667                 this.select(this.focusObjects[0]).elementClass === Const.OBJECT_CLASS_POINT) {
4668                 // If an element has focus we do not hide its infobox
4669                 return this;
4670             }
4671             if (this.infobox.hiddenByParent === val) {
4672                 this.infobox.hiddenByParent = !val;
4673                 this.infobox.prepareUpdate().updateVisibility(val).updateRenderer();
4674             }
4675             return this;
4676         },
4677 
4678         // Alias for displayInfobox to be backwards compatible.
4679         // The method showInfobox clashes with the board attribute showInfobox
4680         showInfobox: function (val) {
4681             return this.displayInfobox(val);
4682         },
4683 
4684         /**
4685          * Changes the text of the info box to show the given coordinates.
4686          * @param {Number} x
4687          * @param {Number} y
4688          * @param {JXG.GeometryElement} [el] The element the mouse is pointing at
4689          * @returns {JXG.Board} Reference to the board.
4690          */
4691         highlightInfobox: function (x, y, el) {
4692             this.highlightCustomInfobox('(' + x + ', ' + y + ')', el);
4693             return this;
4694         },
4695 
4696         /**
4697          * Changes the text of the info box to what is provided via text.
4698          * @param {String} text
4699          * @param {JXG.GeometryElement} [el]
4700          * @returns {JXG.Board} Reference to the board.
4701          */
4702         highlightCustomInfobox: function (text, el) {
4703             this.infobox.setText(text);
4704             return this;
4705         },
4706 
4707         /**
4708          * Remove highlighting of all elements.
4709          * @returns {JXG.Board} Reference to the board.
4710          */
4711         dehighlightAll: function () {
4712             var el,
4713                 pEl,
4714                 stillHighlighted = {},
4715                 needsDeHighlight = false;
4716 
4717             for (el in this.highlightedObjects) {
4718                 if (this.highlightedObjects.hasOwnProperty(el)) {
4719 
4720                     pEl = this.highlightedObjects[el];
4721                     if (this.focusObjects.indexOf(el) < 0) { // Element does not have focus
4722                         if (this.hasMouseHandlers || this.hasPointerHandlers) {
4723                             pEl.noHighlight();
4724                         }
4725                         needsDeHighlight = true;
4726                     } else {
4727                         stillHighlighted[el] = pEl;
4728                     }
4729                     // In highlightedObjects should only be objects which fulfill all these conditions
4730                     // And in case of complex elements, like a turtle based fractal, it should be faster to
4731                     // just de-highlight the element instead of checking hasPoint...
4732                     // if ((!Type.exists(pEl.hasPoint)) || !pEl.hasPoint(x, y) || !pEl.visPropCalc.visible)
4733                 }
4734             }
4735 
4736             this.highlightedObjects = stillHighlighted;
4737 
4738             // We do not need to redraw during dehighlighting in CanvasRenderer
4739             // because we are redrawing anyhow
4740             //  -- We do need to redraw during dehighlighting. Otherwise objects won't be dehighlighted until
4741             // another object is highlighted.
4742             if (this.renderer.type === 'canvas' && needsDeHighlight) {
4743                 this.prepareUpdate();
4744                 this.renderer.suspendRedraw(this);
4745                 this.updateRenderer();
4746                 this.renderer.unsuspendRedraw();
4747             }
4748 
4749             return this;
4750         },
4751 
4752         /**
4753          * Returns the input parameters in an array. This method looks pointless and it really is, but it had a purpose
4754          * once.
4755          * @private
4756          * @param {Number} x X coordinate in screen coordinates
4757          * @param {Number} y Y coordinate in screen coordinates
4758          * @returns {Array} Coordinates [x, y] of the mouse in screen coordinates.
4759          * @see JXG.Board#getUsrCoordsOfMouse
4760          */
4761         getScrCoordsOfMouse: function (x, y) {
4762             return [x, y];
4763         },
4764 
4765         /**
4766          * This method calculates the user coords of the current mouse coordinates.
4767          * @param {Event} evt Event object containing the mouse coordinates.
4768          * @returns {Array} Coordinates [x, y] of the mouse in user coordinates.
4769          * @example
4770          * board.on('up', function (evt) {
4771          *         var a = board.getUsrCoordsOfMouse(evt),
4772          *             x = a[0],
4773          *             y = a[1],
4774          *             somePoint = board.create('point', [x,y], {name:'SomePoint',size:4});
4775          *             // Shorter version:
4776          *             //somePoint = board.create('point', a, {name:'SomePoint',size:4});
4777          *         });
4778          *
4779          * </pre><div id='JXG48d5066b-16ba-4920-b8ea-a4f8eff6b746' class='jxgbox' style='width: 300px; height: 300px;'></div>
4780          * <script type='text/javascript'>
4781          *     (function() {
4782          *         var board = JXG.JSXGraph.initBoard('JXG48d5066b-16ba-4920-b8ea-a4f8eff6b746',
4783          *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
4784          *     board.on('up', function (evt) {
4785          *             var a = board.getUsrCoordsOfMouse(evt),
4786          *                 x = a[0],
4787          *                 y = a[1],
4788          *                 somePoint = board.create('point', [x,y], {name:'SomePoint',size:4});
4789          *                 // Shorter version:
4790          *                 //somePoint = board.create('point', a, {name:'SomePoint',size:4});
4791          *             });
4792          *
4793          *     })();
4794          *
4795          * </script><pre>
4796          *
4797          * @see JXG.Board#getScrCoordsOfMouse
4798          * @see JXG.Board#getAllUnderMouse
4799          */
4800         getUsrCoordsOfMouse: function (evt) {
4801             var cPos = this.getCoordsTopLeftCorner(),
4802                 absPos = Env.getPosition(evt, null, this.document),
4803                 x = absPos[0] - cPos[0],
4804                 y = absPos[1] - cPos[1],
4805                 newCoords = new Coords(Const.COORDS_BY_SCREEN, [x, y], this);
4806 
4807             return newCoords.usrCoords.slice(1);
4808         },
4809 
4810         /**
4811          * Collects all elements under current mouse position plus current user coordinates of mouse cursor.
4812          * @param {Event} evt Event object containing the mouse coordinates.
4813          * @returns {Array} Array of elements at the current mouse position plus current user coordinates of mouse.
4814          * @see JXG.Board#getUsrCoordsOfMouse
4815          * @see JXG.Board#getAllObjectsUnderMouse
4816          */
4817         getAllUnderMouse: function (evt) {
4818             var elList = this.getAllObjectsUnderMouse(evt);
4819             elList.push(this.getUsrCoordsOfMouse(evt));
4820 
4821             return elList;
4822         },
4823 
4824         /**
4825          * Collects all elements under current mouse position.
4826          * @param {Event} evt Event object containing the mouse coordinates.
4827          * @returns {Array} Array of elements at the current mouse position.
4828          * @see JXG.Board#getAllUnderMouse
4829          */
4830         getAllObjectsUnderMouse: function (evt) {
4831             var cPos = this.getCoordsTopLeftCorner(),
4832                 absPos = Env.getPosition(evt, null, this.document),
4833                 dx = absPos[0] - cPos[0],
4834                 dy = absPos[1] - cPos[1],
4835                 elList = [],
4836                 el,
4837                 pEl,
4838                 len = this.objectsList.length;
4839 
4840             for (el = 0; el < len; el++) {
4841                 pEl = this.objectsList[el];
4842                 if (pEl.visPropCalc.visible && pEl.hasPoint && pEl.hasPoint(dx, dy)) {
4843                     elList[elList.length] = pEl;
4844                 }
4845             }
4846 
4847             return elList;
4848         },
4849 
4850         /**
4851          * Update the coords object of all elements which possess this
4852          * property. This is necessary after changing the viewport.
4853          * @returns {JXG.Board} Reference to this board.
4854          **/
4855         updateCoords: function () {
4856             var el,
4857                 ob,
4858                 len = this.objectsList.length;
4859 
4860             for (ob = 0; ob < len; ob++) {
4861                 el = this.objectsList[ob];
4862 
4863                 if (Type.exists(el.coords)) {
4864                     if (el.evalVisProp('frozen')) {
4865                         if (el.is3D) {
4866                             el.element2D.coords.screen2usr();
4867                         } else {
4868                             el.coords.screen2usr();
4869                         }
4870                     } else {
4871                         if (el.is3D) {
4872                             el.element2D.coords.usr2screen();
4873                         } else {
4874                             el.coords.usr2screen();
4875                             if (Type.exists(el.actualCoords)) {
4876                                 el.actualCoords.usr2screen();
4877 
4878                             }
4879                         }
4880                     }
4881                 }
4882             }
4883             return this;
4884         },
4885 
4886         /**
4887          * Moves the origin and initializes an update of all elements.
4888          * @param {Number} x
4889          * @param {Number} y
4890          * @param {Boolean} [diff=false]
4891          * @returns {JXG.Board} Reference to this board.
4892          */
4893         moveOrigin: function (x, y, diff) {
4894             var ox, oy, ul, lr;
4895             if (Type.exists(x) && Type.exists(y)) {
4896                 ox = this.origin.scrCoords[1];
4897                 oy = this.origin.scrCoords[2];
4898 
4899                 this.origin.scrCoords[1] = x;
4900                 this.origin.scrCoords[2] = y;
4901 
4902                 if (diff) {
4903                     this.origin.scrCoords[1] -= this.drag_dx;
4904                     this.origin.scrCoords[2] -= this.drag_dy;
4905                 }
4906 
4907                 ul = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this).usrCoords;
4908                 lr = new Coords(
4909                     Const.COORDS_BY_SCREEN,
4910                     [this.canvasWidth, this.canvasHeight],
4911                     this
4912                 ).usrCoords;
4913                 if (
4914                     ul[1] < this.maxboundingbox[0] - Mat.eps ||
4915                     ul[2] > this.maxboundingbox[1] + Mat.eps ||
4916                     lr[1] > this.maxboundingbox[2] + Mat.eps ||
4917                     lr[2] < this.maxboundingbox[3] - Mat.eps
4918                 ) {
4919                     this.origin.scrCoords[1] = ox;
4920                     this.origin.scrCoords[2] = oy;
4921                 }
4922             }
4923 
4924             this.updateCoords().clearTraces().fullUpdate();
4925             this.triggerEventHandlers(['boundingbox']);
4926 
4927             return this;
4928         },
4929 
4930         /**
4931          * Add conditional updates to the elements.
4932          * @param {String} str String containing conditional update in geonext syntax
4933          */
4934         addConditions: function (str) {
4935             var term,
4936                 m,
4937                 left,
4938                 right,
4939                 name,
4940                 el,
4941                 property,
4942                 functions = [],
4943                 // plaintext = 'var el, x, y, c, rgbo;\n',
4944                 i = str.indexOf('<data>'),
4945                 j = str.indexOf('<' + '/data>'),
4946                 xyFun = function (board, el, f, what) {
4947                     return function () {
4948                         var e, t;
4949 
4950                         e = board.select(el.id);
4951                         t = e.coords.usrCoords[what];
4952 
4953                         if (what === 2) {
4954                             e.setPositionDirectly(Const.COORDS_BY_USER, [f(), t]);
4955                         } else {
4956                             e.setPositionDirectly(Const.COORDS_BY_USER, [t, f()]);
4957                         }
4958                         e.prepareUpdate().update();
4959                     };
4960                 },
4961                 visFun = function (board, el, f) {
4962                     return function () {
4963                         var e, v;
4964 
4965                         e = board.select(el.id);
4966                         v = f();
4967 
4968                         e.setAttribute({ visible: v });
4969                     };
4970                 },
4971                 colFun = function (board, el, f, what) {
4972                     return function () {
4973                         var e, v;
4974 
4975                         e = board.select(el.id);
4976                         v = f();
4977 
4978                         if (what === 'strokewidth') {
4979                             e.visProp.strokewidth = v;
4980                         } else {
4981                             v = Color.rgba2rgbo(v);
4982                             e.visProp[what + 'color'] = v[0];
4983                             e.visProp[what + 'opacity'] = v[1];
4984                         }
4985                     };
4986                 },
4987                 posFun = function (board, el, f) {
4988                     return function () {
4989                         var e = board.select(el.id);
4990 
4991                         e.position = f();
4992                     };
4993                 },
4994                 styleFun = function (board, el, f) {
4995                     return function () {
4996                         var e = board.select(el.id);
4997 
4998                         e.setStyle(f());
4999                     };
5000                 };
5001 
5002             if (i < 0) {
5003                 return;
5004             }
5005 
5006             while (i >= 0) {
5007                 term = str.slice(i + 6, j); // throw away <data>
5008                 m = term.indexOf('=');
5009                 left = term.slice(0, m);
5010                 right = term.slice(m + 1);
5011                 m = left.indexOf('.');   // Resulting variable names must not contain dots, e.g. ' Steuern akt.'
5012                 name = left.slice(0, m); //.replace(/\s+$/,''); // do NOT cut out name (with whitespace)
5013                 el = this.elementsByName[Type.unescapeHTML(name)];
5014 
5015                 property = left
5016                     .slice(m + 1)
5017                     .replace(/\s+/g, '')
5018                     .toLowerCase(); // remove whitespace in property
5019                 right = Type.createFunction(right, this, '', true);
5020 
5021                 // Debug
5022                 if (!Type.exists(this.elementsByName[name])) {
5023                     JXG.debug('debug conditions: |' + name + '| undefined');
5024                 } else {
5025                     // plaintext += 'el = this.objects[\'' + el.id + '\'];\n';
5026 
5027                     switch (property) {
5028                         case 'x':
5029                             functions.push(xyFun(this, el, right, 2));
5030                             break;
5031                         case 'y':
5032                             functions.push(xyFun(this, el, right, 1));
5033                             break;
5034                         case 'visible':
5035                             functions.push(visFun(this, el, right));
5036                             break;
5037                         case 'position':
5038                             functions.push(posFun(this, el, right));
5039                             break;
5040                         case 'stroke':
5041                             functions.push(colFun(this, el, right, 'stroke'));
5042                             break;
5043                         case 'style':
5044                             functions.push(styleFun(this, el, right));
5045                             break;
5046                         case 'strokewidth':
5047                             functions.push(colFun(this, el, right, 'strokewidth'));
5048                             break;
5049                         case 'fill':
5050                             functions.push(colFun(this, el, right, 'fill'));
5051                             break;
5052                         case 'label':
5053                             break;
5054                         default:
5055                             JXG.debug(
5056                                 'property "' +
5057                                 property +
5058                                 '" in conditions not yet implemented:' +
5059                                 right
5060                             );
5061                             break;
5062                     }
5063                 }
5064                 str = str.slice(j + 7); // cut off '</data>'
5065                 i = str.indexOf('<data>');
5066                 j = str.indexOf('<' + '/data>');
5067             }
5068 
5069             this.updateConditions = function () {
5070                 var i;
5071 
5072                 for (i = 0; i < functions.length; i++) {
5073                     functions[i]();
5074                 }
5075 
5076                 this.prepareUpdate().updateElements();
5077                 return true;
5078             };
5079             this.updateConditions();
5080         },
5081 
5082         /**
5083          * Computes the commands in the conditions-section of the gxt file.
5084          * It is evaluated after an update, before the unsuspendRedraw.
5085          * The function is generated in
5086          * @see JXG.Board#addConditions
5087          * @private
5088          */
5089         updateConditions: function () {
5090             return false;
5091         },
5092 
5093         /**
5094          * Calculates adequate snap sizes.
5095          * @returns {JXG.Board} Reference to the board.
5096          */
5097         calculateSnapSizes: function () {
5098             var p1, p2,
5099                 bbox = this.getBoundingBox(),
5100                 gridStep = Type.evaluate(this.options.grid.majorStep),
5101                 gridX = Type.evaluate(this.options.grid.gridX),
5102                 gridY = Type.evaluate(this.options.grid.gridY),
5103                 x, y;
5104 
5105             if (!Type.isArray(gridStep)) {
5106                 gridStep = [gridStep, gridStep];
5107             }
5108             if (gridStep.length < 2) {
5109                 gridStep = [gridStep[0], gridStep[0]];
5110             }
5111             if (Type.exists(gridX)) {
5112                 gridStep[0] = gridX;
5113             }
5114             if (Type.exists(gridY)) {
5115                 gridStep[1] = gridY;
5116             }
5117 
5118             if (gridStep[0] === 'auto') {
5119                 gridStep[0] = 1;
5120             } else {
5121                 gridStep[0] = Type.parseNumber(gridStep[0], Math.abs(bbox[1] - bbox[3]), 1 / this.unitX);
5122             }
5123             if (gridStep[1] === 'auto') {
5124                 gridStep[1] = 1;
5125             } else {
5126                 gridStep[1] = Type.parseNumber(gridStep[1], Math.abs(bbox[0] - bbox[2]), 1 / this.unitY);
5127             }
5128 
5129             p1 = new Coords(Const.COORDS_BY_USER, [0, 0], this);
5130             p2 = new Coords(
5131                 Const.COORDS_BY_USER,
5132                 [gridStep[0], gridStep[1]],
5133                 this
5134             );
5135             x = p1.scrCoords[1] - p2.scrCoords[1];
5136             y = p1.scrCoords[2] - p2.scrCoords[2];
5137 
5138             this.options.grid.snapSizeX = gridStep[0];
5139             while (Math.abs(x) > 25) {
5140                 this.options.grid.snapSizeX *= 2;
5141                 x /= 2;
5142             }
5143 
5144             this.options.grid.snapSizeY = gridStep[1];
5145             while (Math.abs(y) > 25) {
5146                 this.options.grid.snapSizeY *= 2;
5147                 y /= 2;
5148             }
5149 
5150             return this;
5151         },
5152 
5153         /**
5154          * Apply update on all objects with the new zoom-factors. Clears all traces.
5155          * @returns {JXG.Board} Reference to the board.
5156          */
5157         applyZoom: function () {
5158             this.updateCoords().calculateSnapSizes().clearTraces().fullUpdate();
5159 
5160             return this;
5161         },
5162 
5163         /**
5164          * Zooms into the board by the factors board.attr.zoom.factorX and board.attr.zoom.factorY and applies the zoom.
5165          * The zoom operation is centered at x, y.
5166          * @param {Number} [x]
5167          * @param {Number} [y]
5168          * @returns {JXG.Board} Reference to the board
5169          */
5170         zoomIn: function (x, y) {
5171             var bb = this.getBoundingBox(),
5172                 zX = this.attr.zoom.factorx,
5173                 zY = this.attr.zoom.factory,
5174                 dX = (bb[2] - bb[0]) * (1.0 - 1.0 / zX),
5175                 dY = (bb[1] - bb[3]) * (1.0 - 1.0 / zY),
5176                 lr = 0.5,
5177                 tr = 0.5,
5178                 mi = this.attr.zoom.eps || this.attr.zoom.min || 0.001; // this.attr.zoom.eps is deprecated
5179 
5180             if (
5181                 (this.zoomX > this.attr.zoom.max && zX > 1.0) ||
5182                 (this.zoomY > this.attr.zoom.max && zY > 1.0) ||
5183                 (this.zoomX < mi && zX < 1.0) || // zoomIn is used for all zooms on touch devices
5184                 (this.zoomY < mi && zY < 1.0)
5185             ) {
5186                 return this;
5187             }
5188 
5189             if (Type.isNumber(x) && Type.isNumber(y)) {
5190                 lr = (x - bb[0]) / (bb[2] - bb[0]);
5191                 tr = (bb[1] - y) / (bb[1] - bb[3]);
5192             }
5193 
5194             this.setBoundingBox(
5195                 [
5196                     bb[0] + dX * lr,
5197                     bb[1] - dY * tr,
5198                     bb[2] - dX * (1 - lr),
5199                     bb[3] + dY * (1 - tr)
5200                 ],
5201                 this.keepaspectratio,
5202                 'update'
5203             );
5204             return this.applyZoom();
5205         },
5206 
5207         /**
5208          * Zooms out of the board by the factors board.attr.zoom.factorX and board.attr.zoom.factorY and applies the zoom.
5209          * The zoom operation is centered at x, y.
5210          *
5211          * @param {Number} [x]
5212          * @param {Number} [y]
5213          * @returns {JXG.Board} Reference to the board
5214          */
5215         zoomOut: function (x, y) {
5216             var bb = this.getBoundingBox(),
5217                 zX = this.attr.zoom.factorx,
5218                 zY = this.attr.zoom.factory,
5219                 dX = (bb[2] - bb[0]) * (1.0 - zX),
5220                 dY = (bb[1] - bb[3]) * (1.0 - zY),
5221                 lr = 0.5,
5222                 tr = 0.5,
5223                 mi = this.attr.zoom.eps || this.attr.zoom.min || 0.001; // this.attr.zoom.eps is deprecated
5224 
5225             if (this.zoomX < mi || this.zoomY < mi) {
5226                 return this;
5227             }
5228 
5229             if (Type.isNumber(x) && Type.isNumber(y)) {
5230                 lr = (x - bb[0]) / (bb[2] - bb[0]);
5231                 tr = (bb[1] - y) / (bb[1] - bb[3]);
5232             }
5233 
5234             this.setBoundingBox(
5235                 [
5236                     bb[0] + dX * lr,
5237                     bb[1] - dY * tr,
5238                     bb[2] - dX * (1 - lr),
5239                     bb[3] + dY * (1 - tr)
5240                 ],
5241                 this.keepaspectratio,
5242                 'update'
5243             );
5244 
5245             return this.applyZoom();
5246         },
5247 
5248         /**
5249          * Reset the zoom level to the original zoom level from initBoard();
5250          * Additionally, if the board as been initialized with a boundingBox (which is the default),
5251          * restore the viewport to the original viewport during initialization. Otherwise,
5252          * (i.e. if the board as been initialized with unitX/Y and originX/Y),
5253          * just set the zoom level to 100%.
5254          *
5255          * @returns {JXG.Board} Reference to the board
5256          */
5257         zoom100: function () {
5258             var bb, dX, dY;
5259 
5260             if (Type.exists(this.attr.boundingbox)) {
5261                 this.setBoundingBox(this.attr.boundingbox, this.keepaspectratio, 'reset');
5262             } else {
5263                 // Board has been set up with unitX/Y and originX/Y
5264                 bb = this.getBoundingBox();
5265                 dX = (bb[2] - bb[0]) * (1.0 - this.zoomX) * 0.5;
5266                 dY = (bb[1] - bb[3]) * (1.0 - this.zoomY) * 0.5;
5267                 this.setBoundingBox(
5268                     [bb[0] + dX, bb[1] - dY, bb[2] - dX, bb[3] + dY],
5269                     this.keepaspectratio,
5270                     'reset'
5271                 );
5272             }
5273             return this.applyZoom();
5274         },
5275 
5276         /**
5277          * Zooms the board so every visible point is shown. Keeps aspect ratio.
5278          * @returns {JXG.Board} Reference to the board
5279          */
5280         zoomAllPoints: function () {
5281             var el,
5282                 border,
5283                 borderX,
5284                 borderY,
5285                 pEl,
5286                 minX = 0,
5287                 maxX = 0,
5288                 minY = 0,
5289                 maxY = 0,
5290                 len = this.objectsList.length;
5291 
5292             for (el = 0; el < len; el++) {
5293                 pEl = this.objectsList[el];
5294 
5295                 if (Type.isPoint(pEl) && pEl.visPropCalc.visible) {
5296                     if (pEl.coords.usrCoords[1] < minX) {
5297                         minX = pEl.coords.usrCoords[1];
5298                     } else if (pEl.coords.usrCoords[1] > maxX) {
5299                         maxX = pEl.coords.usrCoords[1];
5300                     }
5301                     if (pEl.coords.usrCoords[2] > maxY) {
5302                         maxY = pEl.coords.usrCoords[2];
5303                     } else if (pEl.coords.usrCoords[2] < minY) {
5304                         minY = pEl.coords.usrCoords[2];
5305                     }
5306                 }
5307             }
5308 
5309             border = 50;
5310             borderX = border / this.unitX;
5311             borderY = border / this.unitY;
5312 
5313             this.setBoundingBox(
5314                 [minX - borderX, maxY + borderY, maxX + borderX, minY - borderY],
5315                 this.keepaspectratio,
5316                 'update'
5317             );
5318 
5319             return this.applyZoom();
5320         },
5321 
5322         /**
5323          * Reset the bounding box and the zoom level to 100% such that a given set of elements is
5324          * within the board's viewport.
5325          * @param {Array} elements A set of elements given by id, reference, or name.
5326          * @returns {JXG.Board} Reference to the board.
5327          */
5328         zoomElements: function (elements) {
5329             var i, e,
5330                 box,
5331                 newBBox = [Infinity, -Infinity, -Infinity, Infinity],
5332                 cx, cy,
5333                 dx, dy,
5334                 d;
5335 
5336             if (!Type.isArray(elements) || elements.length === 0) {
5337                 return this;
5338             }
5339 
5340             for (i = 0; i < elements.length; i++) {
5341                 e = this.select(elements[i]);
5342 
5343                 box = e.bounds();
5344                 if (Type.isArray(box)) {
5345                     if (box[0] < newBBox[0]) {
5346                         newBBox[0] = box[0];
5347                     }
5348                     if (box[1] > newBBox[1]) {
5349                         newBBox[1] = box[1];
5350                     }
5351                     if (box[2] > newBBox[2]) {
5352                         newBBox[2] = box[2];
5353                     }
5354                     if (box[3] < newBBox[3]) {
5355                         newBBox[3] = box[3];
5356                     }
5357                 }
5358             }
5359 
5360             if (Type.isArray(newBBox)) {
5361                 cx = 0.5 * (newBBox[0] + newBBox[2]);
5362                 cy = 0.5 * (newBBox[1] + newBBox[3]);
5363                 dx = 1.5 * (newBBox[2] - newBBox[0]) * 0.5;
5364                 dy = 1.5 * (newBBox[1] - newBBox[3]) * 0.5;
5365                 d = Math.max(dx, dy);
5366                 this.setBoundingBox(
5367                     [cx - d, cy + d, cx + d, cy - d],
5368                     this.keepaspectratio,
5369                     'update'
5370                 );
5371             }
5372 
5373             return this;
5374         },
5375 
5376         /**
5377          * Sets the zoom level to <tt>fX</tt> resp <tt>fY</tt>.
5378          * @param {Number} fX
5379          * @param {Number} fY
5380          * @returns {JXG.Board} Reference to the board.
5381          */
5382         setZoom: function (fX, fY) {
5383             var oX = this.attr.zoom.factorx,
5384                 oY = this.attr.zoom.factory;
5385 
5386             this.attr.zoom.factorx = fX / this.zoomX;
5387             this.attr.zoom.factory = fY / this.zoomY;
5388 
5389             this.zoomIn();
5390 
5391             this.attr.zoom.factorx = oX;
5392             this.attr.zoom.factory = oY;
5393 
5394             return this;
5395         },
5396 
5397         /**
5398          * Inner, recursive method of removeObject.
5399          *
5400          * @param {JXG.GeometryElement|Array} object The object to remove or array of objects to be removed.
5401          * The element(s) is/are given by name, id or a reference.
5402          * @param {Boolean} [saveMethod=false] If saveMethod=true, the algorithm runs through all elements
5403          * and tests if the element to be deleted is a child element. If this is the case, it will be
5404          * removed from the list of child elements. If saveMethod=false (default), the element
5405          * is removed from the lists of child elements of all its ancestors.
5406          * The latter should be much faster.
5407          * @returns {JXG.Board} Reference to the board
5408          * @private
5409          */
5410         _removeObj: function (object, saveMethod) {
5411             var el, i;
5412 
5413             if (Type.isArray(object)) {
5414                 for (i = 0; i < object.length; i++) {
5415                     this._removeObj(object[i], saveMethod);
5416                 }
5417 
5418                 return this;
5419             }
5420 
5421             object = this.select(object);
5422 
5423             // If the object which is about to be removed is unknown or a string, do nothing.
5424             // it is a string if a string was given and could not be resolved to an element.
5425             if (!Type.exists(object) || Type.isString(object)) {
5426                 return this;
5427             }
5428 
5429             try {
5430                 // remove all children.
5431                 for (el in object.childElements) {
5432                     if (object.childElements.hasOwnProperty(el)) {
5433                         object.childElements[el].board._removeObj(object.childElements[el]);
5434                     }
5435                 }
5436 
5437                 // Remove all children in elements like turtle
5438                 for (el in object.objects) {
5439                     if (object.objects.hasOwnProperty(el)) {
5440                         object.objects[el].board._removeObj(object.objects[el]);
5441                     }
5442                 }
5443 
5444                 // Remove the element from the childElement list and the descendant list of all elements.
5445                 if (saveMethod) {
5446                     // Running through all objects has quadratic complexity if many objects are deleted.
5447                     for (el in this.objects) {
5448                         if (this.objects.hasOwnProperty(el)) {
5449                             if (
5450                                 Type.exists(this.objects[el].childElements) &&
5451                                 Type.exists(
5452                                     this.objects[el].childElements.hasOwnProperty(object.id)
5453                                 )
5454                             ) {
5455                                 delete this.objects[el].childElements[object.id];
5456                                 delete this.objects[el].descendants[object.id];
5457                             }
5458                         }
5459                     }
5460                 } else if (Type.exists(object.ancestors)) {
5461                     // Running through the ancestors should be much more efficient.
5462                     for (el in object.ancestors) {
5463                         if (object.ancestors.hasOwnProperty(el)) {
5464                             if (
5465                                 Type.exists(object.ancestors[el].childElements) &&
5466                                 Type.exists(
5467                                     object.ancestors[el].childElements.hasOwnProperty(object.id)
5468                                 )
5469                             ) {
5470                                 delete object.ancestors[el].childElements[object.id];
5471                                 delete object.ancestors[el].descendants[object.id];
5472                             }
5473                         }
5474                     }
5475                 }
5476 
5477                 // remove the object itself from our control structures
5478                 if (object._pos > -1) {
5479                     this.objectsList.splice(object._pos, 1);
5480                     for (i = object._pos; i < this.objectsList.length; i++) {
5481                         this.objectsList[i]._pos--;
5482                     }
5483                 } else if (object.type !== Const.OBJECT_TYPE_TURTLE) {
5484                     JXG.debug(
5485                         'Board.removeObject: object ' + object.id + ' not found in list.'
5486                     );
5487                 }
5488 
5489                 delete this.objects[object.id];
5490                 delete this.elementsByName[object.name];
5491 
5492                 if (object.visProp && object.evalVisProp('trace')) {
5493                     object.clearTrace();
5494                 }
5495 
5496                 // the object deletion itself is handled by the object.
5497                 if (Type.exists(object.remove)) {
5498                     object.remove();
5499                 }
5500             } catch (e) {
5501                 JXG.debug(object.id + ': Could not be removed: ' + e);
5502             }
5503 
5504             return this;
5505         },
5506 
5507         /**
5508          * Removes object from board and renderer.
5509          * <p>
5510          * <b>Performance hints:</b> It is recommended to use the object's id.
5511          * If many elements are removed, it is best to call <tt>board.suspendUpdate()</tt>
5512          * before looping through the elements to be removed and call
5513          * <tt>board.unsuspendUpdate()</tt> after the loop. Further, it is advisable to loop
5514          * in reverse order, i.e. remove the object in reverse order of their creation time.
5515          * @param {JXG.GeometryElement|Array} object The object to remove or array of objects to be removed.
5516          * The element(s) is/are given by name, id or a reference.
5517          * @param {Boolean} saveMethod If true, the algorithm runs through all elements
5518          * and tests if the element to be deleted is a child element. If yes, it will be
5519          * removed from the list of child elements. If false (default), the element
5520          * is removed from the lists of child elements of all its ancestors.
5521          * This should be much faster.
5522          * @returns {JXG.Board} Reference to the board
5523          */
5524         removeObject: function (object, saveMethod) {
5525             var i;
5526 
5527             this.renderer.suspendRedraw(this);
5528             if (Type.isArray(object)) {
5529                 for (i = 0; i < object.length; i++) {
5530                     this._removeObj(object[i], saveMethod);
5531                 }
5532             } else {
5533                 this._removeObj(object, saveMethod);
5534             }
5535             this.renderer.unsuspendRedraw();
5536 
5537             this.update();
5538             return this;
5539         },
5540 
5541         /**
5542          * Removes the ancestors of an object an the object itself from board and renderer.
5543          * @param {JXG.GeometryElement} object The object to remove.
5544          * @returns {JXG.Board} Reference to the board
5545          */
5546         removeAncestors: function (object) {
5547             var anc;
5548 
5549             for (anc in object.ancestors) {
5550                 if (object.ancestors.hasOwnProperty(anc)) {
5551                     this.removeAncestors(object.ancestors[anc]);
5552                 }
5553             }
5554 
5555             this.removeObject(object);
5556 
5557             return this;
5558         },
5559 
5560         /**
5561          * Initialize some objects which are contained in every GEONExT construction by default,
5562          * but are not contained in the gxt files.
5563          * @returns {JXG.Board} Reference to the board
5564          */
5565         initGeonextBoard: function () {
5566             var p1, p2, p3;
5567 
5568             p1 = this.create('point', [0, 0], {
5569                 id: this.id + 'g00e0',
5570                 name: 'Ursprung',
5571                 withLabel: false,
5572                 visible: false,
5573                 fixed: true
5574             });
5575 
5576             p2 = this.create('point', [1, 0], {
5577                 id: this.id + 'gX0e0',
5578                 name: 'Punkt_1_0',
5579                 withLabel: false,
5580                 visible: false,
5581                 fixed: true
5582             });
5583 
5584             p3 = this.create('point', [0, 1], {
5585                 id: this.id + 'gY0e0',
5586                 name: 'Punkt_0_1',
5587                 withLabel: false,
5588                 visible: false,
5589                 fixed: true
5590             });
5591 
5592             this.create('line', [p1, p2], {
5593                 id: this.id + 'gXLe0',
5594                 name: 'X-Achse',
5595                 withLabel: false,
5596                 visible: false
5597             });
5598 
5599             this.create('line', [p1, p3], {
5600                 id: this.id + 'gYLe0',
5601                 name: 'Y-Achse',
5602                 withLabel: false,
5603                 visible: false
5604             });
5605 
5606             return this;
5607         },
5608 
5609         /**
5610          * Change the height and width of the board's container.
5611          * After doing so, {@link JXG.JSXGraph.setBoundingBox} is called using
5612          * the actual size of the bounding box and the actual value of keepaspectratio.
5613          * If setBoundingbox() should not be called automatically,
5614          * call resizeContainer with dontSetBoundingBox == true.
5615          * @param {Number} canvasWidth New width of the container.
5616          * @param {Number} canvasHeight New height of the container.
5617          * @param {Boolean} [dontset=false] If true do not set the CSS width and height of the DOM element.
5618          * @param {Boolean} [dontSetBoundingBox=false] If true do not call setBoundingBox(), but keep view centered around original visible center.
5619          * @returns {JXG.Board} Reference to the board
5620          */
5621         resizeContainer: function (canvasWidth, canvasHeight, dontset, dontSetBoundingBox) {
5622             var box,
5623                 oldWidth, oldHeight,
5624                 oX, oY;
5625 
5626             oldWidth = this.canvasWidth;
5627             oldHeight = this.canvasHeight;
5628 
5629             if (!dontSetBoundingBox) {
5630                 box = this.getBoundingBox();    // This is the actual bounding box.
5631             }
5632 
5633             // this.canvasWidth = Math.max(parseFloat(canvasWidth), Mat.eps);
5634             // this.canvasHeight = Math.max(parseFloat(canvasHeight), Mat.eps);
5635             this.canvasWidth = parseFloat(canvasWidth);
5636             this.canvasHeight = parseFloat(canvasHeight);
5637 
5638             if (!dontset) {
5639                 this.containerObj.style.width = this.canvasWidth + 'px';
5640                 this.containerObj.style.height = this.canvasHeight + 'px';
5641             }
5642             this.renderer.resize(this.canvasWidth, this.canvasHeight);
5643 
5644             if (!dontSetBoundingBox) {
5645                 this.setBoundingBox(box, this.keepaspectratio, 'keep');
5646             } else {
5647                 oX = (this.canvasWidth - oldWidth) * 0.5;
5648                 oY = (this.canvasHeight - oldHeight) * 0.5;
5649 
5650                 this.moveOrigin(
5651                     this.origin.scrCoords[1] + oX,
5652                     this.origin.scrCoords[2] + oY
5653                 );
5654             }
5655 
5656             return this;
5657         },
5658 
5659         /**
5660          * Lists the dependencies graph in a new HTML-window.
5661          * @returns {JXG.Board} Reference to the board
5662          */
5663         showDependencies: function () {
5664             var el, t, c, f, i;
5665 
5666             t = '<p>\n';
5667             for (el in this.objects) {
5668                 if (this.objects.hasOwnProperty(el)) {
5669                     i = 0;
5670                     for (c in this.objects[el].childElements) {
5671                         if (this.objects[el].childElements.hasOwnProperty(c)) {
5672                             i += 1;
5673                         }
5674                     }
5675                     if (i >= 0) {
5676                         t += '<strong>' + this.objects[el].id + ':<' + '/strong> ';
5677                     }
5678 
5679                     for (c in this.objects[el].childElements) {
5680                         if (this.objects[el].childElements.hasOwnProperty(c)) {
5681                             t +=
5682                                 this.objects[el].childElements[c].id +
5683                                 '(' +
5684                                 this.objects[el].childElements[c].name +
5685                                 ')' +
5686                                 ', ';
5687                         }
5688                     }
5689                     t += '<p>\n';
5690                 }
5691             }
5692             t += '<' + '/p>\n';
5693             f = window.open();
5694             f.document.open();
5695             f.document.write(t);
5696             f.document.close();
5697             return this;
5698         },
5699 
5700         /**
5701          * Lists the XML code of the construction in a new HTML-window.
5702          * @returns {JXG.Board} Reference to the board
5703          */
5704         showXML: function () {
5705             var f = window.open('');
5706             f.document.open();
5707             f.document.write('<pre>' + Type.escapeHTML(this.xmlString) + '<' + '/pre>');
5708             f.document.close();
5709             return this;
5710         },
5711 
5712         /**
5713          * Sets for all objects the needsUpdate flag to 'true'.
5714          * @param{JXG.GeometryElement} [drag=undefined] Optional element that is dragged.
5715          * @returns {JXG.Board} Reference to the board
5716          */
5717         prepareUpdate: function (drag) {
5718             var el, i,
5719                 pEl,
5720                 len = this.objectsList.length;
5721 
5722             /*
5723             if (this.attr.updatetype === 'hierarchical') {
5724                 return this;
5725             }
5726             */
5727 
5728             for (el = 0; el < len; el++) {
5729                 pEl = this.objectsList[el];
5730                 if (this._change3DView ||
5731                     (Type.exists(drag) && drag.elType === 'view3d_slider')
5732                 ) {
5733                     // The 3D view has changed. No elements are recomputed,
5734                     // only 3D elements are projected to the new view.
5735                     pEl.needsUpdate =
5736                         pEl.visProp.element3d ||
5737                         pEl.elType === 'view3d' ||
5738                         pEl.elType === 'view3d_slider' ||
5739                         this.needsFullUpdate;
5740 
5741                     // Special case sphere3d in central projection:
5742                     // We have to update the defining points of the ellipse
5743                     if (pEl.visProp.element3d &&
5744                         pEl.visProp.element3d.type === Const.OBJECT_TYPE_SPHERE3D
5745                         ) {
5746                         for (i = 0; i < pEl.parents.length; i++) {
5747                             this.objects[pEl.parents[i]].needsUpdate = true;
5748                         }
5749                     }
5750                 } else {
5751                     pEl.needsUpdate = pEl.needsRegularUpdate || this.needsFullUpdate;
5752                 }
5753             }
5754 
5755             for (el in this.groups) {
5756                 if (this.groups.hasOwnProperty(el)) {
5757                     pEl = this.groups[el];
5758                     pEl.needsUpdate = pEl.needsRegularUpdate || this.needsFullUpdate;
5759                 }
5760             }
5761 
5762             return this;
5763         },
5764 
5765         /**
5766          * Runs through all elements and calls their update() method.
5767          * @param {JXG.GeometryElement} drag Element that caused the update.
5768          * @returns {JXG.Board} Reference to the board
5769          */
5770         updateElements: function (drag) {
5771             var el, pEl;
5772             //var childId, i = 0;
5773 
5774             drag = this.select(drag);
5775 
5776             /*
5777             if (Type.exists(drag)) {
5778                 for (el = 0; el < this.objectsList.length; el++) {
5779                     pEl = this.objectsList[el];
5780                     if (pEl.id === drag.id) {
5781                         i = el;
5782                         break;
5783                     }
5784                 }
5785             }
5786             */
5787             for (el = 0; el < this.objectsList.length; el++) {
5788                 pEl = this.objectsList[el];
5789                 if (this.needsFullUpdate && pEl.elementClass === Const.OBJECT_CLASS_TEXT) {
5790                     pEl.updateSize();
5791                 }
5792 
5793                 // For updates of an element we distinguish if the dragged element is updated or
5794                 // other elements are updated.
5795                 // The difference lies in the treatment of gliders and points based on transformations.
5796                 pEl.update(!Type.exists(drag) || pEl.id !== drag.id).updateVisibility();
5797             }
5798 
5799             // update groups last
5800             for (el in this.groups) {
5801                 if (this.groups.hasOwnProperty(el)) {
5802                     this.groups[el].update(drag);
5803                 }
5804             }
5805 
5806             return this;
5807         },
5808 
5809         /**
5810          * Runs through all elements and calls their update() method.
5811          * @returns {JXG.Board} Reference to the board
5812          */
5813         updateRenderer: function () {
5814             var el,
5815                 len = this.objectsList.length;
5816 
5817             if (!this.renderer) {
5818                 return;
5819             }
5820 
5821             /*
5822             objs = this.objectsList.slice(0);
5823             objs.sort(function (a, b) {
5824                 if (a.visProp.layer < b.visProp.layer) {
5825                     return -1;
5826                 } else if (a.visProp.layer === b.visProp.layer) {
5827                     return b.lastDragTime.getTime() - a.lastDragTime.getTime();
5828                 } else {
5829                     return 1;
5830                 }
5831             });
5832             */
5833 
5834             if (this.renderer.type === 'canvas') {
5835                 this.updateRendererCanvas();
5836             } else {
5837                 for (el = 0; el < len; el++) {
5838                     this.objectsList[el].updateRenderer();
5839                 }
5840             }
5841             return this;
5842         },
5843 
5844         /**
5845          * Runs through all elements and calls their update() method.
5846          * This is a special version for the CanvasRenderer.
5847          * Here, we have to do our own layer handling.
5848          * @returns {JXG.Board} Reference to the board
5849          */
5850         updateRendererCanvas: function () {
5851             var el, pEl,
5852                 olen = this.objectsList.length,
5853                 // i, minim, lay,
5854                 // layers = this.options.layer,
5855                 // len = this.options.layer.numlayers,
5856                 // last = Number.NEGATIVE_INFINITY.toExponential,
5857                 depth_order_layers = [],
5858                 objects_sorted,
5859                 // Sort the elements for the canvas rendering according to
5860                 // their layer, _pos, depthOrder (with this priority)
5861                 // @private
5862                 _compareFn = function(a, b) {
5863                     if (a.visProp.layer !== b.visProp.layer) {
5864                         return a.visProp.layer - b.visProp.layer;
5865                     }
5866 
5867                     // The objects are in the same layer, but the layer is not depth ordered
5868                     if (depth_order_layers.indexOf(a.visProp.layer) === -1) {
5869                         return a._pos - b._pos;
5870                     }
5871 
5872                     // The objects are in the same layer and the layer is depth ordered
5873                     // We have to sort 2D elements according to the zIndices of
5874                     // their 3D parents.
5875                     if (!a.visProp.element3d && !b.visProp.element3d) {
5876                         return a._pos - b._pos;
5877                     }
5878 
5879                     if (a.visProp.element3d && !b.visProp.element3d) {
5880                         return -1;
5881                     }
5882 
5883                     if (b.visProp.element3d && !a.visProp.element3d) {
5884                         return 1;
5885                     }
5886 
5887                     return a.visProp.element3d.zIndex - b.visProp.element3d.zIndex;
5888                 };
5889 
5890             // Only one view3d element is supported. Get the depth orderer layers and
5891             // update the zIndices of the 3D elements.
5892             for (el = 0; el < olen; el++) {
5893                 pEl = this.objectsList[el];
5894                 if (pEl.elType === 'view3d' && pEl.evalVisProp('depthorder.enabled')) {
5895                     depth_order_layers = pEl.evalVisProp('depthorder.layers');
5896                     pEl.updateRenderer();
5897                     break;
5898                 }
5899             }
5900 
5901             objects_sorted = this.objectsList.toSorted(_compareFn);
5902             olen = objects_sorted.length;
5903             for (el = 0; el < olen; el++) {
5904                 objects_sorted[el].prepareUpdate().updateRenderer();
5905             }
5906 
5907             // for (i = 0; i < len; i++) {
5908             //     minim = Number.POSITIVE_INFINITY;
5909 
5910             //     for (lay in layers) {
5911             //         if (layers.hasOwnProperty(lay)) {
5912             //             if (layers[lay] > last && layers[lay] < minim) {
5913             //                 minim = layers[lay];
5914             //             }
5915             //         }
5916             //     }
5917 
5918             //     for (el = 0; el < olen; el++) {
5919             //         pEl = this.objectsList[el];
5920             //         if (pEl.visProp.layer === minim) {
5921             //             pEl.prepareUpdate().updateRenderer();
5922             //         }
5923             //     }
5924             //     last = minim;
5925             // }
5926 
5927             return this;
5928         },
5929 
5930         /**
5931          * Please use {@link JXG.Board.on} instead.
5932          * @param {Function} hook A function to be called by the board after an update occurred.
5933          * @param {String} [m='update'] When the hook is to be called. Possible values are <i>mouseup</i>, <i>mousedown</i> and <i>update</i>.
5934          * @param {Object} [context=board] Determines the execution context the hook is called. This parameter is optional, default is the
5935          * board object the hook is attached to.
5936          * @returns {Number} Id of the hook, required to remove the hook from the board.
5937          * @deprecated
5938          */
5939         addHook: function (hook, m, context) {
5940             JXG.deprecated('Board.addHook()', 'Board.on()');
5941             m = Type.def(m, 'update');
5942 
5943             context = Type.def(context, this);
5944 
5945             this.hooks.push([m, hook]);
5946             this.on(m, hook, context);
5947 
5948             return this.hooks.length - 1;
5949         },
5950 
5951         /**
5952          * Alias of {@link JXG.Board.on}.
5953          */
5954         addEvent: JXG.shortcut(JXG.Board.prototype, 'on'),
5955 
5956         /**
5957          * Please use {@link JXG.Board.off} instead.
5958          * @param {Number|function} id The number you got when you added the hook or a reference to the event handler.
5959          * @returns {JXG.Board} Reference to the board
5960          * @deprecated
5961          */
5962         removeHook: function (id) {
5963             JXG.deprecated('Board.removeHook()', 'Board.off()');
5964             if (this.hooks[id]) {
5965                 this.off(this.hooks[id][0], this.hooks[id][1]);
5966                 this.hooks[id] = null;
5967             }
5968 
5969             return this;
5970         },
5971 
5972         /**
5973          * Alias of {@link JXG.Board.off}.
5974          */
5975         removeEvent: JXG.shortcut(JXG.Board.prototype, 'off'),
5976 
5977         /**
5978          * Runs through all hooked functions and calls them.
5979          * @returns {JXG.Board} Reference to the board
5980          * @deprecated
5981          */
5982         updateHooks: function (m) {
5983             var arg = Array.prototype.slice.call(arguments, 0);
5984 
5985             JXG.deprecated('Board.updateHooks()', 'Board.triggerEventHandlers()');
5986 
5987             arg[0] = Type.def(arg[0], 'update');
5988             this.triggerEventHandlers([arg[0]], arguments);
5989 
5990             return this;
5991         },
5992 
5993         /**
5994          * Adds a dependent board to this board.
5995          * @param {JXG.Board} board A reference to board which will be updated after an update of this board occurred.
5996          * @returns {JXG.Board} Reference to the board
5997          */
5998         addChild: function (board) {
5999             if (Type.exists(board) && Type.exists(board.containerObj)) {
6000                 this.dependentBoards.push(board);
6001                 this.update();
6002             }
6003             return this;
6004         },
6005 
6006         /**
6007          * Deletes a board from the list of dependent boards.
6008          * @param {JXG.Board} board Reference to the board which will be removed.
6009          * @returns {JXG.Board} Reference to the board
6010          */
6011         removeChild: function (board) {
6012             var i;
6013 
6014             for (i = this.dependentBoards.length - 1; i >= 0; i--) {
6015                 if (this.dependentBoards[i] === board) {
6016                     this.dependentBoards.splice(i, 1);
6017                 }
6018             }
6019             return this;
6020         },
6021 
6022         /**
6023          * Runs through most elements and calls their update() method and update the conditions.
6024          * @param {JXG.GeometryElement} [drag] Element that caused the update.
6025          * @returns {JXG.Board} Reference to the board
6026          */
6027         update: function (drag) {
6028             var i, len, b, insert, storeActiveEl;
6029 
6030             if (this.inUpdate || this.isSuspendedUpdate) {
6031                 return this;
6032             }
6033             this.inUpdate = true;
6034 
6035             if (
6036                 this.attr.minimizereflow === 'all' &&
6037                 this.containerObj &&
6038                 this.renderer.type !== 'vml'
6039             ) {
6040                 storeActiveEl = this.document.activeElement; // Store focus element
6041                 insert = this.renderer.removeToInsertLater(this.containerObj);
6042             }
6043 
6044             if (this.attr.minimizereflow === 'svg' && this.renderer.type === 'svg') {
6045                 storeActiveEl = this.document.activeElement;
6046                 insert = this.renderer.removeToInsertLater(this.renderer.svgRoot);
6047             }
6048 
6049             this.prepareUpdate(drag).updateElements(drag).updateConditions();
6050 
6051             this.renderer.suspendRedraw(this);
6052             this.updateRenderer();
6053             this.renderer.unsuspendRedraw();
6054             this.triggerEventHandlers(['update'], []);
6055 
6056             if (insert) {
6057                 insert();
6058                 storeActiveEl.focus(); // Restore focus element
6059             }
6060 
6061             // To resolve dependencies between boards
6062             // for (var board in JXG.boards) {
6063             len = this.dependentBoards.length;
6064             for (i = 0; i < len; i++) {
6065                 b = this.dependentBoards[i];
6066                 if (Type.exists(b) && b !== this) {
6067                     b.updateQuality = this.updateQuality;
6068                     b.prepareUpdate().updateElements().updateConditions();
6069                     b.renderer.suspendRedraw(this);
6070                     b.updateRenderer();
6071                     b.renderer.unsuspendRedraw();
6072                     b.triggerEventHandlers(['update'], []);
6073                 }
6074             }
6075 
6076             this.inUpdate = false;
6077             return this;
6078         },
6079 
6080         /**
6081          * Runs through all elements and calls their update() method and update the conditions.
6082          * This is necessary after zooming and changing the bounding box.
6083          * @returns {JXG.Board} Reference to the board
6084          */
6085         fullUpdate: function () {
6086             this.needsFullUpdate = true;
6087             this.update();
6088             this.needsFullUpdate = false;
6089             return this;
6090         },
6091 
6092         /**
6093          * Adds a grid to the board according to the settings given in board.options.
6094          * @returns {JXG.Board} Reference to the board.
6095          */
6096         addGrid: function () {
6097             this.create('grid', []);
6098 
6099             return this;
6100         },
6101 
6102         /**
6103          * Removes all grids assigned to this board. Warning: This method also removes all objects depending on one or
6104          * more of the grids.
6105          * @returns {JXG.Board} Reference to the board object.
6106          */
6107         removeGrids: function () {
6108             var i;
6109 
6110             for (i = 0; i < this.grids.length; i++) {
6111                 this.removeObject(this.grids[i]);
6112             }
6113 
6114             this.grids.length = 0;
6115             this.update(); // required for canvas renderer
6116 
6117             return this;
6118         },
6119 
6120         /**
6121          * Creates a new geometric element of type elementType.
6122          * @param {String} elementType Type of the element to be constructed given as a string e.g. 'point' or 'circle'.
6123          * @param {Array} parents Array of parent elements needed to construct the element e.g. coordinates for a point or two
6124          * points to construct a line. This highly depends on the elementType that is constructed. See the corresponding JXG.create*
6125          * methods for a list of possible parameters.
6126          * @param {Object} [attributes] An object containing the attributes to be set. This also depends on the elementType.
6127          * Common attributes are name, visible, strokeColor.
6128          * @returns {Object} Reference to the created element. This is usually a GeometryElement, but can be an array containing
6129          * two or more elements.
6130          */
6131         create: function (elementType, parents, attributes) {
6132             var el, i;
6133 
6134             elementType = elementType.toLowerCase();
6135 
6136             if (!Type.exists(parents)) {
6137                 parents = [];
6138             }
6139 
6140             if (!Type.exists(attributes)) {
6141                 attributes = {};
6142             }
6143 
6144             for (i = 0; i < parents.length; i++) {
6145                 if (
6146                     Type.isString(parents[i]) &&
6147                     !(elementType === 'text' && i === 2) &&
6148                     !(elementType === 'solidofrevolution3d' && i === 2) &&
6149                     !(elementType === 'text3d' && (i === 2 || i === 4)) &&
6150                     !(
6151                         (elementType === 'input' ||
6152                             elementType === 'checkbox' ||
6153                             elementType === 'button') &&
6154                         (i === 2 || i === 3)
6155                     ) &&
6156                     !(elementType === 'curve' /*&& i > 0*/) && // Allow curve plots with jessiecode, parents[0] is the
6157                                                                // variable name
6158                     !(elementType === 'functiongraph') && // Prevent problems with function terms like 'x', 'y'
6159                     !(elementType === 'implicitcurve')
6160                 ) {
6161                     if (i > 0 && parents[0].elType === 'view3d') {
6162                         // 3D elements are based on 3D elements, only
6163                         parents[i] = parents[0].select(parents[i]);
6164                     } else {
6165                         parents[i] = this.select(parents[i]);
6166                     }
6167                 }
6168             }
6169 
6170             if (Type.isFunction(JXG.elements[elementType])) {
6171                 el = JXG.elements[elementType](this, parents, attributes);
6172             } else {
6173                 throw new Error('JSXGraph: create: Unknown element type given: ' + elementType);
6174             }
6175 
6176             if (!Type.exists(el)) {
6177                 JXG.debug('JSXGraph: create: failure creating ' + elementType);
6178                 return el;
6179             }
6180 
6181             if (el.prepareUpdate && el.update && el.updateRenderer) {
6182                 el.fullUpdate();
6183             }
6184             return el;
6185         },
6186 
6187         /**
6188          * Deprecated name for {@link JXG.Board.create}.
6189          * @deprecated
6190          */
6191         createElement: function () {
6192             JXG.deprecated('Board.createElement()', 'Board.create()');
6193             return this.create.apply(this, arguments);
6194         },
6195 
6196         /**
6197          * Delete the elements drawn as part of a trace of an element.
6198          * @returns {JXG.Board} Reference to the board
6199          */
6200         clearTraces: function () {
6201             var el;
6202 
6203             for (el = 0; el < this.objectsList.length; el++) {
6204                 this.objectsList[el].clearTrace();
6205             }
6206 
6207             this.numTraces = 0;
6208             return this;
6209         },
6210 
6211         /**
6212          * Stop updates of the board.
6213          * @returns {JXG.Board} Reference to the board
6214          */
6215         suspendUpdate: function () {
6216             if (!this.inUpdate) {
6217                 this.isSuspendedUpdate = true;
6218             }
6219             return this;
6220         },
6221 
6222         /**
6223          * Enable updates of the board.
6224          * @returns {JXG.Board} Reference to the board
6225          */
6226         unsuspendUpdate: function () {
6227             if (this.isSuspendedUpdate) {
6228                 this.isSuspendedUpdate = false;
6229                 this.fullUpdate();
6230             }
6231             return this;
6232         },
6233 
6234         /**
6235          * Set the bounding box of the board.
6236          * @param {Array} bbox New bounding box [x1,y1,x2,y2]
6237          * @param {Boolean} [keepaspectratio=false] If set to true, the aspect ratio will be 1:1, but
6238          * the resulting viewport may be larger.
6239          * @param {String} [setZoom='reset'] Reset, keep or update the zoom level of the board. 'reset'
6240          * sets {@link JXG.Board#zoomX} and {@link JXG.Board#zoomY} to the start values (or 1.0).
6241          * 'update' adapts these values accoring to the new bounding box and 'keep' does nothing.
6242          * @returns {JXG.Board} Reference to the board
6243          */
6244         setBoundingBox: function (bbox, keepaspectratio, setZoom) {
6245             var h, w, ux, uy,
6246                 offX = 0,
6247                 offY = 0,
6248                 zoom_ratio = 1,
6249                 ratio, dx, dy, prev_w, prev_h,
6250                 dim = Env.getDimensions(this.containerObj, this.document);
6251 
6252             if (!Type.isArray(bbox)) {
6253                 return this;
6254             }
6255 
6256             if (
6257                 bbox[0] < this.maxboundingbox[0] - Mat.eps ||
6258                 bbox[1] > this.maxboundingbox[1] + Mat.eps ||
6259                 bbox[2] > this.maxboundingbox[2] + Mat.eps ||
6260                 bbox[3] < this.maxboundingbox[3] - Mat.eps
6261             ) {
6262                 return this;
6263             }
6264 
6265             if (!Type.exists(setZoom)) {
6266                 setZoom = 'reset';
6267             }
6268 
6269             ux = this.unitX;
6270             uy = this.unitY;
6271             this.canvasWidth = parseFloat(dim.width);   // parseInt(dim.width, 10);
6272             this.canvasHeight = parseFloat(dim.height); // parseInt(dim.height, 10);
6273             w = this.canvasWidth;
6274             h = this.canvasHeight;
6275             if (keepaspectratio) {
6276                 if (this.keepaspectratio) {
6277                     ratio = ux / uy;        // Keep this ratio if keepaspectratio was true
6278                     if (isNaN(ratio)) {
6279                         ratio = 1.0;
6280                     }
6281                 } else {
6282                     ratio = 1.0;
6283                 }
6284                 if (setZoom === 'keep') {
6285                     zoom_ratio = this.zoomX / this.zoomY;
6286                 }
6287                 dx = bbox[2] - bbox[0];
6288                 dy = bbox[1] - bbox[3];
6289                 prev_w = ux * dx;
6290                 prev_h = uy * dy;
6291                 if (w >= h) {
6292                     if (prev_w >= prev_h) {
6293                         this.unitY = h / dy;
6294                         this.unitX = this.unitY * ratio;
6295                     } else {
6296                         // Switch dominating interval
6297                         this.unitY = h / Math.abs(dx) * Mat.sign(dy) / zoom_ratio;
6298                         this.unitX = this.unitY * ratio;
6299                     }
6300                 } else {
6301                     if (prev_h > prev_w) {
6302                         this.unitX = w / dx;
6303                         this.unitY = this.unitX / ratio;
6304                     } else {
6305                         // Switch dominating interval
6306                         this.unitX = w / Math.abs(dy) * Mat.sign(dx) * zoom_ratio;
6307                         this.unitY = this.unitX / ratio;
6308                     }
6309                 }
6310                 // Add the additional units in equal portions left and right
6311                 offX = (w / this.unitX - dx) * 0.5;
6312                 // Add the additional units in equal portions above and below
6313                 offY = (h / this.unitY - dy) * 0.5;
6314                 this.keepaspectratio = true;
6315             } else {
6316                 this.unitX = w / (bbox[2] - bbox[0]);
6317                 this.unitY = h / (bbox[1] - bbox[3]);
6318                 this.keepaspectratio = false;
6319             }
6320 
6321             this.moveOrigin(-this.unitX * (bbox[0] - offX), this.unitY * (bbox[1] + offY));
6322 
6323             if (setZoom === 'update') {
6324                 this.zoomX *= this.unitX / ux;
6325                 this.zoomY *= this.unitY / uy;
6326             } else if (setZoom === 'reset') {
6327                 this.zoomX = Type.exists(this.attr.zoomx) ? this.attr.zoomx : 1.0;
6328                 this.zoomY = Type.exists(this.attr.zoomy) ? this.attr.zoomy : 1.0;
6329             }
6330 
6331             return this;
6332         },
6333 
6334         /**
6335          * Get the bounding box of the board.
6336          * @returns {Array} bounding box [x1,y1,x2,y2] upper left corner, lower right corner
6337          */
6338         getBoundingBox: function () {
6339             var ul = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this).usrCoords,
6340                 lr = new Coords(
6341                     Const.COORDS_BY_SCREEN,
6342                     [this.canvasWidth, this.canvasHeight],
6343                     this
6344                 ).usrCoords;
6345             return [ul[1], ul[2], lr[1], lr[2]];
6346         },
6347 
6348         /**
6349          * Sets the value of attribute <tt>key</tt> to <tt>value</tt>.
6350          * @param {String} key The attribute's name.
6351          * @param value The new value
6352          * @private
6353          */
6354         _set: function (key, value) {
6355             key = key.toLocaleLowerCase();
6356 
6357             if (
6358                 value !== null &&
6359                 Type.isObject(value) &&
6360                 !Type.exists(value.id) &&
6361                 !Type.exists(value.name)
6362             ) {
6363                 // value is of type {prop: val, prop: val,...}
6364                 // Convert these attributes to lowercase, too
6365                 // this.attr[key] = {};
6366                 // for (el in value) {
6367                 //     if (value.hasOwnProperty(el)) {
6368                 //         this.attr[key][el.toLocaleLowerCase()] = value[el];
6369                 //     }
6370                 // }
6371                 Type.mergeAttr(this.attr[key], value);
6372             } else {
6373                 this.attr[key] = value;
6374             }
6375         },
6376 
6377         /**
6378          * Sets an arbitrary number of attributes. This method has one or more
6379          * parameters of the following types:
6380          * <ul>
6381          * <li> object: {key1:value1,key2:value2,...}
6382          * <li> string: 'key:value'
6383          * <li> array: ['key', value]
6384          * </ul>
6385          * Some board attributes are immutable, like e.g. the renderer type.
6386          *
6387          * @param {Object} attributes An object with attributes.
6388          * @returns {JXG.Board} Reference to the board
6389          *
6390          * @example
6391          * const board = JXG.JSXGraph.initBoard('jxgbox', {
6392          *     boundingbox: [-5, 5, 5, -5],
6393          *     keepAspectRatio: false,
6394          *     axis:true,
6395          *     showFullscreen: true,
6396          *     showScreenshot: true,
6397          *     showCopyright: false
6398          * });
6399          *
6400          * board.setAttribute({
6401          *     animationDelay: 10,
6402          *     boundingbox: [-10, 5, 10, -5],
6403          *     defaultAxes: {
6404          *         x: { strokeColor: 'blue', ticks: { strokeColor: 'blue'}}
6405          *     },
6406          *     description: 'test',
6407          *     fullscreen: {
6408          *         scale: 0.5
6409          *     },
6410          *     intl: {
6411          *         enabled: true,
6412          *         locale: 'de-DE'
6413          *     }
6414          * });
6415          *
6416          * board.setAttribute({
6417          *     selection: {
6418          *         enabled: true,
6419          *         fillColor: 'blue'
6420          *     },
6421          *     showInfobox: false,
6422          *     zoomX: 0.5,
6423          *     zoomY: 2,
6424          *     fullscreen: { symbol: 'x' },
6425          *     screenshot: { symbol: 'y' },
6426          *     showCopyright: true,
6427          *     showFullscreen: false,
6428          *     showScreenshot: false,
6429          *     showZoom: false,
6430          *     showNavigation: false
6431          * });
6432          * board.setAttribute('showCopyright:false');
6433          *
6434          * var p = board.create('point', [1, 1], {size: 10,
6435          *     label: {
6436          *         fontSize: 24,
6437          *         highlightStrokeOpacity: 0.1,
6438          *         offset: [5, 0]
6439          *     }
6440          * });
6441          *
6442          *
6443          * </pre><div id="JXGea7b8e09-beac-4d95-9a0c-5fc1c761ffbc" class="jxgbox" style="width: 300px; height: 300px;"></div>
6444          * <script type="text/javascript">
6445          *     (function() {
6446          *     const board = JXG.JSXGraph.initBoard('JXGea7b8e09-beac-4d95-9a0c-5fc1c761ffbc', {
6447          *         boundingbox: [-5, 5, 5, -5],
6448          *         keepAspectRatio: false,
6449          *         axis:true,
6450          *         showFullscreen: true,
6451          *         showScreenshot: true,
6452          *         showCopyright: false
6453          *     });
6454          *
6455          *     board.setAttribute({
6456          *         animationDelay: 10,
6457          *         boundingbox: [-10, 5, 10, -5],
6458          *         defaultAxes: {
6459          *             x: { strokeColor: 'blue', ticks: { strokeColor: 'blue'}}
6460          *         },
6461          *         description: 'test',
6462          *         fullscreen: {
6463          *             scale: 0.5
6464          *         },
6465          *         intl: {
6466          *             enabled: true,
6467          *             locale: 'de-DE'
6468          *         }
6469          *     });
6470          *
6471          *     board.setAttribute({
6472          *         selection: {
6473          *             enabled: true,
6474          *             fillColor: 'blue'
6475          *         },
6476          *         showInfobox: false,
6477          *         zoomX: 0.5,
6478          *         zoomY: 2,
6479          *         fullscreen: { symbol: 'x' },
6480          *         screenshot: { symbol: 'y' },
6481          *         showCopyright: true,
6482          *         showFullscreen: false,
6483          *         showScreenshot: false,
6484          *         showZoom: false,
6485          *         showNavigation: false
6486          *     });
6487          *
6488          *     board.setAttribute('showCopyright:false');
6489          *
6490          *     var p = board.create('point', [1, 1], {size: 10,
6491          *         label: {
6492          *             fontSize: 24,
6493          *             highlightStrokeOpacity: 0.1,
6494          *             offset: [5, 0]
6495          *         }
6496          *     });
6497          *
6498          *
6499          *     })();
6500          *
6501          * </script><pre>
6502          *
6503          *
6504          */
6505         setAttribute: function (attr) {
6506             var i, arg, pair,
6507                 key, value, oldvalue,// j, le,
6508                 node,
6509                 attributes = {};
6510 
6511             // Normalize the user input
6512             for (i = 0; i < arguments.length; i++) {
6513                 arg = arguments[i];
6514                 if (Type.isString(arg)) {
6515                     // pairRaw is string of the form 'key:value'
6516                     pair = arg.split(":");
6517                     attributes[Type.trim(pair[0])] = Type.trim(pair[1]);
6518                 } else if (!Type.isArray(arg)) {
6519                     // pairRaw consists of objects of the form {key1:value1,key2:value2,...}
6520                     JXG.extend(attributes, arg);
6521                 } else {
6522                     // pairRaw consists of array [key,value]
6523                     attributes[arg[0]] = arg[1];
6524                 }
6525             }
6526 
6527             for (i in attributes) {
6528                 if (attributes.hasOwnProperty(i)) {
6529                     key = i.replace(/\s+/g, "").toLowerCase();
6530                     value = attributes[i];
6531                 }
6532                 value = (value.toLowerCase && value.toLowerCase() === 'false')
6533                     ? false
6534                     : value;
6535 
6536                 oldvalue = this.attr[key];
6537                 if (oldvalue === value) {
6538                     continue;
6539                 }
6540                 switch (key) {
6541                     case 'axis':
6542                         if (value === false) {
6543                             if (Type.exists(this.defaultAxes)) {
6544                                 this.defaultAxes.x.setAttribute({ visible: false });
6545                                 this.defaultAxes.y.setAttribute({ visible: false });
6546                             }
6547                         } else {
6548                             // TODO
6549                         }
6550                         break;
6551                     case 'boundingbox':
6552                         this.setBoundingBox(value, this.keepaspectratio);
6553                         this._set(key, value);
6554                         break;
6555                     case 'defaultaxes':
6556                         if (Type.exists(this.defaultAxes.x) && Type.exists(value.x)) {
6557                             this.defaultAxes.x.setAttribute(value.x);
6558                         }
6559                         if (Type.exists(this.defaultAxes.y) && Type.exists(value.y)) {
6560                             this.defaultAxes.y.setAttribute(value.y);
6561                         }
6562                         break;
6563                     case 'title':
6564                         this.document.getElementById(this.container + '_ARIAlabel')
6565                             .innerHTML = value;
6566                         this._set(key, value);
6567                         break;
6568                     case 'keepaspectratio':
6569                         this._set(key, value);
6570                         this.setBoundingBox(this.getBoundingBox(), value, 'keep');
6571                         break;
6572 
6573                     /* eslint-disable no-fallthrough */
6574                     case 'document':
6575                     case 'maxboundingbox':
6576                         this[key] = value;
6577                         this._set(key, value);
6578                         break;
6579 
6580                     case 'zoomx':
6581                     case 'zoomy':
6582                         this[key] = value;
6583                         this._set(key, value);
6584                         this.setZoom(this.attr.zoomx, this.attr.zoomy);
6585                         break;
6586 
6587                     case 'registerevents':
6588                     case 'renderer':
6589                         // immutable, i.e. ignored
6590                         break;
6591 
6592                     case 'fullscreen':
6593                     case 'screenshot':
6594                         node = this.containerObj.ownerDocument.getElementById(
6595                             this.container + '_navigation_' + key);
6596                         if (node && Type.exists(value.symbol)) {
6597                             node.innerHTML = Type.evaluate(value.symbol);
6598                         }
6599                         this._set(key, value);
6600                         break;
6601 
6602                     case 'selection':
6603                         value.visible = false;
6604                         value.withLines = false;
6605                         value.vertices = { visible: false };
6606                         this._set(key, value);
6607                         break;
6608 
6609                     case 'showcopyright':
6610                         if (this.renderer.type === 'svg') {
6611                             node = this.containerObj.ownerDocument.getElementById(
6612                                 this.renderer.uniqName('licenseText')
6613                             );
6614                             if (node) {
6615                                 node.style.display = ((Type.evaluate(value)) ? 'inline' : 'none');
6616                             } else if (Type.evaluate(value)) {
6617                                 this.renderer.displayCopyright(Const.licenseText, parseInt(this.options.text.fontSize, 10));
6618                             }
6619                         }
6620 
6621                     default:
6622                         if (Type.exists(this.attr[key])) {
6623                             this._set(key, value);
6624                         }
6625                         break;
6626                     /* eslint-enable no-fallthrough */
6627                 }
6628             }
6629 
6630             // Redraw navbar to handle the remaining show* attributes
6631             this.containerObj.ownerDocument.getElementById(
6632                 this.container + "_navigationbar"
6633             ).remove();
6634             this.renderer.drawNavigationBar(this, this.attr.navbar);
6635 
6636             this.triggerEventHandlers(["attribute"], [attributes, this]);
6637             this.fullUpdate();
6638 
6639             return this;
6640         },
6641 
6642         /**
6643          * Adds an animation. Animations are controlled by the boards, so the boards need to be aware of the
6644          * animated elements. This function tells the board about new elements to animate.
6645          * @param {JXG.GeometryElement} element The element which is to be animated.
6646          * @returns {JXG.Board} Reference to the board
6647          */
6648         addAnimation: function (element) {
6649             var that = this;
6650 
6651             this.animationObjects[element.id] = element;
6652 
6653             if (!this.animationIntervalCode) {
6654                 this.animationIntervalCode = window.setInterval(function () {
6655                     that.animate();
6656                 }, element.board.attr.animationdelay);
6657             }
6658 
6659             return this;
6660         },
6661 
6662         /**
6663          * Cancels all running animations.
6664          * @returns {JXG.Board} Reference to the board
6665          */
6666         stopAllAnimation: function () {
6667             var el;
6668 
6669             for (el in this.animationObjects) {
6670                 if (
6671                     this.animationObjects.hasOwnProperty(el) &&
6672                     Type.exists(this.animationObjects[el])
6673                 ) {
6674                     this.animationObjects[el] = null;
6675                     delete this.animationObjects[el];
6676                 }
6677             }
6678 
6679             window.clearInterval(this.animationIntervalCode);
6680             delete this.animationIntervalCode;
6681 
6682             return this;
6683         },
6684 
6685         /**
6686          * General purpose animation function. This currently only supports moving points from one place to another. This
6687          * is faster than managing the animation per point, especially if there is more than one animated point at the same time.
6688          * @returns {JXG.Board} Reference to the board
6689          */
6690         animate: function () {
6691             var props,
6692                 el,
6693                 o,
6694                 newCoords,
6695                 r,
6696                 p,
6697                 c,
6698                 cbtmp,
6699                 count = 0,
6700                 obj = null;
6701 
6702             for (el in this.animationObjects) {
6703                 if (
6704                     this.animationObjects.hasOwnProperty(el) &&
6705                     Type.exists(this.animationObjects[el])
6706                 ) {
6707                     count += 1;
6708                     o = this.animationObjects[el];
6709 
6710                     if (o.animationPath) {
6711                         if (Type.isFunction(o.animationPath)) {
6712                             newCoords = o.animationPath(
6713                                 new Date().getTime() - o.animationStart
6714                             );
6715                         } else {
6716                             newCoords = o.animationPath.pop();
6717                         }
6718 
6719                         if (
6720                             !Type.exists(newCoords) ||
6721                             (!Type.isArray(newCoords) && isNaN(newCoords))
6722                         ) {
6723                             delete o.animationPath;
6724                         } else {
6725                             o.setPositionDirectly(Const.COORDS_BY_USER, newCoords);
6726                             o.fullUpdate();
6727                             obj = o;
6728                         }
6729                     }
6730                     if (o.animationData) {
6731                         c = 0;
6732 
6733                         for (r in o.animationData) {
6734                             if (o.animationData.hasOwnProperty(r)) {
6735                                 p = o.animationData[r].pop();
6736 
6737                                 if (!Type.exists(p)) {
6738                                     delete o.animationData[p];
6739                                 } else {
6740                                     c += 1;
6741                                     props = {};
6742                                     props[r] = p;
6743                                     o.setAttribute(props);
6744                                 }
6745                             }
6746                         }
6747 
6748                         if (c === 0) {
6749                             delete o.animationData;
6750                         }
6751                     }
6752 
6753                     if (!Type.exists(o.animationData) && !Type.exists(o.animationPath)) {
6754                         this.animationObjects[el] = null;
6755                         delete this.animationObjects[el];
6756 
6757                         if (Type.exists(o.animationCallback)) {
6758                             cbtmp = o.animationCallback;
6759                             o.animationCallback = null;
6760                             cbtmp();
6761                         }
6762                     }
6763                 }
6764             }
6765 
6766             if (count === 0) {
6767                 window.clearInterval(this.animationIntervalCode);
6768                 delete this.animationIntervalCode;
6769             } else {
6770                 this.update(obj);
6771             }
6772 
6773             return this;
6774         },
6775 
6776         /**
6777          * Migrate the dependency properties of the point src
6778          * to the point dest and delete the point src.
6779          * For example, a circle around the point src
6780          * receives the new center dest. The old center src
6781          * will be deleted.
6782          * @param {JXG.Point} src Original point which will be deleted
6783          * @param {JXG.Point} dest New point with the dependencies of src.
6784          * @param {Boolean} copyName Flag which decides if the name of the src element is copied to the
6785          *  dest element.
6786          * @returns {JXG.Board} Reference to the board
6787          */
6788         migratePoint: function (src, dest, copyName) {
6789             var child,
6790                 childId,
6791                 prop,
6792                 found,
6793                 i,
6794                 srcLabelId,
6795                 srcHasLabel = false;
6796 
6797             src = this.select(src);
6798             dest = this.select(dest);
6799 
6800             if (Type.exists(src.label)) {
6801                 srcLabelId = src.label.id;
6802                 srcHasLabel = true;
6803                 this.removeObject(src.label);
6804             }
6805 
6806             for (childId in src.childElements) {
6807                 if (src.childElements.hasOwnProperty(childId)) {
6808                     child = src.childElements[childId];
6809                     found = false;
6810 
6811                     for (prop in child) {
6812                         if (child.hasOwnProperty(prop)) {
6813                             if (child[prop] === src) {
6814                                 child[prop] = dest;
6815                                 found = true;
6816                             }
6817                         }
6818                     }
6819 
6820                     if (found) {
6821                         delete src.childElements[childId];
6822                     }
6823 
6824                     for (i = 0; i < child.parents.length; i++) {
6825                         if (child.parents[i] === src.id) {
6826                             child.parents[i] = dest.id;
6827                         }
6828                     }
6829 
6830                     dest.addChild(child);
6831                 }
6832             }
6833 
6834             // The destination object should receive the name
6835             // and the label of the originating (src) object
6836             if (copyName) {
6837                 if (srcHasLabel) {
6838                     delete dest.childElements[srcLabelId];
6839                     delete dest.descendants[srcLabelId];
6840                 }
6841 
6842                 if (dest.label) {
6843                     this.removeObject(dest.label);
6844                 }
6845 
6846                 delete this.elementsByName[dest.name];
6847                 dest.name = src.name;
6848                 if (srcHasLabel) {
6849                     dest.createLabel();
6850                 }
6851             }
6852 
6853             this.removeObject(src);
6854 
6855             if (Type.exists(dest.name) && dest.name !== '') {
6856                 this.elementsByName[dest.name] = dest;
6857             }
6858 
6859             this.fullUpdate();
6860 
6861             return this;
6862         },
6863 
6864         /**
6865          * Initializes color blindness simulation.
6866          * @param {String} deficiency Describes the color blindness deficiency which is simulated. Accepted values are 'protanopia', 'deuteranopia', and 'tritanopia'.
6867          * @returns {JXG.Board} Reference to the board
6868          */
6869         emulateColorblindness: function (deficiency) {
6870             var e, o;
6871 
6872             if (!Type.exists(deficiency)) {
6873                 deficiency = 'none';
6874             }
6875 
6876             if (this.currentCBDef === deficiency) {
6877                 return this;
6878             }
6879 
6880             for (e in this.objects) {
6881                 if (this.objects.hasOwnProperty(e)) {
6882                     o = this.objects[e];
6883 
6884                     if (deficiency !== 'none') {
6885                         if (this.currentCBDef === 'none') {
6886                             // this could be accomplished by JXG.extend, too. But do not use
6887                             // JXG.deepCopy as this could result in an infinite loop because in
6888                             // visProp there could be geometry elements which contain the board which
6889                             // contains all objects which contain board etc.
6890                             o.visPropOriginal = {
6891                                 strokecolor: o.visProp.strokecolor,
6892                                 fillcolor: o.visProp.fillcolor,
6893                                 highlightstrokecolor: o.visProp.highlightstrokecolor,
6894                                 highlightfillcolor: o.visProp.highlightfillcolor
6895                             };
6896                         }
6897                         o.setAttribute({
6898                             strokecolor: Color.rgb2cb(
6899                                 o.eval(o.visPropOriginal.strokecolor),
6900                                 deficiency
6901                             ),
6902                             fillcolor: Color.rgb2cb(
6903                                 o.eval(o.visPropOriginal.fillcolor),
6904                                 deficiency
6905                             ),
6906                             highlightstrokecolor: Color.rgb2cb(
6907                                 o.eval(o.visPropOriginal.highlightstrokecolor),
6908                                 deficiency
6909                             ),
6910                             highlightfillcolor: Color.rgb2cb(
6911                                 o.eval(o.visPropOriginal.highlightfillcolor),
6912                                 deficiency
6913                             )
6914                         });
6915                     } else if (Type.exists(o.visPropOriginal)) {
6916                         JXG.extend(o.visProp, o.visPropOriginal);
6917                     }
6918                 }
6919             }
6920             this.currentCBDef = deficiency;
6921             this.update();
6922 
6923             return this;
6924         },
6925 
6926         /**
6927          * Select a single or multiple elements at once.
6928          * @param {String|Object|function} str The name, id or a reference to a JSXGraph element on this board. An object will
6929          * be used as a filter to return multiple elements at once filtered by the properties of the object.
6930          * @param {Boolean} onlyByIdOrName If true (default:false) elements are only filtered by their id, name or groupId.
6931          * The advanced filters consisting of objects or functions are ignored.
6932          * @returns {JXG.GeometryElement|JXG.Composition}
6933          * @example
6934          * // select the element with name A
6935          * board.select('A');
6936          *
6937          * // select all elements with strokecolor set to 'red' (but not '#ff0000')
6938          * board.select({
6939          *   strokeColor: 'red'
6940          * });
6941          *
6942          * // select all points on or below the x axis and make them black.
6943          * board.select({
6944          *   elementClass: JXG.OBJECT_CLASS_POINT,
6945          *   Y: function (v) {
6946          *     return v <= 0;
6947          *   }
6948          * }).setAttribute({color: 'black'});
6949          *
6950          * // select all elements
6951          * board.select(function (el) {
6952          *   return true;
6953          * });
6954          */
6955         select: function (str, onlyByIdOrName) {
6956             var flist,
6957                 olist,
6958                 i,
6959                 l,
6960                 s = str;
6961 
6962             if (s === null) {
6963                 return s;
6964             }
6965 
6966             // It's a string, most likely an id or a name.
6967             if (Type.isString(s) && s !== '') {
6968                 // Search by ID
6969                 if (Type.exists(this.objects[s])) {
6970                     s = this.objects[s];
6971                     // Search by name
6972                 } else if (Type.exists(this.elementsByName[s])) {
6973                     s = this.elementsByName[s];
6974                     // Search by group ID
6975                 } else if (Type.exists(this.groups[s])) {
6976                     s = this.groups[s];
6977                 }
6978 
6979                 // It's a function or an object, but not an element
6980             } else if (
6981                 !onlyByIdOrName &&
6982                 (Type.isFunction(s) || (Type.isObject(s) && !Type.isFunction(s.setAttribute)))
6983             ) {
6984                 flist = Type.filterElements(this.objectsList, s);
6985 
6986                 olist = {};
6987                 l = flist.length;
6988                 for (i = 0; i < l; i++) {
6989                     olist[flist[i].id] = flist[i];
6990                 }
6991                 s = new Composition(olist);
6992 
6993                 // It's an element which has been deleted (and still hangs around, e.g. in an attractor list
6994             } else if (
6995                 Type.isObject(s) &&
6996                 Type.exists(s.id) &&
6997                 !Type.exists(this.objects[s.id])
6998             ) {
6999                 s = null;
7000             }
7001 
7002             return s;
7003         },
7004 
7005         /**
7006          * Checks if the given point is inside the boundingbox.
7007          * @param {Number|JXG.Coords} x User coordinate or {@link JXG.Coords} object.
7008          * @param {Number} [y] User coordinate. May be omitted in case <tt>x</tt> is a {@link JXG.Coords} object.
7009          * @returns {Boolean}
7010          */
7011         hasPoint: function (x, y) {
7012             var px = x,
7013                 py = y,
7014                 bbox = this.getBoundingBox();
7015 
7016             if (Type.exists(x) && Type.isArray(x.usrCoords)) {
7017                 px = x.usrCoords[1];
7018                 py = x.usrCoords[2];
7019             }
7020 
7021             return !!(
7022                 Type.isNumber(px) &&
7023                 Type.isNumber(py) &&
7024                 bbox[0] < px &&
7025                 px < bbox[2] &&
7026                 bbox[1] > py &&
7027                 py > bbox[3]
7028             );
7029         },
7030 
7031         /**
7032          * Update CSS transformations of type scaling. It is used to correct the mouse position
7033          * in {@link JXG.Board.getMousePosition}.
7034          * The inverse transformation matrix is updated on each mouseDown and touchStart event.
7035          *
7036          * It is up to the user to call this method after an update of the CSS transformation
7037          * in the DOM.
7038          */
7039         updateCSSTransforms: function () {
7040             var obj = this.containerObj,
7041                 o = obj,
7042                 o2 = obj;
7043 
7044             this.cssTransMat = Env.getCSSTransformMatrix(o);
7045 
7046             // Newer variant of walking up the tree.
7047             // We walk up all parent nodes and collect possible CSS transforms.
7048             // Works also for ShadowDOM
7049             if (Type.exists(o.getRootNode)) {
7050                 o = o.parentNode === o.getRootNode() ? o.parentNode.host : o.parentNode;
7051                 while (o) {
7052                     this.cssTransMat = Mat.matMatMult(Env.getCSSTransformMatrix(o), this.cssTransMat);
7053                     o = o.parentNode === o.getRootNode() ? o.parentNode.host : o.parentNode;
7054                 }
7055                 this.cssTransMat = Mat.inverse(this.cssTransMat);
7056             } else {
7057                 /*
7058                  * This is necessary for IE11
7059                  */
7060                 o = o.offsetParent;
7061                 while (o) {
7062                     this.cssTransMat = Mat.matMatMult(Env.getCSSTransformMatrix(o), this.cssTransMat);
7063 
7064                     o2 = o2.parentNode;
7065                     while (o2 !== o) {
7066                         this.cssTransMat = Mat.matMatMult(Env.getCSSTransformMatrix(o), this.cssTransMat);
7067                         o2 = o2.parentNode;
7068                     }
7069                     o = o.offsetParent;
7070                 }
7071                 this.cssTransMat = Mat.inverse(this.cssTransMat);
7072             }
7073             return this;
7074         },
7075 
7076         /**
7077          * Start selection mode. This function can either be triggered from outside or by
7078          * a down event together with correct key pressing. The default keys are
7079          * shift+ctrl. But this can be changed in the options.
7080          *
7081          * Starting from out side can be realized for example with a button like this:
7082          * <pre>
7083          * 	<button onclick='board.startSelectionMode()'>Start</button>
7084          * </pre>
7085          * @example
7086          * //
7087          * // Set a new bounding box from the selection rectangle
7088          * //
7089          * var board = JXG.JSXGraph.initBoard('jxgbox', {
7090          *         boundingBox:[-3,2,3,-2],
7091          *         keepAspectRatio: false,
7092          *         axis:true,
7093          *         selection: {
7094          *             enabled: true,
7095          *             needShift: false,
7096          *             needCtrl: true,
7097          *             withLines: false,
7098          *             vertices: {
7099          *                 visible: false
7100          *             },
7101          *             fillColor: '#ffff00',
7102          *         }
7103          *      });
7104          *
7105          * var f = function f(x) { return Math.cos(x); },
7106          *     curve = board.create('functiongraph', [f]);
7107          *
7108          * board.on('stopselecting', function(){
7109          *     var box = board.stopSelectionMode(),
7110          *
7111          *         // bbox has the coordinates of the selection rectangle.
7112          *         // Attention: box[i].usrCoords have the form [1, x, y], i.e.
7113          *         // are homogeneous coordinates.
7114          *         bbox = box[0].usrCoords.slice(1).concat(box[1].usrCoords.slice(1));
7115          *
7116          *         // Set a new bounding box
7117          *         board.setBoundingBox(bbox, false);
7118          *  });
7119          *
7120          *
7121          * </pre><div class='jxgbox' id='JXG11eff3a6-8c50-11e5-b01d-901b0e1b8723' style='width: 300px; height: 300px;'></div>
7122          * <script type='text/javascript'>
7123          *     (function() {
7124          *     //
7125          *     // Set a new bounding box from the selection rectangle
7126          *     //
7127          *     var board = JXG.JSXGraph.initBoard('JXG11eff3a6-8c50-11e5-b01d-901b0e1b8723', {
7128          *             boundingBox:[-3,2,3,-2],
7129          *             keepAspectRatio: false,
7130          *             axis:true,
7131          *             selection: {
7132          *                 enabled: true,
7133          *                 needShift: false,
7134          *                 needCtrl: true,
7135          *                 withLines: false,
7136          *                 vertices: {
7137          *                     visible: false
7138          *                 },
7139          *                 fillColor: '#ffff00',
7140          *             }
7141          *        });
7142          *
7143          *     var f = function f(x) { return Math.cos(x); },
7144          *         curve = board.create('functiongraph', [f]);
7145          *
7146          *     board.on('stopselecting', function(){
7147          *         var box = board.stopSelectionMode(),
7148          *
7149          *             // bbox has the coordinates of the selection rectangle.
7150          *             // Attention: box[i].usrCoords have the form [1, x, y], i.e.
7151          *             // are homogeneous coordinates.
7152          *             bbox = box[0].usrCoords.slice(1).concat(box[1].usrCoords.slice(1));
7153          *
7154          *             // Set a new bounding box
7155          *             board.setBoundingBox(bbox, false);
7156          *      });
7157          *     })();
7158          *
7159          * </script><pre>
7160          *
7161          */
7162         startSelectionMode: function () {
7163             this.selectingMode = true;
7164             this.selectionPolygon.setAttribute({ visible: true });
7165             this.selectingBox = [
7166                 [0, 0],
7167                 [0, 0]
7168             ];
7169             this._setSelectionPolygonFromBox();
7170             this.selectionPolygon.fullUpdate();
7171         },
7172 
7173         /**
7174          * Finalize the selection: disable selection mode and return the coordinates
7175          * of the selection rectangle.
7176          * @returns {Array} Coordinates of the selection rectangle. The array
7177          * contains two {@link JXG.Coords} objects. One the upper left corner and
7178          * the second for the lower right corner.
7179          */
7180         stopSelectionMode: function () {
7181             this.selectingMode = false;
7182             this.selectionPolygon.setAttribute({ visible: false });
7183             return [
7184                 this.selectionPolygon.vertices[0].coords,
7185                 this.selectionPolygon.vertices[2].coords
7186             ];
7187         },
7188 
7189         /**
7190          * Start the selection of a region.
7191          * @private
7192          * @param  {Array} pos Screen coordiates of the upper left corner of the
7193          * selection rectangle.
7194          */
7195         _startSelecting: function (pos) {
7196             this.isSelecting = true;
7197             this.selectingBox = [
7198                 [pos[0], pos[1]],
7199                 [pos[0], pos[1]]
7200             ];
7201             this._setSelectionPolygonFromBox();
7202         },
7203 
7204         /**
7205          * Update the selection rectangle during a move event.
7206          * @private
7207          * @param  {Array} pos Screen coordiates of the move event
7208          */
7209         _moveSelecting: function (pos) {
7210             if (this.isSelecting) {
7211                 this.selectingBox[1] = [pos[0], pos[1]];
7212                 this._setSelectionPolygonFromBox();
7213                 this.selectionPolygon.fullUpdate();
7214             }
7215         },
7216 
7217         /**
7218          * Update the selection rectangle during an up event. Stop selection.
7219          * @private
7220          * @param  {Object} evt Event object
7221          */
7222         _stopSelecting: function (evt) {
7223             var pos = this.getMousePosition(evt);
7224 
7225             this.isSelecting = false;
7226             this.selectingBox[1] = [pos[0], pos[1]];
7227             this._setSelectionPolygonFromBox();
7228         },
7229 
7230         /**
7231          * Update the Selection rectangle.
7232          * @private
7233          */
7234         _setSelectionPolygonFromBox: function () {
7235             var A = this.selectingBox[0],
7236                 B = this.selectingBox[1];
7237 
7238             this.selectionPolygon.vertices[0].setPositionDirectly(JXG.COORDS_BY_SCREEN, [
7239                 A[0],
7240                 A[1]
7241             ]);
7242             this.selectionPolygon.vertices[1].setPositionDirectly(JXG.COORDS_BY_SCREEN, [
7243                 A[0],
7244                 B[1]
7245             ]);
7246             this.selectionPolygon.vertices[2].setPositionDirectly(JXG.COORDS_BY_SCREEN, [
7247                 B[0],
7248                 B[1]
7249             ]);
7250             this.selectionPolygon.vertices[3].setPositionDirectly(JXG.COORDS_BY_SCREEN, [
7251                 B[0],
7252                 A[1]
7253             ]);
7254         },
7255 
7256         /**
7257          * Test if a down event should start a selection. Test if the
7258          * required keys are pressed. If yes, {@link JXG.Board.startSelectionMode} is called.
7259          * @param  {Object} evt Event object
7260          */
7261         _testForSelection: function (evt) {
7262             if (this._isRequiredKeyPressed(evt, 'selection')) {
7263                 if (!Type.exists(this.selectionPolygon)) {
7264                     this._createSelectionPolygon(this.attr);
7265                 }
7266                 this.startSelectionMode();
7267             }
7268         },
7269 
7270         /**
7271          * Create the internal selection polygon, which will be available as board.selectionPolygon.
7272          * @private
7273          * @param  {Object} attr board attributes, e.g. the subobject board.attr.
7274          * @returns {Object} pointer to the board to enable chaining.
7275          */
7276         _createSelectionPolygon: function (attr) {
7277             var selectionattr;
7278 
7279             if (!Type.exists(this.selectionPolygon)) {
7280                 selectionattr = Type.copyAttributes(attr, Options, 'board', 'selection');
7281                 if (selectionattr.enabled === true) {
7282                     this.selectionPolygon = this.create(
7283                         'polygon',
7284                         [
7285                             [0, 0],
7286                             [0, 0],
7287                             [0, 0],
7288                             [0, 0]
7289                         ],
7290                         selectionattr
7291                     );
7292                 }
7293             }
7294 
7295             return this;
7296         },
7297 
7298         /* **************************
7299          *     EVENT DEFINITION
7300          * for documentation purposes
7301          * ************************** */
7302 
7303         //region Event handler documentation
7304 
7305         /**
7306          * @event
7307          * @description Whenever the {@link JXG.Board#setAttribute} is called.
7308          * @name JXG.Board#attribute
7309          * @param {Event} e The browser's event object.
7310          */
7311         __evt__attribute: function (e) { },
7312 
7313         /**
7314          * @event
7315          * @description Whenever the user starts to touch or click the board.
7316          * @name JXG.Board#down
7317          * @param {Event} e The browser's event object.
7318          */
7319         __evt__down: function (e) { },
7320 
7321         /**
7322          * @event
7323          * @description Whenever the user starts to click on the board.
7324          * @name JXG.Board#mousedown
7325          * @param {Event} e The browser's event object.
7326          */
7327         __evt__mousedown: function (e) { },
7328 
7329         /**
7330          * @event
7331          * @description Whenever the user taps the pen on the board.
7332          * @name JXG.Board#pendown
7333          * @param {Event} e The browser's event object.
7334          */
7335         __evt__pendown: function (e) { },
7336 
7337         /**
7338          * @event
7339          * @description Whenever the user starts to click on the board with a
7340          * device sending pointer events.
7341          * @name JXG.Board#pointerdown
7342          * @param {Event} e The browser's event object.
7343          */
7344         __evt__pointerdown: function (e) { },
7345 
7346         /**
7347          * @event
7348          * @description Whenever the user starts to touch the board.
7349          * @name JXG.Board#touchstart
7350          * @param {Event} e The browser's event object.
7351          */
7352         __evt__touchstart: function (e) { },
7353 
7354         /**
7355          * @event
7356          * @description Whenever the user stops to touch or click the board.
7357          * @name JXG.Board#up
7358          * @param {Event} e The browser's event object.
7359          */
7360         __evt__up: function (e) { },
7361 
7362         /**
7363          * @event
7364          * @description Whenever the user releases the mousebutton over the board.
7365          * @name JXG.Board#mouseup
7366          * @param {Event} e The browser's event object.
7367          */
7368         __evt__mouseup: function (e) { },
7369 
7370         /**
7371          * @event
7372          * @description Whenever the user releases the mousebutton over the board with a
7373          * device sending pointer events.
7374          * @name JXG.Board#pointerup
7375          * @param {Event} e The browser's event object.
7376          */
7377         __evt__pointerup: function (e) { },
7378 
7379         /**
7380          * @event
7381          * @description Whenever the user stops touching the board.
7382          * @name JXG.Board#touchend
7383          * @param {Event} e The browser's event object.
7384          */
7385         __evt__touchend: function (e) { },
7386 
7387         /**
7388          * @event
7389          * @description Whenever the user clicks on the board.
7390          * @name JXG.Board#click
7391          * @see JXG.Board#clickDelay
7392          * @param {Event} e The browser's event object.
7393          */
7394         __evt__click: function (e) { },
7395 
7396         /**
7397          * @event
7398          * @description Whenever the user double clicks on the board.
7399          * This event works on desktop browser, but is undefined
7400          * on mobile browsers.
7401          * @name JXG.Board#dblclick
7402          * @see JXG.Board#clickDelay
7403          * @see JXG.Board#dblClickSuppressClick
7404          * @param {Event} e The browser's event object.
7405          */
7406         __evt__dblclick: function (e) { },
7407 
7408         /**
7409          * @event
7410          * @description Whenever the user clicks on the board with a mouse device.
7411          * @name JXG.Board#mouseclick
7412          * @param {Event} e The browser's event object.
7413          */
7414         __evt__mouseclick: function (e) { },
7415 
7416         /**
7417          * @event
7418          * @description Whenever the user double clicks on the board with a mouse device.
7419          * @name JXG.Board#mousedblclick
7420          * @see JXG.Board#clickDelay
7421          * @param {Event} e The browser's event object.
7422          */
7423         __evt__mousedblclick: function (e) { },
7424 
7425         /**
7426          * @event
7427          * @description Whenever the user clicks on the board with a pointer device.
7428          * @name JXG.Board#pointerclick
7429          * @param {Event} e The browser's event object.
7430          */
7431         __evt__pointerclick: function (e) { },
7432 
7433         /**
7434          * @event
7435          * @description Whenever the user double clicks on the board with a pointer device.
7436          * This event works on desktop browser, but is undefined
7437          * on mobile browsers.
7438          * @name JXG.Board#pointerdblclick
7439          * @see JXG.Board#clickDelay
7440          * @param {Event} e The browser's event object.
7441          */
7442         __evt__pointerdblclick: function (e) { },
7443 
7444         /**
7445          * @event
7446          * @description This event is fired whenever the user is moving the finger or mouse pointer over the board.
7447          * @name JXG.Board#move
7448          * @param {Event} e The browser's event object.
7449          * @param {Number} mode The mode the board currently is in
7450          * @see JXG.Board#mode
7451          */
7452         __evt__move: function (e, mode) { },
7453 
7454         /**
7455          * @event
7456          * @description This event is fired whenever the user is moving the mouse over the board.
7457          * @name JXG.Board#mousemove
7458          * @param {Event} e The browser's event object.
7459          * @param {Number} mode The mode the board currently is in
7460          * @see JXG.Board#mode
7461          */
7462         __evt__mousemove: function (e, mode) { },
7463 
7464         /**
7465          * @event
7466          * @description This event is fired whenever the user is moving the pen over the board.
7467          * @name JXG.Board#penmove
7468          * @param {Event} e The browser's event object.
7469          * @param {Number} mode The mode the board currently is in
7470          * @see JXG.Board#mode
7471          */
7472         __evt__penmove: function (e, mode) { },
7473 
7474         /**
7475          * @event
7476          * @description This event is fired whenever the user is moving the mouse over the board with a
7477          * device sending pointer events.
7478          * @name JXG.Board#pointermove
7479          * @param {Event} e The browser's event object.
7480          * @param {Number} mode The mode the board currently is in
7481          * @see JXG.Board#mode
7482          */
7483         __evt__pointermove: function (e, mode) { },
7484 
7485         /**
7486          * @event
7487          * @description This event is fired whenever the user is moving the finger over the board.
7488          * @name JXG.Board#touchmove
7489          * @param {Event} e The browser's event object.
7490          * @param {Number} mode The mode the board currently is in
7491          * @see JXG.Board#mode
7492          */
7493         __evt__touchmove: function (e, mode) { },
7494 
7495         /**
7496          * @event
7497          * @description This event is fired whenever the user is moving an element over the board by
7498          * pressing arrow keys on a keyboard.
7499          * @name JXG.Board#keymove
7500          * @param {Event} e The browser's event object.
7501          * @param {Number} mode The mode the board currently is in
7502          * @see JXG.Board#mode
7503          */
7504         __evt__keymove: function (e, mode) { },
7505 
7506         /**
7507          * @event
7508          * @description Whenever an element is highlighted this event is fired.
7509          * @name JXG.Board#hit
7510          * @param {Event} e The browser's event object.
7511          * @param {JXG.GeometryElement} el The hit element.
7512          * @param target
7513          *
7514          * @example
7515          * var c = board.create('circle', [[1, 1], 2]);
7516          * board.on('hit', function(evt, el) {
7517          *     console.log('Hit element', el);
7518          * });
7519          *
7520          * </pre><div id='JXG19eb31ac-88e6-11e8-bcb5-901b0e1b8723' class='jxgbox' style='width: 300px; height: 300px;'></div>
7521          * <script type='text/javascript'>
7522          *     (function() {
7523          *         var board = JXG.JSXGraph.initBoard('JXG19eb31ac-88e6-11e8-bcb5-901b0e1b8723',
7524          *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
7525          *     var c = board.create('circle', [[1, 1], 2]);
7526          *     board.on('hit', function(evt, el) {
7527          *         console.log('Hit element', el);
7528          *     });
7529          *
7530          *     })();
7531          *
7532          * </script><pre>
7533          */
7534         __evt__hit: function (e, el, target) { },
7535 
7536         /**
7537          * @event
7538          * @description Whenever an element is highlighted this event is fired.
7539          * @name JXG.Board#mousehit
7540          * @see JXG.Board#hit
7541          * @param {Event} e The browser's event object.
7542          * @param {JXG.GeometryElement} el The hit element.
7543          * @param target
7544          */
7545         __evt__mousehit: function (e, el, target) { },
7546 
7547         /**
7548          * @event
7549          * @description This board is updated.
7550          * @name JXG.Board#update
7551          */
7552         __evt__update: function () { },
7553 
7554         /**
7555          * @event
7556          * @description The bounding box of the board has changed.
7557          * @name JXG.Board#boundingbox
7558          */
7559         __evt__boundingbox: function () { },
7560 
7561         /**
7562          * @event
7563          * @description Select a region is started during a down event or by calling
7564          * {@link JXG.Board.startSelectionMode}
7565          * @name JXG.Board#startselecting
7566          */
7567         __evt__startselecting: function () { },
7568 
7569         /**
7570          * @event
7571          * @description Select a region is started during a down event
7572          * from a device sending mouse events or by calling
7573          * {@link JXG.Board.startSelectionMode}.
7574          * @name JXG.Board#mousestartselecting
7575          */
7576         __evt__mousestartselecting: function () { },
7577 
7578         /**
7579          * @event
7580          * @description Select a region is started during a down event
7581          * from a device sending pointer events or by calling
7582          * {@link JXG.Board.startSelectionMode}.
7583          * @name JXG.Board#pointerstartselecting
7584          */
7585         __evt__pointerstartselecting: function () { },
7586 
7587         /**
7588          * @event
7589          * @description Select a region is started during a down event
7590          * from a device sending touch events or by calling
7591          * {@link JXG.Board.startSelectionMode}.
7592          * @name JXG.Board#touchstartselecting
7593          */
7594         __evt__touchstartselecting: function () { },
7595 
7596         /**
7597          * @event
7598          * @description Selection of a region is stopped during an up event.
7599          * @name JXG.Board#stopselecting
7600          */
7601         __evt__stopselecting: function () { },
7602 
7603         /**
7604          * @event
7605          * @description Selection of a region is stopped during an up event
7606          * from a device sending mouse events.
7607          * @name JXG.Board#mousestopselecting
7608          */
7609         __evt__mousestopselecting: function () { },
7610 
7611         /**
7612          * @event
7613          * @description Selection of a region is stopped during an up event
7614          * from a device sending pointer events.
7615          * @name JXG.Board#pointerstopselecting
7616          */
7617         __evt__pointerstopselecting: function () { },
7618 
7619         /**
7620          * @event
7621          * @description Selection of a region is stopped during an up event
7622          * from a device sending touch events.
7623          * @name JXG.Board#touchstopselecting
7624          */
7625         __evt__touchstopselecting: function () { },
7626 
7627         /**
7628          * @event
7629          * @description A move event while selecting of a region is active.
7630          * @name JXG.Board#moveselecting
7631          */
7632         __evt__moveselecting: function () { },
7633 
7634         /**
7635          * @event
7636          * @description A move event while selecting of a region is active
7637          * from a device sending mouse events.
7638          * @name JXG.Board#mousemoveselecting
7639          */
7640         __evt__mousemoveselecting: function () { },
7641 
7642         /**
7643          * @event
7644          * @description Select a region is started during a down event
7645          * from a device sending mouse events.
7646          * @name JXG.Board#pointermoveselecting
7647          */
7648         __evt__pointermoveselecting: function () { },
7649 
7650         /**
7651          * @event
7652          * @description Select a region is started during a down event
7653          * from a device sending touch events.
7654          * @name JXG.Board#touchmoveselecting
7655          */
7656         __evt__touchmoveselecting: function () { },
7657 
7658         /**
7659          * @ignore
7660          */
7661         __evt: function () { },
7662 
7663         //endregion
7664 
7665         /**
7666          * Expand the JSXGraph construction to fullscreen.
7667          * In order to preserve the proportions of the JSXGraph element,
7668          * a wrapper div is created which is set to fullscreen.
7669          * This function is called when fullscreen mode is triggered
7670          * <b>and</b> when it is closed.
7671          * <p>
7672          * The wrapping div has the CSS class 'jxgbox_wrap_private' which is
7673          * defined in the file 'jsxgraph.css'
7674          * <p>
7675          * This feature is not available on iPhones (as of December 2021).
7676          *
7677          * @param {String} id (Optional) id of the div element which is brought to fullscreen.
7678          * If not provided, this defaults to the JSXGraph div. However, it may be necessary for the aspect ratio trick
7679          * which using padding-bottom/top and an out div element. Then, the id of the outer div has to be supplied.
7680          *
7681          * @return {JXG.Board} Reference to the board
7682          *
7683          * @example
7684          * <div id='jxgbox' class='jxgbox' style='width:500px; height:200px;'></div>
7685          * <button onClick='board.toFullscreen()'>Fullscreen</button>
7686          *
7687          * <script language='Javascript' type='text/javascript'>
7688          * var board = JXG.JSXGraph.initBoard('jxgbox', {axis:true, boundingbox:[-5,5,5,-5]});
7689          * var p = board.create('point', [0, 1]);
7690          * </script>
7691          *
7692          * </pre><div id='JXGd5bab8b6-fd40-11e8-ab14-901b0e1b8723' class='jxgbox' style='width: 300px; height: 300px;'></div>
7693          * <script type='text/javascript'>
7694          *      var board_d5bab8b6;
7695          *     (function() {
7696          *         var board = JXG.JSXGraph.initBoard('JXGd5bab8b6-fd40-11e8-ab14-901b0e1b8723',
7697          *             {boundingbox:[-5,5,5,-5], axis: true, showcopyright: false, shownavigation: false});
7698          *         var p = board.create('point', [0, 1]);
7699          *         board_d5bab8b6 = board;
7700          *     })();
7701          * </script>
7702          * <button onClick='board_d5bab8b6.toFullscreen()'>Fullscreen</button>
7703          * <pre>
7704          *
7705          * @example
7706          * <div id='outer' style='max-width: 500px; margin: 0 auto;'>
7707          * <div id='jxgbox' class='jxgbox' style='height: 0; padding-bottom: 100%'></div>
7708          * </div>
7709          * <button onClick='board.toFullscreen('outer')'>Fullscreen</button>
7710          *
7711          * <script language='Javascript' type='text/javascript'>
7712          * var board = JXG.JSXGraph.initBoard('jxgbox', {
7713          *     axis:true,
7714          *     boundingbox:[-5,5,5,-5],
7715          *     fullscreen: { id: 'outer' },
7716          *     showFullscreen: true
7717          * });
7718          * var p = board.create('point', [-2, 3], {});
7719          * </script>
7720          *
7721          * </pre><div id='JXG7103f6b_outer' style='max-width: 500px; margin: 0 auto;'>
7722          * <div id='JXG7103f6be-6993-4ff8-8133-c78e50a8afac' class='jxgbox' style='height: 0; padding-bottom: 100%;'></div>
7723          * </div>
7724          * <button onClick='board_JXG7103f6be.toFullscreen('JXG7103f6b_outer')'>Fullscreen</button>
7725          * <script type='text/javascript'>
7726          *     var board_JXG7103f6be;
7727          *     (function() {
7728          *         var board = JXG.JSXGraph.initBoard('JXG7103f6be-6993-4ff8-8133-c78e50a8afac',
7729          *             {boundingbox: [-8, 8, 8,-8], axis: true, fullscreen: { id: 'JXG7103f6b_outer' }, showFullscreen: true,
7730          *              showcopyright: false, shownavigation: false});
7731          *     var p = board.create('point', [-2, 3], {});
7732          *     board_JXG7103f6be = board;
7733          *     })();
7734          *
7735          * </script><pre>
7736          *
7737          *
7738          */
7739         toFullscreen: function (id) {
7740             var wrap_id,
7741                 wrap_node,
7742                 inner_node,
7743                 dim,
7744                 doc = this.document,
7745                 fullscreenElement;
7746 
7747             id = id || this.container;
7748             this._fullscreen_inner_id = id;
7749             inner_node = doc.getElementById(id);
7750             wrap_id = 'fullscreenwrap_' + id;
7751 
7752             if (!Type.exists(inner_node._cssFullscreenStore)) {
7753                 // Store the actual, absolute size of the div
7754                 // This is used in scaleJSXGraphDiv
7755                 dim = this.containerObj.getBoundingClientRect();
7756                 inner_node._cssFullscreenStore = {
7757                     w: dim.width,
7758                     h: dim.height
7759                 };
7760             }
7761 
7762             // Wrap a div around the JSXGraph div.
7763             // It is removed when fullscreen mode is closed.
7764             if (doc.getElementById(wrap_id)) {
7765                 wrap_node = doc.getElementById(wrap_id);
7766             } else {
7767                 wrap_node = document.createElement('div');
7768                 wrap_node.classList.add('JXG_wrap_private');
7769                 wrap_node.setAttribute('id', wrap_id);
7770                 inner_node.parentNode.insertBefore(wrap_node, inner_node);
7771                 wrap_node.appendChild(inner_node);
7772             }
7773 
7774             // Trigger fullscreen mode
7775             wrap_node.requestFullscreen =
7776                 wrap_node.requestFullscreen ||
7777                 wrap_node.webkitRequestFullscreen ||
7778                 wrap_node.mozRequestFullScreen ||
7779                 wrap_node.msRequestFullscreen;
7780 
7781             if (doc.fullscreenElement !== undefined) {
7782                 fullscreenElement = doc.fullscreenElement;
7783             } else if (doc.webkitFullscreenElement !== undefined) {
7784                 fullscreenElement = doc.webkitFullscreenElement;
7785             } else {
7786                 fullscreenElement = doc.msFullscreenElement;
7787             }
7788 
7789             if (fullscreenElement === null) {
7790                 // Start fullscreen mode
7791                 if (wrap_node.requestFullscreen) {
7792                     wrap_node.requestFullscreen();
7793                     this.startFullscreenResizeObserver(wrap_node);
7794                 }
7795             } else {
7796                 this.stopFullscreenResizeObserver(wrap_node);
7797                 if (Type.exists(document.exitFullscreen)) {
7798                     document.exitFullscreen();
7799                 } else if (Type.exists(document.webkitExitFullscreen)) {
7800                     document.webkitExitFullscreen();
7801                 }
7802             }
7803 
7804             return this;
7805         },
7806 
7807         /**
7808          * If fullscreen mode is toggled, the possible CSS transformations
7809          * which are applied to the JSXGraph canvas have to be reread.
7810          * Otherwise the position of upper left corner is wrongly interpreted.
7811          *
7812          * @param  {Object} evt fullscreen event object (unused)
7813          */
7814         fullscreenListener: function (evt) {
7815             var inner_id,
7816                 inner_node,
7817                 fullscreenElement,
7818                 doc = this.document;
7819 
7820             inner_id = this._fullscreen_inner_id;
7821             if (!Type.exists(inner_id)) {
7822                 return;
7823             }
7824 
7825             if (doc.fullscreenElement !== undefined) {
7826                 fullscreenElement = doc.fullscreenElement;
7827             } else if (doc.webkitFullscreenElement !== undefined) {
7828                 fullscreenElement = doc.webkitFullscreenElement;
7829             } else {
7830                 fullscreenElement = doc.msFullscreenElement;
7831             }
7832 
7833             inner_node = doc.getElementById(inner_id);
7834             // If full screen mode is started we have to remove CSS margin around the JSXGraph div.
7835             // Otherwise, the positioning of the fullscreen div will be false.
7836             // When leaving the fullscreen mode, the margin is put back in.
7837             if (fullscreenElement) {
7838                 // Just entered fullscreen mode
7839 
7840                 // Store the original data.
7841                 // Further, the CSS margin has to be removed when in fullscreen mode,
7842                 // and must be restored later.
7843                 //
7844                 // Obsolete:
7845                 // It is used in AbstractRenderer.updateText to restore the scaling matrix
7846                 // which is removed by MathJax.
7847                 inner_node._cssFullscreenStore.id = fullscreenElement.id;
7848                 inner_node._cssFullscreenStore.isFullscreen = true;
7849                 inner_node._cssFullscreenStore.margin = inner_node.style.margin;
7850                 inner_node._cssFullscreenStore.width = inner_node.style.width;
7851                 inner_node._cssFullscreenStore.height = inner_node.style.height;
7852                 inner_node._cssFullscreenStore.transform = inner_node.style.transform;
7853                 // Be sure to replace relative width / height units by absolute units
7854                 inner_node.style.width = inner_node._cssFullscreenStore.w + 'px';
7855                 inner_node.style.height = inner_node._cssFullscreenStore.h + 'px';
7856                 inner_node.style.margin = '';
7857 
7858                 // Do the shifting and scaling via CSS properties
7859                 // We do this after fullscreen mode has been established to get the correct size
7860                 // of the JSXGraph div.
7861                 Env.scaleJSXGraphDiv(fullscreenElement.id, inner_id, doc,
7862                     Type.evaluate(this.attr.fullscreen.scale));
7863 
7864                 // Clear this.doc.fullscreenElement, because Safari doesn't to it and
7865                 // when leaving full screen mode it is still set.
7866                 fullscreenElement = null;
7867             } else if (Type.exists(inner_node._cssFullscreenStore)) {
7868                 // Just left the fullscreen mode
7869 
7870                 inner_node._cssFullscreenStore.isFullscreen = false;
7871                 inner_node.style.margin = inner_node._cssFullscreenStore.margin;
7872                 inner_node.style.width = inner_node._cssFullscreenStore.width;
7873                 inner_node.style.height = inner_node._cssFullscreenStore.height;
7874                 inner_node.style.transform = inner_node._cssFullscreenStore.transform;
7875                 inner_node._cssFullscreenStore = null;
7876 
7877                 // Remove the wrapper div
7878                 inner_node.parentElement.replaceWith(inner_node);
7879             }
7880 
7881             this.updateCSSTransforms();
7882         },
7883 
7884         /**
7885          * Start resize observer to handle
7886          * orientation changes in fullscreen mode.
7887          *
7888          * @param {Object} node DOM object which is in fullscreen mode. It is the wrapper element
7889          * around the JSXGraph div.
7890          * @returns {JXG.Board} Reference to the board
7891          * @private
7892          * @see JXG.Board#toFullscreen
7893          *
7894          */
7895         startFullscreenResizeObserver: function(node) {
7896             var that = this;
7897 
7898             if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {
7899                 return this;
7900             }
7901 
7902             this.resizeObserver = new ResizeObserver(function (entries) {
7903                 var inner_id,
7904                     fullscreenElement,
7905                     doc = that.document;
7906 
7907                 if (!that._isResizing) {
7908                     that._isResizing = true;
7909                     window.setTimeout(function () {
7910                         try {
7911                             inner_id = that._fullscreen_inner_id;
7912                             if (doc.fullscreenElement !== undefined) {
7913                                 fullscreenElement = doc.fullscreenElement;
7914                             } else if (doc.webkitFullscreenElement !== undefined) {
7915                                 fullscreenElement = doc.webkitFullscreenElement;
7916                             } else {
7917                                 fullscreenElement = doc.msFullscreenElement;
7918                             }
7919                             if (fullscreenElement !== null) {
7920                                 Env.scaleJSXGraphDiv(fullscreenElement.id, inner_id, doc,
7921                                     Type.evaluate(that.attr.fullscreen.scale));
7922                             }
7923                         } catch (err) {
7924                             that.stopFullscreenResizeObserver(node);
7925                         } finally {
7926                             that._isResizing = false;
7927                         }
7928                     }, that.attr.resize.throttle);
7929                 }
7930             });
7931             this.resizeObserver.observe(node);
7932             return this;
7933         },
7934 
7935         /**
7936          * Remove resize observer to handle orientation changes in fullscreen mode.
7937          * @param {Object} node DOM object which is in fullscreen mode. It is the wrapper element
7938          * around the JSXGraph div.
7939          * @returns {JXG.Board} Reference to the board
7940          * @private
7941          * @see JXG.Board#toFullscreen
7942          */
7943         stopFullscreenResizeObserver: function(node) {
7944             if (!Env.isBrowser || !this.attr.resize || !this.attr.resize.enabled) {
7945                 return this;
7946             }
7947 
7948             if (Type.exists(this.resizeObserver)) {
7949                 this.resizeObserver.unobserve(node);
7950             }
7951             return this;
7952         },
7953 
7954         /**
7955          * Add user activity to the array 'board.userLog'.
7956          *
7957          * @param {String} type Event type, e.g. 'drag'
7958          * @param {Object} obj JSXGraph element object
7959          *
7960          * @see JXG.Board#userLog
7961          * @return {JXG.Board} Reference to the board
7962          */
7963         addLogEntry: function (type, obj, pos) {
7964             var t, id,
7965                 last = this.userLog.length - 1;
7966 
7967             if (Type.exists(obj.elementClass)) {
7968                 id = obj.id;
7969             }
7970             if (Type.evaluate(this.attr.logging.enabled)) {
7971                 t = (new Date()).getTime();
7972                 if (last >= 0 &&
7973                     this.userLog[last].type === type &&
7974                     this.userLog[last].id === id &&
7975                     // Distinguish consecutive drag events of
7976                     // the same element
7977                     t - this.userLog[last].end < 500) {
7978 
7979                     this.userLog[last].end = t;
7980                     this.userLog[last].endpos = pos;
7981                 } else {
7982                     this.userLog.push({
7983                         type: type,
7984                         id: id,
7985                         start: t,
7986                         startpos: pos,
7987                         end: t,
7988                         endpos: pos,
7989                         bbox: this.getBoundingBox(),
7990                         canvas: [this.canvasWidth, this.canvasHeight],
7991                         zoom: [this.zoomX, this.zoomY]
7992                     });
7993                 }
7994             }
7995             return this;
7996         },
7997 
7998         /**
7999          * Function to animate a curve rolling on another curve.
8000          * @param {Curve} c1 JSXGraph curve building the floor where c2 rolls
8001          * @param {Curve} c2 JSXGraph curve which rolls on c1.
8002          * @param {number} start_c1 The parameter t such that c1(t) touches c2. This is the start position of the
8003          *                          rolling process
8004          * @param {Number} stepsize Increase in t in each step for the curve c1
8005          * @param {Number} direction
8006          * @param {Number} time Delay time for setInterval()
8007          * @param {Array} pointlist Array of points which are rolled in each step. This list should contain
8008          *      all points which define c2 and gliders on c2.
8009          *
8010          * @example
8011          *
8012          * // Line which will be the floor to roll upon.
8013          * var line = board.create('curve', [function (t) { return t;}, function (t){ return 1;}], {strokeWidth:6});
8014          * // Center of the rolling circle
8015          * var C = board.create('point',[0,2],{name:'C'});
8016          * // Starting point of the rolling circle
8017          * var P = board.create('point',[0,1],{name:'P', trace:true});
8018          * // Circle defined as a curve. The circle 'starts' at P, i.e. circle(0) = P
8019          * var circle = board.create('curve',[
8020          *           function (t){var d = P.Dist(C),
8021          *                           beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);
8022          *                       t += beta;
8023          *                       return C.X()+d*Math.cos(t);
8024          *           },
8025          *           function (t){var d = P.Dist(C),
8026          *                           beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);
8027          *                       t += beta;
8028          *                       return C.Y()+d*Math.sin(t);
8029          *           },
8030          *           0,2*Math.PI],
8031          *           {strokeWidth:6, strokeColor:'green'});
8032          *
8033          * // Point on circle
8034          * var B = board.create('glider',[0,2,circle],{name:'B', color:'blue',trace:false});
8035          * var roll = board.createRoulette(line, circle, 0, Math.PI/20, 1, 100, [C,P,B]);
8036          * roll.start() // Start the rolling, to be stopped by roll.stop()
8037          *
8038          * </pre><div class='jxgbox' id='JXGe5e1b53c-a036-4a46-9e35-190d196beca5' style='width: 300px; height: 300px;'></div>
8039          * <script type='text/javascript'>
8040          * var brd = JXG.JSXGraph.initBoard('JXGe5e1b53c-a036-4a46-9e35-190d196beca5', {boundingbox: [-5, 5, 5, -5], axis: true, showcopyright:false, shownavigation: false});
8041          * // Line which will be the floor to roll upon.
8042          * var line = brd.create('curve', [function (t) { return t;}, function (t){ return 1;}], {strokeWidth:6});
8043          * // Center of the rolling circle
8044          * var C = brd.create('point',[0,2],{name:'C'});
8045          * // Starting point of the rolling circle
8046          * var P = brd.create('point',[0,1],{name:'P', trace:true});
8047          * // Circle defined as a curve. The circle 'starts' at P, i.e. circle(0) = P
8048          * var circle = brd.create('curve',[
8049          *           function (t){var d = P.Dist(C),
8050          *                           beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);
8051          *                       t += beta;
8052          *                       return C.X()+d*Math.cos(t);
8053          *           },
8054          *           function (t){var d = P.Dist(C),
8055          *                           beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);
8056          *                       t += beta;
8057          *                       return C.Y()+d*Math.sin(t);
8058          *           },
8059          *           0,2*Math.PI],
8060          *           {strokeWidth:6, strokeColor:'green'});
8061          *
8062          * // Point on circle
8063          * var B = brd.create('glider',[0,2,circle],{name:'B', color:'blue',trace:false});
8064          * var roll = brd.createRoulette(line, circle, 0, Math.PI/20, 1, 100, [C,P,B]);
8065          * roll.start() // Start the rolling, to be stopped by roll.stop()
8066          * </script><pre>
8067          */
8068         createRoulette: function (c1, c2, start_c1, stepsize, direction, time, pointlist) {
8069             var brd = this,
8070                 Roulette = function () {
8071                     var alpha = 0,
8072                         Tx = 0,
8073                         Ty = 0,
8074                         t1 = start_c1,
8075                         t2 = Numerics.root(
8076                             function (t) {
8077                                 var c1x = c1.X(t1),
8078                                     c1y = c1.Y(t1),
8079                                     c2x = c2.X(t),
8080                                     c2y = c2.Y(t);
8081 
8082                                 return (c1x - c2x) * (c1x - c2x) + (c1y - c2y) * (c1y - c2y);
8083                             },
8084                             [0, Math.PI * 2]
8085                         ),
8086                         t1_new = 0.0,
8087                         t2_new = 0.0,
8088                         c1dist,
8089                         rotation = brd.create(
8090                             'transform',
8091                             [
8092                                 function () {
8093                                     return alpha;
8094                                 }
8095                             ],
8096                             { type: 'rotate' }
8097                         ),
8098                         rotationLocal = brd.create(
8099                             'transform',
8100                             [
8101                                 function () {
8102                                     return alpha;
8103                                 },
8104                                 function () {
8105                                     return c1.X(t1);
8106                                 },
8107                                 function () {
8108                                     return c1.Y(t1);
8109                                 }
8110                             ],
8111                             { type: 'rotate' }
8112                         ),
8113                         translate = brd.create(
8114                             'transform',
8115                             [
8116                                 function () {
8117                                     return Tx;
8118                                 },
8119                                 function () {
8120                                     return Ty;
8121                                 }
8122                             ],
8123                             { type: 'translate' }
8124                         ),
8125                         // arc length via Simpson's rule.
8126                         arclen = function (c, a, b) {
8127                             var cpxa = Numerics.D(c.X)(a),
8128                                 cpya = Numerics.D(c.Y)(a),
8129                                 cpxb = Numerics.D(c.X)(b),
8130                                 cpyb = Numerics.D(c.Y)(b),
8131                                 cpxab = Numerics.D(c.X)((a + b) * 0.5),
8132                                 cpyab = Numerics.D(c.Y)((a + b) * 0.5),
8133                                 fa = Mat.hypot(cpxa, cpya),
8134                                 fb = Mat.hypot(cpxb, cpyb),
8135                                 fab = Mat.hypot(cpxab, cpyab);
8136 
8137                             return ((fa + 4 * fab + fb) * (b - a)) / 6;
8138                         },
8139                         exactDist = function (t) {
8140                             return c1dist - arclen(c2, t2, t);
8141                         },
8142                         beta = Math.PI / 18,
8143                         beta9 = beta * 9,
8144                         interval = null;
8145 
8146                     this.rolling = function () {
8147                         var h, g, hp, gp, z;
8148 
8149                         t1_new = t1 + direction * stepsize;
8150 
8151                         // arc length between c1(t1) and c1(t1_new)
8152                         c1dist = arclen(c1, t1, t1_new);
8153 
8154                         // find t2_new such that arc length between c2(t2) and c1(t2_new) equals c1dist.
8155                         t2_new = Numerics.root(exactDist, t2);
8156 
8157                         // c1(t) as complex number
8158                         h = new Complex(c1.X(t1_new), c1.Y(t1_new));
8159 
8160                         // c2(t) as complex number
8161                         g = new Complex(c2.X(t2_new), c2.Y(t2_new));
8162 
8163                         hp = new Complex(Numerics.D(c1.X)(t1_new), Numerics.D(c1.Y)(t1_new));
8164                         gp = new Complex(Numerics.D(c2.X)(t2_new), Numerics.D(c2.Y)(t2_new));
8165 
8166                         // z is angle between the tangents of c1 at t1_new, and c2 at t2_new
8167                         z = Complex.C.div(hp, gp);
8168 
8169                         alpha = Math.atan2(z.imaginary, z.real);
8170                         // Normalizing the quotient
8171                         z.div(Complex.C.abs(z));
8172                         z.mult(g);
8173                         Tx = h.real - z.real;
8174 
8175                         // T = h(t1_new)-g(t2_new)*h'(t1_new)/g'(t2_new);
8176                         Ty = h.imaginary - z.imaginary;
8177 
8178                         // -(10-90) degrees: make corners roll smoothly
8179                         if (alpha < -beta && alpha > -beta9) {
8180                             alpha = -beta;
8181                             rotationLocal.applyOnce(pointlist);
8182                         } else if (alpha > beta && alpha < beta9) {
8183                             alpha = beta;
8184                             rotationLocal.applyOnce(pointlist);
8185                         } else {
8186                             rotation.applyOnce(pointlist);
8187                             translate.applyOnce(pointlist);
8188                             t1 = t1_new;
8189                             t2 = t2_new;
8190                         }
8191                         brd.update();
8192                     };
8193 
8194                     this.start = function () {
8195                         if (time > 0) {
8196                             interval = window.setInterval(this.rolling, time);
8197                         }
8198                         return this;
8199                     };
8200 
8201                     this.stop = function () {
8202                         window.clearInterval(interval);
8203                         return this;
8204                     };
8205                     return this;
8206                 };
8207             return new Roulette();
8208         }
8209     }
8210 );
8211 
8212 export default JXG.Board;
8213