1 /*
  2     Copyright 2008-2016
  3         Matthias Ehmann,
  4         Michael Gerhaeuser,
  5         Carsten Miller,
  6         Bianca Valentin,
  7         Alfred Wassermann,
  8         Peter Wilfahrt
  9 
 10     This file is part of JSXGraph.
 11 
 12     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
 13 
 14     You can redistribute it and/or modify it under the terms of the
 15 
 16       * GNU Lesser General Public License as published by
 17         the Free Software Foundation, either version 3 of the License, or
 18         (at your option) any later version
 19       OR
 20       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
 21 
 22     JSXGraph is distributed in the hope that it will be useful,
 23     but WITHOUT ANY WARRANTY; without even the implied warranty of
 24     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 25     GNU Lesser General Public License for more details.
 26 
 27     You should have received a copy of the GNU Lesser General Public License and
 28     the MIT License along with JSXGraph. If not, see <http://www.gnu.org/licenses/>
 29     and <http://opensource.org/licenses/MIT/>.
 30  */
 31 
 32 
 33 /*global JXG: true, define: true, html_sanitize: true*/
 34 /*jslint nomen: true, plusplus: true*/
 35 
 36 /* depends:
 37  jxg
 38  base/constants
 39  */
 40 
 41 /**
 42  * @fileoverview type.js contains several functions to help deal with javascript's weak types. This file mainly consists
 43  * of detector functions which verify if a variable is or is not of a specific type and converter functions that convert
 44  * variables to another type or normalize the type of a variable.
 45  */
 46 
 47 define([
 48     'jxg', 'base/constants'
 49 ], function (JXG, Const) {
 50 
 51     "use strict";
 52 
 53     JXG.extend(JXG, /** @lends JXG */ {
 54         /**
 55          * Checks if the given string is an id within the given board.
 56          * @param {JXG.Board} board
 57          * @param {String} s
 58          * @returns {Boolean}
 59          */
 60         isId: function (board, s) {
 61             return (typeof s === 'string') && !!board.objects[s];
 62         },
 63 
 64         /**
 65          * Checks if the given string is a name within the given board.
 66          * @param {JXG.Board} board
 67          * @param {String} s
 68          * @returns {Boolean}
 69          */
 70         isName: function (board, s) {
 71             return typeof s === 'string' && !!board.elementsByName[s];
 72         },
 73 
 74         /**
 75          * Checks if the given string is a group id within the given board.
 76          * @param {JXG.Board} board
 77          * @param {String} s
 78          * @returns {Boolean}
 79          */
 80         isGroup: function (board, s) {
 81             return typeof s === 'string' && !!board.groups[s];
 82         },
 83 
 84         /**
 85          * Checks if the value of a given variable is of type string.
 86          * @param v A variable of any type.
 87          * @returns {Boolean} True, if v is of type string.
 88          */
 89         isString: function (v) {
 90             return typeof v === "string";
 91         },
 92 
 93         /**
 94          * Checks if the value of a given variable is of type number.
 95          * @param v A variable of any type.
 96          * @returns {Boolean} True, if v is of type number.
 97          */
 98         isNumber: function (v) {
 99             return typeof v === "number" || Object.prototype.toString.call(v) === '[Object Number]';
100         },
101 
102         /**
103          * Checks if a given variable references a function.
104          * @param v A variable of any type.
105          * @returns {Boolean} True, if v is a function.
106          */
107         isFunction: function (v) {
108             return typeof v === "function";
109         },
110 
111         /**
112          * Checks if a given variable references an array.
113          * @param v A variable of any type.
114          * @returns {Boolean} True, if v is of type array.
115          */
116         isArray: function (v) {
117             var r;
118 
119             // use the ES5 isArray() method and if that doesn't exist use a fallback.
120             if (Array.isArray) {
121                 r = Array.isArray(v);
122             } else {
123                 r = (v !== null && typeof v === "object" && typeof v.splice === 'function' && typeof v.join === 'function');
124             }
125 
126             return r;
127         },
128 
129         /**
130          * Tests if the input variable is an Object
131          * @param v
132          */
133         isObject: function (v) {
134             return typeof v === 'object' && !JXG.isArray(v);
135         },
136 
137         /**
138          * Checks if a given variable is a reference of a JSXGraph Point element.
139          * @param v A variable of any type.
140          * @returns {Boolean} True, if v is of type JXG.Point.
141          */
142         isPoint: function (v) {
143             if (v !== null && typeof v === 'object') {
144                 return (v.elementClass === Const.OBJECT_CLASS_POINT);
145             }
146 
147             return false;
148         },
149 
150         /**
151          * Checks if a given variable is a reference of a JSXGraph Point element or an array of length at least two or
152          * a function returning an array of length two or three.
153          * @param {JXG.Board} board
154          * @param v A variable of any type.
155          * @returns {Boolean} True, if v is of type JXG.Point.
156          */
157         isPointType: function (board, v) {
158             var val;
159 
160             if (this.isArray(v)) {
161                 return true;
162             }
163             if (this.isFunction(v)) {
164                 val = v();
165                 if (this.isArray(val) && val.length > 1) {
166                     return true;
167                 }
168             }
169             v = board.select(v);
170             return this.isPoint(v);
171         },
172 
173         /**
174          * Checks if a given variable is neither undefined nor null. You should not use this together with global
175          * variables!
176          * @param v A variable of any type.
177          * @returns {Boolean} True, if v is neither undefined nor null.
178          */
179         exists: (function (undef) {
180             return function (v) {
181                 return !(v === undef || v === null);
182             };
183         }()),
184 
185         /**
186          * Handle default parameters.
187          * @param v Given value
188          * @param d Default value
189          * @returns <tt>d</tt>, if <tt>v</tt> is undefined or null.
190          */
191         def: function (v, d) {
192             if (JXG.exists(v)) {
193                 return v;
194             }
195 
196             return d;
197         },
198 
199         /**
200          * Converts a string containing either <strong>true</strong> or <strong>false</strong> into a boolean value.
201          * @param {String} s String containing either <strong>true</strong> or <strong>false</strong>.
202          * @returns {Boolean} String typed boolean value converted to boolean.
203          */
204         str2Bool: function (s) {
205             if (!JXG.exists(s)) {
206                 return true;
207             }
208 
209             if (typeof s === 'boolean') {
210                 return s;
211             }
212 
213             if (JXG.isString(s)) {
214                 return (s.toLowerCase() === 'true');
215             }
216 
217             return false;
218         },
219 
220         /**
221          * Convert a String, a number or a function into a function. This method is used in Transformation.js
222          * @param {JXG.Board} board Reference to a JSXGraph board. It is required to resolve dependencies given
223          * by a GEONE<sub>X</sub>T string, thus it must be a valid reference only in case one of the param
224          * values is of type string.
225          * @param {Array} param An array containing strings, numbers, or functions.
226          * @param {Number} n Length of <tt>param</tt>.
227          * @returns {Function} A function taking one parameter k which specifies the index of the param element
228          * to evaluate.
229          */
230         createEvalFunction: function (board, param, n) {
231             var f = [], i;
232 
233             for (i = 0; i < n; i++) {
234                 f[i] = JXG.createFunction(param[i], board, '', true);
235             }
236 
237             return function (k) {
238                 return f[k]();
239             };
240         },
241 
242         /**
243          * Convert a String, number or function into a function.
244          * @param {String|Number|Function} term A variable of type string, function or number.
245          * @param {JXG.Board} board Reference to a JSXGraph board. It is required to resolve dependencies given
246          * by a GEONE<sub>X</sub>T string, thus it must be a valid reference only in case one of the param
247          * values is of type string.
248          * @param {String} variableName Only required if evalGeonext is set to true. Describes the variable name
249          * of the variable in a GEONE<sub>X</sub>T string given as term.
250          * @param {Boolean} [evalGeonext=true] Set this true, if term should be treated as a GEONE<sub>X</sub>T string.
251          * @returns {Function} A function evaluation the value given by term or null if term is not of type string,
252          * function or number.
253          */
254         createFunction: function (term, board, variableName, evalGeonext) {
255             var f = null;
256 
257             if ((!JXG.exists(evalGeonext) || evalGeonext) && JXG.isString(term)) {
258                 // Convert GEONExT syntax into  JavaScript syntax
259                 //newTerm = JXG.GeonextParser.geonext2JS(term, board);
260                 //return new Function(variableName,'return ' + newTerm + ';');
261 
262                 //term = JXG.GeonextParser.replaceNameById(term, board);
263                 //term = JXG.GeonextParser.geonext2JS(term, board);
264                 f = board.jc.snippet(term, true, variableName, true);
265             } else if (JXG.isFunction(term)) {
266                 f = term;
267             } else if (JXG.isNumber(term)) {
268                 /** @ignore */
269                 f = function () {
270                     return term;
271                 };
272             } else if (JXG.isString(term)) {
273                 // In case of string function like fontsize
274                 /** @ignore */
275                 f = function () {
276                     return term;
277                 };
278             }
279 
280             if (f !== null) {
281                 f.origin = term;
282             }
283 
284             return f;
285         },
286 
287         /**
288          *  Test if the parents array contains existing points. If instead parents contains coordinate arrays or function returning coordinate arrays
289          *  free points with these coordinates are created.
290          *
291          * @param {JXG.Board} board Board object
292          * @param {Array} parents Array containing parent elements for a new object. This array may contain
293          *    <ul>
294          *      <li> {@link JXG.Point} objects
295          *      <li> {@link JXG.Element#name} of {@link JXG.Point} objects
296          *      <li> {@link JXG.Element#id} of {@link JXG.Point} objects
297          *      <li> Coordinates of points given as array of numbers of length two or three, e.g. [2, 3].
298          *      <li> Coordinates of points given as array of functions of length two or three. Each function returns one coordinate, e.g.
299          *           [function(){ return 2; }, function(){ return 3; }]
300          *      <li> Function returning coordinates, e.g. function() { return [2, 3]; }
301          *    </ul>
302          *  In the last three cases a new point will be created.
303          * @param {String} attrClass Main attribute class of newly created points, see {@link JXG@copyAttributes}
304          * @param {Array} attrArray List of subtype attributes for the newly created points. The list of subtypes is mapped to the list of new points.
305          * @returns {Array} List of newly created {@link JXG.Point} elements or false if not all returned elements are points.
306          */
307         providePoints: function (board, parents, attributes, attrClass, attrArray) {
308             var i, j,
309                 len,
310                 lenAttr = 0,
311                 points = [], attr, val;
312 
313             if (!this.isArray(parents)) {
314                 parents = [parents];
315             }
316             len = parents.length;
317             if (JXG.exists(attrArray)) {
318                 lenAttr = attrArray.length;
319             }
320             if (lenAttr === 0) {
321                 attr = this.copyAttributes(attributes, board.options, attrClass);
322             }
323 
324             for (i = 0; i < len; ++i) {
325                 if (lenAttr > 0) {
326                     j = Math.min(i, lenAttr - 1);
327                     attr = this.copyAttributes(attributes, board.options, attrClass, attrArray[j]);
328                 }
329                 if (this.isArray(parents[i]) && parents[i].length > 1) {
330                     points.push(board.create('point', parents[i], attr));
331                 } else if (this.isFunction(parents[i])) {
332                     val = parents[i]();
333                     if (this.isArray(val) && (val.length > 1)) {
334                         points.push(board.create('point', [parents[i]], attr));
335                     }
336                 } else {
337                     points.push(board.select(parents[i]));
338                 }
339 
340                 if (!this.isPoint(points[i])) {
341                     return false;
342                 }
343             }
344 
345             return points;
346         },
347 
348         /**
349          * Generates a function which calls the function fn in the scope of owner.
350          * @param {Function} fn Function to call.
351          * @param {Object} owner Scope in which fn is executed.
352          * @returns {Function} A function with the same signature as fn.
353          */
354         bind: function (fn, owner) {
355             return function () {
356                 return fn.apply(owner, arguments);
357             };
358         },
359 
360         /**
361          * If <tt>val</tt> is a function, it will be evaluated without giving any parameters, else the input value
362          * is just returned.
363          * @param val Could be anything. Preferably a number or a function.
364          * @returns If <tt>val</tt> is a function, it is evaluated and the result is returned. Otherwise <tt>val</tt> is returned.
365          */
366         evaluate: function (val) {
367             if (JXG.isFunction(val)) {
368                 return val();
369             }
370 
371             return val;
372         },
373 
374         /**
375          * Search an array for a given value.
376          * @param {Array} array
377          * @param value
378          * @param {String} [sub] Use this property if the elements of the array are objects.
379          * @returns {Number} The index of the first appearance of the given value, or
380          * <tt>-1</tt> if the value was not found.
381          */
382         indexOf: function (array, value, sub) {
383             var i, s = JXG.exists(sub);
384 
385             if (Array.indexOf && !s) {
386                 return array.indexOf(value);
387             }
388 
389             for (i = 0; i < array.length; i++) {
390                 if ((s && array[i][sub] === value) || (!s && array[i] === value)) {
391                     return i;
392                 }
393             }
394 
395             return -1;
396         },
397 
398         /**
399          * Eliminates duplicate entries in an array consisting of numbers and strings.
400          * @param {Array} a An array of numbers and/or strings.
401          * @returns {Array} The array with duplicate entries eliminated.
402          */
403         eliminateDuplicates: function (a) {
404             var i,
405                 len = a.length,
406                 result = [],
407                 obj = {};
408 
409             for (i = 0; i < len; i++) {
410                 obj[a[i]] = 0;
411             }
412 
413             for (i in obj) {
414                 if (obj.hasOwnProperty(i)) {
415                     result.push(i);
416                 }
417             }
418 
419             return result;
420         },
421 
422         /**
423          * Swaps to array elements.
424          * @param {Array} arr
425          * @param {Number} i
426          * @param {Number} j
427          * @returns {Array} Reference to the given array.
428          */
429         swap: function (arr, i, j) {
430             var tmp;
431 
432             tmp = arr[i];
433             arr[i] = arr[j];
434             arr[j] = tmp;
435 
436             return arr;
437         },
438 
439         /**
440          * Generates a copy of an array and removes the duplicate entries. The original
441          * Array will be altered.
442          * @param {Array} arr
443          * @returns {Array}
444          */
445         uniqueArray: function (arr) {
446             var i, j, isArray, ret = [];
447 
448             if (arr.length === 0) {
449                 return [];
450             }
451 
452             for (i = 0; i < arr.length; i++) {
453                 isArray = JXG.isArray(arr[i]);
454 
455                 for (j = i + 1; j < arr.length; j++) {
456                     if (isArray && JXG.cmpArrays(arr[i], arr[j])) {
457                         arr[i] = [];
458                     } else if (!isArray && arr[i] === arr[j]) {
459                         arr[i] = '';
460                     }
461                 }
462             }
463 
464             j = 0;
465 
466             for (i = 0; i < arr.length; i++) {
467                 isArray = JXG.isArray(arr[i]);
468 
469                 if (!isArray && arr[i] !== '') {
470                     ret[j] = arr[i];
471                     j += 1;
472                 } else if (isArray && arr[i].length !== 0) {
473                     ret[j] = (arr[i].slice(0));
474                     j += 1;
475                 }
476             }
477 
478             arr = ret;
479             return ret;
480         },
481 
482         /**
483          * Checks if an array contains an element equal to <tt>val</tt> but does not check the type!
484          * @param {Array} arr
485          * @param val
486          * @returns {Boolean}
487          */
488         isInArray: function (arr, val) {
489             return JXG.indexOf(arr, val) > -1;
490         },
491 
492         /**
493          * Converts an array of {@link JXG.Coords} objects into a coordinate matrix.
494          * @param {Array} coords
495          * @param {Boolean} split
496          * @returns {Array}
497          */
498         coordsArrayToMatrix: function (coords, split) {
499             var i,
500                 x = [],
501                 m = [];
502 
503             for (i = 0; i < coords.length; i++) {
504                 if (split) {
505                     x.push(coords[i].usrCoords[1]);
506                     m.push(coords[i].usrCoords[2]);
507                 } else {
508                     m.push([coords[i].usrCoords[1], coords[i].usrCoords[2]]);
509                 }
510             }
511 
512             if (split) {
513                 m = [x, m];
514             }
515 
516             return m;
517         },
518 
519         /**
520          * Compare two arrays.
521          * @param {Array} a1
522          * @param {Array} a2
523          * @returns {Boolean} <tt>true</tt>, if the arrays coefficients are of same type and value.
524          */
525         cmpArrays: function (a1, a2) {
526             var i;
527 
528             // trivial cases
529             if (a1 === a2) {
530                 return true;
531             }
532 
533             if (a1.length !== a2.length) {
534                 return false;
535             }
536 
537             for (i = 0; i < a1.length; i++) {
538                 if (this.isArray(a1[i]) && this.isArray(a2[i])) {
539                     if (!this.cmpArrays(a1[i], a2[i])) {
540                         return false;
541                     }
542                 }
543                 else if (a1[i] !== a2[i]) {
544                     return false;
545                 }
546             }
547 
548             return true;
549         },
550 
551         /**
552          * Removes an element from the given array
553          * @param {Array} ar
554          * @param el
555          * @returns {Array}
556          */
557         removeElementFromArray: function (ar, el) {
558             var i;
559 
560             for (i = 0; i < ar.length; i++) {
561                 if (ar[i] === el) {
562                     ar.splice(i, 1);
563                     return ar;
564                 }
565             }
566 
567             return ar;
568         },
569 
570         /**
571          * Truncate a number <tt>n</tt> after <tt>p</tt> decimals.
572          * @param {Number} n
573          * @param {Number} p
574          * @returns {Number}
575          */
576         trunc: function (n, p) {
577             p = JXG.def(p, 0);
578 
579             /*jslint bitwise: true*/
580 
581             /*
582              * The performance gain of this bitwise trick is marginal and the behavior
583              * is different from toFixed: toFixed rounds, the bitweise operation truncateds
584              */
585             //if (p === 0) {
586             //    n = ~n;
587             //    n = ~n;
588             //} else {
589             n = n.toFixed(p);
590             //}
591 
592             return n;
593         },
594 
595         /**
596          * Truncate a number <tt>val</tt> automatically.
597          * @param val
598          * @returns {Number}
599          */
600         autoDigits: function (val) {
601             var x = Math.abs(val);
602 
603             if (x > 0.1) {
604                 x = val.toFixed(2);
605             } else if (x >= 0.01) {
606                 x = val.toFixed(4);
607             } else if (x >= 0.0001) {
608                 x = val.toFixed(6);
609             } else {
610                 x = val;
611             }
612             return x;
613         },
614 
615         /**
616          * Extracts the keys of a given object.
617          * @param object The object the keys are to be extracted
618          * @param onlyOwn If true, hasOwnProperty() is used to verify that only keys are collected
619          * the object owns itself and not some other object in the prototype chain.
620          * @returns {Array} All keys of the given object.
621          */
622         keys: function (object, onlyOwn) {
623             var keys = [], property;
624 
625             // the caller decides if we use hasOwnProperty
626             /*jslint forin:true*/
627             for (property in object) {
628                 if (onlyOwn) {
629                     if (object.hasOwnProperty(property)) {
630                         keys.push(property);
631                     }
632                 } else {
633                     keys.push(property);
634                 }
635             }
636             /*jslint forin:false*/
637 
638             return keys;
639         },
640 
641         /**
642          * This outputs an object with a base class reference to the given object. This is useful if
643          * you need a copy of an e.g. attributes object and want to overwrite some of the attributes
644          * without changing the original object.
645          * @param {Object} obj Object to be embedded.
646          * @returns {Object} An object with a base class reference to <tt>obj</tt>.
647          */
648         clone: function (obj) {
649             var cObj = {};
650 
651             cObj.prototype = obj;
652 
653             return cObj;
654         },
655 
656         /**
657          * Embeds an existing object into another one just like {@link #clone} and copies the contents of the second object
658          * to the new one. Warning: The copied properties of obj2 are just flat copies.
659          * @param {Object} obj Object to be copied.
660          * @param {Object} obj2 Object with data that is to be copied to the new one as well.
661          * @returns {Object} Copy of given object including some new/overwritten data from obj2.
662          */
663         cloneAndCopy: function (obj, obj2) {
664             var r,
665                 cObj = function () {};
666 
667             cObj.prototype = obj;
668 
669             // no hasOwnProperty on purpose
670             /*jslint forin:true*/
671             /*jshint forin:true*/
672 
673             for (r in obj2) {
674                 cObj[r] = obj2[r];
675             }
676 
677             /*jslint forin:false*/
678             /*jshint forin:false*/
679 
680             return cObj;
681         },
682 
683         /**
684          * Recursively merges obj2 into obj1. Contrary to {@link JXG#deepCopy} this won't create a new object
685          * but instead will
686          * @param {Object} obj1
687          * @param {Object} obj2
688          * @returns {Object}
689          */
690         merge: function (obj1, obj2) {
691             var i, j;
692 
693             for (i in obj2) {
694                 if (obj2.hasOwnProperty(i)) {
695                     if (this.isArray(obj2[i])) {
696                         if (!obj1[i]) {
697                             obj1[i] = [];
698                         }
699 
700                         for (j = 0; j < obj2[i].length; j++) {
701                             if (typeof obj2[i][j] === 'object') {
702                                 obj1[i][j] = this.merge(obj1[i][j], obj2[i][j]);
703                             } else {
704                                 obj1[i][j] = obj2[i][j];
705                             }
706                         }
707                     } else if (typeof obj2[i] === 'object') {
708                         if (!obj1[i]) {
709                             obj1[i] = {};
710                         }
711 
712                         obj1[i] = this.merge(obj1[i], obj2[i]);
713                     } else {
714                         obj1[i] = obj2[i];
715                     }
716                 }
717             }
718 
719             return obj1;
720         },
721 
722         /**
723          * Creates a deep copy of an existing object, i.e. arrays or sub-objects are copied component resp.
724          * element-wise instead of just copying the reference. If a second object is supplied, the two objects
725          * are merged into one object. The properties of the second object have priority.
726          * @param {Object} obj This object will be copied.
727          * @param {Object} obj2 This object will merged into the newly created object
728          * @param {Boolean} [toLower=false] If true the keys are convert to lower case. This is needed for visProp, see JXG#copyAttributes
729          * @returns {Object} copy of obj or merge of obj and obj2.
730          */
731         deepCopy: function (obj, obj2, toLower) {
732             var c, i, prop, i2;
733 
734             toLower = toLower || false;
735 
736             if (typeof obj !== 'object' || obj === null) {
737                 return obj;
738             }
739 
740             // missing hasOwnProperty is on purpose in this function
741             if (this.isArray(obj)) {
742                 c = [];
743                 for (i = 0; i < obj.length; i++) {
744                     prop = obj[i];
745                     if (typeof prop === 'object') {
746                         // We certainly do not want to recurse into a JSXGraph object.
747                         // This would for sure result in an infinite recursion.
748                         // As alternative we copy the id of the object.
749                         if (this.exists(prop.board)) {
750                             c[i] = prop.id;
751                         } else {
752                             c[i] = this.deepCopy(prop);
753                         }
754                     } else {
755                         c[i] = prop;
756                     }
757                 }
758             } else {
759                 c = {};
760                 for (i in obj) {
761                     i2 = toLower ? i.toLowerCase() : i;
762                     prop = obj[i];
763                     if (prop !== null && typeof prop === 'object') {
764                         if (this.exists(prop.board)) {
765                             c[i2] = prop.id;
766                         } else {
767                             c[i2] = this.deepCopy(prop);
768                         }
769                     } else {
770                         c[i2] = prop;
771                     }
772                 }
773 
774                 for (i in obj2) {
775                     i2 = toLower ? i.toLowerCase() : i;
776 
777                     prop = obj2[i];
778                     if (typeof prop === 'object') {
779                         if (JXG.isArray(prop) || !JXG.exists(c[i2])) {
780                             c[i2] = this.deepCopy(prop);
781                         } else {
782                             c[i2] = this.deepCopy(c[i2], prop, toLower);
783                         }
784                     } else {
785                         c[i2] = prop;
786                     }
787                 }
788             }
789 
790             return c;
791         },
792 
793         /**
794          * Generates an attributes object that is filled with default values from the Options object
795          * and overwritten by the user speciified attributes.
796          * @param {Object} attributes user specified attributes
797          * @param {Object} options defaults options
798          * @param {String} s variable number of strings, e.g. 'slider', subtype 'point1'.
799          * @returns {Object} The resulting attributes object
800          */
801         copyAttributes: function (attributes, options, s) {
802             var a, i, len, o, isAvail,
803                 primitives = {
804                     'circle': 1,
805                     'curve': 1,
806                     'image': 1,
807                     'line': 1,
808                     'point': 1,
809                     'polygon': 1,
810                     'text': 1,
811                     'ticks': 1,
812                     'integral': 1
813                 };
814 
815 
816             len = arguments.length;
817             if (len < 3 || primitives[s]) {
818                 // default options from Options.elements
819                 a = JXG.deepCopy(options.elements, null, true);
820             } else {
821                 a = {};
822             }
823 
824             // Only the layer of the main element is set.
825             if (len < 4 && this.exists(s) && this.exists(options.layer[s])) {
826                 a.layer = options.layer[s];
827             }
828 
829             // default options from specific elements
830             o = options;
831             isAvail = true;
832             for (i = 2; i < len; i++) {
833                 if (JXG.exists(o[arguments[i]])) {
834                     o = o[arguments[i]];
835                 } else {
836                     isAvail = false;
837                     break;
838                 }
839             }
840             if (isAvail) {
841                 a = JXG.deepCopy(a, o, true);
842             }
843 
844             // options from attributes
845             o = attributes;
846             isAvail = true;
847             for (i = 3; i < len; i++) {
848                 if (JXG.exists(o[arguments[i]])) {
849                     o = o[arguments[i]];
850                 } else {
851                     isAvail = false;
852                     break;
853                 }
854             }
855             if (isAvail) {
856                 this.extend(a, o, null, true);
857             }
858 
859             // Special treatment of labels
860             o = options;
861             isAvail = true;
862             for (i = 2; i < len; i++) {
863                 if (JXG.exists(o[arguments[i]])) {
864                     o = o[arguments[i]];
865                 } else {
866                     isAvail = false;
867                     break;
868                 }
869             }
870             if (isAvail && JXG.exists(o.label)) {
871                 a.label =  JXG.deepCopy(o.label, a.label);
872             }
873             a.label = JXG.deepCopy(options.label, a.label);
874 
875             return a;
876         },
877 
878         /**
879          * Copy all prototype methods from object "superObject" to object
880          * "subObject". The constructor of superObject will be available
881          * in subObject as subObject.constructor[constructorName].
882          * @param {Object} subObj A JavaScript object which receives new methods.
883          * @param {Object} superObj A JavaScript object which lends its prototype methods to subObject
884          * @returns {String} constructorName Under this name the constructor of superObj will be available
885          * in subObject.
886          * @private
887          */
888         copyPrototypeMethods: function (subObject, superObject, constructorName) {
889             var key;
890 
891             subObject.prototype[constructorName] = superObject.prototype.constructor;
892             for (key in superObject.prototype)  {
893                 subObject.prototype[key] = superObject.prototype[key];
894             }
895         },
896 
897         /**
898          * Converts a JavaScript object into a JSON string.
899          * @param {Object} obj A JavaScript object, functions will be ignored.
900          * @param {Boolean} [noquote=false] No quotes around the name of a property.
901          * @returns {String} The given object stored in a JSON string.
902          */
903         toJSON: function (obj, noquote) {
904             var list, prop, i, s, val;
905 
906             noquote = JXG.def(noquote, false);
907 
908             // check for native JSON support:
909             if (typeof JSON && JSON.stringify && !noquote) {
910                 try {
911                     s = JSON.stringify(obj);
912                     return s;
913                 } catch (e) {
914                     // if something goes wrong, e.g. if obj contains functions we won't return
915                     // and use our own implementation as a fallback
916                 }
917             }
918 
919             switch (typeof obj) {
920             case 'object':
921                 if (obj) {
922                     list = [];
923 
924                     if (JXG.isArray(obj)) {
925                         for (i = 0; i < obj.length; i++) {
926                             list.push(JXG.toJSON(obj[i], noquote));
927                         }
928 
929                         return '[' + list.join(',') + ']';
930                     }
931 
932                     for (prop in obj) {
933                         if (obj.hasOwnProperty(prop)) {
934                             try {
935                                 val = JXG.toJSON(obj[prop], noquote);
936                             } catch (e2) {
937                                 val = '';
938                             }
939 
940                             if (noquote) {
941                                 list.push(prop + ':' + val);
942                             } else {
943                                 list.push('"' + prop + '":' + val);
944                             }
945                         }
946                     }
947 
948                     return '{' + list.join(',') + '} ';
949                 }
950                 return 'null';
951             case 'string':
952                 return '\'' + obj.replace(/(["'])/g, '\\$1') + '\'';
953             case 'number':
954             case 'boolean':
955                 return obj.toString();
956             }
957 
958             return '0';
959         },
960 
961         /**
962          * Resets visPropOld.
963          * @param {JXG.GeometryElement} el
964          * @returns {GeometryElement}
965          */
966         clearVisPropOld: function (el) {
967             el.visPropOld = {
968                 strokecolor: '',
969                 strokeopacity: '',
970                 strokewidth: '',
971                 fillcolor: '',
972                 fillopacity: '',
973                 shadow: false,
974                 firstarrow: false,
975                 lastarrow: false,
976                 cssclass: '',
977                 fontsize: -1,
978                 left: -100000,
979                 top: -100000
980             };
981 
982             return el;
983         },
984 
985         /**
986          * Checks if an object contains a key, whose value equals to val.
987          * @param {Object} obj
988          * @param val
989          * @returns {Boolean}
990          */
991         isInObject: function (obj, val) {
992             var el;
993 
994             for (el in obj) {
995                 if (obj.hasOwnProperty(el)) {
996                     if (obj[el] === val) {
997                         return true;
998                     }
999                 }
1000             }
1001 
1002             return false;
1003         },
1004 
1005         /**
1006          * Replaces all occurences of & by &amp;, > by &gt;, and < by &lt;.
1007          * @param {String} str
1008          * @returns {String}
1009          */
1010         escapeHTML: function (str) {
1011             return str.replace(/&/g, '&').replace(/</g, '<').replace(/>/g, '>');
1012         },
1013 
1014         /**
1015          * Eliminates all substrings enclosed by < and > and replaces all occurences of
1016          * &amp; by &, &gt; by >, and &lt; by <.
1017          * @param {String} str
1018          * @returns {String}
1019          */
1020         unescapeHTML: function (str) {
1021             // this regex is NOT insecure. We are replacing everything found with ''
1022             /*jslint regexp:true*/
1023             return str.replace(/<\/?[^>]+>/gi, '').replace(/&/g, '&').replace(/</g, '<').replace(/>/g, '>');
1024         },
1025 
1026         /**
1027          * Makes a string lower case except for the first character which will be upper case.
1028          * @param {String} str Arbitrary string
1029          * @returns {String} The capitalized string.
1030          */
1031         capitalize: function (str) {
1032             return str.charAt(0).toUpperCase() + str.substring(1).toLowerCase();
1033         },
1034 
1035         /**
1036          * Make numbers given as strings nicer by removing all unnecessary leading and trailing zeroes.
1037          * @param {String} str
1038          * @returns {String}
1039          */
1040         trimNumber: function (str) {
1041             str = str.replace(/^0+/, '');
1042             str = str.replace(/0+$/, '');
1043 
1044             if (str[str.length - 1] === '.' || str[str.length - 1] === ',') {
1045                 str = str.slice(0, -1);
1046             }
1047 
1048             if (str[0] === '.' || str[0] === ',') {
1049                 str = "0" + str;
1050             }
1051 
1052             return str;
1053         },
1054 
1055         /**
1056          * Filter an array of elements.
1057          * @param {Array} list
1058          * @param {Object|function} filter
1059          * @returns {Array}
1060          */
1061         filterElements: function (list, filter) {
1062             var i, f, item, flower, value, visPropValue, pass,
1063                 l = list.length,
1064                 result = [];
1065 
1066             if (typeof filter !== 'function' && typeof filter !== 'object') {
1067                 return result;
1068             }
1069 
1070             for (i = 0; i < l; i++) {
1071                 pass = true;
1072                 item = list[i];
1073 
1074                 if (typeof filter === 'object') {
1075                     for (f in filter) {
1076                         if (filter.hasOwnProperty(f)) {
1077                             flower = f.toLowerCase();
1078 
1079                             if (typeof item[f] === 'function') {
1080                                 value = item[f]();
1081                             } else {
1082                                 value = item[f];
1083                             }
1084 
1085                             if (item.visProp && typeof item.visProp[flower] === 'function') {
1086                                 visPropValue = item.visProp[flower]();
1087                             } else {
1088                                 visPropValue = item.visProp && item.visProp[flower];
1089                             }
1090 
1091                             if (typeof filter[f] === 'function') {
1092                                 pass = filter[f](value) || filter[f](visPropValue);
1093                             } else {
1094                                 pass = (value === filter[f] || visPropValue === filter[f]);
1095                             }
1096 
1097                             if (!pass) {
1098                                 break;
1099                             }
1100                         }
1101                     }
1102                 } else if (typeof filter === 'function') {
1103                     pass = filter(item);
1104                 }
1105 
1106                 if (pass) {
1107                     result.push(item);
1108                 }
1109             }
1110 
1111             return result;
1112         },
1113 
1114         /**
1115          * Remove all leading and trailing whitespaces from a given string.
1116          * @param {String} str
1117          * @returns {String}
1118          */
1119         trim: function (str) {
1120             str = str.replace(/^\s+/, '');
1121             str = str.replace(/\s+$/, '');
1122 
1123             return str;
1124         },
1125 
1126         /**
1127          * Convert HTML tags to entities or use html_sanitize if the google caja html sanitizer is available.
1128          * @param {String} str
1129          * @param {Boolean} caja
1130          * @returns {String} Sanitized string
1131          */
1132         sanitizeHTML: function (str, caja) {
1133             if (typeof html_sanitize === 'function' && caja) {
1134                 return html_sanitize(str, function () {}, function (id) { return id; });
1135             }
1136 
1137             if (str) {
1138                 str = str.replace(/</g, '<').replace(/>/g, '>');
1139             }
1140 
1141             return str;
1142         },
1143 
1144         /**
1145          * If <tt>s</tt> is a slider, it returns the sliders value, otherwise it just returns the given value.
1146          * @param {*} s
1147          * @returns {*} s.Value() if s is an element of type slider, s otherwise
1148          */
1149         evalSlider: function (s) {
1150             if (s && s.type === Const.OBJECT_TYPE_GLIDER && typeof s.Value === 'function') {
1151                 s = s.Value();
1152             }
1153 
1154             return s;
1155         }
1156     });
1157 
1158     return JXG;
1159 });
1160