1 /*
  2     Copyright 2008-2017
  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*/
 34 /*jslint nomen: true, plusplus: true*/
 35 
 36 /* depends:
 37  jxg
 38  base/constants
 39  base/coords
 40  math/statistics
 41  utils/type
 42  base/element
 43   elements:
 44    segment
 45    transform
 46  */
 47 
 48 define([
 49     'jxg', 'base/constants', 'base/coords', 'math/statistics', 'math/geometry', 'utils/type', 'base/element', 'base/line', 'base/transformation'
 50 ], function (JXG, Const, Coords, Statistics, Geometry, Type, GeometryElement, Line, Transform) {
 51 
 52     "use strict";
 53 
 54     /**
 55      * Creates a new instance of JXG.Polygon.
 56      * @class Polygon stores all style and functional properties that are required
 57      * to draw and to interactact with a polygon.
 58      * @param {JXG.Board} board Reference to the board the polygon is to be drawn on.
 59      * @param {Array} vertices Unique identifiers for the points defining the polygon.
 60      * Last point must be first point. Otherwise, the first point will be added at the list.
 61      * @param {Object} attributes An object which contains properties as given in {@link JXG.Options.elements}
 62      * and {@link JXG.Options.polygon}.
 63      * @constructor
 64      * @extends JXG.GeometryElement
 65      */
 66 
 67     JXG.Polygon = function (board, vertices, attributes) {
 68         this.constructor(board, attributes, Const.OBJECT_TYPE_POLYGON, Const.OBJECT_CLASS_AREA);
 69 
 70         var i, l, len, j,
 71             attr_line = Type.copyAttributes(attributes, board.options, 'polygon', 'borders');
 72 
 73         this.withLines = attributes.withlines;
 74         this.attr_line = attr_line;
 75 
 76         /**
 77          * References to the points defining the polygon. The last vertex is the same as the first vertex.
 78          * @type Array
 79          */
 80         this.vertices = [];
 81         for (i = 0; i < vertices.length; i++) {
 82             this.vertices[i] = this.board.select(vertices[i]);
 83         }
 84 
 85         // Close the polygon
 86         if (this.vertices.length > 0 && this.vertices[this.vertices.length - 1].id !== this.vertices[0].id) {
 87             this.vertices.push(this.vertices[0]);
 88         }
 89 
 90         /**
 91          * References to the border lines of the polygon.
 92          * @type Array
 93          */
 94         this.borders = [];
 95 
 96         if (this.withLines) {
 97             len = this.vertices.length - 1;
 98             for (j = 0; j < len; j++) {
 99                 // This sets the "correct" labels for the first triangle of a construction.
100                 i = (j + 1) % len;
101                 attr_line.id = attr_line.ids && attr_line.ids[i];
102                 attr_line.name = attr_line.names && attr_line.names[i];
103                 attr_line.strokecolor = (Type.isArray(attr_line.colors) && attr_line.colors[i % attr_line.colors.length]) ||
104                                             attr_line.strokecolor;
105                 attr_line.visible = Type.exists(attributes.borders.visible) ? attributes.borders.visible : attributes.visible;
106 
107                 if (attr_line.strokecolor === false) {
108                     attr_line.strokecolor = 'none';
109                 }
110 
111                 l = board.create('segment', [this.vertices[i], this.vertices[i + 1]], attr_line);
112                 l.dump = false;
113                 this.borders[i] = l;
114                 l.parentPolygon = this;
115             }
116         }
117         this.inherits.push(this.vertices, this.borders);
118 
119         // Register polygon at board
120         // This needs to be done BEFORE the points get this polygon added in their descendants list
121         this.id = this.board.setId(this, 'Py');
122 
123         // Add polygon as child to defining points
124         for (i = 0; i < this.vertices.length - 1; i++) {
125             this.board.select(this.vertices[i]).addChild(this);
126         }
127 
128         this.board.renderer.drawPolygon(this);
129         this.board.finalizeAdding(this);
130 
131         this.createGradient();
132         this.elType = 'polygon';
133 
134         // create label
135         this.createLabel();
136 
137         this.methodMap = JXG.deepCopy(this.methodMap, {
138             borders: 'borders',
139             vertices: 'vertices',
140             A: 'Area',
141             Area: 'Area',
142             Perimeter: 'Perimeter',
143             L: 'Perimeter',
144             Length: 'Perimeter',
145             boundingBox: 'boundingBox',
146             bounds: 'bounds',
147             addPoints: 'addPoints',
148             insertPoints: 'insertPoints',
149             removePoints: 'removePoints'
150         });
151     };
152 
153     JXG.Polygon.prototype = new GeometryElement();
154 
155     JXG.extend(JXG.Polygon.prototype, /** @lends JXG.Polygon.prototype */ {
156         /**
157          * Checks whether (x,y) is near the polygon.
158          * @param {Number} x Coordinate in x direction, screen coordinates.
159          * @param {Number} y Coordinate in y direction, screen coordinates.
160          * @returns {Boolean} Returns true, if (x,y) is inside or at the boundary the polygon, otherwise false.
161          */
162         hasPoint: function (x, y) {
163 
164             var i, j, len, c = false;
165 
166             if (Type.evaluate(this.visProp.hasinnerpoints)) {
167                 // All points of the polygon trigger hasPoint: inner and boundary points
168                 len = this.vertices.length;
169                 // See http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
170                 // for a reference of Jordan method
171                 for (i = 0, j = len - 2; i < len - 1; j = i++) {
172                     if (((this.vertices[i].coords.scrCoords[2] > y) !== (this.vertices[j].coords.scrCoords[2] > y)) &&
173                             (x < (this.vertices[j].coords.scrCoords[1] - this.vertices[i].coords.scrCoords[1]) * (y - this.vertices[i].coords.scrCoords[2]) /
174                             (this.vertices[j].coords.scrCoords[2] - this.vertices[i].coords.scrCoords[2]) + this.vertices[i].coords.scrCoords[1])) {
175                         c = !c;
176                     }
177                 }
178                 if (c) {
179                     return true;
180                 }
181             }
182 
183             // Only boundary points trigger hasPoint
184             // We additionally test the boundary also in case hasInnerPoints.
185             // Since even if the above test has failed, the strokewidth may be large and (x, y) may
186             // be inside of hasPoint() of a vertices.
187             len = this.borders.length;
188             for (i = 0; i < len; i++) {
189                 if (this.borders[i].hasPoint(x, y)) {
190                     c = true;
191                     break;
192                 }
193             }
194 
195             return c;
196         },
197 
198         /**
199          * Uses the boards renderer to update the polygon.
200          */
201         updateRenderer: function () {
202             var wasReal, i, len;
203 
204             if (!this.needsUpdate) {
205                 return this;
206             }
207 
208             if (this.visPropCalc.visible) {
209                 wasReal = this.isReal;
210 
211                 len = this.vertices.length;
212                 this.isReal = true;
213                 for (i = 0; i < len; ++i) {
214                     if (!this.vertices[i].isReal) {
215                         this.isReal = false;
216                         break;
217                     }
218                 }
219 
220                 if (wasReal && !this.isReal) {
221                     this.updateVisibility(false);
222                 }
223             }
224 
225             if (this.visPropCalc.visible) {
226                 this.board.renderer.updatePolygon(this);
227             }
228 
229             /* Update the label if visible. */
230             if (this.hasLabel && this.visPropCalc.visible && this.label &&
231                 this.label.visPropCalc.visible && this.isReal) {
232 
233                 this.label.update();
234                 this.board.renderer.updateText(this.label);
235             }
236 
237             // Update rendNode display
238             this.setDisplayRendNode();
239             // if (this.visPropCalc.visible !== this.visPropOld.visible) {
240             //     this.board.renderer.display(this, this.visPropCalc.visible);
241             //     this.visPropOld.visible = this.visPropCalc.visible;
242             //
243             //     if (this.hasLabel) {
244             //         this.board.renderer.display(this.label, this.label.visPropCalc.visible);
245             //     }
246             // }
247 
248             this.needsUpdate = false;
249             return this;
250         },
251 
252         /**
253          * return TextAnchor
254          */
255         getTextAnchor: function () {
256             var a, b, x, y, i;
257 
258             if (this.vertices.length === 0) {
259                 return new Coords(Const.COORDS_BY_USER, [1, 0, 0], this.board);
260             }
261 
262             a = this.vertices[0].X();
263             b = this.vertices[0].Y();
264             x = a;
265             y = b;
266             for (i = 0; i < this.vertices.length; i++) {
267                 if (this.vertices[i].X() < a) {
268                     a = this.vertices[i].X();
269                 }
270 
271                 if (this.vertices[i].X() > x) {
272                     x = this.vertices[i].X();
273                 }
274 
275                 if (this.vertices[i].Y() > b) {
276                     b = this.vertices[i].Y();
277                 }
278 
279                 if (this.vertices[i].Y() < y) {
280                     y = this.vertices[i].Y();
281                 }
282             }
283 
284             return new Coords(Const.COORDS_BY_USER, [(a + x) * 0.5, (b + y) * 0.5], this.board);
285         },
286 
287         getLabelAnchor: JXG.shortcut(JXG.Polygon.prototype, 'getTextAnchor'),
288 
289         // documented in geometry element
290         cloneToBackground: function () {
291             var copy = {}, er;
292 
293             copy.id = this.id + 'T' + this.numTraces;
294             this.numTraces++;
295             copy.vertices = this.vertices;
296             copy.visProp = Type.deepCopy(this.visProp, this.visProp.traceattributes, true);
297             copy.visProp.layer = this.board.options.layer.trace;
298             copy.board = this.board;
299             Type.clearVisPropOld(copy);
300 
301             er = this.board.renderer.enhancedRendering;
302             this.board.renderer.enhancedRendering = true;
303             this.board.renderer.drawPolygon(copy);
304             this.board.renderer.enhancedRendering = er;
305             this.traces[copy.id] = copy.rendNode;
306 
307             return this;
308         },
309 
310         /**
311          * Hide the polygon including its border lines. It will still exist but not visible on the board.
312          * @param {Boolean} [borderless=false] If set to true, the polygon is treated as a polygon without
313          * borders, i.e. the borders will not be hidden.
314          */
315         hideElement: function (borderless) {
316             var i;
317 
318             JXG.deprecated('Element.hideElement()', 'Element.setDisplayRendNode()');
319 
320             this.visPropCalc.visible = false;
321             this.board.renderer.display(this, false);
322 
323             if (!borderless) {
324                 for (i = 0; i < this.borders.length; i++) {
325                     this.borders[i].hideElement();
326                 }
327             }
328 
329             if (this.hasLabel && Type.exists(this.label)) {
330                 this.label.hiddenByParent = true;
331                 if (this.label.visPropCalc.visible) {
332                     this.label.hideElement();
333                 }
334             }
335         },
336 
337         /**
338          * Make the element visible.
339          * @param {Boolean} [borderless=false] If set to true, the polygon is treated as a polygon without
340          * borders, i.e. the borders will not be shown.
341          */
342         showElement: function (borderless) {
343             var i;
344 
345             JXG.deprecated('Element.showElement()', 'Element.setDisplayRendNode()');
346 
347             this.visPropCalc.visible = true;
348             this.board.renderer.display(this, true);
349 
350             if (!borderless) {
351                 for (i = 0; i < this.borders.length; i++) {
352                     this.borders[i].showElement().updateRenderer();
353                 }
354             }
355 
356             if (Type.exists(this.label) && this.hasLabel && this.label.hiddenByParent) {
357                 this.label.hiddenByParent = false;
358                 if (!this.label.visPropCalc.visible) {
359                     this.label.showElement().updateRenderer();
360                 }
361             }
362             return this;
363         },
364 
365         /**
366          * Area of (not self-intersecting) polygon
367          * @returns {Number} Area of (not self-intersecting) polygon
368          */
369         Area: function () {
370             return Math.abs(Geometry.signedPolygon(this.vertices, true));
371         },
372 
373         /**
374          * Perimeter of polygon.
375          * @returns {Number} Perimeter of polygon in user units.
376          *
377          * @example
378          * var p = [[0.0, 2.0], [2.0, 1.0], [4.0, 6.0], [1.0, 3.0]];
379          *
380          * var pol = board.create('polygon', p, {hasInnerPoints: true});
381          * var t = board.create('text', [5, 5, function() { return pol.Perimeter(); }]);
382          * </pre><div class="jxgbox" id="b10b734d-89fc-4b9d-b4a7-e3f0c1c6bf77" style="width: 400px; height: 400px;"></div>
383          * <script type="text/javascript">
384          *  (function () {
385          *   var board = JXG.JSXGraph.initBoard('b10b734d-89fc-4b9d-b4a7-e3f0c1c6bf77', {boundingbox: [-1, 9, 9, -1], axis: false, showcopyright: false, shownavigation: false}),
386          *       p = [[0.0, 2.0], [2.0, 1.0], [4.0, 6.0], [1.0, 4.0]],
387          *       cc1 = board.create('polygon', p, {hasInnerPoints: true}),
388          *       t = board.create('text', [5, 5, function() { return cc1.Perimeter(); }]);
389          *  })();
390          * </script><pre>
391          *
392          */
393         Perimeter: function() {
394             var i,
395                 len = this.vertices.length,
396                 val = 0.0;
397 
398             for (i = 1; i < len; ++i) {
399                 val += this.vertices[i].Dist(this.vertices[i - 1]);
400             }
401 
402             return val;
403         },
404 
405         /**
406          * Bounding box of a polygon. The bounding box is an array of four numbers: the first two numbers
407          * determine the upper left corner, the last two number determine the lower right corner of the bounding box.
408          *
409          * The width and height of a polygon can then determined like this:
410          * @example
411          * var box = polygon.boundingBox();
412          * var width = box[2] - box[0];
413          * var height = box[1] - box[3];
414          *
415          * @returns {Array} Array containing four numbers: [minX, maxY, maxX, minY]
416          */
417         boundingBox: function () {
418             var box = [0, 0, 0, 0], i, v,
419                 le = this.vertices.length - 1;
420 
421             if (le === 0) {
422                 return box;
423             }
424             box[0] = this.vertices[0].X();
425             box[2] = box[0];
426             box[1] = this.vertices[0].Y();
427             box[3] = box[1];
428 
429             for (i = 1; i < le; ++i) {
430                 v = this.vertices[i].X();
431                 if (v < box[0]) {
432                     box[0] = v;
433                 } else if (v > box[2]) {
434                     box[2] = v;
435                 }
436 
437                 v = this.vertices[i].Y();
438                 if (v > box[1]) {
439                     box[1] = v;
440                 } else if (v < box[3]) {
441                     box[3] = v;
442                 }
443             }
444 
445             return box;
446         },
447 
448         // already documented in GeometryElement
449         bounds: function () {
450             return this.boundingBox();
451         },
452 
453         /**
454          * This method removes the SVG or VML nodes of the lines and the filled area from the renderer, to remove
455          * the object completely you should use {@link JXG.Board#removeObject}.
456          */
457         remove: function () {
458             var i;
459 
460             for (i = 0; i < this.borders.length; i++) {
461                 this.board.removeObject(this.borders[i]);
462             }
463 
464             GeometryElement.prototype.remove.call(this);
465         },
466 
467         /**
468          * Finds the index to a given point reference.
469          * @param {JXG.Point} p Reference to an element of type {@link JXG.Point}
470          */
471         findPoint: function (p) {
472             var i;
473 
474             if (!Type.isPoint(p)) {
475                 return -1;
476             }
477 
478             for (i = 0; i < this.vertices.length; i++) {
479                 if (this.vertices[i].id === p.id) {
480                     return i;
481                 }
482             }
483 
484             return -1;
485         },
486 
487         /**
488          * Add more points to the polygon. The new points will be inserted at the end.
489          * @param {JXG.Point} p Arbitrary number of points
490          * @returns {JXG.Polygon} Reference to the polygon
491          */
492         addPoints: function (p) {
493             var args = Array.prototype.slice.call(arguments);
494 
495             return this.insertPoints.apply(this, [this.vertices.length - 2].concat(args));
496         },
497 
498         /**
499          * Adds more points to the vertex list of the polygon, starting with index <tt><i</tt>
500          * @param {Number} idx The position where the new vertices are inserted, starting with 0.
501          * @param {JXG.Point} p Arbitrary number of points to insert.
502          * @returns {JXG.Polygon} Reference to the polygon object
503          */
504         insertPoints: function (idx, p) {
505             var i, npoints = [], tmp;
506 
507             if (arguments.length === 0) {
508                 return this;
509             }
510 
511 
512             if (idx < 0 || idx > this.vertices.length - 2) {
513                 return this;
514             }
515 
516             for (i = 1; i < arguments.length; i++) {
517                 if (Type.isPoint(arguments[i])) {
518                     npoints.push(arguments[i]);
519                 }
520             }
521 
522             tmp = this.vertices.slice(0, idx + 1).concat(npoints);
523             this.vertices = tmp.concat(this.vertices.slice(idx + 1));
524 
525             if (this.withLines) {
526                 tmp = this.borders.slice(0, idx);
527                 this.board.removeObject(this.borders[idx]);
528 
529                 for (i = 0; i < npoints.length; i++) {
530                     tmp.push(this.board.create('segment', [this.vertices[idx + i], this.vertices[idx + i + 1]], this.attr_line));
531                 }
532 
533                 tmp.push(this.board.create('segment', [this.vertices[idx + npoints.length], this.vertices[idx + npoints.length + 1]], this.attr_line));
534                 this.borders = tmp.concat(this.borders.slice(idx + 1));
535             }
536 
537             this.board.update();
538 
539             return this;
540         },
541 
542         /**
543          * Removes given set of vertices from the polygon
544          * @param {JXG.Point} p Arbitrary number of vertices as {@link JXG.Point} elements or index numbers
545          * @returns {JXG.Polygon} Reference to the polygon
546          */
547         removePoints: function (p) {
548             var i, j, idx, nvertices = [], nborders = [],
549                 nidx = [], partition = [];
550 
551             // partition:
552             // in order to keep the borders which could be recycled, we have to partition
553             // the set of removed points. I.e. if the points 1, 2, 5, 6, 7, 10 are removed,
554             // the partitions are
555             //       1-2, 5-7, 10-10
556             // this gives us the borders, that can be removed and the borders we have to create.
557 
558 
559             // remove the last vertex which is identical to the first
560             this.vertices = this.vertices.slice(0, this.vertices.length - 1);
561 
562             // collect all valid parameters as indices in nidx
563             for (i = 0; i < arguments.length; i++) {
564                 idx = arguments[i];
565                 if (Type.isPoint(idx)) {
566                     idx = this.findPoint(idx);
567                 }
568 
569                 if (Type.isNumber(idx) && idx > -1 && idx < this.vertices.length && Type.indexOf(nidx, idx) === -1) {
570                     nidx.push(idx);
571                 }
572             }
573 
574             // remove the polygon from each removed point's children
575             for (i = 0; i < nidx.length; i++) {
576                 this.vertices[nidx[i]].removeChild(this);
577             }
578 
579             // sort the elements to be eliminated
580             nidx = nidx.sort();
581             nvertices = this.vertices.slice();
582             nborders = this.borders.slice();
583 
584             // initialize the partition
585             if (this.withLines) {
586                 partition.push([nidx[nidx.length - 1]]);
587             }
588 
589             // run through all existing vertices and copy all remaining ones to nvertices
590             // compute the partition
591             for (i = nidx.length - 1; i > -1; i--) {
592                 nvertices[nidx[i]] = -1;
593 
594                 if (this.withLines && (nidx[i] - 1 > nidx[i - 1])) {
595                     partition[partition.length - 1][1] = nidx[i];
596                     partition.push([nidx[i - 1]]);
597                 }
598             }
599 
600             // finalize the partition computation
601             if (this.withLines) {
602                 partition[partition.length - 1][1] = nidx[0];
603             }
604 
605             // update vertices
606             this.vertices = [];
607             for (i = 0; i < nvertices.length; i++) {
608                 if (Type.isPoint(nvertices[i])) {
609                     this.vertices.push(nvertices[i]);
610                 }
611             }
612             if (this.vertices[this.vertices.length - 1].id !== this.vertices[0].id) {
613                 this.vertices.push(this.vertices[0]);
614             }
615 
616             // delete obsolete and create missing borders
617             if (this.withLines) {
618                 for (i = 0; i < partition.length; i++) {
619                     for (j = partition[i][1] - 1; j < partition[i][0] + 1; j++) {
620                         // special cases
621                         if (j < 0) {
622                             // first vertex is removed, so the last border has to be removed, too
623                             j = 0;
624                             this.board.removeObject(this.borders[nborders.length - 1]);
625                             nborders[nborders.length - 1] = -1;
626                         } else if (j > nborders.length - 1) {
627                             j = nborders.length - 1;
628                         }
629 
630                         this.board.removeObject(this.borders[j]);
631                         nborders[j] = -1;
632                     }
633 
634                     // only create the new segment if it's not the closing border. the closing border is getting a special treatment at the end
635                     // the if clause is newer than the min/max calls inside createSegment; i'm sure this makes the min/max calls obsolete, but
636                     // just to be sure...
637                     if (partition[i][1] !== 0 && partition[i][0] !== nvertices.length - 1) {
638                         nborders[partition[i][0] - 1] = this.board.create('segment', [nvertices[Math.max(partition[i][1] - 1, 0)], nvertices[Math.min(partition[i][0] + 1, this.vertices.length - 1)]], this.attr_line);
639                     }
640                 }
641 
642                 this.borders = [];
643                 for (i = 0; i < nborders.length; i++) {
644                     if (nborders[i] !== -1) {
645                         this.borders.push(nborders[i]);
646                     }
647                 }
648 
649                 // if the first and/or the last vertex is removed, the closing border is created at the end.
650                 if (partition[0][1] === this.vertices.length - 1 || partition[partition.length - 1][1] === 0) {
651                     this.borders.push(this.board.create('segment', [this.vertices[0], this.vertices[this.vertices.length - 2]], this.attr_line));
652                 }
653             }
654 
655             this.board.update();
656 
657             return this;
658         },
659 
660         // documented in element.js
661         getParents: function () {
662             this.setParents(this.vertices);
663             return this.parents;
664         },
665 
666         getAttributes: function () {
667             var attr = GeometryElement.prototype.getAttributes.call(this), i;
668 
669             if (this.withLines) {
670                 attr.lines = attr.lines || {};
671                 attr.lines.ids = [];
672                 attr.lines.colors = [];
673 
674                 for (i = 0; i < this.borders.length; i++) {
675                     attr.lines.ids.push(this.borders[i].id);
676                     attr.lines.colors.push(this.borders[i].visProp.strokecolor);
677                 }
678             }
679 
680             return attr;
681         },
682 
683         snapToGrid: function () {
684             var i, force;
685 
686             if (Type.evaluate(this.visProp.snaptogrid)) {
687                 force = true;
688             } else {
689                 force = false;
690             }
691 
692             for (i = 0; i < this.vertices.length; i++) {
693                 this.vertices[i].handleSnapToGrid(force, true);
694             }
695 
696         },
697 
698         /**
699          * Moves the polygon by the difference of two coordinates.
700          * @param {Number} method The type of coordinates used here. Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
701          * @param {Array} coords coordinates in screen/user units
702          * @param {Array} oldcoords previous coordinates in screen/user units
703          * @returns {JXG.Polygon} this element
704          */
705         setPositionDirectly: function (method, coords, oldcoords) {
706             var dc, t, i, len,
707                 c = new Coords(method, coords, this.board),
708                 oldc = new Coords(method, oldcoords, this.board);
709 
710             len = this.vertices.length - 1;
711             for (i = 0; i < len; i++) {
712                 if (!this.vertices[i].draggable()) {
713                     return this;
714                 }
715             }
716 
717             dc = Statistics.subtract(c.usrCoords, oldc.usrCoords);
718             t = this.board.create('transform', dc.slice(1), {type: 'translate'});
719             t.applyOnce(this.vertices.slice(0, -1));
720 
721             return this;
722         },
723 
724         /**
725         * Algorithm by Sutherland and Hodgman to compute the intersection of two convex polygons.
726         * The polygon itself is the clipping polygon, it expects as parameter a polygon to be clipped.
727         * See <a href="https://en.wikipedia.org/wiki/Sutherland%E2%80%93Hodgman_algorithm">wikipedia entry</a>.
728         * Called by {@link JXG.Polygon#intersect}.
729         *
730         * @private
731         *
732         * @param {JXG.Polygon} polygon Polygon which will be clipped.
733         *
734         * @returns {Array} of (normalized homogeneous user) coordinates (i.e. [z, x, y], where z==1 in most cases,
735         *   representing the vertices of the intersection polygon.
736         *
737         */
738         sutherlandHodgman: function(polygon) {
739             // First the two polygons are sorted counter clockwise
740             var clip = JXG.Math.Geometry.sortVertices(this.vertices),   // "this" is the clipping polygon
741                 subject = JXG.Math.Geometry.sortVertices(polygon.vertices), // "polygon" is the subject polygon
742 
743                 lenClip = clip.length - 1,
744                 lenSubject = subject.length - 1,
745                 lenIn,
746 
747                 outputList = [],
748                 inputList, i, j, S, E, cross,
749 
750 
751                 // Determines if the point c3 is right of the line through c1 and c2.
752                 // Since the polygons are sorted counter clockwise, "right of" and therefore >= is needed here
753                 isInside = function(c1, c2, c3) {
754                     return ((c2[1] - c1[1]) * (c3[2] - c1[2]) - (c2[2] - c1[2]) * (c3[1] - c1[1])) >= 0;
755                 };
756 
757             for (i = 0; i < lenSubject; i++) {
758                 outputList.push(subject[i]);
759             }
760 
761             for (i = 0; i < lenClip; i++) {
762                 inputList = outputList.slice(0);
763                 lenIn = inputList.length;
764                 outputList = [];
765 
766                 S = inputList[lenIn - 1];
767 
768                 for (j = 0; j < lenIn; j++) {
769                     E = inputList[j];
770                     if (isInside(clip[i], clip[i + 1], E)) {
771                         if (!isInside(clip[i], clip[i + 1], S)) {
772                             cross = JXG.Math.Geometry.meetSegmentSegment(S, E, clip[i], clip[i + 1]);
773                             cross[0][1] /= cross[0][0];
774                             cross[0][2] /= cross[0][0];
775                             cross[0][0] = 1;
776                             outputList.push(cross[0]);
777                         }
778                         outputList.push(E);
779                     } else if (isInside(clip[i], clip[i + 1], S)) {
780                         cross = JXG.Math.Geometry.meetSegmentSegment(S, E, clip[i], clip[i + 1]);
781                         cross[0][1] /= cross[0][0];
782                         cross[0][2] /= cross[0][0];
783                         cross[0][0] = 1;
784                         outputList.push(cross[0]);
785                     }
786                     S = E;
787                 }
788             }
789 
790             return outputList;
791         },
792 
793         /**
794          * Generic method for the intersection of this polygon with another polygon.
795          * The parent object is the clipping polygon, it expects as parameter a polygon to be clipped.
796          * Both polygons have to be convex.
797          * Calls {@link JXG.Polygon#sutherlandHodgman}.
798          *
799          * @param {JXG.Polygon} polygon Polygon which will be clipped.
800          *
801          * @returns {Array} of (normalized homogeneous user) coordinates (i.e. [z, x, y], where z==1 in most cases,
802          *   representing the vertices of the intersection polygon.
803          *
804          * @example
805          *  // Static intersection of two polygons pol1 and pol2
806          *  var pol1 = board.create('polygon', [[-2, 3], [-4, -3], [2, 0], [4, 4]], {
807          *                name:'pol1', withLabel: true,
808          *                fillColor: 'yellow'
809          *             });
810          *  var pol2 = board.create('polygon', [[-2, -3], [-4, 1], [0, 4], [5, 1]], {
811          *                name:'pol2', withLabel: true
812          *             });
813          *
814          *  // Static version:
815          *  // the intersection polygon does not adapt to changes of pol1 or pol2.
816          *  var pol3 = board.create('polygon', pol1.intersect(pol2), {fillColor: 'blue'});
817          * </pre><div class="jxgbox" id="d1fe5ea9-309f-494a-af07-ee3d033acb7c" style="width: 300px; height: 300px;"></div>
818          * <script type="text/javascript">
819          *   (function() {
820          *       var board = JXG.JSXGraph.initBoard('d1fe5ea9-309f-494a-af07-ee3d033acb7c', {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
821          *       // Intersect two polygons pol1 and pol2
822          *       var pol1 = board.create('polygon', [[-2, 3], [-4, -3], [2, 0], [4, 4]], {
823          *                name:'pol1', withLabel: true,
824          *                fillColor: 'yellow'
825          *             });
826          *       var pol2 = board.create('polygon', [[-2, -3], [-4, 1], [0, 4], [5, 1]], {
827          *                name:'pol2', withLabel: true
828          *             });
829          *
830          *       // Static version: the intersection polygon does not adapt to changes of pol1 or pol2.
831          *       var pol3 = board.create('polygon', pol1.intersect(pol2), {fillColor: 'blue'});
832          *   })();
833          * </script><pre>
834          *
835          * @example
836          *  // Dynamic intersection of two polygons pol1 and pol2
837          *  var pol1 = board.create('polygon', [[-2, 3], [-4, -3], [2, 0], [4, 4]], {
838          *                name:'pol1', withLabel: true,
839          *                fillColor: 'yellow'
840          *             });
841          *  var pol2 = board.create('polygon', [[-2, -3], [-4, 1], [0, 4], [5, 1]], {
842          *                name:'pol2', withLabel: true
843          *             });
844          *
845          *  // Dynamic version:
846          *  // the intersection polygon does  adapt to changes of pol1 or pol2.
847          *  // For this a curve element is used.
848          *  var curve = board.create('curve', [[],[]], {fillColor: 'blue', fillOpacity: 0.4});
849          *  curve.updateDataArray = function() {
850          *      var mat = JXG.Math.transpose(pol1.intersect(pol2));
851          *
852          *      if (mat.length == 3) {
853          *          this.dataX = mat[1];
854          *          this.dataY = mat[2];
855          *      } else {
856          *          this.dataX = [];
857          *          this.dataY = [];
858          *      }
859          *  };
860          *  board.update();
861          * </pre><div class="jxgbox" id="f870d516-ca1a-4140-8fe3-5d64fb42e5f2" style="width: 300px; height: 300px;"></div>
862          * <script type="text/javascript">
863          *   (function() {
864          *       var board = JXG.JSXGraph.initBoard('f870d516-ca1a-4140-8fe3-5d64fb42e5f2', {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
865          *       // Intersect two polygons pol1 and pol2
866          *       var pol1 = board.create('polygon', [[-2, 3], [-4, -3], [2, 0], [4, 4]], {
867          *                name:'pol1', withLabel: true,
868          *                fillColor: 'yellow'
869          *             });
870          *       var pol2 = board.create('polygon', [[-2, -3], [-4, 1], [0, 4], [5, 1]], {
871          *                name:'pol2', withLabel: true
872          *             });
873          *
874          *  // Dynamic version:
875          *  // the intersection polygon does  adapt to changes of pol1 or pol2.
876          *  // For this a curve element is used.
877          *    var curve = board.create('curve', [[],[]], {fillColor: 'blue', fillOpacity: 0.4});
878          *    curve.updateDataArray = function() {
879          *        var mat = JXG.Math.transpose(pol1.intersect(pol2));
880          *
881          *        if (mat.length == 3) {
882          *            this.dataX = mat[1];
883          *            this.dataY = mat[2];
884          *        } else {
885          *            this.dataX = [];
886          *            this.dataY = [];
887          *        }
888          *    };
889          *    board.update();
890          *   })();
891          * </script><pre>
892          *
893          */
894         intersect: function(polygon) {
895             return this.sutherlandHodgman(polygon);
896         }
897 
898 
899     });
900 
901 
902     /**
903      * @class A polygon is an area enclosed by a set of border lines which are determined by
904      * <ul>
905      *    <li> a list of points or
906      *    <li> a list of coordinate arrays or
907      *    <li> a function returning a list of coordinate arrays.
908      * </ul>
909      * Each two consecutive points of the list define a line.
910      * @pseudo
911      * @constructor
912      * @name Polygon
913      * @type Polygon
914      * @augments JXG.Polygon
915      * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
916      * @param {Array} vertices The polygon's vertices. If the first and the last vertex don't match the first one will be
917      * added to the array by the creator.
918      * @example
919      * var p1 = board.create('point', [0.0, 2.0]);
920      * var p2 = board.create('point', [2.0, 1.0]);
921      * var p3 = board.create('point', [4.0, 6.0]);
922      * var p4 = board.create('point', [1.0, 4.0]);
923      *
924      * var pol = board.create('polygon', [p1, p2, p3, p4]);
925      * </pre><div class="jxgbox" id="682069e9-9e2c-4f63-9b73-e26f8a2b2bb1" style="width: 400px; height: 400px;"></div>
926      * <script type="text/javascript">
927      *  (function () {
928      *   var board = JXG.JSXGraph.initBoard('682069e9-9e2c-4f63-9b73-e26f8a2b2bb1', {boundingbox: [-1, 9, 9, -1], axis: false, showcopyright: false, shownavigation: false}),
929      *       p1 = board.create('point', [0.0, 2.0]),
930      *       p2 = board.create('point', [2.0, 1.0]),
931      *       p3 = board.create('point', [4.0, 6.0]),
932      *       p4 = board.create('point', [1.0, 4.0]),
933      *       cc1 = board.create('polygon', [p1, p2, p3, p4]);
934      *  })();
935      * </script><pre>
936      *
937      * @example
938      * var p = [[0.0, 2.0], [2.0, 1.0], [4.0, 6.0], [1.0, 3.0]];
939      *
940      * var pol = board.create('polygon', p, {hasInnerPoints: true});
941      * </pre><div class="jxgbox" id="9f9a5946-112a-4768-99ca-f30792bcdefb" style="width: 400px; height: 400px;"></div>
942      * <script type="text/javascript">
943      *  (function () {
944      *   var board = JXG.JSXGraph.initBoard('9f9a5946-112a-4768-99ca-f30792bcdefb', {boundingbox: [-1, 9, 9, -1], axis: false, showcopyright: false, shownavigation: false}),
945      *       p = [[0.0, 2.0], [2.0, 1.0], [4.0, 6.0], [1.0, 4.0]],
946      *       cc1 = board.create('polygon', p, {hasInnerPoints: true});
947      *  })();
948      * </script><pre>
949      *
950      * @example
951      *   var f1 = function() { return [0.0, 2.0]; },
952      *       f2 = function() { return [2.0, 1.0]; },
953      *       f3 = function() { return [4.0, 6.0]; },
954      *       f4 = function() { return [1.0, 4.0]; },
955      *       cc1 = board.create('polygon', [f1, f2, f3, f4]);
956      *
957      * </pre><div class="jxgbox" id="ceb09915-b783-44db-adff-7877ae3534c8" style="width: 400px; height: 400px;"></div>
958      * <script type="text/javascript">
959      *  (function () {
960      *   var board = JXG.JSXGraph.initBoard('ceb09915-b783-44db-adff-7877ae3534c8', {boundingbox: [-1, 9, 9, -1], axis: false, showcopyright: false, shownavigation: false}),
961      *       f1 = function() { return [0.0, 2.0]; },
962      *       f2 = function() { return [2.0, 1.0]; },
963      *       f3 = function() { return [4.0, 6.0]; },
964      *       f4 = function() { return [1.0, 4.0]; },
965      *       cc1 = board.create('polygon', [f1, f2, f3, f4]);
966      *  })();
967      * </script><pre>
968      */
969     JXG.createPolygon = function (board, parents, attributes) {
970         var el, i, points = [],
971             attr, p;
972 
973         points = Type.providePoints(board, parents, attributes, 'polygon', ['vertices']);
974         if (points === false) {
975             throw new Error("JSXGraph: Can't create polygon with parent types other than 'point' and 'coordinate arrays' or a function returning an array of coordinates");
976         }
977 
978         attr = Type.copyAttributes(attributes, board.options, 'polygon');
979         el = new JXG.Polygon(board, points, attr);
980         el.isDraggable = true;
981 
982         return el;
983     };
984 
985 
986     /**
987      * @class Constructs a regular polygon. It needs two points which define the base line and the number of vertices.
988      * @pseudo
989      * @description Constructs a regular polygon. It needs two points which define the base line and the number of vertices, or a set of points.
990      * @constructor
991      * @name RegularPolygon
992      * @type Polygon
993      * @augments Polygon
994      * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
995      * @param {JXG.Point_JXG.Point_Number} p1,p2,n The constructed regular polygon has n vertices and the base line defined by p1 and p2.
996      * @example
997      * var p1 = board.create('point', [0.0, 2.0]);
998      * var p2 = board.create('point', [2.0, 1.0]);
999      *
1000      * var pol = board.create('regularpolygon', [p1, p2, 5]);
1001      * </pre><div class="jxgbox" id="682069e9-9e2c-4f63-9b73-e26f8a2b2bb1" style="width: 400px; height: 400px;"></div>
1002      * <script type="text/javascript">
1003      *  (function () {
1004      *   var board = JXG.JSXGraph.initBoard('682069e9-9e2c-4f63-9b73-e26f8a2b2bb1', {boundingbox: [-1, 9, 9, -1], axis: false, showcopyright: false, shownavigation: false}),
1005      *       p1 = board.create('point', [0.0, 2.0]),
1006      *       p2 = board.create('point', [2.0, 1.0]),
1007      *       cc1 = board.create('regularpolygon', [p1, p2, 5]);
1008      *  })();
1009      * </script><pre>
1010      * @example
1011      * var p1 = board.create('point', [0.0, 2.0]);
1012      * var p2 = board.create('point', [4.0,4.0]);
1013      * var p3 = board.create('point', [2.0,0.0]);
1014      *
1015      * var pol = board.create('regularpolygon', [p1, p2, p3]);
1016      * </pre><div class="jxgbox" id="096a78b3-bd50-4bac-b958-3be5e7df17ed" style="width: 400px; height: 400px;"></div>
1017      * <script type="text/javascript">
1018      * (function () {
1019      *   var board = JXG.JSXGraph.initBoard('096a78b3-bd50-4bac-b958-3be5e7df17ed', {boundingbox: [-1, 9, 9, -1], axis: false, showcopyright: false, shownavigation: false}),
1020      *       p1 = board.create('point', [0.0, 2.0]),
1021      *       p2 = board.create('point', [4.0, 4.0]),
1022      *       p3 = board.create('point', [2.0,0.0]),
1023      *       cc1 = board.create('regularpolygon', [p1, p2, p3]);
1024      * })();
1025      * </script><pre>
1026      */
1027     JXG.createRegularPolygon = function (board, parents, attributes) {
1028         var el, i, n,
1029             p = [], rot, c, len, pointsExist, attr;
1030 
1031         len = parents.length;
1032         n = parents[len - 1];
1033 
1034         if (Type.isNumber(n) && (parents.length !== 3 || n < 3)) {
1035             throw new Error("JSXGraph: A regular polygon needs two point types and a number > 2 as input.");
1036         }
1037 
1038         if (Type.isNumber(board.select(n))) { // Regular polygon given by 2 points and a number
1039             len--;
1040             pointsExist = false;
1041         } else {                              // Regular polygon given by n points
1042             n = len;
1043             pointsExist = true;
1044         }
1045 
1046         p = Type.providePoints(board, parents.slice(0, len), attributes, 'regularpolygon', ['vertices']);
1047         if (p === false) {
1048             throw new Error("JSXGraph: Can't create regular polygon with parent types other than 'point' and 'coordinate arrays' or a function returning an array of coordinates");
1049         }
1050 
1051         attr = Type.copyAttributes(attributes, board.options, 'regularpolygon', 'vertices');
1052         for (i = 2; i < n; i++) {
1053             rot = board.create('transform', [Math.PI * (2 - (n - 2) / n), p[i - 1]], {type: 'rotate'});
1054             if (pointsExist) {
1055                 p[i].addTransform(p[i - 2], rot);
1056                 p[i].fullUpdate();
1057             } else {
1058                 if (Type.isArray(attr.ids) && attr.ids.length >= n - 2) {
1059                     attr.id = attr.ids[i - 2];
1060                 }
1061                 p[i] = board.create('point', [p[i - 2], rot], attr);
1062                 p[i].type = Const.OBJECT_TYPE_CAS;
1063 
1064                 // The next two lines of code are needed to make regular polgonmes draggable
1065                 // The new helper points are set to be draggable.
1066                 p[i].isDraggable = true;
1067                 p[i].visProp.fixed = false;
1068             }
1069         }
1070 
1071         attr = Type.copyAttributes(attributes, board.options, 'regularpolygon');
1072         el = board.create('polygon', p, attr);
1073         el.elType = 'regularpolygon';
1074 
1075         return el;
1076     };
1077 
1078     JXG.registerElement('polygon', JXG.createPolygon);
1079     JXG.registerElement('regularpolygon', JXG.createRegularPolygon);
1080 
1081     return {
1082         Polygon: JXG.Polygon,
1083         createPolygon: JXG.createPolygon,
1084         createRegularPolygon: JXG.createRegularPolygon
1085     };
1086 });
1087