1 /*
  2     Copyright 2008,2009
  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: you can redistribute it and/or modify
 13     it under the terms of the GNU Lesser General Public License as published by
 14     the Free Software Foundation, either version 3 of the License, or
 15     (at your option) any later version.
 16 
 17     JSXGraph is distributed in the hope that it will be useful,
 18     but WITHOUT ANY WARRANTY; without even the implied warranty of
 19     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 20     GNU Lesser General Public License for more details.
 21 
 22     You should have received a copy of the GNU Lesser General Public License
 23     along with JSXGraph.  If not, see <http://www.gnu.org/licenses/>.
 24 */
 25 
 26 /**
 27  * Creates a new instance of JXG.Polygon.
 28  * @class Polygon stores all style and functional properties that are required
 29  * to draw and to interactact with a polygon.
 30  * @param {JXG.Board} board Reference to the board the polygon is to be drawn on.
 31  * @param {Array} vertices Unique identifiers for the points defining the polygon.
 32  * Last point must be first point. Otherwise, the first point will be added at the list.
 33  * @param {Object} attributes An object which contains properties as given in {@link JXG.Options.elements}
 34  * and {@link JXG.Options.polygon}.
 35  * @constructor
 36  * @extends JXG.GeometryElement
 37  */
 38 
 39 JXG.Polygon = function (board, vertices, attributes) {
 40     this.constructor(board, attributes, JXG.OBJECT_TYPE_POLYGON, JXG.OBJECT_CLASS_AREA);
 41 
 42     var i, vertex, l,
 43         attr_line = JXG.copyAttributes(attributes, board.options, 'polygon', 'borders');
 44 
 45     this.withLines = attributes.withlines;
 46     this.attr_line = attr_line;
 47 
 48     /**
 49      * References to the points defining the polygon. The last vertex is the same as the first vertex.
 50      * @type Array
 51      */
 52     this.vertices = [];
 53     for(i=0; i<vertices.length; i++) {
 54        vertex = JXG.getRef(this.board, vertices[i]);
 55        this.vertices[i] = vertex;
 56     }
 57 
 58     if(this.vertices[this.vertices.length-1] != this.vertices[0]) {
 59         this.vertices.push(this.vertices[0]);
 60     }
 61 
 62     /**
 63      * References to the border lines of the polygon.
 64      * @type Array
 65      */
 66     this.borders = [];
 67     if (this.withLines) {
 68         for(i = 0; i < this.vertices.length - 1; i++) {
 69             attr_line.id = attr_line.ids && attr_line.ids[i];
 70             attr_line.strokecolor = JXG.isArray(attr_line.colors) && attr_line.colors[i % attr_line.colors.length] || attr_line.strokecolor;
 71             if (attr_line.strokecolor===false) attr_line.strokecolor = 'none';
 72             l = JXG.createSegment(board, [this.vertices[i], this.vertices[i+1]], attr_line);
 73             l.dump = false;
 74             this.borders[i] = l;
 75             l.parentPolygon = this;
 76         }
 77     }
 78 
 79     // Add polygon as child to defining points
 80     for(i=0; i<this.vertices.length-1; i++) { // last vertex is first vertex
 81         vertex = JXG.getReference(this.board, this.vertices[i]);
 82         vertex.addChild(this);
 83     }
 84 
 85     // create label
 86     this.createLabel();
 87 
 88     /* Register polygon at board */
 89     this.id = this.board.setId(this, 'Py');
 90     this.board.renderer.drawPolygon(this);
 91     this.board.finalizeAdding(this);
 92 
 93     this.methodMap.borders = 'borders';
 94     this.methodMap.vertices = 'vertices';
 95 
 96     this.elType = 'polygon';
 97 };
 98 JXG.Polygon.prototype = new JXG.GeometryElement;
 99 
100 
101 JXG.extend(JXG.Polygon.prototype, /** @lends JXG.Polygon.prototype */ {
102     /**
103      * Checks whether (x,y) is near the polygon.
104      * @param {Number} x Coordinate in x direction, screen coordinates.
105      * @param {Number} y Coordinate in y direction, screen coordinates.
106      * @return {Boolean} Returns true, if (x,y) is inside or at the boundary the polygon, otherwise false.
107      */
108     hasPoint: function (x,y) {
109 
110         var i, j, len, c = false;
111 
112         if (this.visProp.hasinnerpoints) {
113             // All points of the polygon trigger hasPoint: inner and boundary points
114             len = this.vertices.length;
115             // See http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html for a reference
116             for (i=0, j=len-2; i<len-1; j=i++) { // last vertex is first vertex
117                 if (((this.vertices[i].coords.scrCoords[2] > y) != (this.vertices[j].coords.scrCoords[2] > y))
118                     && (x < (this.vertices[j].coords.scrCoords[1] - this.vertices[i].coords.scrCoords[1]) * (y - this.vertices[i].coords.scrCoords[2])
119                         / (this.vertices[j].coords.scrCoords[2] - this.vertices[i].coords.scrCoords[2]) + this.vertices[i].coords.scrCoords[1])) {
120                     c = !c;
121                 }
122             }
123         } else {
124             // Only boundary points trigger hasPoint
125             len = this.borders.length;
126             for (i=0; i<len; i++) {
127                 if (this.borders[i].hasPoint(x,y)) {
128                     c = true;
129                     break;
130                 }
131             }
132         }
133 
134         return c;
135     },
136 
137     /**
138      * Uses the boards renderer to update the polygon.
139      */
140     updateRenderer: function () {
141         if (this.needsUpdate) {
142             this.board.renderer.updatePolygon(this);
143             this.needsUpdate = false;
144         }
145         if(this.hasLabel && this.label.content.visProp.visible) {
146             //this.label.setCoordinates(this.coords);
147             this.label.content.update();
148             //this.board.renderer.updateLabel(this.label);
149             this.board.renderer.updateText(this.label.content);
150         }
151     },
152 
153     /**
154      * return TextAnchor
155      */
156     getTextAnchor: function() {
157         var a = this.vertices[0].X(),
158             b = this.vertices[0].Y(),
159             x = a,
160             y = b,
161             i;
162 
163         for (i = 0; i < this.vertices.length; i++) {
164             if (this.vertices[i].X() < a)
165                 a = this.vertices[i].X();
166             if (this.vertices[i].X() > x)
167                 x = this.vertices[i].X();
168             if (this.vertices[i].Y() > b)
169                 b = this.vertices[i].Y();
170             if (this.vertices[i].Y() < y)
171                 y = this.vertices[i].Y();
172         }
173 
174         return new JXG.Coords(JXG.COORDS_BY_USER, [(a + x)*0.5, (b + y)*0.5], this.board);
175     },
176 
177     getLabelAnchor: JXG.shortcut(JXG.Polygon.prototype, 'getTextAnchor'),
178 
179     // documented in geometry element
180     cloneToBackground: function() {
181         var copy = {}, er;
182 
183         copy.id = this.id + 'T' + this.numTraces;
184         this.numTraces++;
185         copy.vertices = this.vertices;
186         copy.visProp = JXG.deepCopy(this.visProp, this.visProp.traceattributes, true);
187         copy.visProp.layer = this.board.options.layer.trace;
188         copy.board = this.board;
189         JXG.clearVisPropOld(copy);
190 
191         er = this.board.renderer.enhancedRendering;
192         this.board.renderer.enhancedRendering = true;
193         this.board.renderer.drawPolygon(copy);
194         this.board.renderer.enhancedRendering = er;
195         this.traces[copy.id] = copy.rendNode;
196 
197         return this;
198     },
199 
200     /**
201      * Hide the polygon including its border lines. It will still exist but not visible on the board.
202      */
203     hideElement: function() {
204         var i;
205 
206         this.visProp.visible = false;
207         this.board.renderer.hide(this);
208 
209         for(i = 0; i < this.borders.length; i++) {
210             this.borders[i].hideElement();
211         }
212 
213         if (this.hasLabel && JXG.exists(this.label)) {
214             this.label.hiddenByParent = true;
215             if(this.label.content.visProp.visible) {
216                 this.board.renderer.hide(this.label.content);
217             }
218         }
219     },
220 
221     /**
222      * Make the element visible.
223      */
224     showElement: function() {
225         var i;
226 
227         this.visProp.visible = true;
228         this.board.renderer.show(this);
229 
230         for(i = 0; i < this.borders.length; i++) {
231             this.borders[i].showElement();
232         }
233 
234         if (this.hasLabel && JXG.exists(this.label)) {
235             if(this.label.content.visProp.visible) {
236                 this.board.renderer.show(this.label.content);
237             }
238         }
239     },
240 
241     /**
242      * returns the area of the polygon
243      */
244     Area: function() {
245         //Surveyor's Formula
246         var area = 0, i;
247 
248         for (i = 0; i < this.vertices.length - 1; i++) {
249             area += (this.vertices[i].X()*this.vertices[i+1].Y()-this.vertices[i+1].X()*this.vertices[i].Y()); // last vertex is first vertex
250         }
251         area /= 2.0;
252         return Math.abs(area);
253     },
254 
255     /**
256      * This method removes the SVG or VML nodes of the lines and the filled area from the renderer, to remove
257      * the object completely you should use {@link JXG.Board#removeObject}.
258      */
259     remove: function () {
260         var i;
261 
262         for (i = 0; i < this.borders.length; i++) {
263             this.board.removeObject(this.borders[i]);
264         }
265         this.board.renderer.remove(this.rendNode);
266     },
267 
268     /**
269      * Finds the index to a given point reference.
270      * @param {JXG.Point} p Reference to an element of type {@link JXG.Point}
271      */
272     findPoint: function (p) {
273         var i;
274 
275         if (!JXG.isPoint(p)) {
276             return -1;
277         }
278 
279         for (i = 0; i < this.vertices.length; i++) {
280             if (this.vertices[i].id === p.id) {
281                 return i;
282             }
283         }
284 
285         return -1;
286     },
287 
288     /**
289      * Add more points to the polygon. The new points will be inserted at the end.
290      * @param {%} % Arbitrary number of points
291      * @returns {JXG.Polygon} Reference to the polygon
292      */
293     addPoints: function () {
294         var args = Array.prototype.slice.call(arguments);
295 
296         return this.insertPoints.apply(this, [this.vertices.length-2].concat(args));
297     },
298 
299     /**
300      * Adds more points to the vertex list of the polygon, starting with index <tt><i</tt>
301      * @param {Number} i The position where the new vertices are inserted, starting with 0.
302      * @param {%} % Arbitrary number of points to insert.
303      * @returns {JXG.Polygon} Reference to the polygon object
304      */
305     insertPoints: function () {
306         var idx, i, npoints = [], tmp;
307 
308         if (arguments.length === 0) {
309             return this;
310         }
311 
312         idx = arguments[0];
313 
314         if (idx < 0 || idx > this.vertices.length-2) {
315             return this;
316         }
317 
318         for (i = 1; i < arguments.length; i++) {
319             if (JXG.isPoint(arguments[i])) {
320                 npoints.push(arguments[i]);
321             }
322         }
323 
324         tmp = this.vertices.slice(0, idx+1).concat(npoints);
325         this.vertices = tmp.concat(this.vertices.slice(idx+1));
326 
327         if (this.withLines) {
328             tmp = this.borders.slice(0, idx);
329             this.board.removeObject(this.borders[idx]);
330 
331             for (i = 0; i < npoints.length; i++) {
332                 tmp.push(JXG.createSegment(this.board, [this.vertices[idx+i], this.vertices[idx+i+1]], this.attr_line));
333             }
334             tmp.push(JXG.createSegment(this.board, [this.vertices[idx+npoints.length], this.vertices[idx+npoints.length+1]], this.attr_line));
335 
336             this.borders = tmp.concat(this.borders.slice(idx));
337         }
338 
339         this.board.update();
340 
341         return this;
342     },
343 
344     /**
345      * Removes given set of vertices from the polygon
346      * @param {%} % Arbitrary number of vertices as {@link JXG.Point} elements or index numbers
347      * @returns {JXG.Polygon} Reference to the polygon
348      */
349     removePoints: function () {
350         var i, j, idx, nvertices = [], nborders = [],
351             nidx = [], partition = [];
352 
353         // partition:
354         // in order to keep the borders which could be recycled, we have to partition
355         // the set of removed points. I.e. if the points 1, 2, 5, 6, 7, 10 are removed,
356         // the partition is
357         //       1-2, 5-7, 10-10
358         // this gives us the borders, that can be removed and the borders we have to create.
359 
360 
361         // remove the last vertex which is identical to the first
362         this.vertices = this.vertices.slice(0, this.vertices.length-1);
363 
364         // collect all valid parameters as indices in nidx
365         for (i = 0; i < arguments.length; i++) {
366             if (JXG.isPoint(arguments[i])) {
367                 idx = this.findPoint(arguments[i]);
368             }
369 
370             if (JXG.isNumber(idx) && idx > -1 && idx < this.vertices.length && JXG.indexOf(nidx, idx) === -1) {
371                 nidx.push(idx);
372             }
373         }
374 
375         // sort the elements to be eliminated
376         nidx = nidx.sort();
377         nvertices = this.vertices.slice();
378         nborders = this.borders.slice();
379 
380         // initialize the partition
381         if (this.withLines) {
382             partition.push([nidx[nidx.length-1]]);
383         }
384 
385         // run through all existing vertices and copy all remaining ones to nvertices
386         // compute the partition
387         for (i = nidx.length-1; i > -1; i--) {
388             nvertices[nidx[i]] = -1;
389 
390             if (this.withLines && (nidx[i] - 1 > nidx[i-1])) {
391                 partition[partition.length-1][1] = nidx[i];
392                 partition.push([nidx[i-1]]);
393             }
394         }
395 
396         // finalize the partition computation
397         if (this.withLines) {
398             partition[partition.length-1][1] = nidx[0];
399         }
400 
401         // update vertices
402         this.vertices = [];
403         for (i = 0; i < nvertices.length; i++) {
404             if (JXG.isPoint(nvertices[i])) {
405                 this.vertices.push(nvertices[i]);
406             }
407         }
408         if (this.vertices[this.vertices.length-1].id !== this.vertices[0].id) {
409             this.vertices.push(this.vertices[0]);
410         }
411 
412         // delete obsolete and create missing borders
413         if (this.withLines) {
414             for (i = 0; i < partition.length; i++) {
415                 for (j = partition[i][1] - 1; j < partition[i][0] + 1; j++) {
416                     // special cases
417                     if (j < 0) {
418                         // first vertex is removed, so the last border has to be removed, too
419                         j = 0;
420                         this.board.removeObject(this.borders[nborders.length-1]);
421                         nborders[nborders.length-1] = -1;
422                     } else if (j > nborders.length-1) {
423                         j = nborders.length-1;
424                     }
425 
426                     this.board.removeObject(this.borders[j]);
427                     nborders[j] = -1;
428                 }
429 
430                 // only create the new segment if it's not the closing border. the closing border is getting a special treatment at the end
431                 // the if clause is newer than the min/max calls inside createSegment; i'm sure this makes the min/max calls obsolete, but
432                 // just to be sure...
433                 if (partition[i][1] !== 0 && partition[i][0] !== nvertices.length-1) {
434                     nborders[partition[i][0] - 1] = JXG.createSegment(this.board, [nvertices[Math.max(partition[i][1]-1, 0)], nvertices[Math.min(partition[i][0]+1, this.vertices.length-1)]], this.attr_line);
435                 }
436             }
437 
438             this.borders = [];
439             for (i = 0; i < nborders.length; i++) {
440                 if (nborders[i] !== -1) {
441                     this.borders.push(nborders[i]);
442                 }
443             }
444 
445             // if the first and/or the last vertex is removed, the closing border is created at the end.
446             if (partition[0][1] === 5 || partition[partition.length-1][1] === 0) {
447                 this.borders.push(JXG.createSegment(this.board, [this.vertices[0], this.vertices[this.vertices.length-2]], this.attr_line));
448             }
449         }
450 
451         this.board.update();
452 
453         return this;
454     },
455 
456     getParents: function () {
457         var p = [], i;
458 
459         for (i = 0; i < this.vertices.length; i++) {
460             p.push(this.vertices[i].id);
461         }
462         return p;
463     },
464 
465     getAttributes: function () {
466         var attr = JXG.GeometryElement.prototype.getAttributes.call(this), i;
467 
468         if (this.withLines) {
469             attr.lines = attr.lines || {};
470             attr.lines.ids = [];
471             attr.lines.colors = [];
472 
473             for (i = 0; i < this.borders.length; i++) {
474                 attr.lines.ids.push(this.borders[i].id);
475                 attr.lines.colors.push(this.borders[i].visProp.strokecolor);
476             }
477         }
478 
479         return attr;
480     }
481 });
482 
483 
484 /**
485  * @class A polygon is an area enclosed by a set of border lines which are determined by a list of points. Each two
486  * consecutive points of the list define a line.
487  * @pseudo
488  * @constructor
489  * @name Polygon
490  * @type Polygon
491  * @augments JXG.Polygon
492  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
493  * @param {Array} vertices The polygon's vertices. If the first and the last vertex don't match the first one will be
494  * added to the array by the creator.
495  * @example
496  * var p1 = board.create('point', [0.0, 2.0]);
497  * var p2 = board.create('point', [2.0, 1.0]);
498  * var p3 = board.create('point', [4.0, 6.0]);
499  * var p4 = board.create('point', [1.0, 3.0]);
500  *
501  * var pol = board.create('polygon', [p1, p2, p3, p4]);
502  * </pre><div id="682069e9-9e2c-4f63-9b73-e26f8a2b2bb1" style="width: 400px; height: 400px;"></div>
503  * <script type="text/javascript">
504  *  (function () {
505  *   var board = JXG.JSXGraph.initBoard('682069e9-9e2c-4f63-9b73-e26f8a2b2bb1', {boundingbox: [-1, 9, 9, -1], axis: false, showcopyright: false, shownavigation: false}),
506  *       p1 = board.create('point', [0.0, 2.0]),
507  *       p2 = board.create('point', [2.0, 1.0]),
508  *       p3 = board.create('point', [4.0, 6.0]),
509  *       p4 = board.create('point', [1.0, 3.0]),
510  *       cc1 = board.create('polygon', [p1, p2, p3, p4]);
511  *  })();
512  * </script><pre>
513  */
514 JXG.createPolygon = function(board, parents, attributes) {
515     var el, i, attr = JXG.copyAttributes(attributes, board.options, 'polygon');
516 
517     // Sind alles Punkte?
518     for(i = 0; i < parents.length; i++) {
519         parents[i] = JXG.getReference(board, parents[i]);
520         if(!JXG.isPoint(parents[i]))
521             throw new Error("JSXGraph: Can't create polygon with parent types other than 'point'.");
522     }
523 
524     el = new JXG.Polygon(board, parents, attr);
525 
526     return el;
527 };
528 
529 
530 /**
531  * @class Constructs a regular polygon. It needs two points which define the base line and the number of vertices.
532  * @pseudo
533  * @description Constructs a regular polygon. It needs two points which define the base line and the number of vertices, or a set of points.
534  * @constructor
535  * @name RegularPolygon
536  * @type Polygon
537  * @augments Polygon
538  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
539  * @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.
540  * @example
541  * var p1 = board.create('point', [0.0, 2.0]);
542  * var p2 = board.create('point', [2.0, 1.0]);
543  *
544  * var pol = board.create('regularpolygon', [p1, p2, 5]);
545  * </pre><div id="682069e9-9e2c-4f63-9b73-e26f8a2b2bb1" style="width: 400px; height: 400px;"></div>
546  * <script type="text/javascript">
547  *  (function () {
548  *   var board = JXG.JSXGraph.initBoard('682069e9-9e2c-4f63-9b73-e26f8a2b2bb1', {boundingbox: [-1, 9, 9, -1], axis: false, showcopyright: false, shownavigation: false}),
549  *       p1 = board.create('point', [0.0, 2.0]),
550  *       p2 = board.create('point', [2.0, 1.0]),
551  *       cc1 = board.create('regularpolygon', [p1, p2, 5]);
552  *  })();
553  * </script><pre>
554  * @example
555  * var p1 = board.create('point', [0.0, 2.0]);
556  * var p2 = board.create('point', [4.0,4.0]);
557  * var p3 = board.create('point', [2.0,0.0]);
558  *
559  * var pol = board.create('regularpolygon', [p1, p2, p3]);
560  * </pre><div id="096a78b3-bd50-4bac-b958-3be5e7df17ed" style="width: 400px; height: 400px;"></div>
561  * <script type="text/javascript">
562  * (function () {
563  *   var board = JXG.JSXGraph.initBoard('096a78b3-bd50-4bac-b958-3be5e7df17ed', {boundingbox: [-1, 9, 9, -1], axis: false, showcopyright: false, shownavigation: false}),
564  *       p1 = board.create('point', [0.0, 2.0]),
565  *       p2 = board.create('point', [4.0, 4.0]),
566  *       p3 = board.create('point', [2.0,0.0]),
567  *       cc1 = board.create('regularpolygon', [p1, p2, p3]);
568  * })();
569  * </script><pre>
570  */
571 JXG.createRegularPolygon = function(board, parents, attributes) {
572     var el, i, n, p = [], rot, c, len, pointsExist, attr;
573 
574     if (JXG.isNumber(parents[parents.length-1]) && parents.length!=3) {
575         throw new Error("JSXGraph: A regular polygon needs two points and a number as input.");
576     }
577 
578     len = parents.length;
579     n = parents[len-1];
580     if ((!JXG.isNumber(n) && !JXG.isPoint(JXG.getReference(board, n))) || n<3) {
581         throw new Error("JSXGraph: The third parameter has to be number greater than 2 or a point.");
582     }
583 
584     if (JXG.isPoint(JXG.getReference(board, n))) {  // Regular polygon given by n points
585         n = len;
586         pointsExist = true;
587     } else {
588         len--;
589         pointsExist = false;
590     }
591 
592     // The first two parent elements have to be points
593     for(i=0; i<len; i++) {
594         parents[i] = JXG.getReference(board, parents[i]);
595         if(!JXG.isPoint(parents[i]))
596             throw new Error("JSXGraph: Can't create regular polygon if the first two parameters aren't points.");
597     }
598 
599     p[0] = parents[0];
600     p[1] = parents[1];
601     attr = JXG.copyAttributes(attributes, board.options, 'polygon', 'vertices');
602     for (i=2;i<n;i++) {
603         rot = board.create('transform', [Math.PI*(2.0-(n-2)/n),p[i-1]], {type:'rotate'});
604         if (pointsExist) {
605             p[i] = parents[i];
606             p[i].addTransform(parents[i-2],rot);
607         } else {
608             if (JXG.isArray(attr.ids) && attr.ids.length >= n-2) {
609                 attr.id = attr.ids[i-2];
610             }
611             p[i] = board.create('point',[p[i-2],rot], attr);
612 			p[i].type = JXG.OBJECT_TYPE_CAS;
613         }
614     }
615     attr = JXG.copyAttributes(attributes, board.options, 'polygon');
616     el = board.create('polygon', p, attr);
617 
618     el.elType = 'regularpolygon';
619 
620     return el;
621 };
622 
623 JXG.JSXGraph.registerElement('polygon', JXG.createPolygon);
624 JXG.JSXGraph.registerElement('regularpolygon', JXG.createRegularPolygon);
625