1 /*
  2     Copyright 2008-2015
  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  math/geometry
 39  math/math
 40  base/coords
 41  base/constants
 42  utils/type
 43   elements:
 44    point
 45    curve
 46    circumcentre
 47    transform
 48  */
 49 
 50 define([
 51     'jxg', 'math/geometry', 'math/math', 'math/statistics', 'base/coords', 'base/constants', 'utils/type', 'base/point', 'base/curve',
 52     'base/transformation', 'element/composition'
 53 ], function (JXG, Geometry, Mat, Statistics, Coords, Const, Type, Point, Curve, Transform, Compositions) {
 54 
 55     "use strict";
 56 
 57     /**
 58      * @class A circular sector is a subarea of the area enclosed by a circle. It is enclosed by two radii and an arc.
 59      * @pseudo
 60      * @name Sector
 61      * @augments JXG.Curve
 62      * @constructor
 63      * @type JXG.Curve
 64      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
 65      *
 66      * First possiblity of input parameters are:
 67      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 A sector is defined by three points: The sector's center <tt>p1</tt>,
 68      * a second point <tt>p2</tt> defining the radius and a third point <tt>p3</tt> defining the angle of the sector. The
 69      * Sector is always drawn counter clockwise from <tt>p2</tt> to <tt>p3</tt>
 70      *
 71      * Second possibility of input parameters are:
 72      * @param {JXG.Line_JXG.Line_array,number_array,number_number,function} line, line2, coords1 or direction1, coords2 or direction2, radius The sector is defined by two lines.
 73      * The two legs which define the sector are given by two coordinates arrays which are project initially two the two lines or by two directions (+/- 1).
 74      * The last parameter is the radius of the sector.
 75      *
 76      *
 77      * @example
 78      * // Create a sector out of three free points
 79      * var p1 = board.create('point', [1.5, 5.0]),
 80      *     p2 = board.create('point', [1.0, 0.5]),
 81      *     p3 = board.create('point', [5.0, 3.0]),
 82      *
 83      *     a = board.create('sector', [p1, p2, p3]);
 84      * </pre><div id="49f59123-f013-4681-bfd9-338b89893156" style="width: 300px; height: 300px;"></div>
 85      * <script type="text/javascript">
 86      * (function () {
 87      *   var board = JXG.JSXGraph.initBoard('49f59123-f013-4681-bfd9-338b89893156', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
 88      *     p1 = board.create('point', [1.5, 5.0]),
 89      *     p2 = board.create('point', [1.0, 0.5]),
 90      *     p3 = board.create('point', [5.0, 3.0]),
 91      *
 92      *     a = board.create('sector', [p1, p2, p3]);
 93      * })();
 94      * </script><pre>
 95      *
 96      * @example
 97      * // Create a sector out of two lines, two directions and a radius
 98      * var p1 = board.create('point', [-1, 4]),
 99      *  p2 = board.create('point', [4, 1]),
100      *  q1 = board.create('point', [-2, -3]),
101      *  q2 = board.create('point', [4,3]),
102      *
103      *  li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
104      *  li2 = board.create('line', [q1,q2], {lastArrow:true}),
105      *
106      *  sec1 = board.create('sector', [li1, li2, [5.5, 0], [4, 3], 3]),
107      *  sec2 = board.create('sector', [li1, li2, 1, -1, 4]);
108      *
109      * </pre><div id="bb9e2809-9895-4ff1-adfa-c9c71d50aa53" style="width: 300px; height: 300px;"></div>
110      * <script type="text/javascript">
111      * (function () {
112      *   var board = JXG.JSXGraph.initBoard('bb9e2809-9895-4ff1-adfa-c9c71d50aa53', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
113      *     p1 = board.create('point', [-1, 4]),
114      *     p2 = board.create('point', [4, 1]),
115      *     q1 = board.create('point', [-2, -3]),
116      *     q2 = board.create('point', [4,3]),
117      *
118      *     li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
119      *     li2 = board.create('line', [q1,q2], {lastArrow:true}),
120      *
121      *     sec1 = board.create('sector', [li1, li2, [5.5, 0], [4, 3], 3]),
122      *     sec2 = board.create('sector', [li1, li2, 1, -1, 4]);
123      * })();
124      * </script><pre>
125      */
126     JXG.createSector = function (board, parents, attributes) {
127         var el, i, attr,
128             type = 'invalid',
129             s, v,
130             attrPoints = ['center', 'radiuspoint', 'anglepoint'],
131             points;
132 
133         // Three points?
134         if (parents[0].elementClass === Const.OBJECT_CLASS_LINE &&
135                 parents[1].elementClass === Const.OBJECT_CLASS_LINE &&
136                 (Type.isArray(parents[2]) || Type.isNumber(parents[2])) &&
137                 (Type.isArray(parents[3]) || Type.isNumber(parents[3])) &&
138                 (Type.isNumber(parents[4]) || Type.isFunction(parents[4]))) {
139 
140             type = '2lines';
141 
142         } else {
143             points = Type.providePoints(board, parents, attributes, 'sector', attrPoints);
144             if (points === false) {
145                 throw new Error("JSXGraph: Can't create Sector with parent types '" +
146                     (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" +
147                     (typeof parents[2]) + "'.");
148             }
149 
150             type = '3points';
151         }
152 
153         attr = Type.copyAttributes(attributes, board.options, 'sector');
154         el = board.create('curve', [[0], [0]], attr);
155         el.type = Const.OBJECT_TYPE_SECTOR;
156         el.elType = 'sector';
157 
158         if (type === '2lines') {
159             el.Radius = function () {
160                 return Type.evaluate(parents[4]);
161             };
162 
163             el.line1 = board.select(parents[0]);
164             el.line2 = board.select(parents[1]);
165 
166             el.line1.addChild(el);
167             el.line2.addChild(el);
168             el.parents = [parents[0].id, parents[1].id];
169 
170             el.point1 = {visProp: {}};
171             el.point2 = {visProp: {}};
172             el.point3 = {visProp: {}};
173 
174             /* Intersection point */
175             s = Geometry.meetLineLine(el.line1.stdform, el.line2.stdform, 0, board);
176 
177             if (Type.isArray(parents[2])) {
178                 /* project p1 to l1 */
179                 if (parents[2].length === 2) {
180                     parents[2] = [1].concat(parents[2]);
181                 }
182                 /*
183                 v = [0, el.line1.stdform[1], el.line1.stdform[2]];
184                 v = Mat.crossProduct(v, parents[2]);
185                 v = Geometry.meetLineLine(v, el.line1.stdform, 0, board);
186                 */
187                 v = Geometry.projectPointToLine({coords: {usrCoords: parents[2]}}, el.line1, board);
188                 v = Statistics.subtract(v.usrCoords, s.usrCoords);
189                 el.direction1 = (Mat.innerProduct(v, [0, el.line1.stdform[2], -el.line1.stdform[1]], 3) >= 0) ? +1 : -1;
190             } else {
191                 el.direction1 = (parents[2] >= 0) ? 1 : -1;
192             }
193 
194             if (Type.isArray(parents[3])) {
195                 /* project p2 to l2 */
196                 if (parents[3].length === 2) {
197                     parents[3] = [1].concat(parents[3]);
198                 }
199                 /*
200                 v = [0, el.line2.stdform[1], el.line2.stdform[2]];
201                 v = Mat.crossProduct(v, parents[3]);
202                 v = Geometry.meetLineLine(v, el.line2.stdform, 0, board);
203                 */
204                 v = Geometry.projectPointToLine({coords: {usrCoords: parents[3]}}, el.line2, board);
205                 v = Statistics.subtract(v.usrCoords, s.usrCoords);
206                 el.direction2 = (Mat.innerProduct(v, [0, el.line2.stdform[2], -el.line2.stdform[1]], 3) >= 0) ? +1 : -1;
207             } else {
208                 el.direction2 = (parents[3] >= 0) ? 1 : -1;
209             }
210 
211             el.updateDataArray = function () {
212                 var r, l1, l2,
213                     A = [0, 0, 0],
214                     B = [0, 0, 0],
215                     C = [0, 0, 0],
216                     ar;
217 
218                 l1 = this.line1;
219                 l2 = this.line2;
220 
221                 // Intersection point of the lines
222                 B = Mat.crossProduct(l1.stdform, l2.stdform);
223 
224                 if (Math.abs(B[0]) > Mat.eps * Mat.eps) {
225                     B[1] /= B[0];
226                     B[2] /= B[0];
227                     B[0] /= B[0];
228                 }
229                 // First point
230                 r = this.direction1 * this.Radius();
231                 A = Statistics.add(B, [0, r * l1.stdform[2], -r * l1.stdform[1]]);
232 
233                 // Second point
234                 r = this.direction2 * this.Radius();
235                 C = Statistics.add(B, [0, r * l2.stdform[2], -r * l2.stdform[1]]);
236 
237                 this.point2.coords = new Coords(Const.COORDS_BY_USER, A, el.board);
238                 this.point1.coords = new Coords(Const.COORDS_BY_USER, B, el.board);
239                 this.point3.coords = new Coords(Const.COORDS_BY_USER, C, el.board);
240 
241                 if (Math.abs(A[0]) < Mat.eps || Math.abs(B[0]) < Mat.eps || Math.abs(C[0]) < Mat.eps) {
242                     this.dataX = [NaN];
243                     this.dataY = [NaN];
244                     return;
245                 }
246 
247                 ar = Geometry.bezierArc(A, B, C, true, 1);
248 
249                 this.dataX = ar[0];
250                 this.dataY = ar[1];
251 
252                 this.bezierDegree = 3;
253             };
254 
255             el.methodMap = JXG.deepCopy(el.methodMap, {
256                 radius: 'getRadius',
257                 getRadius: 'getRadius',
258                 setRadius: 'setRadius'
259             });
260 
261             el.prepareUpdate().update();
262 
263         // end '2lines'
264 
265         } else if (type === '3points') {
266 
267             /**
268             * Midpoint of the sector.
269             * @memberOf Sector.prototype
270             * @name point1
271             * @type JXG.Point
272             */
273             el.point1 = points[0];
274 
275             /**
276             * This point together with {@link Sector#point1} defines the radius..
277             * @memberOf Sector.prototype
278             * @name point2
279             * @type JXG.Point
280             */
281             el.point2 = points[1];
282 
283             /**
284             * Defines the sector's angle.
285             * @memberOf Sector.prototype
286             * @name point3
287             * @type JXG.Point
288             */
289             el.point3 = points[2];
290 
291             /* Add arc as child to defining points */
292             el.point1.addChild(el);
293             el.point2.addChild(el);
294             el.point3.addChild(el);
295 
296             // useDirection is necessary for circumCircleSectors
297             el.useDirection = attributes.usedirection;
298             el.parents = [points[0].id, points[1].id, points[2].id];
299 
300             /**
301             * Defines the sectors orientation in case of circumCircleSectors.
302             * @memberOf Sector.prototype
303             * @name point4
304             * @type JXG.Point
305             */
306             if (Type.exists(points[3])) {
307                 el.point4 = points[3];
308                 el.point4.addChild(el);
309             }
310 
311             el.methodMap = JXG.deepCopy(el.methodMap, {
312                 arc: 'arc',
313                 center: 'center',
314                 radiuspoint: 'radiuspoint',
315                 anglepoint: 'anglepoint',
316                 radius: 'getRadius',
317                 getRadius: 'getRadius',
318                 setRadius: 'setRadius'
319             });
320 
321             /**
322             * documented in JXG.Curve
323             * @ignore
324             */
325             el.updateDataArray = function () {
326                 var ar, det, p0c, p1c, p2c,
327                     A = this.point2,
328                     B = this.point1,
329                     C = this.point3,
330                     phi, sgn = 1;
331 
332                 if (!A.isReal || !B.isReal || !C.isReal) {
333                     this.dataX = [NaN];
334                     this.dataY = [NaN];
335                     return;
336                 }
337 
338                 phi = Geometry.rad(A, B, C);
339                 if ((this.visProp.selection === 'minor' && phi > Math.PI) ||
340                         (this.visProp.selection === 'major' && phi < Math.PI)) {
341                     sgn = -1;
342                 }
343 
344                 // This is true for circumCircleSectors. In that case there is
345                 // a fourth parent element: [midpoint, point1, point3, point2]
346                 if (this.useDirection && Type.exists(this.point4)) {
347                     p0c = this.point2.coords.usrCoords;
348                     p1c = this.point4.coords.usrCoords;
349                     p2c = this.point3.coords.usrCoords;
350                     det = (p0c[1] - p2c[1]) * (p0c[2] - p1c[2]) - (p0c[2] - p2c[2]) * (p0c[1] - p1c[1]);
351 
352                     if (det >= 0.0) {
353                         C = this.point2;
354                         A = this.point3;
355                     }
356                 }
357 
358                 A = A.coords.usrCoords;
359                 B = B.coords.usrCoords;
360                 C = C.coords.usrCoords;
361 
362                 ar = Geometry.bezierArc(A, B, C, true, sgn);
363 
364                 this.dataX = ar[0];
365                 this.dataY = ar[1];
366                 this.bezierDegree = 3;
367             };
368 
369             /**
370             * Returns the radius of the sector.
371             * @memberOf Sector.prototype
372             * @name Radius
373             * @function
374             * @returns {Number} The distance between {@link Sector#point1} and {@link Sector#point2}.
375             */
376             el.Radius = function () {
377                 return this.point2.Dist(this.point1);
378             };
379 
380             attr = Type.copyAttributes(attributes, board.options, 'sector', 'arc');
381             attr.withLabel = false;
382             attr.name += '_arc';
383             el.arc = board.create('arc', [el.point1, el.point2, el.point3], attr);
384             el.addChild(el.arc);
385         }   // end '3points'
386 
387         el.center = el.point1;
388         el.radiuspoint = el.point2;
389         el.anglepoint = el.point3;
390 
391         // Default hasPoint method. Documented in geometry element
392         el.hasPointCurve = function (x, y) {
393             var angle, alpha, beta,
394                 prec = this.board.options.precision.hasPoint / (this.board.unitX),
395                 checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),
396                 r = this.Radius(),
397                 dist = this.center.coords.distance(Const.COORDS_BY_USER, checkPoint),
398                 has = (Math.abs(dist - r) < prec);
399 
400             if (has) {
401                 angle = Geometry.rad(this.point2, this.center, checkPoint.usrCoords.slice(1));
402                 alpha = 0;
403                 beta = Geometry.rad(this.point2, this.center, this.point3);
404 
405                 if (angle < alpha || angle > beta) {
406                     has = false;
407                 }
408             }
409 
410             return has;
411         };
412 
413         /**
414         * Checks whether (x,y) is within the area defined by the sector.
415         * @memberOf Sector.prototype
416         * @name hasPointSector
417         * @function
418         * @param {Number} x Coordinate in x direction, screen coordinates.
419         * @param {Number} y Coordinate in y direction, screen coordinates.
420         * @returns {Boolean} True if (x,y) is within the sector defined by the arc, False otherwise.
421         */
422         el.hasPointSector = function (x, y) {
423             var angle,
424                 checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),
425                 r = this.Radius(),
426                 dist = this.point1.coords.distance(Const.COORDS_BY_USER, checkPoint),
427                 alpha,
428                 beta,
429                 has = (dist < r);
430 
431             if (has) {
432                 angle = Geometry.rad(this.radiuspoint, this.center, checkPoint.usrCoords.slice(1));
433                 alpha = 0.0;
434                 beta = Geometry.rad(this.radiuspoint, this.center, this.anglepoint);
435 
436                 if ((this.visProp.selection === 'minor' && beta > Math.PI) ||
437                         (this.visProp.selection === 'major' && beta < Math.PI)) {
438                     alpha = beta;
439                     beta = 2 * Math.PI;
440                 }
441                 //if (angle > Geometry.rad(this.point2, this.point1, this.point3)) {
442                 if (angle < alpha || angle > beta) {
443                     has = false;
444                 }
445             }
446             return has;
447         };
448 
449         el.hasPoint = function (x, y) {
450             if (this.visProp.highlightonsector || this.visProp.hasinnerpoints) {
451                 return this.hasPointSector(x, y);
452             }
453 
454             return this.hasPointCurve(x, y);
455         };
456 
457         // documented in GeometryElement
458         el.getTextAnchor = function () {
459             return this.point1.coords;
460         };
461 
462         // documented in GeometryElement
463         // this method is very similar to arc.getLabelAnchor()
464         // there are some additions in the arc version though, mainly concerning
465         // "major" and "minor" arcs. but maybe these methods can be merged.
466         el.getLabelAnchor = function () {
467             var coords, vecx, vecy, len,
468                 angle = Geometry.rad(this.point2, this.point1, this.point3),
469                 dx = 13 / this.board.unitX,
470                 dy = 13 / this.board.unitY,
471                 p2c = this.point2.coords.usrCoords,
472                 pmc = this.point1.coords.usrCoords,
473                 bxminusax = p2c[1] - pmc[1],
474                 byminusay = p2c[2] - pmc[2];
475 
476             // If this is uncommented, the angle label can not be dragged
477             //if (Type.exists(this.label)) {
478             //    this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);
479             //}
480 
481             if ((this.visProp.selection === 'minor' && angle > Math.PI) ||
482                     (this.visProp.selection === 'major' && angle < Math.PI)) {
483                 angle = -(2 * Math.PI - angle);
484             }
485 
486             coords = new Coords(Const.COORDS_BY_USER, [
487                 pmc[1] + Math.cos(angle * 0.5) * bxminusax - Math.sin(angle * 0.5) * byminusay,
488                 pmc[2] + Math.sin(angle * 0.5) * bxminusax + Math.cos(angle * 0.5) * byminusay
489             ], this.board);
490 
491             vecx = coords.usrCoords[1] - pmc[1];
492             vecy = coords.usrCoords[2] - pmc[2];
493 
494             len = Math.sqrt(vecx * vecx + vecy * vecy);
495             vecx = vecx * (len + dx) / len;
496             vecy = vecy * (len + dy) / len;
497 
498             return new Coords(Const.COORDS_BY_USER, [pmc[1] + vecx, pmc[2] + vecy], this.board);
499         };
500 
501         /**
502          * Overwrite the Radius method of the sector.
503          * Used in {@link GeometryElement#setAttribute}.
504          * @param {Number, Function} value New radius.
505          */
506         el.setRadius = function (value) {
507             el.Radius = function () {
508                 return Type.evaluate(value);
509             };
510         };
511 
512         /**
513          * deprecated
514          * @ignore
515          */
516         el.getRadius = function () {
517             return this.Radius();
518         };
519 
520         /**
521          * Moves the sector by the difference of two coordinates.
522          * @param {Number} method The type of coordinates used here. Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
523          * @param {Array} coords coordinates in screen/user units
524          * @param {Array} oldcoords previous coordinates in screen/user units
525          * @returns {JXG.Curve} this element
526          */
527         if (type === '3points') {
528             el.setPositionDirectly = function (method, coords, oldcoords) {
529                 var dc, t, i, len,
530                     c = new Coords(method, coords, this.board),
531                     oldc = new Coords(method, oldcoords, this.board);
532 
533                 if (!el.point1.draggable() || !el.point2.draggable() || !el.point3.draggable()) {
534                     return this;
535                 }
536 
537                 dc = Statistics.subtract(c.usrCoords, oldc.usrCoords);
538                 t = this.board.create('transform', dc.slice(1), {type: 'translate'});
539                 t.applyOnce([el.point1, el.point2, el.point3]);
540 
541                 return this;
542             };
543         }
544 
545         el.prepareUpdate().update();
546 
547         return el;
548     };
549 
550     JXG.registerElement('sector', JXG.createSector);
551 
552 
553     /**
554      * @class A circumcircle sector is different from a {@link Sector} mostly in the way the parent elements are interpreted.
555      * At first, the circum centre is determined from the three given points. Then the sector is drawn from <tt>p1</tt> through
556      * <tt>p2</tt> to <tt>p3</tt>.
557      * @pseudo
558      * @name CircumcircleSector
559      * @augments Sector
560      * @constructor
561      * @type Sector
562      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
563      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 A circumcircle sector is defined by the circumcircle which is determined
564      * by these three given points. The circumcircle sector is always drawn from <tt>p1</tt> through <tt>p2</tt> to <tt>p3</tt>.
565      * @example
566      * // Create an arc out of three free points
567      * var p1 = board.create('point', [1.5, 5.0]),
568      *     p2 = board.create('point', [1.0, 0.5]),
569      *     p3 = board.create('point', [5.0, 3.0]),
570      *
571      *     a = board.create('circumcirclesector', [p1, p2, p3]);
572      * </pre><div id="695cf0d6-6d7a-4d4d-bfc9-34c6aa28cd04" style="width: 300px; height: 300px;"></div>
573      * <script type="text/javascript">
574      * (function () {
575  *   var board = JXG.JSXGraph.initBoard('695cf0d6-6d7a-4d4d-bfc9-34c6aa28cd04', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
576  *     p1 = board.create('point', [1.5, 5.0]),
577  *     p2 = board.create('point', [1.0, 0.5]),
578  *     p3 = board.create('point', [5.0, 3.0]),
579  *
580  *     a = board.create('circumcirclesector', [p1, p2, p3]);
581  * })();
582      * </script><pre>
583      */
584     JXG.createCircumcircleSector = function (board, parents, attributes) {
585         var el, mp, attr, points, i;
586 
587         points = Type.providePoints(board, parents, attributes, 'point');
588         if (points === false) {
589             throw new Error("JSXGraph: Can't create circumcircle sector with parent types '" +
590                 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" + (typeof parents[2]) + "'.");
591         }
592 
593         mp = board.create('circumcenter', points.slice(0, 3), attr);
594         mp.dump = false;
595 
596         attr = Type.copyAttributes(attributes, board.options, 'circumcirclesector');
597         el = board.create('sector', [mp, points[0], points[2], points[1]], attr);
598 
599         el.elType = 'circumcirclesector';
600         el.parents = [points[0].id, points[1].id, points[2].id];
601 
602         /**
603          * Center of the circumcirclesector
604          * @memberOf CircumcircleSector.prototype
605          * @name center
606          * @type Circumcenter
607          */
608         el.center = mp;
609         el.subs = {
610             center: mp
611         };
612 
613         return el;
614     };
615 
616     JXG.registerElement('circumcirclesector', JXG.createCircumcircleSector);
617 
618     /**
619      * @class A minor sector is a sector of a circle having measure less than or equal to
620      * 180 degrees (pi radians). It is defined by a center, one point that
621      * defines the radius, and a third point that defines the angle of the sector.
622      * @pseudo
623      * @name MinorSector
624      * @augments Curve
625      * @constructor
626      * @type JXG.Curve
627      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
628      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor sector is a sector of a circle around p1 having measure less than or equal to
629      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
630      * @example
631      * // Create sector out of three free points
632      * var p1 = board.create('point', [2.0, 2.0]);
633      * var p2 = board.create('point', [1.0, 0.5]);
634      * var p3 = board.create('point', [3.5, 1.0]);
635      *
636      * var a = board.create('minorsector', [p1, p2, p3]);
637      * </pre><div id="af27ddcc-265f-428f-90dd-d31ace945800" style="width: 300px; height: 300px;"></div>
638      * <script type="text/javascript">
639      * (function () {
640      *   var board = JXG.JSXGraph.initBoard('af27ddcc-265f-428f-90dd-d31ace945800', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
641      *       p1 = board.create('point', [2.0, 2.0]),
642      *       p2 = board.create('point', [1.0, 0.5]),
643      *       p3 = board.create('point', [3.5, 1.0]),
644      *
645      *       a = board.create('minorsector', [p1, p2, p3]);
646      * })();
647      * </script><pre>
648      */
649     JXG.createMinorSector = function (board, parents, attributes) {
650         attributes.selection = 'minor';
651         return JXG.createSector(board, parents, attributes);
652     };
653 
654     JXG.registerElement('minorsector', JXG.createMinorSector);
655 
656     /**
657      * @class A major sector is a sector of a circle having measure greater than or equal to
658      * 180 degrees (pi radians). It is defined by a center, one point that
659      * defines the radius, and a third point that defines the angle of the sector.
660      * @pseudo
661      * @name MajorSector
662      * @augments Curve
663      * @constructor
664      * @type JXG.Curve
665      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
666      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Major sector is a sector of a circle around p1 having measure greater than or equal to
667      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
668      * @example
669      * // Create an arc out of three free points
670      * var p1 = board.create('point', [2.0, 2.0]);
671      * var p2 = board.create('point', [1.0, 0.5]);
672      * var p3 = board.create('point', [3.5, 1.0]);
673      *
674      * var a = board.create('majorsector', [p1, p2, p3]);
675      * </pre><div id="83c6561f-7561-4047-b98d-036248a00932" style="width: 300px; height: 300px;"></div>
676      * <script type="text/javascript">
677      * (function () {
678      *   var board = JXG.JSXGraph.initBoard('83c6561f-7561-4047-b98d-036248a00932', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
679      *       p1 = board.create('point', [2.0, 2.0]),
680      *       p2 = board.create('point', [1.0, 0.5]),
681      *       p3 = board.create('point', [3.5, 1.0]),
682      *
683      *       a = board.create('majorsector', [p1, p2, p3]);
684      * })();
685      * </script><pre>
686      */
687     JXG.createMajorSector = function (board, parents, attributes) {
688         attributes.selection = 'major';
689         return JXG.createSector(board, parents, attributes);
690     };
691 
692     JXG.registerElement('majorsector', JXG.createMajorSector);
693 
694     /**
695      * @class The angle element is used to denote an angle defined by three points. Visually it is just a {@link Sector}
696      * element with a radius not defined by the parent elements but by an attribute <tt>radius</tt>. As opposed to the sector,
697      * an angle has two angle points and no radius point.
698      * Sector is displayed if type=="sector".
699      * If type=="square", instead of a sector a parallelogram is displayed.
700      * In case of type=="auto", a square is displayed if the angle is near orthogonal.
701      * If no name is provided the angle label is automatically set to a lower greek letter.
702      * @pseudo
703      * @name Angle
704      * @augments Sector
705      * @constructor
706      * @type Sector
707      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
708      * First possiblity of input parameters are:
709      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 An angle is always drawn counterclockwise from <tt>p1</tt> to
710      * <tt>p3</tt> around <tt>p2</tt>.
711      *
712      * Second possibility of input parameters are:
713      * @param {JXG.Line_JXG.Line_array|number_array|number} line, line2, coords1 or direction1, coords2 or direction2, radius The angle is defined by two lines.
714      * The two legs which define the angle are given by two coordinate arrays.
715      * The points given by these coordinate arrays are projected initially (i.e. only once) onto the two lines.
716      * The other possibility is to supply directions (+/- 1).
717      *
718      * @example
719      * // Create an angle out of three free points
720      * var p1 = board.create('point', [5.0, 3.0]),
721      *     p2 = board.create('point', [1.0, 0.5]),
722      *     p3 = board.create('point', [1.5, 5.0]),
723      *
724      *     a = board.create('angle', [p1, p2, p3]);
725      * </pre><div id="a34151f9-bb26-480a-8d6e-9b8cbf789ae5" style="width: 300px; height: 300px;"></div>
726      * <script type="text/javascript">
727      * (function () {
728      *   var board = JXG.JSXGraph.initBoard('a34151f9-bb26-480a-8d6e-9b8cbf789ae5', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
729      *     p1 = board.create('point', [5.0, 3.0]),
730      *     p2 = board.create('point', [1.0, 0.5]),
731      *     p3 = board.create('point', [1.5, 5.0]),
732      *
733      *     a = board.create('angle', [p1, p2, p3]);
734      * })();
735      * </script><pre>
736      *
737      * @example
738      * // Create an angle out of two lines and two directions
739      * var p1 = board.create('point', [-1, 4]),
740      *  p2 = board.create('point', [4, 1]),
741      *  q1 = board.create('point', [-2, -3]),
742      *  q2 = board.create('point', [4,3]),
743      *
744      *  li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
745      *  li2 = board.create('line', [q1,q2], {lastArrow:true}),
746      *
747      *  a1 = board.create('angle', [li1, li2, [5.5, 0], [4, 3]], { radius:1 }),
748      *  a2 = board.create('angle', [li1, li2, 1, -1], { radius:2 });
749      *
750      * </pre><div id="3a667ddd-63dc-4594-b5f1-afac969b371f" style="width: 300px; height: 300px;"></div>
751      * <script type="text/javascript">
752      * (function () {
753      *   var board = JXG.JSXGraph.initBoard('3a667ddd-63dc-4594-b5f1-afac969b371f', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
754      *     p1 = board.create('point', [-1, 4]),
755      *     p2 = board.create('point', [4, 1]),
756      *     q1 = board.create('point', [-2, -3]),
757      *     q2 = board.create('point', [4,3]),
758      *
759      *     li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
760      *     li2 = board.create('line', [q1,q2], {lastArrow:true}),
761      *
762      *     a1 = board.create('angle', [li1, li2, [5.5, 0], [4, 3]], { radius:1 }),
763      *     a2 = board.create('angle', [li1, li2, 1, -1], { radius:2 });
764      * })();
765      * </script><pre>
766      */
767     JXG.createAngle = function (board, parents, attributes) {
768         var el, radius, text, attr, attrsub,
769             i, dot, points,
770             type = 'invalid';
771 
772         // Two lines or three points?
773         if (parents[0].elementClass === Const.OBJECT_CLASS_LINE &&
774                 parents[1].elementClass === Const.OBJECT_CLASS_LINE &&
775                 (Type.isArray(parents[2]) || Type.isNumber(parents[2])) &&
776                 (Type.isArray(parents[3]) || Type.isNumber(parents[3]))) {
777 
778             type = '2lines';
779         } else {
780             points = Type.providePoints(board, parents, attributes, 'point');
781             if (points === false) {
782                 throw new Error("JSXGraph: Can't create angle with parent types '" +
783                     (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" + (typeof parents[2]) + "'.");
784             }
785             type = '3points';
786         }
787 
788         attr = Type.copyAttributes(attributes, board.options, 'angle');
789 
790         //  If empty, create a new name
791         if (!Type.exists(attr.name) || attr.name === '') {
792             attr.name = board.generateName({type: Const.OBJECT_TYPE_ANGLE});
793         }
794 
795         if (Type.exists(attr.radius)) {
796             radius = attr.radius;
797         } else {
798             radius = 0;
799         }
800 
801         if (type === '2lines') {
802             parents.push(radius);
803             el = board.create('sector', parents, attr);
804             el.updateDataArraySector = el.updateDataArray;
805 
806             // TODO
807             el.setAngle = function (val) {};
808             el.free = function (val) {};
809 
810         } else {
811             el = board.create('sector', [points[1], points[0], points[2]], attr);
812             el.arc.visProp.priv = true;
813 
814             /**
815              * The point defining the radius of the angle element. Alias for {@link Angle.prototype#radiuspoint}.
816              * @type JXG.Point
817              * @name point
818              * @memberOf Angle.prototype
819              */
820             el.point = el.point2 = el.radiuspoint = points[0];
821 
822             /**
823              * Helper point for angles of type 'square'.
824              * @type JXG.Point
825              * @name pointsquare
826              * @memberOf Angle.prototype
827              */
828             el.pointsquare = el.point3 = el.anglepoint = points[2];
829 
830             el.Radius = function () {
831                 return Type.evaluate(radius);
832             };
833 
834             el.updateDataArraySector = function () {
835                 var A = this.point2,
836                     B = this.point1,
837                     C = this.point3,
838                     r = this.Radius(),
839                     d = B.Dist(A),
840                     ar,
841                     phi,
842                     sgn = 1;
843 
844                 phi = Geometry.rad(A, B, C);
845                 if ((this.visProp.selection === 'minor' && phi > Math.PI) ||
846                         (this.visProp.selection === 'major' && phi < Math.PI)) {
847                     sgn = -1;
848                 }
849 
850                 A = A.coords.usrCoords;
851                 B = B.coords.usrCoords;
852                 C = C.coords.usrCoords;
853 
854                 A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
855                 C = [1, B[1] + (C[1] - B[1]) * r / d, B[2] + (C[2] - B[2]) * r / d];
856 
857                 ar = Geometry.bezierArc(A, B, C, true, sgn);
858 
859                 this.dataX = ar[0];
860                 this.dataY = ar[1];
861                 this.bezierDegree = 3;
862             };
863 
864             /**
865             * Set an angle to a prescribed value given in radians. This is only possible if the third point of the angle, i.e.
866             * the anglepoint is a free point.
867             * @name setAngle
868             * @function
869             * @param {Number|Function} val Number or Function which returns the size of the angle in Radians
870             * @returns {Object} Pointer to the angle element..
871             * @memberOf Angle.prototype
872             */
873             el.setAngle = function (val) {
874                 var t,
875                     p = this.anglepoint,
876                     q = this.radiuspoint;
877 
878                 if (p.draggable()) {
879                     t = this.board.create('transform', [val, this.center], {type: 'rotate'});
880                     p.addTransform(q, t);
881                     p.isDraggable = false;
882                     p.parents = [q];
883                 }
884                 return this;
885             };
886 
887             /**
888             * Frees an angle from a prescribed value. This is only relevant if the angle size has been set by
889             * setAngle() previously. The anglepoint is set to a free point.
890             * @name free
891             * @function
892             * @returns {Object} Pointer to the angle element..
893             * @memberOf Angle.prototype
894             */
895             el.free = function () {
896                 var p = this.anglepoint;
897                 if (p.transformations.length > 0) {
898                     p.transformations.pop();
899                     p.isDraggable = true;
900                     p.parents = [];
901                 }
902                 return this;
903             };
904 
905             el.parents = [points[0].id, points[1].id, points[2].id]; // Important: This overwrites the parents order in underlying sector
906 
907         } // end '3points'
908 
909         // GEONExT compatible labels.
910         if (JXG.exists(el.visProp.text)) {
911             el.label.setText(el.visProp.text);
912         }
913 
914         el.elType = 'angle';
915         el.type = Const.OBJECT_TYPE_ANGLE;
916         // el.parents = [points[0].id, points[1].id, points[2].id];
917         el.subs = {};
918 
919         el.updateDataArraySquare = function () {
920             var A, B, C,
921                 r = this.Radius(),
922                 d1, d2,
923                 v, l1, l2;
924 
925 
926             if (type === '2lines') {
927                 // This is necessary to update this.point1, this.point2, this.point3.
928                 this.updateDataArraySector();
929             }
930 
931             A = this.point2;
932             B = this.point1;
933             C = this.point3;
934 
935             A = A.coords.usrCoords;
936             B = B.coords.usrCoords;
937             C = C.coords.usrCoords;
938 
939             d1 = Geometry.distance(A, B, 3);
940             d2 = Geometry.distance(C, B, 3);
941 
942             // In case of type=='2lines' this is redundant, because r == d1 == d2
943             A = [1, B[1] + (A[1] - B[1]) * r / d1, B[2] + (A[2] - B[2]) * r / d1];
944             C = [1, B[1] + (C[1] - B[1]) * r / d2, B[2] + (C[2] - B[2]) * r / d2];
945 
946             v = Mat.crossProduct(C, B);
947             l1 = [-A[1] * v[1] - A[2] * v[2], A[0] * v[1], A[0] * v[2]];
948             v = Mat.crossProduct(A, B);
949             l2 = [-C[1] * v[1] - C[2] * v[2], C[0] * v[1], C[0] * v[2]];
950 
951             v = Mat.crossProduct(l1, l2);
952             v[1] /= v[0];
953             v[2] /= v[0];
954 
955             this.dataX = [B[1], A[1], v[1], C[1], B[1]];
956             this.dataY = [B[2], A[2], v[2], C[2], B[2]];
957 
958             this.bezierDegree = 1;
959         };
960 
961         el.updateDataArrayNone = function () {
962             this.dataX = [NaN];
963             this.dataY = [NaN];
964             this.bezierDegree = 1;
965         };
966 
967         el.updateDataArray = function () {
968             var type = this.visProp.type,
969                 deg = Geometry.trueAngle(this.point2, this.point1, this.point3);
970 
971             if ((this.visProp.selection === 'minor' && deg > 180.0) ||
972                     (this.visProp.selection === 'major' && deg < 180.0)) {
973                 deg = 360.0 - deg;
974             }
975 
976             if (Math.abs(deg - 90.0) < this.visProp.orthosensitivity + Mat.eps) {
977                 type = this.visProp.orthotype;
978             }
979 
980             if (type === 'none') {
981                 this.updateDataArrayNone();
982             } else if (type === 'square') {
983                 this.updateDataArraySquare();
984             } else if (type === 'sector') {
985                 this.updateDataArraySector();
986             } else if (type === 'sectordot') {
987                 this.updateDataArraySector();
988                 if (!this.dot.visProp.visible) {
989                     this.dot.setAttribute({visible: true});
990                 }
991             }
992 
993             if (!this.visProp.visible || (type !== 'sectordot' && this.dot.visProp.visible)) {
994                 this.dot.setAttribute({visible: false});
995             }
996         };
997 
998         /**
999          * Indicates a right angle. Invisible by default, use <tt>dot.visible: true</tt> to show.
1000          * Though this dot indicates a right angle, it can be visible even if the angle is not a right
1001          * one.
1002          * @type JXG.Point
1003          * @name dot
1004          * @memberOf Angle.prototype
1005          */
1006         attrsub = Type.copyAttributes(attributes, board.options, 'angle', 'dot');
1007         el.dot = board.create('point', [function () {
1008             var A, B, r, d, a2, co, si, mat,
1009                 point1, point2, point3;
1010 
1011             if (Type.exists(el.dot) && !el.dot.visProp.visible) {
1012                 return [0, 0];
1013             }
1014 
1015             A = el.point2.coords.usrCoords;
1016             B = el.point1.coords.usrCoords;
1017             r = el.Radius();
1018             d = Geometry.distance(A, B, 3);
1019             a2 = Geometry.rad(el.point2, el.point1, el.point3);
1020 
1021             if ((el.visProp.selection === 'minor' && a2 > Math.PI) ||
1022                     (el.visProp.selection === 'major' && a2 < Math.PI)) {
1023                 a2 = -(2 * Math.PI - a2);
1024             }
1025             a2 *= 0.5;
1026 
1027             co = Math.cos(a2);
1028             si = Math.sin(a2);
1029 
1030             A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
1031 
1032             mat = [
1033                 [1, 0, 0],
1034                 [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],
1035                 [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5,  co * 0.5]
1036             ];
1037             return Mat.matVecMult(mat, A);
1038         }], attrsub);
1039 
1040         el.dot.dump = false;
1041         el.subs.dot = el.dot;
1042 
1043         if (type === '2lines') {
1044             for (i = 0; i < 2; i++) {
1045                 board.select(parents[i]).addChild(el.dot);
1046             }
1047         } else {
1048             for (i = 0; i < 3; i++) {
1049                 board.select(points[i]).addChild(el.dot);
1050             }
1051         }
1052 
1053         // documented in GeometryElement
1054         el.getLabelAnchor = function () {
1055             var vec, dx = 12, dy = 12,
1056                 A, B, r, d, a2, co, si, mat;
1057 
1058             // If this is uncommented, the angle label can not be dragged
1059             //if (Type.exists(this.label)) {
1060             //    this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);
1061             //}
1062 
1063             if (Type.exists(this.label.visProp.fontSize)) {
1064                 dx = this.label.visProp.fontSize;
1065                 dy = this.label.visProp.fontSize;
1066             }
1067             dx /= this.board.unitX;
1068             dy /= this.board.unitY;
1069 
1070             A = el.point2.coords.usrCoords;
1071             B = el.point1.coords.usrCoords;
1072             r = el.Radius();
1073             d = Geometry.distance(A, B, 3);
1074             a2 = Geometry.rad(el.point2, el.point1, el.point3);
1075             if ((el.visProp.selection === 'minor' && a2 > Math.PI) ||
1076                     (el.visProp.selection === 'major' && a2 < Math.PI)) {
1077                 a2 = -(2 * Math.PI - a2);
1078             }
1079             a2 *= 0.5;
1080             co = Math.cos(a2);
1081             si = Math.sin(a2);
1082 
1083             A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
1084 
1085             mat = [
1086                 [1, 0, 0],
1087                 [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],
1088                 [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5,  co * 0.5]
1089             ];
1090             vec = Mat.matVecMult(mat, A);
1091             vec[1] /= vec[0];
1092             vec[2] /= vec[0];
1093             vec[0] /= vec[0];
1094 
1095             d = Geometry.distance(vec, B, 3);
1096             vec = [vec[0], B[1] + (vec[1] - B[1]) * (r + dx) / d,  B[2] + (vec[2] - B[2]) * (r + dx) / d];
1097 
1098             return new Coords(Const.COORDS_BY_USER, vec, this.board);
1099         };
1100 
1101         el.Value = function () {
1102             return Geometry.rad(this.point2, this.point1, this.point3);
1103         };
1104 
1105         el.methodMap = Type.deepCopy(el.methodMap, {
1106             Value: 'Value',
1107             setAngle: 'setAngle',
1108             free: 'free'
1109         });
1110 
1111         return el;
1112     };
1113 
1114     JXG.registerElement('angle', JXG.createAngle);
1115 
1116     /**
1117      * @class A non-reflex angle is the acute or obtuse instance of an angle. 
1118      * It is defined by a center, one point that
1119      * defines the radius, and a third point that defines the angle of the sector.
1120      * @pseudo
1121      * @name NonReflexAngle
1122      * @augments Sector
1123      * @constructor
1124      * @type Sector
1125      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
1126      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor sector is a sector of a circle around p1 having measure less than or equal to
1127      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
1128      * @example
1129      * // Create a non-reflex angle out of three free points
1130      * var p1 = board.create('point', [5.0, 3.0]),
1131      *     p2 = board.create('point', [1.0, 0.5]),
1132      *     p3 = board.create('point', [1.5, 5.0]),
1133      *
1134      *     a = board.create('nonreflexangle', [p1, p2, p3], {radius: 2});
1135      * </pre><div id="d0ab6d6b-63a7-48b2-8749-b02bb5e744f9" style="width: 300px; height: 300px;"></div>
1136      * <script type="text/javascript">
1137      * (function () {
1138      *   var board = JXG.JSXGraph.initBoard('d0ab6d6b-63a7-48b2-8749-b02bb5e744f9', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
1139      *     p1 = board.create('point', [5.0, 3.0]),
1140      *     p2 = board.create('point', [1.0, 0.5]),
1141      *     p3 = board.create('point', [1.5, 5.0]),
1142      *
1143      *     a = board.create('nonreflexangle', [p1, p2, p3], {radius: 2});
1144      * })();
1145      * </script><pre>
1146      */
1147     JXG.createNonreflexAngle = function (board, parents, attributes) {
1148         attributes.selection = 'minor';
1149         return JXG.createAngle(board, parents, attributes);
1150     };
1151 
1152     JXG.registerElement('nonreflexangle', JXG.createNonreflexAngle);
1153 
1154     /**
1155      * @class A reflex angle is the neither acute nor obtuse instance of an angle. 
1156      * It is defined by a center, one point that
1157      * defines the radius, and a third point that defines the angle of the sector.
1158      * @pseudo
1159      * @name ReflexAngle
1160      * @augments Sector
1161      * @constructor
1162      * @type Sector
1163      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
1164      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor sector is a sector of a circle around p1 having measure less than or equal to
1165      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
1166      * @example
1167      * // Create a non-reflex angle out of three free points
1168      * var p1 = board.create('point', [5.0, 3.0]),
1169      *     p2 = board.create('point', [1.0, 0.5]),
1170      *     p3 = board.create('point', [1.5, 5.0]),
1171      *
1172      *     a = board.create('reflexangle', [p1, p2, p3], {radius: 2});
1173      * </pre><div id="f2a577f2-553d-4f9f-a895-2d6d4b8c60e8" style="width: 300px; height: 300px;"></div>
1174      * <script type="text/javascript">
1175      * (function () {
1176      *   var board = JXG.JSXGraph.initBoard('f2a577f2-553d-4f9f-a895-2d6d4b8c60e8', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
1177      *     p1 = board.create('point', [5.0, 3.0]),
1178      *     p2 = board.create('point', [1.0, 0.5]),
1179      *     p3 = board.create('point', [1.5, 5.0]),
1180      *
1181      *     a = board.create('reflexangle', [p1, p2, p3], {radius: 2});
1182      * })();
1183      * </script><pre>
1184      */
1185     JXG.createReflexAngle = function (board, parents, attributes) {
1186         attributes.selection = 'major';
1187         return JXG.createAngle(board, parents, attributes);
1188     };
1189 
1190     JXG.registerElement('reflexangle', JXG.createReflexAngle);
1191 
1192 
1193     return {
1194         createSector: JXG.createSector,
1195         createCircumcircleSector: JXG.createCircumcircleSector,
1196         createMinorSector: JXG.createMinorSector,
1197         createMajorSector: JXG.createMajorSector,
1198         createAngle: JXG.createAngle,
1199         createReflexAngle: JXG.createReflexAngle,
1200         createNonreflexAngle: JXG.createNonreflexAngle
1201     };
1202 });
1203