1 /*
  2     Copyright 2008-2016
  3         Matthias Ehmann,
  4         Michael Gerhaeuser,
  5         Carsten Miller,
  6         Bianca Valentin,
  7         Alfred Wassermann,
  8         Peter Wilfahrt
  9 
 10     This file is part of JSXGraph.
 11 
 12     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
 13 
 14     You can redistribute it and/or modify it under the terms of the
 15 
 16       * GNU Lesser General Public License as published by
 17         the Free Software Foundation, either version 3 of the License, or
 18         (at your option) any later version
 19       OR
 20       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
 21 
 22     JSXGraph is distributed in the hope that it will be useful,
 23     but WITHOUT ANY WARRANTY; without even the implied warranty of
 24     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 25     GNU Lesser General Public License for more details.
 26 
 27     You should have received a copy of the GNU Lesser General Public License and
 28     the MIT License along with JSXGraph. If not, see <http://www.gnu.org/licenses/>
 29     and <http://opensource.org/licenses/MIT/>.
 30  */
 31 
 32 
 33 /*global JXG: true, define: true*/
 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 class="jxgbox"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 class="jxgbox"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.setParents(parents);
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.setParents(points);
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 ((this.visProp.selection === 'minor' && beta > Math.PI) ||
406                         (this.visProp.selection === 'major' && beta < Math.PI)) {
407                     alpha = beta;
408                     beta = 2 * Math.PI;
409                 }
410 
411                 if (angle < alpha || angle > beta) {
412                     has = false;
413                 }
414             }
415 
416             return has;
417         };
418 
419         /**
420         * Checks whether (x,y) is within the area defined by the sector.
421         * @memberOf Sector.prototype
422         * @name hasPointSector
423         * @function
424         * @param {Number} x Coordinate in x direction, screen coordinates.
425         * @param {Number} y Coordinate in y direction, screen coordinates.
426         * @returns {Boolean} True if (x,y) is within the sector defined by the arc, False otherwise.
427         */
428         el.hasPointSector = function (x, y) {
429             var angle,
430                 checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),
431                 r = this.Radius(),
432                 dist = this.point1.coords.distance(Const.COORDS_BY_USER, checkPoint),
433                 alpha,
434                 beta,
435                 has = (dist < r);
436 
437             if (has) {
438                 angle = Geometry.rad(this.radiuspoint, this.center, checkPoint.usrCoords.slice(1));
439                 alpha = 0.0;
440                 beta = Geometry.rad(this.radiuspoint, this.center, this.anglepoint);
441 
442                 if ((this.visProp.selection === 'minor' && beta > Math.PI) ||
443                         (this.visProp.selection === 'major' && beta < Math.PI)) {
444                     alpha = beta;
445                     beta = 2 * Math.PI;
446                 }
447                 //if (angle > Geometry.rad(this.point2, this.point1, this.point3)) {
448                 if (angle < alpha || angle > beta) {
449                     has = false;
450                 }
451             }
452             return has;
453         };
454 
455         el.hasPoint = function (x, y) {
456             if (this.visProp.highlightonsector || this.visProp.hasinnerpoints) {
457                 return this.hasPointSector(x, y);
458             }
459 
460             return this.hasPointCurve(x, y);
461         };
462 
463         // documented in GeometryElement
464         el.getTextAnchor = function () {
465             return this.point1.coords;
466         };
467 
468         // documented in GeometryElement
469         // this method is very similar to arc.getLabelAnchor()
470         // there are some additions in the arc version though, mainly concerning
471         // "major" and "minor" arcs. but maybe these methods can be merged.
472         el.getLabelAnchor = function () {
473             var coords, vecx, vecy, len,
474                 angle = Geometry.rad(this.point2, this.point1, this.point3),
475                 dx = 13 / this.board.unitX,
476                 dy = 13 / this.board.unitY,
477                 p2c = this.point2.coords.usrCoords,
478                 pmc = this.point1.coords.usrCoords,
479                 bxminusax = p2c[1] - pmc[1],
480                 byminusay = p2c[2] - pmc[2];
481 
482             // If this is uncommented, the angle label can not be dragged
483             //if (Type.exists(this.label)) {
484             //    this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);
485             //}
486 
487             if ((this.visProp.selection === 'minor' && angle > Math.PI) ||
488                     (this.visProp.selection === 'major' && angle < Math.PI)) {
489                 angle = -(2 * Math.PI - angle);
490             }
491 
492             coords = new Coords(Const.COORDS_BY_USER, [
493                 pmc[1] + Math.cos(angle * 0.5) * bxminusax - Math.sin(angle * 0.5) * byminusay,
494                 pmc[2] + Math.sin(angle * 0.5) * bxminusax + Math.cos(angle * 0.5) * byminusay
495             ], this.board);
496 
497             vecx = coords.usrCoords[1] - pmc[1];
498             vecy = coords.usrCoords[2] - pmc[2];
499 
500             len = Math.sqrt(vecx * vecx + vecy * vecy);
501             vecx = vecx * (len + dx) / len;
502             vecy = vecy * (len + dy) / len;
503 
504             return new Coords(Const.COORDS_BY_USER, [pmc[1] + vecx, pmc[2] + vecy], this.board);
505         };
506 
507         /**
508          * Overwrite the Radius method of the sector.
509          * Used in {@link GeometryElement#setAttribute}.
510          * @param {Number, Function} value New radius.
511          */
512         el.setRadius = function (value) {
513             el.Radius = function () {
514                 return Type.evaluate(value);
515             };
516         };
517 
518         /**
519          * @deprecated
520          * @ignore
521          */
522         el.getRadius = function () {
523             JXG.deprecated('Sector.getRadius()', 'Sector.Radius()');
524             return this.Radius();
525         };
526 
527         /**
528          * Moves the sector by the difference of two coordinates.
529          * @param {Number} method The type of coordinates used here. Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
530          * @param {Array} coords coordinates in screen/user units
531          * @param {Array} oldcoords previous coordinates in screen/user units
532          * @returns {JXG.Curve} this element
533          */
534         if (type === '3points') {
535             el.setPositionDirectly = function (method, coords, oldcoords) {
536                 var dc, t, i, len,
537                     c = new Coords(method, coords, this.board),
538                     oldc = new Coords(method, oldcoords, this.board);
539 
540                 if (!el.point1.draggable() || !el.point2.draggable() || !el.point3.draggable()) {
541                     return this;
542                 }
543 
544                 dc = Statistics.subtract(c.usrCoords, oldc.usrCoords);
545                 t = this.board.create('transform', dc.slice(1), {type: 'translate'});
546                 t.applyOnce([el.point1, el.point2, el.point3]);
547 
548                 return this;
549             };
550         }
551 
552         el.prepareUpdate().update();
553 
554         return el;
555     };
556 
557     JXG.registerElement('sector', JXG.createSector);
558 
559 
560     /**
561      * @class A circumcircle sector is different from a {@link Sector} mostly in the way the parent elements are interpreted.
562      * At first, the circum centre is determined from the three given points. Then the sector is drawn from <tt>p1</tt> through
563      * <tt>p2</tt> to <tt>p3</tt>.
564      * @pseudo
565      * @name CircumcircleSector
566      * @augments Sector
567      * @constructor
568      * @type Sector
569      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
570      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 A circumcircle sector is defined by the circumcircle which is determined
571      * by these three given points. The circumcircle sector is always drawn from <tt>p1</tt> through <tt>p2</tt> to <tt>p3</tt>.
572      * @example
573      * // Create an arc out of three free points
574      * var p1 = board.create('point', [1.5, 5.0]),
575      *     p2 = board.create('point', [1.0, 0.5]),
576      *     p3 = board.create('point', [5.0, 3.0]),
577      *
578      *     a = board.create('circumcirclesector', [p1, p2, p3]);
579      * </pre><div class="jxgbox"id="695cf0d6-6d7a-4d4d-bfc9-34c6aa28cd04" style="width: 300px; height: 300px;"></div>
580      * <script type="text/javascript">
581      * (function () {
582  *   var board = JXG.JSXGraph.initBoard('695cf0d6-6d7a-4d4d-bfc9-34c6aa28cd04', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
583  *     p1 = board.create('point', [1.5, 5.0]),
584  *     p2 = board.create('point', [1.0, 0.5]),
585  *     p3 = board.create('point', [5.0, 3.0]),
586  *
587  *     a = board.create('circumcirclesector', [p1, p2, p3]);
588  * })();
589      * </script><pre>
590      */
591     JXG.createCircumcircleSector = function (board, parents, attributes) {
592         var el, mp, attr, points, i;
593 
594         points = Type.providePoints(board, parents, attributes, 'point');
595         if (points === false) {
596             throw new Error("JSXGraph: Can't create circumcircle sector with parent types '" +
597                 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" + (typeof parents[2]) + "'.");
598         }
599 
600         mp = board.create('circumcenter', points.slice(0, 3), attr);
601         mp.dump = false;
602 
603         attr = Type.copyAttributes(attributes, board.options, 'circumcirclesector');
604         el = board.create('sector', [mp, points[0], points[2], points[1]], attr);
605 
606         el.elType = 'circumcirclesector';
607         el.setParents(points);
608 
609         /**
610          * Center of the circumcirclesector
611          * @memberOf CircumcircleSector.prototype
612          * @name center
613          * @type Circumcenter
614          */
615         el.center = mp;
616         el.subs = {
617             center: mp
618         };
619 
620         return el;
621     };
622 
623     JXG.registerElement('circumcirclesector', JXG.createCircumcircleSector);
624 
625     /**
626      * @class A minor sector is a sector of a circle having measure less than or equal to
627      * 180 degrees (pi radians). It is defined by a center, one point that
628      * defines the radius, and a third point that defines the angle of the sector.
629      * @pseudo
630      * @name MinorSector
631      * @augments Curve
632      * @constructor
633      * @type JXG.Curve
634      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
635      * @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
636      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
637      * @example
638      * // Create sector out of three free points
639      * var p1 = board.create('point', [2.0, 2.0]);
640      * var p2 = board.create('point', [1.0, 0.5]);
641      * var p3 = board.create('point', [3.5, 1.0]);
642      *
643      * var a = board.create('minorsector', [p1, p2, p3]);
644      * </pre><div class="jxgbox"id="af27ddcc-265f-428f-90dd-d31ace945800" style="width: 300px; height: 300px;"></div>
645      * <script type="text/javascript">
646      * (function () {
647      *   var board = JXG.JSXGraph.initBoard('af27ddcc-265f-428f-90dd-d31ace945800', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
648      *       p1 = board.create('point', [2.0, 2.0]),
649      *       p2 = board.create('point', [1.0, 0.5]),
650      *       p3 = board.create('point', [3.5, 1.0]),
651      *
652      *       a = board.create('minorsector', [p1, p2, p3]);
653      * })();
654      * </script><pre>
655      */
656     JXG.createMinorSector = function (board, parents, attributes) {
657         attributes.selection = 'minor';
658         return JXG.createSector(board, parents, attributes);
659     };
660 
661     JXG.registerElement('minorsector', JXG.createMinorSector);
662 
663     /**
664      * @class A major sector is a sector of a circle having measure greater than or equal to
665      * 180 degrees (pi radians). It is defined by a center, one point that
666      * defines the radius, and a third point that defines the angle of the sector.
667      * @pseudo
668      * @name MajorSector
669      * @augments Curve
670      * @constructor
671      * @type JXG.Curve
672      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
673      * @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
674      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
675      * @example
676      * // Create an arc out of three free points
677      * var p1 = board.create('point', [2.0, 2.0]);
678      * var p2 = board.create('point', [1.0, 0.5]);
679      * var p3 = board.create('point', [3.5, 1.0]);
680      *
681      * var a = board.create('majorsector', [p1, p2, p3]);
682      * </pre><div class="jxgbox"id="83c6561f-7561-4047-b98d-036248a00932" style="width: 300px; height: 300px;"></div>
683      * <script type="text/javascript">
684      * (function () {
685      *   var board = JXG.JSXGraph.initBoard('83c6561f-7561-4047-b98d-036248a00932', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
686      *       p1 = board.create('point', [2.0, 2.0]),
687      *       p2 = board.create('point', [1.0, 0.5]),
688      *       p3 = board.create('point', [3.5, 1.0]),
689      *
690      *       a = board.create('majorsector', [p1, p2, p3]);
691      * })();
692      * </script><pre>
693      */
694     JXG.createMajorSector = function (board, parents, attributes) {
695         attributes.selection = 'major';
696         return JXG.createSector(board, parents, attributes);
697     };
698 
699     JXG.registerElement('majorsector', JXG.createMajorSector);
700 
701     /**
702      * @class The angle element is used to denote an angle defined by three points. Visually it is just a {@link Sector}
703      * element with a radius not defined by the parent elements but by an attribute <tt>radius</tt>. As opposed to the sector,
704      * an angle has two angle points and no radius point.
705      * Sector is displayed if type=="sector".
706      * If type=="square", instead of a sector a parallelogram is displayed.
707      * In case of type=="auto", a square is displayed if the angle is near orthogonal.
708      * If no name is provided the angle label is automatically set to a lower greek letter.
709      * @pseudo
710      * @name Angle
711      * @augments Sector
712      * @constructor
713      * @type Sector
714      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
715      * First possiblity of input parameters are:
716      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 An angle is always drawn counterclockwise from <tt>p1</tt> to
717      * <tt>p3</tt> around <tt>p2</tt>.
718      *
719      * Second possibility of input parameters are:
720      * @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.
721      * The two legs which define the angle are given by two coordinate arrays.
722      * The points given by these coordinate arrays are projected initially (i.e. only once) onto the two lines.
723      * The other possibility is to supply directions (+/- 1).
724      *
725      * @example
726      * // Create an angle out of three free points
727      * var p1 = board.create('point', [5.0, 3.0]),
728      *     p2 = board.create('point', [1.0, 0.5]),
729      *     p3 = board.create('point', [1.5, 5.0]),
730      *
731      *     a = board.create('angle', [p1, p2, p3]),
732      *     t = board.create('text', [4, 4, function() { return a.Value().toFixed(2); }]);
733      * </pre><div class="jxgbox"id="a34151f9-bb26-480a-8d6e-9b8cbf789ae5" style="width: 300px; height: 300px;"></div>
734      * <script type="text/javascript">
735      * (function () {
736      *   var board = JXG.JSXGraph.initBoard('a34151f9-bb26-480a-8d6e-9b8cbf789ae5', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
737      *     p1 = board.create('point', [5.0, 3.0]),
738      *     p2 = board.create('point', [1.0, 0.5]),
739      *     p3 = board.create('point', [1.5, 5.0]),
740      *
741      *     a = board.create('angle', [p1, p2, p3]),
742      *     t = board.create('text', [4, 4, function() { return a.Value().toFixed(2); }]);
743      * })();
744      * </script><pre>
745      *
746      * @example
747      * // Create an angle out of two lines and two directions
748      * var p1 = board.create('point', [-1, 4]),
749      *  p2 = board.create('point', [4, 1]),
750      *  q1 = board.create('point', [-2, -3]),
751      *  q2 = board.create('point', [4,3]),
752      *
753      *  li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
754      *  li2 = board.create('line', [q1,q2], {lastArrow:true}),
755      *
756      *  a1 = board.create('angle', [li1, li2, [5.5, 0], [4, 3]], { radius:1 }),
757      *  a2 = board.create('angle', [li1, li2, 1, -1], { radius:2 });
758      *
759      *
760      * </pre><div class="jxgbox"id="3a667ddd-63dc-4594-b5f1-afac969b371f" style="width: 300px; height: 300px;"></div>
761      * <script type="text/javascript">
762      * (function () {
763      *   var board = JXG.JSXGraph.initBoard('3a667ddd-63dc-4594-b5f1-afac969b371f', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
764      *     p1 = board.create('point', [-1, 4]),
765      *     p2 = board.create('point', [4, 1]),
766      *     q1 = board.create('point', [-2, -3]),
767      *     q2 = board.create('point', [4,3]),
768      *
769      *     li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
770      *     li2 = board.create('line', [q1,q2], {lastArrow:true}),
771      *
772      *     a1 = board.create('angle', [li1, li2, [5.5, 0], [4, 3]], { radius:1 }),
773      *     a2 = board.create('angle', [li1, li2, 1, -1], { radius:2 });
774      * })();
775      * </script><pre>
776      */
777     JXG.createAngle = function (board, parents, attributes) {
778         var el, radius, text, attr, attrsub,
779             i, dot, points,
780             type = 'invalid';
781 
782         // Two lines or three points?
783         if (parents[0].elementClass === Const.OBJECT_CLASS_LINE &&
784                 parents[1].elementClass === Const.OBJECT_CLASS_LINE &&
785                 (Type.isArray(parents[2]) || Type.isNumber(parents[2])) &&
786                 (Type.isArray(parents[3]) || Type.isNumber(parents[3]))) {
787 
788             type = '2lines';
789         } else {
790             points = Type.providePoints(board, parents, attributes, 'point');
791             if (points === false) {
792                 throw new Error("JSXGraph: Can't create angle with parent types '" +
793                     (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" + (typeof parents[2]) + "'.");
794             }
795             type = '3points';
796         }
797 
798         attr = Type.copyAttributes(attributes, board.options, 'angle');
799 
800         //  If empty, create a new name
801         if (!Type.exists(attr.name) || attr.name === '') {
802             attr.name = board.generateName({type: Const.OBJECT_TYPE_ANGLE});
803         }
804 
805         if (Type.exists(attr.radius)) {
806             radius = attr.radius;
807         } else {
808             radius = 0;
809         }
810 
811         if (type === '2lines') {
812             parents.push(radius);
813             el = board.create('sector', parents, attr);
814             el.updateDataArraySector = el.updateDataArray;
815 
816             // TODO
817             el.setAngle = function (val) {};
818             el.free = function (val) {};
819 
820         } else {
821             el = board.create('sector', [points[1], points[0], points[2]], attr);
822             el.arc.visProp.priv = true;
823 
824             /**
825              * The point defining the radius of the angle element. Alias for {@link Angle.prototype#radiuspoint}.
826              * @type JXG.Point
827              * @name point
828              * @memberOf Angle.prototype
829              */
830             el.point = el.point2 = el.radiuspoint = points[0];
831 
832             /**
833              * Helper point for angles of type 'square'.
834              * @type JXG.Point
835              * @name pointsquare
836              * @memberOf Angle.prototype
837              */
838             el.pointsquare = el.point3 = el.anglepoint = points[2];
839 
840             el.Radius = function () {
841                 return Type.evaluate(radius);
842             };
843 
844             el.updateDataArraySector = function () {
845                 var A = this.point2,
846                     B = this.point1,
847                     C = this.point3,
848                     r = this.Radius(),
849                     d = B.Dist(A),
850                     ar,
851                     phi,
852                     sgn = 1;
853 
854                 phi = Geometry.rad(A, B, C);
855                 if ((this.visProp.selection === 'minor' && phi > Math.PI) ||
856                         (this.visProp.selection === 'major' && phi < Math.PI)) {
857                     sgn = -1;
858                 }
859 
860                 A = A.coords.usrCoords;
861                 B = B.coords.usrCoords;
862                 C = C.coords.usrCoords;
863 
864                 A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
865                 C = [1, B[1] + (C[1] - B[1]) * r / d, B[2] + (C[2] - B[2]) * r / d];
866 
867                 ar = Geometry.bezierArc(A, B, C, true, sgn);
868 
869                 this.dataX = ar[0];
870                 this.dataY = ar[1];
871                 this.bezierDegree = 3;
872             };
873 
874             /**
875             * Set an angle to a prescribed value given in radians. This is only possible if the third point of the angle, i.e.
876             * the anglepoint is a free point.
877             * @name setAngle
878             * @function
879             * @param {Number|Function} val Number or Function which returns the size of the angle in Radians
880             * @returns {Object} Pointer to the angle element..
881             * @memberOf Angle.prototype
882             *
883             * @example
884             * var p1, p2, p3, c, a, s;
885             *
886             * p1 = board.create('point',[0,0]);
887             * p2 = board.create('point',[5,0]);
888             * p3 = board.create('point',[0,5]);
889             *
890             * c1 = board.create('circle',[p1, p2]);
891             *
892             * a = board.create('angle',[p2, p1, p3], {radius:3});
893             *
894             * a.setAngle(function() {
895             *     return Math.PI / 3;
896             * });
897             * board.update();
898             *
899             * </pre><div id="987c-394f-11e6-af4a-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
900             * <script type="text/javascript">
901             *     (function() {
902             *         var board = JXG.JSXGraph.initBoard('987c-394f-11e6-af4a-901b0e1b8723',
903             *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
904             *     var p1, p2, p3, c, a, s;
905             *
906             *     p1 = board.create('point',[0,0]);
907             *     p2 = board.create('point',[5,0]);
908             *     p3 = board.create('point',[0,5]);
909             *
910             *     c1 = board.create('circle',[p1, p2]);
911             *
912             *     a = board.create('angle',[p2, p1, p3], {radius: 3});
913             *
914             *     a.setAngle(function() {
915             *         return Math.PI / 3;
916             *     });
917             *     board.update();
918             *
919             *     })();
920             *
921             * </script><pre>
922             *
923             * @example
924             * var p1, p2, p3, c, a, s;
925             *
926             * p1 = board.create('point',[0,0]);
927             * p2 = board.create('point',[5,0]);
928             * p3 = board.create('point',[0,5]);
929             *
930             * c1 = board.create('circle',[p1, p2]);
931             *
932             * a = board.create('angle',[p2, p1, p3], {radius:3});
933             * s = board.create('slider',[[-2,1], [2,1], [0, Math.PI*0.5, 2*Math.PI]]);
934             *
935             * a.setAngle(function() {
936             *     return s.Value();
937             * });
938             * board.update();
939             *
940             * </pre><div id="99957b1c-394f-11e6-af4a-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
941             * <script type="text/javascript">
942             *     (function() {
943             *         var board = JXG.JSXGraph.initBoard('99957b1c-394f-11e6-af4a-901b0e1b8723',
944             *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
945             *     var p1, p2, p3, c, a, s;
946             *
947             *     p1 = board.create('point',[0,0]);
948             *     p2 = board.create('point',[5,0]);
949             *     p3 = board.create('point',[0,5]);
950             *
951             *     c1 = board.create('circle',[p1, p2]);
952             *
953             *     a = board.create('angle',[p2, p1, p3], {radius: 3});
954             *     s = board.create('slider',[[-2,1], [2,1], [0, Math.PI*0.5, 2*Math.PI]]);
955             *
956             *     a.setAngle(function() {
957             *         return s.Value();
958             *     });
959             *     board.update();
960             *
961             *     })();
962             *
963             * </script><pre>
964             *
965             */
966             el.setAngle = function (val) {
967                 var t,
968                     p = this.anglepoint,
969                     q = this.radiuspoint;
970 
971                 if (p.draggable()) {
972                     t = this.board.create('transform', [val, this.center], {type: 'rotate'});
973                     p.addTransform(q, t);
974                     p.isDraggable = false;
975                     p.setParents(q);
976                 }
977                 return this;
978             };
979 
980             /**
981             * Frees an angle from a prescribed value. This is only relevant if the angle size has been set by
982             * setAngle() previously. The anglepoint is set to a free point.
983             * @name free
984             * @function
985             * @returns {Object} Pointer to the angle element..
986             * @memberOf Angle.prototype
987             */
988             el.free = function () {
989                 var p = this.anglepoint;
990                 if (p.transformations.length > 0) {
991                     p.transformations.pop();
992                     p.isDraggable = true;
993                     p.parents = [];
994                 }
995                 return this;
996             };
997 
998             el.setParents(points); // Important: This overwrites the parents order in underlying sector
999 
1000         } // end '3points'
1001 
1002         // GEONExT compatible labels.
1003         if (JXG.exists(el.visProp.text)) {
1004             el.label.setText(el.visProp.text);
1005         }
1006 
1007         el.elType = 'angle';
1008         el.type = Const.OBJECT_TYPE_ANGLE;
1009         el.subs = {};
1010 
1011         el.updateDataArraySquare = function () {
1012             var A, B, C,
1013                 r = this.Radius(),
1014                 d1, d2,
1015                 v, l1, l2;
1016 
1017 
1018             if (type === '2lines') {
1019                 // This is necessary to update this.point1, this.point2, this.point3.
1020                 this.updateDataArraySector();
1021             }
1022 
1023             A = this.point2;
1024             B = this.point1;
1025             C = this.point3;
1026 
1027             A = A.coords.usrCoords;
1028             B = B.coords.usrCoords;
1029             C = C.coords.usrCoords;
1030 
1031             d1 = Geometry.distance(A, B, 3);
1032             d2 = Geometry.distance(C, B, 3);
1033 
1034             // In case of type=='2lines' this is redundant, because r == d1 == d2
1035             A = [1, B[1] + (A[1] - B[1]) * r / d1, B[2] + (A[2] - B[2]) * r / d1];
1036             C = [1, B[1] + (C[1] - B[1]) * r / d2, B[2] + (C[2] - B[2]) * r / d2];
1037 
1038             v = Mat.crossProduct(C, B);
1039             l1 = [-A[1] * v[1] - A[2] * v[2], A[0] * v[1], A[0] * v[2]];
1040             v = Mat.crossProduct(A, B);
1041             l2 = [-C[1] * v[1] - C[2] * v[2], C[0] * v[1], C[0] * v[2]];
1042 
1043             v = Mat.crossProduct(l1, l2);
1044             v[1] /= v[0];
1045             v[2] /= v[0];
1046 
1047             this.dataX = [B[1], A[1], v[1], C[1], B[1]];
1048             this.dataY = [B[2], A[2], v[2], C[2], B[2]];
1049 
1050             this.bezierDegree = 1;
1051         };
1052 
1053         el.updateDataArrayNone = function () {
1054             this.dataX = [NaN];
1055             this.dataY = [NaN];
1056             this.bezierDegree = 1;
1057         };
1058 
1059         el.updateDataArray = function () {
1060             var type = this.visProp.type,
1061                 deg = Geometry.trueAngle(this.point2, this.point1, this.point3);
1062 
1063             if ((this.visProp.selection === 'minor' && deg > 180.0) ||
1064                     (this.visProp.selection === 'major' && deg < 180.0)) {
1065                 deg = 360.0 - deg;
1066             }
1067 
1068             if (Math.abs(deg - 90.0) < this.visProp.orthosensitivity + Mat.eps) {
1069                 type = this.visProp.orthotype;
1070             }
1071 
1072             if (type === 'none') {
1073                 this.updateDataArrayNone();
1074             } else if (type === 'square') {
1075                 this.updateDataArraySquare();
1076             } else if (type === 'sector') {
1077                 this.updateDataArraySector();
1078             } else if (type === 'sectordot') {
1079                 this.updateDataArraySector();
1080                 if (!this.dot.visProp.visible) {
1081                     this.dot.setAttribute({visible: true});
1082                 }
1083             }
1084 
1085             if (!this.visProp.visible || (type !== 'sectordot' && this.dot.visProp.visible)) {
1086                 this.dot.setAttribute({visible: false});
1087             }
1088         };
1089 
1090         /**
1091          * Indicates a right angle. Invisible by default, use <tt>dot.visible: true</tt> to show.
1092          * Though this dot indicates a right angle, it can be visible even if the angle is not a right
1093          * one.
1094          * @type JXG.Point
1095          * @name dot
1096          * @memberOf Angle.prototype
1097          */
1098         attrsub = Type.copyAttributes(attributes, board.options, 'angle', 'dot');
1099         el.dot = board.create('point', [function () {
1100             var A, B, r, d, a2, co, si, mat,
1101                 point1, point2, point3;
1102 
1103             if (Type.exists(el.dot) && !el.dot.visProp.visible) {
1104                 return [0, 0];
1105             }
1106 
1107             A = el.point2.coords.usrCoords;
1108             B = el.point1.coords.usrCoords;
1109             r = el.Radius();
1110             d = Geometry.distance(A, B, 3);
1111             a2 = Geometry.rad(el.point2, el.point1, el.point3);
1112 
1113             if ((el.visProp.selection === 'minor' && a2 > Math.PI) ||
1114                     (el.visProp.selection === 'major' && a2 < Math.PI)) {
1115                 a2 = -(2 * Math.PI - a2);
1116             }
1117             a2 *= 0.5;
1118 
1119             co = Math.cos(a2);
1120             si = Math.sin(a2);
1121 
1122             A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
1123 
1124             mat = [
1125                 [1, 0, 0],
1126                 [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],
1127                 [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5,  co * 0.5]
1128             ];
1129             return Mat.matVecMult(mat, A);
1130         }], attrsub);
1131 
1132         el.dot.dump = false;
1133         el.subs.dot = el.dot;
1134 
1135         if (type === '2lines') {
1136             for (i = 0; i < 2; i++) {
1137                 board.select(parents[i]).addChild(el.dot);
1138             }
1139         } else {
1140             for (i = 0; i < 3; i++) {
1141                 board.select(points[i]).addChild(el.dot);
1142             }
1143         }
1144 
1145         // documented in GeometryElement
1146         el.getLabelAnchor = function () {
1147             var vec, dx = 12, dy = 12,
1148                 A, B, r, d, a2, co, si, mat;
1149 
1150             // If this is uncommented, the angle label can not be dragged
1151             //if (Type.exists(this.label)) {
1152             //    this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);
1153             //}
1154 
1155             if (Type.exists(this.label.visProp.fontSize)) {
1156                 dx = this.label.visProp.fontSize;
1157                 dy = this.label.visProp.fontSize;
1158             }
1159             dx /= this.board.unitX;
1160             dy /= this.board.unitY;
1161 
1162             A = el.point2.coords.usrCoords;
1163             B = el.point1.coords.usrCoords;
1164             r = el.Radius();
1165             d = Geometry.distance(A, B, 3);
1166             a2 = Geometry.rad(el.point2, el.point1, el.point3);
1167             if ((el.visProp.selection === 'minor' && a2 > Math.PI) ||
1168                     (el.visProp.selection === 'major' && a2 < Math.PI)) {
1169                 a2 = -(2 * Math.PI - a2);
1170             }
1171             a2 *= 0.5;
1172             co = Math.cos(a2);
1173             si = Math.sin(a2);
1174 
1175             A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
1176 
1177             mat = [
1178                 [1, 0, 0],
1179                 [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],
1180                 [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5,  co * 0.5]
1181             ];
1182             vec = Mat.matVecMult(mat, A);
1183             vec[1] /= vec[0];
1184             vec[2] /= vec[0];
1185             vec[0] /= vec[0];
1186 
1187             d = Geometry.distance(vec, B, 3);
1188             vec = [vec[0], B[1] + (vec[1] - B[1]) * (r + dx) / d,  B[2] + (vec[2] - B[2]) * (r + dx) / d];
1189 
1190             return new Coords(Const.COORDS_BY_USER, vec, this.board);
1191         };
1192 
1193         /**
1194          * Returns the value of the angle in Radians.
1195          * @memberOf Angle.prototype
1196          * @name Value
1197          * @function
1198          * @returns {Number} The angle value in Radians
1199          */
1200         el.Value = function () {
1201             return Geometry.rad(this.point2, this.point1, this.point3);
1202         };
1203 
1204         el.methodMap = Type.deepCopy(el.methodMap, {
1205             Value: 'Value',
1206             setAngle: 'setAngle',
1207             free: 'free'
1208         });
1209 
1210         return el;
1211     };
1212 
1213     JXG.registerElement('angle', JXG.createAngle);
1214 
1215     /**
1216      * @class A non-reflex angle is the acute or obtuse instance of an angle.
1217      * It is defined by a center, one point that
1218      * defines the radius, and a third point that defines the angle of the sector.
1219      * @pseudo
1220      * @name NonReflexAngle
1221      * @augments Angle
1222      * @constructor
1223      * @type Sector
1224      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
1225      * @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
1226      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
1227      * @example
1228      * // Create a non-reflex angle out of three free points
1229      * var p1 = board.create('point', [5.0, 3.0]),
1230      *     p2 = board.create('point', [1.0, 0.5]),
1231      *     p3 = board.create('point', [1.5, 5.0]),
1232      *
1233      *     a = board.create('nonreflexangle', [p1, p2, p3], {radius: 2}),
1234      *     t = board.create('text', [4, 4, function() { return a.Value().toFixed(2); }]);
1235      * </pre><div class="jxgbox"id="d0ab6d6b-63a7-48b2-8749-b02bb5e744f9" style="width: 300px; height: 300px;"></div>
1236      * <script type="text/javascript">
1237      * (function () {
1238      *   var board = JXG.JSXGraph.initBoard('d0ab6d6b-63a7-48b2-8749-b02bb5e744f9', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
1239      *     p1 = board.create('point', [5.0, 3.0]),
1240      *     p2 = board.create('point', [1.0, 0.5]),
1241      *     p3 = board.create('point', [1.5, 5.0]),
1242      *
1243      *     a = board.create('nonreflexangle', [p1, p2, p3], {radius: 2}),
1244      *     t = board.create('text', [4, 4, function() { return a.Value().toFixed(2); }]);
1245      * })();
1246      * </script><pre>
1247      */
1248     JXG.createNonreflexAngle = function (board, parents, attributes) {
1249         var el;
1250 
1251         attributes.selection = 'minor';
1252         el = JXG.createAngle(board, parents, attributes);
1253 
1254         el.Value = function () {
1255             var v = Geometry.rad(this.point2, this.point1, this.point3);
1256             return (v < Math.PI) ? v : 2.0 * Math.PI - v;
1257         };
1258         return el;
1259     };
1260 
1261     JXG.registerElement('nonreflexangle', JXG.createNonreflexAngle);
1262 
1263     /**
1264      * @class A reflex angle is the neither acute nor obtuse instance of an angle.
1265      * It is defined by a center, one point that
1266      * defines the radius, and a third point that defines the angle of the sector.
1267      * @pseudo
1268      * @name ReflexAngle
1269      * @augments Angle
1270      * @constructor
1271      * @type Sector
1272      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
1273      * @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
1274      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
1275      * @example
1276      * // Create a non-reflex angle out of three free points
1277      * var p1 = board.create('point', [5.0, 3.0]),
1278      *     p2 = board.create('point', [1.0, 0.5]),
1279      *     p3 = board.create('point', [1.5, 5.0]),
1280      *
1281      *     a = board.create('reflexangle', [p1, p2, p3], {radius: 2}),
1282      *     t = board.create('text', [4, 4, function() { return a.Value().toFixed(2); }]);
1283      * </pre><div class="jxgbox"id="f2a577f2-553d-4f9f-a895-2d6d4b8c60e8" style="width: 300px; height: 300px;"></div>
1284      * <script type="text/javascript">
1285      * (function () {
1286      * var board = JXG.JSXGraph.initBoard('f2a577f2-553d-4f9f-a895-2d6d4b8c60e8', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
1287      *     p1 = board.create('point', [5.0, 3.0]),
1288      *     p2 = board.create('point', [1.0, 0.5]),
1289      *     p3 = board.create('point', [1.5, 5.0]),
1290      *
1291      *     a = board.create('reflexangle', [p1, p2, p3], {radius: 2}),
1292      *     t = board.create('text', [4, 4, function() { return a.Value().toFixed(2); }]);
1293      * })();
1294      * </script><pre>
1295      */
1296     JXG.createReflexAngle = function (board, parents, attributes) {
1297         var el;
1298 
1299         attributes.selection = 'major';
1300         el = JXG.createAngle(board, parents, attributes);
1301 
1302         el.Value = function () {
1303             var v = Geometry.rad(this.point2, this.point1, this.point3);
1304             return (v >= Math.PI) ? v : 2.0 * Math.PI - v;
1305         };
1306         return el;
1307     };
1308 
1309     JXG.registerElement('reflexangle', JXG.createReflexAngle);
1310 
1311     return {
1312         createSector: JXG.createSector,
1313         createCircumcircleSector: JXG.createCircumcircleSector,
1314         createMinorSector: JXG.createMinorSector,
1315         createMajorSector: JXG.createMajorSector,
1316         createAngle: JXG.createAngle,
1317         createReflexAngle: JXG.createReflexAngle,
1318         createNonreflexAngle: JXG.createNonreflexAngle
1319     };
1320 });
1321