1 /*
  2     Copyright 2008-2023
  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 <https://www.gnu.org/licenses/>
 29     and <https://opensource.org/licenses/MIT/>.
 30  */
 31 
 32 /*global JXG: true, define: true*/
 33 /*jslint nomen: true, plusplus: true*/
 34 
 35 import JXG from "../jxg";
 36 import Geometry from "../math/geometry";
 37 import Mat from "../math/math";
 38 import Statistics from "../math/statistics";
 39 import Coords from "../base/coords";
 40 import Const from "../base/constants";
 41 import Type from "../utils/type";
 42 
 43 /**
 44  * @class A circular sector is a subarea of the area enclosed by a circle. It is enclosed by two radii and an arc.
 45  * @pseudo
 46  * @name Sector
 47  * @augments JXG.Curve
 48  * @constructor
 49  * @type JXG.Curve
 50  * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
 51  *
 52  * First possibility of input parameters are:
 53  * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 A sector is defined by three points: The sector's center <tt>p1</tt>,
 54  * a second point <tt>p2</tt> defining the radius and a third point <tt>p3</tt> defining the angle of the sector. The
 55  * Sector is always drawn counter clockwise from <tt>p2</tt> to <tt>p3</tt>.
 56  * <p>
 57  * In this case, the sector will have an arc as sub-object.
 58  * <p>
 59  * Second possibility of input parameters are:
 60  * @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.
 61  * 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).
 62  * The last parameter is the radius of the sector.
 63  * <p>In this case, the sector will <b>not</b> have an arc as sub-object.
 64  *
 65  * @example
 66  * // Create a sector out of three free points
 67  * var p1 = board.create('point', [1.5, 5.0]),
 68  *     p2 = board.create('point', [1.0, 0.5]),
 69  *     p3 = board.create('point', [5.0, 3.0]),
 70  *
 71  *     a = board.create('sector', [p1, p2, p3]);
 72  * </pre><div class="jxgbox" id="JXG49f59123-f013-4681-bfd9-338b89893156" style="width: 300px; height: 300px;"></div>
 73  * <script type="text/javascript">
 74  * (function () {
 75  *   var board = JXG.JSXGraph.initBoard('JXG49f59123-f013-4681-bfd9-338b89893156', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
 76  *     p1 = board.create('point', [1.5, 5.0]),
 77  *     p2 = board.create('point', [1.0, 0.5]),
 78  *     p3 = board.create('point', [5.0, 3.0]),
 79  *
 80  *     a = board.create('sector', [p1, p2, p3]);
 81  * })();
 82  * </script><pre>
 83  *
 84  * @example
 85  * // Create a sector out of two lines, two directions and a radius
 86  * var p1 = board.create('point', [-1, 4]),
 87  *  p2 = board.create('point', [4, 1]),
 88  *  q1 = board.create('point', [-2, -3]),
 89  *  q2 = board.create('point', [4,3]),
 90  *
 91  *  li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
 92  *  li2 = board.create('line', [q1,q2], {lastArrow:true}),
 93  *
 94  *  sec1 = board.create('sector', [li1, li2, [5.5, 0], [4, 3], 3]),
 95  *  sec2 = board.create('sector', [li1, li2, 1, -1, 4]);
 96  *
 97  * </pre><div class="jxgbox" id="JXGbb9e2809-9895-4ff1-adfa-c9c71d50aa53" style="width: 300px; height: 300px;"></div>
 98  * <script type="text/javascript">
 99  * (function () {
100  *   var board = JXG.JSXGraph.initBoard('JXGbb9e2809-9895-4ff1-adfa-c9c71d50aa53', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
101  *     p1 = board.create('point', [-1, 4]),
102  *     p2 = board.create('point', [4, 1]),
103  *     q1 = board.create('point', [-2, -3]),
104  *     q2 = board.create('point', [4,3]),
105  *
106  *     li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
107  *     li2 = board.create('line', [q1,q2], {lastArrow:true}),
108  *
109  *     sec1 = board.create('sector', [li1, li2, [5.5, 0], [4, 3], 3]),
110  *     sec2 = board.create('sector', [li1, li2, 1, -1, 4]);
111  * })();
112  * </script><pre>
113  *
114  * @example
115  * var t = board.create('transform', [2, 1.5], {type: 'scale'});
116  * var s1 = board.create('sector', [[-3.5,-3], [-3.5, -2], [-3.5,-4]], {
117  *                 anglePoint: {visible:true}, center: {visible: true}, radiusPoint: {visible: true},
118  *                 fillColor: 'yellow', strokeColor: 'black'});
119  * var s2 = board.create('curve', [s1, t], {fillColor: 'yellow', strokeColor: 'black'});
120  *
121  * </pre><div id="JXG2e70ee14-6339-11e8-9fb9-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
122  * <script type="text/javascript">
123  *     (function() {
124  *         var board = JXG.JSXGraph.initBoard('JXG2e70ee14-6339-11e8-9fb9-901b0e1b8723',
125  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
126  *     var t = board.create('transform', [2, 1.5], {type: 'scale'});
127  *     var s1 = board.create('sector', [[-3.5,-3], [-3.5, -2], [-3.5,-4]], {
128  *                     anglePoint: {visible:true}, center: {visible: true}, radiusPoint: {visible: true},
129  *                     fillColor: 'yellow', strokeColor: 'black'});
130  *     var s2 = board.create('curve', [s1, t], {fillColor: 'yellow', strokeColor: 'black'});
131  *
132  *     })();
133  *
134  * </script><pre>
135  *
136  * @example
137  * var A = board.create('point', [3, -2]),
138  *     B = board.create('point', [-2, -2]),
139  *     C = board.create('point', [0, 4]);
140  *
141  * var angle = board.create('sector', [B, A, C], {
142  *         strokeWidth: 0,
143  *         arc: {
144  *         	visible: true,
145  *         	strokeWidth: 3,
146  *           lastArrow: {size: 4},
147  *           firstArrow: {size: 4}
148  *         }
149  *       });
150  * //angle.arc.setAttribute({firstArrow: false});
151  * angle.arc.setAttribute({lastArrow: false});
152  *
153  * </pre><div id="JXGca37b99e-1510-49fa-ac9e-efd60e956104" class="jxgbox" style="width: 300px; height: 300px;"></div>
154  * <script type="text/javascript">
155  *     (function() {
156  *         var board = JXG.JSXGraph.initBoard('JXGca37b99e-1510-49fa-ac9e-efd60e956104',
157  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
158  *     var A = board.create('point', [3, -2]),
159  *         B = board.create('point', [-2, -2]),
160  *         C = board.create('point', [0, 4]);
161  *
162  *     var angle = board.create('sector', [B, A, C], {
163  *             strokeWidth: 0,
164  *             arc: {
165  *             	visible: true,
166  *             	strokeWidth: 3,
167  *               lastArrow: {size: 4},
168  *               firstArrow: {size: 4}
169  *             }
170  *           });
171  *     //angle.arc.setAttribute({firstArrow: false});
172  *     angle.arc.setAttribute({lastArrow: false});
173  *
174  *     })();
175  *
176  * </script><pre>
177  *
178  *
179  */
180 JXG.createSector = function (board, parents, attributes) {
181     var el,
182         attr,
183         i,
184         type = "invalid",
185         s,
186         v,
187         attrPoints = ["center", "radiusPoint", "anglePoint"],
188         points;
189 
190     // Three points?
191     if (
192         parents[0].elementClass === Const.OBJECT_CLASS_LINE &&
193         parents[1].elementClass === Const.OBJECT_CLASS_LINE &&
194         (Type.isArray(parents[2]) || Type.isNumber(parents[2])) &&
195         (Type.isArray(parents[3]) || Type.isNumber(parents[3])) &&
196         (Type.isNumber(parents[4]) || Type.isFunction(parents[4]) || Type.isString(parents[4]))
197     ) {
198         type = "2lines";
199     } else {
200         points = Type.providePoints(board, parents, attributes, "sector", attrPoints);
201         if (points === false) {
202             throw new Error(
203                 "JSXGraph: Can't create Sector with parent types '" +
204                     typeof parents[0] +
205                     "' and '" +
206                     typeof parents[1] +
207                     "' and '" +
208                     typeof parents[2] +
209                     "'."
210             );
211         }
212         type = "3points";
213     }
214 
215     attr = Type.copyAttributes(attributes, board.options, "sector");
216     el = board.create("curve", [[0], [0]], attr);
217     el.type = Const.OBJECT_TYPE_SECTOR;
218     el.elType = "sector";
219 
220     /**
221      * Sets radius if the attribute `radius` has value 'auto'.
222      * Sets a radius between 20 and 50 points, depending on the distance
223      * between the center and the radius point.
224      * This function is used in {@link Angle}.
225      *
226      * @name autoRadius
227      * @memberof Sector.prototype
228      * @function
229      * @returns {Number} returns a radius value in user coordinates.
230      * @private
231      */
232     el.autoRadius = function () {
233         var r1 = 20 / el.board.unitX, // 20px
234             r2 = Infinity,
235             r3 = 50 / el.board.unitX; // 50px
236 
237         if (Type.isPoint(el.center)) {
238             // This does not work for 2-lines sectors / angles
239             r2 = el.center.Dist(el.point2) * 0.3333;
240         }
241 
242         return Math.max(r1, Math.min(r2, r3));
243     };
244 
245     if (type === "2lines") {
246         /**
247          * @ignore
248          */
249         el.Radius = function () {
250             var r = Type.evaluate(parents[4]);
251             if (r === "auto") {
252                 return this.autoRadius();
253             }
254             return r;
255         };
256 
257         el.line1 = board.select(parents[0]);
258         el.line2 = board.select(parents[1]);
259 
260         el.line1.addChild(el);
261         el.line2.addChild(el);
262         el.setParents(parents);
263 
264         el.point1 = { visProp: {} };
265         el.point2 = { visProp: {} };
266         el.point3 = { visProp: {} };
267 
268         /* Intersection point */
269         s = Geometry.meetLineLine(el.line1.stdform, el.line2.stdform, 0, board);
270 
271         if (Type.isArray(parents[2])) {
272             /* project p1 to l1 */
273             if (parents[2].length === 2) {
274                 parents[2] = [1].concat(parents[2]);
275             }
276             /*
277                 v = [0, el.line1.stdform[1], el.line1.stdform[2]];
278                 v = Mat.crossProduct(v, parents[2]);
279                 v = Geometry.meetLineLine(v, el.line1.stdform, 0, board);
280                 */
281             v = Geometry.projectPointToLine(
282                 { coords: { usrCoords: parents[2] } },
283                 el.line1,
284                 board
285             );
286             v = Statistics.subtract(v.usrCoords, s.usrCoords);
287             el.direction1 =
288                 Mat.innerProduct(v, [0, el.line1.stdform[2], -el.line1.stdform[1]], 3) >= 0
289                     ? +1
290                     : -1;
291         } else {
292             el.direction1 = parents[2] >= 0 ? 1 : -1;
293         }
294 
295         if (Type.isArray(parents[3])) {
296             /* project p2 to l2 */
297             if (parents[3].length === 2) {
298                 parents[3] = [1].concat(parents[3]);
299             }
300             /*
301                 v = [0, el.line2.stdform[1], el.line2.stdform[2]];
302                 v = Mat.crossProduct(v, parents[3]);
303                 v = Geometry.meetLineLine(v, el.line2.stdform, 0, board);
304                 */
305             v = Geometry.projectPointToLine(
306                 { coords: { usrCoords: parents[3] } },
307                 el.line2,
308                 board
309             );
310             v = Statistics.subtract(v.usrCoords, s.usrCoords);
311             el.direction2 =
312                 Mat.innerProduct(v, [0, el.line2.stdform[2], -el.line2.stdform[1]], 3) >= 0
313                     ? +1
314                     : -1;
315         } else {
316             el.direction2 = parents[3] >= 0 ? 1 : -1;
317         }
318 
319         /**
320          * @class
321          * @ignore
322          */
323         el.updateDataArray = function () {
324             var r,
325                 l1,
326                 l2,
327                 A = [0, 0, 0],
328                 B = [0, 0, 0],
329                 C = [0, 0, 0],
330                 ar;
331 
332             l1 = this.line1;
333             l2 = this.line2;
334 
335             // Intersection point of the lines
336             B = Mat.crossProduct(l1.stdform, l2.stdform);
337 
338             if (Math.abs(B[0]) > Mat.eps * Mat.eps) {
339                 B[1] /= B[0];
340                 B[2] /= B[0];
341                 B[0] /= B[0];
342             }
343             // First point
344             r = this.direction1 * this.Radius();
345             A = Statistics.add(B, [0, r * l1.stdform[2], -r * l1.stdform[1]]);
346 
347             // Second point
348             r = this.direction2 * this.Radius();
349             C = Statistics.add(B, [0, r * l2.stdform[2], -r * l2.stdform[1]]);
350 
351             this.point2.coords = new Coords(Const.COORDS_BY_USER, A, el.board);
352             this.point1.coords = new Coords(Const.COORDS_BY_USER, B, el.board);
353             this.point3.coords = new Coords(Const.COORDS_BY_USER, C, el.board);
354 
355             if (
356                 Math.abs(A[0]) < Mat.eps ||
357                 Math.abs(B[0]) < Mat.eps ||
358                 Math.abs(C[0]) < Mat.eps
359             ) {
360                 this.dataX = [NaN];
361                 this.dataY = [NaN];
362                 return;
363             }
364 
365             ar = Geometry.bezierArc(A, B, C, true, 1);
366 
367             this.dataX = ar[0];
368             this.dataY = ar[1];
369 
370             this.bezierDegree = 3;
371         };
372 
373         // Arc does not work yet, since point1, point2 and point3 are
374         // virtual points.
375         //
376         // attr = Type.copyAttributes(attributes, board.options, "arc");
377         // attr = Type.copyAttributes(attr, board.options, "sector", "arc");
378         // attr.withLabel = false;
379         // attr.name += "_arc";
380         // // el.arc = board.create("arc", [el.point1, el.point2, el.point3], attr);
381         // // The arc's radius is always the radius of sector.
382         // // This is important for angles.
383         // el.updateDataArray();
384         // el.arc = board.create("arc", [
385         //     function() {
386         //         return el.point1.coords.usrCoords;
387         //     }, // Center
388         //     function() {
389         //         var d = el.point2.coords.distance(Const.COORDS_BY_USER, el.point1.coords);
390         //         if (d === 0) {
391         //             return [el.point1.coords.usrCoords[1], el.point1.coords.usrCoords[2]];
392         //         }
393         //         return [
394         //             el.point1.coords.usrCoords[1] + el.Radius() * (el.point2.coords.usrCoords[1] - el.point1.coords.usrCoords[1]) / d,
395         //             el.point1.coords.usrCoords[2] + el.Radius() * (el.point2.coords.usrCoords[2] - el.point1.coords.usrCoords[2]) / d
396         //         ];
397         //     },
398         //     function() {
399         //         return el.point3.coords.usrCoords;
400         //     }, // Center
401         // ], attr);
402         // el.addChild(el.arc);
403 
404         // end '2lines'
405     } else if (type === "3points") {
406         /**
407          * Midpoint of the sector.
408          * @memberOf Sector.prototype
409          * @name point1
410          * @type JXG.Point
411          */
412         el.point1 = points[0];
413 
414         /**
415          * This point together with {@link Sector#point1} defines the radius.
416          * @memberOf Sector.prototype
417          * @name point2
418          * @type JXG.Point
419          */
420         el.point2 = points[1];
421 
422         /**
423          * Defines the sector's angle.
424          * @memberOf Sector.prototype
425          * @name point3
426          * @type JXG.Point
427          */
428         el.point3 = points[2];
429 
430         /* Add arc as child to defining points */
431         for (i = 0; i < 3; i++) {
432             if (Type.exists(points[i]._is_new)) {
433                 el.addChild(points[i]);
434                 delete points[i]._is_new;
435             } else {
436                 points[i].addChild(el);
437             }
438         }
439 
440         // useDirection is necessary for circumCircleSectors
441         el.useDirection = attributes.usedirection;
442         el.setParents(points);
443 
444         /**
445          * Defines the sectors orientation in case of circumCircleSectors.
446          * @memberOf Sector.prototype
447          * @name point4
448          * @type JXG.Point
449          */
450         if (Type.exists(points[3])) {
451             el.point4 = points[3];
452             el.point4.addChild(el);
453         }
454 
455         el.methodMap = JXG.deepCopy(el.methodMap, {
456             arc: "arc",
457             center: "center",
458             radiuspoint: "radiuspoint",
459             anglepoint: "anglepoint"
460         });
461 
462         /**
463          * @class
464          * @ignore
465          */
466         el.updateDataArray = function () {
467             var ar,
468                 det,
469                 p0c,
470                 p1c,
471                 p2c,
472                 A = this.point2,
473                 B = this.point1,
474                 C = this.point3,
475                 phi,
476                 sgn = 1,
477                 vp_s = Type.evaluate(this.visProp.selection);
478 
479             if (!A.isReal || !B.isReal || !C.isReal) {
480                 this.dataX = [NaN];
481                 this.dataY = [NaN];
482                 return;
483             }
484 
485             phi = Geometry.rad(A, B, C);
486             if ((vp_s === "minor" && phi > Math.PI) || (vp_s === "major" && phi < Math.PI)) {
487                 sgn = -1;
488             }
489 
490             // This is true for circumCircleSectors. In that case there is
491             // a fourth parent element: [midpoint, point1, point3, point2]
492             if (this.useDirection && Type.exists(this.point4)) {
493                 p0c = this.point2.coords.usrCoords;
494                 p1c = this.point4.coords.usrCoords;
495                 p2c = this.point3.coords.usrCoords;
496                 det =
497                     (p0c[1] - p2c[1]) * (p0c[2] - p1c[2]) -
498                     (p0c[2] - p2c[2]) * (p0c[1] - p1c[1]);
499 
500                 if (det >= 0.0) {
501                     C = this.point2;
502                     A = this.point3;
503                 }
504             }
505 
506             A = A.coords.usrCoords;
507             B = B.coords.usrCoords;
508             C = C.coords.usrCoords;
509 
510             ar = Geometry.bezierArc(A, B, C, true, sgn);
511 
512             this.dataX = ar[0];
513             this.dataY = ar[1];
514             this.bezierDegree = 3;
515         };
516 
517         /**
518          * Returns the radius of the sector.
519          * @memberOf Sector.prototype
520          * @name Radius
521          * @function
522          * @returns {Number} The distance between {@link Sector#point1} and {@link Sector#point2}.
523          */
524         el.Radius = function () {
525             return this.point2.Dist(this.point1);
526         };
527     } // end '3points'
528 
529     el.center = el.point1;
530     el.radiuspoint = el.point2;
531     el.anglepoint = el.point3;
532 
533     attr = Type.copyAttributes(attributes, board.options, "arc");
534     attr = Type.copyAttributes(attr, board.options, "sector", "arc");
535     attr.withLabel = false;
536     attr.name += "_arc";
537 
538     if (type === "2lines") {
539         el.updateDataArray();
540         el.arc = board.create("arc", [
541             function() {
542                 return el.point1.coords.usrCoords;
543             }, // Center
544             function() {
545                 var d = el.point2.coords.distance(Const.COORDS_BY_USER, el.point1.coords);
546                 if (d === 0) {
547                     return [el.point1.coords.usrCoords[1], el.point1.coords.usrCoords[2]];
548                 }
549                 return [
550                     el.point1.coords.usrCoords[1] + el.Radius() * (el.point2.coords.usrCoords[1] - el.point1.coords.usrCoords[1]) / d,
551                     el.point1.coords.usrCoords[2] + el.Radius() * (el.point2.coords.usrCoords[2] - el.point1.coords.usrCoords[2]) / d
552                 ];
553             },
554             function() {
555                 return el.point3.coords.usrCoords;
556             } // Center
557         ], attr);
558     } else {
559         // The arc's radius is always the radius of sector.
560         // This is important for angles.
561         el.arc = board.create("arc", [
562             el.point1, // Center
563             function() {
564                 var d = el.point2.Dist(el.point1);
565                 if (d === 0) {
566                     return [el.point1.X(), el.point1.Y()];
567                 }
568                 return [
569                     el.point1.X() + el.Radius() * (el.point2.X() - el.point1.X()) / d,
570                     el.point1.Y() + el.Radius() * (el.point2.Y() - el.point1.Y()) / d
571                 ];
572             },
573             el.point3
574         ], attr);
575     }
576     el.addChild(el.arc);
577 
578     // Default hasPoint method. Documented in geometry element
579     el.hasPointCurve = function (x, y) {
580         var angle,
581             alpha,
582             beta,
583             prec,
584             type,
585             checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),
586             r = this.Radius(),
587             dist = this.center.coords.distance(Const.COORDS_BY_USER, checkPoint),
588             has,
589             vp_s = Type.evaluate(this.visProp.selection);
590 
591         if (Type.isObject(Type.evaluate(this.visProp.precision))) {
592             type = this.board._inputDevice;
593             prec = Type.evaluate(this.visProp.precision[type]);
594         } else {
595             // 'inherit'
596             prec = this.board.options.precision.hasPoint;
597         }
598         prec /= Math.min(Math.abs(this.board.unitX), Math.abs(this.board.unitY));
599         has = Math.abs(dist - r) < prec;
600         if (has) {
601             angle = Geometry.rad(this.point2, this.center, checkPoint.usrCoords.slice(1));
602             alpha = 0;
603             beta = Geometry.rad(this.point2, this.center, this.point3);
604 
605             if ((vp_s === "minor" && beta > Math.PI) || (vp_s === "major" && beta < Math.PI)) {
606                 alpha = beta;
607                 beta = 2 * Math.PI;
608             }
609 
610             if (angle < alpha || angle > beta) {
611                 has = false;
612             }
613         }
614 
615         return has;
616     };
617 
618     /**
619      * Checks whether (x,y) is within the area defined by the sector.
620      * @memberOf Sector.prototype
621      * @name hasPointSector
622      * @function
623      * @param {Number} x Coordinate in x direction, screen coordinates.
624      * @param {Number} y Coordinate in y direction, screen coordinates.
625      * @returns {Boolean} True if (x,y) is within the sector defined by the arc, False otherwise.
626      */
627     el.hasPointSector = function (x, y) {
628         var angle,
629             checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),
630             r = this.Radius(),
631             dist = this.point1.coords.distance(Const.COORDS_BY_USER, checkPoint),
632             alpha,
633             beta,
634             has = dist < r,
635             vp_s = Type.evaluate(this.visProp.selection);
636 
637         if (has) {
638             angle = Geometry.rad(this.radiuspoint, this.center, checkPoint.usrCoords.slice(1));
639             alpha = 0.0;
640             beta = Geometry.rad(this.radiuspoint, this.center, this.anglepoint);
641 
642             if ((vp_s === "minor" && beta > Math.PI) || (vp_s === "major" && beta < Math.PI)) {
643                 alpha = beta;
644                 beta = 2 * Math.PI;
645             }
646             //if (angle > Geometry.rad(this.point2, this.point1, this.point3)) {
647             if (angle < alpha || angle > beta) {
648                 has = false;
649             }
650         }
651         return has;
652     };
653 
654     el.hasPoint = function (x, y) {
655         if (
656             Type.evaluate(this.visProp.highlightonsector) ||
657             Type.evaluate(this.visProp.hasinnerpoints)
658         ) {
659             return this.hasPointSector(x, y);
660         }
661 
662         return this.hasPointCurve(x, y);
663     };
664 
665     // documented in GeometryElement
666     el.getTextAnchor = function () {
667         return this.point1.coords;
668     };
669 
670     // documented in GeometryElement
671     // this method is very similar to arc.getLabelAnchor()
672     // there are some additions in the arc version though, mainly concerning
673     // "major" and "minor" arcs. but maybe these methods can be merged.
674     /**
675      * @class
676      * @ignore
677      */
678     el.getLabelAnchor = function () {
679         var coords,
680             vec,
681             vecx,
682             vecy,
683             len,
684             angle = Geometry.rad(this.point2, this.point1, this.point3),
685             dx = 13 / this.board.unitX,
686             dy = 13 / this.board.unitY,
687             p2c = this.point2.coords.usrCoords,
688             pmc = this.point1.coords.usrCoords,
689             bxminusax = p2c[1] - pmc[1],
690             byminusay = p2c[2] - pmc[2],
691             vp_s = Type.evaluate(this.visProp.selection),
692             l_vp = this.label ? this.label.visProp : this.visProp.label;
693 
694         // If this is uncommented, the angle label can not be dragged
695         //if (Type.exists(this.label)) {
696         //    this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);
697         //}
698 
699         if ((vp_s === "minor" && angle > Math.PI) || (vp_s === "major" && angle < Math.PI)) {
700             angle = -(2 * Math.PI - angle);
701         }
702 
703         coords = new Coords(
704             Const.COORDS_BY_USER,
705             [
706                 pmc[1] + Math.cos(angle * 0.5) * bxminusax - Math.sin(angle * 0.5) * byminusay,
707                 pmc[2] + Math.sin(angle * 0.5) * bxminusax + Math.cos(angle * 0.5) * byminusay
708             ],
709             this.board
710         );
711 
712         vecx = coords.usrCoords[1] - pmc[1];
713         vecy = coords.usrCoords[2] - pmc[2];
714 
715         len = Mat.hypot(vecx, vecy);
716         vecx = (vecx * (len + dx)) / len;
717         vecy = (vecy * (len + dy)) / len;
718         vec = [pmc[1] + vecx, pmc[2] + vecy];
719 
720         l_vp.position = Geometry.calcLabelQuadrant(Geometry.rad([1, 0], [0, 0], vec));
721 
722         return new Coords(Const.COORDS_BY_USER, vec, this.board);
723     };
724 
725     /**
726      * Overwrite the Radius method of the sector.
727      * Used in {@link GeometryElement#setAttribute}.
728      * @memberOf Sector.prototype
729      * @name setRadius
730      * @param {Number|Function} value New radius.
731      * @function
732      */
733     el.setRadius = function (val) {
734         var res,
735             e = Type.evaluate(val);
736 
737         if (val === 'auto' || e === 'auto') {
738             res = 'auto';
739         } else if (Type.isNumber(val)) {
740             res = 'number';
741         } else if (Type.isFunction(val) && !Type.isString(e)) {
742             res = 'function';
743         } else {
744             res = 'undefined';
745         }
746         if (res !== 'undefined') {
747             this.visProp.radius = val;
748         }
749 
750         /**
751          * @ignore
752          */
753         el.Radius = function () {
754             var r = Type.evaluate(val);
755             if (r === "auto") {
756                 return this.autoRadius();
757             }
758             return r;
759         };
760     };
761 
762     /**
763      * @deprecated
764      * @ignore
765      */
766     el.getRadius = function () {
767         JXG.deprecated("Sector.getRadius()", "Sector.Radius()");
768         return this.Radius();
769     };
770 
771     /**
772      * Length of the sector's arc or the angle in various units, see {@link Arc#Value}.
773      * @memberOf Sector.prototype
774      * @name Value
775      * @function
776      * @param {String} unit
777      * @returns {Number} The arc length or the angle value in various units.
778      * @see Arc#Value
779      */
780     el.Value = function(unit) {
781         return this.arc.Value(unit);
782     };
783 
784     /**
785      * Arc length.
786      * @memberOf Sector.prototype
787      * @name L
788      * @returns {Number} Length of the sector's arc.
789      * @function
790      * @see Arc#L
791      */
792     el.L = function() {
793         return this.arc.L();
794     };
795 
796     /**
797      * Area of the sector.
798      * @memberOf Sector.prototype
799      * @name Area
800      * @function
801      * @returns {Number} The area of the sector.
802      */
803     el.Area = function () {
804         var r = this.Radius();
805 
806         return 0.5 * r * r * this.Value('radians');
807     };
808 
809     /**
810      * Sector perimeter, i.e. arc length plus 2 * radius.
811      * @memberOf Sector.prototype
812      * @name Perimeter
813      * @function
814      * @returns {Number} Perimeter of sector.
815      */
816     el.Perimeter = function () {
817         return this.L() + 2 * this.Radius();
818     };
819 
820     if (type === "3points") {
821         /**
822          * Moves the sector by the difference of two coordinates.
823          * @memberOf Sector.prototype
824          * @name setPositionDirectly
825          * @function
826          * @param {Number} method The type of coordinates used here. Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
827          * @param {Array} coords coordinates in screen/user units
828          * @param {Array} oldcoords previous coordinates in screen/user units
829          * @returns {JXG.Curve} this element
830          * @private
831          */
832         el.setPositionDirectly = function (method, coords, oldcoords) {
833             var dc, t,
834                 c = new Coords(method, coords, this.board),
835                 oldc = new Coords(method, oldcoords, this.board);
836 
837             if (!el.point1.draggable() || !el.point2.draggable() || !el.point3.draggable()) {
838                 return this;
839             }
840 
841             dc = Statistics.subtract(c.usrCoords, oldc.usrCoords);
842             t = this.board.create("transform", dc.slice(1), { type: "translate" });
843             t.applyOnce([el.point1, el.point2, el.point3]);
844 
845             return this;
846         };
847     }
848 
849     el.methodMap = JXG.deepCopy(el.methodMap, {
850         radius: "Radius",
851         getRadius: "Radius",
852         setRadius: "setRadius",
853         Value: "Value",
854         L: "L",
855         Area: "Area",
856         Perimeter: "Perimeter"
857     });
858 
859     return el;
860 };
861 
862 JXG.registerElement("sector", JXG.createSector);
863 
864 /**
865  * @class A circumcircle sector is different from a {@link Sector} mostly in the way the parent elements are interpreted.
866  * At first, the circum center is determined from the three given points. Then the sector is drawn from <tt>p1</tt> through
867  * <tt>p2</tt> to <tt>p3</tt>.
868  * @pseudo
869  * @name CircumcircleSector
870  * @augments Sector
871  * @constructor
872  * @type Sector
873  * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
874  * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 A circumcircle sector is defined by the circumcircle which is determined
875  * by these three given points. The circumcircle sector is always drawn from <tt>p1</tt> through <tt>p2</tt> to <tt>p3</tt>.
876  * @example
877  * // Create an arc out of three free points
878  * var p1 = board.create('point', [1.5, 5.0]),
879  *     p2 = board.create('point', [1.0, 0.5]),
880  *     p3 = board.create('point', [5.0, 3.0]),
881  *
882  *     a = board.create('circumcirclesector', [p1, p2, p3]);
883  * </pre><div class="jxgbox" id="JXG695cf0d6-6d7a-4d4d-bfc9-34c6aa28cd04" style="width: 300px; height: 300px;"></div>
884  * <script type="text/javascript">
885  * (function () {
886  *   var board = JXG.JSXGraph.initBoard('JXG695cf0d6-6d7a-4d4d-bfc9-34c6aa28cd04', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
887  *     p1 = board.create('point', [1.5, 5.0]),
888  *     p2 = board.create('point', [1.0, 0.5]),
889  *     p3 = board.create('point', [5.0, 3.0]),
890  *
891  *     a = board.create('circumcirclesector', [p1, p2, p3]);
892  * })();
893  * </script><pre>
894  */
895 JXG.createCircumcircleSector = function (board, parents, attributes) {
896     var el, mp, attr, points;
897 
898     points = Type.providePoints(board, parents, attributes, "point");
899     if (points === false) {
900         throw new Error(
901             "JSXGraph: Can't create circumcircle sector with parent types '" +
902                 typeof parents[0] +
903                 "' and '" +
904                 typeof parents[1] +
905                 "' and '" +
906                 typeof parents[2] +
907                 "'."
908         );
909     }
910 
911     mp = board.create("circumcenter", points.slice(0, 3), attr);
912     mp.dump = false;
913 
914     attr = Type.copyAttributes(attributes, board.options, "circumcirclesector");
915     el = board.create("sector", [mp, points[0], points[2], points[1]], attr);
916 
917     el.elType = "circumcirclesector";
918     el.setParents(points);
919 
920     /**
921      * Center of the circumcirclesector
922      * @memberOf CircumcircleSector.prototype
923      * @name center
924      * @type Circumcenter
925      */
926     el.center = mp;
927     el.subs = {
928         center: mp
929     };
930 
931     return el;
932 };
933 
934 JXG.registerElement("circumcirclesector", JXG.createCircumcircleSector);
935 
936 /**
937  * @class A minor sector is a sector of a circle having measure less than or equal to
938  * 180 degrees (pi radians). It is defined by a center, one point that
939  * defines the radius, and a third point that defines the angle of the sector.
940  * @pseudo
941  * @name MinorSector
942  * @augments Curve
943  * @constructor
944  * @type JXG.Curve
945  * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
946  * @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
947  * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
948  * @example
949  * // Create sector out of three free points
950  * var p1 = board.create('point', [2.0, 2.0]);
951  * var p2 = board.create('point', [1.0, 0.5]);
952  * var p3 = board.create('point', [3.5, 1.0]);
953  *
954  * var a = board.create('minorsector', [p1, p2, p3]);
955  * </pre><div class="jxgbox" id="JXGaf27ddcc-265f-428f-90dd-d31ace945800" style="width: 300px; height: 300px;"></div>
956  * <script type="text/javascript">
957  * (function () {
958  *   var board = JXG.JSXGraph.initBoard('JXGaf27ddcc-265f-428f-90dd-d31ace945800', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
959  *       p1 = board.create('point', [2.0, 2.0]),
960  *       p2 = board.create('point', [1.0, 0.5]),
961  *       p3 = board.create('point', [3.5, 1.0]),
962  *
963  *       a = board.create('minorsector', [p1, p2, p3]);
964  * })();
965  * </script><pre>
966  *
967  * @example
968  * var A = board.create('point', [3, -2]),
969  *     B = board.create('point', [-2, -2]),
970  *     C = board.create('point', [0, 4]);
971  *
972  * var angle = board.create('minorsector', [B, A, C], {
973  *         strokeWidth: 0,
974  *         arc: {
975  *         	visible: true,
976  *         	strokeWidth: 3,
977  *           lastArrow: {size: 4},
978  *           firstArrow: {size: 4}
979  *         }
980  *       });
981  * //angle.arc.setAttribute({firstArrow: false});
982  * angle.arc.setAttribute({lastArrow: false});
983  *
984  *
985  * </pre><div id="JXGdddf3c8f-4b0c-4268-8171-8fcd30e71f60" class="jxgbox" style="width: 300px; height: 300px;"></div>
986  * <script type="text/javascript">
987  *     (function() {
988  *         var board = JXG.JSXGraph.initBoard('JXGdddf3c8f-4b0c-4268-8171-8fcd30e71f60',
989  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
990  *     var A = board.create('point', [3, -2]),
991  *         B = board.create('point', [-2, -2]),
992  *         C = board.create('point', [0, 4]);
993  *
994  *     var angle = board.create('minorsector', [B, A, C], {
995  *             strokeWidth: 0,
996  *             arc: {
997  *             	visible: true,
998  *             	strokeWidth: 3,
999  *               lastArrow: {size: 4},
1000  *               firstArrow: {size: 4}
1001  *             }
1002  *           });
1003  *     //angle.arc.setAttribute({firstArrow: false});
1004  *     angle.arc.setAttribute({lastArrow: false});
1005  *
1006  *
1007  *     })();
1008  *
1009  * </script><pre>
1010  *
1011  */
1012 JXG.createMinorSector = function (board, parents, attributes) {
1013     attributes.selection = "minor";
1014     return JXG.createSector(board, parents, attributes);
1015 };
1016 
1017 JXG.registerElement("minorsector", JXG.createMinorSector);
1018 
1019 /**
1020  * @class A major sector is a sector of a circle having measure greater than or equal to
1021  * 180 degrees (pi radians). It is defined by a center, one point that
1022  * defines the radius, and a third point that defines the angle of the sector.
1023  * @pseudo
1024  * @name MajorSector
1025  * @augments Curve
1026  * @constructor
1027  * @type JXG.Curve
1028  * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
1029  * @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
1030  * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
1031  * @example
1032  * // Create an arc out of three free points
1033  * var p1 = board.create('point', [2.0, 2.0]);
1034  * var p2 = board.create('point', [1.0, 0.5]);
1035  * var p3 = board.create('point', [3.5, 1.0]);
1036  *
1037  * var a = board.create('majorsector', [p1, p2, p3]);
1038  * </pre><div class="jxgbox" id="JXG83c6561f-7561-4047-b98d-036248a00932" style="width: 300px; height: 300px;"></div>
1039  * <script type="text/javascript">
1040  * (function () {
1041  *   var board = JXG.JSXGraph.initBoard('JXG83c6561f-7561-4047-b98d-036248a00932', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
1042  *       p1 = board.create('point', [2.0, 2.0]),
1043  *       p2 = board.create('point', [1.0, 0.5]),
1044  *       p3 = board.create('point', [3.5, 1.0]),
1045  *
1046  *       a = board.create('majorsector', [p1, p2, p3]);
1047  * })();
1048  * </script><pre>
1049  */
1050 JXG.createMajorSector = function (board, parents, attributes) {
1051     attributes.selection = "major";
1052     return JXG.createSector(board, parents, attributes);
1053 };
1054 
1055 JXG.registerElement("majorsector", JXG.createMajorSector);
1056 
1057 /**
1058  * @class The angle element is used to denote an angle defined by three points. Visually it is just a {@link Sector}
1059  * element with a radius not defined by the parent elements but by an attribute <tt>radius</tt>. As opposed to the sector,
1060  * an angle has two angle points and no radius point.
1061  * Sector is displayed if type=="sector".
1062  * If type=="square", instead of a sector a parallelogram is displayed.
1063  * In case of type=="auto", a square is displayed if the angle is near orthogonal.
1064  * If no name is provided the angle label is automatically set to a lower greek letter.
1065  * @pseudo
1066  * @name Angle
1067  * @augments Sector
1068  * @constructor
1069  * @type Sector
1070  * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
1071  * First possibility of input parameters are:
1072  * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 An angle is always drawn counterclockwise from <tt>p1</tt> to
1073  * <tt>p3</tt> around <tt>p2</tt>.
1074  *
1075  * Second possibility of input parameters are:
1076  * @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.
1077  * The two legs which define the angle are given by two coordinate arrays.
1078  * The points given by these coordinate arrays are projected initially (i.e. only once) onto the two lines.
1079  * The other possibility is to supply directions (+/- 1).
1080  *
1081  * @example
1082  * // Create an angle out of three free points
1083  * var p1 = board.create('point', [5.0, 3.0]),
1084  *     p2 = board.create('point', [1.0, 0.5]),
1085  *     p3 = board.create('point', [1.5, 5.0]),
1086  *
1087  *     a = board.create('angle', [p1, p2, p3]),
1088  *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
1089  * </pre><div class="jxgbox" id="JXGa34151f9-bb26-480a-8d6e-9b8cbf789ae5" style="width: 300px; height: 300px;"></div>
1090  * <script type="text/javascript">
1091  * (function () {
1092  *   var board = JXG.JSXGraph.initBoard('JXGa34151f9-bb26-480a-8d6e-9b8cbf789ae5', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
1093  *     p1 = board.create('point', [5.0, 3.0]),
1094  *     p2 = board.create('point', [1.0, 0.5]),
1095  *     p3 = board.create('point', [1.5, 5.0]),
1096  *
1097  *     a = board.create('angle', [p1, p2, p3]),
1098  *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
1099  * })();
1100  * </script><pre>
1101  *
1102  * @example
1103  * // Create an angle out of two lines and two directions
1104  * var p1 = board.create('point', [-1, 4]),
1105  *  p2 = board.create('point', [4, 1]),
1106  *  q1 = board.create('point', [-2, -3]),
1107  *  q2 = board.create('point', [4,3]),
1108  *
1109  *  li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
1110  *  li2 = board.create('line', [q1,q2], {lastArrow:true}),
1111  *
1112  *  a1 = board.create('angle', [li1, li2, [5.5, 0], [4, 3]], { radius:1 }),
1113  *  a2 = board.create('angle', [li1, li2, 1, -1], { radius:2 });
1114  *
1115  *
1116  * </pre><div class="jxgbox" id="JXG3a667ddd-63dc-4594-b5f1-afac969b371f" style="width: 300px; height: 300px;"></div>
1117  * <script type="text/javascript">
1118  * (function () {
1119  *   var board = JXG.JSXGraph.initBoard('JXG3a667ddd-63dc-4594-b5f1-afac969b371f', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
1120  *     p1 = board.create('point', [-1, 4]),
1121  *     p2 = board.create('point', [4, 1]),
1122  *     q1 = board.create('point', [-2, -3]),
1123  *     q2 = board.create('point', [4,3]),
1124  *
1125  *     li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
1126  *     li2 = board.create('line', [q1,q2], {lastArrow:true}),
1127  *
1128  *     a1 = board.create('angle', [li1, li2, [5.5, 0], [4, 3]], { radius:1 }),
1129  *     a2 = board.create('angle', [li1, li2, 1, -1], { radius:2 });
1130  * })();
1131  * </script><pre>
1132  *
1133  *
1134  * @example
1135  * // Display the angle value instead of the name
1136  * var p1 = board.create('point', [0,2]);
1137  * var p2 = board.create('point', [0,0]);
1138  * var p3 = board.create('point', [-2,0.2]);
1139  *
1140  * var a = board.create('angle', [p1, p2, p3], {
1141  * 	 radius: 1,
1142  *   name: function() {
1143  *   	return JXG.Math.Geometry.trueAngle(p1, p2, p3).toFixed(1) + '°';
1144  *   }});
1145  *
1146  * </pre><div id="JXGc813f601-8dd3-4030-9892-25c6d8671512" class="jxgbox" style="width: 300px; height: 300px;"></div>
1147  * <script type="text/javascript">
1148  *     (function() {
1149  *         var board = JXG.JSXGraph.initBoard('JXGc813f601-8dd3-4030-9892-25c6d8671512',
1150  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
1151  *
1152  *     var p1 = board.create('point', [0,2]);
1153  *     var p2 = board.create('point', [0,0]);
1154  *     var p3 = board.create('point', [-2,0.2]);
1155  *
1156  *     var a = board.create('angle', [p1, p2, p3], {
1157  *     	radius: 1,
1158  *       name: function() {
1159  *       	return JXG.Math.Geometry.trueAngle(p1, p2, p3).toFixed(1) + '°';
1160  *       }});
1161  *
1162  *     })();
1163  *
1164  * </script><pre>
1165  *
1166  *
1167  * @example
1168  * // Apply a transformation to an angle.
1169  * var t = board.create('transform', [2, 1.5], {type: 'scale'});
1170  * var an1 = board.create('angle', [[-4,3.9], [-3, 4], [-3, 3]]);
1171  * var an2 = board.create('curve', [an1, t]);
1172  *
1173  * </pre><div id="JXG4c8d9ed8-6339-11e8-9fb9-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
1174  * <script type="text/javascript">
1175  *     (function() {
1176  *         var board = JXG.JSXGraph.initBoard('JXG4c8d9ed8-6339-11e8-9fb9-901b0e1b8723',
1177  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
1178  *     var t = board.create('transform', [2, 1.5], {type: 'scale'});
1179  *     var an1 = board.create('angle', [[-4,3.9], [-3, 4], [-3, 3]]);
1180  *     var an2 = board.create('curve', [an1, t]);
1181  *
1182  *     })();
1183  *
1184  * </script><pre>
1185  *
1186  */
1187 JXG.createAngle = function (board, parents, attributes) {
1188     var el,
1189         radius, attr, attrsub,
1190         i, points,
1191         type = "invalid";
1192 
1193     // Two lines or three points?
1194     if (
1195         parents[0].elementClass === Const.OBJECT_CLASS_LINE &&
1196         parents[1].elementClass === Const.OBJECT_CLASS_LINE &&
1197         (Type.isArray(parents[2]) || Type.isNumber(parents[2])) &&
1198         (Type.isArray(parents[3]) || Type.isNumber(parents[3]))
1199     ) {
1200         type = "2lines";
1201     } else {
1202         attr = {
1203             name: ''
1204         };
1205         points = Type.providePoints(board, parents, attr, "point");
1206         if (points === false) {
1207             throw new Error(
1208                 "JSXGraph: Can't create angle with parent types '" +
1209                     typeof parents[0] +
1210                     "' and '" +
1211                     typeof parents[1] +
1212                     "' and '" +
1213                     typeof parents[2] +
1214                     "'."
1215             );
1216         }
1217         type = "3points";
1218     }
1219 
1220     attr = Type.copyAttributes(attributes, board.options, "angle");
1221 
1222     //  If empty, create a new name
1223     if (!Type.exists(attr.name) || attr.name === "") {
1224         attr.name = board.generateName({ type: Const.OBJECT_TYPE_ANGLE });
1225     }
1226 
1227     if (Type.exists(attr.radius)) {
1228         radius = attr.radius;
1229     } else {
1230         radius = 0;
1231     }
1232 
1233     board.suspendUpdate(); // Necessary for immediate availability of radius.
1234     if (type === "2lines") {
1235         parents.push(radius);
1236         el = board.create("sector", parents, attr);
1237         /**
1238          * @class
1239          * @ignore
1240          */
1241         el.updateDataArraySector = el.updateDataArray;
1242 
1243         // TODO
1244         /**
1245          * @class
1246          * @ignore
1247          */
1248         el.setAngle = function (val) {};
1249         /**
1250          * @class
1251          * @ignore
1252          */
1253         el.free = function (val) {};
1254     } else {
1255         el = board.create("sector", [points[1], points[0], points[2]], attr);
1256         el.arc.visProp.priv = true;
1257 
1258         /**
1259          * The point defining the radius of the angle element.
1260          * Alias for {@link Sector#radiuspoint}.
1261          * @type JXG.Point
1262          * @name point
1263          * @memberOf Angle.prototype
1264          *
1265          */
1266         el.point = el.point2 = el.radiuspoint = points[0];
1267 
1268         /**
1269          * Helper point for angles of type 'square'.
1270          * @type JXG.Point
1271          * @name pointsquare
1272          * @memberOf Angle.prototype
1273          */
1274         el.pointsquare = el.point3 = el.anglepoint = points[2];
1275 
1276         /**
1277          * @ignore
1278          */
1279         el.Radius = function () {
1280             // Set the angle radius, also @see @link Sector#autoRadius
1281             var r = Type.evaluate(radius);
1282             if (r === "auto") {
1283                 return el.autoRadius();
1284             }
1285             return r;
1286         };
1287 
1288         /**
1289          * @class
1290          * @ignore
1291          */
1292         el.updateDataArraySector = function () {
1293             var A = this.point2,
1294                 B = this.point1,
1295                 C = this.point3,
1296                 r = this.Radius(),
1297                 d = B.Dist(A),
1298                 ar,
1299                 phi,
1300                 sgn = 1,
1301                 vp_s = Type.evaluate(this.visProp.selection);
1302 
1303             phi = Geometry.rad(A, B, C);
1304             if ((vp_s === "minor" && phi > Math.PI) || (vp_s === "major" && phi < Math.PI)) {
1305                 sgn = -1;
1306             }
1307 
1308             A = A.coords.usrCoords;
1309             B = B.coords.usrCoords;
1310             C = C.coords.usrCoords;
1311 
1312             A = [1, B[1] + ((A[1] - B[1]) * r) / d, B[2] + ((A[2] - B[2]) * r) / d];
1313             C = [1, B[1] + ((C[1] - B[1]) * r) / d, B[2] + ((C[2] - B[2]) * r) / d];
1314 
1315             ar = Geometry.bezierArc(A, B, C, true, sgn);
1316 
1317             this.dataX = ar[0];
1318             this.dataY = ar[1];
1319             this.bezierDegree = 3;
1320         };
1321 
1322         /**
1323          * Set an angle to a prescribed value given in radians.
1324          * This is only possible if the third point of the angle, i.e.
1325          * the anglepoint is a free point.
1326          * Removing the constraint again is done by calling "angle.free()".
1327          *
1328          * Changing the angle requires to call the method "free()":
1329          *
1330          * <pre>
1331          * angle.setAngle(Math.PI / 6);
1332          * // ...
1333          * angle.free().setAngle(Math.PI / 4);
1334          * </pre>
1335          *
1336          * @name setAngle
1337          * @memberof Angle.prototype
1338          * @function
1339          * @param {Number|Function} val Number or Function which returns the size of the angle in Radians
1340          * @returns {Object} Pointer to the angle element..
1341          * @see Angle#free
1342          *
1343          * @example
1344          * var p1, p2, p3, c, a, s;
1345          *
1346          * p1 = board.create('point',[0,0]);
1347          * p2 = board.create('point',[5,0]);
1348          * p3 = board.create('point',[0,5]);
1349          *
1350          * c1 = board.create('circle',[p1, p2]);
1351          *
1352          * a = board.create('angle',[p2, p1, p3], {radius:3});
1353          *
1354          * a.setAngle(function() {
1355          *     return Math.PI / 3;
1356          * });
1357          * board.update();
1358          *
1359          * </pre><div id="JXG987c-394f-11e6-af4a-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
1360          * <script type="text/javascript">
1361          *     (function() {
1362          *         var board = JXG.JSXGraph.initBoard('JXG987c-394f-11e6-af4a-901b0e1b8723',
1363          *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
1364          *     var p1, p2, p3, c, a, s;
1365          *
1366          *     p1 = board.create('point',[0,0]);
1367          *     p2 = board.create('point',[5,0]);
1368          *     p3 = board.create('point',[0,5]);
1369          *
1370          *     c1 = board.create('circle',[p1, p2]);
1371          *
1372          *     a = board.create('angle',[p2, p1, p3], {radius: 3});
1373          *
1374          *     a.setAngle(function() {
1375          *         return Math.PI / 3;
1376          *     });
1377          *     board.update();
1378          *
1379          *     })();
1380          *
1381          * </script><pre>
1382          *
1383          * @example
1384          * var p1, p2, p3, c, a, s;
1385          *
1386          * p1 = board.create('point',[0,0]);
1387          * p2 = board.create('point',[5,0]);
1388          * p3 = board.create('point',[0,5]);
1389          *
1390          * c1 = board.create('circle',[p1, p2]);
1391          *
1392          * a = board.create('angle',[p2, p1, p3], {radius:3});
1393          * s = board.create('slider',[[-2,1], [2,1], [0, Math.PI*0.5, 2*Math.PI]]);
1394          *
1395          * a.setAngle(function() {
1396          *     return s.Value();
1397          * });
1398          * board.update();
1399          *
1400          * </pre><div id="JXG99957b1c-394f-11e6-af4a-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
1401          * <script type="text/javascript">
1402          *     (function() {
1403          *         var board = JXG.JSXGraph.initBoard('JXG99957b1c-394f-11e6-af4a-901b0e1b8723',
1404          *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
1405          *     var p1, p2, p3, c, a, s;
1406          *
1407          *     p1 = board.create('point',[0,0]);
1408          *     p2 = board.create('point',[5,0]);
1409          *     p3 = board.create('point',[0,5]);
1410          *
1411          *     c1 = board.create('circle',[p1, p2]);
1412          *
1413          *     a = board.create('angle',[p2, p1, p3], {radius: 3});
1414          *     s = board.create('slider',[[-2,1], [2,1], [0, Math.PI*0.5, 2*Math.PI]]);
1415          *
1416          *     a.setAngle(function() {
1417          *         return s.Value();
1418          *     });
1419          *     board.update();
1420          *
1421          *     })();
1422          *
1423          * </script><pre>
1424          *
1425          */
1426         el.setAngle = function (val) {
1427             var t1, t2,
1428                 val2,
1429                 p = this.anglepoint,
1430                 q = this.radiuspoint;
1431 
1432             if (p.draggable()) {
1433                 t1 = this.board.create("transform", [val, this.center], {
1434                     type: "rotate"
1435                 });
1436                 p.addTransform(q, t1);
1437                 // Immediately apply the transformation.
1438                 // This prevents that jumping elements can be watched.
1439                 t1.update();
1440                 p.moveTo(Mat.matVecMult(t1.matrix, q.coords.usrCoords));
1441 
1442                 if (Type.isFunction(val)) {
1443                     /**
1444                      * @ignore
1445                      */
1446                     val2 = function () {
1447                         return Math.PI * 2 - val();
1448                     };
1449                 } else {
1450                     /**
1451                      * @ignore
1452                      */
1453                     val2 = function () {
1454                         return Math.PI * 2 - val;
1455                     };
1456                 }
1457                 t2 = this.board.create("transform", [val2, this.center], {
1458                     type: "rotate"
1459                 });
1460                 p.coords.on("update", function () {
1461                     t2.update();
1462                     q.moveTo(Mat.matVecMult(t2.matrix, p.coords.usrCoords));
1463                 });
1464 
1465                 p.setParents(q);
1466             }
1467             return this;
1468         };
1469 
1470         /**
1471          * Frees an angle from a prescribed value. This is only relevant if the angle size has been set by
1472          * "setAngle()" previously. The anglepoint is set to a free point.
1473          * @name free
1474          * @function
1475          * @memberof Angle.prototype
1476          * @returns {Object} Pointer to the angle element..
1477          * @see Angle#setAngle
1478          */
1479         el.free = function () {
1480             var p = this.anglepoint;
1481 
1482             if (p.transformations.length > 0) {
1483                 p.transformations.pop();
1484                 p.isDraggable = true;
1485                 p.parents = [];
1486 
1487                 p.coords.off("update");
1488             }
1489 
1490             return this;
1491         };
1492 
1493         el.setParents(points); // Important: This overwrites the parents order in underlying sector
1494     } // end '3points'
1495 
1496     // GEONExT compatible labels.
1497     if (Type.exists(el.visProp.text)) {
1498         el.label.setText(Type.evaluate(el.visProp.text));
1499     }
1500 
1501     el.elType = "angle";
1502     el.type = Const.OBJECT_TYPE_ANGLE;
1503     el.subs = {};
1504 
1505     /**
1506      * @class
1507      * @ignore
1508      */
1509     el.updateDataArraySquare = function () {
1510         var A, B, C,
1511             d1, d2, v, l1, l2,
1512             r = this.Radius();
1513 
1514         if (type === "2lines") {
1515             // This is necessary to update this.point1, this.point2, this.point3.
1516             this.updateDataArraySector();
1517         }
1518 
1519         A = this.point2;
1520         B = this.point1;
1521         C = this.point3;
1522 
1523         A = A.coords.usrCoords;
1524         B = B.coords.usrCoords;
1525         C = C.coords.usrCoords;
1526 
1527         d1 = Geometry.distance(A, B, 3);
1528         d2 = Geometry.distance(C, B, 3);
1529 
1530         // In case of type=='2lines' this is redundant, because r == d1 == d2
1531         A = [1, B[1] + ((A[1] - B[1]) * r) / d1, B[2] + ((A[2] - B[2]) * r) / d1];
1532         C = [1, B[1] + ((C[1] - B[1]) * r) / d2, B[2] + ((C[2] - B[2]) * r) / d2];
1533 
1534         v = Mat.crossProduct(C, B);
1535         l1 = [-A[1] * v[1] - A[2] * v[2], A[0] * v[1], A[0] * v[2]];
1536         v = Mat.crossProduct(A, B);
1537         l2 = [-C[1] * v[1] - C[2] * v[2], C[0] * v[1], C[0] * v[2]];
1538 
1539         v = Mat.crossProduct(l1, l2);
1540         v[1] /= v[0];
1541         v[2] /= v[0];
1542 
1543         this.dataX = [B[1], A[1], v[1], C[1], B[1]];
1544         this.dataY = [B[2], A[2], v[2], C[2], B[2]];
1545 
1546         this.bezierDegree = 1;
1547     };
1548 
1549     /**
1550      * @class
1551      * @ignore
1552      */
1553     el.updateDataArrayNone = function () {
1554         this.dataX = [NaN];
1555         this.dataY = [NaN];
1556         this.bezierDegree = 1;
1557     };
1558 
1559     /**
1560      * @class
1561      * @ignore
1562      */
1563     el.updateDataArray = function () {
1564         var type = Type.evaluate(this.visProp.type),
1565             deg = Geometry.trueAngle(this.point2, this.point1, this.point3),
1566             vp_s = Type.evaluate(this.visProp.selection);
1567 
1568         if ((vp_s === "minor" && deg > 180.0) || (vp_s === "major" && deg < 180.0)) {
1569             deg = 360.0 - deg;
1570         }
1571 
1572         if (Math.abs(deg - 90.0) < Type.evaluate(this.visProp.orthosensitivity) + Mat.eps) {
1573             type = Type.evaluate(this.visProp.orthotype);
1574         }
1575 
1576         if (type === "none") {
1577             this.updateDataArrayNone();
1578         } else if (type === "square") {
1579             this.updateDataArraySquare();
1580         } else if (type === "sector") {
1581             this.updateDataArraySector();
1582         } else if (type === "sectordot") {
1583             this.updateDataArraySector();
1584             if (!this.dot.visProp.visible) {
1585                 this.dot.setAttribute({ visible: true });
1586             }
1587         }
1588 
1589         if (!this.visProp.visible || (type !== "sectordot" && this.dot.visProp.visible)) {
1590             this.dot.setAttribute({ visible: false });
1591         }
1592     };
1593 
1594     attrsub = Type.copyAttributes(attributes, board.options, "angle", "dot");
1595     /**
1596      * Indicates a right angle. Invisible by default, use <tt>dot.visible: true</tt> to show.
1597      * Though this dot indicates a right angle, it can be visible even if the angle is not a right
1598      * one.
1599      * @type JXG.Point
1600      * @name dot
1601      * @memberOf Angle.prototype
1602      */
1603     el.dot = board.create(
1604         "point",
1605         [
1606             function () {
1607                 var A, B, r, d, a2, co, si, mat, vp_s;
1608 
1609                 if (Type.exists(el.dot) && !el.dot.visProp.visible) {
1610                     return [0, 0];
1611                 }
1612 
1613                 A = el.point2.coords.usrCoords;
1614                 B = el.point1.coords.usrCoords;
1615                 r = el.Radius();
1616                 d = Geometry.distance(A, B, 3);
1617                 a2 = Geometry.rad(el.point2, el.point1, el.point3);
1618 
1619                 vp_s = Type.evaluate(el.visProp.selection);
1620                 if ((vp_s === "minor" && a2 > Math.PI) || (vp_s === "major" && a2 < Math.PI)) {
1621                     a2 = -(2 * Math.PI - a2);
1622                 }
1623                 a2 *= 0.5;
1624 
1625                 co = Math.cos(a2);
1626                 si = Math.sin(a2);
1627 
1628                 A = [1, B[1] + ((A[1] - B[1]) * r) / d, B[2] + ((A[2] - B[2]) * r) / d];
1629 
1630                 mat = [
1631                     [1, 0, 0],
1632                     [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],
1633                     [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5, co * 0.5]
1634                 ];
1635                 return Mat.matVecMult(mat, A);
1636             }
1637         ],
1638         attrsub
1639     );
1640 
1641     el.dot.dump = false;
1642     el.subs.dot = el.dot;
1643 
1644     if (type === "2lines") {
1645         for (i = 0; i < 2; i++) {
1646             board.select(parents[i]).addChild(el.dot);
1647         }
1648     } else {
1649         for (i = 0; i < 3; i++) {
1650             board.select(points[i]).addChild(el.dot);
1651         }
1652     }
1653     board.unsuspendUpdate();
1654 
1655     /**
1656      * Returns the value of the angle.
1657      * @memberOf Angle.prototype
1658      * @name Value
1659      * @function
1660      * @param {String} [unit='length'] Unit of the returned values. Possible units are
1661      * <ul>
1662      * <li> 'radians' (default): angle value in radians
1663      * <li> 'degrees': angle value in degrees
1664      * <li> 'semicircle': angle value in radians as a multiple of π, e.g. if the angle is 1.5π, 1.5 will be returned.
1665      * <li> 'circle': angle value in radians as a multiple of 2π
1666      * <li> 'length': length of the arc line of the angle
1667      * </ul>
1668      * It is sufficient to supply the first three characters of the unit, e.g. 'len'.
1669      * @returns {Number} angle value in various units.
1670      * @see Sector#L
1671      * @example
1672      * var A, B, C, ang,
1673      *     r = 0.5;
1674      * A = board.create("point", [3, 0]);
1675      * B = board.create("point", [0, 0]);
1676      * C = board.create("point", [2, 2]);
1677      * ang = board.create("angle", [A, B, C], {radius: r});
1678      *
1679      * console.log(ang.Value());
1680      * // Output Math.PI * 0.25
1681      *
1682      * console.log(ang.Value('radian'));
1683      * // Output Math.PI * 0.25
1684      *
1685      * console.log(ang.Value('degree');
1686      * // Output 45
1687      *
1688      * console.log(ang.Value('semicircle'));
1689      * // Output 0.25
1690      *
1691      * console.log(ang.Value('circle'));
1692      * // Output 0.125
1693      *
1694      * console.log(ang.Value('length'));
1695      * // Output r * Math.PI * 0.25
1696      *
1697      * console.log(ang.L());
1698      * // Output r * Math.PI * 0.25
1699      *
1700      */
1701     el.Value = function(unit) {
1702         unit = unit || 'radians';
1703         if (unit === '') {
1704             unit = 'radians';
1705         }
1706         return el.arc.Value(unit);
1707     };
1708 
1709     // documented in GeometryElement
1710     /**
1711      * @class
1712      * @ignore
1713      */
1714     el.getLabelAnchor = function () {
1715         var vec,
1716             dx = 12,
1717             A, B, r, d, a2, co, si, mat,
1718             vp_s = Type.evaluate(el.visProp.selection),
1719             l_vp = this.label ? this.label.visProp : this.visProp.label;
1720 
1721         // If this is uncommented, the angle label can not be dragged
1722         //if (Type.exists(this.label)) {
1723         //    this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);
1724         //}
1725 
1726         if (Type.exists(this.label) && Type.exists(this.label.visProp.fontsize)) {
1727             dx = Type.evaluate(this.label.visProp.fontsize);
1728         }
1729         dx /= this.board.unitX;
1730 
1731         A = el.point2.coords.usrCoords;
1732         B = el.point1.coords.usrCoords;
1733         r = el.Radius();
1734         d = Geometry.distance(A, B, 3);
1735         a2 = Geometry.rad(el.point2, el.point1, el.point3);
1736         if ((vp_s === "minor" && a2 > Math.PI) || (vp_s === "major" && a2 < Math.PI)) {
1737             a2 = -(2 * Math.PI - a2);
1738         }
1739         a2 *= 0.5;
1740         co = Math.cos(a2);
1741         si = Math.sin(a2);
1742 
1743         A = [1, B[1] + ((A[1] - B[1]) * r) / d, B[2] + ((A[2] - B[2]) * r) / d];
1744 
1745         mat = [
1746             [1, 0, 0],
1747             [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],
1748             [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5, co * 0.5]
1749         ];
1750         vec = Mat.matVecMult(mat, A);
1751         vec[1] /= vec[0];
1752         vec[2] /= vec[0];
1753         vec[0] /= vec[0];
1754 
1755         d = Geometry.distance(vec, B, 3);
1756         vec = [
1757             vec[0],
1758             B[1] + ((vec[1] - B[1]) * (r + dx)) / d,
1759             B[2] + ((vec[2] - B[2]) * (r + dx)) / d
1760         ];
1761 
1762         l_vp.position = Geometry.calcLabelQuadrant(Geometry.rad([1, 0], [0, 0], vec));
1763 
1764         return new Coords(Const.COORDS_BY_USER, vec, this.board);
1765     };
1766 
1767     el.methodMap = Type.deepCopy(el.methodMap, {
1768         setAngle: "setAngle",
1769         Value: "Value",
1770         free: "free"
1771     });
1772 
1773     return el;
1774 };
1775 
1776 JXG.registerElement("angle", JXG.createAngle);
1777 
1778 /**
1779  * @class A non-reflex angle is the acute or obtuse instance of an angle.
1780  * It is defined by a center, one point that
1781  * defines the radius, and a third point that defines the angle of the sector.
1782  * @pseudo
1783  * @name NonReflexAngle
1784  * @augments Angle
1785  * @constructor
1786  * @type Sector
1787  * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
1788  * @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
1789  * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
1790  * @example
1791  * // Create a non-reflex angle out of three free points
1792  * var p1 = board.create('point', [5.0, 3.0]),
1793  *     p2 = board.create('point', [1.0, 0.5]),
1794  *     p3 = board.create('point', [1.5, 5.0]),
1795  *
1796  *     a = board.create('nonreflexangle', [p1, p2, p3], {radius: 2}),
1797  *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
1798  * </pre><div class="jxgbox" id="JXGd0ab6d6b-63a7-48b2-8749-b02bb5e744f9" style="width: 300px; height: 300px;"></div>
1799  * <script type="text/javascript">
1800  * (function () {
1801  *   var board = JXG.JSXGraph.initBoard('JXGd0ab6d6b-63a7-48b2-8749-b02bb5e744f9', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
1802  *     p1 = board.create('point', [5.0, 3.0]),
1803  *     p2 = board.create('point', [1.0, 0.5]),
1804  *     p3 = board.create('point', [1.5, 5.0]),
1805  *
1806  *     a = board.create('nonreflexangle', [p1, p2, p3], {radius: 2}),
1807  *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
1808  * })();
1809  * </script><pre>
1810  */
1811 JXG.createNonreflexAngle = function (board, parents, attributes) {
1812     var el;
1813 
1814     attributes.selection = "minor";
1815     attributes = Type.copyAttributes(attributes, board.options, 'nonreflexangle');
1816     el = JXG.createAngle(board, parents, attributes);
1817 
1818     // Documented in createAngle
1819     el.Value = function (unit) {
1820         var rad = Geometry.rad(this.point2, this.point1, this.point3);
1821         unit = unit || 'radians';
1822         if (unit === '') {
1823             unit = 'radians';
1824         }
1825         rad = (rad < Math.PI) ? rad : 2.0 * Math.PI - rad;
1826 
1827         return this.arc.Value(unit, rad);
1828     };
1829     return el;
1830 };
1831 
1832 JXG.registerElement("nonreflexangle", JXG.createNonreflexAngle);
1833 
1834 /**
1835  * @class A reflex angle is the neither acute nor obtuse instance of an angle.
1836  * It is defined by a center, one point that
1837  * defines the radius, and a third point that defines the angle of the sector.
1838  * @pseudo
1839  * @name ReflexAngle
1840  * @augments Angle
1841  * @constructor
1842  * @type Sector
1843  * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
1844  * @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
1845  * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
1846  * @example
1847  * // Create a non-reflex angle out of three free points
1848  * var p1 = board.create('point', [5.0, 3.0]),
1849  *     p2 = board.create('point', [1.0, 0.5]),
1850  *     p3 = board.create('point', [1.5, 5.0]),
1851  *
1852  *     a = board.create('reflexangle', [p1, p2, p3], {radius: 2}),
1853  *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
1854  * </pre><div class="jxgbox" id="JXGf2a577f2-553d-4f9f-a895-2d6d4b8c60e8" style="width: 300px; height: 300px;"></div>
1855  * <script type="text/javascript">
1856  * (function () {
1857  * var board = JXG.JSXGraph.initBoard('JXGf2a577f2-553d-4f9f-a895-2d6d4b8c60e8', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
1858  *     p1 = board.create('point', [5.0, 3.0]),
1859  *     p2 = board.create('point', [1.0, 0.5]),
1860  *     p3 = board.create('point', [1.5, 5.0]),
1861  *
1862  *     a = board.create('reflexangle', [p1, p2, p3], {radius: 2}),
1863  *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
1864  * })();
1865  * </script><pre>
1866  */
1867 JXG.createReflexAngle = function (board, parents, attributes) {
1868     var el;
1869 
1870     attributes.selection = "major";
1871     attributes = Type.copyAttributes(attributes, board.options, 'reflexangle');
1872     el = JXG.createAngle(board, parents, attributes);
1873 
1874     // Documented in createAngle
1875     el.Value = function (unit) {
1876         var rad = Geometry.rad(this.point2, this.point1, this.point3);
1877         unit = unit || 'radians';
1878         if (unit === '') {
1879             unit = 'radians';
1880         }
1881         rad = (rad >= Math.PI) ? rad : 2.0 * Math.PI - rad;
1882 
1883         return this.arc.Value(unit, rad);
1884     };
1885 
1886     return el;
1887 };
1888 
1889 JXG.registerElement("reflexangle", JXG.createReflexAngle);
1890