1 /*
  2     Copyright 2008-2022
  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/circle
 42  utils/type
 43  base/constants
 44   elements:
 45    curve
 46    midpoint
 47    circumcenter
 48  */
 49 
 50 /**
 51  * @fileoverview In this file the geometry object Arc is defined. Arc stores all
 52  * style and functional properties that are required to draw an arc on a board.
 53  */
 54 
 55 define([
 56     'jxg', 'math/geometry', 'math/math', 'base/coords', 'base/circle', 'utils/type', 'base/constants'
 57 ], function (JXG, Geometry, Mat, Coords, Circle, Type, Const) {
 58 
 59     "use strict";
 60 
 61     /**
 62      * @class An arc is a segment of the circumference of a circle. It is defined by a center, one point that
 63      * defines the radius, and a third point that defines the angle of the arc.
 64      *
 65      * @pseudo
 66      * @name Arc
 67      * @augments Curve
 68      * @constructor
 69      * @type JXG.Curve
 70      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
 71      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The result will be an arc of a circle around p1 through p2. The arc is drawn
 72      * counter-clockwise from p2 to p3.
 73      * @example
 74      * // Create an arc out of three free points
 75      * var p1 = board.create('point', [2.0, 2.0]);
 76      * var p2 = board.create('point', [1.0, 0.5]);
 77      * var p3 = board.create('point', [3.5, 1.0]);
 78      *
 79      * var a = board.create('arc', [p1, p2, p3]);
 80      * board.create('text',[1,6,function(){return 'arclength: '+Math.round(a.Value()*100)/100}])
 81      * </pre><div class="jxgbox" id="JXG114ef584-4a5e-4686-8392-c97501befb5b" style="width: 300px; height: 300px;"></div>
 82      * <script type="text/javascript">
 83      * (function () {
 84      *   var board = JXG.JSXGraph.initBoard('JXG114ef584-4a5e-4686-8392-c97501befb5b', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
 85      *       p1 = board.create('point', [2.0, 2.0]),
 86      *       p2 = board.create('point', [1.0, 0.5]),
 87      *       p3 = board.create('point', [3.5, 1.0]),
 88      *
 89      *       a = board.create('arc', [p1, p2, p3]);
 90      *       board.create('text',[1,6,function(){return 'arclength: '+Math.round(a.Value()*100)/100}])
 91      * })();
 92      * </script><pre>
 93      *
 94      * @example
 95      * var t = board.create('transform', [2, 1.5], {type: 'scale'});
 96      * var a1 = board.create('arc', [[1, 1], [0, 1], [1, 0]], {strokeColor: 'red'});
 97      * var a2 = board.create('curve', [a1, t], {strokeColor: 'red'});
 98      *
 99      * </pre><div id="JXG1949da46-6339-11e8-9fb9-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
100      * <script type="text/javascript">
101      *     (function() {
102      *         var board = JXG.JSXGraph.initBoard('JXG1949da46-6339-11e8-9fb9-901b0e1b8723',
103      *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
104      *     var t = board.create('transform', [2, 1.5], {type: 'scale'});
105      *     var a1 = board.create('arc', [[1, 1], [0, 1], [1, 0]], {strokeColor: 'red'});
106      *     var a2 = board.create('curve', [a1, t], {strokeColor: 'red'});
107      *
108      *     })();
109      *
110      * </script><pre>
111      *
112      */
113     JXG.createArc = function (board, parents, attributes) {
114         var el, attr, points;
115 
116         points = Type.providePoints(board, parents, attributes, 'arc', ['center', 'radiusPoint', 'anglePoint']);
117         if (points === false || points.length < 3) {
118             throw new Error("JSXGraph: Can't create Arc with parent types '" +
119                 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" +
120                 (typeof parents[2]) + "'." +
121                 "\nPossible parent types: [point,point,point], [arc, transformation]");
122         }
123 
124         attr = Type.copyAttributes(attributes, board.options, 'arc');
125         el = board.create('curve', [[0], [0]], attr);
126 
127         el.elType = 'arc';
128         el.setParents(points);
129 
130         /**
131          * documented in JXG.GeometryElement
132          * @ignore
133          */
134         el.type = Const.OBJECT_TYPE_ARC;
135 
136         /**
137          * Center of the arc.
138          * @memberOf Arc.prototype
139          * @name center
140          * @type JXG.Point
141          */
142         el.center = points[0];
143 
144         /**
145          * Point defining the arc's radius.
146          * @memberOf Arc.prototype
147          * @name radiuspoint
148          * @type JXG.Point
149          */
150         el.radiuspoint = points[1];
151         el.point2 = el.radiuspoint;
152 
153         /**
154          * The point defining the arc's angle.
155          * @memberOf Arc.prototype
156          * @name anglepoint
157          * @type JXG.Point
158          */
159         el.anglepoint = points[2];
160         el.point3 = el.anglepoint;
161 
162         // Add arc as child to defining points
163         // or vice versa if the points are provided as coordinates
164         if (Type.exists(el.center._is_new)) {
165             el.addChild(el.center);
166             delete el.center._is_new;
167         } else {
168             el.center.addChild(el);
169         }
170         if (Type.exists(el.radiuspoint._is_new)) {
171             el.addChild(el.radiuspoint);
172             delete el.radiuspoint._is_new;
173         } else {
174             el.radiuspoint.addChild(el);
175         }
176         if (Type.exists(el.anglepoint._is_new)) {
177             el.addChild(el.anglepoint);
178             delete el.anglepoint._is_new;
179         } else {
180             el.anglepoint.addChild(el);
181         }
182 
183         // should be documented in options
184         el.useDirection = attr.usedirection;
185 
186         // documented in JXG.Curve
187         el.updateDataArray = function () {
188             var ar, phi, det, p0c, p1c, p2c,
189                 sgn = 1,
190                 A = this.radiuspoint,
191                 B = this.center,
192                 C = this.anglepoint,
193                 ev_s = Type.evaluate(this.visProp.selection);
194 
195             phi = Geometry.rad(A, B, C);
196             if ((ev_s === 'minor' && phi > Math.PI) ||
197                     (ev_s === 'major' && phi < Math.PI)) {
198                 sgn = -1;
199             }
200 
201             // This is true for circumCircleArcs. In that case there is
202             // a fourth parent element: [center, point1, point3, point2]
203             if (this.useDirection) {
204                 p0c = points[1].coords.usrCoords;
205                 p1c = points[3].coords.usrCoords;
206                 p2c = points[2].coords.usrCoords;
207                 det = (p0c[1] - p2c[1]) * (p0c[2] - p1c[2]) - (p0c[2] - p2c[2]) * (p0c[1] - p1c[1]);
208 
209                 if (det < 0) {
210                     this.radiuspoint = points[1];
211                     this.anglepoint = points[2];
212                 } else {
213                     this.radiuspoint = points[2];
214                     this.anglepoint = points[1];
215                 }
216             }
217 
218             A = A.coords.usrCoords;
219             B = B.coords.usrCoords;
220             C = C.coords.usrCoords;
221 
222             ar = Geometry.bezierArc(A, B, C, false, sgn);
223 
224             this.dataX = ar[0];
225             this.dataY = ar[1];
226 
227             this.bezierDegree = 3;
228 
229             this.updateStdform();
230             this.updateQuadraticform();
231         };
232 
233         /**
234          * Determines the arc's current radius. I.e. the distance between {@link Arc#center} and {@link Arc#radiuspoint}.
235          * @memberOf Arc.prototype
236          * @name Radius
237          * @function
238          * @returns {Number} The arc's radius
239          */
240         el.Radius = function () {
241             return this.radiuspoint.Dist(this.center);
242         };
243 
244         /**
245          * @deprecated Use {@link Arc#Radius}
246          * @memberOf Arc.prototype
247          * @name getRadius
248          * @function
249          * @returns {Number}
250          */
251         el.getRadius = function () {
252             JXG.deprecated('Arc.getRadius()', 'Arc.Radius()');
253             return this.Radius();
254         };
255 
256         /**
257          * Returns the length of the arc.
258          * @memberOf Arc.prototype
259          * @name Value
260          * @function
261          * @returns {Number} The arc length
262          */
263         el.Value = function () {
264             return this.Radius() * Geometry.rad(this.radiuspoint, this.center, this.anglepoint);
265         };
266 
267         // documented in geometry element
268         el.hasPoint = function (x, y) {
269             var dist, checkPoint,
270                 has,
271                 invMat, c,
272                 prec, type,
273                 r = this.Radius();
274 
275             if (Type.evaluate(this.visProp.hasinnerpoints)) {
276                 return this.hasPointSector(x, y);
277             }
278 
279             if (Type.isObject(Type.evaluate(this.visProp.precision))) {
280                 type = this.board._inputDevice;
281                 prec = Type.evaluate(this.visProp.precision[type]);
282             } else {
283                 // 'inherit'
284                 prec = this.board.options.precision.hasPoint;
285             }
286             prec /= Math.min(this.board.unitX, this.board.unitY);
287             checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board);
288 
289             if (this.transformations.length > 0) {
290                 // Transform the mouse/touch coordinates
291                 // back to the original position of the curve.
292                 this.updateTransformMatrix();
293                 invMat = Mat.inverse(this.transformMat);
294                 c = Mat.matVecMult(invMat, checkPoint.usrCoords);
295                 checkPoint = new Coords(Const.COORDS_BY_USER, c, this.board);
296             }
297 
298             dist = this.center.coords.distance(Const.COORDS_BY_USER, checkPoint);
299             has = (Math.abs(dist - r) < prec);
300 
301             /**
302              * At that point we know that the user has touched the circle line.
303              * Now, we have to check, if the user has hit the arc path.
304              */
305             if (has) {
306                 has = Geometry.coordsOnArc(this, checkPoint);
307             }
308             return has;
309         };
310 
311         /**
312          * Checks whether (x,y) is within the sector defined by the arc.
313          * @memberOf Arc.prototype
314          * @name hasPointSector
315          * @function
316          * @param {Number} x Coordinate in x direction, screen coordinates.
317          * @param {Number} y Coordinate in y direction, screen coordinates.
318          * @returns {Boolean} True if (x,y) is within the sector defined by the arc, False otherwise.
319          */
320         el.hasPointSector = function (x, y) {
321             var checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),
322                 r = this.Radius(),
323                 dist = this.center.coords.distance(Const.COORDS_BY_USER, checkPoint),
324                 has = (dist < r);
325 
326             if (has) {
327                 has = Geometry.coordsOnArc(this, checkPoint);
328             }
329             return has;
330         };
331 
332         // documented in geometry element
333         el.getTextAnchor = function () {
334             return this.center.coords;
335         };
336 
337         // documented in geometry element
338         el.getLabelAnchor = function () {
339             var coords, vec, vecx, vecy, len,
340                 angle = Geometry.rad(this.radiuspoint, this.center, this.anglepoint),
341                 dx = 10 / this.board.unitX,
342                 dy = 10 / this.board.unitY,
343                 p2c = this.point2.coords.usrCoords,
344                 pmc = this.center.coords.usrCoords,
345                 bxminusax = p2c[1] - pmc[1],
346                 byminusay = p2c[2] - pmc[2],
347                 ev_s = Type.evaluate(this.visProp.selection),
348                 l_vp = this.label ? this.label.visProp : this.visProp.label;
349 
350             // If this is uncommented, the angle label can not be dragged
351             //if (Type.exists(this.label)) {
352             //    this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);
353             //}
354 
355             if ((ev_s === 'minor' && angle > Math.PI) ||
356                     (ev_s === 'major' && angle < Math.PI)) {
357                 angle = -(2 * Math.PI - angle);
358             }
359 
360             coords = new Coords(Const.COORDS_BY_USER, [
361                 pmc[1] + Math.cos(angle * 0.5) * bxminusax - Math.sin(angle * 0.5) * byminusay,
362                 pmc[2] + Math.sin(angle * 0.5) * bxminusax + Math.cos(angle * 0.5) * byminusay
363             ], this.board);
364 
365             vecx = coords.usrCoords[1] - pmc[1];
366             vecy = coords.usrCoords[2] - pmc[2];
367 
368             len = Math.sqrt(vecx * vecx + vecy * vecy);
369             vecx = vecx * (len + dx) / len;
370             vecy = vecy * (len + dy) / len;
371             vec = [pmc[1] + vecx, pmc[2] + vecy];
372 
373             l_vp.position = Geometry.calcLabelQuadrant(Geometry.rad([1,0],[0,0],vec));
374 
375             return new Coords(Const.COORDS_BY_USER, vec, this.board);
376         };
377 
378         // documentation in jxg.circle
379         el.updateQuadraticform = Circle.Circle.prototype.updateQuadraticform;
380 
381         // documentation in jxg.circle
382         el.updateStdform = Circle.Circle.prototype.updateStdform;
383 
384         el.methodMap = JXG.deepCopy(el.methodMap, {
385             getRadius: 'getRadius',
386             radius: 'Radius',
387             center: 'center',
388             radiuspoint: 'radiuspoint',
389             anglepoint: 'anglepoint',
390             Value: 'Value'
391         });
392 
393         el.prepareUpdate().update();
394         return el;
395     };
396 
397     JXG.registerElement('arc', JXG.createArc);
398 
399     /**
400      * @class A semicircle is a special arc defined by two points. The arc hits both points.
401      * @pseudo
402      * @name Semicircle
403      * @augments Arc
404      * @constructor
405      * @type Arc
406      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
407      * @param {JXG.Point_JXG.Point} p1,p2 The result will be a composition of an arc drawn clockwise from <tt>p1</tt> and
408      * <tt>p2</tt> and the midpoint of <tt>p1</tt> and <tt>p2</tt>.
409      * @example
410      * // Create an arc out of three free points
411      * var p1 = board.create('point', [4.5, 2.0]);
412      * var p2 = board.create('point', [1.0, 0.5]);
413      *
414      * var a = board.create('semicircle', [p1, p2]);
415      * </pre><div class="jxgbox" id="JXG5385d349-75d7-4078-b732-9ae808db1b0e" style="width: 300px; height: 300px;"></div>
416      * <script type="text/javascript">
417      * (function () {
418      *   var board = JXG.JSXGraph.initBoard('JXG5385d349-75d7-4078-b732-9ae808db1b0e', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
419      *       p1 = board.create('point', [4.5, 2.0]),
420      *       p2 = board.create('point', [1.0, 0.5]),
421      *
422      *       sc = board.create('semicircle', [p1, p2]);
423      * })();
424      * </script><pre>
425      */
426     JXG.createSemicircle = function (board, parents, attributes) {
427         var el, mp, attr, points;
428 
429         // we need 2 points
430         points = Type.providePoints(board, parents, attributes, 'point');
431         if (points === false || points.length !== 2) {
432             throw new Error("JSXGraph: Can't create Semicircle with parent types '" +
433                 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "'." +
434                 "\nPossible parent types: [point,point]");
435         }
436 
437         attr = Type.copyAttributes(attributes, board.options, 'semicircle', 'center');
438         mp = board.create('midpoint', points, attr);
439         mp.dump = false;
440 
441         attr = Type.copyAttributes(attributes, board.options, 'semicircle');
442         el = board.create('arc', [mp, points[1], points[0]], attr);
443         el.elType = 'semicircle';
444         el.setParents([points[0].id, points[1].id]);
445         el.subs = {
446             midpoint: mp
447         };
448         el.inherits.push(mp);
449 
450         /**
451          * The midpoint of the two defining points.
452          * @memberOf Semicircle.prototype
453          * @name midpoint
454          * @type Midpoint
455          */
456         el.midpoint = el.center = mp;
457 
458         return el;
459     };
460 
461     JXG.registerElement('semicircle', JXG.createSemicircle);
462 
463     /**
464      * @class A circumcircle arc is an {@link Arc} defined by three points. All three points lie on the arc.
465      * @pseudo
466      * @name CircumcircleArc
467      * @augments Arc
468      * @constructor
469      * @type Arc
470      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
471      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The result will be a composition of an arc of the circumcircle of
472      * <tt>p1</tt>, <tt>p2</tt>, and <tt>p3</tt> and the midpoint of the circumcircle of the three points. The arc is drawn
473      * counter-clockwise from <tt>p1</tt> over <tt>p2</tt> to <tt>p3</tt>.
474      * @example
475      * // Create a circum circle arc out of three free points
476      * var p1 = board.create('point', [2.0, 2.0]);
477      * var p2 = board.create('point', [1.0, 0.5]);
478      * var p3 = board.create('point', [3.5, 1.0]);
479      *
480      * var a = board.create('circumcirclearc', [p1, p2, p3]);
481      * </pre><div class="jxgbox" id="JXG87125fd4-823a-41c1-88ef-d1a1369504e3" style="width: 300px; height: 300px;"></div>
482      * <script type="text/javascript">
483      * (function () {
484      *   var board = JXG.JSXGraph.initBoard('JXG87125fd4-823a-41c1-88ef-d1a1369504e3', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
485      *       p1 = board.create('point', [2.0, 2.0]),
486      *       p2 = board.create('point', [1.0, 0.5]),
487      *       p3 = board.create('point', [3.5, 1.0]),
488      *
489      *       cca = board.create('circumcirclearc', [p1, p2, p3]);
490      * })();
491      * </script><pre>
492      */
493     JXG.createCircumcircleArc = function (board, parents, attributes) {
494         var el, mp, attr, points;
495 
496         // We need three points
497         points = Type.providePoints(board, parents, attributes, 'point');
498         if (points === false || points.length !== 3) {
499             throw new Error("JSXGraph: create Circumcircle Arc with parent types '" +
500                 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" + (typeof parents[2]) + "'." +
501                 "\nPossible parent types: [point,point,point]");
502         }
503 
504         attr = Type.copyAttributes(attributes, board.options, 'circumcirclearc', 'center');
505         mp = board.create('circumcenter', points, attr);
506         mp.dump = false;
507 
508         attr = Type.copyAttributes(attributes, board.options, 'circumcirclearc');
509         attr.usedirection = true;
510         el = board.create('arc', [mp, points[0], points[2], points[1]], attr);
511 
512         el.elType = 'circumcirclearc';
513         el.setParents([points[0].id, points[1].id, points[2].id]);
514         el.subs = {
515             center: mp
516         };
517         el.inherits.push(mp);
518 
519         /**
520          * The midpoint of the circumcircle of the three points defining the circumcircle arc.
521          * @memberOf CircumcircleArc.prototype
522          * @name center
523          * @type Circumcenter
524          */
525         el.center = mp;
526 
527         return el;
528     };
529 
530     JXG.registerElement('circumcirclearc', JXG.createCircumcircleArc);
531 
532     /**
533      * @class A minor arc is a segment of the circumference of a circle having measure less than or equal to
534      * 180 degrees (pi radians). It is defined by a center, one point that
535      * defines the radius, and a third point that defines the angle of the arc.
536      * @pseudo
537      * @name MinorArc
538      * @augments Curve
539      * @constructor
540      * @type JXG.Curve
541      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
542      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor arc is an arc of a circle around p1 having measure less than or equal to
543      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
544      * @example
545      * // Create an arc out of three free points
546      * var p1 = board.create('point', [2.0, 2.0]);
547      * var p2 = board.create('point', [1.0, 0.5]);
548      * var p3 = board.create('point', [3.5, 1.0]);
549      *
550      * var a = board.create('arc', [p1, p2, p3]);
551      * </pre><div class="jxgbox" id="JXG64ba7ca2-8728-45f3-96e5-3c7a4414de2f" style="width: 300px; height: 300px;"></div>
552      * <script type="text/javascript">
553      * (function () {
554      *   var board = JXG.JSXGraph.initBoard('JXG64ba7ca2-8728-45f3-96e5-3c7a4414de2f', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
555      *       p1 = board.create('point', [2.0, 2.0]),
556      *       p2 = board.create('point', [1.0, 0.5]),
557      *       p3 = board.create('point', [3.5, 1.0]),
558      *
559      *       a = board.create('minorarc', [p1, p2, p3]);
560      * })();
561      * </script><pre>
562      */
563 
564     JXG.createMinorArc = function (board, parents, attributes) {
565         attributes.selection = 'minor';
566         return JXG.createArc(board, parents, attributes);
567     };
568 
569     JXG.registerElement('minorarc', JXG.createMinorArc);
570 
571     /**
572      * @class A major arc is a segment of the circumference of a circle having measure greater than or equal to
573      * 180 degrees (pi radians). It is defined by a center, one point that
574      * defines the radius, and a third point that defines the angle of the arc.
575      * @pseudo
576      * @name MajorArc
577      * @augments Curve
578      * @constructor
579      * @type JXG.Curve
580      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
581      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Major arc is an arc of a circle around p1 having measure greater than or equal to
582      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
583      * @example
584      * // Create an arc out of three free points
585      * var p1 = board.create('point', [2.0, 2.0]);
586      * var p2 = board.create('point', [1.0, 0.5]);
587      * var p3 = board.create('point', [3.5, 1.0]);
588      *
589      * var a = board.create('minorarc', [p1, p2, p3]);
590      * </pre><div class="jxgbox" id="JXG17a10d38-5629-40a4-b150-f41806edee9f" style="width: 300px; height: 300px;"></div>
591      * <script type="text/javascript">
592      * (function () {
593      *   var board = JXG.JSXGraph.initBoard('JXG17a10d38-5629-40a4-b150-f41806edee9f', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
594      *       p1 = board.create('point', [2.0, 2.0]),
595      *       p2 = board.create('point', [1.0, 0.5]),
596      *       p3 = board.create('point', [3.5, 1.0]),
597      *
598      *       a = board.create('majorarc', [p1, p2, p3]);
599      * })();
600      * </script><pre>
601      */
602     JXG.createMajorArc = function (board, parents, attributes) {
603         attributes.selection = 'major';
604         return JXG.createArc(board, parents, attributes);
605     };
606 
607     JXG.registerElement('majorarc', JXG.createMajorArc);
608 
609     return {
610         createArc: JXG.createArc,
611         createSemicircle: JXG.createSemicircle,
612         createCircumcircleArc: JXG.createCircumcircleArc,
613         createMinorArc: JXG.createMinorArc,
614         createMajorArc: JXG.createMajorArc
615     };
616 });
617