      1 /*
      2     Copyright 2008-2015
      3         Matthias Ehmann,
      4         Michael Gerhaeuser,
      5         Carsten Miller,
      6         Bianca Valentin,
      7         Alfred Wassermann,
      8         Peter Wilfahrt
      9
     10     This file is part of JSXGraph.
     11
     12     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
     13
     14     You can redistribute it and/or modify it under the terms of the
     15
     16       * GNU Lesser General Public License as published by
     17         the Free Software Foundation, either version 3 of the License, or
     18         (at your option) any later version
     19       OR
     20       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
     21
     22     JSXGraph is distributed in the hope that it will be useful,
     23     but WITHOUT ANY WARRANTY; without even the implied warranty of
     24     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     25     GNU Lesser General Public License for more details.
     26
     27     You should have received a copy of the GNU Lesser General Public License and
     28     the MIT License along with JSXGraph. If not, see <http://www.gnu.org/licenses/>
     29     and <http://opensource.org/licenses/MIT/>.
     30  */
     31
     32
     33 /*global JXG: true, define: true*/
     34 /*jslint nomen: true, plusplus: true*/
     35
     36 /* depends:
     37  jxg
     38  math/geometry
     39  math/math
     40  base/coords
     41  base/constants
     42  utils/type
     43   elements:
     44    point
     45    curve
     46    circumcentre
     47    transform
     48  */
     49
     50 define([
     51     'jxg', 'math/geometry', 'math/math', 'math/statistics', 'base/coords', 'base/constants', 'utils/type', 'base/point', 'base/curve',
     52     'base/transformation', 'element/composition'
     53 ], function (JXG, Geometry, Mat, Statistics, Coords, Const, Type, Point, Curve, Transform, Compositions) {
     54
     55     "use strict";
     56
     57     /**
     58      * @class A circular sector is a subarea of the area enclosed by a circle. It is enclosed by two radii and an arc.
     59      * @pseudo
     60      * @name Sector
     61      * @augments JXG.Curve
     62      * @constructor
     63      * @type JXG.Curve
     64      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
     65      *
     66      * First possiblity of input parameters are:
     67      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 A sector is defined by three points: The sector's center <tt>p1</tt>,
     68      * a second point <tt>p2</tt> defining the radius and a third point <tt>p3</tt> defining the angle of the sector. The
     69      * Sector is always drawn counter clockwise from <tt>p2</tt> to <tt>p3</tt>
     70      *
     71      * Second possibility of input parameters are:
     72      * @param {JXG.Line_JXG.Line_array,number_array,number_number,function} line, line2, coords1 or direction1, coords2 or direction2, radius The sector is defined by two lines.
     73      * The two legs which define the sector are given by two coordinates arrays which are project initially two the two lines or by two directions (+/- 1).
     74      * The last parameter is the radius of the sector.
     75      *
     76      *
     77      * @example
     78      * // Create a sector out of three free points
     79      * var p1 = board.create('point', [1.5, 5.0]),
     80      *     p2 = board.create('point', [1.0, 0.5]),
     81      *     p3 = board.create('point', [5.0, 3.0]),
     82      *
     83      *     a = board.create('sector', [p1, p2, p3]);
     84      * </pre><div id="49f59123-f013-4681-bfd9-338b89893156" style="width: 300px; height: 300px;"></div>
     85      * <script type="text/javascript">
     86      * (function () {
     87      *   var board = JXG.JSXGraph.initBoard('49f59123-f013-4681-bfd9-338b89893156', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
     88      *     p1 = board.create('point', [1.5, 5.0]),
     89      *     p2 = board.create('point', [1.0, 0.5]),
     90      *     p3 = board.create('point', [5.0, 3.0]),
     91      *
     92      *     a = board.create('sector', [p1, p2, p3]);
     93      * })();
     94      * </script><pre>
     95      *
     96      * @example
     97      * // Create a sector out of two lines, two directions and a radius
     98      * var p1 = board.create('point', [-1, 4]),
     99      *  p2 = board.create('point', [4, 1]),
    100      *  q1 = board.create('point', [-2, -3]),
    101      *  q2 = board.create('point', [4,3]),
    102      *
    103      *  li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
    104      *  li2 = board.create('line', [q1,q2], {lastArrow:true}),
    105      *
    106      *  sec1 = board.create('sector', [li1, li2, [5.5, 0], [4, 3], 3]),
    107      *  sec2 = board.create('sector', [li1, li2, 1, -1, 4]);
    108      *
    109      * </pre><div id="bb9e2809-9895-4ff1-adfa-c9c71d50aa53" style="width: 300px; height: 300px;"></div>
    110      * <script type="text/javascript">
    111      * (function () {
    112      *   var board = JXG.JSXGraph.initBoard('bb9e2809-9895-4ff1-adfa-c9c71d50aa53', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    113      *     p1 = board.create('point', [-1, 4]),
    114      *     p2 = board.create('point', [4, 1]),
    115      *     q1 = board.create('point', [-2, -3]),
    116      *     q2 = board.create('point', [4,3]),
    117      *
    118      *     li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
    119      *     li2 = board.create('line', [q1,q2], {lastArrow:true}),
    120      *
    121      *     sec1 = board.create('sector', [li1, li2, [5.5, 0], [4, 3], 3]),
    122      *     sec2 = board.create('sector', [li1, li2, 1, -1, 4]);
    123      * })();
    124      * </script><pre>
    125      */
    126     JXG.createSector = function (board, parents, attributes) {
    127         var el, i, attr,
    128             type = 'invalid',
    129             s, v,
    130             attrPoints = ['center', 'radiuspoint', 'anglepoint'],
    131             points;
    132
    133         // Three points?
    134         if (parents[0].elementClass === Const.OBJECT_CLASS_LINE &&
    135                 parents[1].elementClass === Const.OBJECT_CLASS_LINE &&
    136                 (Type.isArray(parents[2]) || Type.isNumber(parents[2])) &&
    137                 (Type.isArray(parents[3]) || Type.isNumber(parents[3])) &&
    138                 (Type.isNumber(parents[4]) || Type.isFunction(parents[4]))) {
    139
    140             type = '2lines';
    141
    142         } else {
    143             points = Type.providePoints(board, parents, attributes, 'sector', attrPoints);
    144             if (points === false) {
    145                 throw new Error("JSXGraph: Can't create Sector with parent types '" +
    146                     (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" +
    147                     (typeof parents[2]) + "'.");
    148             }
    149
    150             type = '3points';
    151         }
    152
    153         attr = Type.copyAttributes(attributes, board.options, 'sector');
    154         el = board.create('curve', [[0], [0]], attr);
    155         el.type = Const.OBJECT_TYPE_SECTOR;
    156         el.elType = 'sector';
    157
    158         if (type === '2lines') {
    159             el.Radius = function () {
    160                 return Type.evaluate(parents[4]);
    161             };
    162
    163             el.line1 = board.select(parents[0]);
    164             el.line2 = board.select(parents[1]);
    165
    166             el.line1.addChild(el);
    167             el.line2.addChild(el);
    168             el.parents = [parents[0].id, parents[1].id];
    169
    170             el.point1 = {visProp: {}};
    171             el.point2 = {visProp: {}};
    172             el.point3 = {visProp: {}};
    173
    174             /* Intersection point */
    175             s = Geometry.meetLineLine(el.line1.stdform, el.line2.stdform, 0, board);
    176
    177             if (Type.isArray(parents[2])) {
    178                 /* project p1 to l1 */
    179                 if (parents[2].length === 2) {
    180                     parents[2] = [1].concat(parents[2]);
    181                 }
    182                 /*
    183                 v = [0, el.line1.stdform[1], el.line1.stdform[2]];
    184                 v = Mat.crossProduct(v, parents[2]);
    185                 v = Geometry.meetLineLine(v, el.line1.stdform, 0, board);
    186                 */
    187                 v = Geometry.projectPointToLine({coords: {usrCoords: parents[2]}}, el.line1, board);
    188                 v = Statistics.subtract(v.usrCoords, s.usrCoords);
    189                 el.direction1 = (Mat.innerProduct(v, [0, el.line1.stdform[2], -el.line1.stdform[1]], 3) >= 0) ? +1 : -1;
    190             } else {
    191                 el.direction1 = (parents[2] >= 0) ? 1 : -1;
    192             }
    193
    194             if (Type.isArray(parents[3])) {
    195                 /* project p2 to l2 */
    196                 if (parents[3].length === 2) {
    197                     parents[3] = [1].concat(parents[3]);
    198                 }
    199                 /*
    200                 v = [0, el.line2.stdform[1], el.line2.stdform[2]];
    201                 v = Mat.crossProduct(v, parents[3]);
    202                 v = Geometry.meetLineLine(v, el.line2.stdform, 0, board);
    203                 */
    204                 v = Geometry.projectPointToLine({coords: {usrCoords: parents[3]}}, el.line2, board);
    205                 v = Statistics.subtract(v.usrCoords, s.usrCoords);
    206                 el.direction2 = (Mat.innerProduct(v, [0, el.line2.stdform[2], -el.line2.stdform[1]], 3) >= 0) ? +1 : -1;
    207             } else {
    208                 el.direction2 = (parents[3] >= 0) ? 1 : -1;
    209             }
    210
    211             el.updateDataArray = function () {
    212                 var r, l1, l2,
    213                     A = [0, 0, 0],
    214                     B = [0, 0, 0],
    215                     C = [0, 0, 0],
    216                     ar;
    217
    218                 l1 = this.line1;
    219                 l2 = this.line2;
    220
    221                 // Intersection point of the lines
    222                 B = Mat.crossProduct(l1.stdform, l2.stdform);
    223
    224                 if (Math.abs(B[0]) > Mat.eps * Mat.eps) {
    225                     B[1] /= B[0];
    226                     B[2] /= B[0];
    227                     B[0] /= B[0];
    228                 }
    229                 // First point
    230                 r = this.direction1 * this.Radius();
    231                 A = Statistics.add(B, [0, r * l1.stdform[2], -r * l1.stdform[1]]);
    232
    233                 // Second point
    234                 r = this.direction2 * this.Radius();
    235                 C = Statistics.add(B, [0, r * l2.stdform[2], -r * l2.stdform[1]]);
    236
    237                 this.point2.coords = new Coords(Const.COORDS_BY_USER, A, el.board);
    238                 this.point1.coords = new Coords(Const.COORDS_BY_USER, B, el.board);
    239                 this.point3.coords = new Coords(Const.COORDS_BY_USER, C, el.board);
    240
    241                 if (Math.abs(A[0]) < Mat.eps || Math.abs(B[0]) < Mat.eps || Math.abs(C[0]) < Mat.eps) {
    242                     this.dataX = [NaN];
    243                     this.dataY = [NaN];
    244                     return;
    245                 }
    246
    247                 ar = Geometry.bezierArc(A, B, C, true, 1);
    248
    249                 this.dataX = ar[0];
    250                 this.dataY = ar[1];
    251
    252                 this.bezierDegree = 3;
    253             };
    254
    255             el.methodMap = JXG.deepCopy(el.methodMap, {
    256                 radius: 'getRadius',
    257                 getRadius: 'getRadius',
    258                 setRadius: 'setRadius'
    259             });
    260
    261             el.prepareUpdate().update();
    262
    263         // end '2lines'
    264
    265         } else if (type === '3points') {
    266
    267             /**
    268             * Midpoint of the sector.
    269             * @memberOf Sector.prototype
    270             * @name point1
    271             * @type JXG.Point
    272             */
    273             el.point1 = points[0];
    274
    275             /**
    276             * This point together with {@link Sector#point1} defines the radius..
    277             * @memberOf Sector.prototype
    278             * @name point2
    279             * @type JXG.Point
    280             */
    281             el.point2 = points[1];
    282
    283             /**
    284             * Defines the sector's angle.
    285             * @memberOf Sector.prototype
    286             * @name point3
    287             * @type JXG.Point
    288             */
    289             el.point3 = points[2];
    290
    291             /* Add arc as child to defining points */
    292             el.point1.addChild(el);
    293             el.point2.addChild(el);
    294             el.point3.addChild(el);
    295
    296             // useDirection is necessary for circumCircleSectors
    297             el.useDirection = attributes.usedirection;
    298             el.parents = [points[0].id, points[1].id, points[2].id];
    299
    300             /**
    301             * Defines the sectors orientation in case of circumCircleSectors.
    302             * @memberOf Sector.prototype
    303             * @name point4
    304             * @type JXG.Point
    305             */
    306             if (Type.exists(points[3])) {
    307                 el.point4 = points[3];
    308                 el.point4.addChild(el);
    309             }
    310
    311             el.methodMap = JXG.deepCopy(el.methodMap, {
    312                 arc: 'arc',
    313                 center: 'center',
    314                 radiuspoint: 'radiuspoint',
    315                 anglepoint: 'anglepoint',
    316                 radius: 'getRadius',
    317                 getRadius: 'getRadius',
    318                 setRadius: 'setRadius'
    319             });
    320
    321             /**
    322             * documented in JXG.Curve
    323             * @ignore
    324             */
    325             el.updateDataArray = function () {
    326                 var ar, det, p0c, p1c, p2c,
    327                     A = this.point2,
    328                     B = this.point1,
    329                     C = this.point3,
    330                     phi, sgn = 1;
    331
    332                 if (!A.isReal || !B.isReal || !C.isReal) {
    333                     this.dataX = [NaN];
    334                     this.dataY = [NaN];
    335                     return;
    336                 }
    337
    338                 phi = Geometry.rad(A, B, C);
    339                 if ((this.visProp.selection === 'minor' && phi > Math.PI) ||
    340                         (this.visProp.selection === 'major' && phi < Math.PI)) {
    341                     sgn = -1;
    342                 }
    343
    344                 // This is true for circumCircleSectors. In that case there is
    345                 // a fourth parent element: [midpoint, point1, point3, point2]
    346                 if (this.useDirection && Type.exists(this.point4)) {
    347                     p0c = this.point2.coords.usrCoords;
    348                     p1c = this.point4.coords.usrCoords;
    349                     p2c = this.point3.coords.usrCoords;
    350                     det = (p0c[1] - p2c[1]) * (p0c[2] - p1c[2]) - (p0c[2] - p2c[2]) * (p0c[1] - p1c[1]);
    351
    352                     if (det >= 0.0) {
    353                         C = this.point2;
    354                         A = this.point3;
    355                     }
    356                 }
    357
    358                 A = A.coords.usrCoords;
    359                 B = B.coords.usrCoords;
    360                 C = C.coords.usrCoords;
    361
    362                 ar = Geometry.bezierArc(A, B, C, true, sgn);
    363
    364                 this.dataX = ar[0];
    365                 this.dataY = ar[1];
    366                 this.bezierDegree = 3;
    367             };
    368
    369             /**
    370             * Returns the radius of the sector.
    371             * @memberOf Sector.prototype
    372             * @name Radius
    373             * @function
    374             * @returns {Number} The distance between {@link Sector#point1} and {@link Sector#point2}.
    375             */
    376             el.Radius = function () {
    377                 return this.point2.Dist(this.point1);
    378             };
    379
    380             attr = Type.copyAttributes(attributes, board.options, 'sector', 'arc');
    381             attr.withLabel = false;
    382             attr.name += '_arc';
    383             el.arc = board.create('arc', [el.point1, el.point2, el.point3], attr);
    384             el.addChild(el.arc);
    385         }   // end '3points'
    386
    387         el.center = el.point1;
    388         el.radiuspoint = el.point2;
    389         el.anglepoint = el.point3;
    390
    391         // Default hasPoint method. Documented in geometry element
    392         el.hasPointCurve = function (x, y) {
    393             var angle, alpha, beta,
    394                 prec = this.board.options.precision.hasPoint / (this.board.unitX),
    395                 checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),
    396                 r = this.Radius(),
    397                 dist = this.center.coords.distance(Const.COORDS_BY_USER, checkPoint),
    398                 has = (Math.abs(dist - r) < prec);
    399
    400             if (has) {
    401                 angle = Geometry.rad(this.point2, this.center, checkPoint.usrCoords.slice(1));
    402                 alpha = 0;
    403                 beta = Geometry.rad(this.point2, this.center, this.point3);
    404
    405                 if (angle < alpha || angle > beta) {
    406                     has = false;
    407                 }
    408             }
    409
    410             return has;
    411         };
    412
    413         /**
    414         * Checks whether (x,y) is within the area defined by the sector.
    415         * @memberOf Sector.prototype
    416         * @name hasPointSector
    417         * @function
    418         * @param {Number} x Coordinate in x direction, screen coordinates.
    419         * @param {Number} y Coordinate in y direction, screen coordinates.
    420         * @returns {Boolean} True if (x,y) is within the sector defined by the arc, False otherwise.
    421         */
    422         el.hasPointSector = function (x, y) {
    423             var angle,
    424                 checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),
    425                 r = this.Radius(),
    426                 dist = this.point1.coords.distance(Const.COORDS_BY_USER, checkPoint),
    427                 alpha,
    428                 beta,
    429                 has = (dist < r);
    430
    431             if (has) {
    432                 angle = Geometry.rad(this.radiuspoint, this.center, checkPoint.usrCoords.slice(1));
    433                 alpha = 0.0;
    434                 beta = Geometry.rad(this.radiuspoint, this.center, this.anglepoint);
    435
    436                 if ((this.visProp.selection === 'minor' && beta > Math.PI) ||
    437                         (this.visProp.selection === 'major' && beta < Math.PI)) {
    438                     alpha = beta;
    439                     beta = 2 * Math.PI;
    440                 }
    441                 //if (angle > Geometry.rad(this.point2, this.point1, this.point3)) {
    442                 if (angle < alpha || angle > beta) {
    443                     has = false;
    444                 }
    445             }
    446             return has;
    447         };
    448
    449         el.hasPoint = function (x, y) {
    450             if (this.visProp.highlightonsector || this.visProp.hasinnerpoints) {
    451                 return this.hasPointSector(x, y);
    452             }
    453
    454             return this.hasPointCurve(x, y);
    455         };
    456
    457         // documented in GeometryElement
    458         el.getTextAnchor = function () {
    459             return this.point1.coords;
    460         };
    461
    462         // documented in GeometryElement
    463         // this method is very similar to arc.getLabelAnchor()
    464         // there are some additions in the arc version though, mainly concerning
    465         // "major" and "minor" arcs. but maybe these methods can be merged.
    466         el.getLabelAnchor = function () {
    467             var coords, vecx, vecy, len,
    468                 angle = Geometry.rad(this.point2, this.point1, this.point3),
    469                 dx = 13 / this.board.unitX,
    470                 dy = 13 / this.board.unitY,
    471                 p2c = this.point2.coords.usrCoords,
    472                 pmc = this.point1.coords.usrCoords,
    473                 bxminusax = p2c[1] - pmc[1],
    474                 byminusay = p2c[2] - pmc[2];
    475
    476             // If this is uncommented, the angle label can not be dragged
    477             //if (Type.exists(this.label)) {
    478             //    this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);
    479             //}
    480
    481             if ((this.visProp.selection === 'minor' && angle > Math.PI) ||
    482                     (this.visProp.selection === 'major' && angle < Math.PI)) {
    483                 angle = -(2 * Math.PI - angle);
    484             }
    485
    486             coords = new Coords(Const.COORDS_BY_USER, [
    487                 pmc[1] + Math.cos(angle * 0.5) * bxminusax - Math.sin(angle * 0.5) * byminusay,
    488                 pmc[2] + Math.sin(angle * 0.5) * bxminusax + Math.cos(angle * 0.5) * byminusay
    489             ], this.board);
    490
    491             vecx = coords.usrCoords[1] - pmc[1];
    492             vecy = coords.usrCoords[2] - pmc[2];
    493
    494             len = Math.sqrt(vecx * vecx + vecy * vecy);
    495             vecx = vecx * (len + dx) / len;
    496             vecy = vecy * (len + dy) / len;
    497
    498             return new Coords(Const.COORDS_BY_USER, [pmc[1] + vecx, pmc[2] + vecy], this.board);
    499         };
    500
    501         /**
    502          * Overwrite the Radius method of the sector.
    503          * Used in {@link GeometryElement#setAttribute}.
    504          * @param {Number, Function} value New radius.
    505          */
    506         el.setRadius = function (value) {
    507             el.Radius = function () {
    508                 return Type.evaluate(value);
    509             };
    510         };
    511
    512         /**
    513          * deprecated
    514          * @ignore
    515          */
    516         el.getRadius = function () {
    517             return this.Radius();
    518         };
    519
    520         /**
    521          * Moves the sector by the difference of two coordinates.
    522          * @param {Number} method The type of coordinates used here. Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
    523          * @param {Array} coords coordinates in screen/user units
    524          * @param {Array} oldcoords previous coordinates in screen/user units
    525          * @returns {JXG.Curve} this element
    526          */
    527         if (type === '3points') {
    528             el.setPositionDirectly = function (method, coords, oldcoords) {
    529                 var dc, t, i, len,
    530                     c = new Coords(method, coords, this.board),
    531                     oldc = new Coords(method, oldcoords, this.board);
    532
    533                 if (!el.point1.draggable() || !el.point2.draggable() || !el.point3.draggable()) {
    534                     return this;
    535                 }
    536
    537                 dc = Statistics.subtract(c.usrCoords, oldc.usrCoords);
    538                 t = this.board.create('transform', dc.slice(1), {type: 'translate'});
    539                 t.applyOnce([el.point1, el.point2, el.point3]);
    540
    541                 return this;
    542             };
    543         }
    544
    545         el.prepareUpdate().update();
    546
    547         return el;
    548     };
    549
    550     JXG.registerElement('sector', JXG.createSector);
    551
    552
    553     /**
    554      * @class A circumcircle sector is different from a {@link Sector} mostly in the way the parent elements are interpreted.
    555      * At first, the circum centre is determined from the three given points. Then the sector is drawn from <tt>p1</tt> through
    556      * <tt>p2</tt> to <tt>p3</tt>.
    557      * @pseudo
    558      * @name CircumcircleSector
    559      * @augments Sector
    560      * @constructor
    561      * @type Sector
    562      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    563      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 A circumcircle sector is defined by the circumcircle which is determined
    564      * by these three given points. The circumcircle sector is always drawn from <tt>p1</tt> through <tt>p2</tt> to <tt>p3</tt>.
    565      * @example
    566      * // Create an arc out of three free points
    567      * var p1 = board.create('point', [1.5, 5.0]),
    568      *     p2 = board.create('point', [1.0, 0.5]),
    569      *     p3 = board.create('point', [5.0, 3.0]),
    570      *
    571      *     a = board.create('circumcirclesector', [p1, p2, p3]);
    572      * </pre><div id="695cf0d6-6d7a-4d4d-bfc9-34c6aa28cd04" style="width: 300px; height: 300px;"></div>
    573      * <script type="text/javascript">
    574      * (function () {
    575  *   var board = JXG.JSXGraph.initBoard('695cf0d6-6d7a-4d4d-bfc9-34c6aa28cd04', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    576  *     p1 = board.create('point', [1.5, 5.0]),
    577  *     p2 = board.create('point', [1.0, 0.5]),
    578  *     p3 = board.create('point', [5.0, 3.0]),
    579  *
    580  *     a = board.create('circumcirclesector', [p1, p2, p3]);
    581  * })();
    582      * </script><pre>
    583      */
    584     JXG.createCircumcircleSector = function (board, parents, attributes) {
    585         var el, mp, attr, points, i;
    586
    587         points = Type.providePoints(board, parents, attributes, 'point');
    588         if (points === false) {
    589             throw new Error("JSXGraph: Can't create circumcircle sector with parent types '" +
    590                 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" + (typeof parents[2]) + "'.");
    591         }
    592
    593         mp = board.create('circumcenter', points.slice(0, 3), attr);
    594         mp.dump = false;
    595
    596         attr = Type.copyAttributes(attributes, board.options, 'circumcirclesector');
    597         el = board.create('sector', [mp, points[0], points[2], points[1]], attr);
    598
    599         el.elType = 'circumcirclesector';
    600         el.parents = [points[0].id, points[1].id, points[2].id];
    601
    602         /**
    603          * Center of the circumcirclesector
    604          * @memberOf CircumcircleSector.prototype
    605          * @name center
    606          * @type Circumcenter
    607          */
    608         el.center = mp;
    609         el.subs = {
    610             center: mp
    611         };
    612
    613         return el;
    614     };
    615
    616     JXG.registerElement('circumcirclesector', JXG.createCircumcircleSector);
    617
    618     /**
    619      * @class A minor sector is a sector of a circle having measure less than or equal to
    620      * 180 degrees (pi radians). It is defined by a center, one point that
    621      * defines the radius, and a third point that defines the angle of the sector.
    622      * @pseudo
    623      * @name MinorSector
    624      * @augments Curve
    625      * @constructor
    626      * @type JXG.Curve
    627      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    628      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor sector is a sector of a circle around p1 having measure less than or equal to
    629      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
    630      * @example
    631      * // Create sector out of three free points
    632      * var p1 = board.create('point', [2.0, 2.0]);
    633      * var p2 = board.create('point', [1.0, 0.5]);
    634      * var p3 = board.create('point', [3.5, 1.0]);
    635      *
    636      * var a = board.create('minorsector', [p1, p2, p3]);
    637      * </pre><div id="af27ddcc-265f-428f-90dd-d31ace945800" style="width: 300px; height: 300px;"></div>
    638      * <script type="text/javascript">
    639      * (function () {
    640      *   var board = JXG.JSXGraph.initBoard('af27ddcc-265f-428f-90dd-d31ace945800', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    641      *       p1 = board.create('point', [2.0, 2.0]),
    642      *       p2 = board.create('point', [1.0, 0.5]),
    643      *       p3 = board.create('point', [3.5, 1.0]),
    644      *
    645      *       a = board.create('minorsector', [p1, p2, p3]);
    646      * })();
    647      * </script><pre>
    648      */
    649     JXG.createMinorSector = function (board, parents, attributes) {
    650         attributes.selection = 'minor';
    651         return JXG.createSector(board, parents, attributes);
    652     };
    653
    654     JXG.registerElement('minorsector', JXG.createMinorSector);
    655
    656     /**
    657      * @class A major sector is a sector of a circle having measure greater than or equal to
    658      * 180 degrees (pi radians). It is defined by a center, one point that
    659      * defines the radius, and a third point that defines the angle of the sector.
    660      * @pseudo
    661      * @name MajorSector
    662      * @augments Curve
    663      * @constructor
    664      * @type JXG.Curve
    665      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    666      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Major sector is a sector of a circle around p1 having measure greater than or equal to
    667      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
    668      * @example
    669      * // Create an arc out of three free points
    670      * var p1 = board.create('point', [2.0, 2.0]);
    671      * var p2 = board.create('point', [1.0, 0.5]);
    672      * var p3 = board.create('point', [3.5, 1.0]);
    673      *
    674      * var a = board.create('majorsector', [p1, p2, p3]);
    675      * </pre><div id="83c6561f-7561-4047-b98d-036248a00932" style="width: 300px; height: 300px;"></div>
    676      * <script type="text/javascript">
    677      * (function () {
    678      *   var board = JXG.JSXGraph.initBoard('83c6561f-7561-4047-b98d-036248a00932', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    679      *       p1 = board.create('point', [2.0, 2.0]),
    680      *       p2 = board.create('point', [1.0, 0.5]),
    681      *       p3 = board.create('point', [3.5, 1.0]),
    682      *
    683      *       a = board.create('majorsector', [p1, p2, p3]);
    684      * })();
    685      * </script><pre>
    686      */
    687     JXG.createMajorSector = function (board, parents, attributes) {
    688         attributes.selection = 'major';
    689         return JXG.createSector(board, parents, attributes);
    690     };
    691
    692     JXG.registerElement('majorsector', JXG.createMajorSector);
    693
    694     /**
    695      * @class The angle element is used to denote an angle defined by three points. Visually it is just a {@link Sector}
    696      * element with a radius not defined by the parent elements but by an attribute <tt>radius</tt>. As opposed to the sector,
    697      * an angle has two angle points and no radius point.
    698      * Sector is displayed if type=="sector".
    699      * If type=="square", instead of a sector a parallelogram is displayed.
    700      * In case of type=="auto", a square is displayed if the angle is near orthogonal.
    701      * If no name is provided the angle label is automatically set to a lower greek letter.
    702      * @pseudo
    703      * @name Angle
    704      * @augments Sector
    705      * @constructor
    706      * @type Sector
    707      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    708      * First possiblity of input parameters are:
    709      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 An angle is always drawn counterclockwise from <tt>p1</tt> to
    710      * <tt>p3</tt> around <tt>p2</tt>.
    711      *
    712      * Second possibility of input parameters are:
    713      * @param {JXG.Line_JXG.Line_array|number_array|number} line, line2, coords1 or direction1, coords2 or direction2, radius The angle is defined by two lines.
    714      * The two legs which define the angle are given by two coordinate arrays.
    715      * The points given by these coordinate arrays are projected initially (i.e. only once) onto the two lines.
    716      * The other possibility is to supply directions (+/- 1).
    717      *
    718      * @example
    719      * // Create an angle out of three free points
    720      * var p1 = board.create('point', [5.0, 3.0]),
    721      *     p2 = board.create('point', [1.0, 0.5]),
    722      *     p3 = board.create('point', [1.5, 5.0]),
    723      *
    724      *     a = board.create('angle', [p1, p2, p3]);
    725      * </pre><div id="a34151f9-bb26-480a-8d6e-9b8cbf789ae5" style="width: 300px; height: 300px;"></div>
    726      * <script type="text/javascript">
    727      * (function () {
    728      *   var board = JXG.JSXGraph.initBoard('a34151f9-bb26-480a-8d6e-9b8cbf789ae5', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    729      *     p1 = board.create('point', [5.0, 3.0]),
    730      *     p2 = board.create('point', [1.0, 0.5]),
    731      *     p3 = board.create('point', [1.5, 5.0]),
    732      *
    733      *     a = board.create('angle', [p1, p2, p3]);
    734      * })();
    735      * </script><pre>
    736      *
    737      * @example
    738      * // Create an angle out of two lines and two directions
    739      * var p1 = board.create('point', [-1, 4]),
    740      *  p2 = board.create('point', [4, 1]),
    741      *  q1 = board.create('point', [-2, -3]),
    742      *  q2 = board.create('point', [4,3]),
    743      *
    744      *  li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
    745      *  li2 = board.create('line', [q1,q2], {lastArrow:true}),
    746      *
    747      *  a1 = board.create('angle', [li1, li2, [5.5, 0], [4, 3]], { radius:1 }),
    748      *  a2 = board.create('angle', [li1, li2, 1, -1], { radius:2 });
    749      *
    750      * </pre><div id="3a667ddd-63dc-4594-b5f1-afac969b371f" style="width: 300px; height: 300px;"></div>
    751      * <script type="text/javascript">
    752      * (function () {
    753      *   var board = JXG.JSXGraph.initBoard('3a667ddd-63dc-4594-b5f1-afac969b371f', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    754      *     p1 = board.create('point', [-1, 4]),
    755      *     p2 = board.create('point', [4, 1]),
    756      *     q1 = board.create('point', [-2, -3]),
    757      *     q2 = board.create('point', [4,3]),
    758      *
    759      *     li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
    760      *     li2 = board.create('line', [q1,q2], {lastArrow:true}),
    761      *
    762      *     a1 = board.create('angle', [li1, li2, [5.5, 0], [4, 3]], { radius:1 }),
    763      *     a2 = board.create('angle', [li1, li2, 1, -1], { radius:2 });
    764      * })();
    765      * </script><pre>
    766      */
    767     JXG.createAngle = function (board, parents, attributes) {
    768         var el, radius, text, attr, attrsub,
    769             i, dot, points,
    770             type = 'invalid';
    771
    772         // Two lines or three points?
    773         if (parents[0].elementClass === Const.OBJECT_CLASS_LINE &&
    774                 parents[1].elementClass === Const.OBJECT_CLASS_LINE &&
    775                 (Type.isArray(parents[2]) || Type.isNumber(parents[2])) &&
    776                 (Type.isArray(parents[3]) || Type.isNumber(parents[3]))) {
    777
    778             type = '2lines';
    779         } else {
    780             points = Type.providePoints(board, parents, attributes, 'point');
    781             if (points === false) {
    782                 throw new Error("JSXGraph: Can't create angle with parent types '" +
    783                     (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" + (typeof parents[2]) + "'.");
    784             }
    785             type = '3points';
    786         }
    787
    788         attr = Type.copyAttributes(attributes, board.options, 'angle');
    789
    790         //  If empty, create a new name
    791         if (!Type.exists(attr.name) || attr.name === '') {
    792             attr.name = board.generateName({type: Const.OBJECT_TYPE_ANGLE});
    793         }
    794
    795         if (Type.exists(attr.radius)) {
    796             radius = attr.radius;
    797         } else {
    798             radius = 0;
    799         }
    800
    801         if (type === '2lines') {
    802             parents.push(radius);
    803             el = board.create('sector', parents, attr);
    804             el.updateDataArraySector = el.updateDataArray;
    805
    806             // TODO
    807             el.setAngle = function (val) {};
    808             el.free = function (val) {};
    809
    810         } else {
    811             el = board.create('sector', [points[1], points[0], points[2]], attr);
    812             el.arc.visProp.priv = true;
    813
    814             /**
    815              * The point defining the radius of the angle element. Alias for {@link Angle.prototype#radiuspoint}.
    816              * @type JXG.Point
    817              * @name point
    818              * @memberOf Angle.prototype
    819              */
    820             el.point = el.point2 = el.radiuspoint = points[0];
    821
    822             /**
    823              * Helper point for angles of type 'square'.
    824              * @type JXG.Point
    825              * @name pointsquare
    826              * @memberOf Angle.prototype
    827              */
    828             el.pointsquare = el.point3 = el.anglepoint = points[2];
    829
    830             el.Radius = function () {
    831                 return Type.evaluate(radius);
    832             };
    833
    834             el.updateDataArraySector = function () {
    835                 var A = this.point2,
    836                     B = this.point1,
    837                     C = this.point3,
    838                     r = this.Radius(),
    839                     d = B.Dist(A),
    840                     ar,
    841                     phi,
    842                     sgn = 1;
    843
    844                 phi = Geometry.rad(A, B, C);
    845                 if ((this.visProp.selection === 'minor' && phi > Math.PI) ||
    846                         (this.visProp.selection === 'major' && phi < Math.PI)) {
    847                     sgn = -1;
    848                 }
    849
    850                 A = A.coords.usrCoords;
    851                 B = B.coords.usrCoords;
    852                 C = C.coords.usrCoords;
    853
    854                 A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
    855                 C = [1, B[1] + (C[1] - B[1]) * r / d, B[2] + (C[2] - B[2]) * r / d];
    856
    857                 ar = Geometry.bezierArc(A, B, C, true, sgn);
    858
    859                 this.dataX = ar[0];
    860                 this.dataY = ar[1];
    861                 this.bezierDegree = 3;
    862             };
    863
    864             /**
    865             * Set an angle to a prescribed value given in radians. This is only possible if the third point of the angle, i.e.
    866             * the anglepoint is a free point.
    867             * @name setAngle
    868             * @function
    869             * @param {Number|Function} val Number or Function which returns the size of the angle in Radians
    870             * @returns {Object} Pointer to the angle element..
    871             * @memberOf Angle.prototype
    872             */
    873             el.setAngle = function (val) {
    874                 var t,
    875                     p = this.anglepoint,
    876                     q = this.radiuspoint;
    877
    878                 if (p.draggable()) {
    879                     t = this.board.create('transform', [val, this.center], {type: 'rotate'});
    880                     p.addTransform(q, t);
    881                     p.isDraggable = false;
    882                     p.parents = [q];
    883                 }
    884                 return this;
    885             };
    886
    887             /**
    888             * Frees an angle from a prescribed value. This is only relevant if the angle size has been set by
    889             * setAngle() previously. The anglepoint is set to a free point.
    890             * @name free
    891             * @function
    892             * @returns {Object} Pointer to the angle element..
    893             * @memberOf Angle.prototype
    894             */
    895             el.free = function () {
    896                 var p = this.anglepoint;
    897                 if (p.transformations.length > 0) {
    898                     p.transformations.pop();
    899                     p.isDraggable = true;
    900                     p.parents = [];
    901                 }
    902                 return this;
    903             };
    904
    905             el.parents = [points[0].id, points[1].id, points[2].id]; // Important: This overwrites the parents order in underlying sector
    906
    907         } // end '3points'
    908
    909         // GEONExT compatible labels.
    910         if (JXG.exists(el.visProp.text)) {
    911             el.label.setText(el.visProp.text);
    912         }
    913
    914         el.elType = 'angle';
    915         el.type = Const.OBJECT_TYPE_ANGLE;
    916         // el.parents = [points[0].id, points[1].id, points[2].id];
    917         el.subs = {};
    918
    919         el.updateDataArraySquare = function () {
    920             var A, B, C,
    921                 r = this.Radius(),
    922                 d1, d2,
    923                 v, l1, l2;
    924
    925
    926             if (type === '2lines') {
    927                 // This is necessary to update this.point1, this.point2, this.point3.
    928                 this.updateDataArraySector();
    929             }
    930
    931             A = this.point2;
    932             B = this.point1;
    933             C = this.point3;
    934
    935             A = A.coords.usrCoords;
    936             B = B.coords.usrCoords;
    937             C = C.coords.usrCoords;
    938
    939             d1 = Geometry.distance(A, B, 3);
    940             d2 = Geometry.distance(C, B, 3);
    941
    942             // In case of type=='2lines' this is redundant, because r == d1 == d2
    943             A = [1, B[1] + (A[1] - B[1]) * r / d1, B[2] + (A[2] - B[2]) * r / d1];
    944             C = [1, B[1] + (C[1] - B[1]) * r / d2, B[2] + (C[2] - B[2]) * r / d2];
    945
    946             v = Mat.crossProduct(C, B);
    947             l1 = [-A[1] * v[1] - A[2] * v[2], A[0] * v[1], A[0] * v[2]];
    948             v = Mat.crossProduct(A, B);
    949             l2 = [-C[1] * v[1] - C[2] * v[2], C[0] * v[1], C[0] * v[2]];
    950
    951             v = Mat.crossProduct(l1, l2);
    952             v[1] /= v[0];
    953             v[2] /= v[0];
    954
    955             this.dataX = [B[1], A[1], v[1], C[1], B[1]];
    956             this.dataY = [B[2], A[2], v[2], C[2], B[2]];
    957
    958             this.bezierDegree = 1;
    959         };
    960
    961         el.updateDataArrayNone = function () {
    962             this.dataX = [NaN];
    963             this.dataY = [NaN];
    964             this.bezierDegree = 1;
    965         };
    966
    967         el.updateDataArray = function () {
    968             var type = this.visProp.type,
    969                 deg = Geometry.trueAngle(this.point2, this.point1, this.point3);
    970
    971             if ((this.visProp.selection === 'minor' && deg > 180.0) ||
    972                     (this.visProp.selection === 'major' && deg < 180.0)) {
    973                 deg = 360.0 - deg;
    974             }
    975
    976             if (Math.abs(deg - 90.0) < this.visProp.orthosensitivity + Mat.eps) {
    977                 type = this.visProp.orthotype;
    978             }
    979
    980             if (type === 'none') {
    981                 this.updateDataArrayNone();
    982             } else if (type === 'square') {
    983                 this.updateDataArraySquare();
    984             } else if (type === 'sector') {
    985                 this.updateDataArraySector();
    986             } else if (type === 'sectordot') {
    987                 this.updateDataArraySector();
    988                 if (!this.dot.visProp.visible) {
    989                     this.dot.setAttribute({visible: true});
    990                 }
    991             }
    992
    993             if (!this.visProp.visible || (type !== 'sectordot' && this.dot.visProp.visible)) {
    994                 this.dot.setAttribute({visible: false});
    995             }
    996         };
    997
    998         /**
    999          * Indicates a right angle. Invisible by default, use <tt>dot.visible: true</tt> to show.
    1000          * Though this dot indicates a right angle, it can be visible even if the angle is not a right
    1001          * one.
    1002          * @type JXG.Point
    1003          * @name dot
    1004          * @memberOf Angle.prototype
    1005          */
    1006         attrsub = Type.copyAttributes(attributes, board.options, 'angle', 'dot');
    1007         el.dot = board.create('point', [function () {
    1008             var A, B, r, d, a2, co, si, mat,
    1009                 point1, point2, point3;
    1010
    1011             if (Type.exists(el.dot) && !el.dot.visProp.visible) {
    1012                 return [0, 0];
    1013             }
    1014
    1015             A = el.point2.coords.usrCoords;
    1016             B = el.point1.coords.usrCoords;
    1017             r = el.Radius();
    1018             d = Geometry.distance(A, B, 3);
    1019             a2 = Geometry.rad(el.point2, el.point1, el.point3);
    1020
    1021             if ((el.visProp.selection === 'minor' && a2 > Math.PI) ||
    1022                     (el.visProp.selection === 'major' && a2 < Math.PI)) {
    1023                 a2 = -(2 * Math.PI - a2);
    1024             }
    1025             a2 *= 0.5;
    1026
    1027             co = Math.cos(a2);
    1028             si = Math.sin(a2);
    1029
    1030             A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
    1031
    1032             mat = [
    1033                 [1, 0, 0],
    1034                 [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],
    1035                 [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5,  co * 0.5]
    1036             ];
    1037             return Mat.matVecMult(mat, A);
    1038         }], attrsub);
    1039
    1040         el.dot.dump = false;
    1041         el.subs.dot = el.dot;
    1042
    1043         if (type === '2lines') {
    1044             for (i = 0; i < 2; i++) {
    1045                 board.select(parents[i]).addChild(el.dot);
    1046             }
    1047         } else {
    1048             for (i = 0; i < 3; i++) {
    1049                 board.select(points[i]).addChild(el.dot);
    1050             }
    1051         }
    1052
    1053         // documented in GeometryElement
    1054         el.getLabelAnchor = function () {
    1055             var vec, dx = 12, dy = 12,
    1056                 A, B, r, d, a2, co, si, mat;
    1057
    1058             // If this is uncommented, the angle label can not be dragged
    1059             //if (Type.exists(this.label)) {
    1060             //    this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);
    1061             //}
    1062
    1063             if (Type.exists(this.label.visProp.fontSize)) {
    1064                 dx = this.label.visProp.fontSize;
    1065                 dy = this.label.visProp.fontSize;
    1066             }
    1067             dx /= this.board.unitX;
    1068             dy /= this.board.unitY;
    1069
    1070             A = el.point2.coords.usrCoords;
    1071             B = el.point1.coords.usrCoords;
    1072             r = el.Radius();
    1073             d = Geometry.distance(A, B, 3);
    1074             a2 = Geometry.rad(el.point2, el.point1, el.point3);
    1075             if ((el.visProp.selection === 'minor' && a2 > Math.PI) ||
    1076                     (el.visProp.selection === 'major' && a2 < Math.PI)) {
    1077                 a2 = -(2 * Math.PI - a2);
    1078             }
    1079             a2 *= 0.5;
    1080             co = Math.cos(a2);
    1081             si = Math.sin(a2);
    1082
    1083             A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
    1084
    1085             mat = [
    1086                 [1, 0, 0],
    1087                 [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],
    1088                 [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5,  co * 0.5]
    1089             ];
    1090             vec = Mat.matVecMult(mat, A);
    1091             vec[1] /= vec[0];
    1092             vec[2] /= vec[0];
    1093             vec[0] /= vec[0];
    1094
    1095             d = Geometry.distance(vec, B, 3);
    1096             vec = [vec[0], B[1] + (vec[1] - B[1]) * (r + dx) / d,  B[2] + (vec[2] - B[2]) * (r + dx) / d];
    1097
    1098             return new Coords(Const.COORDS_BY_USER, vec, this.board);
    1099         };
    1100
    1101         el.Value = function () {
    1102             return Geometry.rad(this.point2, this.point1, this.point3);
    1103         };
    1104
    1105         el.methodMap = Type.deepCopy(el.methodMap, {
    1106             Value: 'Value',
    1107             setAngle: 'setAngle',
    1108             free: 'free'
    1109         });
    1110
    1111         return el;
    1112     };
    1113
    1114     JXG.registerElement('angle', JXG.createAngle);
    1115
    1116     /**
    1117      * @class A non-reflex angle is the acute or obtuse instance of an angle.
    1118      * It is defined by a center, one point that
    1119      * defines the radius, and a third point that defines the angle of the sector.
    1120      * @pseudo
    1121      * @name NonReflexAngle
    1122      * @augments Sector
    1123      * @constructor
    1124      * @type Sector
    1125      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    1126      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor sector is a sector of a circle around p1 having measure less than or equal to
    1127      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
    1128      * @example
    1129      * // Create a non-reflex angle out of three free points
    1130      * var p1 = board.create('point', [5.0, 3.0]),
    1131      *     p2 = board.create('point', [1.0, 0.5]),
    1132      *     p3 = board.create('point', [1.5, 5.0]),
    1133      *
    1134      *     a = board.create('nonreflexangle', [p1, p2, p3], {radius: 2});
    1135      * </pre><div id="d0ab6d6b-63a7-48b2-8749-b02bb5e744f9" style="width: 300px; height: 300px;"></div>
    1136      * <script type="text/javascript">
    1137      * (function () {
    1138      *   var board = JXG.JSXGraph.initBoard('d0ab6d6b-63a7-48b2-8749-b02bb5e744f9', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    1139      *     p1 = board.create('point', [5.0, 3.0]),
    1140      *     p2 = board.create('point', [1.0, 0.5]),
    1141      *     p3 = board.create('point', [1.5, 5.0]),
    1142      *
    1143      *     a = board.create('nonreflexangle', [p1, p2, p3], {radius: 2});
    1144      * })();
    1145      * </script><pre>
    1146      */
    1147     JXG.createNonreflexAngle = function (board, parents, attributes) {
    1148         attributes.selection = 'minor';
    1149         return JXG.createAngle(board, parents, attributes);
    1150     };
    1151
    1152     JXG.registerElement('nonreflexangle', JXG.createNonreflexAngle);
    1153
    1154     /**
    1155      * @class A reflex angle is the neither acute nor obtuse instance of an angle.
    1156      * It is defined by a center, one point that
    1157      * defines the radius, and a third point that defines the angle of the sector.
    1158      * @pseudo
    1159      * @name ReflexAngle
    1160      * @augments Sector
    1161      * @constructor
    1162      * @type Sector
    1163      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    1164      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor sector is a sector of a circle around p1 having measure less than or equal to
    1165      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
    1166      * @example
    1167      * // Create a non-reflex angle out of three free points
    1168      * var p1 = board.create('point', [5.0, 3.0]),
    1169      *     p2 = board.create('point', [1.0, 0.5]),
    1170      *     p3 = board.create('point', [1.5, 5.0]),
    1171      *
    1172      *     a = board.create('reflexangle', [p1, p2, p3], {radius: 2});
    1173      * </pre><div id="f2a577f2-553d-4f9f-a895-2d6d4b8c60e8" style="width: 300px; height: 300px;"></div>
    1174      * <script type="text/javascript">
    1175      * (function () {
    1176      *   var board = JXG.JSXGraph.initBoard('f2a577f2-553d-4f9f-a895-2d6d4b8c60e8', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    1177      *     p1 = board.create('point', [5.0, 3.0]),
    1178      *     p2 = board.create('point', [1.0, 0.5]),
    1179      *     p3 = board.create('point', [1.5, 5.0]),
    1180      *
    1181      *     a = board.create('reflexangle', [p1, p2, p3], {radius: 2});
    1182      * })();
    1183      * </script><pre>
    1184      */
    1185     JXG.createReflexAngle = function (board, parents, attributes) {
    1186         attributes.selection = 'major';
    1187         return JXG.createAngle(board, parents, attributes);
    1188     };
    1189
    1190     JXG.registerElement('reflexangle', JXG.createReflexAngle);
    1191
    1192
    1193     return {
    1194         createSector: JXG.createSector,
    1195         createCircumcircleSector: JXG.createCircumcircleSector,
    1196         createMinorSector: JXG.createMinorSector,
    1197         createMajorSector: JXG.createMajorSector,
    1198         createAngle: JXG.createAngle,
    1199         createReflexAngle: JXG.createReflexAngle,
    1200         createNonreflexAngle: JXG.createNonreflexAngle
    1201     };
    1202 });
    1203