      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