      1 /*
      2     Copyright 2008-2017
      3         Matthias Ehmann,
      4         Michael Gerhaeuser,
      5         Carsten Miller,
      6         Bianca Valentin,
      7         Alfred Wassermann,
      8         Peter Wilfahrt
      9
     10     This file is part of JSXGraph.
     11
     12     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
     13
     14     You can redistribute it and/or modify it under the terms of the
     15
     16       * GNU Lesser General Public License as published by
     17         the Free Software Foundation, either version 3 of the License, or
     18         (at your option) any later version
     19       OR
     20       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
     21
     22     JSXGraph is distributed in the hope that it will be useful,
     23     but WITHOUT ANY WARRANTY; without even the implied warranty of
     24     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     25     GNU Lesser General Public License for more details.
     26
     27     You should have received a copy of the GNU Lesser General Public License and
     28     the MIT License along with JSXGraph. If not, see <http://www.gnu.org/licenses/>
     29     and <http://opensource.org/licenses/MIT/>.
     30  */
     31
     32
     33 /*global JXG: true, define: true*/
     34 /*jslint nomen: true, plusplus: true*/
     35
     36 /* depends:
     37  jxg
     38  math/geometry
     39  math/math
     40  base/coords
     41  base/constants
     42  utils/type
     43   elements:
     44    point
     45    curve
     46    circumcentre
     47    transform
     48  */
     49
     50 define([
     51     'jxg', 'math/geometry', 'math/math', 'math/statistics', 'base/coords', 'base/constants', 'utils/type', 'base/point', 'base/curve',
     52     'base/transformation', 'element/composition'
     53 ], function (JXG, Geometry, Mat, Statistics, Coords, Const, Type, Point, Curve, Transform, Compositions) {
     54
     55     "use strict";
     56
     57     /**
     58      * @class A circular sector is a subarea of the area enclosed by a circle. It is enclosed by two radii and an arc.
     59      * @pseudo
     60      * @name Sector
     61      * @augments JXG.Curve
     62      * @constructor
     63      * @type JXG.Curve
     64      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
     65      *
     66      * First possiblity of input parameters are:
     67      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 A sector is defined by three points: The sector's center <tt>p1</tt>,
     68      * a second point <tt>p2</tt> defining the radius and a third point <tt>p3</tt> defining the angle of the sector. The
     69      * Sector is always drawn counter clockwise from <tt>p2</tt> to <tt>p3</tt>
     70      *
     71      * Second possibility of input parameters are:
     72      * @param {JXG.Line_JXG.Line_array,number_array,number_number,function} line, line2, coords1 or direction1, coords2 or direction2, radius The sector is defined by two lines.
     73      * The two legs which define the sector are given by two coordinates arrays which are project initially two the two lines or by two directions (+/- 1).
     74      * The last parameter is the radius of the sector.
     75      *
     76      *
     77      * @example
     78      * // Create a sector out of three free points
     79      * var p1 = board.create('point', [1.5, 5.0]),
     80      *     p2 = board.create('point', [1.0, 0.5]),
     81      *     p3 = board.create('point', [5.0, 3.0]),
     82      *
     83      *     a = board.create('sector', [p1, p2, p3]);
     84      * </pre><div class="jxgbox" id="49f59123-f013-4681-bfd9-338b89893156" style="width: 300px; height: 300px;"></div>
     85      * <script type="text/javascript">
     86      * (function () {
     87      *   var board = JXG.JSXGraph.initBoard('49f59123-f013-4681-bfd9-338b89893156', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
     88      *     p1 = board.create('point', [1.5, 5.0]),
     89      *     p2 = board.create('point', [1.0, 0.5]),
     90      *     p3 = board.create('point', [5.0, 3.0]),
     91      *
     92      *     a = board.create('sector', [p1, p2, p3]);
     93      * })();
     94      * </script><pre>
     95      *
     96      * @example
     97      * // Create a sector out of two lines, two directions and a radius
     98      * var p1 = board.create('point', [-1, 4]),
     99      *  p2 = board.create('point', [4, 1]),
    100      *  q1 = board.create('point', [-2, -3]),
    101      *  q2 = board.create('point', [4,3]),
    102      *
    103      *  li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
    104      *  li2 = board.create('line', [q1,q2], {lastArrow:true}),
    105      *
    106      *  sec1 = board.create('sector', [li1, li2, [5.5, 0], [4, 3], 3]),
    107      *  sec2 = board.create('sector', [li1, li2, 1, -1, 4]);
    108      *
    109      * </pre><div class="jxgbox" id="bb9e2809-9895-4ff1-adfa-c9c71d50aa53" style="width: 300px; height: 300px;"></div>
    110      * <script type="text/javascript">
    111      * (function () {
    112      *   var board = JXG.JSXGraph.initBoard('bb9e2809-9895-4ff1-adfa-c9c71d50aa53', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    113      *     p1 = board.create('point', [-1, 4]),
    114      *     p2 = board.create('point', [4, 1]),
    115      *     q1 = board.create('point', [-2, -3]),
    116      *     q2 = board.create('point', [4,3]),
    117      *
    118      *     li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
    119      *     li2 = board.create('line', [q1,q2], {lastArrow:true}),
    120      *
    121      *     sec1 = board.create('sector', [li1, li2, [5.5, 0], [4, 3], 3]),
    122      *     sec2 = board.create('sector', [li1, li2, 1, -1, 4]);
    123      * })();
    124      * </script><pre>
    125      */
    126     JXG.createSector = function (board, parents, attributes) {
    127         var el, i, attr,
    128             type = 'invalid',
    129             s, v,
    130             attrPoints = ['center', 'radiuspoint', 'anglepoint'],
    131             points;
    132
    133         // Three points?
    134         if (parents[0].elementClass === Const.OBJECT_CLASS_LINE &&
    135                 parents[1].elementClass === Const.OBJECT_CLASS_LINE &&
    136                 (Type.isArray(parents[2]) || Type.isNumber(parents[2])) &&
    137                 (Type.isArray(parents[3]) || Type.isNumber(parents[3])) &&
    138                 (Type.isNumber(parents[4]) || Type.isFunction(parents[4]))) {
    139
    140             type = '2lines';
    141
    142         } else {
    143             points = Type.providePoints(board, parents, attributes, 'sector', attrPoints);
    144             if (points === false) {
    145                 throw new Error("JSXGraph: Can't create Sector with parent types '" +
    146                     (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" +
    147                     (typeof parents[2]) + "'.");
    148             }
    149
    150             type = '3points';
    151         }
    152
    153         attr = Type.copyAttributes(attributes, board.options, 'sector');
    154         el = board.create('curve', [[0], [0]], attr);
    155         el.type = Const.OBJECT_TYPE_SECTOR;
    156         el.elType = 'sector';
    157
    158         if (type === '2lines') {
    159             el.Radius = function () {
    160                 return Type.evaluate(parents[4]);
    161             };
    162
    163             el.line1 = board.select(parents[0]);
    164             el.line2 = board.select(parents[1]);
    165
    166             el.line1.addChild(el);
    167             el.line2.addChild(el);
    168             el.setParents(parents);
    169
    170             el.point1 = {visProp: {}};
    171             el.point2 = {visProp: {}};
    172             el.point3 = {visProp: {}};
    173
    174             /* Intersection point */
    175             s = Geometry.meetLineLine(el.line1.stdform, el.line2.stdform, 0, board);
    176
    177             if (Type.isArray(parents[2])) {
    178                 /* project p1 to l1 */
    179                 if (parents[2].length === 2) {
    180                     parents[2] = [1].concat(parents[2]);
    181                 }
    182                 /*
    183                 v = [0, el.line1.stdform[1], el.line1.stdform[2]];
    184                 v = Mat.crossProduct(v, parents[2]);
    185                 v = Geometry.meetLineLine(v, el.line1.stdform, 0, board);
    186                 */
    187                 v = Geometry.projectPointToLine({coords: {usrCoords: parents[2]}}, el.line1, board);
    188                 v = Statistics.subtract(v.usrCoords, s.usrCoords);
    189                 el.direction1 = (Mat.innerProduct(v, [0, el.line1.stdform[2], -el.line1.stdform[1]], 3) >= 0) ? +1 : -1;
    190             } else {
    191                 el.direction1 = (parents[2] >= 0) ? 1 : -1;
    192             }
    193
    194             if (Type.isArray(parents[3])) {
    195                 /* project p2 to l2 */
    196                 if (parents[3].length === 2) {
    197                     parents[3] = [1].concat(parents[3]);
    198                 }
    199                 /*
    200                 v = [0, el.line2.stdform[1], el.line2.stdform[2]];
    201                 v = Mat.crossProduct(v, parents[3]);
    202                 v = Geometry.meetLineLine(v, el.line2.stdform, 0, board);
    203                 */
    204                 v = Geometry.projectPointToLine({coords: {usrCoords: parents[3]}}, el.line2, board);
    205                 v = Statistics.subtract(v.usrCoords, s.usrCoords);
    206                 el.direction2 = (Mat.innerProduct(v, [0, el.line2.stdform[2], -el.line2.stdform[1]], 3) >= 0) ? +1 : -1;
    207             } else {
    208                 el.direction2 = (parents[3] >= 0) ? 1 : -1;
    209             }
    210
    211             el.updateDataArray = function () {
    212                 var r, l1, l2,
    213                     A = [0, 0, 0],
    214                     B = [0, 0, 0],
    215                     C = [0, 0, 0],
    216                     ar;
    217
    218                 l1 = this.line1;
    219                 l2 = this.line2;
    220
    221                 // Intersection point of the lines
    222                 B = Mat.crossProduct(l1.stdform, l2.stdform);
    223
    224                 if (Math.abs(B[0]) > Mat.eps * Mat.eps) {
    225                     B[1] /= B[0];
    226                     B[2] /= B[0];
    227                     B[0] /= B[0];
    228                 }
    229                 // First point
    230                 r = this.direction1 * this.Radius();
    231                 A = Statistics.add(B, [0, r * l1.stdform[2], -r * l1.stdform[1]]);
    232
    233                 // Second point
    234                 r = this.direction2 * this.Radius();
    235                 C = Statistics.add(B, [0, r * l2.stdform[2], -r * l2.stdform[1]]);
    236
    237                 this.point2.coords = new Coords(Const.COORDS_BY_USER, A, el.board);
    238                 this.point1.coords = new Coords(Const.COORDS_BY_USER, B, el.board);
    239                 this.point3.coords = new Coords(Const.COORDS_BY_USER, C, el.board);
    240
    241                 if (Math.abs(A[0]) < Mat.eps || Math.abs(B[0]) < Mat.eps || Math.abs(C[0]) < Mat.eps) {
    242                     this.dataX = [NaN];
    243                     this.dataY = [NaN];
    244                     return;
    245                 }
    246
    247                 ar = Geometry.bezierArc(A, B, C, true, 1);
    248
    249                 this.dataX = ar[0];
    250                 this.dataY = ar[1];
    251
    252                 this.bezierDegree = 3;
    253             };
    254
    255             el.methodMap = JXG.deepCopy(el.methodMap, {
    256                 radius: 'getRadius',
    257                 getRadius: 'getRadius',
    258                 setRadius: 'setRadius'
    259             });
    260
    261             el.prepareUpdate().update();
    262
    263         // end '2lines'
    264
    265         } else if (type === '3points') {
    266
    267             /**
    268             * Midpoint of the sector.
    269             * @memberOf Sector.prototype
    270             * @name point1
    271             * @type JXG.Point
    272             */
    273             el.point1 = points[0];
    274
    275             /**
    276             * This point together with {@link Sector#point1} defines the radius..
    277             * @memberOf Sector.prototype
    278             * @name point2
    279             * @type JXG.Point
    280             */
    281             el.point2 = points[1];
    282
    283             /**
    284             * Defines the sector's angle.
    285             * @memberOf Sector.prototype
    286             * @name point3
    287             * @type JXG.Point
    288             */
    289             el.point3 = points[2];
    290
    291             /* Add arc as child to defining points */
    292             el.point1.addChild(el);
    293             el.point2.addChild(el);
    294             el.point3.addChild(el);
    295
    296             // useDirection is necessary for circumCircleSectors
    297             el.useDirection = attributes.usedirection;
    298             el.setParents(points);
    299
    300             /**
    301             * Defines the sectors orientation in case of circumCircleSectors.
    302             * @memberOf Sector.prototype
    303             * @name point4
    304             * @type JXG.Point
    305             */
    306             if (Type.exists(points[3])) {
    307                 el.point4 = points[3];
    308                 el.point4.addChild(el);
    309             }
    310
    311             el.methodMap = JXG.deepCopy(el.methodMap, {
    312                 arc: 'arc',
    313                 center: 'center',
    314                 radiuspoint: 'radiuspoint',
    315                 anglepoint: 'anglepoint',
    316                 radius: 'getRadius',
    317                 getRadius: 'getRadius',
    318                 setRadius: 'setRadius'
    319             });
    320
    321             /**
    322             * documented in JXG.Curve
    323             * @ignore
    324             */
    325             el.updateDataArray = function () {
    326                 var ar, det, p0c, p1c, p2c,
    327                     A = this.point2,
    328                     B = this.point1,
    329                     C = this.point3,
    330                     phi, sgn = 1,
    331                     vp_s = Type.evaluate(this.visProp.selection);
    332
    333                 if (!A.isReal || !B.isReal || !C.isReal) {
    334                     this.dataX = [NaN];
    335                     this.dataY = [NaN];
    336                     return;
    337                 }
    338
    339                 phi = Geometry.rad(A, B, C);
    340                 if ((vp_s === 'minor' && phi > Math.PI) ||
    341                         (vp_s === 'major' && phi < Math.PI)) {
    342                     sgn = -1;
    343                 }
    344
    345                 // This is true for circumCircleSectors. In that case there is
    346                 // a fourth parent element: [midpoint, point1, point3, point2]
    347                 if (this.useDirection && Type.exists(this.point4)) {
    348                     p0c = this.point2.coords.usrCoords;
    349                     p1c = this.point4.coords.usrCoords;
    350                     p2c = this.point3.coords.usrCoords;
    351                     det = (p0c[1] - p2c[1]) * (p0c[2] - p1c[2]) - (p0c[2] - p2c[2]) * (p0c[1] - p1c[1]);
    352
    353                     if (det >= 0.0) {
    354                         C = this.point2;
    355                         A = this.point3;
    356                     }
    357                 }
    358
    359                 A = A.coords.usrCoords;
    360                 B = B.coords.usrCoords;
    361                 C = C.coords.usrCoords;
    362
    363                 ar = Geometry.bezierArc(A, B, C, true, sgn);
    364
    365                 this.dataX = ar[0];
    366                 this.dataY = ar[1];
    367                 this.bezierDegree = 3;
    368             };
    369
    370             /**
    371             * Returns the radius of the sector.
    372             * @memberOf Sector.prototype
    373             * @name Radius
    374             * @function
    375             * @returns {Number} The distance between {@link Sector#point1} and {@link Sector#point2}.
    376             */
    377             el.Radius = function () {
    378                 return this.point2.Dist(this.point1);
    379             };
    380
    381             attr = Type.copyAttributes(attributes, board.options, 'sector', 'arc');
    382             attr.withLabel = false;
    383             attr.name += '_arc';
    384             el.arc = board.create('arc', [el.point1, el.point2, el.point3], attr);
    385             el.addChild(el.arc);
    386         }   // end '3points'
    387
    388         el.center = el.point1;
    389         el.radiuspoint = el.point2;
    390         el.anglepoint = el.point3;
    391
    392         // Default hasPoint method. Documented in geometry element
    393         el.hasPointCurve = function (x, y) {
    394             var angle, alpha, beta,
    395                 prec,
    396                 checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),
    397                 r = this.Radius(),
    398                 dist = this.center.coords.distance(Const.COORDS_BY_USER, checkPoint),
    399                 has,
    400                 vp_s = Type.evaluate(this.visProp.selection);
    401
    402             prec = this.board.options.precision.hasPoint / Math.min(this.board.unitX, this.board.unitY);
    403             has = (Math.abs(dist - r) < prec);
    404             if (has) {
    405                 angle = Geometry.rad(this.point2, this.center, checkPoint.usrCoords.slice(1));
    406                 alpha = 0;
    407                 beta = Geometry.rad(this.point2, this.center, this.point3);
    408
    409                 if ((vp_s === 'minor' && beta > Math.PI) ||
    410                         (vp_s === 'major' && beta < Math.PI)) {
    411                     alpha = beta;
    412                     beta = 2 * Math.PI;
    413                 }
    414
    415                 if (angle < alpha || angle > beta) {
    416                     has = false;
    417                 }
    418             }
    419
    420             return has;
    421         };
    422
    423         /**
    424         * Checks whether (x,y) is within the area defined by the sector.
    425         * @memberOf Sector.prototype
    426         * @name hasPointSector
    427         * @function
    428         * @param {Number} x Coordinate in x direction, screen coordinates.
    429         * @param {Number} y Coordinate in y direction, screen coordinates.
    430         * @returns {Boolean} True if (x,y) is within the sector defined by the arc, False otherwise.
    431         */
    432         el.hasPointSector = function (x, y) {
    433             var angle,
    434                 checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board),
    435                 r = this.Radius(),
    436                 dist = this.point1.coords.distance(Const.COORDS_BY_USER, checkPoint),
    437                 alpha,
    438                 beta,
    439                 has = (dist < r),
    440                 vp_s = Type.evaluate(this.visProp.selection);
    441
    442             if (has) {
    443                 angle = Geometry.rad(this.radiuspoint, this.center, checkPoint.usrCoords.slice(1));
    444                 alpha = 0.0;
    445                 beta = Geometry.rad(this.radiuspoint, this.center, this.anglepoint);
    446
    447                 if ((vp_s === 'minor' && beta > Math.PI) ||
    448                         (vp_s === 'major' && beta < Math.PI)) {
    449                     alpha = beta;
    450                     beta = 2 * Math.PI;
    451                 }
    452                 //if (angle > Geometry.rad(this.point2, this.point1, this.point3)) {
    453                 if (angle < alpha || angle > beta) {
    454                     has = false;
    455                 }
    456             }
    457             return has;
    458         };
    459
    460         el.hasPoint = function (x, y) {
    461             if (Type.evaluate(this.visProp.highlightonsector) ||
    462                     Type.evaluate(this.visProp.hasinnerpoints)) {
    463                 return this.hasPointSector(x, y);
    464             }
    465
    466             return this.hasPointCurve(x, y);
    467         };
    468
    469         // documented in GeometryElement
    470         el.getTextAnchor = function () {
    471             return this.point1.coords;
    472         };
    473
    474         // documented in GeometryElement
    475         // this method is very similar to arc.getLabelAnchor()
    476         // there are some additions in the arc version though, mainly concerning
    477         // "major" and "minor" arcs. but maybe these methods can be merged.
    478         el.getLabelAnchor = function () {
    479             var coords, vecx, vecy, len,
    480                 angle = Geometry.rad(this.point2, this.point1, this.point3),
    481                 dx = 13 / this.board.unitX,
    482                 dy = 13 / this.board.unitY,
    483                 p2c = this.point2.coords.usrCoords,
    484                 pmc = this.point1.coords.usrCoords,
    485                 bxminusax = p2c[1] - pmc[1],
    486                 byminusay = p2c[2] - pmc[2],
    487                 vp_s = Type.evaluate(this.visProp.selection);
    488
    489             // If this is uncommented, the angle label can not be dragged
    490             //if (Type.exists(this.label)) {
    491             //    this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);
    492             //}
    493
    494             if ((vp_s === 'minor' && angle > Math.PI) ||
    495                     (vp_s === 'major' && angle < Math.PI)) {
    496                 angle = -(2 * Math.PI - angle);
    497             }
    498
    499             coords = new Coords(Const.COORDS_BY_USER, [
    500                 pmc[1] + Math.cos(angle * 0.5) * bxminusax - Math.sin(angle * 0.5) * byminusay,
    501                 pmc[2] + Math.sin(angle * 0.5) * bxminusax + Math.cos(angle * 0.5) * byminusay
    502             ], this.board);
    503
    504             vecx = coords.usrCoords[1] - pmc[1];
    505             vecy = coords.usrCoords[2] - pmc[2];
    506
    507             len = Math.sqrt(vecx * vecx + vecy * vecy);
    508             vecx = vecx * (len + dx) / len;
    509             vecy = vecy * (len + dy) / len;
    510
    511             return new Coords(Const.COORDS_BY_USER, [pmc[1] + vecx, pmc[2] + vecy], this.board);
    512         };
    513
    514         /**
    515          * Overwrite the Radius method of the sector.
    516          * Used in {@link GeometryElement#setAttribute}.
    517          * @param {Number, Function} value New radius.
    518          */
    519         el.setRadius = function (value) {
    520             el.Radius = function () {
    521                 return Type.evaluate(value);
    522             };
    523         };
    524
    525         /**
    526          * @deprecated
    527          * @ignore
    528          */
    529         el.getRadius = function () {
    530             JXG.deprecated('Sector.getRadius()', 'Sector.Radius()');
    531             return this.Radius();
    532         };
    533
    534         /**
    535          * Moves the sector by the difference of two coordinates.
    536          * @param {Number} method The type of coordinates used here. Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
    537          * @param {Array} coords coordinates in screen/user units
    538          * @param {Array} oldcoords previous coordinates in screen/user units
    539          * @returns {JXG.Curve} this element
    540          */
    541         if (type === '3points') {
    542             el.setPositionDirectly = function (method, coords, oldcoords) {
    543                 var dc, t, i, len,
    544                     c = new Coords(method, coords, this.board),
    545                     oldc = new Coords(method, oldcoords, this.board);
    546
    547                 if (!el.point1.draggable() || !el.point2.draggable() || !el.point3.draggable()) {
    548                     return this;
    549                 }
    550
    551                 dc = Statistics.subtract(c.usrCoords, oldc.usrCoords);
    552                 t = this.board.create('transform', dc.slice(1), {type: 'translate'});
    553                 t.applyOnce([el.point1, el.point2, el.point3]);
    554
    555                 return this;
    556             };
    557         }
    558
    559         el.prepareUpdate().update();
    560
    561         return el;
    562     };
    563
    564     JXG.registerElement('sector', JXG.createSector);
    565
    566
    567     /**
    568      * @class A circumcircle sector is different from a {@link Sector} mostly in the way the parent elements are interpreted.
    569      * At first, the circum centre is determined from the three given points. Then the sector is drawn from <tt>p1</tt> through
    570      * <tt>p2</tt> to <tt>p3</tt>.
    571      * @pseudo
    572      * @name CircumcircleSector
    573      * @augments Sector
    574      * @constructor
    575      * @type Sector
    576      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    577      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 A circumcircle sector is defined by the circumcircle which is determined
    578      * by these three given points. The circumcircle sector is always drawn from <tt>p1</tt> through <tt>p2</tt> to <tt>p3</tt>.
    579      * @example
    580      * // Create an arc out of three free points
    581      * var p1 = board.create('point', [1.5, 5.0]),
    582      *     p2 = board.create('point', [1.0, 0.5]),
    583      *     p3 = board.create('point', [5.0, 3.0]),
    584      *
    585      *     a = board.create('circumcirclesector', [p1, p2, p3]);
    586      * </pre><div class="jxgbox" id="695cf0d6-6d7a-4d4d-bfc9-34c6aa28cd04" style="width: 300px; height: 300px;"></div>
    587      * <script type="text/javascript">
    588      * (function () {
    589  *   var board = JXG.JSXGraph.initBoard('695cf0d6-6d7a-4d4d-bfc9-34c6aa28cd04', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    590  *     p1 = board.create('point', [1.5, 5.0]),
    591  *     p2 = board.create('point', [1.0, 0.5]),
    592  *     p3 = board.create('point', [5.0, 3.0]),
    593  *
    594  *     a = board.create('circumcirclesector', [p1, p2, p3]);
    595  * })();
    596      * </script><pre>
    597      */
    598     JXG.createCircumcircleSector = function (board, parents, attributes) {
    599         var el, mp, attr, points, i;
    600
    601         points = Type.providePoints(board, parents, attributes, 'point');
    602         if (points === false) {
    603             throw new Error("JSXGraph: Can't create circumcircle sector with parent types '" +
    604                 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" + (typeof parents[2]) + "'.");
    605         }
    606
    607         mp = board.create('circumcenter', points.slice(0, 3), attr);
    608         mp.dump = false;
    609
    610         attr = Type.copyAttributes(attributes, board.options, 'circumcirclesector');
    611         el = board.create('sector', [mp, points[0], points[2], points[1]], attr);
    612
    613         el.elType = 'circumcirclesector';
    614         el.setParents(points);
    615
    616         /**
    617          * Center of the circumcirclesector
    618          * @memberOf CircumcircleSector.prototype
    619          * @name center
    620          * @type Circumcenter
    621          */
    622         el.center = mp;
    623         el.subs = {
    624             center: mp
    625         };
    626
    627         return el;
    628     };
    629
    630     JXG.registerElement('circumcirclesector', JXG.createCircumcircleSector);
    631
    632     /**
    633      * @class A minor sector is a sector of a circle having measure less than or equal to
    634      * 180 degrees (pi radians). It is defined by a center, one point that
    635      * defines the radius, and a third point that defines the angle of the sector.
    636      * @pseudo
    637      * @name MinorSector
    638      * @augments Curve
    639      * @constructor
    640      * @type JXG.Curve
    641      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    642      * @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
    643      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
    644      * @example
    645      * // Create sector out of three free points
    646      * var p1 = board.create('point', [2.0, 2.0]);
    647      * var p2 = board.create('point', [1.0, 0.5]);
    648      * var p3 = board.create('point', [3.5, 1.0]);
    649      *
    650      * var a = board.create('minorsector', [p1, p2, p3]);
    651      * </pre><div class="jxgbox" id="af27ddcc-265f-428f-90dd-d31ace945800" style="width: 300px; height: 300px;"></div>
    652      * <script type="text/javascript">
    653      * (function () {
    654      *   var board = JXG.JSXGraph.initBoard('af27ddcc-265f-428f-90dd-d31ace945800', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    655      *       p1 = board.create('point', [2.0, 2.0]),
    656      *       p2 = board.create('point', [1.0, 0.5]),
    657      *       p3 = board.create('point', [3.5, 1.0]),
    658      *
    659      *       a = board.create('minorsector', [p1, p2, p3]);
    660      * })();
    661      * </script><pre>
    662      */
    663     JXG.createMinorSector = function (board, parents, attributes) {
    664         attributes.selection = 'minor';
    665         return JXG.createSector(board, parents, attributes);
    666     };
    667
    668     JXG.registerElement('minorsector', JXG.createMinorSector);
    669
    670     /**
    671      * @class A major sector is a sector of a circle having measure greater than or equal to
    672      * 180 degrees (pi radians). It is defined by a center, one point that
    673      * defines the radius, and a third point that defines the angle of the sector.
    674      * @pseudo
    675      * @name MajorSector
    676      * @augments Curve
    677      * @constructor
    678      * @type JXG.Curve
    679      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    680      * @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
    681      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
    682      * @example
    683      * // Create an arc out of three free points
    684      * var p1 = board.create('point', [2.0, 2.0]);
    685      * var p2 = board.create('point', [1.0, 0.5]);
    686      * var p3 = board.create('point', [3.5, 1.0]);
    687      *
    688      * var a = board.create('majorsector', [p1, p2, p3]);
    689      * </pre><div class="jxgbox" id="83c6561f-7561-4047-b98d-036248a00932" style="width: 300px; height: 300px;"></div>
    690      * <script type="text/javascript">
    691      * (function () {
    692      *   var board = JXG.JSXGraph.initBoard('83c6561f-7561-4047-b98d-036248a00932', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    693      *       p1 = board.create('point', [2.0, 2.0]),
    694      *       p2 = board.create('point', [1.0, 0.5]),
    695      *       p3 = board.create('point', [3.5, 1.0]),
    696      *
    697      *       a = board.create('majorsector', [p1, p2, p3]);
    698      * })();
    699      * </script><pre>
    700      */
    701     JXG.createMajorSector = function (board, parents, attributes) {
    702         attributes.selection = 'major';
    703         return JXG.createSector(board, parents, attributes);
    704     };
    705
    706     JXG.registerElement('majorsector', JXG.createMajorSector);
    707
    708     /**
    709      * @class The angle element is used to denote an angle defined by three points. Visually it is just a {@link Sector}
    710      * element with a radius not defined by the parent elements but by an attribute <tt>radius</tt>. As opposed to the sector,
    711      * an angle has two angle points and no radius point.
    712      * Sector is displayed if type=="sector".
    713      * If type=="square", instead of a sector a parallelogram is displayed.
    714      * In case of type=="auto", a square is displayed if the angle is near orthogonal.
    715      * If no name is provided the angle label is automatically set to a lower greek letter.
    716      * @pseudo
    717      * @name Angle
    718      * @augments Sector
    719      * @constructor
    720      * @type Sector
    721      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    722      * First possiblity of input parameters are:
    723      * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p1 An angle is always drawn counterclockwise from <tt>p1</tt> to
    724      * <tt>p3</tt> around <tt>p2</tt>.
    725      *
    726      * Second possibility of input parameters are:
    727      * @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.
    728      * The two legs which define the angle are given by two coordinate arrays.
    729      * The points given by these coordinate arrays are projected initially (i.e. only once) onto the two lines.
    730      * The other possibility is to supply directions (+/- 1).
    731      *
    732      * @example
    733      * // Create an angle out of three free points
    734      * var p1 = board.create('point', [5.0, 3.0]),
    735      *     p2 = board.create('point', [1.0, 0.5]),
    736      *     p3 = board.create('point', [1.5, 5.0]),
    737      *
    738      *     a = board.create('angle', [p1, p2, p3]),
    739      *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
    740      * </pre><div class="jxgbox" id="a34151f9-bb26-480a-8d6e-9b8cbf789ae5" style="width: 300px; height: 300px;"></div>
    741      * <script type="text/javascript">
    742      * (function () {
    743      *   var board = JXG.JSXGraph.initBoard('a34151f9-bb26-480a-8d6e-9b8cbf789ae5', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    744      *     p1 = board.create('point', [5.0, 3.0]),
    745      *     p2 = board.create('point', [1.0, 0.5]),
    746      *     p3 = board.create('point', [1.5, 5.0]),
    747      *
    748      *     a = board.create('angle', [p1, p2, p3]),
    749      *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
    750      * })();
    751      * </script><pre>
    752      *
    753      * @example
    754      * // Create an angle out of two lines and two directions
    755      * var p1 = board.create('point', [-1, 4]),
    756      *  p2 = board.create('point', [4, 1]),
    757      *  q1 = board.create('point', [-2, -3]),
    758      *  q2 = board.create('point', [4,3]),
    759      *
    760      *  li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
    761      *  li2 = board.create('line', [q1,q2], {lastArrow:true}),
    762      *
    763      *  a1 = board.create('angle', [li1, li2, [5.5, 0], [4, 3]], { radius:1 }),
    764      *  a2 = board.create('angle', [li1, li2, 1, -1], { radius:2 });
    765      *
    766      *
    767      * </pre><div class="jxgbox" id="3a667ddd-63dc-4594-b5f1-afac969b371f" style="width: 300px; height: 300px;"></div>
    768      * <script type="text/javascript">
    769      * (function () {
    770      *   var board = JXG.JSXGraph.initBoard('3a667ddd-63dc-4594-b5f1-afac969b371f', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    771      *     p1 = board.create('point', [-1, 4]),
    772      *     p2 = board.create('point', [4, 1]),
    773      *     q1 = board.create('point', [-2, -3]),
    774      *     q2 = board.create('point', [4,3]),
    775      *
    776      *     li1 = board.create('line', [p1,p2], {strokeColor:'black', lastArrow:true}),
    777      *     li2 = board.create('line', [q1,q2], {lastArrow:true}),
    778      *
    779      *     a1 = board.create('angle', [li1, li2, [5.5, 0], [4, 3]], { radius:1 }),
    780      *     a2 = board.create('angle', [li1, li2, 1, -1], { radius:2 });
    781      * })();
    782      * </script><pre>
    783      */
    784     JXG.createAngle = function (board, parents, attributes) {
    785         var el, radius, text, attr, attrsub,
    786             i, dot, points,
    787             type = 'invalid';
    788
    789         // Two lines or three points?
    790         if (parents[0].elementClass === Const.OBJECT_CLASS_LINE &&
    791                 parents[1].elementClass === Const.OBJECT_CLASS_LINE &&
    792                 (Type.isArray(parents[2]) || Type.isNumber(parents[2])) &&
    793                 (Type.isArray(parents[3]) || Type.isNumber(parents[3]))) {
    794
    795             type = '2lines';
    796         } else {
    797             points = Type.providePoints(board, parents, attributes, 'point');
    798             if (points === false) {
    799                 throw new Error("JSXGraph: Can't create angle with parent types '" +
    800                     (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" + (typeof parents[2]) + "'.");
    801             }
    802             type = '3points';
    803         }
    804
    805         attr = Type.copyAttributes(attributes, board.options, 'angle');
    806
    807         //  If empty, create a new name
    808         if (!Type.exists(attr.name) || attr.name === '') {
    809             attr.name = board.generateName({type: Const.OBJECT_TYPE_ANGLE});
    810         }
    811
    812         if (Type.exists(attr.radius)) {
    813             radius = attr.radius;
    814         } else {
    815             radius = 0;
    816         }
    817
    818         if (type === '2lines') {
    819             parents.push(radius);
    820             el = board.create('sector', parents, attr);
    821             el.updateDataArraySector = el.updateDataArray;
    822
    823             // TODO
    824             el.setAngle = function (val) {};
    825             el.free = function (val) {};
    826
    827         } else {
    828             el = board.create('sector', [points[1], points[0], points[2]], attr);
    829             el.arc.visProp.priv = true;
    830
    831             /**
    832              * The point defining the radius of the angle element. Alias for {@link Angle.prototype#radiuspoint}.
    833              * @type JXG.Point
    834              * @name point
    835              * @memberOf Angle.prototype
    836              */
    837             el.point = el.point2 = el.radiuspoint = points[0];
    838
    839             /**
    840              * Helper point for angles of type 'square'.
    841              * @type JXG.Point
    842              * @name pointsquare
    843              * @memberOf Angle.prototype
    844              */
    845             el.pointsquare = el.point3 = el.anglepoint = points[2];
    846
    847             el.Radius = function () {
    848                 return Type.evaluate(radius);
    849             };
    850
    851             el.updateDataArraySector = function () {
    852                 var A = this.point2,
    853                     B = this.point1,
    854                     C = this.point3,
    855                     r = this.Radius(),
    856                     d = B.Dist(A),
    857                     ar,
    858                     phi,
    859                     sgn = 1,
    860                     vp_s = Type.evaluate(this.visProp.selection);
    861
    862                 phi = Geometry.rad(A, B, C);
    863                 if ((vp_s === 'minor' && phi > Math.PI) ||
    864                         (vp_s === 'major' && phi < Math.PI)) {
    865                     sgn = -1;
    866                 }
    867
    868                 A = A.coords.usrCoords;
    869                 B = B.coords.usrCoords;
    870                 C = C.coords.usrCoords;
    871
    872                 A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
    873                 C = [1, B[1] + (C[1] - B[1]) * r / d, B[2] + (C[2] - B[2]) * r / d];
    874
    875                 ar = Geometry.bezierArc(A, B, C, true, sgn);
    876
    877                 this.dataX = ar[0];
    878                 this.dataY = ar[1];
    879                 this.bezierDegree = 3;
    880             };
    881
    882             /**
    883             * Set an angle to a prescribed value given in radians. This is only possible if the third point of the angle, i.e.
    884             * the anglepoint is a free point.
    885             * @name setAngle
    886             * @function
    887             * @param {Number|Function} val Number or Function which returns the size of the angle in Radians
    888             * @returns {Object} Pointer to the angle element..
    889             * @memberOf Angle.prototype
    890             *
    891             * @example
    892             * var p1, p2, p3, c, a, s;
    893             *
    894             * p1 = board.create('point',[0,0]);
    895             * p2 = board.create('point',[5,0]);
    896             * p3 = board.create('point',[0,5]);
    897             *
    898             * c1 = board.create('circle',[p1, p2]);
    899             *
    900             * a = board.create('angle',[p2, p1, p3], {radius:3});
    901             *
    902             * a.setAngle(function() {
    903             *     return Math.PI / 3;
    904             * });
    905             * board.update();
    906             *
    907             * </pre><div id="987c-394f-11e6-af4a-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
    908             * <script type="text/javascript">
    909             *     (function() {
    910             *         var board = JXG.JSXGraph.initBoard('987c-394f-11e6-af4a-901b0e1b8723',
    911             *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
    912             *     var p1, p2, p3, c, a, s;
    913             *
    914             *     p1 = board.create('point',[0,0]);
    915             *     p2 = board.create('point',[5,0]);
    916             *     p3 = board.create('point',[0,5]);
    917             *
    918             *     c1 = board.create('circle',[p1, p2]);
    919             *
    920             *     a = board.create('angle',[p2, p1, p3], {radius: 3});
    921             *
    922             *     a.setAngle(function() {
    923             *         return Math.PI / 3;
    924             *     });
    925             *     board.update();
    926             *
    927             *     })();
    928             *
    929             * </script><pre>
    930             *
    931             * @example
    932             * var p1, p2, p3, c, a, s;
    933             *
    934             * p1 = board.create('point',[0,0]);
    935             * p2 = board.create('point',[5,0]);
    936             * p3 = board.create('point',[0,5]);
    937             *
    938             * c1 = board.create('circle',[p1, p2]);
    939             *
    940             * a = board.create('angle',[p2, p1, p3], {radius:3});
    941             * s = board.create('slider',[[-2,1], [2,1], [0, Math.PI*0.5, 2*Math.PI]]);
    942             *
    943             * a.setAngle(function() {
    944             *     return s.Value();
    945             * });
    946             * board.update();
    947             *
    948             * </pre><div id="99957b1c-394f-11e6-af4a-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
    949             * <script type="text/javascript">
    950             *     (function() {
    951             *         var board = JXG.JSXGraph.initBoard('99957b1c-394f-11e6-af4a-901b0e1b8723',
    952             *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
    953             *     var p1, p2, p3, c, a, s;
    954             *
    955             *     p1 = board.create('point',[0,0]);
    956             *     p2 = board.create('point',[5,0]);
    957             *     p3 = board.create('point',[0,5]);
    958             *
    959             *     c1 = board.create('circle',[p1, p2]);
    960             *
    961             *     a = board.create('angle',[p2, p1, p3], {radius: 3});
    962             *     s = board.create('slider',[[-2,1], [2,1], [0, Math.PI*0.5, 2*Math.PI]]);
    963             *
    964             *     a.setAngle(function() {
    965             *         return s.Value();
    966             *     });
    967             *     board.update();
    968             *
    969             *     })();
    970             *
    971             * </script><pre>
    972             *
    973             */
    974             el.setAngle = function (val) {
    975                 var t,
    976                     p = this.anglepoint,
    977                     q = this.radiuspoint;
    978
    979                 if (p.draggable()) {
    980                     t = this.board.create('transform', [val, this.center], {type: 'rotate'});
    981                     p.addTransform(q, t);
    982                     p.isDraggable = false;
    983                     p.setParents(q);
    984                 }
    985                 return this;
    986             };
    987
    988             /**
    989             * Frees an angle from a prescribed value. This is only relevant if the angle size has been set by
    990             * setAngle() previously. The anglepoint is set to a free point.
    991             * @name free
    992             * @function
    993             * @returns {Object} Pointer to the angle element..
    994             * @memberOf Angle.prototype
    995             */
    996             el.free = function () {
    997                 var p = this.anglepoint;
    998                 if (p.transformations.length > 0) {
    999                     p.transformations.pop();
    1000                     p.isDraggable = true;
    1001                     p.parents = [];
    1002                 }
    1003                 return this;
    1004             };
    1005
    1006             el.setParents(points); // Important: This overwrites the parents order in underlying sector
    1007
    1008         } // end '3points'
    1009
    1010         // GEONExT compatible labels.
    1011         if (Type.exists(el.visProp.text)) {
    1012             el.label.setText(Type.evaluate(el.visProp.text));
    1013         }
    1014
    1015         el.elType = 'angle';
    1016         el.type = Const.OBJECT_TYPE_ANGLE;
    1017         el.subs = {};
    1018
    1019         el.updateDataArraySquare = function () {
    1020             var A, B, C,
    1021                 r = this.Radius(),
    1022                 d1, d2,
    1023                 v, l1, l2;
    1024
    1025
    1026             if (type === '2lines') {
    1027                 // This is necessary to update this.point1, this.point2, this.point3.
    1028                 this.updateDataArraySector();
    1029             }
    1030
    1031             A = this.point2;
    1032             B = this.point1;
    1033             C = this.point3;
    1034
    1035             A = A.coords.usrCoords;
    1036             B = B.coords.usrCoords;
    1037             C = C.coords.usrCoords;
    1038
    1039             d1 = Geometry.distance(A, B, 3);
    1040             d2 = Geometry.distance(C, B, 3);
    1041
    1042             // In case of type=='2lines' this is redundant, because r == d1 == d2
    1043             A = [1, B[1] + (A[1] - B[1]) * r / d1, B[2] + (A[2] - B[2]) * r / d1];
    1044             C = [1, B[1] + (C[1] - B[1]) * r / d2, B[2] + (C[2] - B[2]) * r / d2];
    1045
    1046             v = Mat.crossProduct(C, B);
    1047             l1 = [-A[1] * v[1] - A[2] * v[2], A[0] * v[1], A[0] * v[2]];
    1048             v = Mat.crossProduct(A, B);
    1049             l2 = [-C[1] * v[1] - C[2] * v[2], C[0] * v[1], C[0] * v[2]];
    1050
    1051             v = Mat.crossProduct(l1, l2);
    1052             v[1] /= v[0];
    1053             v[2] /= v[0];
    1054
    1055             this.dataX = [B[1], A[1], v[1], C[1], B[1]];
    1056             this.dataY = [B[2], A[2], v[2], C[2], B[2]];
    1057
    1058             this.bezierDegree = 1;
    1059         };
    1060
    1061         el.updateDataArrayNone = function () {
    1062             this.dataX = [NaN];
    1063             this.dataY = [NaN];
    1064             this.bezierDegree = 1;
    1065         };
    1066
    1067         el.updateDataArray = function () {
    1068             var type = Type.evaluate(this.visProp.type),
    1069                 deg = Geometry.trueAngle(this.point2, this.point1, this.point3),
    1070                 vp_s = Type.evaluate(this.visProp.selection);
    1071
    1072             if ((vp_s === 'minor' && deg > 180.0) ||
    1073                     (vp_s === 'major' && deg < 180.0)) {
    1074                 deg = 360.0 - deg;
    1075             }
    1076
    1077             if (Math.abs(deg - 90.0) < Type.evaluate(this.visProp.orthosensitivity) + Mat.eps) {
    1078                 type = Type.evaluate(this.visProp.orthotype);
    1079             }
    1080
    1081             if (type === 'none') {
    1082                 this.updateDataArrayNone();
    1083             } else if (type === 'square') {
    1084                 this.updateDataArraySquare();
    1085             } else if (type === 'sector') {
    1086                 this.updateDataArraySector();
    1087             } else if (type === 'sectordot') {
    1088                 this.updateDataArraySector();
    1089                 if (!this.dot.visProp.visible) {
    1090                     this.dot.setAttribute({visible: true});
    1091                 }
    1092             }
    1093
    1094             if (!this.visProp.visible || (type !== 'sectordot' && this.dot.visProp.visible)) {
    1095                 this.dot.setAttribute({visible: false});
    1096             }
    1097         };
    1098
    1099         /**
    1100          * Indicates a right angle. Invisible by default, use <tt>dot.visible: true</tt> to show.
    1101          * Though this dot indicates a right angle, it can be visible even if the angle is not a right
    1102          * one.
    1103          * @type JXG.Point
    1104          * @name dot
    1105          * @memberOf Angle.prototype
    1106          */
    1107         attrsub = Type.copyAttributes(attributes, board.options, 'angle', 'dot');
    1108         el.dot = board.create('point', [function () {
    1109             var A, B, r, d, a2, co, si, mat,
    1110                 point1, point2, point3,
    1111                 vp_s;
    1112
    1113             if (Type.exists(el.dot) && !el.dot.visProp.visible) {
    1114                 return [0, 0];
    1115             }
    1116
    1117             A = el.point2.coords.usrCoords;
    1118             B = el.point1.coords.usrCoords;
    1119             r = el.Radius();
    1120             d = Geometry.distance(A, B, 3);
    1121             a2 = Geometry.rad(el.point2, el.point1, el.point3);
    1122
    1123             vp_s = Type.evaluate(el.visProp.selection);
    1124             if ((vp_s === 'minor' && a2 > Math.PI) ||
    1125                     (vp_s === 'major' && a2 < Math.PI)) {
    1126                 a2 = -(2 * Math.PI - a2);
    1127             }
    1128             a2 *= 0.5;
    1129
    1130             co = Math.cos(a2);
    1131             si = Math.sin(a2);
    1132
    1133             A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
    1134
    1135             mat = [
    1136                 [1, 0, 0],
    1137                 [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],
    1138                 [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5,  co * 0.5]
    1139             ];
    1140             return Mat.matVecMult(mat, A);
    1141         }], attrsub);
    1142
    1143         el.dot.dump = false;
    1144         el.subs.dot = el.dot;
    1145
    1146         if (type === '2lines') {
    1147             for (i = 0; i < 2; i++) {
    1148                 board.select(parents[i]).addChild(el.dot);
    1149             }
    1150         } else {
    1151             for (i = 0; i < 3; i++) {
    1152                 board.select(points[i]).addChild(el.dot);
    1153             }
    1154         }
    1155
    1156         // documented in GeometryElement
    1157         el.getLabelAnchor = function () {
    1158             var vec, dx = 12, dy = 12,
    1159                 A, B, r, d, a2, co, si, mat,
    1160                 vp_s = Type.evaluate(el.visProp.selection);
    1161
    1162             // If this is uncommented, the angle label can not be dragged
    1163             //if (Type.exists(this.label)) {
    1164             //    this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board);
    1165             //}
    1166
    1167             if (Type.exists(this.label.visProp.fontSize)) {
    1168                 dx = dy = Type.evaluate(this.label.visProp.fontSize);
    1169             }
    1170             dx /= this.board.unitX;
    1171             dy /= this.board.unitY;
    1172
    1173             A = el.point2.coords.usrCoords;
    1174             B = el.point1.coords.usrCoords;
    1175             r = el.Radius();
    1176             d = Geometry.distance(A, B, 3);
    1177             a2 = Geometry.rad(el.point2, el.point1, el.point3);
    1178             if ((vp_s === 'minor' && a2 > Math.PI) ||
    1179                     (vp_s === 'major' && a2 < Math.PI)) {
    1180                 a2 = -(2 * Math.PI - a2);
    1181             }
    1182             a2 *= 0.5;
    1183             co = Math.cos(a2);
    1184             si = Math.sin(a2);
    1185
    1186             A = [1, B[1] + (A[1] - B[1]) * r / d, B[2] + (A[2] - B[2]) * r / d];
    1187
    1188             mat = [
    1189                 [1, 0, 0],
    1190                 [B[1] - 0.5 * B[1] * co + 0.5 * B[2] * si, co * 0.5, -si * 0.5],
    1191                 [B[2] - 0.5 * B[1] * si - 0.5 * B[2] * co, si * 0.5,  co * 0.5]
    1192             ];
    1193             vec = Mat.matVecMult(mat, A);
    1194             vec[1] /= vec[0];
    1195             vec[2] /= vec[0];
    1196             vec[0] /= vec[0];
    1197
    1198             d = Geometry.distance(vec, B, 3);
    1199             vec = [vec[0], B[1] + (vec[1] - B[1]) * (r + dx) / d,  B[2] + (vec[2] - B[2]) * (r + dx) / d];
    1200
    1201             return new Coords(Const.COORDS_BY_USER, vec, this.board);
    1202         };
    1203
    1204         /**
    1205          * Returns the value of the angle in Radians.
    1206          * @memberOf Angle.prototype
    1207          * @name Value
    1208          * @function
    1209          * @returns {Number} The angle value in Radians
    1210          */
    1211         el.Value = function () {
    1212             return Geometry.rad(this.point2, this.point1, this.point3);
    1213         };
    1214
    1215         el.methodMap = Type.deepCopy(el.methodMap, {
    1216             Value: 'Value',
    1217             setAngle: 'setAngle',
    1218             free: 'free'
    1219         });
    1220
    1221         return el;
    1222     };
    1223
    1224     JXG.registerElement('angle', JXG.createAngle);
    1225
    1226     /**
    1227      * @class A non-reflex angle is the acute or obtuse instance of an angle.
    1228      * It is defined by a center, one point that
    1229      * defines the radius, and a third point that defines the angle of the sector.
    1230      * @pseudo
    1231      * @name NonReflexAngle
    1232      * @augments Angle
    1233      * @constructor
    1234      * @type Sector
    1235      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    1236      * @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
    1237      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
    1238      * @example
    1239      * // Create a non-reflex angle out of three free points
    1240      * var p1 = board.create('point', [5.0, 3.0]),
    1241      *     p2 = board.create('point', [1.0, 0.5]),
    1242      *     p3 = board.create('point', [1.5, 5.0]),
    1243      *
    1244      *     a = board.create('nonreflexangle', [p1, p2, p3], {radius: 2}),
    1245      *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
    1246      * </pre><div class="jxgbox" id="d0ab6d6b-63a7-48b2-8749-b02bb5e744f9" style="width: 300px; height: 300px;"></div>
    1247      * <script type="text/javascript">
    1248      * (function () {
    1249      *   var board = JXG.JSXGraph.initBoard('d0ab6d6b-63a7-48b2-8749-b02bb5e744f9', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    1250      *     p1 = board.create('point', [5.0, 3.0]),
    1251      *     p2 = board.create('point', [1.0, 0.5]),
    1252      *     p3 = board.create('point', [1.5, 5.0]),
    1253      *
    1254      *     a = board.create('nonreflexangle', [p1, p2, p3], {radius: 2}),
    1255      *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
    1256      * })();
    1257      * </script><pre>
    1258      */
    1259     JXG.createNonreflexAngle = function (board, parents, attributes) {
    1260         var el;
    1261
    1262         attributes.selection = 'minor';
    1263         el = JXG.createAngle(board, parents, attributes);
    1264
    1265         el.Value = function () {
    1266             var v = Geometry.rad(this.point2, this.point1, this.point3);
    1267             return (v < Math.PI) ? v : 2.0 * Math.PI - v;
    1268         };
    1269         return el;
    1270     };
    1271
    1272     JXG.registerElement('nonreflexangle', JXG.createNonreflexAngle);
    1273
    1274     /**
    1275      * @class A reflex angle is the neither acute nor obtuse instance of an angle.
    1276      * It is defined by a center, one point that
    1277      * defines the radius, and a third point that defines the angle of the sector.
    1278      * @pseudo
    1279      * @name ReflexAngle
    1280      * @augments Angle
    1281      * @constructor
    1282      * @type Sector
    1283      * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    1284      * @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
    1285      * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3.
    1286      * @example
    1287      * // Create a non-reflex angle out of three free points
    1288      * var p1 = board.create('point', [5.0, 3.0]),
    1289      *     p2 = board.create('point', [1.0, 0.5]),
    1290      *     p3 = board.create('point', [1.5, 5.0]),
    1291      *
    1292      *     a = board.create('reflexangle', [p1, p2, p3], {radius: 2}),
    1293      *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
    1294      * </pre><div class="jxgbox" id="f2a577f2-553d-4f9f-a895-2d6d4b8c60e8" style="width: 300px; height: 300px;"></div>
    1295      * <script type="text/javascript">
    1296      * (function () {
    1297      * var board = JXG.JSXGraph.initBoard('f2a577f2-553d-4f9f-a895-2d6d4b8c60e8', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}),
    1298      *     p1 = board.create('point', [5.0, 3.0]),
    1299      *     p2 = board.create('point', [1.0, 0.5]),
    1300      *     p3 = board.create('point', [1.5, 5.0]),
    1301      *
    1302      *     a = board.create('reflexangle', [p1, p2, p3], {radius: 2}),
    1303      *     t = board.create('text', [4, 4, function() { return JXG.toFixed(a.Value(), 2); }]);
    1304      * })();
    1305      * </script><pre>
    1306      */
    1307     JXG.createReflexAngle = function (board, parents, attributes) {
    1308         var el;
    1309
    1310         attributes.selection = 'major';
    1311         el = JXG.createAngle(board, parents, attributes);
    1312
    1313         el.Value = function () {
    1314             var v = Geometry.rad(this.point2, this.point1, this.point3);
    1315             return (v >= Math.PI) ? v : 2.0 * Math.PI - v;
    1316         };
    1317         return el;
    1318     };
    1319
    1320     JXG.registerElement('reflexangle', JXG.createReflexAngle);
    1321
    1322     return {
    1323         createSector: JXG.createSector,
    1324         createCircumcircleSector: JXG.createCircumcircleSector,
    1325         createMinorSector: JXG.createMinorSector,
    1326         createMajorSector: JXG.createMajorSector,
    1327         createAngle: JXG.createAngle,
    1328         createReflexAngle: JXG.createReflexAngle,
    1329         createNonreflexAngle: JXG.createNonreflexAngle
    1330     };
    1331 });
    1332