      1 /*
      2     Copyright 2008-2023
      3         Matthias Ehmann,
      4         Michael Gerhaeuser,
      5         Carsten Miller,
      6         Alfred Wassermann
      7
      8     This file is part of JSXGraph.
      9
     10     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
     11
     12     You can redistribute it and/or modify it under the terms of the
     13
     14       * GNU Lesser General Public License as published by
     15         the Free Software Foundation, either version 3 of the License, or
     16         (at your option) any later version
     17       OR
     18       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
     19
     20     JSXGraph is distributed in the hope that it will be useful,
     21     but WITHOUT ANY WARRANTY; without even the implied warranty of
     22     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     23     GNU Lesser General Public License for more details.
     24
     25     You should have received a copy of the GNU Lesser General Public License and
     26     the MIT License along with JSXGraph. If not, see <https://www.gnu.org/licenses/>
     27     and <https://opensource.org/licenses/MIT/>.
     28  */
     29
     30 /*global JXG: true, define: true, console: true, window: true*/
     31 /*jslint nomen: true, plusplus: true*/
     32
     33 /**
     34  * @fileoverview The geometry object CoordsElement is defined in this file.
     35  * This object provides the coordinate handling of points, images and texts.
     36  */
     37
     38 import JXG from "../jxg";
     39 import Mat from "../math/math";
     40 import Geometry from "../math/geometry";
     41 import Numerics from "../math/numerics";
     42 import Statistics from "../math/statistics";
     43 import Coords from "./coords";
     44 import Const from "./constants";
     45 import Type from "../utils/type";
     46
     47 /**
     48  * An element containing coords is the basic geometric element. Based on points lines and circles can be constructed which can be intersected
     49  * which in turn are points again which can be used to construct new lines, circles, polygons, etc. This class holds methods for
     50  * all kind of coordinate elements like points, texts and images.
     51  * @class Creates a new coords element object. Do not use this constructor to create an element.
     52  *
     53  * @private
     54  * @augments JXG.GeometryElement
     55  * @param {Array} coordinates An array with the affine user coordinates of the point.
     56  * {@link JXG.Options#elements}, and - optionally - a name and an id.
     57  */
     58 JXG.CoordsElement = function (coordinates, isLabel) {
     59     var i;
     60
     61     if (!Type.exists(coordinates)) {
     62         coordinates = [1, 0, 0];
     63     }
     64
     65     for (i = 0; i < coordinates.length; ++i) {
     66         coordinates[i] = parseFloat(coordinates[i]);
     67     }
     68
     69     /**
     70      * Coordinates of the element.
     71      * @type JXG.Coords
     72      * @private
     73      */
     74     this.coords = new Coords(Const.COORDS_BY_USER, coordinates, this.board);
     75     this.initialCoords = new Coords(Const.COORDS_BY_USER, coordinates, this.board);
     76
     77     /**
     78      * Relative position on a slide element (line, circle, curve) if element is a glider on this element.
     79      * @type Number
     80      * @private
     81      */
     82     this.position = null;
     83
     84     /**
     85      * True if there the method this.updateConstraint() has been set. It is
     86      * probably different from the prototype function() {return this;}.
     87      * Used in updateCoords fo glider elements.
     88      *
     89      * @see JXG.CoordsElement#updateCoords
     90      * @type Boolean
     91      * @private
     92      */
     93     this.isConstrained = false;
     94
     95     /**
     96      * Determines whether the element slides on a polygon if point is a glider.
     97      * @type Boolean
     98      * @default false
     99      * @private
    100      */
    101     this.onPolygon = false;
    102
    103     /**
    104      * When used as a glider this member stores the object, where to glide on.
    105      * To set the object to glide on use the method
    106      * {@link JXG.Point#makeGlider} and DO NOT set this property directly
    107      * as it will break the dependency tree.
    108      * @type JXG.GeometryElement
    109      */
    110     this.slideObject = null;
    111
    112     /**
    113      * List of elements the element is bound to, i.e. the element glides on.
    114      * Only the last entry is active.
    115      * Use {@link JXG.Point#popSlideObject} to remove the currently active slideObject.
    116      */
    117     this.slideObjects = [];
    118
    119     /**
    120      * A {@link JXG.CoordsElement#updateGlider} call is usually followed
    121      * by a general {@link JXG.Board#update} which calls
    122      * {@link JXG.CoordsElement#updateGliderFromParent}.
    123      * To prevent double updates, {@link JXG.CoordsElement#needsUpdateFromParent}
    124      * is set to false in updateGlider() and reset to true in the following call to
    125      * {@link JXG.CoordsElement#updateGliderFromParent}
    126      * @type Boolean
    127      */
    128     this.needsUpdateFromParent = true;
    129
    130     /**
    131      * Stores the groups of this element in an array of Group.
    132      * @type Array
    133      * @see JXG.Group
    134      * @private
    135      */
    136     this.groups = [];
    137
    138     /*
    139      * Do we need this?
    140      */
    141     this.Xjc = null;
    142     this.Yjc = null;
    143
    144     // documented in GeometryElement
    145     this.methodMap = Type.deepCopy(this.methodMap, {
    146         move: "moveTo",
    147         moveTo: "moveTo",
    148         moveAlong: "moveAlong",
    149         visit: "visit",
    150         glide: "makeGlider",
    151         makeGlider: "makeGlider",
    152         intersect: "makeIntersection",
    153         makeIntersection: "makeIntersection",
    154         X: "X",
    155         Y: "Y",
    156         Coords: "Coords",
    157         free: "free",
    158         setPosition: "setGliderPosition",
    159         setGliderPosition: "setGliderPosition",
    160         addConstraint: "addConstraint",
    161         dist: "Dist",
    162         Dist: "Dist",
    163         onPolygon: "onPolygon",
    164         startAnimation: "startAnimation",
    165         stopAnimation: "stopAnimation"
    166     });
    167
    168     /*
    169      * this.element may have been set by the object constructor.
    170      */
    171     if (Type.exists(this.element)) {
    172         this.addAnchor(coordinates, isLabel);
    173     }
    174     this.isDraggable = true;
    175 };
    176
    177 JXG.extend(
    178     JXG.CoordsElement.prototype,
    179     /** @lends JXG.CoordsElement.prototype */ {
    180         /**
    181          * Dummy function for unconstrained points or gliders.
    182          * @private
    183          */
    184         updateConstraint: function () {
    185             return this;
    186         },
    187
    188         /**
    189          * Updates the coordinates of the element.
    190          * @private
    191          */
    192         updateCoords: function (fromParent) {
    193             if (!this.needsUpdate) {
    194                 return this;
    195             }
    196
    197             if (!Type.exists(fromParent)) {
    198                 fromParent = false;
    199             }
    200
    201             if (!Type.evaluate(this.visProp.frozen)) {
    202                 this.updateConstraint();
    203             }
    204
    205             /*
    206              * We need to calculate the new coordinates no matter of the elements visibility because
    207              * a child could be visible and depend on the coordinates of the element/point (e.g. perpendicular).
    208              *
    209              * Check if the element is a glider and calculate new coords in dependency of this.slideObject.
    210              * This function is called with fromParent==true in case it is a glider element for example if
    211              * the defining elements of the line or circle have been changed.
    212              */
    213             if (this.type === Const.OBJECT_TYPE_GLIDER) {
    214                 if (this.isConstrained) {
    215                     fromParent = false;
    216                 }
    217
    218                 if (fromParent) {
    219                     this.updateGliderFromParent();
    220                 } else {
    221                     this.updateGlider();
    222                 }
    223             }
    224
    225             this.updateTransform(fromParent);
    226
    227             return this;
    228         },
    229
    230         /**
    231          * Update of glider in case of dragging the glider or setting the postion of the glider.
    232          * The relative position of the glider has to be updated.
    233          *
    234          * In case of a glider on a line:
    235          * If the second point is an ideal point, then -1 < this.position < 1,
    236          * this.position==+/-1 equals point2, this.position==0 equals point1
    237          *
    238          * If the first point is an ideal point, then 0 < this.position < 2
    239          * this.position==0  or 2 equals point1, this.position==1 equals point2
    240          *
    241          * @private
    242          */
    243         updateGlider: function () {
    244             var i, d, v,
    245                 p1c, p2c, poly, cc, pos,
    246                 angle, sgn, alpha, beta,
    247                 delta = 2.0 * Math.PI,
    248                 cp, c, invMat,
    249                 newCoords, newPos,
    250                 doRound = false,
    251                 ev_sw,
    252                 snappedTo, snapValues,
    253                 slide = this.slideObject,
    254                 res, cu,
    255                 slides = [],
    256                 isTransformed;
    257
    258             this.needsUpdateFromParent = false;
    259             if (slide.elementClass === Const.OBJECT_CLASS_CIRCLE) {
    260                 if (Type.evaluate(this.visProp.isgeonext)) {
    261                     delta = 1.0;
    262                 }
    263                 newCoords = Geometry.projectPointToCircle(this, slide, this.board);
    264                 newPos =
    265                     Geometry.rad(
    266                         [slide.center.X() + 1.0, slide.center.Y()],
    267                         slide.center,
    268                         this
    269                     ) / delta;
    270             } else if (slide.elementClass === Const.OBJECT_CLASS_LINE) {
    271                 /*
    272                  * onPolygon==true: the point is a slider on a segment and this segment is one of the
    273                  * "borders" of a polygon.
    274                  * This is a GEONExT feature.
    275                  */
    276                 if (this.onPolygon) {
    277                     p1c = slide.point1.coords.usrCoords;
    278                     p2c = slide.point2.coords.usrCoords;
    279                     i = 1;
    280                     d = p2c[i] - p1c[i];
    281
    282                     if (Math.abs(d) < Mat.eps) {
    283                         i = 2;
    284                         d = p2c[i] - p1c[i];
    285                     }
    286
    287                     cc = Geometry.projectPointToLine(this, slide, this.board);
    288                     pos = (cc.usrCoords[i] - p1c[i]) / d;
    289                     poly = slide.parentPolygon;
    290
    291                     if (pos < 0) {
    292                         for (i = 0; i < poly.borders.length; i++) {
    293                             if (slide === poly.borders[i]) {
    294                                 slide =
    295                                     poly.borders[
    296                                         (i - 1 + poly.borders.length) % poly.borders.length
    297                                     ];
    298                                 break;
    299                             }
    300                         }
    301                     } else if (pos > 1.0) {
    302                         for (i = 0; i < poly.borders.length; i++) {
    303                             if (slide === poly.borders[i]) {
    304                                 slide =
    305                                     poly.borders[
    306                                         (i + 1 + poly.borders.length) % poly.borders.length
    307                                     ];
    308                                 break;
    309                             }
    310                         }
    311                     }
    312
    313                     // If the slide object has changed, save the change to the glider.
    314                     if (slide.id !== this.slideObject.id) {
    315                         this.slideObject = slide;
    316                     }
    317                 }
    318
    319                 p1c = slide.point1.coords;
    320                 p2c = slide.point2.coords;
    321
    322                 // Distance between the two defining points
    323                 d = p1c.distance(Const.COORDS_BY_USER, p2c);
    324
    325                 // The defining points are identical
    326                 if (d < Mat.eps) {
    327                     //this.coords.setCoordinates(Const.COORDS_BY_USER, p1c);
    328                     newCoords = p1c;
    329                     doRound = true;
    330                     newPos = 0.0;
    331                 } else {
    332                     newCoords = Geometry.projectPointToLine(this, slide, this.board);
    333                     p1c = p1c.usrCoords.slice(0);
    334                     p2c = p2c.usrCoords.slice(0);
    335
    336                     // The second point is an ideal point
    337                     if (Math.abs(p2c[0]) < Mat.eps) {
    338                         i = 1;
    339                         d = p2c[i];
    340
    341                         if (Math.abs(d) < Mat.eps) {
    342                             i = 2;
    343                             d = p2c[i];
    344                         }
    345
    346                         d = (newCoords.usrCoords[i] - p1c[i]) / d;
    347                         sgn = d >= 0 ? 1 : -1;
    348                         d = Math.abs(d);
    349                         newPos = (sgn * d) / (d + 1);
    350
    351                         // The first point is an ideal point
    352                     } else if (Math.abs(p1c[0]) < Mat.eps) {
    353                         i = 1;
    354                         d = p1c[i];
    355
    356                         if (Math.abs(d) < Mat.eps) {
    357                             i = 2;
    358                             d = p1c[i];
    359                         }
    360
    361                         d = (newCoords.usrCoords[i] - p2c[i]) / d;
    362
    363                         // 1.0 - d/(1-d);
    364                         if (d < 0.0) {
    365                             newPos = (1 - 2.0 * d) / (1.0 - d);
    366                         } else {
    367                             newPos = 1 / (d + 1);
    368                         }
    369                     } else {
    370                         i = 1;
    371                         d = p2c[i] - p1c[i];
    372
    373                         if (Math.abs(d) < Mat.eps) {
    374                             i = 2;
    375                             d = p2c[i] - p1c[i];
    376                         }
    377                         newPos = (newCoords.usrCoords[i] - p1c[i]) / d;
    378                     }
    379                 }
    380
    381                 // Snap the glider to snap values.
    382                 snappedTo = this.findClosestSnapValue(newPos);
    383                 if(snappedTo !== null) {
    384                     snapValues = Type.evaluate(this.visProp.snapvalues);
    385                     newPos = (snapValues[snappedTo] - this._smin) / (this._smax - this._smin);
    386                     this.update(true);
    387                 } else {
    388                     // Snap the glider point of the slider into its appropiate position
    389                     // First, recalculate the new value of this.position
    390                     // Second, call update(fromParent==true) to make the positioning snappier.
    391                     ev_sw = Type.evaluate(this.visProp.snapwidth);
    392                     if (
    393                         Type.evaluate(ev_sw) > 0.0 &&
    394                         Math.abs(this._smax - this._smin) >= Mat.eps
    395                     ) {
    396                         newPos = Math.max(Math.min(newPos, 1), 0);
    397
    398                         v = newPos * (this._smax - this._smin) + this._smin;
    399                         v = Math.round(v / ev_sw) * ev_sw;
    400                         newPos = (v - this._smin) / (this._smax - this._smin);
    401                         this.update(true);
    402                     }
    403                 }
    404
    405                 p1c = slide.point1.coords;
    406                 if (
    407                     !Type.evaluate(slide.visProp.straightfirst) &&
    408                     Math.abs(p1c.usrCoords[0]) > Mat.eps &&
    409                     newPos < 0
    410                 ) {
    411                     newCoords = p1c;
    412                     doRound = true;
    413                     newPos = 0;
    414                 }
    415
    416                 p2c = slide.point2.coords;
    417                 if (
    418                     !Type.evaluate(slide.visProp.straightlast) &&
    419                     Math.abs(p2c.usrCoords[0]) > Mat.eps &&
    420                     newPos > 1
    421                 ) {
    422                     newCoords = p2c;
    423                     doRound = true;
    424                     newPos = 1;
    425                 }
    426             } else if (slide.type === Const.OBJECT_TYPE_TURTLE) {
    427                 // In case, the point is a constrained glider.
    428                 this.updateConstraint();
    429                 res = Geometry.projectPointToTurtle(this, slide, this.board);
    430                 newCoords = res[0];
    431                 newPos = res[1]; // save position for the overwriting below
    432             } else if (slide.elementClass === Const.OBJECT_CLASS_CURVE) {
    433                 if (
    434                     slide.type === Const.OBJECT_TYPE_ARC ||
    435                     slide.type === Const.OBJECT_TYPE_SECTOR
    436                 ) {
    437                     newCoords = Geometry.projectPointToCircle(this, slide, this.board);
    438
    439                     angle = Geometry.rad(slide.radiuspoint, slide.center, this);
    440                     alpha = 0.0;
    441                     beta = Geometry.rad(slide.radiuspoint, slide.center, slide.anglepoint);
    442                     newPos = angle;
    443
    444                     ev_sw = Type.evaluate(slide.visProp.selection);
    445                     if (
    446                         (ev_sw === "minor" && beta > Math.PI) ||
    447                         (ev_sw === "major" && beta < Math.PI)
    448                     ) {
    449                         alpha = beta;
    450                         beta = 2 * Math.PI;
    451                     }
    452
    453                     // Correct the position if we are outside of the sector/arc
    454                     if (angle < alpha || angle > beta) {
    455                         newPos = beta;
    456
    457                         if (
    458                             (angle < alpha && angle > alpha * 0.5) ||
    459                             (angle > beta && angle > beta * 0.5 + Math.PI)
    460                         ) {
    461                             newPos = alpha;
    462                         }
    463
    464                         this.needsUpdateFromParent = true;
    465                         this.updateGliderFromParent();
    466                     }
    467
    468                     delta = beta - alpha;
    469                     if (this.visProp.isgeonext) {
    470                         delta = 1.0;
    471                     }
    472                     if (Math.abs(delta) > Mat.eps) {
    473                         newPos /= delta;
    474                     }
    475                 } else {
    476                     // In case, the point is a constrained glider.
    477                     this.updateConstraint();
    478
    479                     // Handle the case if the curve comes from a transformation of a continuous curve.
    480                     if (slide.transformations.length > 0) {
    481                         isTransformed = false;
    482                         res = slide.getTransformationSource();
    483                         if (res[0]) {
    484                             isTransformed = res[0];
    485                             slides.push(slide);
    486                             slides.push(res[1]);
    487                         }
    488                         // Recurse
    489                         while (res[0] && Type.exists(res[1]._transformationSource)) {
    490                             res = res[1].getTransformationSource();
    491                             slides.push(res[1]);
    492                         }
    493
    494                         cu = this.coords.usrCoords;
    495                         if (isTransformed) {
    496                             for (i = 0; i < slides.length; i++) {
    497                                 slides[i].updateTransformMatrix();
    498                                 invMat = Mat.inverse(slides[i].transformMat);
    499                                 cu = Mat.matVecMult(invMat, cu);
    500                             }
    501                             cp = new Coords(Const.COORDS_BY_USER, cu, this.board).usrCoords;
    502                             c = Geometry.projectCoordsToCurve(
    503                                 cp[1],
    504                                 cp[2],
    505                                 this.position || 0,
    506                                 slides[slides.length - 1],
    507                                 this.board
    508                             );
    509                             // projectPointCurve() already would apply the transformation.
    510                             // Since we are projecting on the original curve, we have to do
    511                             // the transformations "by hand".
    512                             cu = c[0].usrCoords;
    513                             for (i = slides.length - 2; i >= 0; i--) {
    514                                 cu = Mat.matVecMult(slides[i].transformMat, cu);
    515                             }
    516                             c[0] = new Coords(Const.COORDS_BY_USER, cu, this.board);
    517                         } else {
    518                             slide.updateTransformMatrix();
    519                             invMat = Mat.inverse(slide.transformMat);
    520                             cu = Mat.matVecMult(invMat, cu);
    521                             cp = new Coords(Const.COORDS_BY_USER, cu, this.board).usrCoords;
    522                             c = Geometry.projectCoordsToCurve(
    523                                 cp[1],
    524                                 cp[2],
    525                                 this.position || 0,
    526                                 slide,
    527                                 this.board
    528                             );
    529                         }
    530
    531                         newCoords = c[0];
    532                         newPos = c[1];
    533                     } else {
    534                         res = Geometry.projectPointToCurve(this, slide, this.board);
    535                         newCoords = res[0];
    536                         newPos = res[1]; // save position for the overwriting below
    537                     }
    538                 }
    539             } else if (Type.isPoint(slide)) {
    540                 //this.coords.setCoordinates(Const.COORDS_BY_USER, Geometry.projectPointToPoint(this, slide, this.board).usrCoords, false);
    541                 newCoords = Geometry.projectPointToPoint(this, slide, this.board);
    542                 newPos = this.position; // save position for the overwriting below
    543             }
    544
    545             this.coords.setCoordinates(Const.COORDS_BY_USER, newCoords.usrCoords, doRound);
    546             this.position = newPos;
    547         },
    548
    549         /**
    550          * Find the closest entry in snapValues that is within snapValueDistance of pos.
    551          *
    552          * @param {Number} pos Value for which snapping is calculated.
    553          * @returns {Number} Index of the value to snap to, or null.
    554          * @private
    555          */
    556         findClosestSnapValue: function(pos) {
    557             var i, d,
    558                 snapValues, snapValueDistance,
    559                 snappedTo = null;
    560
    561             // Snap the glider to snap values.
    562             snapValues = Type.evaluate(this.visProp.snapvalues);
    563             snapValueDistance = Type.evaluate(this.visProp.snapvaluedistance);
    564
    565             if (Type.isArray(snapValues) &&
    566                 Math.abs(this._smax - this._smin) >= Mat.eps &&
    567                 snapValueDistance > 0.0) {
    568                 for (i = 0; i < snapValues.length; i++) {
    569                     d = Math.abs(pos * (this._smax - this._smin) + this._smin - snapValues[i]);
    570                     if (d < snapValueDistance) {
    571                         snapValueDistance = d;
    572                         snappedTo = i;
    573                     }
    574                 }
    575             }
    576
    577             return snappedTo;
    578         },
    579
    580         /**
    581          * Update of a glider in case a parent element has been updated. That means the
    582          * relative position of the glider stays the same.
    583          * @private
    584          */
    585         updateGliderFromParent: function () {
    586             var p1c, p2c, r, lbda, c,
    587                 slide = this.slideObject,
    588                 slides = [],
    589                 res, i, isTransformed,
    590                 baseangle, alpha, angle, beta,
    591                 delta = 2.0 * Math.PI;
    592
    593             if (!this.needsUpdateFromParent) {
    594                 this.needsUpdateFromParent = true;
    595                 return;
    596             }
    597
    598             if (slide.elementClass === Const.OBJECT_CLASS_CIRCLE) {
    599                 r = slide.Radius();
    600                 if (Type.evaluate(this.visProp.isgeonext)) {
    601                     delta = 1.0;
    602                 }
    603                 c = [
    604                     slide.center.X() + r * Math.cos(this.position * delta),
    605                     slide.center.Y() + r * Math.sin(this.position * delta)
    606                 ];
    607             } else if (slide.elementClass === Const.OBJECT_CLASS_LINE) {
    608                 p1c = slide.point1.coords.usrCoords;
    609                 p2c = slide.point2.coords.usrCoords;
    610
    611                 // If one of the defining points of the line does not exist,
    612                 // the glider should disappear
    613                 if (
    614                     (p1c[0] === 0 && p1c[1] === 0 && p1c[2] === 0) ||
    615                     (p2c[0] === 0 && p2c[1] === 0 && p2c[2] === 0)
    616                 ) {
    617                     c = [0, 0, 0];
    618                     // The second point is an ideal point
    619                 } else if (Math.abs(p2c[0]) < Mat.eps) {
    620                     lbda = Math.min(Math.abs(this.position), 1 - Mat.eps);
    621                     lbda /= 1.0 - lbda;
    622
    623                     if (this.position < 0) {
    624                         lbda = -lbda;
    625                     }
    626
    627                     c = [
    628                         p1c[0] + lbda * p2c[0],
    629                         p1c[1] + lbda * p2c[1],
    630                         p1c[2] + lbda * p2c[2]
    631                     ];
    632                     // The first point is an ideal point
    633                 } else if (Math.abs(p1c[0]) < Mat.eps) {
    634                     lbda = Math.max(this.position, Mat.eps);
    635                     lbda = Math.min(lbda, 2 - Mat.eps);
    636
    637                     if (lbda > 1) {
    638                         lbda = (lbda - 1) / (lbda - 2);
    639                     } else {
    640                         lbda = (1 - lbda) / lbda;
    641                     }
    642
    643                     c = [
    644                         p2c[0] + lbda * p1c[0],
    645                         p2c[1] + lbda * p1c[1],
    646                         p2c[2] + lbda * p1c[2]
    647                     ];
    648                 } else {
    649                     lbda = this.position;
    650                     c = [
    651                         p1c[0] + lbda * (p2c[0] - p1c[0]),
    652                         p1c[1] + lbda * (p2c[1] - p1c[1]),
    653                         p1c[2] + lbda * (p2c[2] - p1c[2])
    654                     ];
    655                 }
    656             } else if (slide.type === Const.OBJECT_TYPE_TURTLE) {
    657                 this.coords.setCoordinates(Const.COORDS_BY_USER, [
    658                     slide.Z(this.position),
    659                     slide.X(this.position),
    660                     slide.Y(this.position)
    661                 ]);
    662                 // In case, the point is a constrained glider.
    663                 this.updateConstraint();
    664                 c = Geometry.projectPointToTurtle(this, slide, this.board)[0].usrCoords;
    665             } else if (slide.elementClass === Const.OBJECT_CLASS_CURVE) {
    666                 // Handle the case if the curve comes from a transformation of a continuous curve.
    667                 isTransformed = false;
    668                 res = slide.getTransformationSource();
    669                 if (res[0]) {
    670                     isTransformed = res[0];
    671                     slides.push(slide);
    672                     slides.push(res[1]);
    673                 }
    674                 // Recurse
    675                 while (res[0] && Type.exists(res[1]._transformationSource)) {
    676                     res = res[1].getTransformationSource();
    677                     slides.push(res[1]);
    678                 }
    679                 if (isTransformed) {
    680                     this.coords.setCoordinates(Const.COORDS_BY_USER, [
    681                         slides[slides.length - 1].Z(this.position),
    682                         slides[slides.length - 1].X(this.position),
    683                         slides[slides.length - 1].Y(this.position)
    684                     ]);
    685                 } else {
    686                     this.coords.setCoordinates(Const.COORDS_BY_USER, [
    687                         slide.Z(this.position),
    688                         slide.X(this.position),
    689                         slide.Y(this.position)
    690                     ]);
    691                 }
    692
    693                 if (
    694                     slide.type === Const.OBJECT_TYPE_ARC ||
    695                     slide.type === Const.OBJECT_TYPE_SECTOR
    696                 ) {
    697                     baseangle = Geometry.rad(
    698                         [slide.center.X() + 1, slide.center.Y()],
    699                         slide.center,
    700                         slide.radiuspoint
    701                     );
    702
    703                     alpha = 0.0;
    704                     beta = Geometry.rad(slide.radiuspoint, slide.center, slide.anglepoint);
    705
    706                     if (
    707                         (slide.visProp.selection === "minor" && beta > Math.PI) ||
    708                         (slide.visProp.selection === "major" && beta < Math.PI)
    709                     ) {
    710                         alpha = beta;
    711                         beta = 2 * Math.PI;
    712                     }
    713
    714                     delta = beta - alpha;
    715                     if (Type.evaluate(this.visProp.isgeonext)) {
    716                         delta = 1.0;
    717                     }
    718                     angle = this.position * delta;
    719
    720                     // Correct the position if we are outside of the sector/arc
    721                     if (angle < alpha || angle > beta) {
    722                         angle = beta;
    723
    724                         if (
    725                             (angle < alpha && angle > alpha * 0.5) ||
    726                             (angle > beta && angle > beta * 0.5 + Math.PI)
    727                         ) {
    728                             angle = alpha;
    729                         }
    730
    731                         this.position = angle;
    732                         if (Math.abs(delta) > Mat.eps) {
    733                             this.position /= delta;
    734                         }
    735                     }
    736
    737                     r = slide.Radius();
    738                     c = [
    739                         slide.center.X() + r * Math.cos(this.position * delta + baseangle),
    740                         slide.center.Y() + r * Math.sin(this.position * delta + baseangle)
    741                     ];
    742                 } else {
    743                     // In case, the point is a constrained glider.
    744                     this.updateConstraint();
    745
    746                     if (isTransformed) {
    747                         c = Geometry.projectPointToCurve(
    748                             this,
    749                             slides[slides.length - 1],
    750                             this.board
    751                         )[0].usrCoords;
    752                         // projectPointCurve() already would do the transformation.
    753                         // But since we are projecting on the original curve, we have to do
    754                         // the transformation "by hand".
    755                         for (i = slides.length - 2; i >= 0; i--) {
    756                             c = new Coords(
    757                                 Const.COORDS_BY_USER,
    758                                 Mat.matVecMult(slides[i].transformMat, c),
    759                                 this.board
    760                             ).usrCoords;
    761                         }
    762                     } else {
    763                         c = Geometry.projectPointToCurve(this, slide, this.board)[0].usrCoords;
    764                     }
    765                 }
    766             } else if (Type.isPoint(slide)) {
    767                 c = Geometry.projectPointToPoint(this, slide, this.board).usrCoords;
    768             }
    769
    770             this.coords.setCoordinates(Const.COORDS_BY_USER, c, false);
    771         },
    772
    773         updateRendererGeneric: function (rendererMethod) {
    774             //var wasReal;
    775
    776             if (!this.needsUpdate || !this.board.renderer) {
    777                 return this;
    778             }
    779
    780             if (this.visPropCalc.visible) {
    781                 //wasReal = this.isReal;
    782                 this.isReal = !isNaN(this.coords.usrCoords[1] + this.coords.usrCoords[2]);
    783                 //Homogeneous coords: ideal point
    784                 this.isReal =
    785                     Math.abs(this.coords.usrCoords[0]) > Mat.eps ? this.isReal : false;
    786
    787                 if (
    788                     // wasReal &&
    789                     !this.isReal
    790                 ) {
    791                     this.updateVisibility(false);
    792                 }
    793             }
    794
    795             // Call the renderer only if element is visible.
    796             // Update the position
    797             if (this.visPropCalc.visible) {
    798                 this.board.renderer[rendererMethod](this);
    799             }
    800
    801             // Update the label if visible.
    802             if (
    803                 this.hasLabel &&
    804                 this.visPropCalc.visible &&
    805                 this.label &&
    806                 this.label.visPropCalc.visible &&
    807                 this.isReal
    808             ) {
    809                 this.label.update();
    810                 this.board.renderer.updateText(this.label);
    811             }
    812
    813             // Update rendNode display
    814             this.setDisplayRendNode();
    815             // if (this.visPropCalc.visible !== this.visPropOld.visible) {
    816             //     this.board.renderer.display(this, this.visPropCalc.visible);
    817             //     this.visPropOld.visible = this.visPropCalc.visible;
    818             //
    819             //     if (this.hasLabel) {
    820             //         this.board.renderer.display(this.label, this.label.visPropCalc.visible);
    821             //     }
    822             // }
    823
    824             this.needsUpdate = false;
    825             return this;
    826         },
    827
    828         /**
    829          * Getter method for x, this is used by for CAS-points to access point coordinates.
    830          * @returns {Number} User coordinate of point in x direction.
    831          */
    832         X: function () {
    833             return this.coords.usrCoords[1];
    834         },
    835
    836         /**
    837          * Getter method for y, this is used by CAS-points to access point coordinates.
    838          * @returns {Number} User coordinate of point in y direction.
    839          */
    840         Y: function () {
    841             return this.coords.usrCoords[2];
    842         },
    843
    844         /**
    845          * Getter method for z, this is used by CAS-points to access point coordinates.
    846          * @returns {Number} User coordinate of point in z direction.
    847          */
    848         Z: function () {
    849             return this.coords.usrCoords[0];
    850         },
    851
    852         /**
    853          * Getter method for coordinates x, y and (optional) z.
    854          * @param {Number|String} [digits='auto'] Truncating rule for the digits in the infobox.
    855          * <ul>
    856          * <li>'auto': done automatically by JXG.autoDigits()
    857          * <li>'none': no truncation
    858          * <li>number: truncate after "number digits" with JXG.toFixed()
    859          * </ul>
    860          * @param {Boolean} [withZ=false] If set to true the return value will be <tt>(x | y | z)</tt> instead of <tt>(x, y)</tt>.
    861          * @returns {String} User coordinates of point.
    862          */
    863         Coords: function(withZ) {
    864             if (withZ) {
    865                 return this.coords.usrCoords.slice();
    866             }
    867             return this.coords.usrCoords.slice(1);
    868         },
    869         // Coords: function (digits, withZ) {
    870         //     var arr, sep;
    871
    872         //     digits = digits || 'auto';
    873
    874         //     if (withZ) {
    875         //         sep = ' | ';
    876         //     } else {
    877         //         sep = ', ';
    878         //     }
    879
    880         //     if (digits === 'none') {
    881         //         arr = [this.X(), sep, this.Y()];
    882         //         if (withZ) {
    883         //             arr.push(sep, this.Z());
    884         //         }
    885
    886         //     } else if (digits === 'auto') {
    887         //         if (this.useLocale()) {
    888         //             arr = [this.formatNumberLocale(this.X()), sep, this.formatNumberLocale(this.Y())];
    889         //             if (withZ) {
    890         //                 arr.push(sep, this.formatNumberLocale(this.Z()));
    891         //             }
    892         //         } else {
    893         //             arr = [Type.autoDigits(this.X()), sep, Type.autoDigits(this.Y())];
    894         //             if (withZ) {
    895         //                 arr.push(sep, Type.autoDigits(this.Z()));
    896         //             }
    897         //         }
    898
    899         //     } else {
    900         //         if (this.useLocale()) {
    901         //             arr = [this.formatNumberLocale(this.X(), digits), sep, this.formatNumberLocale(this.Y(), digits)];
    902         //             if (withZ) {
    903         //                 arr.push(sep, this.formatNumberLocale(this.Z(), digits));
    904         //             }
    905         //         } else {
    906         //             arr = [Type.toFixed(this.X(), digits), sep, Type.toFixed(this.Y(), digits)];
    907         //             if (withZ) {
    908         //                 arr.push(sep, Type.toFixed(this.Z(), digits));
    909         //             }
    910         //         }
    911         //     }
    912
    913         //     return '(' + arr.join('') + ')';
    914         // },
    915
    916         /**
    917          * New evaluation of the function term.
    918          * This is required for CAS-points: Their XTerm() method is
    919          * overwritten in {@link JXG.CoordsElement#addConstraint}.
    920          *
    921          * @returns {Number} User coordinate of point in x direction.
    922          * @private
    923          */
    924         XEval: function () {
    925             return this.coords.usrCoords[1];
    926         },
    927
    928         /**
    929          * New evaluation of the function term.
    930          * This is required for CAS-points: Their YTerm() method is overwritten
    931          * in {@link JXG.CoordsElement#addConstraint}.
    932          *
    933          * @returns {Number} User coordinate of point in y direction.
    934          * @private
    935          */
    936         YEval: function () {
    937             return this.coords.usrCoords[2];
    938         },
    939
    940         /**
    941          * New evaluation of the function term.
    942          * This is required for CAS-points: Their ZTerm() method is overwritten in
    943          * {@link JXG.CoordsElement#addConstraint}.
    944          *
    945          * @returns {Number} User coordinate of point in z direction.
    946          * @private
    947          */
    948         ZEval: function () {
    949             return this.coords.usrCoords[0];
    950         },
    951
    952         /**
    953          * Getter method for the distance to a second point, this is required for CAS-elements.
    954          * Here, function inlining seems to be worthwile (for plotting).
    955          * @param {JXG.Point} point2 The point to which the distance shall be calculated.
    956          * @returns {Number} Distance in user coordinate to the given point
    957          */
    958         Dist: function (point2) {
    959             if (this.isReal && point2.isReal) {
    960                 return this.coords.distance(Const.COORDS_BY_USER, point2.coords);
    961             }
    962             return NaN;
    963         },
    964
    965         /**
    966          * Alias for {@link JXG.Element#handleSnapToGrid}
    967          * @param {Boolean} force force snapping independent of what the snaptogrid attribute says
    968          * @returns {JXG.CoordsElement} Reference to this element
    969          */
    970         snapToGrid: function (force) {
    971             return this.handleSnapToGrid(force);
    972         },
    973
    974         /**
    975          * Let a point snap to the nearest point in distance of
    976          * {@link JXG.Point#attractorDistance}.
    977          * The function uses the coords object of the point as
    978          * its actual position.
    979          * @param {Boolean} force force snapping independent of what the snaptogrid attribute says
    980          * @returns {JXG.Point} Reference to this element
    981          */
    982         handleSnapToPoints: function (force) {
    983             var i,
    984                 pEl,
    985                 pCoords,
    986                 d = 0,
    987                 len,
    988                 dMax = Infinity,
    989                 c = null,
    990                 ev_au,
    991                 ev_ad,
    992                 ev_is2p = Type.evaluate(this.visProp.ignoredsnaptopoints),
    993                 len2,
    994                 j,
    995                 ignore = false;
    996
    997             len = this.board.objectsList.length;
    998
    999             if (ev_is2p) {
    1000                 len2 = ev_is2p.length;
    1001             }
    1002
    1003             if (Type.evaluate(this.visProp.snaptopoints) || force) {
    1004                 ev_au = Type.evaluate(this.visProp.attractorunit);
    1005                 ev_ad = Type.evaluate(this.visProp.attractordistance);
    1006
    1007                 for (i = 0; i < len; i++) {
    1008                     pEl = this.board.objectsList[i];
    1009
    1010                     if (ev_is2p) {
    1011                         ignore = false;
    1012                         for (j = 0; j < len2; j++) {
    1013                             if (pEl === this.board.select(ev_is2p[j])) {
    1014                                 ignore = true;
    1015                                 break;
    1016                             }
    1017                         }
    1018                         if (ignore) {
    1019                             continue;
    1020                         }
    1021                     }
    1022
    1023                     if (Type.isPoint(pEl) && pEl !== this && pEl.visPropCalc.visible) {
    1024                         pCoords = Geometry.projectPointToPoint(this, pEl, this.board);
    1025                         if (ev_au === "screen") {
    1026                             d = pCoords.distance(Const.COORDS_BY_SCREEN, this.coords);
    1027                         } else {
    1028                             d = pCoords.distance(Const.COORDS_BY_USER, this.coords);
    1029                         }
    1030
    1031                         if (d < ev_ad && d < dMax) {
    1032                             dMax = d;
    1033                             c = pCoords;
    1034                         }
    1035                     }
    1036                 }
    1037
    1038                 if (c !== null) {
    1039                     this.coords.setCoordinates(Const.COORDS_BY_USER, c.usrCoords);
    1040                 }
    1041             }
    1042
    1043             return this;
    1044         },
    1045
    1046         /**
    1047          * Alias for {@link JXG.CoordsElement#handleSnapToPoints}.
    1048          *
    1049          * @param {Boolean} force force snapping independent of what the snaptogrid attribute says
    1050          * @returns {JXG.Point} Reference to this element
    1051          */
    1052         snapToPoints: function (force) {
    1053             return this.handleSnapToPoints(force);
    1054         },
    1055
    1056         /**
    1057          * A point can change its type from free point to glider
    1058          * and vice versa. If it is given an array of attractor elements
    1059          * (attribute attractors) and the attribute attractorDistance
    1060          * then the point will be made a glider if it less than attractorDistance
    1061          * apart from one of its attractor elements.
    1062          * If attractorDistance is equal to zero, the point stays in its
    1063          * current form.
    1064          * @returns {JXG.Point} Reference to this element
    1065          */
    1066         handleAttractors: function () {
    1067             var i,
    1068                 el,
    1069                 projCoords,
    1070                 d = 0.0,
    1071                 projection,
    1072                 ev_au = Type.evaluate(this.visProp.attractorunit),
    1073                 ev_ad = Type.evaluate(this.visProp.attractordistance),
    1074                 ev_sd = Type.evaluate(this.visProp.snatchdistance),
    1075                 ev_a = Type.evaluate(this.visProp.attractors),
    1076                 len = ev_a.length;
    1077
    1078             if (ev_ad === 0.0) {
    1079                 return;
    1080             }
    1081
    1082             for (i = 0; i < len; i++) {
    1083                 el = this.board.select(ev_a[i]);
    1084
    1085                 if (Type.exists(el) && el !== this) {
    1086                     if (Type.isPoint(el)) {
    1087                         projCoords = Geometry.projectPointToPoint(this, el, this.board);
    1088                     } else if (el.elementClass === Const.OBJECT_CLASS_LINE) {
    1089                         projection = Geometry.projectCoordsToSegment(
    1090                             this.coords.usrCoords,
    1091                             el.point1.coords.usrCoords,
    1092                             el.point2.coords.usrCoords
    1093                         );
    1094                         if (!Type.evaluate(el.visProp.straightfirst) && projection[1] < 0.0) {
    1095                             projCoords = el.point1.coords;
    1096                         } else if (
    1097                             !Type.evaluate(el.visProp.straightlast) &&
    1098                             projection[1] > 1.0
    1099                         ) {
    1100                             projCoords = el.point2.coords;
    1101                         } else {
    1102                             projCoords = new Coords(
    1103                                 Const.COORDS_BY_USER,
    1104                                 projection[0],
    1105                                 this.board
    1106                             );
    1107                         }
    1108                     } else if (el.elementClass === Const.OBJECT_CLASS_CIRCLE) {
    1109                         projCoords = Geometry.projectPointToCircle(this, el, this.board);
    1110                     } else if (el.elementClass === Const.OBJECT_CLASS_CURVE) {
    1111                         projCoords = Geometry.projectPointToCurve(this, el, this.board)[0];
    1112                     } else if (el.type === Const.OBJECT_TYPE_TURTLE) {
    1113                         projCoords = Geometry.projectPointToTurtle(this, el, this.board)[0];
    1114                     } else if (el.type === Const.OBJECT_TYPE_POLYGON) {
    1115                         projCoords = new Coords(
    1116                             Const.COORDS_BY_USER,
    1117                             Geometry.projectCoordsToPolygon(this.coords.usrCoords, el),
    1118                             this.board
    1119                         );
    1120                     }
    1121
    1122                     if (ev_au === "screen") {
    1123                         d = projCoords.distance(Const.COORDS_BY_SCREEN, this.coords);
    1124                     } else {
    1125                         d = projCoords.distance(Const.COORDS_BY_USER, this.coords);
    1126                     }
    1127
    1128                     if (d < ev_ad) {
    1129                         if (
    1130                             !(
    1131                                 this.type === Const.OBJECT_TYPE_GLIDER &&
    1132                                 (el === this.slideObject ||
    1133                                     (this.slideObject &&
    1134                                         this.onPolygon &&
    1135                                         this.slideObject.parentPolygon === el))
    1136                             )
    1137                         ) {
    1138                             this.makeGlider(el);
    1139                         }
    1140                         break; // bind the point to the first attractor in its list.
    1141                     }
    1142                     if (
    1143                         d >= ev_sd &&
    1144                         (el === this.slideObject ||
    1145                             (this.slideObject &&
    1146                                 this.onPolygon &&
    1147                                 this.slideObject.parentPolygon === el))
    1148                     ) {
    1149                         this.popSlideObject();
    1150                     }
    1151                 }
    1152             }
    1153
    1154             return this;
    1155         },
    1156
    1157         /**
    1158          * Sets coordinates and calls the point's update() method.
    1159          * @param {Number} method The type of coordinates used here.
    1160          * Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
    1161          * @param {Array} coords coordinates <tt>([z], x, y)</tt> in screen/user units
    1162          * @returns {JXG.Point} this element
    1163          */
    1164         setPositionDirectly: function (method, coords) {
    1165             var i,
    1166                 c,
    1167                 dc,
    1168                 oldCoords = this.coords,
    1169                 newCoords;
    1170
    1171             if (this.relativeCoords) {
    1172                 c = new Coords(method, coords, this.board);
    1173                 if (Type.evaluate(this.visProp.islabel)) {
    1174                     dc = Statistics.subtract(c.scrCoords, oldCoords.scrCoords);
    1175                     this.relativeCoords.scrCoords[1] += dc[1];
    1176                     this.relativeCoords.scrCoords[2] += dc[2];
    1177                 } else {
    1178                     dc = Statistics.subtract(c.usrCoords, oldCoords.usrCoords);
    1179                     this.relativeCoords.usrCoords[1] += dc[1];
    1180                     this.relativeCoords.usrCoords[2] += dc[2];
    1181                 }
    1182
    1183                 return this;
    1184             }
    1185
    1186             this.coords.setCoordinates(method, coords);
    1187             this.handleSnapToGrid();
    1188             this.handleSnapToPoints();
    1189             this.handleAttractors();
    1190
    1191             // Update the initial coordinates. This is needed for free points
    1192             // that have a transformation bound to it.
    1193             for (i = this.transformations.length - 1; i >= 0; i--) {
    1194                 if (method === Const.COORDS_BY_SCREEN) {
    1195                     newCoords = new Coords(method, coords, this.board).usrCoords;
    1196                 } else {
    1197                     if (coords.length === 2) {
    1198                         coords = [1].concat(coords);
    1199                     }
    1200                     newCoords = coords;
    1201                 }
    1202                 this.initialCoords.setCoordinates(
    1203                     Const.COORDS_BY_USER,
    1204                     Mat.matVecMult(Mat.inverse(this.transformations[i].matrix), newCoords)
    1205                 );
    1206             }
    1207             this.prepareUpdate().update();
    1208
    1209             // If the user suspends the board updates we need to recalculate the relative position of
    1210             // the point on the slide object. This is done in updateGlider() which is NOT called during the
    1211             // update process triggered by unsuspendUpdate.
    1212             if (this.board.isSuspendedUpdate && this.type === Const.OBJECT_TYPE_GLIDER) {
    1213                 this.updateGlider();
    1214             }
    1215
    1216             return this;
    1217         },
    1218
    1219         /**
    1220          * Translates the point by <tt>tv = (x, y)</tt>.
    1221          * @param {Number} method The type of coordinates used here.
    1222          * Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
    1223          * @param {Array} tv (x, y)
    1224          * @returns {JXG.Point}
    1225          */
    1226         setPositionByTransform: function (method, tv) {
    1227             var t;
    1228
    1229             tv = new Coords(method, tv, this.board);
    1230             t = this.board.create("transform", tv.usrCoords.slice(1), {
    1231                 type: "translate"
    1232             });
    1233
    1234             if (
    1235                 this.transformations.length > 0 &&
    1236                 this.transformations[this.transformations.length - 1].isNumericMatrix
    1237             ) {
    1238                 this.transformations[this.transformations.length - 1].melt(t);
    1239             } else {
    1240                 this.addTransform(this, t);
    1241             }
    1242
    1243             this.prepareUpdate().update();
    1244
    1245             return this;
    1246         },
    1247
    1248         /**
    1249          * Sets coordinates and calls the point's update() method.
    1250          * @param {Number} method The type of coordinates used here.
    1251          * Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
    1252          * @param {Array} coords coordinates in screen/user units
    1253          * @returns {JXG.Point}
    1254          */
    1255         setPosition: function (method, coords) {
    1256             return this.setPositionDirectly(method, coords);
    1257         },
    1258
    1259         /**
    1260          * Sets the position of a glider relative to the defining elements
    1261          * of the {@link JXG.Point#slideObject}.
    1262          * @param {Number} x
    1263          * @returns {JXG.Point} Reference to the point element.
    1264          */
    1265         setGliderPosition: function (x) {
    1266             if (this.type === Const.OBJECT_TYPE_GLIDER) {
    1267                 this.position = x;
    1268                 this.board.update();
    1269             }
    1270
    1271             return this;
    1272         },
    1273
    1274         /**
    1275          * Convert the point to glider and update the construction.
    1276          * To move the point visual onto the glider, a call of board update is necessary.
    1277          * @param {String|Object} slide The object the point will be bound to.
    1278          */
    1279         makeGlider: function (slide) {
    1280             var slideobj = this.board.select(slide),
    1281                 onPolygon = false,
    1282                 min, i, dist;
    1283
    1284             if (slideobj.type === Const.OBJECT_TYPE_POLYGON) {
    1285                 // Search for the closest edge of the polygon.
    1286                 min = Number.MAX_VALUE;
    1287                 for (i = 0; i < slideobj.borders.length; i++) {
    1288                     dist = JXG.Math.Geometry.distPointLine(
    1289                         this.coords.usrCoords,
    1290                         slideobj.borders[i].stdform
    1291                     );
    1292                     if (dist < min) {
    1293                         min = dist;
    1294                         slide = slideobj.borders[i];
    1295                     }
    1296                 }
    1297                 slideobj = this.board.select(slide);
    1298                 onPolygon = true;
    1299             }
    1300
    1301             /* Gliders on Ticks are forbidden */
    1302             if (!Type.exists(slideobj)) {
    1303                 throw new Error("JSXGraph: slide object undefined.");
    1304             } else if (slideobj.type === Const.OBJECT_TYPE_TICKS) {
    1305                 throw new Error("JSXGraph: gliders on ticks are not possible.");
    1306             }
    1307
    1308             this.slideObject = this.board.select(slide);
    1309             this.slideObjects.push(this.slideObject);
    1310             this.addParents(slide);
    1311
    1312             this.type = Const.OBJECT_TYPE_GLIDER;
    1313             this.elType = 'glider';
    1314             this.visProp.snapwidth = -1; // By default, deactivate snapWidth
    1315             this.slideObject.addChild(this);
    1316             this.isDraggable = true;
    1317             this.onPolygon = onPolygon;
    1318
    1319             this.generatePolynomial = function () {
    1320                 return this.slideObject.generatePolynomial(this);
    1321             };
    1322
    1323             // Determine the initial value of this.position
    1324             this.updateGlider();
    1325             this.needsUpdateFromParent = true;
    1326             this.updateGliderFromParent();
    1327
    1328             return this;
    1329         },
    1330
    1331         /**
    1332          * Remove the last slideObject. If there are more than one elements the point is bound to,
    1333          * the second last element is the new active slideObject.
    1334          */
    1335         popSlideObject: function () {
    1336             if (this.slideObjects.length > 0) {
    1337                 this.slideObjects.pop();
    1338
    1339                 // It may not be sufficient to remove the point from
    1340                 // the list of childElement. For complex dependencies
    1341                 // one may have to go to the list of ancestor and descendants.  A.W.
    1342                 // Yes indeed, see #51 on github bug tracker
    1343                 //   delete this.slideObject.childElements[this.id];
    1344                 this.slideObject.removeChild(this);
    1345
    1346                 if (this.slideObjects.length === 0) {
    1347                     this.type = this._org_type;
    1348                     if (this.type === Const.OBJECT_TYPE_POINT) {
    1349                         this.elType = "point";
    1350                     } else if (this.elementClass === Const.OBJECT_CLASS_TEXT) {
    1351                         this.elType = "text";
    1352                     } else if (this.type === Const.OBJECT_TYPE_IMAGE) {
    1353                         this.elType = "image";
    1354                     } else if (this.type === Const.OBJECT_TYPE_FOREIGNOBJECT) {
    1355                         this.elType = "foreignobject";
    1356                     }
    1357
    1358                     this.slideObject = null;
    1359                 } else {
    1360                     this.slideObject = this.slideObjects[this.slideObjects.length - 1];
    1361                 }
    1362             }
    1363         },
    1364
    1365         /**
    1366          * Converts a calculated element into a free element,
    1367          * i.e. it will delete all ancestors and transformations and,
    1368          * if the element is currently a glider, will remove the slideObject reference.
    1369          */
    1370         free: function () {
    1371             var ancestorId, ancestor;
    1372             // child;
    1373
    1374             if (this.type !== Const.OBJECT_TYPE_GLIDER) {
    1375                 // remove all transformations
    1376                 this.transformations.length = 0;
    1377
    1378                 delete this.updateConstraint;
    1379                 this.isConstrained = false;
    1380                 // this.updateConstraint = function () {
    1381                 //     return this;
    1382                 // };
    1383
    1384                 if (!this.isDraggable) {
    1385                     this.isDraggable = true;
    1386
    1387                     if (this.elementClass === Const.OBJECT_CLASS_POINT) {
    1388                         this.type = Const.OBJECT_TYPE_POINT;
    1389                         this.elType = "point";
    1390                     }
    1391
    1392                     this.XEval = function () {
    1393                         return this.coords.usrCoords[1];
    1394                     };
    1395
    1396                     this.YEval = function () {
    1397                         return this.coords.usrCoords[2];
    1398                     };
    1399
    1400                     this.ZEval = function () {
    1401                         return this.coords.usrCoords[0];
    1402                     };
    1403
    1404                     this.Xjc = null;
    1405                     this.Yjc = null;
    1406                 } else {
    1407                     return;
    1408                 }
    1409             }
    1410
    1411             // a free point does not depend on anything. And instead of running through tons of descendants and ancestor
    1412             // structures, where we eventually are going to visit a lot of objects twice or thrice with hard to read and
    1413             // comprehend code, just run once through all objects and delete all references to this point and its label.
    1414             for (ancestorId in this.board.objects) {
    1415                 if (this.board.objects.hasOwnProperty(ancestorId)) {
    1416                     ancestor = this.board.objects[ancestorId];
    1417
    1418                     if (ancestor.descendants) {
    1419                         delete ancestor.descendants[this.id];
    1420                         delete ancestor.childElements[this.id];
    1421
    1422                         if (this.hasLabel) {
    1423                             delete ancestor.descendants[this.label.id];
    1424                             delete ancestor.childElements[this.label.id];
    1425                         }
    1426                     }
    1427                 }
    1428             }
    1429
    1430             // A free point does not depend on anything. Remove all ancestors.
    1431             this.ancestors = {}; // only remove the reference
    1432             this.parents = [];
    1433
    1434             // Completely remove all slideObjects of the element
    1435             this.slideObject = null;
    1436             this.slideObjects = [];
    1437             if (this.elementClass === Const.OBJECT_CLASS_POINT) {
    1438                 this.type = Const.OBJECT_TYPE_POINT;
    1439                 this.elType = "point";
    1440             } else if (this.elementClass === Const.OBJECT_CLASS_TEXT) {
    1441                 this.type = this._org_type;
    1442                 this.elType = "text";
    1443             } else if (this.elementClass === Const.OBJECT_CLASS_OTHER) {
    1444                 this.type = this._org_type;
    1445                 this.elType = "image";
    1446             }
    1447         },
    1448
    1449         /**
    1450          * Convert the point to CAS point and call update().
    1451          * @param {Array} terms [[zterm], xterm, yterm] defining terms for the z, x and y coordinate.
    1452          * The z-coordinate is optional and it is used for homogeneous coordinates.
    1453          * The coordinates may be either <ul>
    1454          *   <li>a JavaScript function,</li>
    1455          *   <li>a string containing GEONExT syntax. This string will be converted into a JavaScript
    1456          *     function here,</li>
    1457          *   <li>a Number</li>
    1458          *   <li>a pointer to a slider object. This will be converted into a call of the Value()-method
    1459          *     of this slider.</li>
    1460          *   </ul>
    1461          * @see JXG.GeonextParser#geonext2JS
    1462          */
    1463         addConstraint: function (terms) {
    1464             var i, v,
    1465                 newfuncs = [],
    1466                 what = ["X", "Y"],
    1467                 makeConstFunction = function (z) {
    1468                     return function () {
    1469                         return z;
    1470                     };
    1471                 },
    1472                 makeSliderFunction = function (a) {
    1473                     return function () {
    1474                         return a.Value();
    1475                     };
    1476                 };
    1477
    1478             if (this.elementClass === Const.OBJECT_CLASS_POINT) {
    1479                 this.type = Const.OBJECT_TYPE_CAS;
    1480             }
    1481
    1482             this.isDraggable = false;
    1483
    1484             for (i = 0; i < terms.length; i++) {
    1485                 v = terms[i];
    1486
    1487                 if (Type.isString(v)) {
    1488                     // Convert GEONExT syntax into JavaScript syntax
    1489                     //t  = JXG.GeonextParser.geonext2JS(v, this.board);
    1490                     //newfuncs[i] = new Function('','return ' + t + ';');
    1491                     //v = GeonextParser.replaceNameById(v, this.board);
    1492                     newfuncs[i] = this.board.jc.snippet(v, true, null, true);
    1493                     this.addParentsFromJCFunctions([newfuncs[i]]);
    1494
    1495                     // Store original term as 'Xjc' or 'Yjc'
    1496                     if (terms.length === 2) {
    1497                         this[what[i] + "jc"] = terms[i];
    1498                     }
    1499                 } else if (Type.isFunction(v)) {
    1500                     newfuncs[i] = v;
    1501                 } else if (Type.isNumber(v)) {
    1502                     newfuncs[i] = makeConstFunction(v);
    1503                 } else if (Type.isObject(v) && Type.isFunction(v.Value)) {
    1504                     // Slider
    1505                     newfuncs[i] = makeSliderFunction(v);
    1506                 }
    1507
    1508                 newfuncs[i].origin = v;
    1509             }
    1510
    1511             // Intersection function
    1512             if (terms.length === 1) {
    1513                 this.updateConstraint = function () {
    1514                     var c = newfuncs[0]();
    1515
    1516                     // Array
    1517                     if (Type.isArray(c)) {
    1518                         this.coords.setCoordinates(Const.COORDS_BY_USER, c);
    1519                         // Coords object
    1520                     } else {
    1521                         this.coords = c;
    1522                     }
    1523                     return this;
    1524                 };
    1525                 // Euclidean coordinates
    1526             } else if (terms.length === 2) {
    1527                 this.XEval = newfuncs[0];
    1528                 this.YEval = newfuncs[1];
    1529                 this.addParents([newfuncs[0].origin, newfuncs[1].origin]);
    1530
    1531                 this.updateConstraint = function () {
    1532                     this.coords.setCoordinates(Const.COORDS_BY_USER, [
    1533                         this.XEval(),
    1534                         this.YEval()
    1535                     ]);
    1536                     return this;
    1537                 };
    1538                 // Homogeneous coordinates
    1539             } else {
    1540                 this.ZEval = newfuncs[0];
    1541                 this.XEval = newfuncs[1];
    1542                 this.YEval = newfuncs[2];
    1543
    1544                 this.addParents([newfuncs[0].origin, newfuncs[1].origin, newfuncs[2].origin]);
    1545
    1546                 this.updateConstraint = function () {
    1547                     this.coords.setCoordinates(Const.COORDS_BY_USER, [
    1548                         this.ZEval(),
    1549                         this.XEval(),
    1550                         this.YEval()
    1551                     ]);
    1552                     return this;
    1553                 };
    1554             }
    1555             this.isConstrained = true;
    1556
    1557             /**
    1558              * We have to do an update. Otherwise, elements relying on this point will receive NaN.
    1559              */
    1560             this.prepareUpdate().update();
    1561             if (!this.board.isSuspendedUpdate) {
    1562                 this.updateVisibility().updateRenderer();
    1563                 if (this.hasLabel) {
    1564                     this.label.fullUpdate();
    1565                 }
    1566             }
    1567
    1568             return this;
    1569         },
    1570
    1571         /**
    1572          * In case there is an attribute "anchor", the element is bound to
    1573          * this anchor element.
    1574          * This is handled with this.relativeCoords. If the element is a label
    1575          * relativeCoords are given in scrCoords, otherwise in usrCoords.
    1576          * @param{Array} coordinates Offset from the anchor element. These are the values for this.relativeCoords.
    1577          * In case of a label, coordinates are screen coordinates. Otherwise, coordinates are user coordinates.
    1578          * @param{Boolean} isLabel Yes/no
    1579          * @private
    1580          */
    1581         addAnchor: function (coordinates, isLabel) {
    1582             if (isLabel) {
    1583                 this.relativeCoords = new Coords(
    1584                     Const.COORDS_BY_SCREEN,
    1585                     coordinates.slice(0, 2),
    1586                     this.board
    1587                 );
    1588             } else {
    1589                 this.relativeCoords = new Coords(Const.COORDS_BY_USER, coordinates, this.board);
    1590             }
    1591             this.element.addChild(this);
    1592             if (isLabel) {
    1593                 this.addParents(this.element);
    1594             }
    1595
    1596             this.XEval = function () {
    1597                 var sx, coords, anchor, ev_o;
    1598
    1599                 if (Type.evaluate(this.visProp.islabel)) {
    1600                     ev_o = Type.evaluate(this.visProp.offset);
    1601                     sx = parseFloat(ev_o[0]);
    1602                     anchor = this.element.getLabelAnchor();
    1603                     coords = new Coords(
    1604                         Const.COORDS_BY_SCREEN,
    1605                         [sx + this.relativeCoords.scrCoords[1] + anchor.scrCoords[1], 0],
    1606                         this.board
    1607                     );
    1608
    1609                     return coords.usrCoords[1];
    1610                 }
    1611
    1612                 anchor = this.element.getTextAnchor();
    1613                 return this.relativeCoords.usrCoords[1] + anchor.usrCoords[1];
    1614             };
    1615
    1616             this.YEval = function () {
    1617                 var sy, coords, anchor, ev_o;
    1618
    1619                 if (Type.evaluate(this.visProp.islabel)) {
    1620                     ev_o = Type.evaluate(this.visProp.offset);
    1621                     sy = -parseFloat(ev_o[1]);
    1622                     anchor = this.element.getLabelAnchor();
    1623                     coords = new Coords(
    1624                         Const.COORDS_BY_SCREEN,
    1625                         [0, sy + this.relativeCoords.scrCoords[2] + anchor.scrCoords[2]],
    1626                         this.board
    1627                     );
    1628
    1629                     return coords.usrCoords[2];
    1630                 }
    1631
    1632                 anchor = this.element.getTextAnchor();
    1633                 return this.relativeCoords.usrCoords[2] + anchor.usrCoords[2];
    1634             };
    1635
    1636             this.ZEval = Type.createFunction(1, this.board, "");
    1637
    1638             this.updateConstraint = function () {
    1639                 this.coords.setCoordinates(Const.COORDS_BY_USER, [
    1640                     this.ZEval(),
    1641                     this.XEval(),
    1642                     this.YEval()
    1643                 ]);
    1644             };
    1645             this.isConstrained = true;
    1646
    1647             this.updateConstraint();
    1648         },
    1649
    1650         /**
    1651          * Applies the transformations of the element.
    1652          * This method applies to text and images. Point transformations are handled differently.
    1653          * @param {Boolean} fromParent True if the drag comes from a child element. Unused.
    1654          * @returns {JXG.CoordsElement} Reference to itself.
    1655          */
    1656         updateTransform: function (fromParent) {
    1657             var i;
    1658
    1659             if (this.transformations.length === 0) {
    1660                 return this;
    1661             }
    1662
    1663             for (i = 0; i < this.transformations.length; i++) {
    1664                 this.transformations[i].update();
    1665             }
    1666
    1667             return this;
    1668         },
    1669
    1670         /**
    1671          * Add transformations to this element.
    1672          * @param {JXG.GeometryElement} el
    1673          * @param {JXG.Transformation|Array} transform Either one {@link JXG.Transformation}
    1674          * or an array of {@link JXG.Transformation}s.
    1675          * @returns {JXG.CoordsElement} Reference to itself.
    1676          */
    1677         addTransform: function (el, transform) {
    1678             var i,
    1679                 list = Type.isArray(transform) ? transform : [transform],
    1680                 len = list.length;
    1681
    1682             // There is only one baseElement possible
    1683             if (this.transformations.length === 0) {
    1684                 this.baseElement = el;
    1685             }
    1686
    1687             for (i = 0; i < len; i++) {
    1688                 this.transformations.push(list[i]);
    1689             }
    1690
    1691             return this;
    1692         },
    1693
    1694         /**
    1695          * Animate the point.
    1696          * @param {Number|Function} direction The direction the glider is animated. Can be +1 or -1.
    1697          * @param {Number|Function} stepCount The number of steps in which the parent element is divided.
    1698          * Must be at least 1.
    1699          * @param {Number|Function} delay Time in msec between two animation steps. Default is 250.
    1700          * @returns {JXG.CoordsElement} Reference to iself.
    1701          *
    1702          * @name Glider#startAnimation
    1703          * @see Glider#stopAnimation
    1704          * @function
    1705          * @example
    1706          * // Divide the circle line into 6 steps and
    1707          * // visit every step 330 msec counterclockwise.
    1708          * var ci = board.create('circle', [[-1,2], [2,1]]);
    1709          * var gl = board.create('glider', [0,2, ci]);
    1710          * gl.startAnimation(-1, 6, 330);
    1711          *
    1712          * </pre><div id="JXG0f35a50e-e99d-11e8-a1ca-04d3b0c2aad3" class="jxgbox" style="width: 300px; height: 300px;"></div>
    1713          * <script type="text/javascript">
    1714          *     (function() {
    1715          *         var board = JXG.JSXGraph.initBoard('JXG0f35a50e-e99d-11e8-a1ca-04d3b0c2aad3',
    1716          *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
    1717          *     // Divide the circle line into 6 steps and
    1718          *     // visit every step 330 msec counterclockwise.
    1719          *     var ci = board.create('circle', [[-1,2], [2,1]]);
    1720          *     var gl = board.create('glider', [0,2, ci]);
    1721          *     gl.startAnimation(-1, 6, 330);
    1722          *
    1723          *     })();
    1724          *
    1725          * </script><pre>
    1726          *
    1727          * @example
    1728          * // Divide the slider area into 20 steps and
    1729          * // visit every step 30 msec.
    1730          * var n = board.create('slider',[[-2,4],[2,4],[1,5,100]],{name:'n'});
    1731          * n.startAnimation(1, 20, 30);
    1732          *
    1733          * </pre><div id="JXG40ce04b8-e99c-11e8-a1ca-04d3b0c2aad3" class="jxgbox" style="width: 300px; height: 300px;"></div>
    1734          * <script type="text/javascript">
    1735          *     (function() {
    1736          *         var board = JXG.JSXGraph.initBoard('JXG40ce04b8-e99c-11e8-a1ca-04d3b0c2aad3',
    1737          *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
    1738          *     // Divide the slider area into 20 steps and
    1739          *     // visit every step 30 msec.
    1740          *     var n = board.create('slider',[[-2,4],[2,4],[1,5,100]],{name:'n'});
    1741          *     n.startAnimation(1, 20, 30);
    1742          *
    1743          *     })();
    1744          * </script><pre>
    1745          *
    1746          */
    1747         startAnimation: function (direction, stepCount, delay) {
    1748             var dir = Type.evaluate(direction),
    1749                 sc = Type.evaluate(stepCount),
    1750                 that = this;
    1751
    1752             delay = Type.evaluate(delay) || 250;
    1753
    1754             if (this.type === Const.OBJECT_TYPE_GLIDER && !Type.exists(this.intervalCode)) {
    1755                 this.intervalCode = window.setInterval(function () {
    1756                     that._anim(dir, sc);
    1757                 }, delay);
    1758
    1759                 if (!Type.exists(this.intervalCount)) {
    1760                     this.intervalCount = 0;
    1761                 }
    1762             }
    1763             return this;
    1764         },
    1765
    1766         /**
    1767          * Stop animation.
    1768          * @name Glider#stopAnimation
    1769          * @see Glider#startAnimation
    1770          * @function
    1771          * @returns {JXG.CoordsElement} Reference to itself.
    1772          */
    1773         stopAnimation: function () {
    1774             if (Type.exists(this.intervalCode)) {
    1775                 window.clearInterval(this.intervalCode);
    1776                 delete this.intervalCode;
    1777             }
    1778
    1779             return this;
    1780         },
    1781
    1782         /**
    1783          * Starts an animation which moves the point along a given path in given time.
    1784          * @param {Array|function} path The path the point is moved on.
    1785          * This can be either an array of arrays or containing x and y values of the points of
    1786          * the path, or an array of points, or a function taking the amount of elapsed time since the animation
    1787          * has started and returns an array containing a x and a y value or NaN.
    1788          * In case of NaN the animation stops.
    1789          * @param {Number} time The time in milliseconds in which to finish the animation
    1790          * @param {Object} [options] Optional settings for the animation.
    1791          * @param {function} [options.callback] A function that is called as soon as the animation is finished.
    1792          * @param {Boolean} [options.interpolate=true] If <tt>path</tt> is an array moveAlong()
    1793          * will interpolate the path
    1794          * using {@link JXG.Math.Numerics.Neville}. Set this flag to false if you don't want to use interpolation.
    1795          * @returns {JXG.CoordsElement} Reference to itself.
    1796          * @see JXG.CoordsElement#moveAlong
    1797          * @see JXG.CoordsElement#moveTo
    1798          * @see JXG.GeometryElement#animate
    1799          */
    1800         moveAlong: function (path, time, options) {
    1801             options = options || {};
    1802
    1803             var i,
    1804                 neville,
    1805                 interpath = [],
    1806                 p = [],
    1807                 delay = this.board.attr.animationdelay,
    1808                 steps = time / delay,
    1809                 len,
    1810                 pos,
    1811                 part,
    1812                 makeFakeFunction = function (i, j) {
    1813                     return function () {
    1814                         return path[i][j];
    1815                     };
    1816                 };
    1817
    1818             if (Type.isArray(path)) {
    1819                 len = path.length;
    1820                 for (i = 0; i < len; i++) {
    1821                     if (Type.isPoint(path[i])) {
    1822                         p[i] = path[i];
    1823                     } else {
    1824                         p[i] = {
    1825                             elementClass: Const.OBJECT_CLASS_POINT,
    1826                             X: makeFakeFunction(i, 0),
    1827                             Y: makeFakeFunction(i, 1)
    1828                         };
    1829                     }
    1830                 }
    1831
    1832                 time = time || 0;
    1833                 if (time === 0) {
    1834                     this.setPosition(Const.COORDS_BY_USER, [
    1835                         p[p.length - 1].X(),
    1836                         p[p.length - 1].Y()
    1837                     ]);
    1838                     return this.board.update(this);
    1839                 }
    1840
    1841                 if (!Type.exists(options.interpolate) || options.interpolate) {
    1842                     neville = Numerics.Neville(p);
    1843                     for (i = 0; i < steps; i++) {
    1844                         interpath[i] = [];
    1845                         interpath[i][0] = neville[0](((steps - i) / steps) * neville[3]());
    1846                         interpath[i][1] = neville[1](((steps - i) / steps) * neville[3]());
    1847                     }
    1848                 } else {
    1849                     len = path.length - 1;
    1850                     for (i = 0; i < steps; ++i) {
    1851                         pos = Math.floor((i / steps) * len);
    1852                         part = (i / steps) * len - pos;
    1853
    1854                         interpath[i] = [];
    1855                         interpath[i][0] = (1.0 - part) * p[pos].X() + part * p[pos + 1].X();
    1856                         interpath[i][1] = (1.0 - part) * p[pos].Y() + part * p[pos + 1].Y();
    1857                     }
    1858                     interpath.push([p[len].X(), p[len].Y()]);
    1859                     interpath.reverse();
    1860                     /*
    1861                     for (i = 0; i < steps; i++) {
    1862                         interpath[i] = [];
    1863                         interpath[i][0] = path[Math.floor((steps - i) / steps * (path.length - 1))][0];
    1864                         interpath[i][1] = path[Math.floor((steps - i) / steps * (path.length - 1))][1];
    1865                     }
    1866                     */
    1867                 }
    1868
    1869                 this.animationPath = interpath;
    1870             } else if (Type.isFunction(path)) {
    1871                 this.animationPath = path;
    1872                 this.animationStart = new Date().getTime();
    1873             }
    1874
    1875             this.animationCallback = options.callback;
    1876             this.board.addAnimation(this);
    1877
    1878             return this;
    1879         },
    1880
    1881         /**
    1882          * Starts an animated point movement towards the given coordinates <tt>where</tt>.
    1883          * The animation is done after <tt>time</tt> milliseconds.
    1884          * If the second parameter is not given or is equal to 0, setPosition() is called, see #setPosition,
    1885          * i.e. the coordinates are changed without animation.
    1886          * @param {Array} where Array containing the x and y coordinate of the target location.
    1887          * @param {Number} [time] Number of milliseconds the animation should last.
    1888          * @param {Object} [options] Optional settings for the animation
    1889          * @param {function} [options.callback] A function that is called as soon as the animation is finished.
    1890          * @param {String} [options.effect='<>'] animation effects like speed fade in and out. possible values are
    1891          * '<>' for speed increase on start and slow down at the end (default) and '--' for constant speed during
    1892          * the whole animation.
    1893          * @returns {JXG.CoordsElement} Reference to itself.
    1894          * @see JXG.CoordsElement#moveAlong
    1895          * @see JXG.CoordsElement#visit
    1896          * @see JXG.GeometryElement#animate
    1897          */
    1898         moveTo: function (where, time, options) {
    1899             options = options || {};
    1900             where = new Coords(Const.COORDS_BY_USER, where, this.board);
    1901
    1902             var i,
    1903                 delay = this.board.attr.animationdelay,
    1904                 steps = Math.ceil(time / delay),
    1905                 coords = [],
    1906                 X = this.coords.usrCoords[1],
    1907                 Y = this.coords.usrCoords[2],
    1908                 dX = where.usrCoords[1] - X,
    1909                 dY = where.usrCoords[2] - Y,
    1910                 /** @ignore */
    1911                 stepFun = function (i) {
    1912                     if (options.effect && options.effect === "<>") {
    1913                         return Math.pow(Math.sin(((i / steps) * Math.PI) / 2), 2);
    1914                     }
    1915                     return i / steps;
    1916                 };
    1917
    1918             if (
    1919                 !Type.exists(time) ||
    1920                 time === 0 ||
    1921                 Math.abs(where.usrCoords[0] - this.coords.usrCoords[0]) > Mat.eps
    1922             ) {
    1923                 this.setPosition(Const.COORDS_BY_USER, where.usrCoords);
    1924                 return this.board.update(this);
    1925             }
    1926
    1927             // In case there is no callback and we are already at the endpoint we can stop here
    1928             if (
    1929                 !Type.exists(options.callback) &&
    1930                 Math.abs(dX) < Mat.eps &&
    1931                 Math.abs(dY) < Mat.eps
    1932             ) {
    1933                 return this;
    1934             }
    1935
    1936             for (i = steps; i >= 0; i--) {
    1937                 coords[steps - i] = [
    1938                     where.usrCoords[0],
    1939                     X + dX * stepFun(i),
    1940                     Y + dY * stepFun(i)
    1941                 ];
    1942             }
    1943
    1944             this.animationPath = coords;
    1945             this.animationCallback = options.callback;
    1946             this.board.addAnimation(this);
    1947
    1948             return this;
    1949         },
    1950
    1951         /**
    1952          * Starts an animated point movement towards the given coordinates <tt>where</tt>. After arriving at
    1953          * <tt>where</tt> the point moves back to where it started. The animation is done after <tt>time</tt>
    1954          * milliseconds.
    1955          * @param {Array} where Array containing the x and y coordinate of the target location.
    1956          * @param {Number} time Number of milliseconds the animation should last.
    1957          * @param {Object} [options] Optional settings for the animation
    1958          * @param {function} [options.callback] A function that is called as soon as the animation is finished.
    1959          * @param {String} [options.effect='<>'] animation effects like speed fade in and out. possible values are
    1960          * '<>' for speed increase on start and slow down at the end (default) and '--' for constant speed during
    1961          * the whole animation.
    1962          * @param {Number} [options.repeat=1] How often this animation should be repeated.
    1963          * @returns {JXG.CoordsElement} Reference to itself.
    1964          * @see JXG.CoordsElement#moveAlong
    1965          * @see JXG.CoordsElement#moveTo
    1966          * @see JXG.GeometryElement#animate
    1967          */
    1968         visit: function (where, time, options) {
    1969             where = new Coords(Const.COORDS_BY_USER, where, this.board);
    1970
    1971             var i,
    1972                 j,
    1973                 steps,
    1974                 delay = this.board.attr.animationdelay,
    1975                 coords = [],
    1976                 X = this.coords.usrCoords[1],
    1977                 Y = this.coords.usrCoords[2],
    1978                 dX = where.usrCoords[1] - X,
    1979                 dY = where.usrCoords[2] - Y,
    1980                 /** @ignore */
    1981                 stepFun = function (i) {
    1982                     var x = i < steps / 2 ? (2 * i) / steps : (2 * (steps - i)) / steps;
    1983
    1984                     if (options.effect && options.effect === "<>") {
    1985                         return Math.pow(Math.sin((x * Math.PI) / 2), 2);
    1986                     }
    1987
    1988                     return x;
    1989                 };
    1990
    1991             // support legacy interface where the third parameter was the number of repeats
    1992             if (Type.isNumber(options)) {
    1993                 options = { repeat: options };
    1994             } else {
    1995                 options = options || {};
    1996                 if (!Type.exists(options.repeat)) {
    1997                     options.repeat = 1;
    1998                 }
    1999             }
    2000
    2001             steps = Math.ceil(time / (delay * options.repeat));
    2002
    2003             for (j = 0; j < options.repeat; j++) {
    2004                 for (i = steps; i >= 0; i--) {
    2005                     coords[j * (steps + 1) + steps - i] = [
    2006                         where.usrCoords[0],
    2007                         X + dX * stepFun(i),
    2008                         Y + dY * stepFun(i)
    2009                     ];
    2010                 }
    2011             }
    2012             this.animationPath = coords;
    2013             this.animationCallback = options.callback;
    2014             this.board.addAnimation(this);
    2015
    2016             return this;
    2017         },
    2018
    2019         /**
    2020          * Animates a glider. Is called by the browser after startAnimation is called.
    2021          * @param {Number} direction The direction the glider is animated.
    2022          * @param {Number} stepCount The number of steps in which the parent element is divided.
    2023          * Must be at least 1.
    2024          * @see #startAnimation
    2025          * @see #stopAnimation
    2026          * @private
    2027          * @returns {JXG.CoordsElement} Reference to itself.
    2028          */
    2029         _anim: function (direction, stepCount) {
    2030             var dX, dY, alpha, startPoint, newX, radius, sp1c, sp2c, res;
    2031
    2032             this.intervalCount += 1;
    2033             if (this.intervalCount > stepCount) {
    2034                 this.intervalCount = 0;
    2035             }
    2036
    2037             if (this.slideObject.elementClass === Const.OBJECT_CLASS_LINE) {
    2038                 sp1c = this.slideObject.point1.coords.scrCoords;
    2039                 sp2c = this.slideObject.point2.coords.scrCoords;
    2040
    2041                 dX = Math.round(((sp2c[1] - sp1c[1]) * this.intervalCount) / stepCount);
    2042                 dY = Math.round(((sp2c[2] - sp1c[2]) * this.intervalCount) / stepCount);
    2043                 if (direction > 0) {
    2044                     startPoint = this.slideObject.point1;
    2045                 } else {
    2046                     startPoint = this.slideObject.point2;
    2047                     dX *= -1;
    2048                     dY *= -1;
    2049                 }
    2050
    2051                 this.coords.setCoordinates(Const.COORDS_BY_SCREEN, [
    2052                     startPoint.coords.scrCoords[1] + dX,
    2053                     startPoint.coords.scrCoords[2] + dY
    2054                 ]);
    2055             } else if (this.slideObject.elementClass === Const.OBJECT_CLASS_CURVE) {
    2056                 if (direction > 0) {
    2057                     newX = Math.round(
    2058                         (this.intervalCount / stepCount) * this.board.canvasWidth
    2059                     );
    2060                 } else {
    2061                     newX = Math.round(
    2062                         ((stepCount - this.intervalCount) / stepCount) * this.board.canvasWidth
    2063                     );
    2064                 }
    2065
    2066                 this.coords.setCoordinates(Const.COORDS_BY_SCREEN, [newX, 0]);
    2067                 res = Geometry.projectPointToCurve(this, this.slideObject, this.board);
    2068                 this.coords = res[0];
    2069                 this.position = res[1];
    2070             } else if (this.slideObject.elementClass === Const.OBJECT_CLASS_CIRCLE) {
    2071                 alpha = 2 * Math.PI;
    2072                 if (direction < 0) {
    2073                     alpha *= this.intervalCount / stepCount;
    2074                 } else {
    2075                     alpha *= (stepCount - this.intervalCount) / stepCount;
    2076                 }
    2077                 radius = this.slideObject.Radius();
    2078
    2079                 this.coords.setCoordinates(Const.COORDS_BY_USER, [
    2080                     this.slideObject.center.coords.usrCoords[1] + radius * Math.cos(alpha),
    2081                     this.slideObject.center.coords.usrCoords[2] + radius * Math.sin(alpha)
    2082                 ]);
    2083             }
    2084
    2085             this.board.update(this);
    2086             return this;
    2087         },
    2088
    2089         // documented in GeometryElement
    2090         getTextAnchor: function () {
    2091             return this.coords;
    2092         },
    2093
    2094         // documented in GeometryElement
    2095         getLabelAnchor: function () {
    2096             return this.coords;
    2097         },
    2098
    2099         // documented in element.js
    2100         getParents: function () {
    2101             var p = [this.Z(), this.X(), this.Y()];
    2102
    2103             if (this.parents.length !== 0) {
    2104                 p = this.parents;
    2105             }
    2106
    2107             if (this.type === Const.OBJECT_TYPE_GLIDER) {
    2108                 p = [this.X(), this.Y(), this.slideObject.id];
    2109             }
    2110
    2111             return p;
    2112         }
    2113     }
    2114 );
    2115
    2116 /**
    2117  * Generic method to create point, text or image.
    2118  * Determines the type of the construction, i.e. free, or constrained by function,
    2119  * transformation or of glider type.
    2120  * @param{Object} Callback Object type, e.g. JXG.Point, JXG.Text or JXG.Image
    2121  * @param{Object} board Link to the board object
    2122  * @param{Array} coords Array with coordinates. This may be: array of numbers, function
    2123  * returning an array of numbers, array of functions returning a number, object and transformation.
    2124  * If the attribute "slideObject" exists, a glider element is constructed.
    2125  * @param{Object} attr Attributes object
    2126  * @param{Object} arg1 Optional argument 1: in case of text this is the text content,
    2127  * in case of an image this is the url.
    2128  * @param{Array} arg2 Optional argument 2: in case of image this is an array containing the size of
    2129  * the image.
    2130  * @returns{Object} returns the created object or false.
    2131  */
    2132 JXG.CoordsElement.create = function (Callback, board, coords, attr, arg1, arg2) {
    2133     var el,
    2134         isConstrained = false,
    2135         i;
    2136
    2137     for (i = 0; i < coords.length; i++) {
    2138         if (Type.isFunction(coords[i]) || Type.isString(coords[i])) {
    2139             isConstrained = true;
    2140         }
    2141     }
    2142
    2143     if (!isConstrained) {
    2144         if (Type.isNumber(coords[0]) && Type.isNumber(coords[1])) {
    2145             el = new Callback(board, coords, attr, arg1, arg2);
    2146
    2147             if (Type.exists(attr.slideobject)) {
    2148                 el.makeGlider(attr.slideobject);
    2149             } else {
    2150                 // Free element
    2151                 el.baseElement = el;
    2152             }
    2153             el.isDraggable = true;
    2154         } else if (Type.isObject(coords[0]) && Type.isTransformationOrArray(coords[1])) {
    2155             // Transformation
    2156             // TODO less general specification of isObject
    2157             el = new Callback(board, [0, 0], attr, arg1, arg2);
    2158             el.addTransform(coords[0], coords[1]);
    2159             el.isDraggable = false;
    2160         } else {
    2161             return false;
    2162         }
    2163     } else {
    2164         el = new Callback(board, [0, 0], attr, arg1, arg2);
    2165         el.addConstraint(coords);
    2166     }
    2167
    2168     el.handleSnapToGrid();
    2169     el.handleSnapToPoints();
    2170     el.handleAttractors();
    2171
    2172     el.addParents(coords);
    2173     return el;
    2174 };
    2175
    2176 export default JXG.CoordsElement;
    2177