      1 /*
      2     Copyright 2008-2023
      3         Matthias Ehmann,
      4         Carsten Miller,
      5         Andreas Walter,
      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 /*global JXG:true, define: true*/
     30
     31 import JXG from "../jxg";
     32 import Const from "../base/constants";
     33 import Mat from "../math/math";
     34 import Geometry from "../math/geometry";
     35 import Type from "../utils/type";
     36 //, GeometryElement3D) {
     37
     38 /**
     39  * A 3D point is the basic geometric element.
     40  * @class Creates a new 3D point object. Do not use this constructor to create a 3D point. Use {@link JXG.View3D#create} with
     41  * type {@link Point3D} instead.
     42  * @augments JXG.GeometryElement3D
     43  * @augments JXG.GeometryElement
     44  * @param {JXG.View3D} view The 3D view the point is drawn on.
     45  * @param {Function|Array} F Array of numbers, array of functions or function returning an array with defines the user coordinates of the point.
     46  * @parame {JXG.GeometryElement3D} slide Object the 3D point should be bound to. If null, the point is a free point.
     47  * @param {Object} attributes An object containing visual properties like in {@link JXG.Options#point3d} and
     48  * {@link JXG.Options#elements}, and optional a name and an id.
     49  * @see JXG.Board#generateName
     50  */
     51 JXG.Point3D = function (view, F, slide, attributes) {
     52     this.constructor(view.board, attributes, Const.OBJECT_TYPE_POINT3D, Const.OBJECT_CLASS_3D);
     53     this.constructor3D(view, "point3d");
     54
     55     this.board.finalizeAdding(this);
     56
     57     /**
     58      * Homogeneous coordinates of a Point3D, i.e. array of length 4: [w, x, y, z]. Usually, w=1 for finite points and w=0 for points
     59      * which are infinitely far.
     60      *
     61      * @example
     62      *   p.coords;
     63      *
     64      * @name Point3D#coords
     65      * @type Array
     66      * @private
     67      */
     68     this.coords = [0, 0, 0, 0];
     69
     70     /**
     71      * Function or array of functions or array of numbers defining the coordinates of the point, used in {@link updateCoords}.
     72      *
     73      * @name Point3D#F
     74      * @function
     75      * @private
     76      *
     77      * @see updateCoords
     78      */
     79     this.F = F;
     80
     81     /**
     82      * Optional slide element, i.e. element the Point3D lives on.
     83      *
     84      * @example
     85      *   p.slide;
     86      *
     87      * @name Point3D#slide
     88      * @type JXG.GeometryElement3D
     89      * @default null
     90      * @private
     91      *
     92      */
     93     this.slide = slide;
     94
     95     /**
     96      * Get x-coordinate of a 3D point.
     97      *
     98      * @name X
     99      * @memberOf Point3D
    100      * @function
    101      * @returns {Number}
    102      *
    103      * @example
    104      *   p.X();
    105      */
    106     this.X = function () {
    107         return this.coords[1];
    108     };
    109
    110     /**
    111      * Get y-coordinate of a 3D point.
    112      *
    113      * @name Y
    114      * @memberOf Point3D
    115      * @function
    116      * @returns Number
    117      *
    118      * @example
    119      *   p.Y();
    120      */
    121     this.Y = function () {
    122         return this.coords[2];
    123     };
    124
    125     /**
    126      * Get z-coordinate of a 3D point.
    127      *
    128      * @name Z
    129      * @memberOf Point3D
    130      * @function
    131      * @returns Number
    132      *
    133      * @example
    134      *   p.Z();
    135      */
    136     this.Z = function () {
    137         return this.coords[3];
    138     };
    139
    140     /**
    141      * Store the last position of the 2D point for the optimizer.
    142      *
    143      * @type Array
    144      * @private
    145      */
    146     this._params = null;
    147
    148     this._c2d = null;
    149
    150     this.methodMap = Type.deepCopy(this.methodMap, {
    151         // TODO
    152     });
    153 };
    154 JXG.Point3D.prototype = new JXG.GeometryElement();
    155 Type.copyPrototypeMethods(JXG.Point3D, JXG.GeometryElement3D, "constructor3D");
    156
    157 JXG.extend(
    158     JXG.Point3D.prototype,
    159     /** @lends JXG.Point3D.prototype */ {
    160         /**
    161          * Update the homogeneous coords array.
    162          *
    163          * @name updateCoords
    164          * @memberOf Point3D
    165          * @function
    166          * @returns {Object} Reference to the Point3D object
    167          * @private
    168          * @example
    169          *    p.updateCoords();
    170          */
    171         updateCoords: function () {
    172             var i;
    173
    174             if (Type.isFunction(this.F)) {
    175                 this.coords = [1].concat(Type.evaluate(this.F));
    176             } else {
    177                 this.coords[0] = 1;
    178                 for (i = 0; i < 3; i++) {
    179                     // Attention: if F is array of numbers, coords are not updated.
    180                     // Otherwise, dragging will not work anymore.
    181                     if (Type.isFunction(this.F[i])) {
    182                         this.coords[i + 1] = Type.evaluate(this.F[i]);
    183                     }
    184                 }
    185             }
    186             return this;
    187         },
    188
    189         /**
    190          * Initialize the coords array.
    191          *
    192          * @private
    193          * @returns {Object} Reference to the Point3D object
    194          */
    195         initCoords: function () {
    196             var i;
    197
    198             if (Type.isFunction(this.F)) {
    199                 this.coords = [1].concat(Type.evaluate(this.F));
    200             } else {
    201                 this.coords[0] = 1;
    202                 for (i = 0; i < 3; i++) {
    203                     this.coords[i + 1] = Type.evaluate(this.F[i]);
    204                 }
    205             }
    206             return this;
    207         },
    208
    209         /**
    210          * Normalize homogeneous coordinates such the the first coordinate (the w-coordinate is equal to 1 or 0)-
    211          *
    212          * @name normalizeCoords
    213          * @memberOf Point3D
    214          * @function
    215          * @returns {Object} Reference to the Point3D object
    216          * @private
    217          * @example
    218          *    p.normalizeCoords();
    219          */
    220         normalizeCoords: function () {
    221             if (Math.abs(this.coords[0]) > Mat.eps) {
    222                 this.coords[1] /= this.coords[0];
    223                 this.coords[2] /= this.coords[0];
    224                 this.coords[3] /= this.coords[0];
    225                 this.coords[0] = 1.0;
    226             }
    227             return this;
    228         },
    229
    230         /**
    231          * Set the position of a 3D point.
    232          *
    233          * @name setPosition
    234          * @memberOf Point3D
    235          * @function
    236          * @param {Array} coords 3D coordinates. Either of the form [x,y,z] (Euclidean) or [w,x,y,z] (homogeneous).
    237          * @param {Boolean} [noevent] If true, no events are triggered.
    238          * @returns {Object} Reference to the Point3D object
    239          *
    240          * @example
    241          *    p.setPosition([1, 3, 4]);
    242          */
    243         setPosition: function (coords, noevent) {
    244             var c = this.coords,
    245                 oc = this.coords.slice(); // Copy of original values
    246
    247             if (coords.length === 3) {
    248                 // Euclidean coordinates
    249                 c[0] = 1.0;
    250                 c[1] = coords[0];
    251                 c[2] = coords[1];
    252                 c[3] = coords[2];
    253             } else {
    254                 // Homogeneous coordinates (normalized)
    255                 c[0] = coords[0];
    256                 c[1] = coords[1];
    257                 c[2] = coords[2];
    258                 c[3] = coords[2];
    259                 this.normalizeCoords();
    260             }
    261
    262             // console.log(el.emitter, !noevent, oc[0] !== c[0] || oc[1] !== c[1] || oc[2] !== c[2] || oc[3] !== c[3]);
    263             // Not yet working
    264             // if (el.emitter && !noevent &&
    265             //     (oc[0] !== c[0] || oc[1] !== c[1] || oc[2] !== c[2] || oc[3] !== c[3])) {
    266             //     this.triggerEventHandlers(['update3D'], [oc]);
    267             // }
    268             return this;
    269         },
    270
    271         update: function (drag) {
    272             var c3d, foot;
    273
    274             // Update is called from two methods:
    275             // Once in setToPosition and
    276             // once in the subsequent board.update
    277             if (
    278                 this.element2D.draggable() &&
    279                 Geometry.distance(this._c2d, this.element2D.coords.usrCoords) !== 0
    280             ) {
    281                 if (this.slide) {
    282                     this.projectCoords2Surface();
    283                 } else {
    284                     if (this.view.isVerticalDrag()) {
    285                         // Drag the point in its vertical to the xy plane
    286                         c3d = this.view.project2DTo3DVertical(this.element2D, this.coords);
    287                     } else {
    288                         // Drag the point in its xy plane
    289                         foot = [1, 0, 0, this.coords[3]];
    290                         c3d = this.view.project2DTo3DPlane(this.element2D, [1, 0, 0, 1], foot);
    291                     }
    292                     if (c3d[0] !== 0) {
    293                         this.coords = this.view.project3DToCube(c3d);
    294                     }
    295                 }
    296             } else {
    297                 this.updateCoords();
    298                 // Update 2D point from its 3D view
    299                 this.element2D.coords.setCoordinates(
    300                     Const.COORDS_BY_USER,
    301                     this.view.project3DTo2D([1, this.X(), this.Y(), this.Z()])
    302                 );
    303             }
    304             this._c2d = this.element2D.coords.usrCoords.slice();
    305
    306             return this;
    307         },
    308
    309         updateRenderer: function () {
    310             this.needsUpdate = false;
    311             return this;
    312         },
    313
    314         projectCoords2Surface: function () {
    315             var n = 2, // # of variables
    316                 m = 2, // number of constraints
    317                 x = [0, 0],
    318                 // Various Cobyla constants, see Cobyla docs in Cobyja.js
    319                 rhobeg = 5.0,
    320                 rhoend = 1.0e-6,
    321                 iprint = 0,
    322                 maxfun = 200,
    323                 surface = this.slide,
    324                 that = this,
    325                 r,
    326                 c3d,
    327                 c2d,
    328                 _minFunc;
    329
    330             if (surface === null) {
    331                 return;
    332             }
    333
    334             _minFunc = function (n, m, x, con) {
    335                 var c3d = [
    336                         1,
    337                         surface.X(x[0], x[1]),
    338                         surface.Y(x[0], x[1]),
    339                         surface.Z(x[0], x[1])
    340                     ],
    341                     c2d = that.view.project3DTo2D(c3d);
    342
    343                 con[0] = that.element2D.X() - c2d[1];
    344                 con[1] = that.element2D.Y() - c2d[2];
    345
    346                 return con[0] * con[0] + con[1] * con[1];
    347             };
    348             if (Type.exists(this._params)) {
    349                 x = this._params.slice();
    350             }
    351             r = Mat.Nlp.FindMinimum(_minFunc, n, m, x, rhobeg, rhoend, iprint, maxfun);
    352
    353             c3d = [1, surface.X(x[0], x[1]), surface.Y(x[0], x[1]), surface.Z(x[0], x[1])];
    354             c2d = this.view.project3DTo2D(c3d);
    355             this._params = x;
    356             this.coords = c3d;
    357             this.element2D.coords.setCoordinates(Const.COORDS_BY_USER, c2d);
    358             this._c2d = c2d;
    359         },
    360
    361         // Not yet working
    362         __evt__update3D: function (oc) {}
    363     }
    364 );
    365
    366 /**
    367  * @class This element is used to provide a constructor for a 3D Point.
    368  * @pseudo
    369  * @description A Point3D object is defined by 3 coordinates [x,y,z].
    370  * <p>
    371  * All numbers can also be provided as functions returning a number.
    372  *
    373  * @name Point3D
    374  * @augments JXG.Point3D
    375  * @constructor
    376  * @throws {Exception} If the element cannot be constructed with the given parent
    377  * objects an exception is thrown.
    378  * @param {number,function_number,function_number,function} x,y,z The coordinates are given as x, y, z consisting of numbers of functions.
    379  * @param {array,function} F Alternatively, the coordinates can be supplied as
    380  *  <ul>
    381  *   <li>array arr=[x,y,z] of length 3 consisting of numbers or
    382  *   <li>function returning an array [x,y,z] of length 3 of numbers.
    383  * </ul>
    384  *
    385  * @example
    386  *    var bound = [-5, 5];
    387  *    var view = board.create('view3d',
    388  *        [[-6, -3], [8, 8],
    389  *        [bound, bound, bound]],
    390  *        {});
    391  *    var p = view.create('point3d', [1, 2, 2], { name:'A', size: 5 });
    392  *    var q = view.create('point3d', function() { return [p.X(), p.Y(), p.Z() - 3]; }, { name:'B', size: 5, fixed: true });
    393  *
    394  * </pre><div id="JXGb9ee8f9f-3d2b-4f73-8221-4f82c09933f1" class="jxgbox" style="width: 300px; height: 300px;"></div>
    395  * <script type="text/javascript">
    396  *     (function() {
    397  *         var board = JXG.JSXGraph.initBoard('JXGb9ee8f9f-3d2b-4f73-8221-4f82c09933f1',
    398  *             {boundingbox: [-8, 8, 8,-8], axis: false, showcopyright: false, shownavigation: false});
    399  *         var bound = [-5, 5];
    400  *         var view = board.create('view3d',
    401  *             [[-6, -3], [8, 8],
    402  *             [bound, bound, bound]],
    403  *             {});
    404  *         var p = view.create('point3d', [1, 2, 2], { name:'A', size: 5 });
    405  *         var q = view.create('point3d', function() { return [p.X(), p.Y(), p.Z() - 3]; }, { name:'B', size: 5 });
    406  *     })();
    407  *
    408  * </script><pre>
    409  *
    410  */
    411 JXG.createPoint3D = function (board, parents, attributes) {
    412     //   parents[0]: view
    413     // followed by
    414     //   parents[1]: function or array
    415     // or
    416     //   parents[1..3]: coordinates
    417
    418     var view = parents[0],
    419         attr, F, slide, c2d, el;
    420
    421     // If the last element of parents is a 3D object,
    422     // the point is a glider on that element.
    423     if (parents.length > 2 && Type.exists(parents[parents.length - 1].is3D)) {
    424         slide = parents.pop();
    425     } else {
    426         slide = null;
    427     }
    428
    429     if (parents.length === 2) {
    430         // [view, array|fun] (Array [x, y, z] | function) returning [x, y, z]
    431         F = parents[1];
    432     } else if (parents.length === 4) {
    433         // [view, x, y, z], (3 numbers | functions)
    434         F = parents.slice(1);
    435     } else {
    436         throw new Error(
    437             "JSXGraph: Can't create point3d with parent types '" +
    438                 typeof parents[0] +
    439                 "' and '" +
    440                 typeof parents[1] +
    441                 "'." +
    442                 "\nPossible parent types: [[x,y,z]], [x,y,z]"
    443         );
    444         //  "\nPossible parent types: [[x,y,z]], [x,y,z], [element,transformation]"); // TODO
    445     }
    446
    447     attr = Type.copyAttributes(attributes, board.options, 'point3d');
    448     el = new JXG.Point3D(view, F, slide, attr);
    449     el.initCoords();
    450
    451     c2d = view.project3DTo2D(el.coords);
    452
    453     attr = el.setAttr2D(attr);
    454     el.element2D = view.create('point', c2d, attr);
    455     el.addChild(el.element2D);
    456     el.inherits.push(el.element2D);
    457     el.element2D.setParents(el);
    458
    459     el._c2d = el.element2D.coords.usrCoords.slice(); // Store a copy of the coordinates to detect dragging
    460
    461     return el;
    462 };
    463
    464 JXG.registerElement("point3d", JXG.createPoint3D);
    465