1 /*
  2     Copyright 2008-2026
  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.js";
 32 import Const from "../base/constants.js";
 33 import Type from "../utils/type.js";
 34 import Mat from "../math/math.js";
 35 import Geometry from "../math/geometry.js";
 36 
 37 /**
 38  * A 3D point is a basic geometric element.
 39  * @class Creates a new 3D point object. Do not use this constructor to create a 3D point. Use {@link JXG.View3D#create} with
 40  * type {@link Point3D} instead.
 41  * @augments JXG.GeometryElement3D
 42  * @augments JXG.GeometryElement
 43  * @param {JXG.View3D} view The 3D view the point is drawn on.
 44  * @param {Function|Array} F Array of numbers, array of functions or function returning an array with defines the user coordinates of the point.
 45  * @param {JXG.GeometryElement3D} slide Object the 3D point should be bound to. If null, the point is a free point.
 46  * @param {Object} attributes An object containing visual properties like in {@link JXG.Options#point3d} and
 47  * {@link JXG.Options#elements}, and optionally a name and an id.
 48  * @see JXG.Board#generateName
 49  */
 50 JXG.Point3D = function (view, F, slide, attributes) {
 51     this.constructor(view.board, attributes, Const.OBJECT_TYPE_POINT3D, Const.OBJECT_CLASS_3D);
 52     this.constructor3D(view, 'point3d');
 53 
 54     this.board.finalizeAdding(this);
 55 
 56     // add the new point to its view's point list
 57     // if (view.visProp.depthorderpoints) {
 58     //     view.points.push(this);
 59     // }
 60 
 61     /**
 62      * Homogeneous coordinates of a Point3D, i.e. array of length 4 containing numbers: [w, x, y, z].
 63      * Usually, w=1 for finite points and w=0 for points which are infinitely far.
 64      * If coordinates of the point are supplied as functions, they are resolved in {@link Point3D#updateCoords} into numbers.
 65      *
 66      * @example
 67      *   p.coords;
 68      *
 69      * @name Point3D#coords
 70      * @type Array
 71      * @private
 72      */
 73     this.coords = [0, 0, 0, 0];
 74     this.initialCoords = [0, 0, 0, 0];
 75 
 76     /**
 77      * Function or array of functions or array of numbers defining the coordinates of the point, used in {@link updateCoords}.
 78      *
 79      * @name Point3D#F
 80      * @function
 81      * @private
 82      *
 83      * @see updateCoords
 84      */
 85     this.F = F;
 86 
 87     /**
 88      * Optional slide element, i.e. element the Point3D lives on.
 89      *
 90      * @example
 91      *   p.slide;
 92      *
 93      * @name Point3D#slide
 94      * @type JXG.GeometryElement3D
 95      * @default null
 96      * @private
 97      *
 98      */
 99     this.slide = slide;
100 
101     /**
102      * In case, the point is a glider, store the preimage of the coordinates in terms of the parametric definition of the host element.
103      * That is, if the host element `slide` is a curve, and the coordinates of the point are equal to `p` and `u = this.position[0]`, then
104      * `p = [slide.X(u), slide.Y(u), slide.Z(u)]`.
105      *
106      * @type Array
107      * @private
108      */
109     this.position = [];
110 
111     /**
112      * An array of coordinates for moveTo().  An in-progress move can be updated or cancelled by updating or clearing this array.  Use moveTo() instead of
113      * accessing this array directly.
114      * @type Array
115      * @private
116      */
117     this.movePath = [];
118     this.moveCallback = null;
119     this.moveInterval = null;
120 
121 
122     this._c2d = null;
123 
124     this.methodMap = Type.deepCopy(this.methodMap, {
125         // TODO
126     });
127 };
128 
129 JXG.Point3D.prototype = new JXG.GeometryElement();
130 Type.copyPrototypeMethods(JXG.Point3D, JXG.GeometryElement3D, 'constructor3D');
131 
132 JXG.extend(
133     JXG.Point3D.prototype,
134     /** @lends JXG.Point3D.prototype */ {
135 
136         /**
137          * Get x-coordinate of a 3D point.
138          *
139          * @name X
140          * @memberOf Point3D
141          * @function
142          * @returns {Number}
143          *
144          * @example
145          *   p.X();
146          */
147         X: function () {
148             return this.coords[1];
149         },
150 
151         /**
152          * Get y-coordinate of a 3D point.
153          *
154          * @name Y
155          * @memberOf Point3D
156          * @function
157          * @returns Number
158          *
159          * @example
160          *   p.Y();
161          */
162         Y: function () {
163             return this.coords[2];
164         },
165 
166         /**
167          * Get z-coordinate of a 3D point.
168          *
169          * @name Z
170          * @memberOf Point3D
171          * @function
172          * @returns Number
173          *
174          * @example
175          *   p.Z();
176          */
177         Z: function () {
178             return this.coords[3];
179         },
180 
181         /**
182          * Get w-coordinate of a 3D point.
183          *
184          * @name W
185          * @memberOf Point3D
186          * @function
187          * @returns Number
188          *
189          * @example
190          *   p.W();
191          */
192         W: function () {
193             return this.coords[0];
194         },
195 
196         /**
197          * Update the array {@link JXG.Point3D#coords} containing the homogeneous coords.
198          *
199          * @name updateCoords
200          * @memberOf Point3D
201          * @function
202          * @returns {Object} Reference to the Point3D object
203          * @private
204          * @see GeometryElement3D#update()
205          * @example
206          *    p.updateCoords();
207          */
208         updateCoords: function () {
209             var i,
210                 s = 0;
211 
212             if (Type.isFunction(this.F)) {
213                 this.coords = Type.evaluate(this.F);
214                 if (this.coords.length === 3) {
215                     this.coords.unshift(1);
216                 }
217             } else {
218                 if (this.F.length === 3) {
219                     this.coords[0] = 1;
220                     s = 1;
221                 }
222                 for (i = 0; i < this.F.length; i++) {
223                     // Attention: if F is array of numbers, coords may not be updated.
224                     // Otherwise, dragging will not work anymore.
225                     if (Type.isFunction(this.F[i])) {
226                         this.coords[s + i] = Type.evaluate(this.F[i]);
227                     }
228                 }
229             }
230 
231             return this;
232         },
233 
234         /**
235          * Initialize the coords array.
236          *
237          * @private
238          * @returns {Object} Reference to the Point3D object
239          */
240         initCoords: function () {
241             var i,
242                 s = 0;
243 
244 
245             if (Type.isFunction(this.F)) {
246                 this.coords = Type.evaluate(this.F);
247                 if (this.coords.length === 3) {
248                     this.coords.unshift(1);
249                 }
250             } else {
251                 if (this.F.length === 3) {
252                     this.coords[0] = 1;
253                     s = 1;
254                 }
255                 for (i = 0; i < this.F.length; i++) {
256                     this.coords[s + i] = Type.evaluate(this.F[i]);
257                 }
258             }
259             this.initialCoords = this.coords.slice();
260 
261             return this;
262         },
263 
264         /**
265          * Normalize homogeneous coordinates such the the first coordinate (the w-coordinate is equal to 1 or 0)-
266          *
267          * @name normalizeCoords
268          * @memberOf Point3D
269          * @function
270          * @returns {Object} Reference to the Point3D object
271          * @private
272          * @example
273          *    p.normalizeCoords();
274          */
275         normalizeCoords: function () {
276             if (Math.abs(this.coords[0]) > 1.e-14) {
277                 this.coords[1] /= this.coords[0];
278                 this.coords[2] /= this.coords[0];
279                 this.coords[3] /= this.coords[0];
280                 this.coords[0] = 1.0;
281             }
282             return this;
283         },
284 
285         /**
286          * Set the position of a 3D point.
287          *
288          * @name setPosition
289          * @memberOf Point3D
290          * @function
291          * @param {Array} coords 3D coordinates. Either of the form [x,y,z] (Euclidean) or [w,x,y,z] (homogeneous).
292          * @param {Boolean} [noevent] If true, no events are triggered (TODO)
293          * @returns {Object} Reference to the Point3D object
294          *
295          * @example
296          *    p.setPosition([1, 3, 4]);
297          */
298         setPosition: function (coords, noevent) {
299             var c = this.coords;
300             // oc = this.coords.slice(); // Copy of original values
301 
302             if (coords.length === 3) {
303                 // Euclidean coordinates
304                 c[0] = 1.0;
305                 c[1] = coords[0];
306                 c[2] = coords[1];
307                 c[3] = coords[2];
308             } else {
309                 // Homogeneous coordinates (normalized)
310                 c[0] = coords[0];
311                 c[1] = coords[1];
312                 c[2] = coords[2];
313                 c[3] = coords[3];
314                 this.normalizeCoords();
315             }
316 
317             // console.log(el.emitter, !noevent, oc[0] !== c[0] || oc[1] !== c[1] || oc[2] !== c[2] || oc[3] !== c[3]);
318             // Not yet working TODO
319             // if (el.emitter && !noevent &&
320             //     (oc[0] !== c[0] || oc[1] !== c[1] || oc[2] !== c[2] || oc[3] !== c[3])) {
321             //     this.triggerEventHandlers(['update3D'], [oc]);
322             // }
323             return this;
324         },
325 
326         // /**
327         //  * Add transformations to this element.
328         //  * @param {JXG.GeometryElement} el
329         //  * @param {JXG.Transformation|Array} transform Either one {@link JXG.Transformation}
330         //  * or an array of {@link JXG.Transformation}s.
331         //  * @returns {JXG.CoordsElement} Reference to itself.
332         //  */
333         addTransform: function (el, transform) {
334             this.addTransformGeneric(el, transform);
335             return this;
336         },
337 
338         updateTransform: function () {
339             var c, i;
340 
341             if (this.transformations.length === 0 || this.baseElement === null) {
342                 return this;
343             }
344 
345             if (this === this.baseElement) {
346                 c = this.initialCoords;
347             } else {
348                 c = this.baseElement.coords;
349             }
350             for (i = 0; i < this.transformations.length; i++) {
351                 this.transformations[i].update();
352                 c = Mat.matVecMult(this.transformations[i].matrix, c);
353             }
354             this.coords = c;
355 
356             return this;
357         },
358 
359         // Already documented in JXG.GeometryElement
360         update: function (drag) {
361             var c3d,         // Homogeneous 3D coordinates
362                 foot, res;
363 
364             if (
365                 this.element2D.draggable() &&
366                 Geometry.distance(this._c2d, this.element2D.coords.usrCoords) !== 0
367             ) {
368                 // Update is called from board.updateElements, e.g. after manipulating a
369                 // a slider or dragging a point.
370                 // Usually this followed by an update call using the other branch below.
371 
372                 if (this.slide /*&& this.slide.type === Const.OBJECT_TYPE_PLANE3D*/) {
373                     // Dragging 3D points with two degrees of freedom on a 3D plane.
374                     // On other slide object we still use the shift key, see below.
375 
376                     this.coords = this.slide.projectScreenCoords([this.element2D.X(), this.element2D.Y()], this.position, this.evalVisProp('cyclic'));
377                     this.element2D.coords.setCoordinates(
378                         Const.COORDS_BY_USER,
379                         this.view.project3DTo2D(this.coords)
380                     );
381                 } else {
382                     if (this.view.isVerticalDrag()) {
383                         // Drag the point in its vertical to the xy plane
384                         // If the point is outside of bbox3d,
385                         // c3d is already corrected.
386                         c3d = this.view.project2DTo3DVertical(this.element2D, this.coords);
387                     } else {
388                         // Drag the point in its xy plane
389                         foot = [1, 0, 0, this.coords[3]];
390                         c3d = this.view.project2DTo3DPlane(this.element2D, [1, 0, 0, 1], foot);
391                     }
392 
393                     if (c3d[0] !== 0) {
394                         // Check if c3d is inside of view.bbox3d
395                         // Otherwise, the coords are now corrected.
396                         res = this.view.project3DToCube(c3d);
397                         this.coords = res[0];
398 
399                         if (res[1]) {
400                             // The 3D coordinates have been corrected, now also correct the 2D element.
401                             this.element2D.coords.setCoordinates(
402                                 Const.COORDS_BY_USER,
403                                 this.view.project3DTo2D(this.coords)
404                             );
405                         }
406                         if (this.slide) {
407                             this.coords = this.slide.projectCoords([1, this.X(), this.Y(), this.Z()], this.position);
408                             this.element2D.coords.setCoordinates(
409                                 Const.COORDS_BY_USER,
410                                 this.view.project3DTo2D(this.coords)
411                             );
412                         }
413                     }
414                 }
415             } else {
416                 // Update 2D point from its 3D view, e.g. when rotating the view
417                 this.updateCoords()
418                     .updateTransform();
419 
420                 if (this.slide) {
421                     this.coords = this.slide.projectCoords([1, this.X(), this.Y(), this.Z()], this.position);
422                 }
423                 c3d = this.coords;
424                 this.element2D.coords.setCoordinates(
425                     Const.COORDS_BY_USER,
426                     this.view.project3DTo2D(c3d)
427                 );
428                 // this.zIndex = Mat.matVecMult(this.view.matrix3DRotShift, c3d)[3];
429                 this.zIndex = Mat.innerProduct(this.view.matrix3DRotShift[3], c3d);
430             }
431             this._c2d = this.element2D.coords.usrCoords.slice();
432 
433             return this;
434         },
435 
436         // Already documented in JXG.GeometryElement
437         updateRenderer: function () {
438             this.needsUpdate = false;
439             return this;
440         },
441 
442         /**
443          * Check whether a point's position is finite, i.e. the first entry is not zero.
444          * @returns {Boolean} True if the first entry of the coordinate vector is not zero; false otherwise.
445          */
446         testIfFinite: function () {
447             return Math.abs(this.coords[0]) > 1.e-12 ? true : false;
448             // return Type.cmpArrays(this.coords, [0, 0, 0, 0]);
449         },
450 
451         /**
452          * Calculate the distance from one point to another. If one of the points is on the plane at infinity, return positive infinity.
453          * @param {JXG.Point3D} pt The point to which the distance is calculated.
454          * @returns {Number} The distance
455          */
456         distance: function (pt) {
457             var eps_sq = 1e-12,
458                 c_this = this.coords,
459                 c_pt = pt.coords;
460 
461             if (c_this[0] * c_this[0] > eps_sq && c_pt[0] * c_pt[0] > eps_sq) {
462                 return Mat.hypot(
463                     c_pt[1] - c_this[1],
464                     c_pt[2] - c_this[2],
465                     c_pt[3] - c_this[3]
466                 );
467             } else {
468                 return Number.POSITIVE_INFINITY;
469             }
470         },
471 
472 
473 
474         /**
475         * Starts an animated point movement towards the given coordinates <tt>where</tt>.
476         * The animation is done after <tt>time</tt> milliseconds.
477         * If the second parameter is not given or is equal to 0, coordinates are changed without animation.
478         * @param {Array} where Array containing the target coordinate in cartesian or homogenous form.
479         * @param {Number} [time] Number of milliseconds the animation should last.
480         * @param {Object} [options] Optional settings for the animation
481         * @param {function} [options.callback] A function that is called as soon as the animation is finished.
482         * @param {String} [options.effect='<>'|'>'|'<'] animation effects like speed fade in and out. possible values are
483         * '<>' for speed increase on start and slow down at the end (default), '<' for speed up, '>' for slow down, and '--' for constant speed during
484         * the whole animation.
485         * @see JXG.Point3D#moveAlong
486         * @see JXG.Point#moveTo
487         * @example
488         * // visit a coordinate, then use callback to visit a second coordinate.
489         * const board = JXG.JSXGraph.initBoard('jxgbox')
490         * var view = board.create(
491         *     'view3d',
492         *     [[-6, -3], [8, 8],
493         *     [[-3, 3], [-3, 3], [-3, 3]]]);
494         *
495         *  let A = view.create('point3d', [0, 0, 0]);
496         *
497         *  // move A with callbacks
498         *  board.create('button', [-4, 4.3, 'callbacks', () => {
499         *    A.moveTo([3, 3, 3], 3000,
500         *       {
501         *          callback: () => A.moveTo([-3, -3, -3], 3000, {
502         *              callback: () => A.moveTo([0, 0, 0],1000), effect: '<'
503         *          }),
504         *          effect: '>'
505         *       })
506         *     }])
507         *
508         *   // move A with async/await
509         *   board.create('button', [-3, 4.3, 'async/await', async () => {
510         *       await A.moveTo([3, 3, 3], 3000, { effect: '>' });
511         *       await A.moveTo([-3, -3, -3], 3000, { effect: '<' });
512         *       A.moveTo([0, 0, 0],1000)
513         *   }])
514         *  </pre><div id="JXG0f35a50e-e99d-11e8-a1ca-cba3b0c2aad4" class="jxgbox" style="width: 300px; height: 300px;"></div>
515         * <script type="text/javascript">
516         * {
517         * const board = JXG.JSXGraph.initBoard('JXG0f35a50e-e99d-11e8-a1ca-cba3b0c2aad4')
518         * var view = board.create(
519         *     'view3d',
520         *     [[-6, -3], [8, 8],
521         *     [[-3, 3], [-3, 3], [-3, 3]]]);
522         *
523         * let A = view.create('point3d', [0, 0, 0]);
524         *  // move A with callbacks
525         *  board.create('button', [-4, 4.3, 'callbacks', () => {
526         *    A.moveTo([3, 3, 3], 3000,
527         *       {
528         *          callback: () => A.moveTo([-3, -3, -3], 3000, {
529         *              callback: () => A.moveTo([0, 0, 0],1000), effect: '<'
530         *          }),
531         *          effect: '>'
532         *       })
533         *     }])
534         *
535         *   // move A with async/await
536         *   board.create('button', [-1, 4.3, 'async/await', async () => {
537         *       await A.moveTo([3, 3, 3], 3000, { effect: '>' });
538         *       await A.moveTo([-3, -3, -3], 3000, { effect: '<' });
539         *       A.moveTo([0, 0, 0],1000)
540         *   }])
541         * }
542         * </script><pre>
543         */
544         moveTo: function (where, time, options) {
545             options = options || {};
546 
547             var i,
548                 steps = Math.ceil(time / this.board.attr.animationdelay),
549                 X = where[0],
550                 Y = where[1],
551                 Z = where[2],
552                 dX = this.coords[1] - X,
553                 dY = this.coords[2] - Y,
554                 dZ = this.coords[3] - Z,
555                 doneCallback = () => { },
556                 stepFun;
557 
558             if (options.callback)
559                 doneCallback = options.callback;  // unload
560 
561 
562             /** @ignore */
563             stepFun = function (i) {
564                 var x = i / steps;  // absolute progress of the animatin
565 
566                 if (options.effect) {
567                     if (options.effect === "<>") {
568                         return Math.pow(Math.sin((x * Math.PI) / 2), 2);
569                     }
570                     if (options.effect === "<") {   // cubic ease in
571                         return x * x * x;
572                     }
573                     if (options.effect === ">") {   // cubic ease out
574                         return 1 - Math.pow(1 - x, 3);
575                     }
576                     if (options.effect === "==") {
577                         return i / steps;       // linear
578                     }
579                     throw new Error("valid effects are '==', '<>', '>', and '<'.");
580                 }
581                 return i / steps;  // default
582             };
583 
584             // immediate move, no time
585             if (
586                 !Type.exists(time) ||
587                 time === 0
588                 // check for tiny move, is this necessary?
589                 // Math.abs(where.usrCoords[0] - this.coords.usrCoords[0]) > Mat.eps
590             ) {
591                 this.setPosition([X, Y, Z], true);  // no event here
592                 return this.board.update(this);
593             }
594 
595             // In case there is no callback and we are already at the endpoint we can stop here
596             if (
597                 !Type.exists(options.callback) &&
598                 Math.abs(dX) < Mat.eps &&
599                 Math.abs(dY) < Mat.eps &&
600                 Math.abs(dZ) < Mat.eps
601             ) {
602                 return this;
603             }
604 
605             this.animationPath = [];
606             for (i = steps; i >= 0; i--) {
607                 this.animationPath[steps - i] = [
608                     X + dX * stepFun(i),
609                     Y + dY * stepFun(i),
610                     Z + dZ * stepFun(i)
611                 ];
612             }
613 
614             return this.moveAlong(this.animationPath, time,
615                 { callback: doneCallback });
616 
617         },
618 
619         /**
620          * Move along a path defined by an array of coordinates
621          * @param {number[][]} [traversePath] Array of path coordinates (either cartesian or homogenous).
622          * @param {number} [time] Number of milliseconds the animation should last.
623          * @param {Object} [options] 'callback' and 'interpolate'.  see {@link JXG.CoordsElement#moveAlong},
624          * @example
625          *const board = JXG.JSXGraph.initBoard('jxgbox')
626          *var view = board.create(
627          *    'view3d',
628          *    [[-6, -3], [8, 8],
629          *    [[-3, 3], [-3, 3], [-3, 3]]]);
630          *
631          * board.create('button', [-4, 4.5, 'start', () => {
632          *      let A = view.create('point3d', [0, 0, 0]);
633          *      A.moveAlong([[3, 3, 3], [-2, -1, -2], [-1, -1, -1], [-1, -2, 1]], 3000,
634          *         { callback: () => board.create('text', [-4, 4, 'done!']) })
635          *}])
636          *
637          * </pre><div id="JXGa45032e5-a517-4f1d-868a-abc698d344cf" class="jxgbox" style="width: 300px; height: 300px;"></div>
638          * <script type="text/javascript">
639          *     (function() {
640          * const board = JXG.JSXGraph.initBoard("JXGa45032e5-a517-4f1d-868a-abc698d344cf")
641          * var view = board.create(
642          *     'view3d',
643          *     [[-6, -3], [8, 8],
644          *     [[-3, 3], [-3, 3], [-3, 3]]]);
645          *
646          * board.create('button', [-4, 4.5, 'start', () => {
647          *      let A = view.create('point3d', [0, 0, 0]);
648          *      A.moveAlong([[3, 3, 3], [-2, -1, -2], [-1, -1, -1], [-1, -2, 1]], 3000,
649          *       { callback: () => board.create('text', [-4, 4, 'done!']) })
650          * }])
651          *
652          * })();
653          *
654          * </script><pre>
655          *
656          */
657         moveAlong: function (traversePath, time, options) {
658             let stepTime = time/traversePath.length;   // will be same as this.board.attr.animationdelay if called by MoveTo
659 
660 
661             // unload the options
662             if (Type.isObject(options)) {
663                 if ('callback' in options)
664                     this.moveCallback = options.callback;
665                 // TODO:add interpolation using Neville.  How?  easiest is add interpolation to path before start
666                 // if ('interpolate' in options) interpolate = options.interpolate;
667             }
668 
669 
670             if (this.movePath.length > 0) {         // existing move in progress
671                 this.movePath = traversePath;       // set the new path and return ??
672                 return;                             // promise is still outstanding
673             }
674 
675             // no move currently in progress
676             this.movePath = traversePath;           // set the new path and return a promise
677             return new Promise((resolve, reject) => {
678                 this.moveInterval = setInterval(() => {
679                     if (this.movePath.length > 0) {
680                         let coord = this.movePath.shift();
681                         this.setPosition(coord, true);  // no events during transit
682                         this.board.update(this);
683                     }
684                     if (this.movePath.length === 0) {   // now shorter than previous test
685                         clearInterval(this.moveInterval);
686                         resolve();
687                         if (Type.isFunction(this.moveCallback)) {
688                             this.moveCallback(); // invoke the callback
689                         }
690                     }
691                 }, stepTime);
692             });
693         },
694 
695 
696 
697 
698         // Not yet working
699         __evt__update3D: function (oc) { }
700     }
701 );
702 
703 /**
704  * @class A Point3D object is defined by three coordinates [x,y,z], or a function returning an array with three numbers.
705  * Alternatively, all numbers can also be provided as functions returning a number.
706  *
707  * @pseudo
708  * @name Point3D
709  * @augments JXG.Point3D
710  * @constructor
711  * @throws {Exception} If the element cannot be constructed with the given parent
712  * objects an exception is thrown.
713  * @param {number,function_number,function_number,function_JXG.GeometryElement3D} x,y,z,[slide=undefined] The coordinates are given as x, y, z consisting of numbers or functions.
714  * If an optional 3D element "slide" is supplied, the point is a glider on that element. At the time of version v1.11, only elements of type line3d are supperted as glider hosts.
715  * @param {array,function_JXG.GeometryElement3D} F,[slide=null] Alternatively, the coordinates can be supplied as
716  *  <ul>
717  *   <li>function returning an array [x,y,z] of length 3 of numbers or
718  *   <li>array arr=[x,y,z] of length 3 consisting of numbers
719  * </ul>
720  * If an optional 3D element "slide" is supplied, the point is a glider on that element.
721  *
722  * @example
723  *    var bound = [-5, 5];
724  *    var view = board.create('view3d',
725  *        [[-6, -3], [8, 8],
726  *        [bound, bound, bound]],
727  *        {});
728  *    var p = view.create('point3d', [1, 2, 2], { name:'A', size: 5 });
729  *    var q = view.create('point3d', function() { return [p.X(), p.Y(), p.Z() - 3]; }, { name:'B', size: 3, fixed: true });
730  *    var w = view.create('point3d', [ () => p.X() + 3, () => p.Y(), () => p.Z() - 2], { name:'C', size: 3, fixed: true });
731  *
732  * </pre><div id="JXGb9ee8f9f-3d2b-4f73-8221-4f82c09933f1" class="jxgbox" style="width: 300px; height: 300px;"></div>
733  * <script type="text/javascript">
734  *     (function() {
735  *         var board = JXG.JSXGraph.initBoard('JXGb9ee8f9f-3d2b-4f73-8221-4f82c09933f1',
736  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
737  *         var bound = [-5, 5];
738  *         var view = board.create('view3d',
739  *             [[-6, -3], [8, 8],
740  *             [bound, bound, bound]],
741  *             {});
742  *         var p = view.create('point3d', [1, 2, 2], { name:'A', size: 5 });
743  *         var q = view.create('point3d', function() { return [p.X(), p.Y(), p.Z() - 3]; }, { name:'B', size: 3 });
744  *         var w = view.create('point3d', [ () => p.X() + 3, () => p.Y(), () => p.Z() - 2], { name:'C', size: 3, fixed: true });
745  *     })();
746  *
747  * </script><pre>
748  *
749  * @example
750  *     // Glider on sphere
751  *     var view = board.create(
752  *         'view3d',
753  *         [[-6, -3], [8, 8],
754  *         [[-3, 3], [-3, 3], [-3, 3]]],
755  *         {
756  *             depthOrder: {
757  *                 enabled: true
758  *             },
759  *             projection: 'central',
760  *             xPlaneRear: {fillOpacity: 0.2, gradient: null},
761  *             yPlaneRear: {fillOpacity: 0.2, gradient: null},
762  *             zPlaneRear: {fillOpacity: 0.2, gradient: null}
763  *         }
764  *     );
765  *
766  *     // Two points
767  *     var center = view.create('point3d', [0, 0, 0], {withLabel: false, size: 2});
768  *     var point = view.create('point3d', [2, 0, 0], {withLabel: false, size: 2});
769  *
770  *     // Sphere
771  *     var sphere = view.create('sphere3d', [center, point], {fillOpacity: 0.8});
772  *
773  *     // Glider on sphere
774  *     var glide = view.create('point3d', [2, 2, 0, sphere], {withLabel: false, color: 'red', size: 4});
775  *     var l1 = view.create('line3d', [glide, center], { strokeWidth: 2, dash: 2 });
776  *
777  * </pre><div id="JXG672fe3c7-e6fd-48e0-9a24-22f51f2dfa71" class="jxgbox" style="width: 300px; height: 300px;"></div>
778  * <script type="text/javascript">
779  *     (function() {
780  *         var board = JXG.JSXGraph.initBoard('JXG672fe3c7-e6fd-48e0-9a24-22f51f2dfa71',
781  *             {boundingbox: [-8, 8, 8,-8], axis: false, showcopyright: false, shownavigation: false});
782  *         var view = board.create(
783  *             'view3d',
784  *             [[-6, -3], [8, 8],
785  *             [[-3, 3], [-3, 3], [-3, 3]]],
786  *             {
787  *                 depthOrder: {
788  *                     enabled: true
789  *                 },
790  *                 projection: 'central',
791  *                 xPlaneRear: {fillOpacity: 0.2, gradient: null},
792  *                 yPlaneRear: {fillOpacity: 0.2, gradient: null},
793  *                 zPlaneRear: {fillOpacity: 0.2, gradient: null}
794  *             }
795  *         );
796  *
797  *         // Two points
798  *         var center = view.create('point3d', [0, 0, 0], {withLabel: false, size: 2});
799  *         var point = view.create('point3d', [2, 0, 0], {withLabel: false, size: 2});
800  *
801  *         // Sphere
802  *         var sphere = view.create('sphere3d', [center, point], {fillOpacity: 0.8});
803  *
804  *         // Glider on sphere
805  *         var glide = view.create('point3d', [2, 2, 0, sphere], {withLabel: false, color: 'red', size: 4});
806  *         var l1 = view.create('line3d', [glide, center], { strokeWidth: 2, dash: 2 });
807  *
808  *     })();
809  *
810  * </script><pre>
811  *
812  */
813 JXG.createPoint3D = function (board, parents, attributes) {
814     //   parents[0]: view
815     // followed by
816     //   parents[1]: function or array
817     // or
818     //   parents[1..3]: coordinates
819 
820     var view = parents[0],
821         attr, F, slide, c2d, el,
822         base = null,
823         transform = null;
824 
825     // If the last element of `parents` is a 3D object,
826     // the point is a glider on that element.
827     if (parents.length > 2 &&
828         Type.exists(parents[parents.length - 1].is3D) &&
829         !Type.isTransformationOrArray(parents[parents.length - 1])
830     ) {
831         slide = parents.pop();
832     } else {
833         slide = null;
834     }
835 
836     if (parents.length === 2) {
837         // [view, array|fun] (Array [x, y, z] | function) returning [x, y, z]
838         F = parents[1];
839     } else if (parents.length === 3 &&
840         Type.isPoint3D(parents[1]) &&
841         Type.isTransformationOrArray(parents[2])
842     ) {
843         F = [0, 0, 0];
844         base = parents[1];
845         transform = parents[2];
846     } else if (parents.length === 4) {
847         // [view, x, y, z], (3 numbers | functions)
848         F = parents.slice(1);
849     } else if (parents.length === 5) {
850         // [view, w, x, y, z], (4 numbers | functions)
851         F = parents.slice(1);
852     } else {
853         throw new Error(
854             "JSXGraph: Can't create point3d with parent types '" +
855             typeof parents[1] +
856             "' and '" +
857             typeof parents[2] +
858             "'." +
859             "\nPossible parent types: [[x,y,z]], [x,y,z], or [[x,y,z], slide], () => [x, y, z], or [point, transformation(s)]"
860         );
861         //  "\nPossible parent types: [[x,y,z]], [x,y,z], [element,transformation]"); // TODO
862     }
863 
864     attr = Type.copyAttributes(attributes, board.options, 'point3d');
865     el = new JXG.Point3D(view, F, slide, attr);
866     el.initCoords();
867     if (base !== null && transform !== null) {
868         el.addTransform(base, transform);
869     }
870 
871     c2d = view.project3DTo2D(el.coords);
872 
873     attr = el.setAttr2D(attr);
874     el.element2D = view.create('point', c2d, attr);
875     el.element2D.view = view;
876     el.addChild(el.element2D);
877     el.inherits.push(el.element2D);
878     el.element2D.setParents(el);
879 
880     // If this point is a glider, record that in the update tree
881     if (el.slide) {
882         el.slide.addChild(el);
883         el.setParents(el.slide);
884     }
885     if (base) {
886         el.setParents(base);
887     }
888 
889     el._c2d = el.element2D.coords.usrCoords.slice(); // Store a copy of the coordinates to detect dragging
890 
891     return el;
892 };
893 
894 JXG.registerElement("point3d", JXG.createPoint3D);
895 
896