1 /*
  2     Copyright 2008-2025
  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 the 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 optional 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[2];
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                 if (this.view.isVerticalDrag()) {
372                     // Drag the point in its vertical to the xy plane
373                     // If the point is outside of bbox3d,
374                     // c3d is already corrected.
375                     c3d = this.view.project2DTo3DVertical(this.element2D, this.coords);
376                 } else {
377                     // Drag the point in its xy plane
378                     foot = [1, 0, 0, this.coords[3]];
379                     c3d = this.view.project2DTo3DPlane(this.element2D, [1, 0, 0, 1], foot);
380                 }
381 
382                 if (c3d[0] !== 0) {
383                     // Check if c3d is inside of view.bbox3d
384                     // Otherwise, the coords are now corrected.
385                     res = this.view.project3DToCube(c3d);
386                     this.coords = res[0];
387 
388                     if (res[1]) {
389                         // The 3D coordinates have been corrected, now
390                         // also correct the 2D element.
391                         this.element2D.coords.setCoordinates(
392                             Const.COORDS_BY_USER,
393                             this.view.project3DTo2D(this.coords)
394                         );
395                     }
396                     if (this.slide) {
397                         this.coords = this.slide.projectCoords([1, this.X(), this.Y(), this.Z()], this.position);
398                         this.element2D.coords.setCoordinates(
399                             Const.COORDS_BY_USER,
400                             this.view.project3DTo2D(this.coords)
401                         );
402                     }
403                 }
404 
405             } else {
406                 // Update 2D point from its 3D view, e.g. when rotating the view
407                 this.updateCoords()
408                     .updateTransform();
409 
410                 if (this.slide) {
411                     this.coords = this.slide.projectCoords([1, this.X(), this.Y(), this.Z()], this.position);
412                 }
413                 c3d = this.coords;
414                 this.element2D.coords.setCoordinates(
415                     Const.COORDS_BY_USER,
416                     this.view.project3DTo2D(c3d)
417                 );
418                 // this.zIndex = Mat.matVecMult(this.view.matrix3DRotShift, c3d)[3];
419                 this.zIndex = Mat.innerProduct(this.view.matrix3DRotShift[3], c3d);
420             }
421             this._c2d = this.element2D.coords.usrCoords.slice();
422 
423             return this;
424         },
425 
426         // Already documented in JXG.GeometryElement
427         updateRenderer: function () {
428             this.needsUpdate = false;
429             return this;
430         },
431 
432         /**
433          * Check whether a point's position is finite, i.e. the first entry is not zero.
434          * @returns {Boolean} True if the first entry of the coordinate vector is not zero; false otherwise.
435          */
436         testIfFinite: function () {
437             return Math.abs(this.coords[0]) > 1.e-12 ? true : false;
438             // return Type.cmpArrays(this.coords, [0, 0, 0, 0]);
439         },
440 
441         /**
442          * Calculate the distance from one point to another. If one of the points is on the plane at infinity, return positive infinity.
443          * @param {JXG.Point3D} pt The point to which the distance is calculated.
444          * @returns {Number} The distance
445          */
446         distance: function (pt) {
447             var eps_sq = 1e-12,
448                 c_this = this.coords,
449                 c_pt = pt.coords;
450 
451             if (c_this[0] * c_this[0] > eps_sq && c_pt[0] * c_pt[0] > eps_sq) {
452                 return Mat.hypot(
453                     c_pt[1] - c_this[1],
454                     c_pt[2] - c_this[2],
455                     c_pt[3] - c_this[3]
456                 );
457             } else {
458                 return Number.POSITIVE_INFINITY;
459             }
460         },
461 
462 
463 
464         /**
465         * Starts an animated point movement towards the given coordinates <tt>where</tt>.
466         * The animation is done after <tt>time</tt> milliseconds.
467         * If the second parameter is not given or is equal to 0, coordinates are changed without animation.
468         * @param {Array} where Array containing the target coordinate in cartesian or homogenous form.
469         * @param {Number} [time] Number of milliseconds the animation should last.
470         * @param {Object} [options] Optional settings for the animation
471         * @param {function} [options.callback] A function that is called as soon as the animation is finished.
472         * @param {String} [options.effect='<>'|'>'|'<'] animation effects like speed fade in and out. possible values are
473         * '<>' for speed increase on start and slow down at the end (default), '<' for speed up, '>' for slow down, and '--' for constant speed during
474         * the whole animation.
475         * @see JXG.Point3D#moveAlong
476         * @see JXG.Point#moveTo
477         * @example
478         * // visit a coordinate, then use callback to visit a second coordinate.
479         * const board = JXG.JSXGraph.initBoard('jxgbox')
480         * var view = board.create(
481         *     'view3d',
482         *     [[-6, -3], [8, 8],
483         *     [[-3, 3], [-3, 3], [-3, 3]]]);
484         *
485         *  let A = view.create('point3d', [0, 0, 0]);
486         *
487         *  // move A with callbacks
488         *  board.create('button', [-4, 4.3, 'callbacks', () => {
489         *    A.moveTo([3, 3, 3], 3000,
490         *       {
491         *          callback: () => A.moveTo([-3, -3, -3], 3000, {
492         *              callback: () => A.moveTo([0, 0, 0],1000), effect: '<'
493         *          }),
494         *          effect: '>'
495         *       })
496         *     }])
497         *
498         *   // move A with async/await
499         *   board.create('button', [-3, 4.3, 'async/await', async () => {
500         *       await A.moveTo([3, 3, 3], 3000, { effect: '>' });
501         *       await A.moveTo([-3, -3, -3], 3000, { effect: '<' });
502         *       A.moveTo([0, 0, 0],1000)
503         *   }])
504         *  </pre><div id="JXG0f35a50e-e99d-11e8-a1ca-cba3b0c2aad4" class="jxgbox" style="width: 300px; height: 300px;"></div>
505         * <script type="text/javascript">
506         * {
507         * const board = JXG.JSXGraph.initBoard('JXG0f35a50e-e99d-11e8-a1ca-cba3b0c2aad4')
508         * var view = board.create(
509         *     'view3d',
510         *     [[-6, -3], [8, 8],
511         *     [[-3, 3], [-3, 3], [-3, 3]]]);
512         *
513         * let A = view.create('point3d', [0, 0, 0]);
514         *  // move A with callbacks
515         *  board.create('button', [-4, 4.3, 'callbacks', () => {
516         *    A.moveTo([3, 3, 3], 3000,
517         *       {
518         *          callback: () => A.moveTo([-3, -3, -3], 3000, {
519         *              callback: () => A.moveTo([0, 0, 0],1000), effect: '<'
520         *          }),
521         *          effect: '>'
522         *       })
523         *     }])
524         *
525         *   // move A with async/await
526         *   board.create('button', [-1, 4.3, 'async/await', async () => {
527         *       await A.moveTo([3, 3, 3], 3000, { effect: '>' });
528         *       await A.moveTo([-3, -3, -3], 3000, { effect: '<' });
529         *       A.moveTo([0, 0, 0],1000)
530         *   }])
531         * }
532         * </script><pre>
533         */
534         moveTo: function (where, time, options) {
535             options = options || {};
536 
537             var i,
538                 steps = Math.ceil(time / this.board.attr.animationdelay),
539                 X = where[0],
540                 Y = where[1],
541                 Z = where[2],
542                 dX = this.coords[1] - X,
543                 dY = this.coords[2] - Y,
544                 dZ = this.coords[3] - Z,
545                 doneCallback = () => { },
546                 stepFun;
547 
548             if (options.callback)
549                 doneCallback = options.callback;  // unload
550 
551 
552             /** @ignore */
553             stepFun = function (i) {
554                 var x = i / steps;  // absolute progress of the animatin
555 
556                 if (options.effect) {
557                     if (options.effect === "<>") {
558                         return Math.pow(Math.sin((x * Math.PI) / 2), 2);
559                     }
560                     if (options.effect === "<") {   // cubic ease in
561                         return x * x * x;
562                     }
563                     if (options.effect === ">") {   // cubic ease out
564                         return 1 - Math.pow(1 - x, 3);
565                     }
566                     if (options.effect === "==") {
567                         return i / steps;       // linear
568                     }
569                     throw new Error("valid effects are '==', '<>', '>', and '<'.");
570                 }
571                 return i / steps;  // default
572             };
573 
574             // immediate move, no time
575             if (
576                 !Type.exists(time) ||
577                 time === 0
578                 // check for tiny move, is this necessary?
579                 // Math.abs(where.usrCoords[0] - this.coords.usrCoords[0]) > Mat.eps
580             ) {
581                 this.setPosition([X, Y, Z], true);  // no event here
582                 return this.board.update(this);
583             }
584 
585             // In case there is no callback and we are already at the endpoint we can stop here
586             if (
587                 !Type.exists(options.callback) &&
588                 Math.abs(dX) < Mat.eps &&
589                 Math.abs(dY) < Mat.eps &&
590                 Math.abs(dZ) < Mat.eps
591             ) {
592                 return this;
593             }
594 
595             this.animationPath = [];
596             for (i = steps; i >= 0; i--) {
597                 this.animationPath[steps - i] = [
598                     X + dX * stepFun(i),
599                     Y + dY * stepFun(i),
600                     Z + dZ * stepFun(i)
601                 ];
602             }
603 
604             return this.moveAlong(this.animationPath, time,
605                 { callback: doneCallback });
606 
607         },
608 
609         /**
610          * Move along a path defined by an array of coordinates
611          * @param {number[][]} [traversePath] Array of path coordinates (either cartesian or homogenous).
612          * @param {number} [time] Number of milliseconds the animation should last.
613          * @param {Object} [options] 'callback' and 'interpolate'.  see {@link JXG.CoordsElement#moveAlong},
614          * @example
615          *const board = JXG.JSXGraph.initBoard('jxgbox')
616          *var view = board.create(
617          *    'view3d',
618          *    [[-6, -3], [8, 8],
619          *    [[-3, 3], [-3, 3], [-3, 3]]]);
620          *
621          * board.create('button', [-4, 4.5, 'start', () => {
622          *      let A = view.create('point3d', [0, 0, 0]);
623          *      A.moveAlong([[3, 3, 3], [-2, -1, -2], [-1, -1, -1], [-1, -2, 1]], 3000,
624          *         { callback: () => board.create('text', [-4, 4, 'done!']) })
625          *}])
626          *
627          * </pre><div id="JXGa45032e5-a517-4f1d-868a-abc698d344cf" class="jxgbox" style="width: 300px; height: 300px;"></div>
628          * <script type="text/javascript">
629          *     (function() {
630          * const board = JXG.JSXGraph.initBoard("JXGa45032e5-a517-4f1d-868a-abc698d344cf")
631          * var view = board.create(
632          *     'view3d',
633          *     [[-6, -3], [8, 8],
634          *     [[-3, 3], [-3, 3], [-3, 3]]]);
635          *
636          * board.create('button', [-4, 4.5, 'start', () => {
637          *      let A = view.create('point3d', [0, 0, 0]);
638          *      A.moveAlong([[3, 3, 3], [-2, -1, -2], [-1, -1, -1], [-1, -2, 1]], 3000,
639          *       { callback: () => board.create('text', [-4, 4, 'done!']) })
640          * }])
641          *
642          * })();
643          *
644          * </script><pre>
645          *
646          */
647         moveAlong: function (traversePath, time, options) {
648             let stepTime = time/traversePath.length;   // will be same as this.board.attr.animationdelay if called by MoveTo
649 
650 
651             // unload the options
652             if (Type.isObject(options)) {
653                 if ('callback' in options)
654                     this.moveCallback = options.callback;
655                 // TODO:add interpolation using Neville.  How?  easiest is add interpolation to path before start
656                 // if ('interpolate' in options) interpolate = options.interpolate;
657             }
658 
659 
660             if (this.movePath.length > 0) {         // existing move in progress
661                 this.movePath = traversePath;       // set the new path and return ??
662                 return;                             // promise is still outstanding
663             }
664 
665             // no move currently in progress
666             this.movePath = traversePath;           // set the new path and return a promise
667             return new Promise((resolve, reject) => {
668                 this.moveInterval = setInterval(() => {
669                     if (this.movePath.length > 0) {
670                         let coord = this.movePath.shift();
671                         this.setPosition(coord, true);  // no events during transit
672                         this.board.update(this);
673                     }
674                     if (this.movePath.length === 0) {   // now shorter than previous test
675                         clearInterval(this.moveInterval);
676                         resolve();
677                         if (Type.isFunction(this.moveCallback)) {
678                             this.moveCallback(); // invoke the callback
679                         }
680                     }
681                 }, stepTime);
682             });
683         },
684 
685 
686 
687 
688         // Not yet working
689         __evt__update3D: function (oc) { }
690     }
691 );
692 
693 /**
694  * @class A Point3D object is defined by three coordinates [x,y,z], or a function returning an array with three numbers.
695  * Alternatively, all numbers can also be provided as functions returning a number.
696  *
697  * @pseudo
698  * @name Point3D
699  * @augments JXG.Point3D
700  * @constructor
701  * @throws {Exception} If the element cannot be constructed with the given parent
702  * objects an exception is thrown.
703  * @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.
704  * 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.
705  * @param {array,function_JXG.GeometryElement3D} F,[slide=null] Alternatively, the coordinates can be supplied as
706  *  <ul>
707  *   <li>function returning an array [x,y,z] of length 3 of numbers or
708  *   <li>array arr=[x,y,z] of length 3 consisting of numbers
709  * </ul>
710  * If an optional 3D element "slide" is supplied, the point is a glider on that element.
711  *
712  * @example
713  *    var bound = [-5, 5];
714  *    var view = board.create('view3d',
715  *        [[-6, -3], [8, 8],
716  *        [bound, bound, bound]],
717  *        {});
718  *    var p = view.create('point3d', [1, 2, 2], { name:'A', size: 5 });
719  *    var q = view.create('point3d', function() { return [p.X(), p.Y(), p.Z() - 3]; }, { name:'B', size: 3, fixed: true });
720  *    var w = view.create('point3d', [ () => p.X() + 3, () => p.Y(), () => p.Z() - 2], { name:'C', size: 3, fixed: true });
721  *
722  * </pre><div id="JXGb9ee8f9f-3d2b-4f73-8221-4f82c09933f1" class="jxgbox" style="width: 300px; height: 300px;"></div>
723  * <script type="text/javascript">
724  *     (function() {
725  *         var board = JXG.JSXGraph.initBoard('JXGb9ee8f9f-3d2b-4f73-8221-4f82c09933f1',
726  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
727  *         var bound = [-5, 5];
728  *         var view = board.create('view3d',
729  *             [[-6, -3], [8, 8],
730  *             [bound, bound, bound]],
731  *             {});
732  *         var p = view.create('point3d', [1, 2, 2], { name:'A', size: 5 });
733  *         var q = view.create('point3d', function() { return [p.X(), p.Y(), p.Z() - 3]; }, { name:'B', size: 3 });
734  *         var w = view.create('point3d', [ () => p.X() + 3, () => p.Y(), () => p.Z() - 2], { name:'C', size: 3, fixed: true });
735  *     })();
736  *
737  * </script><pre>
738  *
739  * @example
740  *     // Glider on sphere
741  *     var view = board.create(
742  *         'view3d',
743  *         [[-6, -3], [8, 8],
744  *         [[-3, 3], [-3, 3], [-3, 3]]],
745  *         {
746  *             depthOrder: {
747  *                 enabled: true
748  *             },
749  *             projection: 'central',
750  *             xPlaneRear: {fillOpacity: 0.2, gradient: null},
751  *             yPlaneRear: {fillOpacity: 0.2, gradient: null},
752  *             zPlaneRear: {fillOpacity: 0.2, gradient: null}
753  *         }
754  *     );
755  *
756  *     // Two points
757  *     var center = view.create('point3d', [0, 0, 0], {withLabel: false, size: 2});
758  *     var point = view.create('point3d', [2, 0, 0], {withLabel: false, size: 2});
759  *
760  *     // Sphere
761  *     var sphere = view.create('sphere3d', [center, point], {fillOpacity: 0.8});
762  *
763  *     // Glider on sphere
764  *     var glide = view.create('point3d', [2, 2, 0, sphere], {withLabel: false, color: 'red', size: 4});
765  *     var l1 = view.create('line3d', [glide, center], { strokeWidth: 2, dash: 2 });
766  *
767  * </pre><div id="JXG672fe3c7-e6fd-48e0-9a24-22f51f2dfa71" class="jxgbox" style="width: 300px; height: 300px;"></div>
768  * <script type="text/javascript">
769  *     (function() {
770  *         var board = JXG.JSXGraph.initBoard('JXG672fe3c7-e6fd-48e0-9a24-22f51f2dfa71',
771  *             {boundingbox: [-8, 8, 8,-8], axis: false, showcopyright: false, shownavigation: false});
772  *         var view = board.create(
773  *             'view3d',
774  *             [[-6, -3], [8, 8],
775  *             [[-3, 3], [-3, 3], [-3, 3]]],
776  *             {
777  *                 depthOrder: {
778  *                     enabled: true
779  *                 },
780  *                 projection: 'central',
781  *                 xPlaneRear: {fillOpacity: 0.2, gradient: null},
782  *                 yPlaneRear: {fillOpacity: 0.2, gradient: null},
783  *                 zPlaneRear: {fillOpacity: 0.2, gradient: null}
784  *             }
785  *         );
786  *
787  *         // Two points
788  *         var center = view.create('point3d', [0, 0, 0], {withLabel: false, size: 2});
789  *         var point = view.create('point3d', [2, 0, 0], {withLabel: false, size: 2});
790  *
791  *         // Sphere
792  *         var sphere = view.create('sphere3d', [center, point], {fillOpacity: 0.8});
793  *
794  *         // Glider on sphere
795  *         var glide = view.create('point3d', [2, 2, 0, sphere], {withLabel: false, color: 'red', size: 4});
796  *         var l1 = view.create('line3d', [glide, center], { strokeWidth: 2, dash: 2 });
797  *
798  *     })();
799  *
800  * </script><pre>
801  *
802  */
803 JXG.createPoint3D = function (board, parents, attributes) {
804     //   parents[0]: view
805     // followed by
806     //   parents[1]: function or array
807     // or
808     //   parents[1..3]: coordinates
809 
810     var view = parents[0],
811         attr, F, slide, c2d, el,
812         base = null,
813         transform = null;
814 
815     // If the last element of `parents` is a 3D object,
816     // the point is a glider on that element.
817     if (parents.length > 2 &&
818         Type.exists(parents[parents.length - 1].is3D) &&
819         !Type.isTransformationOrArray(parents[parents.length - 1])
820     ) {
821         slide = parents.pop();
822     } else {
823         slide = null;
824     }
825 
826     if (parents.length === 2) {
827         // [view, array|fun] (Array [x, y, z] | function) returning [x, y, z]
828         F = parents[1];
829     } else if (parents.length === 3 &&
830         Type.isPoint3D(parents[1]) &&
831         Type.isTransformationOrArray(parents[2])
832     ) {
833         F = [0, 0, 0];
834         base = parents[1];
835         transform = parents[2];
836     } else if (parents.length === 4) {
837         // [view, x, y, z], (3 numbers | functions)
838         F = parents.slice(1);
839     } else if (parents.length === 5) {
840         // [view, w, x, y, z], (4 numbers | functions)
841         F = parents.slice(1);
842     } else {
843         throw new Error(
844             "JSXGraph: Can't create point3d with parent types '" +
845             typeof parents[1] +
846             "' and '" +
847             typeof parents[2] +
848             "'." +
849             "\nPossible parent types: [[x,y,z]], [x,y,z], or [[x,y,z], slide], () => [x, y, z], or [point, transformation(s)]"
850         );
851         //  "\nPossible parent types: [[x,y,z]], [x,y,z], [element,transformation]"); // TODO
852     }
853 
854     attr = Type.copyAttributes(attributes, board.options, 'point3d');
855     el = new JXG.Point3D(view, F, slide, attr);
856     el.initCoords();
857     if (base !== null && transform !== null) {
858         el.addTransform(base, transform);
859     }
860 
861     c2d = view.project3DTo2D(el.coords);
862 
863     attr = el.setAttr2D(attr);
864     el.element2D = view.create('point', c2d, attr);
865     el.element2D.view = view;
866     el.addChild(el.element2D);
867     el.inherits.push(el.element2D);
868     el.element2D.setParents(el);
869 
870     // If this point is a glider, record that in the update tree
871     if (el.slide) {
872         el.slide.addChild(el);
873         el.setParents(el.slide);
874     }
875     if (base) {
876         el.setParents(base);
877     }
878 
879     el._c2d = el.element2D.coords.usrCoords.slice(); // Store a copy of the coordinates to detect dragging
880 
881     return el;
882 };
883 
884 JXG.registerElement("point3d", JXG.createPoint3D);
885 
886