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 /*
 30     Some functionalities in this file were developed as part of a software project
 31     with students. We would like to thank all contributors for their help:
 32 
 33     Winter semester 2023/2024:
 34         Lars Hofmann
 35         Leonhard Iser
 36         Vincent Kulicke
 37         Laura Rinas
 38  */
 39 
 40 /*global JXG:true, define: true*/
 41 
 42 import JXG from "../jxg.js";
 43 import Const from "../base/constants.js";
 44 import Coords from "../base/coords.js";
 45 import Type from "../utils/type.js";
 46 import Mat from "../math/math.js";
 47 import Geometry from "../math/geometry.js";
 48 import Numerics from "../math/numerics.js";
 49 import Env from "../utils/env.js";
 50 import GeometryElement from "../base/element.js";
 51 import Composition from "../base/composition.js";
 52 
 53 /**
 54  * 3D view inside a JXGraph board.
 55  *
 56  * @class Creates a new 3D view. Do not use this constructor to create a 3D view. Use {@link JXG.Board#create} with
 57  * type {@link View3D} instead.
 58  *
 59  * @augments JXG.GeometryElement
 60  * @param {Array} parents Array consisting of lower left corner [x, y] of the view inside the board, [width, height] of the view
 61  * and box size [[x1, x2], [y1,y2], [z1,z2]]. If the view's azimuth=0 and elevation=0, the 3D view will cover a rectangle with lower left corner
 62  * [x,y] and side lengths [w, h] of the board.
 63  */
 64 JXG.View3D = function (board, parents, attributes) {
 65     this.constructor(board, attributes, Const.OBJECT_TYPE_VIEW3D, Const.OBJECT_CLASS_3D);
 66 
 67     /**
 68      * An associative array containing all geometric objects belonging to the view.
 69      * Key is the id of the object and value is a reference to the object.
 70      * @type Object
 71      * @private
 72      */
 73     this.objects = {};
 74 
 75     /**
 76      * An array containing all the elements in the view that are sorted due to their depth order.
 77      * @Type Object
 78      * @private
 79      */
 80     this.depthOrdered = {};
 81 
 82     /**
 83      * TODO: why deleted?
 84      * An array containing all geometric objects in this view in the order of construction.
 85      * @type Array
 86      * @private
 87      */
 88     // this.objectsList = [];
 89 
 90     /**
 91      * An associative array / dictionary to store the objects of the board by name. The name of the object is the key and value is a reference to the object.
 92      * @type Object
 93      * @private
 94      */
 95     this.elementsByName = {};
 96 
 97     /**
 98      * Default axes of the 3D view, contains the axes of the view or null.
 99      *
100      * @type {Object}
101      * @default null
102      */
103     this.defaultAxes = null;
104 
105     /**
106      * The Tait-Bryan angles specifying the view box orientation
107      */
108     this.angles = {
109         az: null,
110         el: null,
111         bank: null
112     };
113 
114     /**
115      * @type {Array}
116      * The view box orientation matrix
117      */
118     this.matrix3DRot = [
119         [1, 0, 0, 0],
120         [0, 1, 0, 0],
121         [0, 0, 1, 0],
122         [0, 0, 0, 1]
123     ];
124 
125     // Used for z-index computation
126     this.matrix3DRotShift = [
127         [1, 0, 0, 0],
128         [0, 1, 0, 0],
129         [0, 0, 1, 0],
130         [0, 0, 0, 1]
131     ];
132 
133     /**
134      * @type  {Array}
135      * @private
136      */
137     // 3D-to-2D transformation matrix
138     this.matrix3D = [
139         [1, 0, 0, 0],
140         [0, 1, 0, 0],
141         [0, 0, 1, 0]
142     ];
143 
144     /**
145      * The 4×4 matrix that maps box coordinates to camera coordinates. These
146      * coordinate systems fit into the View3D coordinate atlas as follows.
147      * <ul>
148      * <li><b>World coordinates.</b> The coordinates used to specify object
149      * positions in a JSXGraph scene.</li>
150      * <li><b>Box coordinates.</b> The world coordinates translated to put the
151      * center of the view box at the origin.
152      * <li><b>Camera coordinates.</b> The coordinate system where the
153      * <code>x</code>, <code>y</code> plane is the screen, the origin is the
154      * center of the screen, and the <code>z</code> axis points out of the
155      * screen, toward the viewer.
156      * <li><b>Focal coordinates.</b> The camera coordinates translated to put
157      * the origin at the focal point, which is set back from the screen by the
158      * focal distance.</li>
159      * </ul>
160      * The <code>boxToCam</code> transformation is exposed to help 3D elements
161      * manage their 2D representations in central projection mode. To map world
162      * coordinates to focal coordinates, use the
163      * {@link JXG.View3D#worldToFocal} method.
164      * @type {Array}
165      */
166     this.boxToCam = [];
167 
168     /**
169      * @type array
170      * @private
171      */
172     // Lower left corner [x, y] of the 3D view if elevation and azimuth are set to 0.
173     this.llftCorner = parents[0];
174 
175     /**
176      * Width and height [w, h] of the 3D view if elevation and azimuth are set to 0.
177      * @type array
178      * @private
179      */
180     this.size = parents[1];
181 
182     /**
183      * Bounding box (cube) [[x1, x2], [y1,y2], [z1,z2]] of the 3D view
184      * @type array
185      */
186     this.bbox3D = parents[2];
187 
188     /**
189      * The distance from the camera to the origin. In other words, the
190      * radius of the sphere where the camera sits.
191      * @type Number
192      */
193     this.r = -1;
194 
195     /**
196      * The distance from the camera to the screen. Computed automatically from
197      * the `fov` property.
198      * @type Number
199      */
200     this.focalDist = -1;
201 
202     /**
203      * Type of projection.
204      * @type String
205      */
206     // Will be set in update().
207     this.projectionType = 'parallel';
208 
209     /**
210      * Whether trackball navigation is currently enabled.
211      * @type String
212      */
213     this.trackballEnabled = false;
214 
215     /**
216      * Store last position of pointer.
217      * This is the successor to use evt.movementX/Y which caused problems on firefox
218      * @type Object
219      * @private
220      */
221     this._lastPos = {
222         x: 0,
223         y: 0
224     };
225 
226     this.timeoutAzimuth = null;
227 
228     this.zIndexMin = Infinity;
229     this.zIndexMax = -Infinity;
230 
231     this.id = this.board.setId(this, 'V');
232     this.board.finalizeAdding(this);
233     this.elType = 'view3d';
234 
235     this.methodMap = Type.deepCopy(this.methodMap, {
236         // TODO
237     });
238 };
239 JXG.View3D.prototype = new GeometryElement();
240 
241 JXG.extend(
242     JXG.View3D.prototype, /** @lends JXG.View3D.prototype */ {
243 
244     /**
245      * Creates a new 3D element of type elementType.
246      * @param {String} elementType Type of the element to be constructed given as a string e.g. 'point3d' or 'surface3d'.
247      * @param {Array} parents Array of parent elements needed to construct the element e.g. coordinates for a 3D point or two
248      * 3D points to construct a line. This highly depends on the elementType that is constructed. See the corresponding JXG.create*
249      * methods for a list of possible parameters.
250      * @param {Object} [attributes] An object containing the attributes to be set. This also depends on the elementType.
251      * Common attributes are name, visible, strokeColor.
252      * @returns {Object} Reference to the created element. This is usually a GeometryElement3D, but can be an array containing
253      * two or more elements.
254      */
255     create: function (elementType, parents, attributes) {
256         var prefix = [],
257             el;
258 
259         if (elementType.indexOf('3d') > 0) {
260             // is3D = true;
261             prefix.push(this);
262         }
263         el = this.board.create(elementType, prefix.concat(parents), attributes);
264 
265         return el;
266     },
267 
268     /**
269      * Select a single or multiple elements at once.
270      * @param {String|Object|function} str The name, id or a reference to a JSXGraph 3D element in the 3D view. An object will
271      * be used as a filter to return multiple elements at once filtered by the properties of the object.
272      * @param {Boolean} onlyByIdOrName If true (default:false) elements are only filtered by their id, name or groupId.
273      * The advanced filters consisting of objects or functions are ignored.
274      * @returns {JXG.GeometryElement3D|JXG.Composition}
275      * @example
276      * // select the element with name A
277      * view.select('A');
278      *
279      * // select all elements with strokecolor set to 'red' (but not '#ff0000')
280      * view.select({
281      *   strokeColor: 'red'
282      * });
283      *
284      * // select all points on or below the x/y plane and make them black.
285      * view.select({
286      *   elType: 'point3d',
287      *   Z: function (v) {
288      *     return v <= 0;
289      *   }
290      * }).setAttribute({color: 'black'});
291      *
292      * // select all elements
293      * view.select(function (el) {
294      *   return true;
295      * });
296      */
297     select: function (str, onlyByIdOrName) {
298         var flist,
299             olist,
300             i,
301             l,
302             s = str;
303 
304         if (s === null) {
305             return s;
306         }
307 
308         if (Type.isString(s) && s !== '') {
309             // It's a string, most likely an id or a name.
310             // Search by ID
311             if (Type.exists(this.objects[s])) {
312                 s = this.objects[s];
313                 // Search by name
314             } else if (Type.exists(this.elementsByName[s])) {
315                 s = this.elementsByName[s];
316                 // // Search by group ID
317                 // } else if (Type.exists(this.groups[s])) {
318                 //     s = this.groups[s];
319             }
320 
321         } else if (
322             !onlyByIdOrName &&
323             (Type.isFunction(s) || (Type.isObject(s) && !Type.isFunction(s.setAttribute)))
324         ) {
325             // It's a function or an object, but not an element
326             flist = Type.filterElements(this.objectsList, s);
327 
328             olist = {};
329             l = flist.length;
330             for (i = 0; i < l; i++) {
331                 olist[flist[i].id] = flist[i];
332             }
333             s = new Composition(olist);
334 
335         } else if (
336             Type.isObject(s) &&
337             Type.exists(s.id) &&
338             !Type.exists(this.objects[s.id])
339         ) {
340             // It's an element which has been deleted (and still hangs around, e.g. in an attractor list)
341             s = null;
342         }
343 
344         return s;
345     },
346 
347     // set the Tait-Bryan angles to specify the current view rotation matrix
348     setAnglesFromRotation: function () {
349         var rem = this.matrix3DRot, // rotation remaining after angle extraction
350             rBank, cosBank, sinBank,
351             cosEl, sinEl,
352             cosAz, sinAz;
353 
354         // extract bank by rotating the view box z axis onto the camera yz plane
355         rBank = Math.sqrt(rem[1][3] * rem[1][3] + rem[2][3] * rem[2][3]);
356         if (rBank > Mat.eps) {
357             cosBank = rem[2][3] / rBank;
358             sinBank = rem[1][3] / rBank;
359         } else {
360             // if the z axis is pointed almost exactly at the screen, we
361             // keep the current bank value
362             cosBank = Math.cos(this.angles.bank);
363             sinBank = Math.sin(this.angles.bank);
364         }
365         rem = Mat.matMatMult([
366             [1, 0, 0, 0],
367             [0, cosBank, -sinBank, 0],
368             [0, sinBank, cosBank, 0],
369             [0, 0, 0, 1]
370         ], rem);
371         this.angles.bank = Math.atan2(sinBank, cosBank);
372 
373         // extract elevation by rotating the view box z axis onto the camera
374         // y axis
375         cosEl = rem[2][3];
376         sinEl = rem[3][3];
377         rem = Mat.matMatMult([
378             [1, 0, 0, 0],
379             [0, 1, 0, 0],
380             [0, 0, cosEl, sinEl],
381             [0, 0, -sinEl, cosEl]
382         ], rem);
383         this.angles.el = Math.atan2(sinEl, cosEl);
384 
385         // extract azimuth
386         cosAz = -rem[1][1];
387         sinAz = rem[3][1];
388         this.angles.az = Math.atan2(sinAz, cosAz);
389         if (this.angles.az < 0) this.angles.az += 2 * Math.PI;
390 
391         this.setSlidersFromAngles();
392     },
393 
394     anglesHaveMoved: function () {
395         return (
396             this._hasMoveAz || this._hasMoveEl ||
397             Math.abs(this.angles.az - this.az_slide.Value()) > Mat.eps ||
398             Math.abs(this.angles.el - this.el_slide.Value()) > Mat.eps ||
399             Math.abs(this.angles.bank - this.bank_slide.Value()) > Mat.eps
400         );
401     },
402 
403     getAnglesFromSliders: function () {
404         this.angles.az = this.az_slide.Value();
405         this.angles.el = this.el_slide.Value();
406         this.angles.bank = this.bank_slide.Value();
407     },
408 
409     setSlidersFromAngles: function () {
410         this.az_slide.setValue(this.angles.az);
411         this.el_slide.setValue(this.angles.el);
412         this.bank_slide.setValue(this.angles.bank);
413     },
414 
415     // return the rotation matrix specified by the current Tait-Bryan angles
416     getRotationFromAngles: function () {
417         var a, e, b, f,
418             cosBank, sinBank,
419             mat = [
420                 [1, 0, 0, 0],
421                 [0, 1, 0, 0],
422                 [0, 0, 1, 0],
423                 [0, 0, 0, 1]
424             ];
425 
426         // mat projects homogeneous 3D coords in View3D
427         // to homogeneous 2D coordinates in the board
428         a = this.angles.az;
429         e = this.angles.el;
430         b = this.angles.bank;
431         f = -Math.sin(e);
432 
433         mat[1][1] = -Math.cos(a);
434         mat[1][2] = Math.sin(a);
435         mat[1][3] = 0;
436 
437         mat[2][1] = f * Math.sin(a);
438         mat[2][2] = f * Math.cos(a);
439         mat[2][3] = Math.cos(e);
440 
441         mat[3][1] = Math.cos(e) * Math.sin(a);
442         mat[3][2] = Math.cos(e) * Math.cos(a);
443         mat[3][3] = Math.sin(e);
444 
445         cosBank = Math.cos(b);
446         sinBank = Math.sin(b);
447         mat = Mat.matMatMult([
448             [1, 0, 0, 0],
449             [0, cosBank, sinBank, 0],
450             [0, -sinBank, cosBank, 0],
451             [0, 0, 0, 1]
452         ], mat);
453 
454         return mat;
455 
456         /* this code, originally from `_updateCentralProjection`, is an
457          * alternate implementation of the azimuth-elevation matrix
458          * computation above. using this implementation instead of the
459          * current one might lead to simpler code in a future refactoring
460         var a, e, up,
461             ax, ay, az, v, nrm,
462             eye, d,
463             func_sphere;
464 
465         // finds the point on the unit sphere with the given azimuth and
466         // elevation, and returns its affine coordinates
467         func_sphere = function (az, el) {
468             return [
469                 Math.cos(az) * Math.cos(el),
470                 -Math.sin(az) * Math.cos(el),
471                 Math.sin(el)
472             ];
473         };
474 
475         a = this.az_slide.Value() + (3 * Math.PI * 0.5); // Sphere
476         e = this.el_slide.Value();
477 
478         // create an up vector and an eye vector which are 90 degrees out of phase
479         up = func_sphere(a, e + Math.PI / 2);
480         eye = func_sphere(a, e);
481         d = [eye[0], eye[1], eye[2]];
482 
483         nrm = Mat.norm(d, 3);
484         az = [d[0] / nrm, d[1] / nrm, d[2] / nrm];
485 
486         nrm = Mat.norm(up, 3);
487         v = [up[0] / nrm, up[1] / nrm, up[2] / nrm];
488 
489         ax = Mat.crossProduct(v, az);
490         ay = Mat.crossProduct(az, ax);
491 
492         this.matrix3DRot[1] = [0, ax[0], ax[1], ax[2]];
493         this.matrix3DRot[2] = [0, ay[0], ay[1], ay[2]];
494         this.matrix3DRot[3] = [0, az[0], az[1], az[2]];
495          */
496     },
497 
498     /**
499      * Project 2D point (x,y) to the virtual trackpad sphere,
500      * see Bell's virtual trackpad, and return z-component of the
501      * number.
502      *
503      * @param {Number} r
504      * @param {Number} x
505      * @param {Number} y
506      * @returns Number
507      * @private
508      */
509     _projectToSphere: function (r, x, y) {
510         var d = Mat.hypot(x, y),
511             t, z;
512 
513         if (d < r * 0.7071067811865475) { // Inside sphere
514             z = Math.sqrt(r * r - d * d);
515         } else {                          // On hyperbola
516             t = r / 1.414213562373095;
517             z = t * t / d;
518         }
519         return z;
520     },
521 
522     /**
523      * Determine 4x4 rotation matrix with Bell's virtual trackball.
524      *
525      * @returns {Array} 4x4 rotation matrix
526      * @private
527      */
528     updateProjectionTrackball: function (Pref) {
529         var R = 100,
530             dx, dy, dr2,
531             p1, p2, x, y, theta, t, d,
532             c, s, n,
533             mat = [
534                 [1, 0, 0, 0],
535                 [0, 1, 0, 0],
536                 [0, 0, 1, 0],
537                 [0, 0, 0, 1]
538             ];
539 
540         if (!Type.exists(this._trackball)) {
541             return this.matrix3DRot;
542         }
543 
544         dx = this._trackball.dx;
545         dy = this._trackball.dy;
546         dr2 = dx * dx + dy * dy;
547         if (dr2 > Mat.eps) {
548             // // Method by Hanson, "The rolling ball", Graphics Gems III, p.51
549             // // Rotation axis:
550             // //     n = (-dy/dr, dx/dr, 0)
551             // // Rotation angle around n:
552             // //     theta = atan(dr / R) approx dr / R
553             // dr = Math.sqrt(dr2);
554             // c = R / Math.hypot(R, dr);  // cos(theta)
555             // t = 1 - c;                  // 1 - cos(theta)
556             // s = dr / Math.hypot(R, dr); // sin(theta)
557             // n = [-dy / dr, dx / dr, 0];
558 
559             // Bell virtual trackpad, see
560             // https://opensource.apple.com/source/X11libs/X11libs-60/mesa/Mesa-7.8.2/progs/util/trackball.c.auto.html
561             // http://scv.bu.edu/documentation/presentations/visualizationworkshop08/materials/opengl/trackball.c.
562             // See also Henriksen, Sporring, Hornaek, "Virtual Trackballs revisited".
563             //
564             R = (this.size[0] * this.board.unitX + this.size[1] * this.board.unitY) * 0.25;
565             x = this._trackball.x;
566             y = this._trackball.y;
567 
568             p2 = [x, y, this._projectToSphere(R, x, y)];
569             x -= dx;
570             y -= dy;
571             p1 = [x, y, this._projectToSphere(R, x, y)];
572 
573             n = Mat.crossProduct(p1, p2);
574             d = Mat.hypot(n[0], n[1], n[2]);
575             n[0] /= d;
576             n[1] /= d;
577             n[2] /= d;
578 
579             t = Geometry.distance(p2, p1, 3) / (2 * R);
580             t = (t > 1.0) ? 1.0 : t;
581             t = (t < -1.0) ? -1.0 : t;
582             theta = 2.0 * Math.asin(t);
583             c = Math.cos(theta);
584             t = 1 - c;
585             s = Math.sin(theta);
586 
587             // Rotation by theta about the axis n. See equation 9.63 of
588             //
589             //   Ian Richard Cole. "Modeling CPV" (thesis). Loughborough
590             //   University. https://hdl.handle.net/2134/18050
591             //
592             mat[1][1] = c + n[0] * n[0] * t;
593             mat[2][1] = n[1] * n[0] * t + n[2] * s;
594             mat[3][1] = n[2] * n[0] * t - n[1] * s;
595 
596             mat[1][2] = n[0] * n[1] * t - n[2] * s;
597             mat[2][2] = c + n[1] * n[1] * t;
598             mat[3][2] = n[2] * n[1] * t + n[0] * s;
599 
600             mat[1][3] = n[0] * n[2] * t + n[1] * s;
601             mat[2][3] = n[1] * n[2] * t - n[0] * s;
602             mat[3][3] = c + n[2] * n[2] * t;
603         }
604 
605         mat = Mat.matMatMult(mat, this.matrix3DRot);
606         return mat;
607     },
608 
609     updateAngleSliderBounds: function () {
610         var az_smax, az_smin,
611             el_smax, el_smin, el_cover,
612             el_smid, el_equiv, el_flip_equiv,
613             el_equiv_loss, el_flip_equiv_loss, el_interval_loss,
614             bank_smax, bank_smin;
615 
616         // update stored trackball toggle
617         this.trackballEnabled = this.evalVisProp('trackball.enabled');
618 
619         // set slider bounds
620         if (this.trackballEnabled) {
621             this.az_slide.setMin(0);
622             this.az_slide.setMax(2 * Math.PI);
623             this.el_slide.setMin(-0.5 * Math.PI);
624             this.el_slide.setMax(0.5 * Math.PI);
625             this.bank_slide.setMin(-Math.PI);
626             this.bank_slide.setMax(Math.PI);
627         } else {
628             this.az_slide.setMin(this.visProp.az.slider.min);
629             this.az_slide.setMax(this.visProp.az.slider.max);
630             this.el_slide.setMin(this.visProp.el.slider.min);
631             this.el_slide.setMax(this.visProp.el.slider.max);
632             this.bank_slide.setMin(this.visProp.bank.slider.min);
633             this.bank_slide.setMax(this.visProp.bank.slider.max);
634         }
635 
636         // get new slider bounds
637         az_smax = this.az_slide._smax;
638         az_smin = this.az_slide._smin;
639         el_smax = this.el_slide._smax;
640         el_smin = this.el_slide._smin;
641         bank_smax = this.bank_slide._smax;
642         bank_smin = this.bank_slide._smin;
643 
644         // wrap and restore angle values
645         if (this.trackballEnabled) {
646             // if we're upside-down, flip the bank angle to reach the same
647             // orientation with an elevation between -pi/2 and pi/2
648             el_cover = Mat.mod(this.angles.el, 2 * Math.PI);
649             if (0.5 * Math.PI < el_cover && el_cover < 1.5 * Math.PI) {
650                 this.angles.el = Math.PI - el_cover;
651                 this.angles.az = Mat.wrap(this.angles.az + Math.PI, az_smin, az_smax);
652                 this.angles.bank = Mat.wrap(this.angles.bank + Math.PI, bank_smin, bank_smax);
653             }
654 
655             // wrap the azimuth and bank angle
656             this.angles.az = Mat.wrap(this.angles.az, az_smin, az_smax);
657             this.angles.el = Mat.wrap(this.angles.el, el_smin, el_smax);
658             this.angles.bank = Mat.wrap(this.angles.bank, bank_smin, bank_smax);
659         } else {
660             // wrap and clamp the elevation into the slider range. if
661             // flipping the elevation gets us closer to the slider interval,
662             // do that, inverting the azimuth and bank angle to compensate
663             el_interval_loss = function (t) {
664                 if (t < el_smin) {
665                     return el_smin - t;
666                 } else if (el_smax < t) {
667                     return t - el_smax;
668                 } else {
669                     return 0;
670                 }
671             };
672             el_smid = 0.5 * (el_smin + el_smax);
673             el_equiv = Mat.wrap(
674                 this.angles.el,
675                 el_smid - Math.PI,
676                 el_smid + Math.PI
677             );
678             el_flip_equiv = Mat.wrap(
679                 Math.PI - this.angles.el,
680                 el_smid - Math.PI,
681                 el_smid + Math.PI
682             );
683             el_equiv_loss = el_interval_loss(el_equiv);
684             el_flip_equiv_loss = el_interval_loss(el_flip_equiv);
685             if (el_equiv_loss <= el_flip_equiv_loss) {
686                 this.angles.el = Mat.clamp(el_equiv, el_smin, el_smax);
687             } else {
688                 this.angles.el = Mat.clamp(el_flip_equiv, el_smin, el_smax);
689                 this.angles.az = Mat.wrap(this.angles.az + Math.PI, az_smin, az_smax);
690                 this.angles.bank = Mat.wrap(this.angles.bank + Math.PI, bank_smin, bank_smax);
691             }
692 
693             // wrap and clamp the azimuth and bank angle into the slider range
694             this.angles.az = Mat.wrapAndClamp(this.angles.az, az_smin, az_smax, 2 * Math.PI);
695             this.angles.bank = Mat.wrapAndClamp(this.angles.bank, bank_smin, bank_smax, 2 * Math.PI);
696 
697             // since we're using `clamp`, angles may have changed
698             this.matrix3DRot = this.getRotationFromAngles();
699         }
700 
701         // restore slider positions
702         this.setSlidersFromAngles();
703     },
704 
705     /**
706      * @private
707      * @returns {Array}
708      */
709     _updateCentralProjection: function () {
710         var zf = 20, // near clip plane
711             zn = 8, // far clip plane
712 
713             // See https://www.mathematik.uni-marburg.de/~thormae/lectures/graphics1/graphics_6_1_eng_web.html
714             // bbox3D is always at the world origin, i.e. T_obj is the unit matrix.
715             // All vectors contain affine coordinates and have length 3
716             // The matrices are of size 4x4.
717             r, A;
718 
719         // set distance from view box center to camera
720         r = this.evalVisProp('r');
721         if (r === 'auto') {
722             r = Mat.hypot(
723                 this.bbox3D[0][0] - this.bbox3D[0][1],
724                 this.bbox3D[1][0] - this.bbox3D[1][1],
725                 this.bbox3D[2][0] - this.bbox3D[2][1]
726             ) * 1.01;
727         }
728 
729         // compute camera transformation
730         // this.boxToCam = this.matrix3DRot.map((row) => row.slice());
731         this.boxToCam = this.matrix3DRot.map(function (row) { return row.slice(); });
732         this.boxToCam[3][0] = -r;
733 
734         // compute focal distance and clip space transformation
735         this.focalDist = 1 / Math.tan(0.5 * this.evalVisProp('fov'));
736         A = [
737             [0, 0, 0, -1],
738             [0, this.focalDist, 0, 0],
739             [0, 0, this.focalDist, 0],
740             [2 * zf * zn / (zn - zf), 0, 0, (zf + zn) / (zn - zf)]
741         ];
742 
743         return Mat.matMatMult(A, this.boxToCam);
744     },
745 
746     // Update 3D-to-2D transformation matrix with the actual azimuth and elevation angles.
747     update: function () {
748         var r = this.r,
749             stretch = [
750                 [1, 0, 0, 0],
751                 [0, -r, 0, 0],
752                 [0, 0, -r, 0],
753                 [0, 0, 0, 1]
754             ],
755             mat2D, objectToClip, size,
756             dx, dy;
757             // objectsList;
758 
759         if (
760             !Type.exists(this.el_slide) ||
761             !Type.exists(this.az_slide) ||
762             !Type.exists(this.bank_slide) ||
763             !this.needsUpdate
764         ) {
765             this.needsUpdate = false;
766             return this;
767         }
768 
769         mat2D = [
770             [1, 0, 0],
771             [0, 1, 0],
772             [0, 0, 1]
773         ];
774 
775         this.projectionType = this.evalVisProp('projection').toLowerCase();
776 
777         // override angle slider bounds when trackball navigation is enabled
778         if (this.trackballEnabled !== this.evalVisProp('trackball.enabled')) {
779             this.updateAngleSliderBounds();
780         }
781 
782         if (this._hasMoveTrackball) {
783             // The trackball has been moved since the last update, so we do
784             // trackball navigation. When the trackball is enabled, a drag
785             // event is interpreted as a trackball movement unless it's
786             // caught by something else, like point dragging. When the
787             // trackball is disabled, the trackball movement flag should
788             // never be set
789             this.matrix3DRot = this.updateProjectionTrackball();
790             this.setAnglesFromRotation();
791         } else if (this.anglesHaveMoved()) {
792             // The trackball hasn't been moved since the last up date, but
793             // the Tait-Bryan angles have been, so we do angle navigation
794             this.getAnglesFromSliders();
795             this.matrix3DRot = this.getRotationFromAngles();
796         }
797 
798         /**
799          * The translation that moves the center of the view box to the origin.
800          */
801         this.shift = [
802             [1, 0, 0, 0],
803             [-0.5 * (this.bbox3D[0][0] + this.bbox3D[0][1]), 1, 0, 0],
804             [-0.5 * (this.bbox3D[1][0] + this.bbox3D[1][1]), 0, 1, 0],
805             [-0.5 * (this.bbox3D[2][0] + this.bbox3D[2][1]), 0, 0, 1]
806         ];
807 
808         switch (this.projectionType) {
809             case 'central': // Central projection
810 
811                 // Add a final transformation to scale and shift the projection
812                 // on the board, usually called viewport.
813                 size = 2 * 0.4;
814                 mat2D[1][1] = this.size[0] / size; // w / d_x
815                 mat2D[2][2] = this.size[1] / size; // h / d_y
816                 mat2D[1][0] = this.llftCorner[0] + mat2D[1][1] * 0.5 * size; // llft_x
817                 mat2D[2][0] = this.llftCorner[1] + mat2D[2][2] * 0.5 * size; // llft_y
818                 // The transformations this.matrix3D and mat2D can not be combined at this point,
819                 // since the projected vectors have to be normalized in between in project3DTo2D
820                 this.viewPortTransform = mat2D;
821                 objectToClip = this._updateCentralProjection();
822                 // this.matrix3D is a 4x4 matrix
823                 this.matrix3D = Mat.matMatMult(objectToClip, this.shift);
824                 break;
825 
826             case 'parallel': // Parallel projection
827             default:
828                 // Add a final transformation to scale and shift the projection
829                 // on the board, usually called viewport.
830                 dx = this.bbox3D[0][1] - this.bbox3D[0][0];
831                 dy = this.bbox3D[1][1] - this.bbox3D[1][0];
832                 mat2D[1][1] = this.size[0] / dx; // w / d_x
833                 mat2D[2][2] = this.size[1] / dy; // h / d_y
834                 mat2D[1][0] = this.llftCorner[0] + mat2D[1][1] * 0.5 * dx; // llft_x
835                 mat2D[2][0] = this.llftCorner[1] + mat2D[2][2] * 0.5 * dy; // llft_y
836 
837                 // Combine all transformations, this.matrix3D is a 3x4 matrix
838                 this.matrix3D = Mat.matMatMult(
839                     mat2D,
840                     Mat.matMatMult(Mat.matMatMult(this.matrix3DRot, stretch), this.shift).slice(0, 3)
841                 );
842         }
843 
844         // Used for zIndex in dept ordering in subsequent update methods of the
845         // 3D elements and in view3d.updateRenderer
846         this.matrix3DRotShift = Mat.matMatMult(this.matrix3DRot, this.shift);
847 
848         return this;
849     },
850 
851     /**
852      * Compares 3D elements according to their z-Index.
853      * @param {JXG.GeometryElement3D} a
854      * @param {JXG.GeometryElement3D} b
855      * @returns Number
856      */
857     compareDepth: function (a, b) {
858         // return a.zIndex - b.zIndex;
859         // if (a.type !== Const.OBJECT_TYPE_PLANE3D && b.type !== Const.OBJECT_TYPE_PLANE3D) {
860         //     return a.zIndex - b.zIndex;
861         // } else if (a.type === Const.OBJECT_TYPE_PLANE3D) {
862         //     let bHesse = Mat.innerProduct(a.point.coords, a.normal, 4);
863         //     let po = Mat.innerProduct(b.coords, a.normal, 4);
864         //     let pos = Mat.innerProduct(this.boxToCam[3], a.normal, 4);
865         // console.log(this.boxToCam[3])
866         //     return pos - po;
867         // } else if (b.type === Const.OBJECT_TYPE_PLANE3D) {
868         //     let bHesse = Mat.innerProduct(b.point.coords, b.normal, 4);
869         //     let po = Mat.innerProduct(a.coords, a.normal, 4);
870         //     let pos = Mat.innerProduct(this.boxToCam[3], b.normal, 4);
871         //     console.log('b', pos, po, bHesse)
872         //     return -pos;
873         // }
874         return a.zIndex - b.zIndex;
875     },
876 
877     updateZIndices: function() {
878         var id, el;
879         for (id in this.objects) {
880             if (this.objects.hasOwnProperty(id)) {
881                 el = this.objects[id];
882                 // Update zIndex of less frequent objects line3d and polygon3d
883                 // The other elements (point3d, face3d) do this in their update method.
884                 if ((el.type === Const.OBJECT_TYPE_LINE3D ||
885                     el.type === Const.OBJECT_TYPE_POLYGON3D
886                     ) &&
887                     Type.exists(el.element2D) &&
888                     el.element2D.evalVisProp('visible')
889                 ) {
890                     el.updateZIndex();
891                 }
892             }
893         }
894     },
895 
896     updateShaders: function() {
897         var id, el, v;
898         for (id in this.objects) {
899             if (this.objects.hasOwnProperty(id)) {
900                 el = this.objects[id];
901                 if (Type.exists(el.shader)) {
902                     v = el.shader();
903                     if (v < this.zIndexMin) {
904                         this.zIndexMin = v;
905                     } else if (v > this.zIndexMax) {
906                         this.zIndexMax = v;
907                     }
908                 }
909             }
910         }
911     },
912 
913     updateDepthOrdering: function () {
914         var id, el,
915             i, j, l, layers, lay;
916 
917         // Collect elements for depth ordering layer-wise
918         layers = this.evalVisProp('depthorder.layers');
919         for (i = 0; i < layers.length; i++) {
920             this.depthOrdered[layers[i]] = [];
921         }
922 
923         for (id in this.objects) {
924             if (this.objects.hasOwnProperty(id)) {
925                 el = this.objects[id];
926                 if ((el.type === Const.OBJECT_TYPE_FACE3D ||
927                     el.type === Const.OBJECT_TYPE_LINE3D ||
928                     // el.type === Const.OBJECT_TYPE_PLANE3D ||
929                     el.type === Const.OBJECT_TYPE_POINT3D ||
930                     el.type === Const.OBJECT_TYPE_POLYGON3D
931                     ) &&
932                     Type.exists(el.element2D) &&
933                     el.element2D.evalVisProp('visible')
934                 ) {
935                     lay = el.element2D.evalVisProp('layer');
936                     if (layers.indexOf(lay) >= 0) {
937                         this.depthOrdered[lay].push(el);
938                     }
939                 }
940             }
941         }
942 
943         if (this.board.renderer && this.board.renderer.type === 'svg') {
944             for (i = 0; i < layers.length; i++) {
945                 lay = layers[i];
946                 this.depthOrdered[lay].sort(this.compareDepth.bind(this));
947                 // DEBUG
948                 // if (this.depthOrdered[lay].length > 0) {
949                 //     for (let k = 0; k < this.depthOrdered[lay].length; k++) {
950                 //         let o = this.depthOrdered[lay][k]
951                 //         console.log(o.visProp.fillcolor, o.zIndex)
952                 //     }
953                 // }
954                 l = this.depthOrdered[lay];
955                 for (j = 0; j < l.length; j++) {
956                     this.board.renderer.setLayer(l[j].element2D, lay);
957                 }
958                 // this.depthOrdered[lay].forEach((el) => this.board.renderer.setLayer(el.element2D, lay));
959                 // Attention: forEach prevents deleting an element
960             }
961         }
962 
963         return this;
964     },
965 
966     updateRenderer: function () {
967         if (!this.needsUpdate) {
968             return this;
969         }
970 
971         // console.time('update')
972         // Handle depth ordering
973         this.depthOrdered = {};
974 
975         if (this.shift !== undefined && this.evalVisProp('depthorder.enabled')) {
976             // Update the zIndices of certain element types.
977             // We do it here in updateRenderer, because the elements' positions
978             // are meanwhile updated.
979             this.updateZIndices();
980 
981             this.updateShaders();
982 
983             if (this.board.renderer && this.board.renderer.type === 'svg') {
984                 // For SVG we update the DOM order
985                 // In canvas we sort the elements in board.updateRendererCanvas
986                 this.updateDepthOrdering();
987             }
988         }
989         // console.timeEnd('update')
990 
991         this.needsUpdate = false;
992         return this;
993     },
994 
995     removeObject: function (object, saveMethod) {
996         var i, el;
997 
998         // this.board.removeObject(object, saveMethod);
999         if (Type.isArray(object)) {
1000             for (i = 0; i < object.length; i++) {
1001                 this.removeObject(object[i]);
1002             }
1003             return this;
1004         }
1005 
1006         object = this.select(object);
1007 
1008         // // If the object which is about to be removed unknown or a string, do nothing.
1009         // // it is a string if a string was given and could not be resolved to an element.
1010         if (!Type.exists(object) || Type.isString(object)) {
1011             return this;
1012         }
1013 
1014         try {
1015             // Remove all children.
1016             for (el in object.childElements) {
1017                 if (object.childElements.hasOwnProperty(el)) {
1018                     this.removeObject(object.childElements[el]);
1019                 }
1020             }
1021 
1022             delete this.objects[object.id];
1023         } catch (e) {
1024             JXG.debug('View3D ' + object.id + ': Could not be removed: ' + e);
1025         }
1026 
1027         // this.update();
1028 
1029         this.board.removeObject(object, saveMethod);
1030 
1031         return this;
1032     },
1033 
1034     /**
1035      * Map world coordinates to focal coordinates. These coordinate systems
1036      * are explained in the {@link JXG.View3D#boxToCam} matrix
1037      * documentation.
1038      *
1039      * @param {Array} pWorld A world space point, in homogeneous coordinates.
1040      * @param {Boolean} [homog=true] Whether to return homogeneous coordinates.
1041      * If false, projects down to ordinary coordinates.
1042      */
1043     worldToFocal: function (pWorld, homog = true) {
1044         var k,
1045             pView = Mat.matVecMult(this.boxToCam, Mat.matVecMult(this.shift, pWorld));
1046         pView[3] -= pView[0] * this.focalDist;
1047         if (homog) {
1048             return pView;
1049         } else {
1050             for (k = 1; k < 4; k++) {
1051                 pView[k] /= pView[0];
1052             }
1053             return pView.slice(1, 4);
1054         }
1055     },
1056 
1057     /**
1058      * Project 3D coordinates to 2D board coordinates
1059      * The 3D coordinates are provides as three numbers x, y, z or one array of length 3.
1060      *
1061      * @param  {Number|Array} x
1062      * @param  {Number[]} y
1063      * @param  {Number[]} z
1064      * @returns {Array} Array of length 3 containing the projection on to the board
1065      * in homogeneous user coordinates.
1066      */
1067     project3DTo2D: function (x, y, z) {
1068         var vec, w;
1069         if (arguments.length === 3) {
1070             vec = [1, x, y, z];
1071         } else {
1072             // Argument is an array
1073             if (x.length === 3) {
1074                 // vec = [1].concat(x);
1075                 vec = x.slice();
1076                 vec.unshift(1);
1077             } else {
1078                 vec = x;
1079             }
1080         }
1081 
1082         w = Mat.matVecMult(this.matrix3D, vec);
1083 
1084         switch (this.projectionType) {
1085             case 'central':
1086                 w[1] /= w[0];
1087                 w[2] /= w[0];
1088                 w[3] /= w[0];
1089                 w[0] /= w[0];
1090                 return Mat.matVecMult(this.viewPortTransform, w.slice(0, 3));
1091 
1092             case 'parallel':
1093             default:
1094                 return w;
1095         }
1096     },
1097 
1098     /**
1099      * We know that v2d * w0 = mat * (1, x, y, d)^T where v2d = (1, b, c, h)^T with unknowns w0, h, x, y.
1100      * Setting R = mat^(-1) gives
1101      *   1/ w0 * (1, x, y, d)^T = R * v2d.
1102      * The first and the last row of this equation allows to determine 1/w0 and h.
1103      *
1104      * @param {Array} mat
1105      * @param {Array} v2d
1106      * @param {Number} d
1107      * @returns Array
1108      * @private
1109      */
1110     _getW0: function (mat, v2d, d) {
1111         var R = Mat.inverse(mat),
1112             R1 = R[0][0] + v2d[1] * R[0][1] + v2d[2] * R[0][2],
1113             R2 = R[3][0] + v2d[1] * R[3][1] + v2d[2] * R[3][2],
1114             w, h, det;
1115 
1116         det = d * R[0][3] - R[3][3];
1117         w = (R2 * R[0][3] - R1 * R[3][3]) / det;
1118         h = (R2 - R1 * d) / det;
1119         return [1 / w, h];
1120     },
1121 
1122     /**
1123      * Project a 2D coordinate to the plane defined by point "foot"
1124      * and the normal vector `normal`.
1125      *
1126      * @param  {JXG.Point} point2d
1127      * @param  {Array} normal Normal of plane
1128      * @param  {Array} foot Foot point of plane
1129      * @returns {Array} of length 4 containing the projected
1130      * point in homogeneous coordinates.
1131      */
1132     project2DTo3DPlane: function (point2d, normal, foot) {
1133         var mat, rhs, d, le, sol,
1134             f = foot.slice(1) || [0, 0, 0],
1135             n = normal.slice(1),
1136             v2d, w0, res;
1137 
1138         le = Mat.norm(n, 3);
1139         d = Mat.innerProduct(f, n, 3) / le;
1140 
1141         if (this.projectionType === 'parallel') {
1142             mat = this.matrix3D.slice(0, 3);     // Copy each row by reference
1143             mat.push([0, n[0], n[1], n[2]]);
1144 
1145             // 2D coordinates of point
1146             rhs = point2d.coords.usrCoords.slice();
1147             rhs.push(d);
1148             try {
1149                 // Prevent singularity in case elevation angle is zero
1150                 if (mat[2][3] === 1.0) {
1151                     mat[2][1] = mat[2][2] = Mat.eps * 0.001;
1152                 }
1153                 sol = Mat.Numerics.Gauss(mat, rhs);
1154             } catch (e) {
1155                 sol = [0, NaN, NaN, NaN];
1156             }
1157         } else {
1158             mat = this.matrix3D;
1159 
1160             // 2D coordinates of point:
1161             rhs = point2d.coords.usrCoords.slice();
1162 
1163             v2d = Mat.Numerics.Gauss(this.viewPortTransform, rhs);
1164             res = this._getW0(mat, v2d, d);
1165             w0 = res[0];
1166             rhs = [
1167                 v2d[0] * w0,
1168                 v2d[1] * w0,
1169                 v2d[2] * w0,
1170                 res[1] * w0
1171             ];
1172             try {
1173                 // Prevent singularity in case elevation angle is zero
1174                 if (mat[2][3] === 1.0) {
1175                     mat[2][1] = mat[2][2] = Mat.eps * 0.001;
1176                 }
1177 
1178                 sol = Mat.Numerics.Gauss(mat, rhs);
1179                 sol[1] /= sol[0];
1180                 sol[2] /= sol[0];
1181                 sol[3] /= sol[0];
1182                 // sol[3] = d;
1183                 sol[0] /= sol[0];
1184             } catch (err) {
1185                 sol = [0, NaN, NaN, NaN];
1186             }
1187         }
1188 
1189         return sol;
1190     },
1191 
1192     /**
1193      * Project a point on the screen to the nearest point, in screen
1194      * distance, on a line segment in 3d space. The inputs must be in
1195      * ordinary coordinates, but the output is in homogeneous coordinates.
1196      *
1197      * @param {Array} pScr The screen coordinates of the point to project.
1198      * @param {Array} end0 The world space coordinates of one end of the
1199      * line segment.
1200      * @param {Array} end1 The world space coordinates of the other end of
1201      * the line segment.
1202      *
1203      * @returns Homogeneous coordinates of the projection
1204      */
1205     projectScreenToSegment: function (pScr, end0, end1) {
1206         var end0_2d = this.project3DTo2D(end0).slice(1, 3),
1207             end1_2d = this.project3DTo2D(end1).slice(1, 3),
1208             dir_2d = [
1209                 end1_2d[0] - end0_2d[0],
1210                 end1_2d[1] - end0_2d[1]
1211             ],
1212             dir_2d_norm_sq = Mat.innerProduct(dir_2d, dir_2d),
1213             diff = [
1214                 pScr[0] - end0_2d[0],
1215                 pScr[1] - end0_2d[1]
1216             ],
1217             s = Mat.innerProduct(diff, dir_2d) / dir_2d_norm_sq, // screen-space affine parameter
1218             mid, mid_2d, mid_diff, m,
1219 
1220             t, // view-space affine parameter
1221             t_clamped, // affine parameter clamped to range
1222             t_clamped_co;
1223 
1224         if (this.projectionType === 'central') {
1225             mid = [
1226                 0.5 * (end0[0] + end1[0]),
1227                 0.5 * (end0[1] + end1[1]),
1228                 0.5 * (end0[2] + end1[2])
1229             ];
1230             mid_2d = this.project3DTo2D(mid).slice(1, 3);
1231             mid_diff = [
1232                 mid_2d[0] - end0_2d[0],
1233                 mid_2d[1] - end0_2d[1]
1234             ];
1235             m = Mat.innerProduct(mid_diff, dir_2d) / dir_2d_norm_sq;
1236 
1237             // the view-space affine parameter s is related to the
1238             // screen-space affine parameter t by a Möbius transformation,
1239             // which is determined by the following relations:
1240             //
1241             // s | t
1242             // -----
1243             // 0 | 0
1244             // m | 1/2
1245             // 1 | 1
1246             //
1247             t = (1 - m) * s / ((1 - 2 * m) * s + m);
1248         } else {
1249             t = s;
1250         }
1251 
1252         t_clamped = Math.min(Math.max(t, 0), 1);
1253         t_clamped_co = 1 - t_clamped;
1254         return [
1255             1,
1256             t_clamped_co * end0[0] + t_clamped * end1[0],
1257             t_clamped_co * end0[1] + t_clamped * end1[1],
1258             t_clamped_co * end0[2] + t_clamped * end1[2]
1259         ];
1260     },
1261 
1262     /**
1263      * Project a 2D coordinate to a new 3D position by keeping
1264      * the 3D x, y coordinates and changing only the z coordinate.
1265      * All horizontal moves of the 2D point are ignored.
1266      *
1267      * @param {JXG.Point} point2d
1268      * @param {Array} base_c3d
1269      * @returns {Array} of length 4 containing the projected
1270      * point in homogeneous coordinates.
1271      */
1272     project2DTo3DVertical: function (point2d, base_c3d) {
1273         var pScr = point2d.coords.usrCoords.slice(1, 3),
1274             end0 = [base_c3d[1], base_c3d[2], this.bbox3D[2][0]],
1275             end1 = [base_c3d[1], base_c3d[2], this.bbox3D[2][1]];
1276 
1277         return this.projectScreenToSegment(pScr, end0, end1);
1278     },
1279 
1280     /**
1281      * Limit 3D coordinates to the bounding cube.
1282      *
1283      * @param {Array} c3d 3D coordinates [x,y,z]
1284      * @returns Array [Array, Boolean] containing [coords, corrected]. coords contains the updated 3D coordinates,
1285      * correct is true if the coords have been changed.
1286      */
1287     project3DToCube: function (c3d) {
1288         var cube = this.bbox3D,
1289             isOut = false;
1290 
1291         if (c3d[1] < cube[0][0]) {
1292             c3d[1] = cube[0][0];
1293             isOut = true;
1294         }
1295         if (c3d[1] > cube[0][1]) {
1296             c3d[1] = cube[0][1];
1297             isOut = true;
1298         }
1299         if (c3d[2] < cube[1][0]) {
1300             c3d[2] = cube[1][0];
1301             isOut = true;
1302         }
1303         if (c3d[2] > cube[1][1]) {
1304             c3d[2] = cube[1][1];
1305             isOut = true;
1306         }
1307         if (c3d[3] <= cube[2][0]) {
1308             c3d[3] = cube[2][0];
1309             isOut = true;
1310         }
1311         if (c3d[3] >= cube[2][1]) {
1312             c3d[3] = cube[2][1];
1313             isOut = true;
1314         }
1315 
1316         return [c3d, isOut];
1317     },
1318 
1319     /**
1320      * Intersect a ray with the bounding cube of the 3D view.
1321      * @param {Array} p 3D coordinates [w,x,y,z]
1322      * @param {Array} dir 3D direction vector of the line (array of length 3 or 4)
1323      * @param {Number} r direction of the ray (positive if r > 0, negative if r < 0).
1324      * @returns Affine ratio of the intersection of the line with the cube.
1325      */
1326     intersectionLineCube: function (p, dir, r) {
1327         var r_n, i, r0, r1, d;
1328 
1329         d = (dir.length === 3) ? dir : dir.slice(1);
1330 
1331         r_n = r;
1332         for (i = 0; i < 3; i++) {
1333             if (d[i] !== 0) {
1334                 r0 = (this.bbox3D[i][0] - p[i + 1]) / d[i];
1335                 r1 = (this.bbox3D[i][1] - p[i + 1]) / d[i];
1336                 if (r < 0) {
1337                     r_n = Math.max(r_n, Math.min(r0, r1));
1338                 } else {
1339                     r_n = Math.min(r_n, Math.max(r0, r1));
1340                 }
1341             }
1342         }
1343         return r_n;
1344     },
1345 
1346     /**
1347      * Test if coordinates are inside of the bounding cube.
1348      * @param {array} p 3D coordinates [[w],x,y,z] of a point.
1349      * @returns Boolean
1350      */
1351     isInCube: function (p, polyhedron) {
1352         var q;
1353         if (p.length === 4) {
1354             if (p[0] === 0) {
1355                 return false;
1356             }
1357             q = p.slice(1);
1358         }
1359         return (
1360             q[0] > this.bbox3D[0][0] - Mat.eps &&
1361             q[0] < this.bbox3D[0][1] + Mat.eps &&
1362             q[1] > this.bbox3D[1][0] - Mat.eps &&
1363             q[1] < this.bbox3D[1][1] + Mat.eps &&
1364             q[2] > this.bbox3D[2][0] - Mat.eps &&
1365             q[2] < this.bbox3D[2][1] + Mat.eps
1366         );
1367     },
1368 
1369     /**
1370      *
1371      * @param {JXG.Plane3D} plane1
1372      * @param {JXG.Plane3D} plane2
1373      * @param {Number} d Right hand side of Hesse normal for plane2 (it can be adjusted)
1374      * @returns {Array} of length 2 containing the coordinates of the defining points of
1375      * of the intersection segment, or false if there is no intersection
1376      */
1377     intersectionPlanePlane: function (plane1, plane2, d) {
1378         var ret = [false, false],
1379             p, q, r, w,
1380             dir;
1381 
1382         d = d || plane2.d;
1383 
1384         // Get one point of the intersection of the two planes
1385         w = Mat.crossProduct(plane1.normal.slice(1), plane2.normal.slice(1));
1386         w.unshift(0);
1387 
1388         p = Mat.Geometry.meet3Planes(
1389             plane1.normal,
1390             plane1.d,
1391             plane2.normal,
1392             d,
1393             w,
1394             0
1395         );
1396 
1397         // Get the direction of the intersecting line of the two planes
1398         dir = Mat.Geometry.meetPlanePlane(
1399             plane1.vec1,
1400             plane1.vec2,
1401             plane2.vec1,
1402             plane2.vec2
1403         );
1404 
1405         // Get the bounding points of the intersecting segment
1406         r = this.intersectionLineCube(p, dir, Infinity);
1407         q = Mat.axpy(r, dir, p);
1408         if (this.isInCube(q)) {
1409             ret[0] = q;
1410         }
1411         r = this.intersectionLineCube(p, dir, -Infinity);
1412         q = Mat.axpy(r, dir, p);
1413         if (this.isInCube(q)) {
1414             ret[1] = q;
1415         }
1416 
1417         return ret;
1418     },
1419 
1420     intersectionPlaneFace: function (plane, face) {
1421         var ret = [],
1422             j, t,
1423             p, crds,
1424             p1, p2, c,
1425             f, le, x1, y1, x2, y2,
1426             dir, vec, w,
1427             mat = [], b = [], sol;
1428 
1429         w = Mat.crossProduct(plane.normal.slice(1), face.normal.slice(1));
1430         w.unshift(0);
1431 
1432         // Get one point of the intersection of the two planes
1433         p = Geometry.meet3Planes(
1434             plane.normal,
1435             plane.d,
1436             face.normal,
1437             face.d,
1438             w,
1439             0
1440         );
1441 
1442         // Get the direction the intersecting line of the two planes
1443         dir = Geometry.meetPlanePlane(
1444             plane.vec1,
1445             plane.vec2,
1446             face.vec1,
1447             face.vec2
1448         );
1449 
1450         f = face.polyhedron.faces[face.faceNumber];
1451         crds = face.polyhedron.coords;
1452         le = f.length;
1453         for (j = 1; j <= le; j++) {
1454             p1 = crds[f[j - 1]];
1455             p2 = crds[f[j % le]];
1456             vec = [0, p2[1] - p1[1], p2[2] - p1[2], p2[3] - p1[3]];
1457 
1458             x1 = Math.random();
1459             y1 = Math.random();
1460             x2 = Math.random();
1461             y2 = Math.random();
1462             mat = [
1463                 [x1 * dir[1] + y1 * dir[3], x1 * (-vec[1]) + y1 * (-vec[3])],
1464                 [x2 * dir[2] + y2 * dir[3], x2 * (-vec[2]) + y2 * (-vec[3])]
1465             ];
1466             b = [
1467                 x1 * (p1[1] - p[1]) + y1 * (p1[3] - p[3]),
1468                 x2 * (p1[2] - p[2]) + y2 * (p1[3] - p[3])
1469             ];
1470 
1471             sol = Numerics.Gauss(mat, b);
1472             t = sol[1];
1473             if (t > -Mat.eps && t < 1 + Mat.eps) {
1474                 c = [1, p1[1] + t * vec[1], p1[2] + t * vec[2], p1[3] + t * vec[3]];
1475                 ret.push(c);
1476             }
1477         }
1478 
1479         return ret;
1480     },
1481 
1482     // TODO:
1483     // - handle non-closed polyhedra
1484     // - handle intersections in vertex, edge, plane
1485     intersectionPlanePolyhedron: function(plane, phdr) {
1486         var i, j, seg,
1487             p, first, pos, pos_akt,
1488             eps = 1e-12,
1489             points = [],
1490             x = [],
1491             y = [],
1492             z = [];
1493 
1494         for (i = 0; i < phdr.numberFaces; i++) {
1495             if (phdr.def.faces[i].length < 3) {
1496                 // We skip intersection with points or lines
1497                 continue;
1498             }
1499 
1500             // seg will be an array consisting of two points
1501             // that span the intersecting segment of the plane
1502             // and the face.
1503             seg = this.intersectionPlaneFace(plane, phdr.faces[i]);
1504 
1505             // Plane intersects the face in less than 2 points
1506             if (seg.length < 2) {
1507                 continue;
1508             }
1509 
1510             if (seg[0].length === 4 && seg[1].length === 4) {
1511                 // This test is necessary to filter out intersection lines which are
1512                 // identical to intersections of axis planes (they would occur twice),
1513                 // i.e. edges of bbox3d.
1514                 for (j = 0; j < points.length; j++) {
1515                     if (
1516                         (Geometry.distance(seg[0], points[j][0], 4) < eps &&
1517                             Geometry.distance(seg[1], points[j][1], 4) < eps) ||
1518                         (Geometry.distance(seg[0], points[j][1], 4) < eps &&
1519                             Geometry.distance(seg[1], points[j][0], 4) < eps)
1520                     ) {
1521                         break;
1522                     }
1523                 }
1524                 if (j === points.length) {
1525                     points.push(seg.slice());
1526                 }
1527             }
1528         }
1529 
1530         // Handle the case that the intersection is the empty set.
1531         if (points.length === 0) {
1532             return { X: x, Y: y, Z: z };
1533         }
1534 
1535         // Concatenate the intersection points to a polygon.
1536         // If all went well, each intersection should appear
1537         // twice in the list.
1538         // __Attention:__ each face has to be planar!!!
1539         // Otherwise the algorithm will fail.
1540         first = 0;
1541         pos = first;
1542         i = 0;
1543         do {
1544             p = points[pos][i];
1545             if (p.length === 4) {
1546                 x.push(p[1]);
1547                 y.push(p[2]);
1548                 z.push(p[3]);
1549             }
1550             i = (i + 1) % 2;
1551             p = points[pos][i];
1552 
1553             pos_akt = pos;
1554             for (j = 0; j < points.length; j++) {
1555                 if (j !== pos && Geometry.distance(p, points[j][0]) < eps) {
1556                     pos = j;
1557                     i = 0;
1558                     break;
1559                 }
1560                 if (j !== pos && Geometry.distance(p, points[j][1]) < eps) {
1561                     pos = j;
1562                     i = 1;
1563                     break;
1564                 }
1565             }
1566             if (pos === pos_akt) {
1567                 console.log('Error face3d intersection update: did not find next', pos, i);
1568                 break;
1569             }
1570         } while (pos !== first);
1571         x.push(x[0]);
1572         y.push(y[0]);
1573         z.push(z[0]);
1574 
1575         return { X: x, Y: y, Z: z };
1576     },
1577 
1578     /**
1579      * Generate mesh for a surface / plane.
1580      * Returns array [dataX, dataY] for a JSXGraph curve's updateDataArray function.
1581      * @param {Array|Function} func
1582      * @param {Array} interval_u
1583      * @param {Array} interval_v
1584      * @returns Array
1585      * @private
1586      *
1587      * @example
1588      *  var el = view.create('curve', [[], []]);
1589      *  el.updateDataArray = function () {
1590      *      var steps_u = this.evalVisProp('stepsu'),
1591      *           steps_v = this.evalVisProp('stepsv'),
1592      *           r_u = Type.evaluate(this.range_u),
1593      *           r_v = Type.evaluate(this.range_v),
1594      *           func, ret;
1595      *
1596      *      if (this.F !== null) {
1597      *          func = this.F;
1598      *      } else {
1599      *          func = [this.X, this.Y, this.Z];
1600      *      }
1601      *      ret = this.view.getMesh(func,
1602      *          r_u.concat([steps_u]),
1603      *          r_v.concat([steps_v]));
1604      *
1605      *      this.dataX = ret[0];
1606      *      this.dataY = ret[1];
1607      *  };
1608      *
1609      */
1610     getMesh: function (func, interval_u, interval_v) {
1611         var i_u, i_v, u, v,
1612             c2d, delta_u, delta_v,
1613             p = [0, 0, 0],
1614             steps_u = Type.evaluate(interval_u[2]),
1615             steps_v = Type.evaluate(interval_v[2]),
1616             dataX = [],
1617             dataY = [];
1618 
1619         delta_u = (Type.evaluate(interval_u[1]) - Type.evaluate(interval_u[0])) / steps_u;
1620         delta_v = (Type.evaluate(interval_v[1]) - Type.evaluate(interval_v[0])) / steps_v;
1621 
1622         for (i_u = 0; i_u <= steps_u; i_u++) {
1623             u = interval_u[0] + delta_u * i_u;
1624             for (i_v = 0; i_v <= steps_v; i_v++) {
1625                 v = interval_v[0] + delta_v * i_v;
1626                 if (Type.isFunction(func)) {
1627                     p = func(u, v);
1628                 } else {
1629                     p = [func[0](u, v), func[1](u, v), func[2](u, v)];
1630                 }
1631                 c2d = this.project3DTo2D(p);
1632                 dataX.push(c2d[1]);
1633                 dataY.push(c2d[2]);
1634             }
1635             dataX.push(NaN);
1636             dataY.push(NaN);
1637         }
1638 
1639         for (i_v = 0; i_v <= steps_v; i_v++) {
1640             v = interval_v[0] + delta_v * i_v;
1641             for (i_u = 0; i_u <= steps_u; i_u++) {
1642                 u = interval_u[0] + delta_u * i_u;
1643                 if (Type.isFunction(func)) {
1644                     p = func(u, v);
1645                 } else {
1646                     p = [func[0](u, v), func[1](u, v), func[2](u, v)];
1647                 }
1648                 c2d = this.project3DTo2D(p);
1649                 dataX.push(c2d[1]);
1650                 dataY.push(c2d[2]);
1651             }
1652             dataX.push(NaN);
1653             dataY.push(NaN);
1654         }
1655 
1656         return [dataX, dataY];
1657     },
1658 
1659     /**
1660      *
1661      */
1662     animateAzimuth: function () {
1663         var s = this.az_slide._smin,
1664             e = this.az_slide._smax,
1665             sdiff = e - s,
1666             newVal = this.az_slide.Value() + 0.1;
1667 
1668         this.az_slide.position = (newVal - s) / sdiff;
1669         if (this.az_slide.position > 1) {
1670             this.az_slide.position = 0.0;
1671         }
1672         this.board._change3DView = true;
1673         this.board.update();
1674         this.board._change3DView = false;
1675 
1676         this.timeoutAzimuth = setTimeout(function () {
1677             this.animateAzimuth();
1678         }.bind(this), 200);
1679     },
1680 
1681     /**
1682      *
1683      */
1684     stopAzimuth: function () {
1685         clearTimeout(this.timeoutAzimuth);
1686         this.timeoutAzimuth = null;
1687     },
1688 
1689     /**
1690      * Check if vertical dragging is enabled and which action is needed.
1691      * Default is shiftKey.
1692      *
1693      * @returns Boolean
1694      * @private
1695      */
1696     isVerticalDrag: function () {
1697         var b = this.board,
1698             key;
1699         if (!this.evalVisProp('verticaldrag.enabled')) {
1700             return false;
1701         }
1702         key = '_' + this.evalVisProp('verticaldrag.key') + 'Key';
1703         return b[key];
1704     },
1705 
1706     /**
1707      * Sets camera view to the given values.
1708      *
1709      * @param {Number} az Value of azimuth.
1710      * @param {Number} el Value of elevation.
1711      * @param {Number} [r] Value of radius.
1712      *
1713      * @returns {Object} Reference to the view.
1714      */
1715     setView: function (az, el, r) {
1716         r = r || this.r;
1717 
1718         this.az_slide.setValue(az);
1719         this.el_slide.setValue(el);
1720         this.r = r;
1721         this.board.update();
1722 
1723         return this;
1724     },
1725 
1726     /**
1727      * Changes view to the next view stored in the attribute `values`.
1728      *
1729      * @see View3D#values
1730      *
1731      * @returns {Object} Reference to the view.
1732      */
1733     nextView: function () {
1734         var views = this.evalVisProp('values'),
1735             n = this.visProp._currentview;
1736 
1737         n = (n + 1) % views.length;
1738         this.setCurrentView(n);
1739 
1740         return this;
1741     },
1742 
1743     /**
1744      * Changes view to the previous view stored in the attribute `values`.
1745      *
1746      * @see View3D#values
1747      *
1748      * @returns {Object} Reference to the view.
1749      */
1750     previousView: function () {
1751         var views = this.evalVisProp('values'),
1752             n = this.visProp._currentview;
1753 
1754         n = (n + views.length - 1) % views.length;
1755         this.setCurrentView(n);
1756 
1757         return this;
1758     },
1759 
1760     /**
1761      * Changes view to the determined view stored in the attribute `values`.
1762      *
1763      * @see View3D#values
1764      *
1765      * @param {Number} n Index of view in attribute `values`.
1766      * @returns {Object} Reference to the view.
1767      */
1768     setCurrentView: function (n) {
1769         var views = this.evalVisProp('values');
1770 
1771         if (n < 0 || n >= views.length) {
1772             n = ((n % views.length) + views.length) % views.length;
1773         }
1774 
1775         this.setView(views[n][0], views[n][1], views[n][2]);
1776         this.visProp._currentview = n;
1777 
1778         return this;
1779     },
1780 
1781     /**
1782      * Controls the navigation in az direction using either the keyboard or a pointer.
1783      *
1784      * @private
1785      *
1786      * @param {event} evt either the keydown or the pointer event
1787      * @returns view
1788      */
1789     _azEventHandler: function (evt) {
1790         var smax = this.az_slide._smax,
1791             smin = this.az_slide._smin,
1792             speed = (smax - smin) / this.board.canvasWidth * (this.evalVisProp('az.pointer.speed')),
1793             delta, // = evt.movementX,
1794             az = this.az_slide.Value(),
1795             el = this.el_slide.Value();
1796 
1797         delta = evt.screenX - this._lastPos.x;
1798         this._lastPos.x = evt.screenX;
1799 
1800         // Doesn't allow navigation if another moving event is triggered
1801         if (this.board.mode === this.board.BOARD_MODE_DRAG) {
1802             return this;
1803         }
1804 
1805         // Calculate new az value if keyboard events are triggered
1806         // Plus if right-button, minus if left-button
1807         if (this.evalVisProp('az.keyboard.enabled')) {
1808             if (evt.key === 'ArrowRight') {
1809                 az = az + this.evalVisProp('az.keyboard.step') * Math.PI / 180;
1810             } else if (evt.key === 'ArrowLeft') {
1811                 az = az - this.evalVisProp('az.keyboard.step') * Math.PI / 180;
1812             }
1813         }
1814 
1815         if (this.evalVisProp('az.pointer.enabled') && (delta !== 0) && evt.key == null) {
1816             // delta *= (Math.abs(delta) > 100) ? 0.03 : 1;
1817             az += delta * speed;
1818         }
1819 
1820         // Project the calculated az value to a usable value in the interval [smin,smax]
1821         // Use modulo if continuous is true
1822         if (this.evalVisProp('az.continuous')) {
1823             az = Mat.wrap(az, smin, smax);
1824         } else {
1825             if (az > 0) {
1826                 az = Math.min(smax, az);
1827             } else if (az < 0) {
1828                 az = Math.max(smin, az);
1829             }
1830         }
1831 
1832         this.setView(az, el);
1833         return this;
1834     },
1835 
1836     /**
1837      * Controls the navigation in el direction using either the keyboard or a pointer.
1838      *
1839      * @private
1840      *
1841      * @param {event} evt either the keydown or the pointer event
1842      * @returns view
1843      */
1844     _elEventHandler: function (evt) {
1845         var smax = this.el_slide._smax,
1846             smin = this.el_slide._smin,
1847             speed = (smax - smin) / this.board.canvasHeight * this.evalVisProp('el.pointer.speed'),
1848             delta, // = evt.movementY,
1849             az = this.az_slide.Value(),
1850             el = this.el_slide.Value();
1851 
1852         delta = evt.screenY - this._lastPos.y;
1853         this._lastPos.y = evt.screenY;
1854 
1855         // Doesn't allow navigation if another moving event is triggered
1856         if (this.board.mode === this.board.BOARD_MODE_DRAG) {
1857             return this;
1858         }
1859 
1860         // Calculate new az value if keyboard events are triggered
1861         // Plus if down-button, minus if up-button
1862         if (this.evalVisProp('el.keyboard.enabled')) {
1863             if (evt.key === 'ArrowUp') {
1864                 el = el - this.evalVisProp('el.keyboard.step') * Math.PI / 180;
1865             } else if (evt.key === 'ArrowDown') {
1866                 el = el + this.evalVisProp('el.keyboard.step') * Math.PI / 180;
1867             }
1868         }
1869 
1870         if (this.evalVisProp('el.pointer.enabled') && (delta !== 0) && evt.key == null) {
1871             // delta *= (Math.abs(delta) > 100) ? 0.05 : 1;
1872             el += delta * speed;
1873         }
1874 
1875         // Project the calculated el value to a usable value in the interval [smin,smax]
1876         // Use modulo if continuous is true and the trackball is disabled
1877         if (this.evalVisProp('el.continuous') && !this.trackballEnabled) {
1878             el = Mat.wrap(el, smin, smax);
1879         } else {
1880             if (el > 0) {
1881                 el = Math.min(smax, el);
1882             } else if (el < 0) {
1883                 el = Math.max(smin, el);
1884             }
1885         }
1886 
1887         this.setView(az, el);
1888 
1889         return this;
1890     },
1891 
1892     /**
1893      * Controls the navigation in bank direction using either the keyboard or a pointer.
1894      *
1895      * @private
1896      *
1897      * @param {event} evt either the keydown or the pointer event
1898      * @returns view
1899      */
1900     _bankEventHandler: function (evt) {
1901         var smax = this.bank_slide._smax,
1902             smin = this.bank_slide._smin,
1903             step, speed,
1904             delta = evt.deltaY, // Wheel event
1905             bank = this.bank_slide.Value();
1906 
1907         // Doesn't allow navigation if another moving event is triggered
1908         if (this.board.mode === this.board.BOARD_MODE_DRAG) {
1909             return this;
1910         }
1911 
1912         // Calculate new bank value if keyboard events are triggered
1913         // Plus if down-button, minus if up-button
1914         if (this.evalVisProp('bank.keyboard.enabled')) {
1915             step = this.evalVisProp('bank.keyboard.step') * Math.PI / 180;
1916             if (evt.key === '.' || evt.key === '<') {
1917                 bank -= step;
1918             } else if (evt.key === ',' || evt.key === '>') {
1919                 bank += step;
1920             }
1921         }
1922 
1923         if (this.evalVisProp('bank.pointer.enabled') && (delta !== 0) && evt.key == null) {
1924             speed = (smax - smin) / this.board.canvasHeight * this.evalVisProp('bank.pointer.speed');
1925             bank += delta * speed;
1926 
1927             // prevent the pointer wheel from scrolling the page
1928             evt.preventDefault();
1929         }
1930 
1931         // Project the calculated bank value to a usable value in the interval [smin,smax]
1932         if (this.evalVisProp('bank.continuous')) {
1933             // in continuous mode, wrap value around slider range
1934             bank = Mat.wrap(bank, smin, smax);
1935         } else {
1936             // in non-continuous mode, clamp value to slider range
1937             bank = Mat.clamp(bank, smin, smax);
1938         }
1939 
1940         this.bank_slide.setValue(bank);
1941         this.board.update();
1942         return this;
1943     },
1944 
1945     /**
1946      * Controls the navigation using either virtual trackball.
1947      *
1948      * @private
1949      *
1950      * @param {event} evt either the keydown or the pointer event
1951      * @returns view
1952      */
1953     _trackballHandler: function (evt) {
1954         var pos = this.board.getMousePosition(evt),
1955             x, y, dx, dy, center;
1956 
1957         center = new Coords(Const.COORDS_BY_USER, [this.llftCorner[0] + this.size[0] * 0.5, this.llftCorner[1] + this.size[1] * 0.5], this.board);
1958         x = pos[0] - center.scrCoords[1];
1959         y = pos[1] - center.scrCoords[2];
1960 
1961         dx = evt.screenX - this._lastPos.x;
1962         dy = evt.screenY - this._lastPos.y;
1963         this._lastPos.x = evt.screenX;
1964         this._lastPos.y = evt.screenY;
1965 
1966         this._trackball = {
1967             dx: dx,
1968             dy: -dy,
1969             x: x,
1970             y: -y
1971         };
1972         this.board.update();
1973         return this;
1974     },
1975 
1976     /**
1977      * Event handler for pointer down event. Triggers handling of all 3D navigation.
1978      *
1979      * @private
1980      * @param {event} evt
1981      * @returns view
1982      */
1983     pointerDownHandler: function (evt) {
1984         var neededButton, neededKey, target;
1985 
1986         this._hasMoveAz = false;
1987         this._hasMoveEl = false;
1988         this._hasMoveBank = false;
1989         this._hasMoveTrackball = false;
1990 
1991         if (this.board.mode !== this.board.BOARD_MODE_NONE) {
1992             return;
1993         }
1994 
1995         this.board._change3DView = true;
1996 
1997         this._lastPos.x = evt.screenX;
1998         this._lastPos.y = evt.screenY;
1999 
2000         if (this.evalVisProp('trackball.enabled')) {
2001             neededButton = this.evalVisProp('trackball.button');
2002             neededKey = this.evalVisProp('trackball.key');
2003 
2004             // Move events for virtual trackball
2005             if (
2006                 (neededButton === -1 || neededButton === evt.button) &&
2007                 (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))
2008             ) {
2009                 // If outside is true then the event listener is bound to the document, otherwise to the div
2010                 target = (this.evalVisProp('trackball.outside')) ? document : this.board.containerObj;
2011                 Env.addEvent(target, 'pointermove', this._trackballHandler, this);
2012                 this._hasMoveTrackball = true;
2013             }
2014         } else {
2015             if (this.evalVisProp('az.pointer.enabled')) {
2016                 neededButton = this.evalVisProp('az.pointer.button');
2017                 neededKey = this.evalVisProp('az.pointer.key');
2018 
2019                 // Move events for azimuth
2020                 if (
2021                     (neededButton === -1 || neededButton === evt.button) &&
2022                     (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))
2023                 ) {
2024                     // If outside is true then the event listener is bound to the document, otherwise to the div
2025                     target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj;
2026                     Env.addEvent(target, 'pointermove', this._azEventHandler, this);
2027                     this._hasMoveAz = true;
2028                 }
2029             }
2030 
2031             if (this.evalVisProp('el.pointer.enabled')) {
2032                 neededButton = this.evalVisProp('el.pointer.button');
2033                 neededKey = this.evalVisProp('el.pointer.key');
2034 
2035                 // Events for elevation
2036                 if (
2037                     (neededButton === -1 || neededButton === evt.button) &&
2038                     (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))
2039                 ) {
2040                     // If outside is true then the event listener is bound to the document, otherwise to the div
2041                     target = (this.evalVisProp('el.pointer.outside')) ? document : this.board.containerObj;
2042                     Env.addEvent(target, 'pointermove', this._elEventHandler, this);
2043                     this._hasMoveEl = true;
2044                 }
2045             }
2046 
2047             if (this.evalVisProp('bank.pointer.enabled')) {
2048                 neededButton = this.evalVisProp('bank.pointer.button');
2049                 neededKey = this.evalVisProp('bank.pointer.key');
2050 
2051                 // Events for bank
2052                 if (
2053                     (neededButton === -1 || neededButton === evt.button) &&
2054                     (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))
2055                 ) {
2056                     // If `outside` is true, we bind the event listener to
2057                     // the document. otherwise, we bind it to the div. we
2058                     // register the event listener as active so it can
2059                     // prevent the pointer wheel from scrolling the page
2060                     target = (this.evalVisProp('bank.pointer.outside')) ? document : this.board.containerObj;
2061                     Env.addEvent(target, 'wheel', this._bankEventHandler, this, { passive: false });
2062                     this._hasMoveBank = true;
2063                 }
2064             }
2065         }
2066         Env.addEvent(document, 'pointerup', this.pointerUpHandler, this);
2067     },
2068 
2069     /**
2070      * Event handler for pointer up event. Triggers handling of all 3D navigation.
2071      *
2072      * @private
2073      * @param {event} evt
2074      * @returns view
2075      */
2076     pointerUpHandler: function (evt) {
2077         var target;
2078 
2079         if (this._hasMoveAz) {
2080             target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj;
2081             Env.removeEvent(target, 'pointermove', this._azEventHandler, this);
2082             this._hasMoveAz = false;
2083         }
2084         if (this._hasMoveEl) {
2085             target = (this.evalVisProp('el.pointer.outside')) ? document : this.board.containerObj;
2086             Env.removeEvent(target, 'pointermove', this._elEventHandler, this);
2087             this._hasMoveEl = false;
2088         }
2089         if (this._hasMoveBank) {
2090             target = (this.evalVisProp('bank.pointer.outside')) ? document : this.board.containerObj;
2091             Env.removeEvent(target, 'wheel', this._bankEventHandler, this);
2092             this._hasMoveBank = false;
2093         }
2094         if (this._hasMoveTrackball) {
2095             target = (this.evalVisProp('trackball.outside')) ? document : this.board.containerObj;
2096             Env.removeEvent(target, 'pointermove', this._trackballHandler, this);
2097             this._hasMoveTrackball = false;
2098         }
2099         Env.removeEvent(document, 'pointerup', this.pointerUpHandler, this);
2100         this.board._change3DView = false;
2101 
2102     }
2103 });
2104 
2105 /**
2106  * @class A View3D element provides the container and the methods to create and display 3D elements.
2107  * @pseudo
2108  * @description  A View3D element provides the container and the methods to create and display 3D elements.
2109  * It is contained in a JSXGraph board.
2110  * <p>
2111  * It is advisable to disable panning of the board by setting the board attribute "pan":
2112  * <pre>
2113  *   pan: {enabled: false}
2114  * </pre>
2115  * Otherwise users will not be able to rotate the scene with their fingers on a touch device.
2116  * <p>
2117  * The start position of the camera can be adjusted by the attributes {@link View3D#az}, {@link View3D#el}, and {@link View3D#bank}.
2118  *
2119  * @name View3D
2120  * @augments JXG.View3D
2121  * @constructor
2122  * @type Object
2123  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
2124  * @param {Array_Array_Array} lower,dim,cube  Here, lower is an array of the form [x, y] and
2125  * dim is an array of the form [w, h].
2126  * The arrays [x, y] and [w, h] define the 2D frame into which the 3D cube is
2127  * (roughly) projected. If the view's azimuth=0 and elevation=0, the 3D view will cover a rectangle with lower left corner
2128  * [x,y] and side lengths [w, h] of the board.
2129  * The array 'cube' is of the form [[x1, x2], [y1, y2], [z1, z2]]
2130  * which determines the coordinate ranges of the 3D cube.
2131  *
2132  * @example
2133  *     var bound = [-4, 6];
2134  *     var view = board.create('view3d',
2135  *         [[-4, -3], [8, 8],
2136  *         [bound, bound, bound]],
2137  *         {
2138  *             projection: 'parallel',
2139  *             trackball: {enabled:true},
2140  *         });
2141  *
2142  *     var curve = view.create('curve3d', [
2143  *         (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2144  *         (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2145  *         (t) => Math.sin(3 * t),
2146  *         [-Math.PI, Math.PI]
2147  *     ], { strokeWidth: 4 });
2148  *
2149  * </pre><div id="JXG9b327a6c-1bd6-4e40-a502-59d024dbfd1b" class="jxgbox" style="width: 300px; height: 300px;"></div>
2150  * <script type="text/javascript">
2151  *     (function() {
2152  *         var board = JXG.JSXGraph.initBoard('JXG9b327a6c-1bd6-4e40-a502-59d024dbfd1b',
2153  *             {boundingbox: [-8, 8, 8,-8], pan: {enabled: false}, axis: false, showcopyright: false, shownavigation: false});
2154  *         var bound = [-4, 6];
2155  *         var view = board.create('view3d',
2156  *             [[-4, -3], [8, 8],
2157  *             [bound, bound, bound]],
2158  *             {
2159  *                 projection: 'parallel',
2160  *                 trackball: {enabled:true},
2161  *             });
2162  *
2163  *         var curve = view.create('curve3d', [
2164  *             (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2165  *             (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2166  *             (t) => Math.sin(3 * t),
2167  *             [-Math.PI, Math.PI]
2168  *         ], { strokeWidth: 4 });
2169  *
2170  *     })();
2171  *
2172  * </script><pre>
2173  *
2174  * @example
2175  *     var bound = [-4, 6];
2176  *     var view = board.create('view3d',
2177  *         [[-4, -3], [8, 8],
2178  *         [bound, bound, bound]],
2179  *         {
2180  *             projection: 'central',
2181  *             trackball: {enabled:true},
2182  *
2183  *             xPlaneRear: { visible: false },
2184  *             yPlaneRear: { visible: false }
2185  *
2186  *         });
2187  *
2188  *     var curve = view.create('curve3d', [
2189  *         (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2190  *         (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2191  *         (t) => Math.sin(3 * t),
2192  *         [-Math.PI, Math.PI]
2193  *     ], { strokeWidth: 4 });
2194  *
2195  * </pre><div id="JXG0dc2493d-fb2f-40d5-bdb8-762ba0ad2007" class="jxgbox" style="width: 300px; height: 300px;"></div>
2196  * <script type="text/javascript">
2197  *     (function() {
2198  *         var board = JXG.JSXGraph.initBoard('JXG0dc2493d-fb2f-40d5-bdb8-762ba0ad2007',
2199  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
2200  *         var bound = [-4, 6];
2201  *         var view = board.create('view3d',
2202  *             [[-4, -3], [8, 8],
2203  *             [bound, bound, bound]],
2204  *             {
2205  *                 projection: 'central',
2206  *                 trackball: {enabled:true},
2207  *
2208  *                 xPlaneRear: { visible: false },
2209  *                 yPlaneRear: { visible: false }
2210  *
2211  *             });
2212  *
2213  *         var curve = view.create('curve3d', [
2214  *             (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2215  *             (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2216  *             (t) => Math.sin(3 * t),
2217  *             [-Math.PI, Math.PI]
2218  *         ], { strokeWidth: 4 });
2219  *
2220  *     })();
2221  *
2222  * </script><pre>
2223  *
2224 * @example
2225  *     var bound = [-4, 6];
2226  *     var view = board.create('view3d',
2227  *         [[-4, -3], [8, 8],
2228  *         [bound, bound, bound]],
2229  *         {
2230  *             projection: 'central',
2231  *             trackball: {enabled:true},
2232  *
2233  *             // Main axes
2234  *             axesPosition: 'border',
2235  *
2236  *             // Axes at the border
2237  *             xAxisBorder: { ticks3d: { ticksDistance: 2} },
2238  *             yAxisBorder: { ticks3d: { ticksDistance: 2} },
2239  *             zAxisBorder: { ticks3d: { ticksDistance: 2} },
2240  *
2241  *             // No axes on planes
2242  *             xPlaneRearYAxis: {visible: false},
2243  *             xPlaneRearZAxis: {visible: false},
2244  *             yPlaneRearXAxis: {visible: false},
2245  *             yPlaneRearZAxis: {visible: false},
2246  *             zPlaneRearXAxis: {visible: false},
2247  *             zPlaneRearYAxis: {visible: false}
2248  *         });
2249  *
2250  *     var curve = view.create('curve3d', [
2251  *         (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2252  *         (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2253  *         (t) => Math.sin(3 * t),
2254  *         [-Math.PI, Math.PI]
2255  *     ], { strokeWidth: 4 });
2256  *
2257  * </pre><div id="JXG586f3551-335c-47e9-8d72-835409f6a103" class="jxgbox" style="width: 300px; height: 300px;"></div>
2258  * <script type="text/javascript">
2259  *     (function() {
2260  *         var board = JXG.JSXGraph.initBoard('JXG586f3551-335c-47e9-8d72-835409f6a103',
2261  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
2262  *         var bound = [-4, 6];
2263  *         var view = board.create('view3d',
2264  *             [[-4, -3], [8, 8],
2265  *             [bound, bound, bound]],
2266  *             {
2267  *                 projection: 'central',
2268  *                 trackball: {enabled:true},
2269  *
2270  *                 // Main axes
2271  *                 axesPosition: 'border',
2272  *
2273  *                 // Axes at the border
2274  *                 xAxisBorder: { ticks3d: { ticksDistance: 2} },
2275  *                 yAxisBorder: { ticks3d: { ticksDistance: 2} },
2276  *                 zAxisBorder: { ticks3d: { ticksDistance: 2} },
2277  *
2278  *                 // No axes on planes
2279  *                 xPlaneRearYAxis: {visible: false},
2280  *                 xPlaneRearZAxis: {visible: false},
2281  *                 yPlaneRearXAxis: {visible: false},
2282  *                 yPlaneRearZAxis: {visible: false},
2283  *                 zPlaneRearXAxis: {visible: false},
2284  *                 zPlaneRearYAxis: {visible: false}
2285  *             });
2286  *
2287  *         var curve = view.create('curve3d', [
2288  *             (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2289  *             (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2290  *             (t) => Math.sin(3 * t),
2291  *             [-Math.PI, Math.PI]
2292  *         ], { strokeWidth: 4 });
2293  *
2294  *     })();
2295  *
2296  * </script><pre>
2297  *
2298  * @example
2299  *     var bound = [-4, 6];
2300  *     var view = board.create('view3d',
2301  *         [[-4, -3], [8, 8],
2302  *         [bound, bound, bound]],
2303  *         {
2304  *             projection: 'central',
2305  *             trackball: {enabled:true},
2306  *
2307  *             axesPosition: 'none'
2308  *         });
2309  *
2310  *     var curve = view.create('curve3d', [
2311  *         (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2312  *         (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2313  *         (t) => Math.sin(3 * t),
2314  *         [-Math.PI, Math.PI]
2315  *     ], { strokeWidth: 4 });
2316  *
2317  * </pre><div id="JXG9a9467e1-f189-4c8c-adb2-d4f49bc7fa26" class="jxgbox" style="width: 300px; height: 300px;"></div>
2318  * <script type="text/javascript">
2319  *     (function() {
2320  *         var board = JXG.JSXGraph.initBoard('JXG9a9467e1-f189-4c8c-adb2-d4f49bc7fa26',
2321  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
2322  *         var bound = [-4, 6];
2323  *         var view = board.create('view3d',
2324  *             [[-4, -3], [8, 8],
2325  *             [bound, bound, bound]],
2326  *             {
2327  *                 projection: 'central',
2328  *                 trackball: {enabled:true},
2329  *
2330  *                 axesPosition: 'none'
2331  *             });
2332  *
2333  *         var curve = view.create('curve3d', [
2334  *             (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2335  *             (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2336  *             (t) => Math.sin(3 * t),
2337  *             [-Math.PI, Math.PI]
2338  *         ], { strokeWidth: 4 });
2339  *
2340  *     })();
2341  *
2342  * </script><pre>
2343  *
2344  * @example
2345  *     var bound = [-4, 6];
2346  *     var view = board.create('view3d',
2347  *         [[-4, -3], [8, 8],
2348  *         [bound, bound, bound]],
2349  *         {
2350  *             projection: 'central',
2351  *             trackball: {enabled:true},
2352  *
2353  *             // Main axes
2354  *             axesPosition: 'border',
2355  *
2356  *             // Axes at the border
2357  *             xAxisBorder: { ticks3d: { ticksDistance: 2} },
2358  *             yAxisBorder: { ticks3d: { ticksDistance: 2} },
2359  *             zAxisBorder: { ticks3d: { ticksDistance: 2} },
2360  *
2361  *             xPlaneRear: {
2362  *                 fillColor: '#fff',
2363  *                 mesh3d: {visible: false}
2364  *             },
2365  *             yPlaneRear: {
2366  *                 fillColor: '#fff',
2367  *                 mesh3d: {visible: false}
2368  *             },
2369  *             zPlaneRear: {
2370  *                 fillColor: '#fff',
2371  *                 mesh3d: {visible: false}
2372  *             },
2373  *             xPlaneFront: {
2374  *                 visible: true,
2375  *                 fillColor: '#fff',
2376  *                 mesh3d: {visible: false}
2377  *             },
2378  *             yPlaneFront: {
2379  *                 visible: true,
2380  *                 fillColor: '#fff',
2381  *                 mesh3d: {visible: false}
2382  *             },
2383  *             zPlaneFront: {
2384  *                 visible: true,
2385  *                 fillColor: '#fff',
2386  *                 mesh3d: {visible: false}
2387  *             },
2388  *
2389  *             // No axes on planes
2390  *             xPlaneRearYAxis: {visible: false},
2391  *             xPlaneRearZAxis: {visible: false},
2392  *             yPlaneRearXAxis: {visible: false},
2393  *             yPlaneRearZAxis: {visible: false},
2394  *             zPlaneRearXAxis: {visible: false},
2395  *             zPlaneRearYAxis: {visible: false},
2396  *             xPlaneFrontYAxis: {visible: false},
2397  *             xPlaneFrontZAxis: {visible: false},
2398  *             yPlaneFrontXAxis: {visible: false},
2399  *             yPlaneFrontZAxis: {visible: false},
2400  *             zPlaneFrontXAxis: {visible: false},
2401  *             zPlaneFrontYAxis: {visible: false}
2402  *
2403  *         });
2404  *
2405  *     var curve = view.create('curve3d', [
2406  *         (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2407  *         (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2408  *         (t) => Math.sin(3 * t),
2409  *         [-Math.PI, Math.PI]
2410  *     ], { strokeWidth: 4 });
2411  *
2412  * </pre><div id="JXGbd41a4e3-1bf7-4764-b675-98b01667103b" class="jxgbox" style="width: 300px; height: 300px;"></div>
2413  * <script type="text/javascript">
2414  *     (function() {
2415  *         var board = JXG.JSXGraph.initBoard('JXGbd41a4e3-1bf7-4764-b675-98b01667103b',
2416  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
2417  *         var bound = [-4, 6];
2418  *         var view = board.create('view3d',
2419  *             [[-4, -3], [8, 8],
2420  *             [bound, bound, bound]],
2421  *             {
2422  *                 projection: 'central',
2423  *                 trackball: {enabled:true},
2424  *
2425  *                 // Main axes
2426  *                 axesPosition: 'border',
2427  *
2428  *                 // Axes at the border
2429  *                 xAxisBorder: { ticks3d: { ticksDistance: 2} },
2430  *                 yAxisBorder: { ticks3d: { ticksDistance: 2} },
2431  *                 zAxisBorder: { ticks3d: { ticksDistance: 2} },
2432  *
2433  *                 xPlaneRear: {
2434  *                     fillColor: '#fff',
2435  *                     mesh3d: {visible: false}
2436  *                 },
2437  *                 yPlaneRear: {
2438  *                     fillColor: '#fff',
2439  *                     mesh3d: {visible: false}
2440  *                 },
2441  *                 zPlaneRear: {
2442  *                     fillColor: '#fff',
2443  *                     mesh3d: {visible: false}
2444  *                 },
2445  *                 xPlaneFront: {
2446  *                     visible: true,
2447  *                     fillColor: '#fff',
2448  *                     mesh3d: {visible: false}
2449  *                 },
2450  *                 yPlaneFront: {
2451  *                     visible: true,
2452  *                     fillColor: '#fff',
2453  *                     mesh3d: {visible: false}
2454  *                 },
2455  *                 zPlaneFront: {
2456  *                     visible: true,
2457  *                     fillColor: '#fff',
2458  *                     mesh3d: {visible: false}
2459  *                 },
2460  *
2461  *                 // No axes on planes
2462  *                 xPlaneRearYAxis: {visible: false},
2463  *                 xPlaneRearZAxis: {visible: false},
2464  *                 yPlaneRearXAxis: {visible: false},
2465  *                 yPlaneRearZAxis: {visible: false},
2466  *                 zPlaneRearXAxis: {visible: false},
2467  *                 zPlaneRearYAxis: {visible: false},
2468  *                 xPlaneFrontYAxis: {visible: false},
2469  *                 xPlaneFrontZAxis: {visible: false},
2470  *                 yPlaneFrontXAxis: {visible: false},
2471  *                 yPlaneFrontZAxis: {visible: false},
2472  *                 zPlaneFrontXAxis: {visible: false},
2473  *                 zPlaneFrontYAxis: {visible: false}
2474  *
2475  *             });
2476  *
2477  *         var curve = view.create('curve3d', [
2478  *             (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2479  *             (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2480  *             (t) => Math.sin(3 * t),
2481  *             [-Math.PI, Math.PI]
2482  *         ], { strokeWidth: 4 });
2483  *     })();
2484  *
2485  * </script><pre>
2486  *
2487  * @example
2488  *  var bound = [-5, 5];
2489  *  var view = board.create('view3d',
2490  *      [[-6, -3],
2491  *       [8, 8],
2492  *       [bound, bound, bound]],
2493  *      {
2494  *          // Main axes
2495  *          axesPosition: 'center',
2496  *          xAxis: { strokeColor: 'blue', strokeWidth: 3},
2497  *
2498  *          // Planes
2499  *          xPlaneRear: { fillColor: 'yellow',  mesh3d: {visible: false}},
2500  *          yPlaneFront: { visible: true, fillColor: 'blue'},
2501  *
2502  *          // Axes on planes
2503  *          xPlaneRearYAxis: {strokeColor: 'red'},
2504  *          xPlaneRearZAxis: {strokeColor: 'red'},
2505  *
2506  *          yPlaneFrontXAxis: {strokeColor: 'blue'},
2507  *          yPlaneFrontZAxis: {strokeColor: 'blue'},
2508  *
2509  *          zPlaneFrontXAxis: {visible: false},
2510  *          zPlaneFrontYAxis: {visible: false}
2511  *      });
2512  *
2513  * </pre><div id="JXGdd06d90e-be5d-4531-8f0b-65fc30b1a7c7" class="jxgbox" style="width: 500px; height: 500px;"></div>
2514  * <script type="text/javascript">
2515  *     (function() {
2516  *         var board = JXG.JSXGraph.initBoard('JXGdd06d90e-be5d-4531-8f0b-65fc30b1a7c7',
2517  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
2518  *         var bound = [-5, 5];
2519  *         var view = board.create('view3d',
2520  *             [[-6, -3], [8, 8],
2521  *             [bound, bound, bound]],
2522  *             {
2523  *                 // Main axes
2524  *                 axesPosition: 'center',
2525  *                 xAxis: { strokeColor: 'blue', strokeWidth: 3},
2526  *                 // Planes
2527  *                 xPlaneRear: { fillColor: 'yellow',  mesh3d: {visible: false}},
2528  *                 yPlaneFront: { visible: true, fillColor: 'blue'},
2529  *                 // Axes on planes
2530  *                 xPlaneRearYAxis: {strokeColor: 'red'},
2531  *                 xPlaneRearZAxis: {strokeColor: 'red'},
2532  *                 yPlaneFrontXAxis: {strokeColor: 'blue'},
2533  *                 yPlaneFrontZAxis: {strokeColor: 'blue'},
2534  *                 zPlaneFrontXAxis: {visible: false},
2535  *                 zPlaneFrontYAxis: {visible: false}
2536  *             });
2537  *     })();
2538  *
2539  * </script><pre>
2540  * @example
2541  * var bound = [-5, 5];
2542  * var view = board.create('view3d',
2543  *     [[-6, -3], [8, 8],
2544  *     [bound, bound, bound]],
2545  *     {
2546  *         projection: 'central',
2547  *         az: {
2548  *             slider: {
2549  *                 visible: true,
2550  *                 point1: {
2551  *                     pos: [5, -4]
2552  *                 },
2553  *                 point2: {
2554  *                     pos: [5, 4]
2555  *                 },
2556  *                 label: {anchorX: 'middle'}
2557  *             }
2558  *         },
2559  *         el: {
2560  *             slider: {
2561  *                 visible: true,
2562  *                 point1: {
2563  *                     pos: [6, -5]
2564  *                 },
2565  *                 point2: {
2566  *                     pos: [6, 3]
2567  *                 },
2568  *                 label: {anchorX: 'middle'}
2569  *             }
2570  *         },
2571  *         bank: {
2572  *             slider: {
2573  *                 visible: true,
2574  *                 point1: {
2575  *                     pos: [7, -6]
2576  *                 },
2577  *                 point2: {
2578  *                     pos: [7, 2]
2579  *                 },
2580  *                 label: {anchorX: 'middle'}
2581  *             }
2582  *         }
2583  *     });
2584  *
2585  *
2586  * </pre><div id="JXGe181cc55-271b-419b-84fd-622326fd1d1a" class="jxgbox" style="width: 300px; height: 300px;"></div>
2587  * <script type="text/javascript">
2588  *     (function() {
2589  *         var board = JXG.JSXGraph.initBoard('JXGe181cc55-271b-419b-84fd-622326fd1d1a',
2590  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
2591  *     var bound = [-5, 5];
2592  *     var view = board.create('view3d',
2593  *         [[-6, -3], [8, 8],
2594  *         [bound, bound, bound]],
2595  *         {
2596  *             projection: 'central',
2597  *             az: {
2598  *                 slider: {
2599  *                     visible: true,
2600  *                     point1: {
2601  *                         pos: [5, -4]
2602  *                     },
2603  *                     point2: {
2604  *                         pos: [5, 4]
2605  *                     },
2606  *                     label: {anchorX: 'middle'}
2607  *                 }
2608  *             },
2609  *             el: {
2610  *                 slider: {
2611  *                     visible: true,
2612  *                     point1: {
2613  *                         pos: [6, -5]
2614  *                     },
2615  *                     point2: {
2616  *                         pos: [6, 3]
2617  *                     },
2618  *                     label: {anchorX: 'middle'}
2619  *                 }
2620  *             },
2621  *             bank: {
2622  *                 slider: {
2623  *                     visible: true,
2624  *                     point1: {
2625  *                         pos: [7, -6]
2626  *                     },
2627  *                     point2: {
2628  *                         pos: [7, 2]
2629  *                     },
2630  *                     label: {anchorX: 'middle'}
2631  *                 }
2632  *             }
2633  *         });
2634  *
2635  *
2636  *     })();
2637  *
2638  * </script><pre>
2639  *
2640  *
2641  */
2642 JXG.createView3D = function (board, parents, attributes) {
2643     var view, attr, attr_az, attr_el, attr_bank,
2644         x, y, w, h,
2645         p1, p2, v,
2646         coords = parents[0], // llft corner
2647         size = parents[1]; // [w, h]
2648 
2649     attr = Type.copyAttributes(attributes, board.options, 'view3d');
2650     view = new JXG.View3D(board, parents, attr);
2651     view.defaultAxes = view.create('axes3d', [], attr);
2652 
2653     x = coords[0];
2654     y = coords[1];
2655     w = size[0];
2656     h = size[1];
2657 
2658     attr_az = Type.copyAttributes(attr, board.options, 'view3d', 'az', 'slider');
2659     attr_az.name = 'az';
2660 
2661     attr_el = Type.copyAttributes(attr, board.options, 'view3d', 'el', 'slider');
2662     attr_el.name = 'el';
2663 
2664     attr_bank = Type.copyAttributes(attr, board.options, 'view3d', 'bank', 'slider');
2665     attr_bank.name = 'bank';
2666 
2667     v = Type.evaluate(attr_az.point1.pos);
2668     if (!Type.isArray(v)) {
2669         // 'auto'
2670         p1 = [x - 1, y - 2];
2671     } else {
2672         p1 = v;
2673     }
2674     v = Type.evaluate(attr_az.point2.pos);
2675     if (!Type.isArray(v)) {
2676         // 'auto'
2677         p2 = [x + w + 1, y - 2];
2678     } else {
2679         p2 = v;
2680     }
2681 
2682     /**
2683      * Slider to adapt azimuth angle
2684      * @name JXG.View3D#az_slide
2685      * @type {Slider}
2686      */
2687     view.az_slide = board.create(
2688         'slider',
2689         [
2690             p1, p2,
2691             [
2692                 Type.evaluate(attr_az.min),
2693                 Type.evaluate(attr_az.start),
2694                 Type.evaluate(attr_az.max)
2695             ]
2696         ],
2697         attr_az
2698     );
2699     view.inherits.push(view.az_slide);
2700     view.az_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate()
2701 
2702     v = Type.evaluate(attr_el.point1.pos);
2703     if (!Type.isArray(v)) {
2704         // 'auto'
2705         p1 = [x - 1, y];
2706     } else {
2707         p1 = v;
2708     }
2709     v = Type.evaluate(attr_el.point2.pos);
2710     if (!Type.isArray(v)) {
2711         // 'auto'
2712         p2 = [x - 1, y + h];
2713     } else {
2714         p2 = v;
2715     }
2716 
2717     /**
2718      * Slider to adapt elevation angle
2719      *
2720      * @name JXG.View3D#el_slide
2721      * @type {Slider}
2722      */
2723     view.el_slide = board.create(
2724         'slider',
2725         [
2726             p1, p2,
2727             [
2728                 Type.evaluate(attr_el.min),
2729                 Type.evaluate(attr_el.start),
2730                 Type.evaluate(attr_el.max)]
2731         ],
2732         attr_el
2733     );
2734     view.inherits.push(view.el_slide);
2735     view.el_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate()
2736 
2737     v = Type.evaluate(attr_bank.point1.pos);
2738     if (!Type.isArray(v)) {
2739         // 'auto'
2740         p1 = [x - 1, y + h + 2];
2741     } else {
2742         p1 = v;
2743     }
2744     v = Type.evaluate(attr_bank.point2.pos);
2745     if (!Type.isArray(v)) {
2746         // 'auto'
2747         p2 = [x + w + 1, y + h + 2];
2748     } else {
2749         p2 = v;
2750     }
2751 
2752     /**
2753      * Slider to adjust bank angle
2754      *
2755      * @name JXG.View3D#bank_slide
2756      * @type {Slider}
2757      */
2758     view.bank_slide = board.create(
2759         'slider',
2760         [
2761             p1, p2,
2762             [
2763                 Type.evaluate(attr_bank.min),
2764                 Type.evaluate(attr_bank.start),
2765                 Type.evaluate(attr_bank.max)
2766             ]
2767         ],
2768         attr_bank
2769     );
2770     view.inherits.push(view.bank_slide);
2771     view.bank_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate()
2772 
2773     // Set special infobox attributes of view3d.infobox
2774     // Using setAttribute() is not possible here, since we have to
2775     // avoid a call of board.update().
2776     // The drawback is that we can not use shortcuts
2777     view.board.infobox.visProp = Type.merge(view.board.infobox.visProp, attr.infobox);
2778 
2779     // 3d infobox: drag direction and coordinates
2780     view.board.highlightInfobox = function (x, y, el) {
2781         var d, i, c3d, foot,
2782             pre = '',
2783             brd = el.board,
2784             arr, infobox,
2785             p = null;
2786 
2787         if (this.mode === this.BOARD_MODE_DRAG) {
2788             // Drag direction is only shown during dragging
2789             if (view.isVerticalDrag()) {
2790                 pre = '<span style="color:black; font-size:200%">\u21C5  </span>';
2791             } else {
2792                 pre = '<span style="color:black; font-size:200%">\u21C4  </span>';
2793             }
2794         }
2795 
2796         // Search 3D parent
2797         for (i = 0; i < el.parents.length; i++) {
2798             p = brd.objects[el.parents[i]];
2799             if (p.is3D) {
2800                 break;
2801             }
2802         }
2803 
2804         if (p && Type.exists(p.element2D)) {
2805             foot = [1, 0, 0, p.coords[3]];
2806             view._w0 = Mat.innerProduct(view.matrix3D[0], foot, 4);
2807 
2808             c3d = view.project2DTo3DPlane(p.element2D, [1, 0, 0, 1], foot);
2809             if (!view.isInCube(c3d)) {
2810                 view.board.highlightCustomInfobox('', p);
2811                 return;
2812             }
2813             d = p.evalVisProp('infoboxdigits');
2814             infobox = view.board.infobox;
2815             if (d === 'auto') {
2816                 if (infobox.useLocale()) {
2817                     arr = [pre, '(', infobox.formatNumberLocale(p.X()), ' | ', infobox.formatNumberLocale(p.Y()), ' | ', infobox.formatNumberLocale(p.Z()), ')'];
2818                 } else {
2819                     arr = [pre, '(', Type.autoDigits(p.X()), ' | ', Type.autoDigits(p.Y()), ' | ', Type.autoDigits(p.Z()), ')'];
2820                 }
2821 
2822             } else {
2823                 if (infobox.useLocale()) {
2824                     arr = [pre, '(', infobox.formatNumberLocale(p.X(), d), ' | ', infobox.formatNumberLocale(p.Y(), d), ' | ', infobox.formatNumberLocale(p.Z(), d), ')'];
2825                 } else {
2826                     arr = [pre, '(', Type.toFixed(p.X(), d), ' | ', Type.toFixed(p.Y(), d), ' | ', Type.toFixed(p.Z(), d), ')'];
2827                 }
2828             }
2829             view.board.highlightCustomInfobox(arr.join(''), p);
2830         } else {
2831             view.board.highlightCustomInfobox('(' + x + ', ' + y + ')', el);
2832         }
2833     };
2834 
2835     // Hack needed to enable addEvent for view3D:
2836     view.BOARD_MODE_NONE = 0x0000;
2837 
2838     // Add events for the keyboard navigation
2839     Env.addEvent(board.containerObj, 'keydown', function (event) {
2840         var neededKey,
2841             catchEvt = false;
2842 
2843         // this.board._change3DView = true;
2844         if (view.evalVisProp('el.keyboard.enabled') &&
2845             (event.key === 'ArrowUp' || event.key === 'ArrowDown')
2846         ) {
2847             neededKey = view.evalVisProp('el.keyboard.key');
2848             if (neededKey === 'none' ||
2849                 (neededKey.indexOf('shift') > -1 && event.shiftKey) ||
2850                 (neededKey.indexOf('ctrl') > -1 && event.ctrlKey)) {
2851                 view._elEventHandler(event);
2852                 catchEvt = true;
2853             }
2854 
2855         }
2856 
2857         if (view.evalVisProp('az.keyboard.enabled') &&
2858             (event.key === 'ArrowLeft' || event.key === 'ArrowRight')
2859         ) {
2860             neededKey = view.evalVisProp('az.keyboard.key');
2861             if (neededKey === 'none' ||
2862                 (neededKey.indexOf('shift') > -1 && event.shiftKey) ||
2863                 (neededKey.indexOf('ctrl') > -1 && event.ctrlKey)
2864             ) {
2865                 view._azEventHandler(event);
2866                 catchEvt = true;
2867             }
2868         }
2869 
2870         if (view.evalVisProp('bank.keyboard.enabled') && (event.key === ',' || event.key === '<' || event.key === '.' || event.key === '>')) {
2871             neededKey = view.evalVisProp('bank.keyboard.key');
2872             if (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && event.shiftKey) || (neededKey.indexOf('ctrl') > -1 && event.ctrlKey)) {
2873                 view._bankEventHandler(event);
2874                 catchEvt = true;
2875             }
2876         }
2877 
2878         if (event.key === 'PageUp') {
2879             view.nextView();
2880             catchEvt = true;
2881         } else if (event.key === 'PageDown') {
2882             view.previousView();
2883             catchEvt = true;
2884         }
2885 
2886         if (catchEvt) {
2887             // We stop event handling only in the case if the keypress could be
2888             // used for the 3D view. If this is not done, input fields et al
2889             // can not be used any more.
2890             event.preventDefault();
2891         }
2892         this.board._change3DView = false;
2893 
2894     }, view);
2895 
2896     // Add events for the pointer navigation
2897     Env.addEvent(board.containerObj, 'pointerdown', view.pointerDownHandler, view);
2898 
2899     // Initialize view rotation matrix
2900     view.getAnglesFromSliders();
2901     view.matrix3DRot = view.getRotationFromAngles();
2902 
2903     // override angle slider bounds when trackball navigation is enabled
2904     view.updateAngleSliderBounds();
2905 
2906     view.board.update();
2907 
2908     return view;
2909 };
2910 
2911 JXG.registerElement("view3d", JXG.createView3D);
2912 
2913 export default JXG.View3D;
2914