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 
236 JXG.View3D.prototype = new GeometryElement();
237 Type.copyMethodMap(JXG.View3D, {
238     // TODO
239 });
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 ((
885                         el.type === Const.OBJECT_TYPE_LINE3D ||
886                         el.type === Const.OBJECT_TYPE_POLYGON3D
887                     ) &&
888                     Type.exists(el.element2D) &&
889                     el.element2D.evalVisProp('visible')
890                 ) {
891                     el.updateZIndex();
892                 }
893             }
894         }
895     },
896 
897     updateShaders: function() {
898         var id, el, v;
899         for (id in this.objects) {
900             if (this.objects.hasOwnProperty(id)) {
901                 el = this.objects[id];
902 
903                 if (el.visPropCalc.visible && Type.exists(el.shader)) {
904                     if (this.board._change3DView && el.evalVisProp('shader.fixed')) {
905                         // In case, 3D view is rotated and the shader is fixed
906                         // we can avoid the call of shader()
907                         v = el.zIndex;
908                     } else {
909                         v = el.shader();
910                     }
911                     if (v < this.zIndexMin) {
912                         this.zIndexMin = v;
913                     } else if (v > this.zIndexMax) {
914                         this.zIndexMax = v;
915                     }
916                 }
917             }
918         }
919     },
920 
921     updateDepthOrdering: function () {
922         var id, el,
923             i, j, l, layers, lay;
924 
925         // Collect elements for depth ordering layer-wise
926         layers = this.evalVisProp('depthorder.layers');
927         for (i = 0; i < layers.length; i++) {
928             this.depthOrdered[layers[i]] = [];
929         }
930 
931         for (id in this.objects) {
932             if (this.objects.hasOwnProperty(id)) {
933                 el = this.objects[id];
934                 if ((el.type === Const.OBJECT_TYPE_FACE3D ||
935                     el.type === Const.OBJECT_TYPE_LINE3D ||
936                     // el.type === Const.OBJECT_TYPE_PLANE3D ||
937                     el.type === Const.OBJECT_TYPE_POINT3D ||
938                     el.type === Const.OBJECT_TYPE_POLYGON3D
939                     ) &&
940                     Type.exists(el.element2D) &&
941                     el.element2D.visPropCalc.visible
942                     // el.element2D.evalVisProp('visible')
943                 ) {
944                     lay = el.element2D.evalVisProp('layer');
945                     if (layers.indexOf(lay) >= 0) {
946                         this.depthOrdered[lay].push(el);
947                     }
948                 }
949             }
950         }
951 
952         if (this.board.renderer && this.board.renderer.type === 'svg') {
953             for (i = 0; i < layers.length; i++) {
954                 lay = layers[i];
955                 this.depthOrdered[lay].sort(this.compareDepth.bind(this));
956                 // DEBUG
957                 // if (this.depthOrdered[lay].length > 0) {
958                 //     for (let k = 0; k < this.depthOrdered[lay].length; k++) {
959                 //         let o = this.depthOrdered[lay][k]
960                 //         console.log(o.visProp.fillcolor, o.zIndex)
961                 //     }
962                 // }
963                 l = this.depthOrdered[lay];
964                 for (j = 0; j < l.length; j++) {
965                     this.board.renderer.setLayer(l[j].element2D, lay);
966                 }
967                 // this.depthOrdered[lay].forEach((el) => this.board.renderer.setLayer(el.element2D, lay));
968                 // Attention: forEach prevents deleting an element
969             }
970         }
971 
972         return this;
973     },
974 
975     updateRenderer: function () {
976         if (!this.needsUpdate) {
977             return this;
978         }
979 
980         // console.time('update')
981         // Handle depth ordering
982         this.depthOrdered = {};
983 
984         if (this.shift !== undefined && this.evalVisProp('depthorder.enabled')) {
985             // Update the zIndices of certain element types.
986             // We do it here in updateRenderer, because the elements' positions
987             // are meanwhile updated.
988             this.updateZIndices();
989 
990             this.updateShaders();
991 
992             if (this.board.renderer && this.board.renderer.type === 'svg') {
993                 // For SVG we update the DOM order here.
994                 // In canvas we sort the elements in board.updateRendererCanvas
995                 this.updateDepthOrdering();
996             }
997         }
998         // console.timeEnd('update')
999 
1000         this.needsUpdate = false;
1001         return this;
1002     },
1003 
1004     removeObject: function (object, saveMethod) {
1005         var i, el, le, o, fst, face;
1006 
1007         // this.board.removeObject(object, saveMethod);
1008         if (Type.isArray(object)) {
1009             for (i = 0; i < object.length; i++) {
1010                 this.removeObject(object[i]);
1011             }
1012             return this;
1013         }
1014 
1015         object = this.select(object);
1016 
1017         // // If the object which is about to be removed unknown or a string, do nothing.
1018         // // it is a string if a string was given and could not be resolved to an element.
1019         if (!Type.exists(object) || Type.isString(object)) {
1020             return this;
1021         }
1022 
1023         try {
1024             // Remove all children.
1025             for (el in object.childElements) {
1026                 if (object.childElements.hasOwnProperty(el)) {
1027                     this.removeObject(object.childElements[el]);
1028                 }
1029             }
1030             if (object.type === Const.OBJECT_TYPE_POLYHEDRON3D) {
1031                 // Special treatment for polyhedron3d.
1032                 // With this we can avoid the time consuming addChild() calls.
1033                 le = object.faces.length;
1034                 if (le > 0) {
1035                     fst = object.faces[0]._pos;
1036                     fst = (object.faces[0].element2D._pos < fst) ? object.faces[0].element2D._pos : fst;
1037                 }
1038                 for (i = 0; i < le; i++) {
1039                     face = object.faces[i];
1040                     delete this.objects[face.id];
1041 
1042                     // this.board.removeObject(face.element2D, saveMethod);
1043                     delete this.board.objects[face.element2D.id];
1044                     delete this.board.elementsByName[face.element2D.name];
1045                     face.element2D.remove();
1046                     this.board.objectsList.splice(face.element2D._pos, 1);
1047 
1048                     delete this.board.objects[face.id];
1049                     delete this.board.elementsByName[face.name];
1050                     face.remove();
1051                     this.board.objectsList.splice(face._pos, 1);
1052                 }
1053                 le = this.board.objectsList.length;
1054                 // Reindex the positions
1055                 for (i = fst; i < this.board.objectsList.length; i++) {
1056                     o = this.board.objectsList[i];
1057                     if (o._pos > -1) { o._pos = i; }
1058                 }
1059                 object.faces = [];
1060             }
1061 
1062             delete this.objects[object.id];
1063         } catch (e) {
1064             JXG.debug('View3D ' + object.id + ': Could not be removed: ' + e);
1065         }
1066 
1067         // this.update();
1068 
1069         this.board.removeObject(object, saveMethod);
1070 
1071         return this;
1072     },
1073 
1074     /**
1075      * Map world coordinates to focal coordinates. These coordinate systems
1076      * are explained in the {@link JXG.View3D#boxToCam} matrix
1077      * documentation.
1078      *
1079      * @param {Array} pWorld A world space point, in homogeneous coordinates.
1080      * @param {Boolean} [homog=true] Whether to return homogeneous coordinates.
1081      * If false, projects down to ordinary coordinates.
1082      */
1083     worldToFocal: function (pWorld, homog = true) {
1084         var k,
1085             pView = Mat.matVecMult(this.boxToCam, Mat.matVecMult(this.shift, pWorld));
1086 
1087         pView[3] -= pView[0] * this.focalDist;
1088         if (homog) {
1089             return pView;
1090         } else {
1091             for (k = 1; k < 4; k++) {
1092                 pView[k] /= pView[0];
1093             }
1094             return pView.slice(1, 4);
1095         }
1096     },
1097 
1098     /**
1099      * Project 3D coordinates to 2D board coordinates
1100      * The 3D coordinates are provides as three numbers x, y, z or one array of length 3.
1101      *
1102      * @param  {Number|Array} x
1103      * @param  {Number[]} y
1104      * @param  {Number[]} z
1105      * @returns {Array} Array of length 3 containing the projection on to the board
1106      * in homogeneous user coordinates.
1107      */
1108     project3DTo2D: function (x, y, z) {
1109         var vec, w;
1110         if (arguments.length === 3) {
1111             vec = [1, x, y, z];
1112         } else {
1113             // Argument is an array
1114             if (x.length === 3) {
1115                 // vec = [1].concat(x);
1116                 vec = x.slice();
1117                 vec.unshift(1);
1118             } else {
1119                 vec = x;
1120             }
1121         }
1122 
1123         w = Mat.matVecMult(this.matrix3D, vec);
1124 
1125         switch (this.projectionType) {
1126             case 'central':
1127                 w[1] /= w[0];
1128                 w[2] /= w[0];
1129                 w[3] /= w[0];
1130                 w[0] /= w[0];
1131                 return Mat.matVecMult(this.viewPortTransform, w.slice(0, 3));
1132 
1133             case 'parallel':
1134             default:
1135                 return w;
1136         }
1137     },
1138 
1139     /**
1140      * We know that v2d * w0 = mat * (1, x, y, d)^T where v2d = (1, b, c, h)^T with unknowns w0, h, x, y.
1141      * Setting R = mat^(-1) gives
1142      *   1/ w0 * (1, x, y, d)^T = R * v2d.
1143      * The first and the last row of this equation allows to determine 1/w0 and h.
1144      *
1145      * @param {Array} mat
1146      * @param {Array} v2d
1147      * @param {Number} d
1148      * @returns Array
1149      * @private
1150      */
1151     _getW0: function (mat, v2d, d) {
1152         var R = Mat.inverse(mat),
1153             R1 = R[0][0] + v2d[1] * R[0][1] + v2d[2] * R[0][2],
1154             R2 = R[3][0] + v2d[1] * R[3][1] + v2d[2] * R[3][2],
1155             w, h, det;
1156 
1157         det = d * R[0][3] - R[3][3];
1158         w = (R2 * R[0][3] - R1 * R[3][3]) / det;
1159         h = (R2 - R1 * d) / det;
1160         return [1 / w, h];
1161     },
1162 
1163     /**
1164      * Project a 2D coordinate to the plane defined by point "foot"
1165      * and the normal vector `normal`.
1166      *
1167      * @param  {JXG.Point} point2d
1168      * @param  {Array} normal Normal of plane
1169      * @param  {Array} foot Foot point of plane
1170      * @returns {Array} of length 4 containing the projected
1171      * point in homogeneous coordinates.
1172      */
1173     project2DTo3DPlane: function (point2d, normal, foot) {
1174         var mat, rhs, d, le, sol,
1175             f = foot.slice(1) || [0, 0, 0],
1176             n = normal.slice(1),
1177             v2d, w0, res;
1178 
1179         le = Mat.norm(n, 3);
1180         d = Mat.innerProduct(f, n, 3) / le;
1181 
1182         if (this.projectionType === 'parallel') {
1183             mat = this.matrix3D.slice(0, 3);     // Copy each row by reference
1184             mat.push([0, n[0], n[1], n[2]]);
1185 
1186             // 2D coordinates of point
1187             rhs = point2d.coords.usrCoords.slice();
1188             rhs.push(d);
1189             try {
1190                 // Prevent singularity in case elevation angle is zero
1191                 if (mat[2][3] === 1.0) {
1192                     mat[2][1] = mat[2][2] = Mat.eps * 0.001;
1193                 }
1194                 sol = Mat.Numerics.Gauss(mat, rhs);
1195             } catch (e) {
1196                 sol = [0, NaN, NaN, NaN];
1197             }
1198         } else {
1199             mat = this.matrix3D;
1200 
1201             // 2D coordinates of point:
1202             rhs = point2d.coords.usrCoords.slice();
1203 
1204             v2d = Mat.Numerics.Gauss(this.viewPortTransform, rhs);
1205             res = this._getW0(mat, v2d, d);
1206             w0 = res[0];
1207             rhs = [
1208                 v2d[0] * w0,
1209                 v2d[1] * w0,
1210                 v2d[2] * w0,
1211                 res[1] * w0
1212             ];
1213             try {
1214                 // Prevent singularity in case elevation angle is zero
1215                 if (mat[2][3] === 1.0) {
1216                     mat[2][1] = mat[2][2] = Mat.eps * 0.001;
1217                 }
1218 
1219                 sol = Mat.Numerics.Gauss(mat, rhs);
1220                 sol[1] /= sol[0];
1221                 sol[2] /= sol[0];
1222                 sol[3] /= sol[0];
1223                 // sol[3] = d;
1224                 sol[0] /= sol[0];
1225             } catch (err) {
1226                 sol = [0, NaN, NaN, NaN];
1227             }
1228         }
1229 
1230         return sol;
1231     },
1232 
1233     /**
1234      * Project a point on the screen to the nearest point, in screen
1235      * distance, on a line segment in 3d space. The inputs and outputs
1236      * are in homogeneous coordinates.
1237      * <p>
1238      * Used in View3d.project2DTo3DVertical() and
1239      * Line3d.projectScreenCoords().
1240      *
1241      * @param {Array} pScr The screen coordinates of the point to project.
1242      * @param {Array} end0 The world space coordinates of one end of the
1243      * line segment (array of length 4).
1244      * @param {Array} end1 The world space coordinates of the other end of
1245      * the line segment (array of length 4).
1246      *
1247      * @returns {Array} Homogeneous coordinates of the projection
1248      */
1249     projectScreenToSegment: function (pScr, end0, end1) {
1250         var end0_2d = this.project3DTo2D(end0).slice(1, 3),
1251             end1_2d = this.project3DTo2D(end1).slice(1, 3),
1252             dir_2d = [
1253                 end1_2d[0] - end0_2d[0],
1254                 end1_2d[1] - end0_2d[1]
1255             ],
1256             dir_2d_norm_sq = Mat.innerProduct(dir_2d, dir_2d),
1257             diff = [
1258                 pScr[0] - end0_2d[0],
1259                 pScr[1] - end0_2d[1]
1260             ],
1261             s = Mat.innerProduct(diff, dir_2d) / dir_2d_norm_sq, // screen-space affine parameter
1262             mid, mid_2d, mid_diff, m,
1263 
1264             t, // view-space affine parameter
1265             t_clamped, // affine parameter clamped to range
1266             t_clamped_co;
1267 
1268         if (this.projectionType === 'central') {
1269             mid = [
1270                 1,
1271                 0.5 * (end0[1] + end1[1]),
1272                 0.5 * (end0[2] + end1[2]),
1273                 0.5 * (end0[3] + end1[3])
1274             ];
1275             mid_2d = this.project3DTo2D(mid).slice(1, 3);
1276             mid_diff = [
1277                 mid_2d[0] - end0_2d[0],
1278                 mid_2d[1] - end0_2d[1]
1279             ];
1280             m = Mat.innerProduct(mid_diff, dir_2d) / dir_2d_norm_sq;
1281 
1282             // the view-space affine parameter s is related to the
1283             // screen-space affine parameter t by a Möbius transformation,
1284             // which is determined by the following relations:
1285             //
1286             // s | t
1287             // -----
1288             // 0 | 0
1289             // m | 1/2
1290             // 1 | 1
1291             //
1292             t = (1 - m) * s / ((1 - 2 * m) * s + m);
1293         } else {
1294             t = s;
1295         }
1296 
1297         t_clamped = Math.min(Math.max(t, 0), 1);
1298         t_clamped_co = 1 - t_clamped;
1299         return [
1300             1,
1301             t_clamped_co * end0[1] + t_clamped * end1[1],
1302             t_clamped_co * end0[2] + t_clamped * end1[2],
1303             t_clamped_co * end0[3] + t_clamped * end1[3]
1304         ];
1305     },
1306 
1307     /**
1308      * Project a 2D coordinate to a new 3D position by keeping
1309      * the 3D x, y coordinates and changing only the z coordinate.
1310      * All horizontal moves of the 2D point are ignored.
1311      *
1312      * @param {JXG.Point} point2d
1313      * @param {Array} base_c3d
1314      * @returns {Array} of length 4 containing the projected
1315      * point in homogeneous coordinates.
1316      */
1317     project2DTo3DVertical: function (point2d, base_c3d) {
1318         var pScr = point2d.coords.usrCoords.slice(1, 3),
1319             end0 = [1, base_c3d[1], base_c3d[2], this.bbox3D[2][0]],
1320             end1 = [1, base_c3d[1], base_c3d[2], this.bbox3D[2][1]];
1321 
1322         return this.projectScreenToSegment(pScr, end0, end1);
1323     },
1324 
1325     /**
1326      * Limit 3D coordinates to the bounding cube.
1327      *
1328      * @param {Array} c3d 3D coordinates [x,y,z]
1329      * @returns Array [Array, Boolean] containing [coords, corrected]. coords contains the updated 3D coordinates,
1330      * correct is true if the coords have been changed.
1331      */
1332     project3DToCube: function (c3d) {
1333         var cube = this.bbox3D,
1334             isOut = false;
1335 
1336         if (c3d[1] < cube[0][0]) {
1337             c3d[1] = cube[0][0];
1338             isOut = true;
1339         }
1340         if (c3d[1] > cube[0][1]) {
1341             c3d[1] = cube[0][1];
1342             isOut = true;
1343         }
1344         if (c3d[2] < cube[1][0]) {
1345             c3d[2] = cube[1][0];
1346             isOut = true;
1347         }
1348         if (c3d[2] > cube[1][1]) {
1349             c3d[2] = cube[1][1];
1350             isOut = true;
1351         }
1352         if (c3d[3] <= cube[2][0]) {
1353             c3d[3] = cube[2][0];
1354             isOut = true;
1355         }
1356         if (c3d[3] >= cube[2][1]) {
1357             c3d[3] = cube[2][1];
1358             isOut = true;
1359         }
1360 
1361         return [c3d, isOut];
1362     },
1363 
1364     /**
1365      * Intersect a ray with the bounding cube of the 3D view.
1366      * @param {Array} p 3D coordinates [w,x,y,z]
1367      * @param {Array} dir 3D direction vector of the line (array of length 3 or 4)
1368      * @param {Number} r direction of the ray (positive if r > 0, negative if r < 0).
1369      * @returns Affine ratio of the intersection of the line with the cube.
1370      */
1371     intersectionLineCube: function (p, dir, r) {
1372         var r_n, i, r0, r1, d;
1373 
1374         d = (dir.length === 3) ? dir : dir.slice(1);
1375 
1376         r_n = r;
1377         for (i = 0; i < 3; i++) {
1378             if (d[i] !== 0) {
1379                 r0 = (this.bbox3D[i][0] - p[i + 1]) / d[i];
1380                 r1 = (this.bbox3D[i][1] - p[i + 1]) / d[i];
1381                 if (r < 0) {
1382                     r_n = Math.max(r_n, Math.min(r0, r1));
1383                 } else {
1384                     r_n = Math.min(r_n, Math.max(r0, r1));
1385                 }
1386             }
1387         }
1388         return r_n;
1389     },
1390 
1391     /**
1392      * Test if coordinates are inside of the bounding cube.
1393      * @param {array} p 3D coordinates [[w],x,y,z] of a point.
1394      * @returns Boolean
1395      */
1396     isInCube: function (p, polyhedron) {
1397         var q;
1398         if (p.length === 4) {
1399             if (p[0] === 0) {
1400                 return false;
1401             }
1402             q = p.slice(1);
1403         }
1404         return (
1405             q[0] > this.bbox3D[0][0] - Mat.eps &&
1406             q[0] < this.bbox3D[0][1] + Mat.eps &&
1407             q[1] > this.bbox3D[1][0] - Mat.eps &&
1408             q[1] < this.bbox3D[1][1] + Mat.eps &&
1409             q[2] > this.bbox3D[2][0] - Mat.eps &&
1410             q[2] < this.bbox3D[2][1] + Mat.eps
1411         );
1412     },
1413 
1414     /**
1415      *
1416      * @param {JXG.Plane3D} plane1
1417      * @param {JXG.Plane3D} plane2
1418      * @param {Number} d Right hand side of Hesse normal for plane2 (it can be adjusted)
1419      * @returns {Array} of length 2 containing the coordinates of the defining points of
1420      * of the intersection segment, or false if there is no intersection
1421      */
1422     intersectionPlanePlane: function (plane1, plane2, d) {
1423         var ret = [false, false],
1424             p, q, r, w,
1425             dir;
1426 
1427         d = d || plane2.d;
1428 
1429         // Get one point of the intersection of the two planes
1430         w = Mat.crossProduct(plane1.normal.slice(1), plane2.normal.slice(1));
1431         w.unshift(0);
1432 
1433         p = Mat.Geometry.meet3Planes(
1434             plane1.normal,
1435             plane1.d,
1436             plane2.normal,
1437             d,
1438             w,
1439             0
1440         );
1441 
1442         // Get the direction of the intersecting line of the two planes
1443         dir = Mat.Geometry.meetPlanePlane(
1444             plane1.vec1,
1445             plane1.vec2,
1446             plane2.vec1,
1447             plane2.vec2
1448         );
1449 
1450         // Get the bounding points of the intersecting segment
1451         r = this.intersectionLineCube(p, dir, Infinity);
1452         q = Mat.axpy(r, dir, p);
1453         if (this.isInCube(q)) {
1454             ret[0] = q;
1455         }
1456         r = this.intersectionLineCube(p, dir, -Infinity);
1457         q = Mat.axpy(r, dir, p);
1458         if (this.isInCube(q)) {
1459             ret[1] = q;
1460         }
1461 
1462         return ret;
1463     },
1464 
1465     intersectionPlaneFace: function (plane, face) {
1466         var ret = [],
1467             j, t,
1468             p, crds,
1469             p1, p2, c,
1470             f, le, x1, y1, x2, y2,
1471             dir, vec, w,
1472             mat = [], b = [], sol;
1473 
1474         w = Mat.crossProduct(plane.normal.slice(1), face.normal.slice(1));
1475         w.unshift(0);
1476 
1477         // Get one point of the intersection of the two planes
1478         p = Geometry.meet3Planes(
1479             plane.normal,
1480             plane.d,
1481             face.normal,
1482             face.d,
1483             w,
1484             0
1485         );
1486 
1487         // Get the direction the intersecting line of the two planes
1488         dir = Geometry.meetPlanePlane(
1489             plane.vec1,
1490             plane.vec2,
1491             face.vec1,
1492             face.vec2
1493         );
1494 
1495         f = face.polyhedron.faces[face.faceNumber];
1496         crds = face.polyhedron.coords;
1497         le = f.length;
1498         for (j = 1; j <= le; j++) {
1499             p1 = crds[f[j - 1]];
1500             p2 = crds[f[j % le]];
1501             vec = [0, p2[1] - p1[1], p2[2] - p1[2], p2[3] - p1[3]];
1502 
1503             x1 = Math.random();
1504             y1 = Math.random();
1505             x2 = Math.random();
1506             y2 = Math.random();
1507             mat = [
1508                 [x1 * dir[1] + y1 * dir[3], x1 * (-vec[1]) + y1 * (-vec[3])],
1509                 [x2 * dir[2] + y2 * dir[3], x2 * (-vec[2]) + y2 * (-vec[3])]
1510             ];
1511             b = [
1512                 x1 * (p1[1] - p[1]) + y1 * (p1[3] - p[3]),
1513                 x2 * (p1[2] - p[2]) + y2 * (p1[3] - p[3])
1514             ];
1515 
1516             sol = Numerics.Gauss(mat, b);
1517             t = sol[1];
1518             if (t > -Mat.eps && t < 1 + Mat.eps) {
1519                 c = [1, p1[1] + t * vec[1], p1[2] + t * vec[2], p1[3] + t * vec[3]];
1520                 ret.push(c);
1521             }
1522         }
1523 
1524         return ret;
1525     },
1526 
1527     // TODO:
1528     // - handle non-closed polyhedra
1529     // - handle intersections in vertex, edge, plane
1530     intersectionPlanePolyhedron: function(plane, phdr) {
1531         var i, j, seg,
1532             p, first, pos, pos_akt,
1533             eps = 1e-12,
1534             points = [],
1535             x = [],
1536             y = [],
1537             z = [];
1538 
1539         for (i = 0; i < phdr.numberFaces; i++) {
1540             if (phdr.def.faces[i].length < 3) {
1541                 // We skip intersection with points or lines
1542                 continue;
1543             }
1544 
1545             // seg will be an array consisting of two points
1546             // that span the intersecting segment of the plane
1547             // and the face.
1548             seg = this.intersectionPlaneFace(plane, phdr.faces[i]);
1549 
1550             // Plane intersects the face in less than 2 points
1551             if (seg.length < 2) {
1552                 continue;
1553             }
1554 
1555             if (seg[0].length === 4 && seg[1].length === 4) {
1556                 // This test is necessary to filter out intersection lines which are
1557                 // identical to intersections of axis planes (they would occur twice),
1558                 // i.e. edges of bbox3d.
1559                 for (j = 0; j < points.length; j++) {
1560                     if (
1561                         (Geometry.distance(seg[0], points[j][0], 4) < eps &&
1562                             Geometry.distance(seg[1], points[j][1], 4) < eps) ||
1563                         (Geometry.distance(seg[0], points[j][1], 4) < eps &&
1564                             Geometry.distance(seg[1], points[j][0], 4) < eps)
1565                     ) {
1566                         break;
1567                     }
1568                 }
1569                 if (j === points.length) {
1570                     points.push(seg.slice());
1571                 }
1572             }
1573         }
1574 
1575         // Handle the case that the intersection is the empty set.
1576         if (points.length === 0) {
1577             return { X: x, Y: y, Z: z };
1578         }
1579 
1580         // Concatenate the intersection points to a polygon.
1581         // If all went well, each intersection should appear
1582         // twice in the list.
1583         // __Attention:__ each face has to be planar!!!
1584         // Otherwise the algorithm will fail.
1585         first = 0;
1586         pos = first;
1587         i = 0;
1588         do {
1589             p = points[pos][i];
1590             if (p.length === 4) {
1591                 x.push(p[1]);
1592                 y.push(p[2]);
1593                 z.push(p[3]);
1594             }
1595             i = (i + 1) % 2;
1596             p = points[pos][i];
1597 
1598             pos_akt = pos;
1599             for (j = 0; j < points.length; j++) {
1600                 if (j !== pos && Geometry.distance(p, points[j][0]) < eps) {
1601                     pos = j;
1602                     i = 0;
1603                     break;
1604                 }
1605                 if (j !== pos && Geometry.distance(p, points[j][1]) < eps) {
1606                     pos = j;
1607                     i = 1;
1608                     break;
1609                 }
1610             }
1611             if (pos === pos_akt) {
1612                 console.log('Error face3d intersection update: did not find next', pos, i);
1613                 break;
1614             }
1615         } while (pos !== first);
1616         x.push(x[0]);
1617         y.push(y[0]);
1618         z.push(z[0]);
1619 
1620         return { X: x, Y: y, Z: z };
1621     },
1622 
1623     /**
1624      * Generate mesh for a surface / plane.
1625      * Returns array [dataX, dataY] for a JSXGraph curve's updateDataArray function.
1626      * @param {Array|Function} func
1627      * @param {Array} interval_u
1628      * @param {Array} interval_v
1629      * @returns Array
1630      * @private
1631      *
1632      * @example
1633      *  var el = view.create('curve', [[], []]);
1634      *  el.updateDataArray = function () {
1635      *      var steps_u = this.evalVisProp('stepsu'),
1636      *           steps_v = this.evalVisProp('stepsv'),
1637      *           r_u = Type.evaluate(this.range_u),
1638      *           r_v = Type.evaluate(this.range_v),
1639      *           func, ret;
1640      *
1641      *      if (this.F !== null) {
1642      *          func = this.F;
1643      *      } else {
1644      *          func = [this.X, this.Y, this.Z];
1645      *      }
1646      *      ret = this.view.getMesh(func,
1647      *          r_u.concat([steps_u]),
1648      *          r_v.concat([steps_v]));
1649      *
1650      *      this.dataX = ret[0];
1651      *      this.dataY = ret[1];
1652      *  };
1653      *
1654      */
1655     getMesh: function (func, interval_u, interval_v) {
1656         var i_u, i_v, u, v,
1657             c2d, delta_u, delta_v,
1658             p = [0, 0, 0],
1659             steps_u = Type.evaluate(interval_u[2]),
1660             steps_v = Type.evaluate(interval_v[2]),
1661             dataX = [],
1662             dataY = [];
1663 
1664         delta_u = (Type.evaluate(interval_u[1]) - Type.evaluate(interval_u[0])) / steps_u;
1665         delta_v = (Type.evaluate(interval_v[1]) - Type.evaluate(interval_v[0])) / steps_v;
1666 
1667         for (i_u = 0; i_u <= steps_u; i_u++) {
1668             u = interval_u[0] + delta_u * i_u;
1669             for (i_v = 0; i_v <= steps_v; i_v++) {
1670                 v = interval_v[0] + delta_v * i_v;
1671                 if (Type.isFunction(func)) {
1672                     p = func(u, v);
1673                 } else {
1674                     p = [func[0](u, v), func[1](u, v), func[2](u, v)];
1675                 }
1676                 c2d = this.project3DTo2D(p);
1677                 dataX.push(c2d[1]);
1678                 dataY.push(c2d[2]);
1679             }
1680             dataX.push(NaN);
1681             dataY.push(NaN);
1682         }
1683 
1684         for (i_v = 0; i_v <= steps_v; i_v++) {
1685             v = interval_v[0] + delta_v * i_v;
1686             for (i_u = 0; i_u <= steps_u; i_u++) {
1687                 u = interval_u[0] + delta_u * i_u;
1688                 if (Type.isFunction(func)) {
1689                     p = func(u, v);
1690                 } else {
1691                     p = [func[0](u, v), func[1](u, v), func[2](u, v)];
1692                 }
1693                 c2d = this.project3DTo2D(p);
1694                 dataX.push(c2d[1]);
1695                 dataY.push(c2d[2]);
1696             }
1697             dataX.push(NaN);
1698             dataY.push(NaN);
1699         }
1700 
1701         return [dataX, dataY];
1702     },
1703 
1704     /**
1705      *
1706      */
1707     animateAzimuth: function () {
1708         var s = this.az_slide._smin,
1709             e = this.az_slide._smax,
1710             sdiff = e - s,
1711             newVal = this.az_slide.Value() + 0.1;
1712 
1713         this.az_slide.position = (newVal - s) / sdiff;
1714         if (this.az_slide.position > 1) {
1715             this.az_slide.position = 0.0;
1716         }
1717         this.board._change3DView = true;
1718         this.board.update();
1719         this.board._change3DView = false;
1720 
1721         this.timeoutAzimuth = setTimeout(function () {
1722             this.animateAzimuth();
1723         }.bind(this), 200);
1724     },
1725 
1726     /**
1727      *
1728      */
1729     stopAzimuth: function () {
1730         clearTimeout(this.timeoutAzimuth);
1731         this.timeoutAzimuth = null;
1732     },
1733 
1734     /**
1735      * Check if vertical dragging is enabled and which action is needed.
1736      * Default is shiftKey.
1737      *
1738      * @returns Boolean
1739      * @private
1740      */
1741     isVerticalDrag: function () {
1742         var b = this.board,
1743             key;
1744         if (!this.evalVisProp('verticaldrag.enabled')) {
1745             return false;
1746         }
1747         key = '_' + this.evalVisProp('verticaldrag.key') + 'Key';
1748         return b[key];
1749     },
1750 
1751     /**
1752      * Sets camera view to the given values.
1753      *
1754      * @param {Number} az Value of azimuth.
1755      * @param {Number} el Value of elevation.
1756      * @param {Number} [r] Value of radius.
1757      *
1758      * @returns {Object} Reference to the view.
1759      */
1760     setView: function (az, el, r) {
1761         r = r || this.r;
1762 
1763         this.az_slide.setValue(az);
1764         this.el_slide.setValue(el);
1765         this.r = r;
1766         this.board.update();
1767 
1768         return this;
1769     },
1770 
1771     /**
1772      * Changes view to the next view stored in the attribute `values`.
1773      *
1774      * @see View3D#values
1775      *
1776      * @returns {Object} Reference to the view.
1777      */
1778     nextView: function () {
1779         var views = this.evalVisProp('values'),
1780             n = this.visProp._currentview;
1781 
1782         n = (n + 1) % views.length;
1783         this.setCurrentView(n);
1784 
1785         return this;
1786     },
1787 
1788     /**
1789      * Changes view to the previous view stored in the attribute `values`.
1790      *
1791      * @see View3D#values
1792      *
1793      * @returns {Object} Reference to the view.
1794      */
1795     previousView: function () {
1796         var views = this.evalVisProp('values'),
1797             n = this.visProp._currentview;
1798 
1799         n = (n + views.length - 1) % views.length;
1800         this.setCurrentView(n);
1801 
1802         return this;
1803     },
1804 
1805     /**
1806      * Changes view to the determined view stored in the attribute `values`.
1807      *
1808      * @see View3D#values
1809      *
1810      * @param {Number} n Index of view in attribute `values`.
1811      * @returns {Object} Reference to the view.
1812      */
1813     setCurrentView: function (n) {
1814         var views = this.evalVisProp('values');
1815 
1816         if (n < 0 || n >= views.length) {
1817             n = ((n % views.length) + views.length) % views.length;
1818         }
1819 
1820         this.setView(views[n][0], views[n][1], views[n][2]);
1821         this.visProp._currentview = n;
1822 
1823         return this;
1824     },
1825 
1826     /**
1827      * Controls 2-degree navigation in az direction using  pointer.
1828      *
1829      * @private
1830      *
1831      * @param {event} evt the pointer event
1832      * @returns view
1833      */
1834     _az_elEventHandler: function (evt) {
1835         var smax = this.az_slide._smax,
1836             smin = this.az_slide._smin,
1837             speed = (smax - smin) / this.board.canvasWidth * (this.evalVisProp('az.pointer.speed')),
1838             deltaX, // = evt.movementX,
1839             deltaY, // = evt.movementY
1840             az = this.az_slide.Value(),
1841             el = this.el_slide.Value();
1842 
1843         deltaX = evt.screenX - this._lastPos.x;
1844         this._lastPos.x = evt.screenX;
1845         deltaY = evt.screenY - this._lastPos.y;
1846         this._lastPos.y = evt.screenY;
1847 
1848         // Doesn't allow navigation if another moving event is triggered
1849         if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) {
1850             return this;
1851         }
1852 
1853         if (this.evalVisProp('az.pointer.enabled') && (deltaX !== 0) && evt.key == null) {
1854             // delta *= (Math.abs(delta) > 100) ? 0.03 : 1;
1855             az += deltaX * speed;
1856         }
1857         if (this.evalVisProp('el.pointer.enabled') && (deltaY !== 0) && evt.key == null) {
1858             el += deltaY * speed;
1859         }
1860 
1861         // Project the calculated az value to a usable value in the interval [smin,smax]
1862         // Use modulo if continuous is true
1863         if (this.evalVisProp('az.continuous')) {
1864             az = Mat.wrap(az, smin, smax);
1865         } else {
1866             if (az > 0) {
1867                 az = Math.min(smax, az);
1868             } else if (az < 0) {
1869                 az = Math.max(smin, az);
1870             }
1871         }
1872         // Project the calculated el value to a usable value in the interval [smin,smax]
1873         // Use modulo if continuous is true and the trackball is disabled
1874         smax = this.el_slide._smax;
1875         smin = this.el_slide._smin;
1876         if (this.evalVisProp('el.continuous') && !this.trackballEnabled) {
1877             el = Mat.wrap(el, smin, smax);
1878         } else {
1879             if (el > 0) {
1880                 el = Math.min(smax, el);
1881             } else if (el < 0) {
1882                 el = Math.max(smin, el);
1883             }
1884         }
1885 
1886         this.setView(az, el);
1887         return this;
1888     },
1889 
1890     /**
1891      * Controls the navigation in az direction using either the keyboard or a pointer.
1892      *
1893      * @private
1894      *
1895      * @param {event} evt either the keydown or the pointer event
1896      * @returns view
1897      */
1898     _azEventHandler: function (evt) {
1899         var smax = this.az_slide._smax,
1900             smin = this.az_slide._smin,
1901             speed = (smax - smin) / this.board.canvasWidth * (this.evalVisProp('az.pointer.speed')),
1902             delta, // = evt.movementX,
1903             az = this.az_slide.Value(),
1904             el = this.el_slide.Value();
1905 
1906         delta = evt.screenX - this._lastPos.x;
1907         this._lastPos.x = evt.screenX;
1908 
1909         // Doesn't allow navigation if another moving event is triggered
1910         if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) {
1911             return this;
1912         }
1913 
1914         // Calculate new az value if keyboard events are triggered
1915         // Plus if right-button, minus if left-button
1916         if (this.evalVisProp('az.keyboard.enabled')) {
1917             if (evt.key === 'ArrowRight') {
1918                 az = az + this.evalVisProp('az.keyboard.step') * Math.PI / 180;
1919             } else if (evt.key === 'ArrowLeft') {
1920                 az = az - this.evalVisProp('az.keyboard.step') * Math.PI / 180;
1921             }
1922         }
1923 
1924         if (this.evalVisProp('az.pointer.enabled') && (delta !== 0) && evt.key == null) {
1925             // delta *= (Math.abs(delta) > 100) ? 0.03 : 1;
1926             az += delta * speed;
1927         }
1928 
1929         // Project the calculated az value to a usable value in the interval [smin,smax]
1930         // Use modulo if continuous is true
1931         if (this.evalVisProp('az.continuous')) {
1932             az = Mat.wrap(az, smin, smax);
1933         } else {
1934             if (az > 0) {
1935                 az = Math.min(smax, az);
1936             } else if (az < 0) {
1937                 az = Math.max(smin, az);
1938             }
1939         }
1940 
1941         this.setView(az, el);
1942         return this;
1943     },
1944 
1945     /**
1946      * Controls the navigation in el direction using either the keyboard or a pointer.
1947      *
1948      * @private
1949      *
1950      * @param {event} evt either the keydown or the pointer event
1951      * @returns view
1952      */
1953     _elEventHandler: function (evt) {
1954         var smax = this.el_slide._smax,
1955             smin = this.el_slide._smin,
1956             speed = (smax - smin) / this.board.canvasHeight * this.evalVisProp('el.pointer.speed'),
1957             delta, // = evt.movementY,
1958             az = this.az_slide.Value(),
1959             el = this.el_slide.Value();
1960 
1961         delta = evt.screenY - this._lastPos.y;
1962         this._lastPos.y = evt.screenY;
1963 
1964         // Doesn't allow navigation if another moving event is triggered
1965         if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) {
1966             return this;
1967         }
1968 
1969         // Calculate new az value if keyboard events are triggered
1970         // Plus if down-button, minus if up-button
1971         if (this.evalVisProp('el.keyboard.enabled')) {
1972             if (evt.key === 'ArrowUp') {
1973                 el = el - this.evalVisProp('el.keyboard.step') * Math.PI / 180;
1974             } else if (evt.key === 'ArrowDown') {
1975                 el = el + this.evalVisProp('el.keyboard.step') * Math.PI / 180;
1976             }
1977         }
1978 
1979         if (this.evalVisProp('el.pointer.enabled') && (delta !== 0) && evt.key == null) {
1980             // delta *= (Math.abs(delta) > 100) ? 0.05 : 1;
1981             el += delta * speed;
1982         }
1983 
1984         // Project the calculated el value to a usable value in the interval [smin,smax]
1985         // Use modulo if continuous is true and the trackball is disabled
1986         if (this.evalVisProp('el.continuous') && !this.trackballEnabled) {
1987             el = Mat.wrap(el, smin, smax);
1988         } else {
1989             if (el > 0) {
1990                 el = Math.min(smax, el);
1991             } else if (el < 0) {
1992                 el = Math.max(smin, el);
1993             }
1994         }
1995 
1996         this.setView(az, el);
1997 
1998         return this;
1999     },
2000 
2001     /**
2002      * Controls the navigation in bank direction using either the keyboard or a pointer.
2003      *
2004      * @private
2005      *
2006      * @param {event} evt either the keydown or the pointer event
2007      * @returns view
2008      */
2009     _bankEventHandler: function (evt) {
2010         var smax = this.bank_slide._smax,
2011             smin = this.bank_slide._smin,
2012             step, speed,
2013             delta = evt.deltaY, // Wheel event
2014             bank = this.bank_slide.Value();
2015 
2016         // Doesn't allow navigation if another moving event is triggered
2017         if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) {
2018             return this;
2019         }
2020 
2021         // Calculate new bank value if keyboard events are triggered
2022         // Plus if down-button, minus if up-button
2023         if (this.evalVisProp('bank.keyboard.enabled')) {
2024             step = this.evalVisProp('bank.keyboard.step') * Math.PI / 180;
2025             if (evt.key === '.' || evt.key === '<') {
2026                 bank -= step;
2027             } else if (evt.key === ',' || evt.key === '>') {
2028                 bank += step;
2029             }
2030         }
2031 
2032         if (this.evalVisProp('bank.pointer.enabled') && (delta !== 0) && evt.key == null) {
2033             speed = (smax - smin) / this.board.canvasHeight * this.evalVisProp('bank.pointer.speed');
2034             bank += delta * speed;
2035 
2036             // prevent the pointer wheel from scrolling the page
2037             evt.preventDefault();
2038         }
2039 
2040         // Project the calculated bank value to a usable value in the interval [smin,smax]
2041         if (this.evalVisProp('bank.continuous')) {
2042             // in continuous mode, wrap value around slider range
2043             bank = Mat.wrap(bank, smin, smax);
2044         } else {
2045             // in non-continuous mode, clamp value to slider range
2046             bank = Mat.clamp(bank, smin, smax);
2047         }
2048 
2049         this.bank_slide.setValue(bank);
2050         this.board.update();
2051         return this;
2052     },
2053 
2054     /**
2055      * Controls the navigation using either virtual trackball.
2056      *
2057      * @private
2058      *
2059      * @param {event} evt either the keydown or the pointer event
2060      * @returns view
2061      */
2062     _trackballHandler: function (evt) {
2063         var pos = this.board.getMousePosition(evt),
2064             x, y, dx, dy, center;
2065 
2066         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);
2067         x = pos[0] - center.scrCoords[1];
2068         y = pos[1] - center.scrCoords[2];
2069 
2070         dx = evt.screenX - this._lastPos.x;
2071         dy = evt.screenY - this._lastPos.y;
2072         this._lastPos.x = evt.screenX;
2073         this._lastPos.y = evt.screenY;
2074 
2075         this._trackball = {
2076             dx: dx,
2077             dy: -dy,
2078             x: x,
2079             y: -y
2080         };
2081         this.board.update();
2082         return this;
2083     },
2084 
2085     /**
2086      * Event handler for pointer down event. Triggers handling of all 3D navigation.
2087      *
2088      * @private
2089      * @param {event} evt
2090      * @returns view
2091      */
2092     pointerDownHandler: function (evt) {
2093         var neededButton, neededKey, target;
2094 
2095         this._hasMoveAzEl = false;
2096         this._hasMoveAz = false;
2097         this._hasMoveEl = false;
2098         this._hasMoveBank = false;
2099         this._hasMoveTrackball = false;
2100 
2101         if (this.board.mode !== this.board.BOARD_MODE_NONE) {
2102             return;
2103         }
2104 
2105         this.board._change3DView = true;
2106 
2107         this._lastPos.x = evt.screenX;
2108         this._lastPos.y = evt.screenY;
2109 
2110         if (this.evalVisProp('trackball.enabled')) {
2111             neededButton = this.evalVisProp('trackball.button');
2112             neededKey = this.evalVisProp('trackball.key');
2113 
2114             // Move events for virtual trackball
2115             if (
2116                 (neededButton === -1 || neededButton === evt.button) &&
2117                 (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))
2118             ) {
2119                 // If outside is true then the event listener is bound to the document, otherwise to the div
2120                 target = (this.evalVisProp('trackball.outside')) ? document : this.board.containerObj;
2121                 Env.addEvent(target, 'pointermove', this._trackballHandler, this);
2122                 this._hasMoveTrackball = true;
2123             }
2124         } else {
2125             if (this.evalVisProp('az.pointer.enabled') && this.evalVisProp('el.pointer.enabled')) {
2126                 neededButton = this.evalVisProp('az.pointer.button');
2127                 neededKey = this.evalVisProp('az.pointer.key');
2128                 if (neededButton === this.evalVisProp('el.pointer.button') &&
2129                     neededKey === this.evalVisProp('el.pointer.key')) {
2130 
2131                     // Move events for azimuth and elevation
2132                     if (
2133                         (neededButton === -1 || neededButton === evt.button) &&
2134                         (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) ||
2135                             (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))
2136                     ) {
2137                         // If outside is true then the event listener is bound to the document, otherwise to the div
2138                         target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj;
2139 
2140                         if (target === ((this.evalVisProp('el.pointer.outside')) ? document : this.board.containerObj)) {
2141                             Env.addEvent(target, 'pointermove', this._az_elEventHandler, this);
2142                             this._hasMoveAzEl = true;
2143                         }
2144                     }
2145                 }
2146             }
2147             if (!this._hasMoveAzEl) {
2148                 if (this.evalVisProp('az.pointer.enabled')) {
2149                     neededButton = this.evalVisProp('az.pointer.button');
2150                     neededKey = this.evalVisProp('az.pointer.key');
2151 
2152                     // Move events for azimuth
2153                     if (
2154                         (neededButton === -1 || neededButton === evt.button) &&
2155                         (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))
2156                     ) {
2157                         // If outside is true then the event listener is bound to the document, otherwise to the div
2158                         target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj;
2159                         Env.addEvent(target, 'pointermove', this._azEventHandler, this);
2160                         this._hasMoveAz = true;
2161                     }
2162                 }
2163 
2164                 if (this.evalVisProp('el.pointer.enabled')) {
2165                     neededButton = this.evalVisProp('el.pointer.button');
2166                     neededKey = this.evalVisProp('el.pointer.key');
2167 
2168                     // Events for elevation
2169                     if (
2170                         (neededButton === -1 || neededButton === evt.button) &&
2171                         (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))
2172                     ) {
2173                         // If outside is true then the event listener is bound to the document, otherwise to the div
2174                         target = (this.evalVisProp('el.pointer.outside')) ? document : this.board.containerObj;
2175                         Env.addEvent(target, 'pointermove', this._elEventHandler, this);
2176                         this._hasMoveEl = true;
2177                     }
2178                 }
2179             }
2180             if (this.evalVisProp('bank.pointer.enabled')) {
2181                 neededButton = this.evalVisProp('bank.pointer.button');
2182                 neededKey = this.evalVisProp('bank.pointer.key');
2183 
2184                 // Events for bank
2185                 if (
2186                     (neededButton === -1 || neededButton === evt.button) &&
2187                     (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey))
2188                 ) {
2189                     // If `outside` is true, we bind the event listener to
2190                     // the document. otherwise, we bind it to the div. we
2191                     // register the event listener as active so it can
2192                     // prevent the pointer wheel from scrolling the page
2193                     target = (this.evalVisProp('bank.pointer.outside')) ? document : this.board.containerObj;
2194                     Env.addEvent(target, 'wheel', this._bankEventHandler, this, { passive: false });
2195                     this._hasMoveBank = true;
2196                 }
2197             }
2198         }
2199         Env.addEvent(document, 'pointerup', this.pointerUpHandler, this);
2200     },
2201 
2202     /**
2203      * Event handler for pointer up event. Triggers handling of all 3D navigation.
2204      *
2205      * @private
2206      * @param {event} evt
2207      * @returns view
2208      */
2209     pointerUpHandler: function (evt) {
2210         var target;
2211 
2212         if (this._hasMoveAzEl) {
2213             target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj;
2214             Env.removeEvent(target, 'pointermove', this._az_elEventHandler, this);
2215             this._hasMoveAzEl = false;
2216         }
2217         if (this._hasMoveAz) {
2218             target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj;
2219             Env.removeEvent(target, 'pointermove', this._azEventHandler, this);
2220             this._hasMoveAz = false;
2221         }
2222         if (this._hasMoveEl) {
2223             target = (this.evalVisProp('el.pointer.outside')) ? document : this.board.containerObj;
2224             Env.removeEvent(target, 'pointermove', this._elEventHandler, this);
2225             this._hasMoveEl = false;
2226         }
2227         if (this._hasMoveBank) {
2228             target = (this.evalVisProp('bank.pointer.outside')) ? document : this.board.containerObj;
2229             Env.removeEvent(target, 'wheel', this._bankEventHandler, this);
2230             this._hasMoveBank = false;
2231         }
2232         if (this._hasMoveTrackball) {
2233             target = (this.evalVisProp('trackball.outside')) ? document : this.board.containerObj;
2234             Env.removeEvent(target, 'pointermove', this._trackballHandler, this);
2235             this._hasMoveTrackball = false;
2236         }
2237         Env.removeEvent(document, 'pointerup', this.pointerUpHandler, this);
2238         this.board._change3DView = false;
2239         this.board.mode = this.board.BOARD_MODE_NONE;
2240     }
2241 });
2242 
2243 /**
2244  * @class A View3D element provides the container and the methods to create and display 3D elements.
2245  * @pseudo
2246  * @description  A View3D element provides the container and the methods to create and display 3D elements.
2247  * It is contained in a JSXGraph board.
2248  * <p>
2249  * It is advisable to disable panning of the board by setting the board attribute "pan":
2250  * <pre>
2251  *   pan: {enabled: false}
2252  * </pre>
2253  * Otherwise users will not be able to rotate the scene with their fingers on a touch device.
2254  * <p>
2255  * The start position of the camera can be adjusted by the attributes {@link View3D#az}, {@link View3D#el}, and {@link View3D#bank}.
2256  *
2257  * @name View3D
2258  * @augments JXG.View3D
2259  * @constructor
2260  * @type Object
2261  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
2262  * @param {Array_Array_Array} lower,dim,cube  Here, lower is an array of the form [x, y] and
2263  * dim is an array of the form [w, h].
2264  * The arrays [x, y] and [w, h] define the 2D frame into which the 3D cube is
2265  * (roughly) projected. If the view's azimuth=0 and elevation=0, the 3D view will cover a rectangle with lower left corner
2266  * [x,y] and side lengths [w, h] of the board.
2267  * The array 'cube' is of the form [[x1, x2], [y1, y2], [z1, z2]]
2268  * which determines the coordinate ranges of the 3D cube.
2269  *
2270  * @example
2271  *     var bound = [-4, 6];
2272  *     var view = board.create('view3d',
2273  *         [[-4, -3], [8, 8],
2274  *         [bound, bound, bound]],
2275  *         {
2276  *             projection: 'parallel',
2277  *             trackball: {enabled:true},
2278  *         });
2279  *
2280  *     var curve = view.create('curve3d', [
2281  *         (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2282  *         (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2283  *         (t) => Math.sin(3 * t),
2284  *         [-Math.PI, Math.PI]
2285  *     ], { strokeWidth: 4 });
2286  *
2287  * </pre><div id="JXG9b327a6c-1bd6-4e40-a502-59d024dbfd1b" class="jxgbox" style="width: 300px; height: 300px;"></div>
2288  * <script type="text/javascript">
2289  *     (function() {
2290  *         var board = JXG.JSXGraph.initBoard('JXG9b327a6c-1bd6-4e40-a502-59d024dbfd1b',
2291  *             {boundingbox: [-8, 8, 8,-8], pan: {enabled: false}, axis: false, showcopyright: false, shownavigation: false});
2292  *         var bound = [-4, 6];
2293  *         var view = board.create('view3d',
2294  *             [[-4, -3], [8, 8],
2295  *             [bound, bound, bound]],
2296  *             {
2297  *                 projection: 'parallel',
2298  *                 trackball: {enabled:true},
2299  *             });
2300  *
2301  *         var curve = view.create('curve3d', [
2302  *             (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2303  *             (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2304  *             (t) => Math.sin(3 * t),
2305  *             [-Math.PI, Math.PI]
2306  *         ], { strokeWidth: 4 });
2307  *
2308  *     })();
2309  *
2310  * </script><pre>
2311  *
2312  * @example
2313  *     var bound = [-4, 6];
2314  *     var view = board.create('view3d',
2315  *         [[-4, -3], [8, 8],
2316  *         [bound, bound, bound]],
2317  *         {
2318  *             projection: 'central',
2319  *             trackball: {enabled:true},
2320  *
2321  *             xPlaneRear: { visible: false },
2322  *             yPlaneRear: { visible: false }
2323  *
2324  *         });
2325  *
2326  *     var curve = view.create('curve3d', [
2327  *         (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2328  *         (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2329  *         (t) => Math.sin(3 * t),
2330  *         [-Math.PI, Math.PI]
2331  *     ], { strokeWidth: 4 });
2332  *
2333  * </pre><div id="JXG0dc2493d-fb2f-40d5-bdb8-762ba0ad2007" class="jxgbox" style="width: 300px; height: 300px;"></div>
2334  * <script type="text/javascript">
2335  *     (function() {
2336  *         var board = JXG.JSXGraph.initBoard('JXG0dc2493d-fb2f-40d5-bdb8-762ba0ad2007',
2337  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
2338  *         var bound = [-4, 6];
2339  *         var view = board.create('view3d',
2340  *             [[-4, -3], [8, 8],
2341  *             [bound, bound, bound]],
2342  *             {
2343  *                 projection: 'central',
2344  *                 trackball: {enabled:true},
2345  *
2346  *                 xPlaneRear: { visible: false },
2347  *                 yPlaneRear: { visible: false }
2348  *
2349  *             });
2350  *
2351  *         var curve = view.create('curve3d', [
2352  *             (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2353  *             (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2354  *             (t) => Math.sin(3 * t),
2355  *             [-Math.PI, Math.PI]
2356  *         ], { strokeWidth: 4 });
2357  *
2358  *     })();
2359  *
2360  * </script><pre>
2361  *
2362 * @example
2363  *     var bound = [-4, 6];
2364  *     var view = board.create('view3d',
2365  *         [[-4, -3], [8, 8],
2366  *         [bound, bound, bound]],
2367  *         {
2368  *             projection: 'central',
2369  *             trackball: {enabled:true},
2370  *
2371  *             // Main axes
2372  *             axesPosition: 'border',
2373  *
2374  *             // Axes at the border
2375  *             xAxisBorder: { ticks3d: { ticksDistance: 2} },
2376  *             yAxisBorder: { ticks3d: { ticksDistance: 2} },
2377  *             zAxisBorder: { ticks3d: { ticksDistance: 2} },
2378  *
2379  *             // No axes on planes
2380  *             xPlaneRearYAxis: {visible: false},
2381  *             xPlaneRearZAxis: {visible: false},
2382  *             yPlaneRearXAxis: {visible: false},
2383  *             yPlaneRearZAxis: {visible: false},
2384  *             zPlaneRearXAxis: {visible: false},
2385  *             zPlaneRearYAxis: {visible: false}
2386  *         });
2387  *
2388  *     var curve = view.create('curve3d', [
2389  *         (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2390  *         (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2391  *         (t) => Math.sin(3 * t),
2392  *         [-Math.PI, Math.PI]
2393  *     ], { strokeWidth: 4 });
2394  *
2395  * </pre><div id="JXG586f3551-335c-47e9-8d72-835409f6a103" class="jxgbox" style="width: 300px; height: 300px;"></div>
2396  * <script type="text/javascript">
2397  *     (function() {
2398  *         var board = JXG.JSXGraph.initBoard('JXG586f3551-335c-47e9-8d72-835409f6a103',
2399  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
2400  *         var bound = [-4, 6];
2401  *         var view = board.create('view3d',
2402  *             [[-4, -3], [8, 8],
2403  *             [bound, bound, bound]],
2404  *             {
2405  *                 projection: 'central',
2406  *                 trackball: {enabled:true},
2407  *
2408  *                 // Main axes
2409  *                 axesPosition: 'border',
2410  *
2411  *                 // Axes at the border
2412  *                 xAxisBorder: { ticks3d: { ticksDistance: 2} },
2413  *                 yAxisBorder: { ticks3d: { ticksDistance: 2} },
2414  *                 zAxisBorder: { ticks3d: { ticksDistance: 2} },
2415  *
2416  *                 // No axes on planes
2417  *                 xPlaneRearYAxis: {visible: false},
2418  *                 xPlaneRearZAxis: {visible: false},
2419  *                 yPlaneRearXAxis: {visible: false},
2420  *                 yPlaneRearZAxis: {visible: false},
2421  *                 zPlaneRearXAxis: {visible: false},
2422  *                 zPlaneRearYAxis: {visible: false}
2423  *             });
2424  *
2425  *         var curve = view.create('curve3d', [
2426  *             (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2427  *             (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2428  *             (t) => Math.sin(3 * t),
2429  *             [-Math.PI, Math.PI]
2430  *         ], { strokeWidth: 4 });
2431  *
2432  *     })();
2433  *
2434  * </script><pre>
2435  *
2436  * @example
2437  *     var bound = [-4, 6];
2438  *     var view = board.create('view3d',
2439  *         [[-4, -3], [8, 8],
2440  *         [bound, bound, bound]],
2441  *         {
2442  *             projection: 'central',
2443  *             trackball: {enabled:true},
2444  *
2445  *             axesPosition: 'none'
2446  *         });
2447  *
2448  *     var curve = view.create('curve3d', [
2449  *         (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2450  *         (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2451  *         (t) => Math.sin(3 * t),
2452  *         [-Math.PI, Math.PI]
2453  *     ], { strokeWidth: 4 });
2454  *
2455  * </pre><div id="JXG9a9467e1-f189-4c8c-adb2-d4f49bc7fa26" class="jxgbox" style="width: 300px; height: 300px;"></div>
2456  * <script type="text/javascript">
2457  *     (function() {
2458  *         var board = JXG.JSXGraph.initBoard('JXG9a9467e1-f189-4c8c-adb2-d4f49bc7fa26',
2459  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
2460  *         var bound = [-4, 6];
2461  *         var view = board.create('view3d',
2462  *             [[-4, -3], [8, 8],
2463  *             [bound, bound, bound]],
2464  *             {
2465  *                 projection: 'central',
2466  *                 trackball: {enabled:true},
2467  *
2468  *                 axesPosition: 'none'
2469  *             });
2470  *
2471  *         var curve = view.create('curve3d', [
2472  *             (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2473  *             (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2474  *             (t) => Math.sin(3 * t),
2475  *             [-Math.PI, Math.PI]
2476  *         ], { strokeWidth: 4 });
2477  *
2478  *     })();
2479  *
2480  * </script><pre>
2481  *
2482  * @example
2483  *     var bound = [-4, 6];
2484  *     var view = board.create('view3d',
2485  *         [[-4, -3], [8, 8],
2486  *         [bound, bound, bound]],
2487  *         {
2488  *             projection: 'central',
2489  *             trackball: {enabled:true},
2490  *
2491  *             // Main axes
2492  *             axesPosition: 'border',
2493  *
2494  *             // Axes at the border
2495  *             xAxisBorder: { ticks3d: { ticksDistance: 2} },
2496  *             yAxisBorder: { ticks3d: { ticksDistance: 2} },
2497  *             zAxisBorder: { ticks3d: { ticksDistance: 2} },
2498  *
2499  *             xPlaneRear: {
2500  *                 fillColor: '#fff',
2501  *                 mesh3d: {visible: false}
2502  *             },
2503  *             yPlaneRear: {
2504  *                 fillColor: '#fff',
2505  *                 mesh3d: {visible: false}
2506  *             },
2507  *             zPlaneRear: {
2508  *                 fillColor: '#fff',
2509  *                 mesh3d: {visible: false}
2510  *             },
2511  *             xPlaneFront: {
2512  *                 visible: true,
2513  *                 fillColor: '#fff',
2514  *                 mesh3d: {visible: false}
2515  *             },
2516  *             yPlaneFront: {
2517  *                 visible: true,
2518  *                 fillColor: '#fff',
2519  *                 mesh3d: {visible: false}
2520  *             },
2521  *             zPlaneFront: {
2522  *                 visible: true,
2523  *                 fillColor: '#fff',
2524  *                 mesh3d: {visible: false}
2525  *             },
2526  *
2527  *             // No axes on planes
2528  *             xPlaneRearYAxis: {visible: false},
2529  *             xPlaneRearZAxis: {visible: false},
2530  *             yPlaneRearXAxis: {visible: false},
2531  *             yPlaneRearZAxis: {visible: false},
2532  *             zPlaneRearXAxis: {visible: false},
2533  *             zPlaneRearYAxis: {visible: false},
2534  *             xPlaneFrontYAxis: {visible: false},
2535  *             xPlaneFrontZAxis: {visible: false},
2536  *             yPlaneFrontXAxis: {visible: false},
2537  *             yPlaneFrontZAxis: {visible: false},
2538  *             zPlaneFrontXAxis: {visible: false},
2539  *             zPlaneFrontYAxis: {visible: false}
2540  *
2541  *         });
2542  *
2543  *     var curve = view.create('curve3d', [
2544  *         (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2545  *         (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2546  *         (t) => Math.sin(3 * t),
2547  *         [-Math.PI, Math.PI]
2548  *     ], { strokeWidth: 4 });
2549  *
2550  * </pre><div id="JXGbd41a4e3-1bf7-4764-b675-98b01667103b" class="jxgbox" style="width: 300px; height: 300px;"></div>
2551  * <script type="text/javascript">
2552  *     (function() {
2553  *         var board = JXG.JSXGraph.initBoard('JXGbd41a4e3-1bf7-4764-b675-98b01667103b',
2554  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
2555  *         var bound = [-4, 6];
2556  *         var view = board.create('view3d',
2557  *             [[-4, -3], [8, 8],
2558  *             [bound, bound, bound]],
2559  *             {
2560  *                 projection: 'central',
2561  *                 trackball: {enabled:true},
2562  *
2563  *                 // Main axes
2564  *                 axesPosition: 'border',
2565  *
2566  *                 // Axes at the border
2567  *                 xAxisBorder: { ticks3d: { ticksDistance: 2} },
2568  *                 yAxisBorder: { ticks3d: { ticksDistance: 2} },
2569  *                 zAxisBorder: { ticks3d: { ticksDistance: 2} },
2570  *
2571  *                 xPlaneRear: {
2572  *                     fillColor: '#fff',
2573  *                     mesh3d: {visible: false}
2574  *                 },
2575  *                 yPlaneRear: {
2576  *                     fillColor: '#fff',
2577  *                     mesh3d: {visible: false}
2578  *                 },
2579  *                 zPlaneRear: {
2580  *                     fillColor: '#fff',
2581  *                     mesh3d: {visible: false}
2582  *                 },
2583  *                 xPlaneFront: {
2584  *                     visible: true,
2585  *                     fillColor: '#fff',
2586  *                     mesh3d: {visible: false}
2587  *                 },
2588  *                 yPlaneFront: {
2589  *                     visible: true,
2590  *                     fillColor: '#fff',
2591  *                     mesh3d: {visible: false}
2592  *                 },
2593  *                 zPlaneFront: {
2594  *                     visible: true,
2595  *                     fillColor: '#fff',
2596  *                     mesh3d: {visible: false}
2597  *                 },
2598  *
2599  *                 // No axes on planes
2600  *                 xPlaneRearYAxis: {visible: false},
2601  *                 xPlaneRearZAxis: {visible: false},
2602  *                 yPlaneRearXAxis: {visible: false},
2603  *                 yPlaneRearZAxis: {visible: false},
2604  *                 zPlaneRearXAxis: {visible: false},
2605  *                 zPlaneRearYAxis: {visible: false},
2606  *                 xPlaneFrontYAxis: {visible: false},
2607  *                 xPlaneFrontZAxis: {visible: false},
2608  *                 yPlaneFrontXAxis: {visible: false},
2609  *                 yPlaneFrontZAxis: {visible: false},
2610  *                 zPlaneFrontXAxis: {visible: false},
2611  *                 zPlaneFrontYAxis: {visible: false}
2612  *
2613  *             });
2614  *
2615  *         var curve = view.create('curve3d', [
2616  *             (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t),
2617  *             (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t),
2618  *             (t) => Math.sin(3 * t),
2619  *             [-Math.PI, Math.PI]
2620  *         ], { strokeWidth: 4 });
2621  *     })();
2622  *
2623  * </script><pre>
2624  *
2625  * @example
2626  *  var bound = [-5, 5];
2627  *  var view = board.create('view3d',
2628  *      [[-6, -3],
2629  *       [8, 8],
2630  *       [bound, bound, bound]],
2631  *      {
2632  *          // Main axes
2633  *          axesPosition: 'center',
2634  *          xAxis: { strokeColor: 'blue', strokeWidth: 3},
2635  *
2636  *          // Planes
2637  *          xPlaneRear: { fillColor: 'yellow',  mesh3d: {visible: false}},
2638  *          yPlaneFront: { visible: true, fillColor: 'blue'},
2639  *
2640  *          // Axes on planes
2641  *          xPlaneRearYAxis: {strokeColor: 'red'},
2642  *          xPlaneRearZAxis: {strokeColor: 'red'},
2643  *
2644  *          yPlaneFrontXAxis: {strokeColor: 'blue'},
2645  *          yPlaneFrontZAxis: {strokeColor: 'blue'},
2646  *
2647  *          zPlaneFrontXAxis: {visible: false},
2648  *          zPlaneFrontYAxis: {visible: false}
2649  *      });
2650  *
2651  * </pre><div id="JXGdd06d90e-be5d-4531-8f0b-65fc30b1a7c7" class="jxgbox" style="width: 500px; height: 500px;"></div>
2652  * <script type="text/javascript">
2653  *     (function() {
2654  *         var board = JXG.JSXGraph.initBoard('JXGdd06d90e-be5d-4531-8f0b-65fc30b1a7c7',
2655  *             {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false});
2656  *         var bound = [-5, 5];
2657  *         var view = board.create('view3d',
2658  *             [[-6, -3], [8, 8],
2659  *             [bound, bound, bound]],
2660  *             {
2661  *                 // Main axes
2662  *                 axesPosition: 'center',
2663  *                 xAxis: { strokeColor: 'blue', strokeWidth: 3},
2664  *                 // Planes
2665  *                 xPlaneRear: { fillColor: 'yellow',  mesh3d: {visible: false}},
2666  *                 yPlaneFront: { visible: true, fillColor: 'blue'},
2667  *                 // Axes on planes
2668  *                 xPlaneRearYAxis: {strokeColor: 'red'},
2669  *                 xPlaneRearZAxis: {strokeColor: 'red'},
2670  *                 yPlaneFrontXAxis: {strokeColor: 'blue'},
2671  *                 yPlaneFrontZAxis: {strokeColor: 'blue'},
2672  *                 zPlaneFrontXAxis: {visible: false},
2673  *                 zPlaneFrontYAxis: {visible: false}
2674  *             });
2675  *     })();
2676  *
2677  * </script><pre>
2678  * @example
2679  * var bound = [-5, 5];
2680  * var view = board.create('view3d',
2681  *     [[-6, -3], [8, 8],
2682  *     [bound, bound, bound]],
2683  *     {
2684  *         projection: 'central',
2685  *         az: {
2686  *             slider: {
2687  *                 visible: true,
2688  *                 point1: {
2689  *                     pos: [5, -4]
2690  *                 },
2691  *                 point2: {
2692  *                     pos: [5, 4]
2693  *                 },
2694  *                 label: {anchorX: 'middle'}
2695  *             }
2696  *         },
2697  *         el: {
2698  *             slider: {
2699  *                 visible: true,
2700  *                 point1: {
2701  *                     pos: [6, -5]
2702  *                 },
2703  *                 point2: {
2704  *                     pos: [6, 3]
2705  *                 },
2706  *                 label: {anchorX: 'middle'}
2707  *             }
2708  *         },
2709  *         bank: {
2710  *             slider: {
2711  *                 visible: true,
2712  *                 point1: {
2713  *                     pos: [7, -6]
2714  *                 },
2715  *                 point2: {
2716  *                     pos: [7, 2]
2717  *                 },
2718  *                 label: {anchorX: 'middle'}
2719  *             }
2720  *         }
2721  *     });
2722  *
2723  *
2724  * </pre><div id="JXGe181cc55-271b-419b-84fd-622326fd1d1a" class="jxgbox" style="width: 300px; height: 300px;"></div>
2725  * <script type="text/javascript">
2726  *     (function() {
2727  *         var board = JXG.JSXGraph.initBoard('JXGe181cc55-271b-419b-84fd-622326fd1d1a',
2728  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
2729  *     var bound = [-5, 5];
2730  *     var view = board.create('view3d',
2731  *         [[-6, -3], [8, 8],
2732  *         [bound, bound, bound]],
2733  *         {
2734  *             projection: 'central',
2735  *             az: {
2736  *                 slider: {
2737  *                     visible: true,
2738  *                     point1: {
2739  *                         pos: [5, -4]
2740  *                     },
2741  *                     point2: {
2742  *                         pos: [5, 4]
2743  *                     },
2744  *                     label: {anchorX: 'middle'}
2745  *                 }
2746  *             },
2747  *             el: {
2748  *                 slider: {
2749  *                     visible: true,
2750  *                     point1: {
2751  *                         pos: [6, -5]
2752  *                     },
2753  *                     point2: {
2754  *                         pos: [6, 3]
2755  *                     },
2756  *                     label: {anchorX: 'middle'}
2757  *                 }
2758  *             },
2759  *             bank: {
2760  *                 slider: {
2761  *                     visible: true,
2762  *                     point1: {
2763  *                         pos: [7, -6]
2764  *                     },
2765  *                     point2: {
2766  *                         pos: [7, 2]
2767  *                     },
2768  *                     label: {anchorX: 'middle'}
2769  *                 }
2770  *             }
2771  *         });
2772  *
2773  *
2774  *     })();
2775  *
2776  * </script><pre>
2777  *
2778  *
2779  */
2780 JXG.createView3D = function (board, parents, attributes) {
2781     var view, attr, attr_az, attr_el, attr_bank,
2782         x, y, w, h,
2783         p1, p2, v,
2784         coords = parents[0], // llft corner
2785         size = parents[1]; // [w, h]
2786 
2787     attr = Type.copyAttributes(attributes, board.options, 'view3d');
2788     view = new JXG.View3D(board, parents, attr);
2789     view.defaultAxes = view.create('axes3d', [], attr);
2790 
2791     x = coords[0];
2792     y = coords[1];
2793     w = size[0];
2794     h = size[1];
2795 
2796     attr_az = Type.copyAttributes(attr, board.options, 'view3d', 'az', 'slider');
2797     attr_az.name = 'az';
2798 
2799     attr_el = Type.copyAttributes(attr, board.options, 'view3d', 'el', 'slider');
2800     attr_el.name = 'el';
2801 
2802     attr_bank = Type.copyAttributes(attr, board.options, 'view3d', 'bank', 'slider');
2803     attr_bank.name = 'bank';
2804 
2805     v = Type.evaluate(attr_az.point1.pos);
2806     if (!Type.isArray(v)) {
2807         // 'auto'
2808         p1 = [x - 1, y - 2];
2809     } else {
2810         p1 = v;
2811     }
2812     v = Type.evaluate(attr_az.point2.pos);
2813     if (!Type.isArray(v)) {
2814         // 'auto'
2815         p2 = [x + w + 1, y - 2];
2816     } else {
2817         p2 = v;
2818     }
2819 
2820     /**
2821      * Slider to adapt azimuth angle
2822      * @name JXG.View3D#az_slide
2823      * @type {Slider}
2824      */
2825     view.az_slide = board.create(
2826         'slider',
2827         [
2828             p1, p2,
2829             [
2830                 Type.evaluate(attr_az.min),
2831                 Type.evaluate(attr_az.start),
2832                 Type.evaluate(attr_az.max)
2833             ]
2834         ],
2835         attr_az
2836     );
2837     view.inherits.push(view.az_slide);
2838     view.az_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate()
2839 
2840     v = Type.evaluate(attr_el.point1.pos);
2841     if (!Type.isArray(v)) {
2842         // 'auto'
2843         p1 = [x - 1, y];
2844     } else {
2845         p1 = v;
2846     }
2847     v = Type.evaluate(attr_el.point2.pos);
2848     if (!Type.isArray(v)) {
2849         // 'auto'
2850         p2 = [x - 1, y + h];
2851     } else {
2852         p2 = v;
2853     }
2854 
2855     /**
2856      * Slider to adapt elevation angle
2857      *
2858      * @name JXG.View3D#el_slide
2859      * @type {Slider}
2860      */
2861     view.el_slide = board.create(
2862         'slider',
2863         [
2864             p1, p2,
2865             [
2866                 Type.evaluate(attr_el.min),
2867                 Type.evaluate(attr_el.start),
2868                 Type.evaluate(attr_el.max)]
2869         ],
2870         attr_el
2871     );
2872     view.inherits.push(view.el_slide);
2873     view.el_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate()
2874 
2875     v = Type.evaluate(attr_bank.point1.pos);
2876     if (!Type.isArray(v)) {
2877         // 'auto'
2878         p1 = [x - 1, y + h + 2];
2879     } else {
2880         p1 = v;
2881     }
2882     v = Type.evaluate(attr_bank.point2.pos);
2883     if (!Type.isArray(v)) {
2884         // 'auto'
2885         p2 = [x + w + 1, y + h + 2];
2886     } else {
2887         p2 = v;
2888     }
2889 
2890     /**
2891      * Slider to adjust bank angle
2892      *
2893      * @name JXG.View3D#bank_slide
2894      * @type {Slider}
2895      */
2896     view.bank_slide = board.create(
2897         'slider',
2898         [
2899             p1, p2,
2900             [
2901                 Type.evaluate(attr_bank.min),
2902                 Type.evaluate(attr_bank.start),
2903                 Type.evaluate(attr_bank.max)
2904             ]
2905         ],
2906         attr_bank
2907     );
2908     view.inherits.push(view.bank_slide);
2909     view.bank_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate()
2910 
2911     // Set special infobox attributes of view3d.infobox
2912     // Using setAttribute() is not possible here, since we have to
2913     // avoid a call of board.update().
2914     // The drawback is that we can not use shortcuts
2915     view.board.infobox.visProp = Type.merge(view.board.infobox.visProp, attr.infobox);
2916 
2917     // 3d infobox: drag direction and coordinates
2918     view.board.highlightInfobox = function (x, y, el) {
2919         var d, i, c3d, foot,
2920             pre = '',
2921             brd = el.board,
2922             arr, infobox,
2923             p = null;
2924 
2925         if (this.mode === this.BOARD_MODE_DRAG) {
2926             // Drag direction is only shown during dragging
2927             if (view.isVerticalDrag()) {
2928                 pre = '<span style="color:black; font-size:200%">\u21C5  </span>';
2929             } else {
2930                 pre = '<span style="color:black; font-size:200%">\u21C4  </span>';
2931             }
2932         }
2933 
2934         // Search 3D parent
2935         for (i = 0; i < el.parents.length; i++) {
2936             p = brd.objects[el.parents[i]];
2937             if (p.is3D) {
2938                 break;
2939             }
2940         }
2941 
2942         if (p && Type.exists(p.element2D)) {
2943             foot = [1, 0, 0, p.coords[3]];
2944             view._w0 = Mat.innerProduct(view.matrix3D[0], foot, 4);
2945 
2946             c3d = view.project2DTo3DPlane(p.element2D, [1, 0, 0, 1], foot);
2947             if (!view.isInCube(c3d)) {
2948                 view.board.highlightCustomInfobox('', p);
2949                 return;
2950             }
2951             d = p.evalVisProp('infoboxdigits');
2952             infobox = view.board.infobox;
2953             if (d === 'auto') {
2954                 if (infobox.useLocale()) {
2955                     arr = [pre, '(', infobox.formatNumberLocale(p.X()), ' | ', infobox.formatNumberLocale(p.Y()), ' | ', infobox.formatNumberLocale(p.Z()), ')'];
2956                 } else {
2957                     arr = [pre, '(', Type.autoDigits(p.X()), ' | ', Type.autoDigits(p.Y()), ' | ', Type.autoDigits(p.Z()), ')'];
2958                 }
2959 
2960             } else {
2961                 if (infobox.useLocale()) {
2962                     arr = [pre, '(', infobox.formatNumberLocale(p.X(), d), ' | ', infobox.formatNumberLocale(p.Y(), d), ' | ', infobox.formatNumberLocale(p.Z(), d), ')'];
2963                 } else {
2964                     arr = [pre, '(', Type.toFixed(p.X(), d), ' | ', Type.toFixed(p.Y(), d), ' | ', Type.toFixed(p.Z(), d), ')'];
2965                 }
2966             }
2967             view.board.highlightCustomInfobox(arr.join(''), p);
2968         } else {
2969             view.board.highlightCustomInfobox('(' + x + ', ' + y + ')', el);
2970         }
2971     };
2972 
2973     // Hack needed to enable addEvent for view3D:
2974     view.BOARD_MODE_NONE = 0x0000;
2975 
2976     // Add events for the keyboard navigation
2977     Env.addEvent(board.containerObj, 'keydown', function (event) {
2978         var neededKey,
2979             catchEvt = false;
2980 
2981         // this.board._change3DView = true;
2982         if (view.evalVisProp('el.keyboard.enabled') &&
2983             (event.key === 'ArrowUp' || event.key === 'ArrowDown')
2984         ) {
2985             neededKey = view.evalVisProp('el.keyboard.key');
2986             if (neededKey === 'none' ||
2987                 (neededKey.indexOf('shift') > -1 && event.shiftKey) ||
2988                 (neededKey.indexOf('ctrl') > -1 && event.ctrlKey)) {
2989                 view._elEventHandler(event);
2990                 catchEvt = true;
2991             }
2992 
2993         }
2994 
2995         if (view.evalVisProp('az.keyboard.enabled') &&
2996             (event.key === 'ArrowLeft' || event.key === 'ArrowRight')
2997         ) {
2998             neededKey = view.evalVisProp('az.keyboard.key');
2999             if (neededKey === 'none' ||
3000                 (neededKey.indexOf('shift') > -1 && event.shiftKey) ||
3001                 (neededKey.indexOf('ctrl') > -1 && event.ctrlKey)
3002             ) {
3003                 view._azEventHandler(event);
3004                 catchEvt = true;
3005             }
3006         }
3007 
3008         if (view.evalVisProp('bank.keyboard.enabled') && (event.key === ',' || event.key === '<' || event.key === '.' || event.key === '>')) {
3009             neededKey = view.evalVisProp('bank.keyboard.key');
3010             if (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && event.shiftKey) || (neededKey.indexOf('ctrl') > -1 && event.ctrlKey)) {
3011                 view._bankEventHandler(event);
3012                 catchEvt = true;
3013             }
3014         }
3015 
3016         if (event.key === 'PageUp') {
3017             view.nextView();
3018             catchEvt = true;
3019         } else if (event.key === 'PageDown') {
3020             view.previousView();
3021             catchEvt = true;
3022         }
3023 
3024         if (catchEvt) {
3025             // We stop event handling only in the case if the keypress could be
3026             // used for the 3D view. If this is not done, input fields et al
3027             // can not be used any more.
3028             event.preventDefault();
3029         }
3030         this.board._change3DView = false;
3031 
3032     }, view);
3033 
3034     // Add events for the pointer navigation
3035     Env.addEvent(board.containerObj, 'pointerdown', view.pointerDownHandler, view);
3036 
3037     // Initialize view rotation matrix
3038     view.getAnglesFromSliders();
3039     view.matrix3DRot = view.getRotationFromAngles();
3040 
3041     // override angle slider bounds when trackball navigation is enabled
3042     view.updateAngleSliderBounds();
3043 
3044     view.board.update();
3045 
3046     return view;
3047 };
3048 
3049 JXG.registerElement("view3d", JXG.createView3D);
3050 
3051 export default JXG.View3D;
3052