1 /* 2 Copyright 2008-2026 3 Matthias Ehmann, 4 Carsten Miller, 5 Andreas Walter, 6 Alfred Wassermann 7 8 This file is part of JSXGraph. 9 10 JSXGraph is free software dual licensed under the GNU LGPL or MIT License. 11 12 You can redistribute it and/or modify it under the terms of the 13 14 * GNU Lesser General Public License as published by 15 the Free Software Foundation, either version 3 of the License, or 16 (at your option) any later version 17 OR 18 * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT 19 20 JSXGraph is distributed in the hope that it will be useful, 21 but WITHOUT ANY WARRANTY; without even the implied warranty of 22 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 23 GNU Lesser General Public License for more details. 24 25 You should have received a copy of the GNU Lesser General Public License and 26 the MIT License along with JSXGraph. If not, see <https://www.gnu.org/licenses/> 27 and <https://opensource.org/licenses/MIT/>. 28 */ 29 /* 30 Some functionalities in this file were developed as part of a software project 31 with students. We would like to thank all contributors for their help: 32 33 Winter semester 2023/2024: 34 Lars Hofmann 35 Leonhard Iser 36 Vincent Kulicke 37 Laura Rinas 38 */ 39 40 /*global JXG:true, define: true*/ 41 42 import JXG from "../jxg.js"; 43 import Const from "../base/constants.js"; 44 import Coords from "../base/coords.js"; 45 import Type from "../utils/type.js"; 46 import Mat from "../math/math.js"; 47 import Geometry from "../math/geometry.js"; 48 import Numerics from "../math/numerics.js"; 49 import Env from "../utils/env.js"; 50 import GeometryElement from "../base/element.js"; 51 import Composition from "../base/composition.js"; 52 53 /** 54 * 3D view inside a JXGraph board. 55 * 56 * @class Creates a new 3D view. Do not use this constructor to create a 3D view. Use {@link JXG.Board#create} with 57 * type {@link View3D} instead. 58 * 59 * @augments JXG.GeometryElement 60 * @param {Array} parents Array consisting of lower left corner [x, y] of the view inside the board, [width, height] of the view 61 * and box size [[x1, x2], [y1,y2], [z1,z2]]. If the view's azimuth=0 and elevation=0, the 3D view will cover a rectangle with lower left corner 62 * [x,y] and side lengths [w, h] of the board. 63 */ 64 JXG.View3D = function (board, parents, attributes) { 65 this.constructor(board, attributes, Const.OBJECT_TYPE_VIEW3D, Const.OBJECT_CLASS_3D); 66 67 /** 68 * An associative array containing all geometric objects belonging to the view. 69 * Key is the id of the object and value is a reference to the object. 70 * @type Object 71 * @private 72 */ 73 this.objects = {}; 74 75 /** 76 * An array containing all the elements in the view that are sorted due to their depth order. 77 * @Type Object 78 * @private 79 */ 80 this.depthOrdered = {}; 81 82 /** 83 * TODO: why deleted? 84 * An array containing all geometric objects in this view in the order of construction. 85 * @type Array 86 * @private 87 */ 88 // this.objectsList = []; 89 90 /** 91 * An associative array / dictionary to store the objects of the board by name. The name of the object is the key and value is a reference to the object. 92 * @type Object 93 * @private 94 */ 95 this.elementsByName = {}; 96 97 /** 98 * Default axes of the 3D view, contains the axes of the view or null. 99 * 100 * @type {Object} 101 * @default null 102 */ 103 this.defaultAxes = null; 104 105 /** 106 * The Tait-Bryan angles specifying the view box orientation 107 */ 108 this.angles = { 109 az: null, 110 el: null, 111 bank: null 112 }; 113 114 /** 115 * @type {Array} 116 * The view box orientation matrix 117 */ 118 this.matrix3DRot = [ 119 [1, 0, 0, 0], 120 [0, 1, 0, 0], 121 [0, 0, 1, 0], 122 [0, 0, 0, 1] 123 ]; 124 125 // Used for z-index computation 126 this.matrix3DRotShift = [ 127 [1, 0, 0, 0], 128 [0, 1, 0, 0], 129 [0, 0, 1, 0], 130 [0, 0, 0, 1] 131 ]; 132 133 /** 134 * @type {Array} 135 * @private 136 */ 137 // 3D-to-2D transformation matrix 138 this.matrix3D = [ 139 [1, 0, 0, 0], 140 [0, 1, 0, 0], 141 [0, 0, 1, 0] 142 ]; 143 144 /** 145 * The 4×4 matrix that maps box coordinates to camera coordinates. These 146 * coordinate systems fit into the View3D coordinate atlas as follows. 147 * <ul> 148 * <li><b>World coordinates.</b> The coordinates used to specify object 149 * positions in a JSXGraph scene.</li> 150 * <li><b>Box coordinates.</b> The world coordinates translated to put the 151 * center of the view box at the origin. 152 * <li><b>Camera coordinates.</b> The coordinate system where the 153 * <code>x</code>, <code>y</code> plane is the screen, the origin is the 154 * center of the screen, and the <code>z</code> axis points out of the 155 * screen, toward the viewer. 156 * <li><b>Focal coordinates.</b> The camera coordinates translated to put 157 * the origin at the focal point, which is set back from the screen by the 158 * focal distance.</li> 159 * </ul> 160 * The <code>boxToCam</code> transformation is exposed to help 3D elements 161 * manage their 2D representations in central projection mode. To map world 162 * coordinates to focal coordinates, use the 163 * {@link JXG.View3D#worldToFocal} method. 164 * @type {Array} 165 */ 166 this.boxToCam = []; 167 168 /** 169 * @type array 170 * @private 171 */ 172 // Lower left corner [x, y] of the 3D view if elevation and azimuth are set to 0. 173 this.llftCorner = parents[0]; 174 175 /** 176 * Width and height [w, h] of the 3D view if elevation and azimuth are set to 0. 177 * @type array 178 * @private 179 */ 180 this.size = parents[1]; 181 182 /** 183 * Bounding box (cube) [[x1, x2], [y1,y2], [z1,z2]] of the 3D view 184 * @type array 185 */ 186 this.bbox3D = parents[2]; 187 188 /** 189 * The distance from the camera to the origin. In other words, the 190 * radius of the sphere where the camera sits. 191 * @type Number 192 */ 193 this.r = -1; 194 195 /** 196 * The distance from the camera to the screen. Computed automatically from 197 * the `fov` property. 198 * @type Number 199 */ 200 this.focalDist = -1; 201 202 /** 203 * Type of projection. 204 * @type String 205 */ 206 // Will be set in update(). 207 this.projectionType = 'parallel'; 208 209 /** 210 * Whether trackball navigation is currently enabled. 211 * @type String 212 */ 213 this.trackballEnabled = false; 214 215 /** 216 * Store last position of pointer. 217 * This is the successor to use evt.movementX/Y which caused problems on firefox 218 * @type Object 219 * @private 220 */ 221 this._lastPos = { 222 x: 0, 223 y: 0 224 }; 225 226 this.timeoutAzimuth = null; 227 228 this.zIndexMin = Infinity; 229 this.zIndexMax = -Infinity; 230 231 this.id = this.board.setId(this, 'V'); 232 this.board.finalizeAdding(this); 233 this.elType = 'view3d'; 234 235 this.methodMap = Type.deepCopy(this.methodMap, { 236 // TODO 237 }); 238 }; 239 JXG.View3D.prototype = new GeometryElement(); 240 241 JXG.extend( 242 JXG.View3D.prototype, /** @lends JXG.View3D.prototype */ { 243 244 /** 245 * Creates a new 3D element of type elementType. 246 * @param {String} elementType Type of the element to be constructed given as a string e.g. 'point3d' or 'surface3d'. 247 * @param {Array} parents Array of parent elements needed to construct the element e.g. coordinates for a 3D point or two 248 * 3D points to construct a line. This highly depends on the elementType that is constructed. See the corresponding JXG.create* 249 * methods for a list of possible parameters. 250 * @param {Object} [attributes] An object containing the attributes to be set. This also depends on the elementType. 251 * Common attributes are name, visible, strokeColor. 252 * @returns {Object} Reference to the created element. This is usually a GeometryElement3D, but can be an array containing 253 * two or more elements. 254 */ 255 create: function (elementType, parents, attributes) { 256 var prefix = [], 257 el; 258 259 if (elementType.indexOf('3d') > 0) { 260 // is3D = true; 261 prefix.push(this); 262 } 263 el = this.board.create(elementType, prefix.concat(parents), attributes); 264 265 return el; 266 }, 267 268 /** 269 * Select a single or multiple elements at once. 270 * @param {String|Object|function} str The name, id or a reference to a JSXGraph 3D element in the 3D view. An object will 271 * be used as a filter to return multiple elements at once filtered by the properties of the object. 272 * @param {Boolean} onlyByIdOrName If true (default:false) elements are only filtered by their id, name or groupId. 273 * The advanced filters consisting of objects or functions are ignored. 274 * @returns {JXG.GeometryElement3D|JXG.Composition} 275 * @example 276 * // select the element with name A 277 * view.select('A'); 278 * 279 * // select all elements with strokecolor set to 'red' (but not '#ff0000') 280 * view.select({ 281 * strokeColor: 'red' 282 * }); 283 * 284 * // select all points on or below the x/y plane and make them black. 285 * view.select({ 286 * elType: 'point3d', 287 * Z: function (v) { 288 * return v <= 0; 289 * } 290 * }).setAttribute({color: 'black'}); 291 * 292 * // select all elements 293 * view.select(function (el) { 294 * return true; 295 * }); 296 */ 297 select: function (str, onlyByIdOrName) { 298 var flist, 299 olist, 300 i, 301 l, 302 s = str; 303 304 if (s === null) { 305 return s; 306 } 307 308 if (Type.isString(s) && s !== '') { 309 // It's a string, most likely an id or a name. 310 // Search by ID 311 if (Type.exists(this.objects[s])) { 312 s = this.objects[s]; 313 // Search by name 314 } else if (Type.exists(this.elementsByName[s])) { 315 s = this.elementsByName[s]; 316 // // Search by group ID 317 // } else if (Type.exists(this.groups[s])) { 318 // s = this.groups[s]; 319 } 320 321 } else if ( 322 !onlyByIdOrName && 323 (Type.isFunction(s) || (Type.isObject(s) && !Type.isFunction(s.setAttribute))) 324 ) { 325 // It's a function or an object, but not an element 326 flist = Type.filterElements(this.objectsList, s); 327 328 olist = {}; 329 l = flist.length; 330 for (i = 0; i < l; i++) { 331 olist[flist[i].id] = flist[i]; 332 } 333 s = new Composition(olist); 334 335 } else if ( 336 Type.isObject(s) && 337 Type.exists(s.id) && 338 !Type.exists(this.objects[s.id]) 339 ) { 340 // It's an element which has been deleted (and still hangs around, e.g. in an attractor list) 341 s = null; 342 } 343 344 return s; 345 }, 346 347 // set the Tait-Bryan angles to specify the current view rotation matrix 348 setAnglesFromRotation: function () { 349 var rem = this.matrix3DRot, // rotation remaining after angle extraction 350 rBank, cosBank, sinBank, 351 cosEl, sinEl, 352 cosAz, sinAz; 353 354 // extract bank by rotating the view box z axis onto the camera yz plane 355 rBank = Math.sqrt(rem[1][3] * rem[1][3] + rem[2][3] * rem[2][3]); 356 if (rBank > Mat.eps) { 357 cosBank = rem[2][3] / rBank; 358 sinBank = rem[1][3] / rBank; 359 } else { 360 // if the z axis is pointed almost exactly at the screen, we 361 // keep the current bank value 362 cosBank = Math.cos(this.angles.bank); 363 sinBank = Math.sin(this.angles.bank); 364 } 365 rem = Mat.matMatMult([ 366 [1, 0, 0, 0], 367 [0, cosBank, -sinBank, 0], 368 [0, sinBank, cosBank, 0], 369 [0, 0, 0, 1] 370 ], rem); 371 this.angles.bank = Math.atan2(sinBank, cosBank); 372 373 // extract elevation by rotating the view box z axis onto the camera 374 // y axis 375 cosEl = rem[2][3]; 376 sinEl = rem[3][3]; 377 rem = Mat.matMatMult([ 378 [1, 0, 0, 0], 379 [0, 1, 0, 0], 380 [0, 0, cosEl, sinEl], 381 [0, 0, -sinEl, cosEl] 382 ], rem); 383 this.angles.el = Math.atan2(sinEl, cosEl); 384 385 // extract azimuth 386 cosAz = -rem[1][1]; 387 sinAz = rem[3][1]; 388 this.angles.az = Math.atan2(sinAz, cosAz); 389 if (this.angles.az < 0) this.angles.az += 2 * Math.PI; 390 391 this.setSlidersFromAngles(); 392 }, 393 394 anglesHaveMoved: function () { 395 return ( 396 this._hasMoveAz || this._hasMoveEl || 397 Math.abs(this.angles.az - this.az_slide.Value()) > Mat.eps || 398 Math.abs(this.angles.el - this.el_slide.Value()) > Mat.eps || 399 Math.abs(this.angles.bank - this.bank_slide.Value()) > Mat.eps 400 ); 401 }, 402 403 getAnglesFromSliders: function () { 404 this.angles.az = this.az_slide.Value(); 405 this.angles.el = this.el_slide.Value(); 406 this.angles.bank = this.bank_slide.Value(); 407 }, 408 409 setSlidersFromAngles: function () { 410 this.az_slide.setValue(this.angles.az); 411 this.el_slide.setValue(this.angles.el); 412 this.bank_slide.setValue(this.angles.bank); 413 }, 414 415 // return the rotation matrix specified by the current Tait-Bryan angles 416 getRotationFromAngles: function () { 417 var a, e, b, f, 418 cosBank, sinBank, 419 mat = [ 420 [1, 0, 0, 0], 421 [0, 1, 0, 0], 422 [0, 0, 1, 0], 423 [0, 0, 0, 1] 424 ]; 425 426 // mat projects homogeneous 3D coords in View3D 427 // to homogeneous 2D coordinates in the board 428 a = this.angles.az; 429 e = this.angles.el; 430 b = this.angles.bank; 431 f = -Math.sin(e); 432 433 mat[1][1] = -Math.cos(a); 434 mat[1][2] = Math.sin(a); 435 mat[1][3] = 0; 436 437 mat[2][1] = f * Math.sin(a); 438 mat[2][2] = f * Math.cos(a); 439 mat[2][3] = Math.cos(e); 440 441 mat[3][1] = Math.cos(e) * Math.sin(a); 442 mat[3][2] = Math.cos(e) * Math.cos(a); 443 mat[3][3] = Math.sin(e); 444 445 cosBank = Math.cos(b); 446 sinBank = Math.sin(b); 447 mat = Mat.matMatMult([ 448 [1, 0, 0, 0], 449 [0, cosBank, sinBank, 0], 450 [0, -sinBank, cosBank, 0], 451 [0, 0, 0, 1] 452 ], mat); 453 454 return mat; 455 456 /* this code, originally from `_updateCentralProjection`, is an 457 * alternate implementation of the azimuth-elevation matrix 458 * computation above. using this implementation instead of the 459 * current one might lead to simpler code in a future refactoring 460 var a, e, up, 461 ax, ay, az, v, nrm, 462 eye, d, 463 func_sphere; 464 465 // finds the point on the unit sphere with the given azimuth and 466 // elevation, and returns its affine coordinates 467 func_sphere = function (az, el) { 468 return [ 469 Math.cos(az) * Math.cos(el), 470 -Math.sin(az) * Math.cos(el), 471 Math.sin(el) 472 ]; 473 }; 474 475 a = this.az_slide.Value() + (3 * Math.PI * 0.5); // Sphere 476 e = this.el_slide.Value(); 477 478 // create an up vector and an eye vector which are 90 degrees out of phase 479 up = func_sphere(a, e + Math.PI / 2); 480 eye = func_sphere(a, e); 481 d = [eye[0], eye[1], eye[2]]; 482 483 nrm = Mat.norm(d, 3); 484 az = [d[0] / nrm, d[1] / nrm, d[2] / nrm]; 485 486 nrm = Mat.norm(up, 3); 487 v = [up[0] / nrm, up[1] / nrm, up[2] / nrm]; 488 489 ax = Mat.crossProduct(v, az); 490 ay = Mat.crossProduct(az, ax); 491 492 this.matrix3DRot[1] = [0, ax[0], ax[1], ax[2]]; 493 this.matrix3DRot[2] = [0, ay[0], ay[1], ay[2]]; 494 this.matrix3DRot[3] = [0, az[0], az[1], az[2]]; 495 */ 496 }, 497 498 /** 499 * Project 2D point (x,y) to the virtual trackpad sphere, 500 * see Bell's virtual trackpad, and return z-component of the 501 * number. 502 * 503 * @param {Number} r 504 * @param {Number} x 505 * @param {Number} y 506 * @returns Number 507 * @private 508 */ 509 _projectToSphere: function (r, x, y) { 510 var d = Mat.hypot(x, y), 511 t, z; 512 513 if (d < r * 0.7071067811865475) { // Inside sphere 514 z = Math.sqrt(r * r - d * d); 515 } else { // On hyperbola 516 t = r / 1.414213562373095; 517 z = t * t / d; 518 } 519 return z; 520 }, 521 522 /** 523 * Determine 4x4 rotation matrix with Bell's virtual trackball. 524 * 525 * @returns {Array} 4x4 rotation matrix 526 * @private 527 */ 528 updateProjectionTrackball: function (Pref) { 529 var R = 100, 530 dx, dy, dr2, 531 p1, p2, x, y, theta, t, d, 532 c, s, n, 533 mat = [ 534 [1, 0, 0, 0], 535 [0, 1, 0, 0], 536 [0, 0, 1, 0], 537 [0, 0, 0, 1] 538 ]; 539 540 if (!Type.exists(this._trackball)) { 541 return this.matrix3DRot; 542 } 543 544 dx = this._trackball.dx; 545 dy = this._trackball.dy; 546 dr2 = dx * dx + dy * dy; 547 if (dr2 > Mat.eps) { 548 // // Method by Hanson, "The rolling ball", Graphics Gems III, p.51 549 // // Rotation axis: 550 // // n = (-dy/dr, dx/dr, 0) 551 // // Rotation angle around n: 552 // // theta = atan(dr / R) approx dr / R 553 // dr = Math.sqrt(dr2); 554 // c = R / Math.hypot(R, dr); // cos(theta) 555 // t = 1 - c; // 1 - cos(theta) 556 // s = dr / Math.hypot(R, dr); // sin(theta) 557 // n = [-dy / dr, dx / dr, 0]; 558 559 // Bell virtual trackpad, see 560 // https://opensource.apple.com/source/X11libs/X11libs-60/mesa/Mesa-7.8.2/progs/util/trackball.c.auto.html 561 // http://scv.bu.edu/documentation/presentations/visualizationworkshop08/materials/opengl/trackball.c. 562 // See also Henriksen, Sporring, Hornaek, "Virtual Trackballs revisited". 563 // 564 R = (this.size[0] * this.board.unitX + this.size[1] * this.board.unitY) * 0.25; 565 x = this._trackball.x; 566 y = this._trackball.y; 567 568 p2 = [x, y, this._projectToSphere(R, x, y)]; 569 x -= dx; 570 y -= dy; 571 p1 = [x, y, this._projectToSphere(R, x, y)]; 572 573 n = Mat.crossProduct(p1, p2); 574 d = Mat.hypot(n[0], n[1], n[2]); 575 n[0] /= d; 576 n[1] /= d; 577 n[2] /= d; 578 579 t = Geometry.distance(p2, p1, 3) / (2 * R); 580 t = (t > 1.0) ? 1.0 : t; 581 t = (t < -1.0) ? -1.0 : t; 582 theta = 2.0 * Math.asin(t); 583 c = Math.cos(theta); 584 t = 1 - c; 585 s = Math.sin(theta); 586 587 // Rotation by theta about the axis n. See equation 9.63 of 588 // 589 // Ian Richard Cole. "Modeling CPV" (thesis). Loughborough 590 // University. https://hdl.handle.net/2134/18050 591 // 592 mat[1][1] = c + n[0] * n[0] * t; 593 mat[2][1] = n[1] * n[0] * t + n[2] * s; 594 mat[3][1] = n[2] * n[0] * t - n[1] * s; 595 596 mat[1][2] = n[0] * n[1] * t - n[2] * s; 597 mat[2][2] = c + n[1] * n[1] * t; 598 mat[3][2] = n[2] * n[1] * t + n[0] * s; 599 600 mat[1][3] = n[0] * n[2] * t + n[1] * s; 601 mat[2][3] = n[1] * n[2] * t - n[0] * s; 602 mat[3][3] = c + n[2] * n[2] * t; 603 } 604 605 mat = Mat.matMatMult(mat, this.matrix3DRot); 606 return mat; 607 }, 608 609 updateAngleSliderBounds: function () { 610 var az_smax, az_smin, 611 el_smax, el_smin, el_cover, 612 el_smid, el_equiv, el_flip_equiv, 613 el_equiv_loss, el_flip_equiv_loss, el_interval_loss, 614 bank_smax, bank_smin; 615 616 // update stored trackball toggle 617 this.trackballEnabled = this.evalVisProp('trackball.enabled'); 618 619 // set slider bounds 620 if (this.trackballEnabled) { 621 this.az_slide.setMin(0); 622 this.az_slide.setMax(2 * Math.PI); 623 this.el_slide.setMin(-0.5 * Math.PI); 624 this.el_slide.setMax(0.5 * Math.PI); 625 this.bank_slide.setMin(-Math.PI); 626 this.bank_slide.setMax(Math.PI); 627 } else { 628 this.az_slide.setMin(this.visProp.az.slider.min); 629 this.az_slide.setMax(this.visProp.az.slider.max); 630 this.el_slide.setMin(this.visProp.el.slider.min); 631 this.el_slide.setMax(this.visProp.el.slider.max); 632 this.bank_slide.setMin(this.visProp.bank.slider.min); 633 this.bank_slide.setMax(this.visProp.bank.slider.max); 634 } 635 636 // get new slider bounds 637 az_smax = this.az_slide._smax; 638 az_smin = this.az_slide._smin; 639 el_smax = this.el_slide._smax; 640 el_smin = this.el_slide._smin; 641 bank_smax = this.bank_slide._smax; 642 bank_smin = this.bank_slide._smin; 643 644 // wrap and restore angle values 645 if (this.trackballEnabled) { 646 // if we're upside-down, flip the bank angle to reach the same 647 // orientation with an elevation between -pi/2 and pi/2 648 el_cover = Mat.mod(this.angles.el, 2 * Math.PI); 649 if (0.5 * Math.PI < el_cover && el_cover < 1.5 * Math.PI) { 650 this.angles.el = Math.PI - el_cover; 651 this.angles.az = Mat.wrap(this.angles.az + Math.PI, az_smin, az_smax); 652 this.angles.bank = Mat.wrap(this.angles.bank + Math.PI, bank_smin, bank_smax); 653 } 654 655 // wrap the azimuth and bank angle 656 this.angles.az = Mat.wrap(this.angles.az, az_smin, az_smax); 657 this.angles.el = Mat.wrap(this.angles.el, el_smin, el_smax); 658 this.angles.bank = Mat.wrap(this.angles.bank, bank_smin, bank_smax); 659 } else { 660 // wrap and clamp the elevation into the slider range. if 661 // flipping the elevation gets us closer to the slider interval, 662 // do that, inverting the azimuth and bank angle to compensate 663 el_interval_loss = function (t) { 664 if (t < el_smin) { 665 return el_smin - t; 666 } else if (el_smax < t) { 667 return t - el_smax; 668 } else { 669 return 0; 670 } 671 }; 672 el_smid = 0.5 * (el_smin + el_smax); 673 el_equiv = Mat.wrap( 674 this.angles.el, 675 el_smid - Math.PI, 676 el_smid + Math.PI 677 ); 678 el_flip_equiv = Mat.wrap( 679 Math.PI - this.angles.el, 680 el_smid - Math.PI, 681 el_smid + Math.PI 682 ); 683 el_equiv_loss = el_interval_loss(el_equiv); 684 el_flip_equiv_loss = el_interval_loss(el_flip_equiv); 685 if (el_equiv_loss <= el_flip_equiv_loss) { 686 this.angles.el = Mat.clamp(el_equiv, el_smin, el_smax); 687 } else { 688 this.angles.el = Mat.clamp(el_flip_equiv, el_smin, el_smax); 689 this.angles.az = Mat.wrap(this.angles.az + Math.PI, az_smin, az_smax); 690 this.angles.bank = Mat.wrap(this.angles.bank + Math.PI, bank_smin, bank_smax); 691 } 692 693 // wrap and clamp the azimuth and bank angle into the slider range 694 this.angles.az = Mat.wrapAndClamp(this.angles.az, az_smin, az_smax, 2 * Math.PI); 695 this.angles.bank = Mat.wrapAndClamp(this.angles.bank, bank_smin, bank_smax, 2 * Math.PI); 696 697 // since we're using `clamp`, angles may have changed 698 this.matrix3DRot = this.getRotationFromAngles(); 699 } 700 701 // restore slider positions 702 this.setSlidersFromAngles(); 703 }, 704 705 /** 706 * @private 707 * @returns {Array} 708 */ 709 _updateCentralProjection: function () { 710 var zf = 20, // near clip plane 711 zn = 8, // far clip plane 712 713 // See https://www.mathematik.uni-marburg.de/~thormae/lectures/graphics1/graphics_6_1_eng_web.html 714 // bbox3D is always at the world origin, i.e. T_obj is the unit matrix. 715 // All vectors contain affine coordinates and have length 3 716 // The matrices are of size 4x4. 717 r, A; 718 719 // set distance from view box center to camera 720 r = this.evalVisProp('r'); 721 if (r === 'auto') { 722 r = Mat.hypot( 723 this.bbox3D[0][0] - this.bbox3D[0][1], 724 this.bbox3D[1][0] - this.bbox3D[1][1], 725 this.bbox3D[2][0] - this.bbox3D[2][1] 726 ) * 1.01; 727 } 728 729 // compute camera transformation 730 // this.boxToCam = this.matrix3DRot.map((row) => row.slice()); 731 this.boxToCam = this.matrix3DRot.map(function (row) { return row.slice(); }); 732 this.boxToCam[3][0] = -r; 733 734 // compute focal distance and clip space transformation 735 this.focalDist = 1 / Math.tan(0.5 * this.evalVisProp('fov')); 736 A = [ 737 [0, 0, 0, -1], 738 [0, this.focalDist, 0, 0], 739 [0, 0, this.focalDist, 0], 740 [2 * zf * zn / (zn - zf), 0, 0, (zf + zn) / (zn - zf)] 741 ]; 742 743 return Mat.matMatMult(A, this.boxToCam); 744 }, 745 746 // Update 3D-to-2D transformation matrix with the actual azimuth and elevation angles. 747 update: function () { 748 var r = this.r, 749 stretch = [ 750 [1, 0, 0, 0], 751 [0, -r, 0, 0], 752 [0, 0, -r, 0], 753 [0, 0, 0, 1] 754 ], 755 mat2D, objectToClip, size, 756 dx, dy; 757 // objectsList; 758 759 if ( 760 !Type.exists(this.el_slide) || 761 !Type.exists(this.az_slide) || 762 !Type.exists(this.bank_slide) || 763 !this.needsUpdate 764 ) { 765 this.needsUpdate = false; 766 return this; 767 } 768 769 mat2D = [ 770 [1, 0, 0], 771 [0, 1, 0], 772 [0, 0, 1] 773 ]; 774 775 this.projectionType = this.evalVisProp('projection').toLowerCase(); 776 777 // override angle slider bounds when trackball navigation is enabled 778 if (this.trackballEnabled !== this.evalVisProp('trackball.enabled')) { 779 this.updateAngleSliderBounds(); 780 } 781 782 if (this._hasMoveTrackball) { 783 // The trackball has been moved since the last update, so we do 784 // trackball navigation. When the trackball is enabled, a drag 785 // event is interpreted as a trackball movement unless it's 786 // caught by something else, like point dragging. When the 787 // trackball is disabled, the trackball movement flag should 788 // never be set 789 this.matrix3DRot = this.updateProjectionTrackball(); 790 this.setAnglesFromRotation(); 791 } else if (this.anglesHaveMoved()) { 792 // The trackball hasn't been moved since the last up date, but 793 // the Tait-Bryan angles have been, so we do angle navigation 794 this.getAnglesFromSliders(); 795 this.matrix3DRot = this.getRotationFromAngles(); 796 } 797 798 /** 799 * The translation that moves the center of the view box to the origin. 800 */ 801 this.shift = [ 802 [1, 0, 0, 0], 803 [-0.5 * (this.bbox3D[0][0] + this.bbox3D[0][1]), 1, 0, 0], 804 [-0.5 * (this.bbox3D[1][0] + this.bbox3D[1][1]), 0, 1, 0], 805 [-0.5 * (this.bbox3D[2][0] + this.bbox3D[2][1]), 0, 0, 1] 806 ]; 807 808 switch (this.projectionType) { 809 case 'central': // Central projection 810 811 // Add a final transformation to scale and shift the projection 812 // on the board, usually called viewport. 813 size = 2 * 0.4; 814 mat2D[1][1] = this.size[0] / size; // w / d_x 815 mat2D[2][2] = this.size[1] / size; // h / d_y 816 mat2D[1][0] = this.llftCorner[0] + mat2D[1][1] * 0.5 * size; // llft_x 817 mat2D[2][0] = this.llftCorner[1] + mat2D[2][2] * 0.5 * size; // llft_y 818 // The transformations this.matrix3D and mat2D can not be combined at this point, 819 // since the projected vectors have to be normalized in between in project3DTo2D 820 this.viewPortTransform = mat2D; 821 objectToClip = this._updateCentralProjection(); 822 // this.matrix3D is a 4x4 matrix 823 this.matrix3D = Mat.matMatMult(objectToClip, this.shift); 824 break; 825 826 case 'parallel': // Parallel projection 827 default: 828 // Add a final transformation to scale and shift the projection 829 // on the board, usually called viewport. 830 dx = this.bbox3D[0][1] - this.bbox3D[0][0]; 831 dy = this.bbox3D[1][1] - this.bbox3D[1][0]; 832 mat2D[1][1] = this.size[0] / dx; // w / d_x 833 mat2D[2][2] = this.size[1] / dy; // h / d_y 834 mat2D[1][0] = this.llftCorner[0] + mat2D[1][1] * 0.5 * dx; // llft_x 835 mat2D[2][0] = this.llftCorner[1] + mat2D[2][2] * 0.5 * dy; // llft_y 836 837 // Combine all transformations, this.matrix3D is a 3x4 matrix 838 this.matrix3D = Mat.matMatMult( 839 mat2D, 840 Mat.matMatMult(Mat.matMatMult(this.matrix3DRot, stretch), this.shift).slice(0, 3) 841 ); 842 } 843 844 // Used for zIndex in dept ordering in subsequent update methods of the 845 // 3D elements and in view3d.updateRenderer 846 this.matrix3DRotShift = Mat.matMatMult(this.matrix3DRot, this.shift); 847 848 return this; 849 }, 850 851 /** 852 * Compares 3D elements according to their z-Index. 853 * @param {JXG.GeometryElement3D} a 854 * @param {JXG.GeometryElement3D} b 855 * @returns Number 856 */ 857 compareDepth: function (a, b) { 858 // return a.zIndex - b.zIndex; 859 // if (a.type !== Const.OBJECT_TYPE_PLANE3D && b.type !== Const.OBJECT_TYPE_PLANE3D) { 860 // return a.zIndex - b.zIndex; 861 // } else if (a.type === Const.OBJECT_TYPE_PLANE3D) { 862 // let bHesse = Mat.innerProduct(a.point.coords, a.normal, 4); 863 // let po = Mat.innerProduct(b.coords, a.normal, 4); 864 // let pos = Mat.innerProduct(this.boxToCam[3], a.normal, 4); 865 // console.log(this.boxToCam[3]) 866 // return pos - po; 867 // } else if (b.type === Const.OBJECT_TYPE_PLANE3D) { 868 // let bHesse = Mat.innerProduct(b.point.coords, b.normal, 4); 869 // let po = Mat.innerProduct(a.coords, a.normal, 4); 870 // let pos = Mat.innerProduct(this.boxToCam[3], b.normal, 4); 871 // console.log('b', pos, po, bHesse) 872 // return -pos; 873 // } 874 return a.zIndex - b.zIndex; 875 }, 876 877 updateZIndices: function() { 878 var id, el; 879 for (id in this.objects) { 880 if (this.objects.hasOwnProperty(id)) { 881 el = this.objects[id]; 882 // Update zIndex of less frequent objects line3d and polygon3d 883 // The other elements (point3d, face3d) do this in their update method. 884 if (( 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 if (el.visPropCalc.visible && Type.exists(el.shader)) { 903 if (this.board._change3DView && el.evalVisProp('shader.fixed')) { 904 // In case, 3D view is rotated and the shader is fixed 905 // we can avoid the call of shader() 906 v = el.zIndex; 907 } else { 908 v = el.shader(); 909 } 910 if (v < this.zIndexMin) { 911 this.zIndexMin = v; 912 } else if (v > this.zIndexMax) { 913 this.zIndexMax = v; 914 } 915 } 916 } 917 } 918 }, 919 920 updateDepthOrdering: function () { 921 var id, el, 922 i, j, l, layers, lay; 923 924 // Collect elements for depth ordering layer-wise 925 layers = this.evalVisProp('depthorder.layers'); 926 for (i = 0; i < layers.length; i++) { 927 this.depthOrdered[layers[i]] = []; 928 } 929 930 for (id in this.objects) { 931 if (this.objects.hasOwnProperty(id)) { 932 el = this.objects[id]; 933 if ((el.type === Const.OBJECT_TYPE_FACE3D || 934 el.type === Const.OBJECT_TYPE_LINE3D || 935 // el.type === Const.OBJECT_TYPE_PLANE3D || 936 el.type === Const.OBJECT_TYPE_POINT3D || 937 el.type === Const.OBJECT_TYPE_POLYGON3D 938 ) && 939 Type.exists(el.element2D) && 940 el.element2D.visPropCalc.visible 941 // el.element2D.evalVisProp('visible') 942 ) { 943 lay = el.element2D.evalVisProp('layer'); 944 if (layers.indexOf(lay) >= 0) { 945 this.depthOrdered[lay].push(el); 946 } 947 } 948 } 949 } 950 951 if (this.board.renderer && this.board.renderer.type === 'svg') { 952 for (i = 0; i < layers.length; i++) { 953 lay = layers[i]; 954 this.depthOrdered[lay].sort(this.compareDepth.bind(this)); 955 // DEBUG 956 // if (this.depthOrdered[lay].length > 0) { 957 // for (let k = 0; k < this.depthOrdered[lay].length; k++) { 958 // let o = this.depthOrdered[lay][k] 959 // console.log(o.visProp.fillcolor, o.zIndex) 960 // } 961 // } 962 l = this.depthOrdered[lay]; 963 for (j = 0; j < l.length; j++) { 964 this.board.renderer.setLayer(l[j].element2D, lay); 965 } 966 // this.depthOrdered[lay].forEach((el) => this.board.renderer.setLayer(el.element2D, lay)); 967 // Attention: forEach prevents deleting an element 968 } 969 } 970 971 return this; 972 }, 973 974 updateRenderer: function () { 975 if (!this.needsUpdate) { 976 return this; 977 } 978 979 // console.time('update') 980 // Handle depth ordering 981 this.depthOrdered = {}; 982 983 if (this.shift !== undefined && this.evalVisProp('depthorder.enabled')) { 984 // Update the zIndices of certain element types. 985 // We do it here in updateRenderer, because the elements' positions 986 // are meanwhile updated. 987 this.updateZIndices(); 988 989 this.updateShaders(); 990 991 if (this.board.renderer && this.board.renderer.type === 'svg') { 992 // For SVG we update the DOM order here. 993 // In canvas we sort the elements in board.updateRendererCanvas 994 this.updateDepthOrdering(); 995 } 996 } 997 // console.timeEnd('update') 998 999 this.needsUpdate = false; 1000 return this; 1001 }, 1002 1003 removeObject: function (object, saveMethod) { 1004 var i, el, le, o, fst, face; 1005 1006 // this.board.removeObject(object, saveMethod); 1007 if (Type.isArray(object)) { 1008 for (i = 0; i < object.length; i++) { 1009 this.removeObject(object[i]); 1010 } 1011 return this; 1012 } 1013 1014 object = this.select(object); 1015 1016 // // If the object which is about to be removed unknown or a string, do nothing. 1017 // // it is a string if a string was given and could not be resolved to an element. 1018 if (!Type.exists(object) || Type.isString(object)) { 1019 return this; 1020 } 1021 1022 try { 1023 // Remove all children. 1024 for (el in object.childElements) { 1025 if (object.childElements.hasOwnProperty(el)) { 1026 this.removeObject(object.childElements[el]); 1027 } 1028 } 1029 if (object.type === Const.OBJECT_TYPE_POLYHEDRON3D) { 1030 // Special treatment for polyhedron3d. 1031 // With this we can avoid the time consuming addChild() calls. 1032 le = object.faces.length; 1033 if (le > 0) { 1034 fst = object.faces[0]._pos; 1035 fst = (object.faces[0].element2D._pos < fst) ? object.faces[0].element2D._pos : fst; 1036 } 1037 for (i = 0; i < le; i++) { 1038 face = object.faces[i]; 1039 delete this.objects[face.id]; 1040 1041 // this.board.removeObject(face.element2D, saveMethod); 1042 delete this.board.objects[face.element2D.id]; 1043 delete this.board.elementsByName[face.element2D.name]; 1044 face.element2D.remove(); 1045 this.board.objectsList.splice(face.element2D._pos, 1); 1046 1047 delete this.board.objects[face.id]; 1048 delete this.board.elementsByName[face.name]; 1049 face.remove(); 1050 this.board.objectsList.splice(face._pos, 1); 1051 } 1052 le = this.board.objectsList.length; 1053 // Reindex the positions 1054 for (i = fst; i < this.board.objectsList.length; i++) { 1055 o = this.board.objectsList[i]; 1056 if (o._pos > -1) { o._pos = i; } 1057 } 1058 object.faces = []; 1059 } 1060 1061 delete this.objects[object.id]; 1062 } catch (e) { 1063 JXG.debug('View3D ' + object.id + ': Could not be removed: ' + e); 1064 } 1065 1066 // this.update(); 1067 1068 this.board.removeObject(object, saveMethod); 1069 1070 return this; 1071 }, 1072 1073 /** 1074 * Map world coordinates to focal coordinates. These coordinate systems 1075 * are explained in the {@link JXG.View3D#boxToCam} matrix 1076 * documentation. 1077 * 1078 * @param {Array} pWorld A world space point, in homogeneous coordinates. 1079 * @param {Boolean} [homog=true] Whether to return homogeneous coordinates. 1080 * If false, projects down to ordinary coordinates. 1081 */ 1082 worldToFocal: function (pWorld, homog = true) { 1083 var k, 1084 pView = Mat.matVecMult(this.boxToCam, Mat.matVecMult(this.shift, pWorld)); 1085 1086 pView[3] -= pView[0] * this.focalDist; 1087 if (homog) { 1088 return pView; 1089 } else { 1090 for (k = 1; k < 4; k++) { 1091 pView[k] /= pView[0]; 1092 } 1093 return pView.slice(1, 4); 1094 } 1095 }, 1096 1097 /** 1098 * Project 3D coordinates to 2D board coordinates 1099 * The 3D coordinates are provides as three numbers x, y, z or one array of length 3. 1100 * 1101 * @param {Number|Array} x 1102 * @param {Number[]} y 1103 * @param {Number[]} z 1104 * @returns {Array} Array of length 3 containing the projection on to the board 1105 * in homogeneous user coordinates. 1106 */ 1107 project3DTo2D: function (x, y, z) { 1108 var vec, w; 1109 if (arguments.length === 3) { 1110 vec = [1, x, y, z]; 1111 } else { 1112 // Argument is an array 1113 if (x.length === 3) { 1114 // vec = [1].concat(x); 1115 vec = x.slice(); 1116 vec.unshift(1); 1117 } else { 1118 vec = x; 1119 } 1120 } 1121 1122 w = Mat.matVecMult(this.matrix3D, vec); 1123 1124 switch (this.projectionType) { 1125 case 'central': 1126 w[1] /= w[0]; 1127 w[2] /= w[0]; 1128 w[3] /= w[0]; 1129 w[0] /= w[0]; 1130 return Mat.matVecMult(this.viewPortTransform, w.slice(0, 3)); 1131 1132 case 'parallel': 1133 default: 1134 return w; 1135 } 1136 }, 1137 1138 /** 1139 * We know that v2d * w0 = mat * (1, x, y, d)^T where v2d = (1, b, c, h)^T with unknowns w0, h, x, y. 1140 * Setting R = mat^(-1) gives 1141 * 1/ w0 * (1, x, y, d)^T = R * v2d. 1142 * The first and the last row of this equation allows to determine 1/w0 and h. 1143 * 1144 * @param {Array} mat 1145 * @param {Array} v2d 1146 * @param {Number} d 1147 * @returns Array 1148 * @private 1149 */ 1150 _getW0: function (mat, v2d, d) { 1151 var R = Mat.inverse(mat), 1152 R1 = R[0][0] + v2d[1] * R[0][1] + v2d[2] * R[0][2], 1153 R2 = R[3][0] + v2d[1] * R[3][1] + v2d[2] * R[3][2], 1154 w, h, det; 1155 1156 det = d * R[0][3] - R[3][3]; 1157 w = (R2 * R[0][3] - R1 * R[3][3]) / det; 1158 h = (R2 - R1 * d) / det; 1159 return [1 / w, h]; 1160 }, 1161 1162 /** 1163 * Project a 2D coordinate to the plane defined by point "foot" 1164 * and the normal vector `normal`. 1165 * 1166 * @param {JXG.Point} point2d 1167 * @param {Array} normal Normal of plane 1168 * @param {Array} foot Foot point of plane 1169 * @returns {Array} of length 4 containing the projected 1170 * point in homogeneous coordinates. 1171 */ 1172 project2DTo3DPlane: function (point2d, normal, foot) { 1173 var mat, rhs, d, le, sol, 1174 f = foot.slice(1) || [0, 0, 0], 1175 n = normal.slice(1), 1176 v2d, w0, res; 1177 1178 le = Mat.norm(n, 3); 1179 d = Mat.innerProduct(f, n, 3) / le; 1180 1181 if (this.projectionType === 'parallel') { 1182 mat = this.matrix3D.slice(0, 3); // Copy each row by reference 1183 mat.push([0, n[0], n[1], n[2]]); 1184 1185 // 2D coordinates of point 1186 rhs = point2d.coords.usrCoords.slice(); 1187 rhs.push(d); 1188 try { 1189 // Prevent singularity in case elevation angle is zero 1190 if (mat[2][3] === 1.0) { 1191 mat[2][1] = mat[2][2] = Mat.eps * 0.001; 1192 } 1193 sol = Mat.Numerics.Gauss(mat, rhs); 1194 } catch (e) { 1195 sol = [0, NaN, NaN, NaN]; 1196 } 1197 } else { 1198 mat = this.matrix3D; 1199 1200 // 2D coordinates of point: 1201 rhs = point2d.coords.usrCoords.slice(); 1202 1203 v2d = Mat.Numerics.Gauss(this.viewPortTransform, rhs); 1204 res = this._getW0(mat, v2d, d); 1205 w0 = res[0]; 1206 rhs = [ 1207 v2d[0] * w0, 1208 v2d[1] * w0, 1209 v2d[2] * w0, 1210 res[1] * w0 1211 ]; 1212 try { 1213 // Prevent singularity in case elevation angle is zero 1214 if (mat[2][3] === 1.0) { 1215 mat[2][1] = mat[2][2] = Mat.eps * 0.001; 1216 } 1217 1218 sol = Mat.Numerics.Gauss(mat, rhs); 1219 sol[1] /= sol[0]; 1220 sol[2] /= sol[0]; 1221 sol[3] /= sol[0]; 1222 // sol[3] = d; 1223 sol[0] /= sol[0]; 1224 } catch (err) { 1225 sol = [0, NaN, NaN, NaN]; 1226 } 1227 } 1228 1229 return sol; 1230 }, 1231 1232 /** 1233 * Project a point on the screen to the nearest point, in screen 1234 * distance, on a line segment in 3d space. The inputs must be in 1235 * ordinary coordinates, but the output is in homogeneous coordinates. 1236 * 1237 * @param {Array} pScr The screen coordinates of the point to project. 1238 * @param {Array} end0 The world space coordinates of one end of the 1239 * line segment (array of length 3). 1240 * @param {Array} end1 The world space coordinates of the other end of 1241 * the line segment (array of length 3). 1242 * 1243 * @returns {Array} Homogeneous coordinates of the projection 1244 */ 1245 projectScreenToSegment: function (pScr, end0, end1) { 1246 var end0_2d = this.project3DTo2D(end0).slice(1, 3), 1247 end1_2d = this.project3DTo2D(end1).slice(1, 3), 1248 dir_2d = [ 1249 end1_2d[0] - end0_2d[0], 1250 end1_2d[1] - end0_2d[1] 1251 ], 1252 dir_2d_norm_sq = Mat.innerProduct(dir_2d, dir_2d), 1253 diff = [ 1254 pScr[0] - end0_2d[0], 1255 pScr[1] - end0_2d[1] 1256 ], 1257 s = Mat.innerProduct(diff, dir_2d) / dir_2d_norm_sq, // screen-space affine parameter 1258 mid, mid_2d, mid_diff, m, 1259 1260 t, // view-space affine parameter 1261 t_clamped, // affine parameter clamped to range 1262 t_clamped_co; 1263 1264 if (this.projectionType === 'central') { 1265 mid = [ 1266 1, 1267 0.5 * (end0[0] + end1[0]), 1268 0.5 * (end0[1] + end1[1]), 1269 0.5 * (end0[2] + end1[2]) 1270 ]; 1271 mid_2d = this.project3DTo2D(mid).slice(1, 3); 1272 mid_diff = [ 1273 mid_2d[0] - end0_2d[0], 1274 mid_2d[1] - end0_2d[1] 1275 ]; 1276 m = Mat.innerProduct(mid_diff, dir_2d) / dir_2d_norm_sq; 1277 1278 // the view-space affine parameter s is related to the 1279 // screen-space affine parameter t by a Möbius transformation, 1280 // which is determined by the following relations: 1281 // 1282 // s | t 1283 // ----- 1284 // 0 | 0 1285 // m | 1/2 1286 // 1 | 1 1287 // 1288 t = (1 - m) * s / ((1 - 2 * m) * s + m); 1289 } else { 1290 t = s; 1291 } 1292 1293 t_clamped = Math.min(Math.max(t, 0), 1); 1294 t_clamped_co = 1 - t_clamped; 1295 return [ 1296 1, 1297 t_clamped_co * end0[0] + t_clamped * end1[0], 1298 t_clamped_co * end0[1] + t_clamped * end1[1], 1299 t_clamped_co * end0[2] + t_clamped * end1[2] 1300 ]; 1301 }, 1302 1303 /** 1304 * Project a 2D coordinate to a new 3D position by keeping 1305 * the 3D x, y coordinates and changing only the z coordinate. 1306 * All horizontal moves of the 2D point are ignored. 1307 * 1308 * @param {JXG.Point} point2d 1309 * @param {Array} base_c3d 1310 * @returns {Array} of length 4 containing the projected 1311 * point in homogeneous coordinates. 1312 */ 1313 project2DTo3DVertical: function (point2d, base_c3d) { 1314 var pScr = point2d.coords.usrCoords.slice(1, 3), 1315 end0 = [base_c3d[1], base_c3d[2], this.bbox3D[2][0]], 1316 end1 = [base_c3d[1], base_c3d[2], this.bbox3D[2][1]]; 1317 1318 return this.projectScreenToSegment(pScr, end0, end1); 1319 }, 1320 1321 /** 1322 * Limit 3D coordinates to the bounding cube. 1323 * 1324 * @param {Array} c3d 3D coordinates [x,y,z] 1325 * @returns Array [Array, Boolean] containing [coords, corrected]. coords contains the updated 3D coordinates, 1326 * correct is true if the coords have been changed. 1327 */ 1328 project3DToCube: function (c3d) { 1329 var cube = this.bbox3D, 1330 isOut = false; 1331 1332 if (c3d[1] < cube[0][0]) { 1333 c3d[1] = cube[0][0]; 1334 isOut = true; 1335 } 1336 if (c3d[1] > cube[0][1]) { 1337 c3d[1] = cube[0][1]; 1338 isOut = true; 1339 } 1340 if (c3d[2] < cube[1][0]) { 1341 c3d[2] = cube[1][0]; 1342 isOut = true; 1343 } 1344 if (c3d[2] > cube[1][1]) { 1345 c3d[2] = cube[1][1]; 1346 isOut = true; 1347 } 1348 if (c3d[3] <= cube[2][0]) { 1349 c3d[3] = cube[2][0]; 1350 isOut = true; 1351 } 1352 if (c3d[3] >= cube[2][1]) { 1353 c3d[3] = cube[2][1]; 1354 isOut = true; 1355 } 1356 1357 return [c3d, isOut]; 1358 }, 1359 1360 /** 1361 * Intersect a ray with the bounding cube of the 3D view. 1362 * @param {Array} p 3D coordinates [w,x,y,z] 1363 * @param {Array} dir 3D direction vector of the line (array of length 3 or 4) 1364 * @param {Number} r direction of the ray (positive if r > 0, negative if r < 0). 1365 * @returns Affine ratio of the intersection of the line with the cube. 1366 */ 1367 intersectionLineCube: function (p, dir, r) { 1368 var r_n, i, r0, r1, d; 1369 1370 d = (dir.length === 3) ? dir : dir.slice(1); 1371 1372 r_n = r; 1373 for (i = 0; i < 3; i++) { 1374 if (d[i] !== 0) { 1375 r0 = (this.bbox3D[i][0] - p[i + 1]) / d[i]; 1376 r1 = (this.bbox3D[i][1] - p[i + 1]) / d[i]; 1377 if (r < 0) { 1378 r_n = Math.max(r_n, Math.min(r0, r1)); 1379 } else { 1380 r_n = Math.min(r_n, Math.max(r0, r1)); 1381 } 1382 } 1383 } 1384 return r_n; 1385 }, 1386 1387 /** 1388 * Test if coordinates are inside of the bounding cube. 1389 * @param {array} p 3D coordinates [[w],x,y,z] of a point. 1390 * @returns Boolean 1391 */ 1392 isInCube: function (p, polyhedron) { 1393 var q; 1394 if (p.length === 4) { 1395 if (p[0] === 0) { 1396 return false; 1397 } 1398 q = p.slice(1); 1399 } 1400 return ( 1401 q[0] > this.bbox3D[0][0] - Mat.eps && 1402 q[0] < this.bbox3D[0][1] + Mat.eps && 1403 q[1] > this.bbox3D[1][0] - Mat.eps && 1404 q[1] < this.bbox3D[1][1] + Mat.eps && 1405 q[2] > this.bbox3D[2][0] - Mat.eps && 1406 q[2] < this.bbox3D[2][1] + Mat.eps 1407 ); 1408 }, 1409 1410 /** 1411 * 1412 * @param {JXG.Plane3D} plane1 1413 * @param {JXG.Plane3D} plane2 1414 * @param {Number} d Right hand side of Hesse normal for plane2 (it can be adjusted) 1415 * @returns {Array} of length 2 containing the coordinates of the defining points of 1416 * of the intersection segment, or false if there is no intersection 1417 */ 1418 intersectionPlanePlane: function (plane1, plane2, d) { 1419 var ret = [false, false], 1420 p, q, r, w, 1421 dir; 1422 1423 d = d || plane2.d; 1424 1425 // Get one point of the intersection of the two planes 1426 w = Mat.crossProduct(plane1.normal.slice(1), plane2.normal.slice(1)); 1427 w.unshift(0); 1428 1429 p = Mat.Geometry.meet3Planes( 1430 plane1.normal, 1431 plane1.d, 1432 plane2.normal, 1433 d, 1434 w, 1435 0 1436 ); 1437 1438 // Get the direction of the intersecting line of the two planes 1439 dir = Mat.Geometry.meetPlanePlane( 1440 plane1.vec1, 1441 plane1.vec2, 1442 plane2.vec1, 1443 plane2.vec2 1444 ); 1445 1446 // Get the bounding points of the intersecting segment 1447 r = this.intersectionLineCube(p, dir, Infinity); 1448 q = Mat.axpy(r, dir, p); 1449 if (this.isInCube(q)) { 1450 ret[0] = q; 1451 } 1452 r = this.intersectionLineCube(p, dir, -Infinity); 1453 q = Mat.axpy(r, dir, p); 1454 if (this.isInCube(q)) { 1455 ret[1] = q; 1456 } 1457 1458 return ret; 1459 }, 1460 1461 intersectionPlaneFace: function (plane, face) { 1462 var ret = [], 1463 j, t, 1464 p, crds, 1465 p1, p2, c, 1466 f, le, x1, y1, x2, y2, 1467 dir, vec, w, 1468 mat = [], b = [], sol; 1469 1470 w = Mat.crossProduct(plane.normal.slice(1), face.normal.slice(1)); 1471 w.unshift(0); 1472 1473 // Get one point of the intersection of the two planes 1474 p = Geometry.meet3Planes( 1475 plane.normal, 1476 plane.d, 1477 face.normal, 1478 face.d, 1479 w, 1480 0 1481 ); 1482 1483 // Get the direction the intersecting line of the two planes 1484 dir = Geometry.meetPlanePlane( 1485 plane.vec1, 1486 plane.vec2, 1487 face.vec1, 1488 face.vec2 1489 ); 1490 1491 f = face.polyhedron.faces[face.faceNumber]; 1492 crds = face.polyhedron.coords; 1493 le = f.length; 1494 for (j = 1; j <= le; j++) { 1495 p1 = crds[f[j - 1]]; 1496 p2 = crds[f[j % le]]; 1497 vec = [0, p2[1] - p1[1], p2[2] - p1[2], p2[3] - p1[3]]; 1498 1499 x1 = Math.random(); 1500 y1 = Math.random(); 1501 x2 = Math.random(); 1502 y2 = Math.random(); 1503 mat = [ 1504 [x1 * dir[1] + y1 * dir[3], x1 * (-vec[1]) + y1 * (-vec[3])], 1505 [x2 * dir[2] + y2 * dir[3], x2 * (-vec[2]) + y2 * (-vec[3])] 1506 ]; 1507 b = [ 1508 x1 * (p1[1] - p[1]) + y1 * (p1[3] - p[3]), 1509 x2 * (p1[2] - p[2]) + y2 * (p1[3] - p[3]) 1510 ]; 1511 1512 sol = Numerics.Gauss(mat, b); 1513 t = sol[1]; 1514 if (t > -Mat.eps && t < 1 + Mat.eps) { 1515 c = [1, p1[1] + t * vec[1], p1[2] + t * vec[2], p1[3] + t * vec[3]]; 1516 ret.push(c); 1517 } 1518 } 1519 1520 return ret; 1521 }, 1522 1523 // TODO: 1524 // - handle non-closed polyhedra 1525 // - handle intersections in vertex, edge, plane 1526 intersectionPlanePolyhedron: function(plane, phdr) { 1527 var i, j, seg, 1528 p, first, pos, pos_akt, 1529 eps = 1e-12, 1530 points = [], 1531 x = [], 1532 y = [], 1533 z = []; 1534 1535 for (i = 0; i < phdr.numberFaces; i++) { 1536 if (phdr.def.faces[i].length < 3) { 1537 // We skip intersection with points or lines 1538 continue; 1539 } 1540 1541 // seg will be an array consisting of two points 1542 // that span the intersecting segment of the plane 1543 // and the face. 1544 seg = this.intersectionPlaneFace(plane, phdr.faces[i]); 1545 1546 // Plane intersects the face in less than 2 points 1547 if (seg.length < 2) { 1548 continue; 1549 } 1550 1551 if (seg[0].length === 4 && seg[1].length === 4) { 1552 // This test is necessary to filter out intersection lines which are 1553 // identical to intersections of axis planes (they would occur twice), 1554 // i.e. edges of bbox3d. 1555 for (j = 0; j < points.length; j++) { 1556 if ( 1557 (Geometry.distance(seg[0], points[j][0], 4) < eps && 1558 Geometry.distance(seg[1], points[j][1], 4) < eps) || 1559 (Geometry.distance(seg[0], points[j][1], 4) < eps && 1560 Geometry.distance(seg[1], points[j][0], 4) < eps) 1561 ) { 1562 break; 1563 } 1564 } 1565 if (j === points.length) { 1566 points.push(seg.slice()); 1567 } 1568 } 1569 } 1570 1571 // Handle the case that the intersection is the empty set. 1572 if (points.length === 0) { 1573 return { X: x, Y: y, Z: z }; 1574 } 1575 1576 // Concatenate the intersection points to a polygon. 1577 // If all went well, each intersection should appear 1578 // twice in the list. 1579 // __Attention:__ each face has to be planar!!! 1580 // Otherwise the algorithm will fail. 1581 first = 0; 1582 pos = first; 1583 i = 0; 1584 do { 1585 p = points[pos][i]; 1586 if (p.length === 4) { 1587 x.push(p[1]); 1588 y.push(p[2]); 1589 z.push(p[3]); 1590 } 1591 i = (i + 1) % 2; 1592 p = points[pos][i]; 1593 1594 pos_akt = pos; 1595 for (j = 0; j < points.length; j++) { 1596 if (j !== pos && Geometry.distance(p, points[j][0]) < eps) { 1597 pos = j; 1598 i = 0; 1599 break; 1600 } 1601 if (j !== pos && Geometry.distance(p, points[j][1]) < eps) { 1602 pos = j; 1603 i = 1; 1604 break; 1605 } 1606 } 1607 if (pos === pos_akt) { 1608 console.log('Error face3d intersection update: did not find next', pos, i); 1609 break; 1610 } 1611 } while (pos !== first); 1612 x.push(x[0]); 1613 y.push(y[0]); 1614 z.push(z[0]); 1615 1616 return { X: x, Y: y, Z: z }; 1617 }, 1618 1619 /** 1620 * Generate mesh for a surface / plane. 1621 * Returns array [dataX, dataY] for a JSXGraph curve's updateDataArray function. 1622 * @param {Array|Function} func 1623 * @param {Array} interval_u 1624 * @param {Array} interval_v 1625 * @returns Array 1626 * @private 1627 * 1628 * @example 1629 * var el = view.create('curve', [[], []]); 1630 * el.updateDataArray = function () { 1631 * var steps_u = this.evalVisProp('stepsu'), 1632 * steps_v = this.evalVisProp('stepsv'), 1633 * r_u = Type.evaluate(this.range_u), 1634 * r_v = Type.evaluate(this.range_v), 1635 * func, ret; 1636 * 1637 * if (this.F !== null) { 1638 * func = this.F; 1639 * } else { 1640 * func = [this.X, this.Y, this.Z]; 1641 * } 1642 * ret = this.view.getMesh(func, 1643 * r_u.concat([steps_u]), 1644 * r_v.concat([steps_v])); 1645 * 1646 * this.dataX = ret[0]; 1647 * this.dataY = ret[1]; 1648 * }; 1649 * 1650 */ 1651 getMesh: function (func, interval_u, interval_v) { 1652 var i_u, i_v, u, v, 1653 c2d, delta_u, delta_v, 1654 p = [0, 0, 0], 1655 steps_u = Type.evaluate(interval_u[2]), 1656 steps_v = Type.evaluate(interval_v[2]), 1657 dataX = [], 1658 dataY = []; 1659 1660 delta_u = (Type.evaluate(interval_u[1]) - Type.evaluate(interval_u[0])) / steps_u; 1661 delta_v = (Type.evaluate(interval_v[1]) - Type.evaluate(interval_v[0])) / steps_v; 1662 1663 for (i_u = 0; i_u <= steps_u; i_u++) { 1664 u = interval_u[0] + delta_u * i_u; 1665 for (i_v = 0; i_v <= steps_v; i_v++) { 1666 v = interval_v[0] + delta_v * i_v; 1667 if (Type.isFunction(func)) { 1668 p = func(u, v); 1669 } else { 1670 p = [func[0](u, v), func[1](u, v), func[2](u, v)]; 1671 } 1672 c2d = this.project3DTo2D(p); 1673 dataX.push(c2d[1]); 1674 dataY.push(c2d[2]); 1675 } 1676 dataX.push(NaN); 1677 dataY.push(NaN); 1678 } 1679 1680 for (i_v = 0; i_v <= steps_v; i_v++) { 1681 v = interval_v[0] + delta_v * i_v; 1682 for (i_u = 0; i_u <= steps_u; i_u++) { 1683 u = interval_u[0] + delta_u * i_u; 1684 if (Type.isFunction(func)) { 1685 p = func(u, v); 1686 } else { 1687 p = [func[0](u, v), func[1](u, v), func[2](u, v)]; 1688 } 1689 c2d = this.project3DTo2D(p); 1690 dataX.push(c2d[1]); 1691 dataY.push(c2d[2]); 1692 } 1693 dataX.push(NaN); 1694 dataY.push(NaN); 1695 } 1696 1697 return [dataX, dataY]; 1698 }, 1699 1700 /** 1701 * 1702 */ 1703 animateAzimuth: function () { 1704 var s = this.az_slide._smin, 1705 e = this.az_slide._smax, 1706 sdiff = e - s, 1707 newVal = this.az_slide.Value() + 0.1; 1708 1709 this.az_slide.position = (newVal - s) / sdiff; 1710 if (this.az_slide.position > 1) { 1711 this.az_slide.position = 0.0; 1712 } 1713 this.board._change3DView = true; 1714 this.board.update(); 1715 this.board._change3DView = false; 1716 1717 this.timeoutAzimuth = setTimeout(function () { 1718 this.animateAzimuth(); 1719 }.bind(this), 200); 1720 }, 1721 1722 /** 1723 * 1724 */ 1725 stopAzimuth: function () { 1726 clearTimeout(this.timeoutAzimuth); 1727 this.timeoutAzimuth = null; 1728 }, 1729 1730 /** 1731 * Check if vertical dragging is enabled and which action is needed. 1732 * Default is shiftKey. 1733 * 1734 * @returns Boolean 1735 * @private 1736 */ 1737 isVerticalDrag: function () { 1738 var b = this.board, 1739 key; 1740 if (!this.evalVisProp('verticaldrag.enabled')) { 1741 return false; 1742 } 1743 key = '_' + this.evalVisProp('verticaldrag.key') + 'Key'; 1744 return b[key]; 1745 }, 1746 1747 /** 1748 * Sets camera view to the given values. 1749 * 1750 * @param {Number} az Value of azimuth. 1751 * @param {Number} el Value of elevation. 1752 * @param {Number} [r] Value of radius. 1753 * 1754 * @returns {Object} Reference to the view. 1755 */ 1756 setView: function (az, el, r) { 1757 r = r || this.r; 1758 1759 this.az_slide.setValue(az); 1760 this.el_slide.setValue(el); 1761 this.r = r; 1762 this.board.update(); 1763 1764 return this; 1765 }, 1766 1767 /** 1768 * Changes view to the next view stored in the attribute `values`. 1769 * 1770 * @see View3D#values 1771 * 1772 * @returns {Object} Reference to the view. 1773 */ 1774 nextView: function () { 1775 var views = this.evalVisProp('values'), 1776 n = this.visProp._currentview; 1777 1778 n = (n + 1) % views.length; 1779 this.setCurrentView(n); 1780 1781 return this; 1782 }, 1783 1784 /** 1785 * Changes view to the previous view stored in the attribute `values`. 1786 * 1787 * @see View3D#values 1788 * 1789 * @returns {Object} Reference to the view. 1790 */ 1791 previousView: function () { 1792 var views = this.evalVisProp('values'), 1793 n = this.visProp._currentview; 1794 1795 n = (n + views.length - 1) % views.length; 1796 this.setCurrentView(n); 1797 1798 return this; 1799 }, 1800 1801 /** 1802 * Changes view to the determined view stored in the attribute `values`. 1803 * 1804 * @see View3D#values 1805 * 1806 * @param {Number} n Index of view in attribute `values`. 1807 * @returns {Object} Reference to the view. 1808 */ 1809 setCurrentView: function (n) { 1810 var views = this.evalVisProp('values'); 1811 1812 if (n < 0 || n >= views.length) { 1813 n = ((n % views.length) + views.length) % views.length; 1814 } 1815 1816 this.setView(views[n][0], views[n][1], views[n][2]); 1817 this.visProp._currentview = n; 1818 1819 return this; 1820 }, 1821 1822 /** 1823 * Controls 2-degree navigation in az direction using pointer. 1824 * 1825 * @private 1826 * 1827 * @param {event} evt the pointer event 1828 * @returns view 1829 */ 1830 _az_elEventHandler: function (evt) { 1831 var smax = this.az_slide._smax, 1832 smin = this.az_slide._smin, 1833 speed = (smax - smin) / this.board.canvasWidth * (this.evalVisProp('az.pointer.speed')), 1834 deltaX, // = evt.movementX, 1835 deltaY, // = evt.movementY 1836 az = this.az_slide.Value(), 1837 el = this.el_slide.Value(); 1838 1839 deltaX = evt.screenX - this._lastPos.x; 1840 this._lastPos.x = evt.screenX; 1841 deltaY = evt.screenY - this._lastPos.y; 1842 this._lastPos.y = evt.screenY; 1843 1844 // Doesn't allow navigation if another moving event is triggered 1845 if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) { 1846 return this; 1847 } 1848 1849 if (this.evalVisProp('az.pointer.enabled') && (deltaX !== 0) && evt.key == null) { 1850 // delta *= (Math.abs(delta) > 100) ? 0.03 : 1; 1851 az += deltaX * speed; 1852 } 1853 if (this.evalVisProp('el.pointer.enabled') && (deltaY !== 0) && evt.key == null) { 1854 el += deltaY * speed; 1855 } 1856 1857 // Project the calculated az value to a usable value in the interval [smin,smax] 1858 // Use modulo if continuous is true 1859 if (this.evalVisProp('az.continuous')) { 1860 az = Mat.wrap(az, smin, smax); 1861 } else { 1862 if (az > 0) { 1863 az = Math.min(smax, az); 1864 } else if (az < 0) { 1865 az = Math.max(smin, az); 1866 } 1867 } 1868 // Project the calculated el value to a usable value in the interval [smin,smax] 1869 // Use modulo if continuous is true and the trackball is disabled 1870 smax = this.el_slide._smax; 1871 smin = this.el_slide._smin; 1872 if (this.evalVisProp('el.continuous') && !this.trackballEnabled) { 1873 el = Mat.wrap(el, smin, smax); 1874 } else { 1875 if (el > 0) { 1876 el = Math.min(smax, el); 1877 } else if (el < 0) { 1878 el = Math.max(smin, el); 1879 } 1880 } 1881 1882 this.setView(az, el); 1883 return this; 1884 }, 1885 1886 /** 1887 * Controls the navigation in az direction using either the keyboard or a pointer. 1888 * 1889 * @private 1890 * 1891 * @param {event} evt either the keydown or the pointer event 1892 * @returns view 1893 */ 1894 _azEventHandler: function (evt) { 1895 var smax = this.az_slide._smax, 1896 smin = this.az_slide._smin, 1897 speed = (smax - smin) / this.board.canvasWidth * (this.evalVisProp('az.pointer.speed')), 1898 delta, // = evt.movementX, 1899 az = this.az_slide.Value(), 1900 el = this.el_slide.Value(); 1901 1902 delta = evt.screenX - this._lastPos.x; 1903 this._lastPos.x = evt.screenX; 1904 1905 // Doesn't allow navigation if another moving event is triggered 1906 if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) { 1907 return this; 1908 } 1909 1910 // Calculate new az value if keyboard events are triggered 1911 // Plus if right-button, minus if left-button 1912 if (this.evalVisProp('az.keyboard.enabled')) { 1913 if (evt.key === 'ArrowRight') { 1914 az = az + this.evalVisProp('az.keyboard.step') * Math.PI / 180; 1915 } else if (evt.key === 'ArrowLeft') { 1916 az = az - this.evalVisProp('az.keyboard.step') * Math.PI / 180; 1917 } 1918 } 1919 1920 if (this.evalVisProp('az.pointer.enabled') && (delta !== 0) && evt.key == null) { 1921 // delta *= (Math.abs(delta) > 100) ? 0.03 : 1; 1922 az += delta * speed; 1923 } 1924 1925 // Project the calculated az value to a usable value in the interval [smin,smax] 1926 // Use modulo if continuous is true 1927 if (this.evalVisProp('az.continuous')) { 1928 az = Mat.wrap(az, smin, smax); 1929 } else { 1930 if (az > 0) { 1931 az = Math.min(smax, az); 1932 } else if (az < 0) { 1933 az = Math.max(smin, az); 1934 } 1935 } 1936 1937 this.setView(az, el); 1938 return this; 1939 }, 1940 1941 /** 1942 * Controls the navigation in el direction using either the keyboard or a pointer. 1943 * 1944 * @private 1945 * 1946 * @param {event} evt either the keydown or the pointer event 1947 * @returns view 1948 */ 1949 _elEventHandler: function (evt) { 1950 var smax = this.el_slide._smax, 1951 smin = this.el_slide._smin, 1952 speed = (smax - smin) / this.board.canvasHeight * this.evalVisProp('el.pointer.speed'), 1953 delta, // = evt.movementY, 1954 az = this.az_slide.Value(), 1955 el = this.el_slide.Value(); 1956 1957 delta = evt.screenY - this._lastPos.y; 1958 this._lastPos.y = evt.screenY; 1959 1960 // Doesn't allow navigation if another moving event is triggered 1961 if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) { 1962 return this; 1963 } 1964 1965 // Calculate new az value if keyboard events are triggered 1966 // Plus if down-button, minus if up-button 1967 if (this.evalVisProp('el.keyboard.enabled')) { 1968 if (evt.key === 'ArrowUp') { 1969 el = el - this.evalVisProp('el.keyboard.step') * Math.PI / 180; 1970 } else if (evt.key === 'ArrowDown') { 1971 el = el + this.evalVisProp('el.keyboard.step') * Math.PI / 180; 1972 } 1973 } 1974 1975 if (this.evalVisProp('el.pointer.enabled') && (delta !== 0) && evt.key == null) { 1976 // delta *= (Math.abs(delta) > 100) ? 0.05 : 1; 1977 el += delta * speed; 1978 } 1979 1980 // Project the calculated el value to a usable value in the interval [smin,smax] 1981 // Use modulo if continuous is true and the trackball is disabled 1982 if (this.evalVisProp('el.continuous') && !this.trackballEnabled) { 1983 el = Mat.wrap(el, smin, smax); 1984 } else { 1985 if (el > 0) { 1986 el = Math.min(smax, el); 1987 } else if (el < 0) { 1988 el = Math.max(smin, el); 1989 } 1990 } 1991 1992 this.setView(az, el); 1993 1994 return this; 1995 }, 1996 1997 /** 1998 * Controls the navigation in bank direction using either the keyboard or a pointer. 1999 * 2000 * @private 2001 * 2002 * @param {event} evt either the keydown or the pointer event 2003 * @returns view 2004 */ 2005 _bankEventHandler: function (evt) { 2006 var smax = this.bank_slide._smax, 2007 smin = this.bank_slide._smin, 2008 step, speed, 2009 delta = evt.deltaY, // Wheel event 2010 bank = this.bank_slide.Value(); 2011 2012 // Doesn't allow navigation if another moving event is triggered 2013 if (this.board.mode === this.board.BOARD_MODE_DRAG || !this.board._change3DView) { 2014 return this; 2015 } 2016 2017 // Calculate new bank value if keyboard events are triggered 2018 // Plus if down-button, minus if up-button 2019 if (this.evalVisProp('bank.keyboard.enabled')) { 2020 step = this.evalVisProp('bank.keyboard.step') * Math.PI / 180; 2021 if (evt.key === '.' || evt.key === '<') { 2022 bank -= step; 2023 } else if (evt.key === ',' || evt.key === '>') { 2024 bank += step; 2025 } 2026 } 2027 2028 if (this.evalVisProp('bank.pointer.enabled') && (delta !== 0) && evt.key == null) { 2029 speed = (smax - smin) / this.board.canvasHeight * this.evalVisProp('bank.pointer.speed'); 2030 bank += delta * speed; 2031 2032 // prevent the pointer wheel from scrolling the page 2033 evt.preventDefault(); 2034 } 2035 2036 // Project the calculated bank value to a usable value in the interval [smin,smax] 2037 if (this.evalVisProp('bank.continuous')) { 2038 // in continuous mode, wrap value around slider range 2039 bank = Mat.wrap(bank, smin, smax); 2040 } else { 2041 // in non-continuous mode, clamp value to slider range 2042 bank = Mat.clamp(bank, smin, smax); 2043 } 2044 2045 this.bank_slide.setValue(bank); 2046 this.board.update(); 2047 return this; 2048 }, 2049 2050 /** 2051 * Controls the navigation using either virtual trackball. 2052 * 2053 * @private 2054 * 2055 * @param {event} evt either the keydown or the pointer event 2056 * @returns view 2057 */ 2058 _trackballHandler: function (evt) { 2059 var pos = this.board.getMousePosition(evt), 2060 x, y, dx, dy, center; 2061 2062 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); 2063 x = pos[0] - center.scrCoords[1]; 2064 y = pos[1] - center.scrCoords[2]; 2065 2066 dx = evt.screenX - this._lastPos.x; 2067 dy = evt.screenY - this._lastPos.y; 2068 this._lastPos.x = evt.screenX; 2069 this._lastPos.y = evt.screenY; 2070 2071 this._trackball = { 2072 dx: dx, 2073 dy: -dy, 2074 x: x, 2075 y: -y 2076 }; 2077 this.board.update(); 2078 return this; 2079 }, 2080 2081 /** 2082 * Event handler for pointer down event. Triggers handling of all 3D navigation. 2083 * 2084 * @private 2085 * @param {event} evt 2086 * @returns view 2087 */ 2088 pointerDownHandler: function (evt) { 2089 var neededButton, neededKey, target; 2090 2091 this._hasMoveAzEl = false; 2092 this._hasMoveAz = false; 2093 this._hasMoveEl = false; 2094 this._hasMoveBank = false; 2095 this._hasMoveTrackball = false; 2096 2097 if (this.board.mode !== this.board.BOARD_MODE_NONE) { 2098 return; 2099 } 2100 2101 this.board._change3DView = true; 2102 2103 this._lastPos.x = evt.screenX; 2104 this._lastPos.y = evt.screenY; 2105 2106 if (this.evalVisProp('trackball.enabled')) { 2107 neededButton = this.evalVisProp('trackball.button'); 2108 neededKey = this.evalVisProp('trackball.key'); 2109 2110 // Move events for virtual trackball 2111 if ( 2112 (neededButton === -1 || neededButton === evt.button) && 2113 (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey)) 2114 ) { 2115 // If outside is true then the event listener is bound to the document, otherwise to the div 2116 target = (this.evalVisProp('trackball.outside')) ? document : this.board.containerObj; 2117 Env.addEvent(target, 'pointermove', this._trackballHandler, this); 2118 this._hasMoveTrackball = true; 2119 } 2120 } else { 2121 if (this.evalVisProp('az.pointer.enabled') && this.evalVisProp('el.pointer.enabled')) { 2122 neededButton = this.evalVisProp('az.pointer.button'); 2123 neededKey = this.evalVisProp('az.pointer.key'); 2124 if (neededButton === this.evalVisProp('el.pointer.button') && 2125 neededKey === this.evalVisProp('el.pointer.key')) { 2126 2127 // Move events for azimuth and elevation 2128 if ( 2129 (neededButton === -1 || neededButton === evt.button) && 2130 (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || 2131 (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey)) 2132 ) { 2133 // If outside is true then the event listener is bound to the document, otherwise to the div 2134 target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj; 2135 2136 if (target === ((this.evalVisProp('el.pointer.outside')) ? document : this.board.containerObj)) { 2137 Env.addEvent(target, 'pointermove', this._az_elEventHandler, this); 2138 this._hasMoveAzEl = true; 2139 } 2140 } 2141 } 2142 } 2143 if (!this._hasMoveAzEl) { 2144 if (this.evalVisProp('az.pointer.enabled')) { 2145 neededButton = this.evalVisProp('az.pointer.button'); 2146 neededKey = this.evalVisProp('az.pointer.key'); 2147 2148 // Move events for azimuth 2149 if ( 2150 (neededButton === -1 || neededButton === evt.button) && 2151 (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey)) 2152 ) { 2153 // If outside is true then the event listener is bound to the document, otherwise to the div 2154 target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj; 2155 Env.addEvent(target, 'pointermove', this._azEventHandler, this); 2156 this._hasMoveAz = true; 2157 } 2158 } 2159 2160 if (this.evalVisProp('el.pointer.enabled')) { 2161 neededButton = this.evalVisProp('el.pointer.button'); 2162 neededKey = this.evalVisProp('el.pointer.key'); 2163 2164 // Events for elevation 2165 if ( 2166 (neededButton === -1 || neededButton === evt.button) && 2167 (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey)) 2168 ) { 2169 // If outside is true then the event listener is bound to the document, otherwise to the div 2170 target = (this.evalVisProp('el.pointer.outside')) ? document : this.board.containerObj; 2171 Env.addEvent(target, 'pointermove', this._elEventHandler, this); 2172 this._hasMoveEl = true; 2173 } 2174 } 2175 } 2176 if (this.evalVisProp('bank.pointer.enabled')) { 2177 neededButton = this.evalVisProp('bank.pointer.button'); 2178 neededKey = this.evalVisProp('bank.pointer.key'); 2179 2180 // Events for bank 2181 if ( 2182 (neededButton === -1 || neededButton === evt.button) && 2183 (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && evt.shiftKey) || (neededKey.indexOf('ctrl') > -1 && evt.ctrlKey)) 2184 ) { 2185 // If `outside` is true, we bind the event listener to 2186 // the document. otherwise, we bind it to the div. we 2187 // register the event listener as active so it can 2188 // prevent the pointer wheel from scrolling the page 2189 target = (this.evalVisProp('bank.pointer.outside')) ? document : this.board.containerObj; 2190 Env.addEvent(target, 'wheel', this._bankEventHandler, this, { passive: false }); 2191 this._hasMoveBank = true; 2192 } 2193 } 2194 } 2195 Env.addEvent(document, 'pointerup', this.pointerUpHandler, this); 2196 }, 2197 2198 /** 2199 * Event handler for pointer up event. Triggers handling of all 3D navigation. 2200 * 2201 * @private 2202 * @param {event} evt 2203 * @returns view 2204 */ 2205 pointerUpHandler: function (evt) { 2206 var target; 2207 2208 if (this._hasMoveAzEl) { 2209 target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj; 2210 Env.removeEvent(target, 'pointermove', this._az_elEventHandler, this); 2211 this._hasMoveAzEl = false; 2212 } 2213 if (this._hasMoveAz) { 2214 target = (this.evalVisProp('az.pointer.outside')) ? document : this.board.containerObj; 2215 Env.removeEvent(target, 'pointermove', this._azEventHandler, this); 2216 this._hasMoveAz = false; 2217 } 2218 if (this._hasMoveEl) { 2219 target = (this.evalVisProp('el.pointer.outside')) ? document : this.board.containerObj; 2220 Env.removeEvent(target, 'pointermove', this._elEventHandler, this); 2221 this._hasMoveEl = false; 2222 } 2223 if (this._hasMoveBank) { 2224 target = (this.evalVisProp('bank.pointer.outside')) ? document : this.board.containerObj; 2225 Env.removeEvent(target, 'wheel', this._bankEventHandler, this); 2226 this._hasMoveBank = false; 2227 } 2228 if (this._hasMoveTrackball) { 2229 target = (this.evalVisProp('trackball.outside')) ? document : this.board.containerObj; 2230 Env.removeEvent(target, 'pointermove', this._trackballHandler, this); 2231 this._hasMoveTrackball = false; 2232 } 2233 Env.removeEvent(document, 'pointerup', this.pointerUpHandler, this); 2234 this.board._change3DView = false; 2235 this.board.mode = this.board.BOARD_MODE_NONE; 2236 } 2237 }); 2238 2239 /** 2240 * @class A View3D element provides the container and the methods to create and display 3D elements. 2241 * @pseudo 2242 * @description A View3D element provides the container and the methods to create and display 3D elements. 2243 * It is contained in a JSXGraph board. 2244 * <p> 2245 * It is advisable to disable panning of the board by setting the board attribute "pan": 2246 * <pre> 2247 * pan: {enabled: false} 2248 * </pre> 2249 * Otherwise users will not be able to rotate the scene with their fingers on a touch device. 2250 * <p> 2251 * The start position of the camera can be adjusted by the attributes {@link View3D#az}, {@link View3D#el}, and {@link View3D#bank}. 2252 * 2253 * @name View3D 2254 * @augments JXG.View3D 2255 * @constructor 2256 * @type Object 2257 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 2258 * @param {Array_Array_Array} lower,dim,cube Here, lower is an array of the form [x, y] and 2259 * dim is an array of the form [w, h]. 2260 * The arrays [x, y] and [w, h] define the 2D frame into which the 3D cube is 2261 * (roughly) projected. If the view's azimuth=0 and elevation=0, the 3D view will cover a rectangle with lower left corner 2262 * [x,y] and side lengths [w, h] of the board. 2263 * The array 'cube' is of the form [[x1, x2], [y1, y2], [z1, z2]] 2264 * which determines the coordinate ranges of the 3D cube. 2265 * 2266 * @example 2267 * var bound = [-4, 6]; 2268 * var view = board.create('view3d', 2269 * [[-4, -3], [8, 8], 2270 * [bound, bound, bound]], 2271 * { 2272 * projection: 'parallel', 2273 * trackball: {enabled:true}, 2274 * }); 2275 * 2276 * var curve = view.create('curve3d', [ 2277 * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t), 2278 * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t), 2279 * (t) => Math.sin(3 * t), 2280 * [-Math.PI, Math.PI] 2281 * ], { strokeWidth: 4 }); 2282 * 2283 * </pre><div id="JXG9b327a6c-1bd6-4e40-a502-59d024dbfd1b" class="jxgbox" style="width: 300px; height: 300px;"></div> 2284 * <script type="text/javascript"> 2285 * (function() { 2286 * var board = JXG.JSXGraph.initBoard('JXG9b327a6c-1bd6-4e40-a502-59d024dbfd1b', 2287 * {boundingbox: [-8, 8, 8,-8], pan: {enabled: false}, axis: false, showcopyright: false, shownavigation: false}); 2288 * var bound = [-4, 6]; 2289 * var view = board.create('view3d', 2290 * [[-4, -3], [8, 8], 2291 * [bound, bound, bound]], 2292 * { 2293 * projection: 'parallel', 2294 * trackball: {enabled:true}, 2295 * }); 2296 * 2297 * var curve = view.create('curve3d', [ 2298 * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t), 2299 * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t), 2300 * (t) => Math.sin(3 * t), 2301 * [-Math.PI, Math.PI] 2302 * ], { strokeWidth: 4 }); 2303 * 2304 * })(); 2305 * 2306 * </script><pre> 2307 * 2308 * @example 2309 * var bound = [-4, 6]; 2310 * var view = board.create('view3d', 2311 * [[-4, -3], [8, 8], 2312 * [bound, bound, bound]], 2313 * { 2314 * projection: 'central', 2315 * trackball: {enabled:true}, 2316 * 2317 * xPlaneRear: { visible: false }, 2318 * yPlaneRear: { visible: false } 2319 * 2320 * }); 2321 * 2322 * var curve = view.create('curve3d', [ 2323 * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t), 2324 * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t), 2325 * (t) => Math.sin(3 * t), 2326 * [-Math.PI, Math.PI] 2327 * ], { strokeWidth: 4 }); 2328 * 2329 * </pre><div id="JXG0dc2493d-fb2f-40d5-bdb8-762ba0ad2007" class="jxgbox" style="width: 300px; height: 300px;"></div> 2330 * <script type="text/javascript"> 2331 * (function() { 2332 * var board = JXG.JSXGraph.initBoard('JXG0dc2493d-fb2f-40d5-bdb8-762ba0ad2007', 2333 * {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false}); 2334 * var bound = [-4, 6]; 2335 * var view = board.create('view3d', 2336 * [[-4, -3], [8, 8], 2337 * [bound, bound, bound]], 2338 * { 2339 * projection: 'central', 2340 * trackball: {enabled:true}, 2341 * 2342 * xPlaneRear: { visible: false }, 2343 * yPlaneRear: { visible: false } 2344 * 2345 * }); 2346 * 2347 * var curve = view.create('curve3d', [ 2348 * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t), 2349 * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t), 2350 * (t) => Math.sin(3 * t), 2351 * [-Math.PI, Math.PI] 2352 * ], { strokeWidth: 4 }); 2353 * 2354 * })(); 2355 * 2356 * </script><pre> 2357 * 2358 * @example 2359 * var bound = [-4, 6]; 2360 * var view = board.create('view3d', 2361 * [[-4, -3], [8, 8], 2362 * [bound, bound, bound]], 2363 * { 2364 * projection: 'central', 2365 * trackball: {enabled:true}, 2366 * 2367 * // Main axes 2368 * axesPosition: 'border', 2369 * 2370 * // Axes at the border 2371 * xAxisBorder: { ticks3d: { ticksDistance: 2} }, 2372 * yAxisBorder: { ticks3d: { ticksDistance: 2} }, 2373 * zAxisBorder: { ticks3d: { ticksDistance: 2} }, 2374 * 2375 * // No axes on planes 2376 * xPlaneRearYAxis: {visible: false}, 2377 * xPlaneRearZAxis: {visible: false}, 2378 * yPlaneRearXAxis: {visible: false}, 2379 * yPlaneRearZAxis: {visible: false}, 2380 * zPlaneRearXAxis: {visible: false}, 2381 * zPlaneRearYAxis: {visible: false} 2382 * }); 2383 * 2384 * var curve = view.create('curve3d', [ 2385 * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t), 2386 * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t), 2387 * (t) => Math.sin(3 * t), 2388 * [-Math.PI, Math.PI] 2389 * ], { strokeWidth: 4 }); 2390 * 2391 * </pre><div id="JXG586f3551-335c-47e9-8d72-835409f6a103" class="jxgbox" style="width: 300px; height: 300px;"></div> 2392 * <script type="text/javascript"> 2393 * (function() { 2394 * var board = JXG.JSXGraph.initBoard('JXG586f3551-335c-47e9-8d72-835409f6a103', 2395 * {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false}); 2396 * var bound = [-4, 6]; 2397 * var view = board.create('view3d', 2398 * [[-4, -3], [8, 8], 2399 * [bound, bound, bound]], 2400 * { 2401 * projection: 'central', 2402 * trackball: {enabled:true}, 2403 * 2404 * // Main axes 2405 * axesPosition: 'border', 2406 * 2407 * // Axes at the border 2408 * xAxisBorder: { ticks3d: { ticksDistance: 2} }, 2409 * yAxisBorder: { ticks3d: { ticksDistance: 2} }, 2410 * zAxisBorder: { ticks3d: { ticksDistance: 2} }, 2411 * 2412 * // No axes on planes 2413 * xPlaneRearYAxis: {visible: false}, 2414 * xPlaneRearZAxis: {visible: false}, 2415 * yPlaneRearXAxis: {visible: false}, 2416 * yPlaneRearZAxis: {visible: false}, 2417 * zPlaneRearXAxis: {visible: false}, 2418 * zPlaneRearYAxis: {visible: false} 2419 * }); 2420 * 2421 * var curve = view.create('curve3d', [ 2422 * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t), 2423 * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t), 2424 * (t) => Math.sin(3 * t), 2425 * [-Math.PI, Math.PI] 2426 * ], { strokeWidth: 4 }); 2427 * 2428 * })(); 2429 * 2430 * </script><pre> 2431 * 2432 * @example 2433 * var bound = [-4, 6]; 2434 * var view = board.create('view3d', 2435 * [[-4, -3], [8, 8], 2436 * [bound, bound, bound]], 2437 * { 2438 * projection: 'central', 2439 * trackball: {enabled:true}, 2440 * 2441 * axesPosition: 'none' 2442 * }); 2443 * 2444 * var curve = view.create('curve3d', [ 2445 * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t), 2446 * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t), 2447 * (t) => Math.sin(3 * t), 2448 * [-Math.PI, Math.PI] 2449 * ], { strokeWidth: 4 }); 2450 * 2451 * </pre><div id="JXG9a9467e1-f189-4c8c-adb2-d4f49bc7fa26" class="jxgbox" style="width: 300px; height: 300px;"></div> 2452 * <script type="text/javascript"> 2453 * (function() { 2454 * var board = JXG.JSXGraph.initBoard('JXG9a9467e1-f189-4c8c-adb2-d4f49bc7fa26', 2455 * {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false}); 2456 * var bound = [-4, 6]; 2457 * var view = board.create('view3d', 2458 * [[-4, -3], [8, 8], 2459 * [bound, bound, bound]], 2460 * { 2461 * projection: 'central', 2462 * trackball: {enabled:true}, 2463 * 2464 * axesPosition: 'none' 2465 * }); 2466 * 2467 * var curve = view.create('curve3d', [ 2468 * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t), 2469 * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t), 2470 * (t) => Math.sin(3 * t), 2471 * [-Math.PI, Math.PI] 2472 * ], { strokeWidth: 4 }); 2473 * 2474 * })(); 2475 * 2476 * </script><pre> 2477 * 2478 * @example 2479 * var bound = [-4, 6]; 2480 * var view = board.create('view3d', 2481 * [[-4, -3], [8, 8], 2482 * [bound, bound, bound]], 2483 * { 2484 * projection: 'central', 2485 * trackball: {enabled:true}, 2486 * 2487 * // Main axes 2488 * axesPosition: 'border', 2489 * 2490 * // Axes at the border 2491 * xAxisBorder: { ticks3d: { ticksDistance: 2} }, 2492 * yAxisBorder: { ticks3d: { ticksDistance: 2} }, 2493 * zAxisBorder: { ticks3d: { ticksDistance: 2} }, 2494 * 2495 * xPlaneRear: { 2496 * fillColor: '#fff', 2497 * mesh3d: {visible: false} 2498 * }, 2499 * yPlaneRear: { 2500 * fillColor: '#fff', 2501 * mesh3d: {visible: false} 2502 * }, 2503 * zPlaneRear: { 2504 * fillColor: '#fff', 2505 * mesh3d: {visible: false} 2506 * }, 2507 * xPlaneFront: { 2508 * visible: true, 2509 * fillColor: '#fff', 2510 * mesh3d: {visible: false} 2511 * }, 2512 * yPlaneFront: { 2513 * visible: true, 2514 * fillColor: '#fff', 2515 * mesh3d: {visible: false} 2516 * }, 2517 * zPlaneFront: { 2518 * visible: true, 2519 * fillColor: '#fff', 2520 * mesh3d: {visible: false} 2521 * }, 2522 * 2523 * // No axes on planes 2524 * xPlaneRearYAxis: {visible: false}, 2525 * xPlaneRearZAxis: {visible: false}, 2526 * yPlaneRearXAxis: {visible: false}, 2527 * yPlaneRearZAxis: {visible: false}, 2528 * zPlaneRearXAxis: {visible: false}, 2529 * zPlaneRearYAxis: {visible: false}, 2530 * xPlaneFrontYAxis: {visible: false}, 2531 * xPlaneFrontZAxis: {visible: false}, 2532 * yPlaneFrontXAxis: {visible: false}, 2533 * yPlaneFrontZAxis: {visible: false}, 2534 * zPlaneFrontXAxis: {visible: false}, 2535 * zPlaneFrontYAxis: {visible: false} 2536 * 2537 * }); 2538 * 2539 * var curve = view.create('curve3d', [ 2540 * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t), 2541 * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t), 2542 * (t) => Math.sin(3 * t), 2543 * [-Math.PI, Math.PI] 2544 * ], { strokeWidth: 4 }); 2545 * 2546 * </pre><div id="JXGbd41a4e3-1bf7-4764-b675-98b01667103b" class="jxgbox" style="width: 300px; height: 300px;"></div> 2547 * <script type="text/javascript"> 2548 * (function() { 2549 * var board = JXG.JSXGraph.initBoard('JXGbd41a4e3-1bf7-4764-b675-98b01667103b', 2550 * {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false}); 2551 * var bound = [-4, 6]; 2552 * var view = board.create('view3d', 2553 * [[-4, -3], [8, 8], 2554 * [bound, bound, bound]], 2555 * { 2556 * projection: 'central', 2557 * trackball: {enabled:true}, 2558 * 2559 * // Main axes 2560 * axesPosition: 'border', 2561 * 2562 * // Axes at the border 2563 * xAxisBorder: { ticks3d: { ticksDistance: 2} }, 2564 * yAxisBorder: { ticks3d: { ticksDistance: 2} }, 2565 * zAxisBorder: { ticks3d: { ticksDistance: 2} }, 2566 * 2567 * xPlaneRear: { 2568 * fillColor: '#fff', 2569 * mesh3d: {visible: false} 2570 * }, 2571 * yPlaneRear: { 2572 * fillColor: '#fff', 2573 * mesh3d: {visible: false} 2574 * }, 2575 * zPlaneRear: { 2576 * fillColor: '#fff', 2577 * mesh3d: {visible: false} 2578 * }, 2579 * xPlaneFront: { 2580 * visible: true, 2581 * fillColor: '#fff', 2582 * mesh3d: {visible: false} 2583 * }, 2584 * yPlaneFront: { 2585 * visible: true, 2586 * fillColor: '#fff', 2587 * mesh3d: {visible: false} 2588 * }, 2589 * zPlaneFront: { 2590 * visible: true, 2591 * fillColor: '#fff', 2592 * mesh3d: {visible: false} 2593 * }, 2594 * 2595 * // No axes on planes 2596 * xPlaneRearYAxis: {visible: false}, 2597 * xPlaneRearZAxis: {visible: false}, 2598 * yPlaneRearXAxis: {visible: false}, 2599 * yPlaneRearZAxis: {visible: false}, 2600 * zPlaneRearXAxis: {visible: false}, 2601 * zPlaneRearYAxis: {visible: false}, 2602 * xPlaneFrontYAxis: {visible: false}, 2603 * xPlaneFrontZAxis: {visible: false}, 2604 * yPlaneFrontXAxis: {visible: false}, 2605 * yPlaneFrontZAxis: {visible: false}, 2606 * zPlaneFrontXAxis: {visible: false}, 2607 * zPlaneFrontYAxis: {visible: false} 2608 * 2609 * }); 2610 * 2611 * var curve = view.create('curve3d', [ 2612 * (t) => (2 + Math.cos(3 * t)) * Math.cos(2 * t), 2613 * (t) => (2 + Math.cos(3 * t)) * Math.sin(2 * t), 2614 * (t) => Math.sin(3 * t), 2615 * [-Math.PI, Math.PI] 2616 * ], { strokeWidth: 4 }); 2617 * })(); 2618 * 2619 * </script><pre> 2620 * 2621 * @example 2622 * var bound = [-5, 5]; 2623 * var view = board.create('view3d', 2624 * [[-6, -3], 2625 * [8, 8], 2626 * [bound, bound, bound]], 2627 * { 2628 * // Main axes 2629 * axesPosition: 'center', 2630 * xAxis: { strokeColor: 'blue', strokeWidth: 3}, 2631 * 2632 * // Planes 2633 * xPlaneRear: { fillColor: 'yellow', mesh3d: {visible: false}}, 2634 * yPlaneFront: { visible: true, fillColor: 'blue'}, 2635 * 2636 * // Axes on planes 2637 * xPlaneRearYAxis: {strokeColor: 'red'}, 2638 * xPlaneRearZAxis: {strokeColor: 'red'}, 2639 * 2640 * yPlaneFrontXAxis: {strokeColor: 'blue'}, 2641 * yPlaneFrontZAxis: {strokeColor: 'blue'}, 2642 * 2643 * zPlaneFrontXAxis: {visible: false}, 2644 * zPlaneFrontYAxis: {visible: false} 2645 * }); 2646 * 2647 * </pre><div id="JXGdd06d90e-be5d-4531-8f0b-65fc30b1a7c7" class="jxgbox" style="width: 500px; height: 500px;"></div> 2648 * <script type="text/javascript"> 2649 * (function() { 2650 * var board = JXG.JSXGraph.initBoard('JXGdd06d90e-be5d-4531-8f0b-65fc30b1a7c7', 2651 * {boundingbox: [-8, 8, 8,-8], axis: false, pan: {enabled: false}, showcopyright: false, shownavigation: false}); 2652 * var bound = [-5, 5]; 2653 * var view = board.create('view3d', 2654 * [[-6, -3], [8, 8], 2655 * [bound, bound, bound]], 2656 * { 2657 * // Main axes 2658 * axesPosition: 'center', 2659 * xAxis: { strokeColor: 'blue', strokeWidth: 3}, 2660 * // Planes 2661 * xPlaneRear: { fillColor: 'yellow', mesh3d: {visible: false}}, 2662 * yPlaneFront: { visible: true, fillColor: 'blue'}, 2663 * // Axes on planes 2664 * xPlaneRearYAxis: {strokeColor: 'red'}, 2665 * xPlaneRearZAxis: {strokeColor: 'red'}, 2666 * yPlaneFrontXAxis: {strokeColor: 'blue'}, 2667 * yPlaneFrontZAxis: {strokeColor: 'blue'}, 2668 * zPlaneFrontXAxis: {visible: false}, 2669 * zPlaneFrontYAxis: {visible: false} 2670 * }); 2671 * })(); 2672 * 2673 * </script><pre> 2674 * @example 2675 * var bound = [-5, 5]; 2676 * var view = board.create('view3d', 2677 * [[-6, -3], [8, 8], 2678 * [bound, bound, bound]], 2679 * { 2680 * projection: 'central', 2681 * az: { 2682 * slider: { 2683 * visible: true, 2684 * point1: { 2685 * pos: [5, -4] 2686 * }, 2687 * point2: { 2688 * pos: [5, 4] 2689 * }, 2690 * label: {anchorX: 'middle'} 2691 * } 2692 * }, 2693 * el: { 2694 * slider: { 2695 * visible: true, 2696 * point1: { 2697 * pos: [6, -5] 2698 * }, 2699 * point2: { 2700 * pos: [6, 3] 2701 * }, 2702 * label: {anchorX: 'middle'} 2703 * } 2704 * }, 2705 * bank: { 2706 * slider: { 2707 * visible: true, 2708 * point1: { 2709 * pos: [7, -6] 2710 * }, 2711 * point2: { 2712 * pos: [7, 2] 2713 * }, 2714 * label: {anchorX: 'middle'} 2715 * } 2716 * } 2717 * }); 2718 * 2719 * 2720 * </pre><div id="JXGe181cc55-271b-419b-84fd-622326fd1d1a" class="jxgbox" style="width: 300px; height: 300px;"></div> 2721 * <script type="text/javascript"> 2722 * (function() { 2723 * var board = JXG.JSXGraph.initBoard('JXGe181cc55-271b-419b-84fd-622326fd1d1a', 2724 * {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false}); 2725 * var bound = [-5, 5]; 2726 * var view = board.create('view3d', 2727 * [[-6, -3], [8, 8], 2728 * [bound, bound, bound]], 2729 * { 2730 * projection: 'central', 2731 * az: { 2732 * slider: { 2733 * visible: true, 2734 * point1: { 2735 * pos: [5, -4] 2736 * }, 2737 * point2: { 2738 * pos: [5, 4] 2739 * }, 2740 * label: {anchorX: 'middle'} 2741 * } 2742 * }, 2743 * el: { 2744 * slider: { 2745 * visible: true, 2746 * point1: { 2747 * pos: [6, -5] 2748 * }, 2749 * point2: { 2750 * pos: [6, 3] 2751 * }, 2752 * label: {anchorX: 'middle'} 2753 * } 2754 * }, 2755 * bank: { 2756 * slider: { 2757 * visible: true, 2758 * point1: { 2759 * pos: [7, -6] 2760 * }, 2761 * point2: { 2762 * pos: [7, 2] 2763 * }, 2764 * label: {anchorX: 'middle'} 2765 * } 2766 * } 2767 * }); 2768 * 2769 * 2770 * })(); 2771 * 2772 * </script><pre> 2773 * 2774 * 2775 */ 2776 JXG.createView3D = function (board, parents, attributes) { 2777 var view, attr, attr_az, attr_el, attr_bank, 2778 x, y, w, h, 2779 p1, p2, v, 2780 coords = parents[0], // llft corner 2781 size = parents[1]; // [w, h] 2782 2783 attr = Type.copyAttributes(attributes, board.options, 'view3d'); 2784 view = new JXG.View3D(board, parents, attr); 2785 view.defaultAxes = view.create('axes3d', [], attr); 2786 2787 x = coords[0]; 2788 y = coords[1]; 2789 w = size[0]; 2790 h = size[1]; 2791 2792 attr_az = Type.copyAttributes(attr, board.options, 'view3d', 'az', 'slider'); 2793 attr_az.name = 'az'; 2794 2795 attr_el = Type.copyAttributes(attr, board.options, 'view3d', 'el', 'slider'); 2796 attr_el.name = 'el'; 2797 2798 attr_bank = Type.copyAttributes(attr, board.options, 'view3d', 'bank', 'slider'); 2799 attr_bank.name = 'bank'; 2800 2801 v = Type.evaluate(attr_az.point1.pos); 2802 if (!Type.isArray(v)) { 2803 // 'auto' 2804 p1 = [x - 1, y - 2]; 2805 } else { 2806 p1 = v; 2807 } 2808 v = Type.evaluate(attr_az.point2.pos); 2809 if (!Type.isArray(v)) { 2810 // 'auto' 2811 p2 = [x + w + 1, y - 2]; 2812 } else { 2813 p2 = v; 2814 } 2815 2816 /** 2817 * Slider to adapt azimuth angle 2818 * @name JXG.View3D#az_slide 2819 * @type {Slider} 2820 */ 2821 view.az_slide = board.create( 2822 'slider', 2823 [ 2824 p1, p2, 2825 [ 2826 Type.evaluate(attr_az.min), 2827 Type.evaluate(attr_az.start), 2828 Type.evaluate(attr_az.max) 2829 ] 2830 ], 2831 attr_az 2832 ); 2833 view.inherits.push(view.az_slide); 2834 view.az_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate() 2835 2836 v = Type.evaluate(attr_el.point1.pos); 2837 if (!Type.isArray(v)) { 2838 // 'auto' 2839 p1 = [x - 1, y]; 2840 } else { 2841 p1 = v; 2842 } 2843 v = Type.evaluate(attr_el.point2.pos); 2844 if (!Type.isArray(v)) { 2845 // 'auto' 2846 p2 = [x - 1, y + h]; 2847 } else { 2848 p2 = v; 2849 } 2850 2851 /** 2852 * Slider to adapt elevation angle 2853 * 2854 * @name JXG.View3D#el_slide 2855 * @type {Slider} 2856 */ 2857 view.el_slide = board.create( 2858 'slider', 2859 [ 2860 p1, p2, 2861 [ 2862 Type.evaluate(attr_el.min), 2863 Type.evaluate(attr_el.start), 2864 Type.evaluate(attr_el.max)] 2865 ], 2866 attr_el 2867 ); 2868 view.inherits.push(view.el_slide); 2869 view.el_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate() 2870 2871 v = Type.evaluate(attr_bank.point1.pos); 2872 if (!Type.isArray(v)) { 2873 // 'auto' 2874 p1 = [x - 1, y + h + 2]; 2875 } else { 2876 p1 = v; 2877 } 2878 v = Type.evaluate(attr_bank.point2.pos); 2879 if (!Type.isArray(v)) { 2880 // 'auto' 2881 p2 = [x + w + 1, y + h + 2]; 2882 } else { 2883 p2 = v; 2884 } 2885 2886 /** 2887 * Slider to adjust bank angle 2888 * 2889 * @name JXG.View3D#bank_slide 2890 * @type {Slider} 2891 */ 2892 view.bank_slide = board.create( 2893 'slider', 2894 [ 2895 p1, p2, 2896 [ 2897 Type.evaluate(attr_bank.min), 2898 Type.evaluate(attr_bank.start), 2899 Type.evaluate(attr_bank.max) 2900 ] 2901 ], 2902 attr_bank 2903 ); 2904 view.inherits.push(view.bank_slide); 2905 view.bank_slide.elType = 'view3d_slider'; // Used in board.prepareUpdate() 2906 2907 // Set special infobox attributes of view3d.infobox 2908 // Using setAttribute() is not possible here, since we have to 2909 // avoid a call of board.update(). 2910 // The drawback is that we can not use shortcuts 2911 view.board.infobox.visProp = Type.merge(view.board.infobox.visProp, attr.infobox); 2912 2913 // 3d infobox: drag direction and coordinates 2914 view.board.highlightInfobox = function (x, y, el) { 2915 var d, i, c3d, foot, 2916 pre = '', 2917 brd = el.board, 2918 arr, infobox, 2919 p = null; 2920 2921 if (this.mode === this.BOARD_MODE_DRAG) { 2922 // Drag direction is only shown during dragging 2923 if (view.isVerticalDrag()) { 2924 pre = '<span style="color:black; font-size:200%">\u21C5 </span>'; 2925 } else { 2926 pre = '<span style="color:black; font-size:200%">\u21C4 </span>'; 2927 } 2928 } 2929 2930 // Search 3D parent 2931 for (i = 0; i < el.parents.length; i++) { 2932 p = brd.objects[el.parents[i]]; 2933 if (p.is3D) { 2934 break; 2935 } 2936 } 2937 2938 if (p && Type.exists(p.element2D)) { 2939 foot = [1, 0, 0, p.coords[3]]; 2940 view._w0 = Mat.innerProduct(view.matrix3D[0], foot, 4); 2941 2942 c3d = view.project2DTo3DPlane(p.element2D, [1, 0, 0, 1], foot); 2943 if (!view.isInCube(c3d)) { 2944 view.board.highlightCustomInfobox('', p); 2945 return; 2946 } 2947 d = p.evalVisProp('infoboxdigits'); 2948 infobox = view.board.infobox; 2949 if (d === 'auto') { 2950 if (infobox.useLocale()) { 2951 arr = [pre, '(', infobox.formatNumberLocale(p.X()), ' | ', infobox.formatNumberLocale(p.Y()), ' | ', infobox.formatNumberLocale(p.Z()), ')']; 2952 } else { 2953 arr = [pre, '(', Type.autoDigits(p.X()), ' | ', Type.autoDigits(p.Y()), ' | ', Type.autoDigits(p.Z()), ')']; 2954 } 2955 2956 } else { 2957 if (infobox.useLocale()) { 2958 arr = [pre, '(', infobox.formatNumberLocale(p.X(), d), ' | ', infobox.formatNumberLocale(p.Y(), d), ' | ', infobox.formatNumberLocale(p.Z(), d), ')']; 2959 } else { 2960 arr = [pre, '(', Type.toFixed(p.X(), d), ' | ', Type.toFixed(p.Y(), d), ' | ', Type.toFixed(p.Z(), d), ')']; 2961 } 2962 } 2963 view.board.highlightCustomInfobox(arr.join(''), p); 2964 } else { 2965 view.board.highlightCustomInfobox('(' + x + ', ' + y + ')', el); 2966 } 2967 }; 2968 2969 // Hack needed to enable addEvent for view3D: 2970 view.BOARD_MODE_NONE = 0x0000; 2971 2972 // Add events for the keyboard navigation 2973 Env.addEvent(board.containerObj, 'keydown', function (event) { 2974 var neededKey, 2975 catchEvt = false; 2976 2977 // this.board._change3DView = true; 2978 if (view.evalVisProp('el.keyboard.enabled') && 2979 (event.key === 'ArrowUp' || event.key === 'ArrowDown') 2980 ) { 2981 neededKey = view.evalVisProp('el.keyboard.key'); 2982 if (neededKey === 'none' || 2983 (neededKey.indexOf('shift') > -1 && event.shiftKey) || 2984 (neededKey.indexOf('ctrl') > -1 && event.ctrlKey)) { 2985 view._elEventHandler(event); 2986 catchEvt = true; 2987 } 2988 2989 } 2990 2991 if (view.evalVisProp('az.keyboard.enabled') && 2992 (event.key === 'ArrowLeft' || event.key === 'ArrowRight') 2993 ) { 2994 neededKey = view.evalVisProp('az.keyboard.key'); 2995 if (neededKey === 'none' || 2996 (neededKey.indexOf('shift') > -1 && event.shiftKey) || 2997 (neededKey.indexOf('ctrl') > -1 && event.ctrlKey) 2998 ) { 2999 view._azEventHandler(event); 3000 catchEvt = true; 3001 } 3002 } 3003 3004 if (view.evalVisProp('bank.keyboard.enabled') && (event.key === ',' || event.key === '<' || event.key === '.' || event.key === '>')) { 3005 neededKey = view.evalVisProp('bank.keyboard.key'); 3006 if (neededKey === 'none' || (neededKey.indexOf('shift') > -1 && event.shiftKey) || (neededKey.indexOf('ctrl') > -1 && event.ctrlKey)) { 3007 view._bankEventHandler(event); 3008 catchEvt = true; 3009 } 3010 } 3011 3012 if (event.key === 'PageUp') { 3013 view.nextView(); 3014 catchEvt = true; 3015 } else if (event.key === 'PageDown') { 3016 view.previousView(); 3017 catchEvt = true; 3018 } 3019 3020 if (catchEvt) { 3021 // We stop event handling only in the case if the keypress could be 3022 // used for the 3D view. If this is not done, input fields et al 3023 // can not be used any more. 3024 event.preventDefault(); 3025 } 3026 this.board._change3DView = false; 3027 3028 }, view); 3029 3030 // Add events for the pointer navigation 3031 Env.addEvent(board.containerObj, 'pointerdown', view.pointerDownHandler, view); 3032 3033 // Initialize view rotation matrix 3034 view.getAnglesFromSliders(); 3035 view.matrix3DRot = view.getRotationFromAngles(); 3036 3037 // override angle slider bounds when trackball navigation is enabled 3038 view.updateAngleSliderBounds(); 3039 3040 view.board.update(); 3041 3042 return view; 3043 }; 3044 3045 JXG.registerElement("view3d", JXG.createView3D); 3046 3047 export default JXG.View3D; 3048