1 /* 2 Copyright 2008-2023 3 Matthias Ehmann, 4 Carsten Miller, 5 Andreas Walter, 6 Alfred Wassermann 7 8 This file is part of JSXGraph. 9 10 JSXGraph is free software dual licensed under the GNU LGPL or MIT License. 11 12 You can redistribute it and/or modify it under the terms of the 13 14 * GNU Lesser General Public License as published by 15 the Free Software Foundation, either version 3 of the License, or 16 (at your option) any later version 17 OR 18 * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT 19 20 JSXGraph is distributed in the hope that it will be useful, 21 but WITHOUT ANY WARRANTY; without even the implied warranty of 22 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 23 GNU Lesser General Public License for more details. 24 25 You should have received a copy of the GNU Lesser General Public License and 26 the MIT License along with JSXGraph. If not, see <https://www.gnu.org/licenses/> 27 and <https://opensource.org/licenses/MIT/>. 28 */ 29 /*global JXG:true, define: true*/ 30 31 import JXG from "../jxg"; 32 import Const from "../base/constants"; 33 import Mat from "../math/math"; 34 import Geometry from "../math/geometry"; 35 import Type from "../utils/type"; 36 //, GeometryElement3D) { 37 38 /** 39 * A 3D point is the basic geometric element. 40 * @class Creates a new 3D point object. Do not use this constructor to create a 3D point. Use {@link JXG.View3D#create} with 41 * type {@link Point3D} instead. 42 * @augments JXG.GeometryElement3D 43 * @augments JXG.GeometryElement 44 * @param {JXG.View3D} view The 3D view the point is drawn on. 45 * @param {Function|Array} F Array of numbers, array of functions or function returning an array with defines the user coordinates of the point. 46 * @parame {JXG.GeometryElement3D} slide Object the 3D point should be bound to. If null, the point is a free point. 47 * @param {Object} attributes An object containing visual properties like in {@link JXG.Options#point3d} and 48 * {@link JXG.Options#elements}, and optional a name and an id. 49 * @see JXG.Board#generateName 50 */ 51 JXG.Point3D = function (view, F, slide, attributes) { 52 this.constructor(view.board, attributes, Const.OBJECT_TYPE_POINT3D, Const.OBJECT_CLASS_3D); 53 this.constructor3D(view, "point3d"); 54 55 this.board.finalizeAdding(this); 56 57 /** 58 * Homogeneous coordinates of a Point3D, i.e. array of length 4: [w, x, y, z]. Usually, w=1 for finite points and w=0 for points 59 * which are infinitely far. 60 * 61 * @example 62 * p.coords; 63 * 64 * @name Point3D#coords 65 * @type Array 66 * @private 67 */ 68 this.coords = [0, 0, 0, 0]; 69 70 /** 71 * Function or array of functions or array of numbers defining the coordinates of the point, used in {@link updateCoords}. 72 * 73 * @name Point3D#F 74 * @function 75 * @private 76 * 77 * @see updateCoords 78 */ 79 this.F = F; 80 81 /** 82 * Optional slide element, i.e. element the Point3D lives on. 83 * 84 * @example 85 * p.slide; 86 * 87 * @name Point3D#slide 88 * @type JXG.GeometryElement3D 89 * @default null 90 * @private 91 * 92 */ 93 this.slide = slide; 94 95 /** 96 * Get x-coordinate of a 3D point. 97 * 98 * @name X 99 * @memberOf Point3D 100 * @function 101 * @returns {Number} 102 * 103 * @example 104 * p.X(); 105 */ 106 this.X = function () { 107 return this.coords[1]; 108 }; 109 110 /** 111 * Get y-coordinate of a 3D point. 112 * 113 * @name Y 114 * @memberOf Point3D 115 * @function 116 * @returns Number 117 * 118 * @example 119 * p.Y(); 120 */ 121 this.Y = function () { 122 return this.coords[2]; 123 }; 124 125 /** 126 * Get z-coordinate of a 3D point. 127 * 128 * @name Z 129 * @memberOf Point3D 130 * @function 131 * @returns Number 132 * 133 * @example 134 * p.Z(); 135 */ 136 this.Z = function () { 137 return this.coords[3]; 138 }; 139 140 /** 141 * Store the last position of the 2D point for the optimizer. 142 * 143 * @type Array 144 * @private 145 */ 146 this._params = null; 147 148 this._c2d = null; 149 150 this.methodMap = Type.deepCopy(this.methodMap, { 151 // TODO 152 }); 153 }; 154 JXG.Point3D.prototype = new JXG.GeometryElement(); 155 Type.copyPrototypeMethods(JXG.Point3D, JXG.GeometryElement3D, "constructor3D"); 156 157 JXG.extend( 158 JXG.Point3D.prototype, 159 /** @lends JXG.Point3D.prototype */ { 160 /** 161 * Update the homogeneous coords array. 162 * 163 * @name updateCoords 164 * @memberOf Point3D 165 * @function 166 * @returns {Object} Reference to the Point3D object 167 * @private 168 * @example 169 * p.updateCoords(); 170 */ 171 updateCoords: function () { 172 var i; 173 174 if (Type.isFunction(this.F)) { 175 this.coords = [1].concat(Type.evaluate(this.F)); 176 } else { 177 this.coords[0] = 1; 178 for (i = 0; i < 3; i++) { 179 // Attention: if F is array of numbers, coords are not updated. 180 // Otherwise, dragging will not work anymore. 181 if (Type.isFunction(this.F[i])) { 182 this.coords[i + 1] = Type.evaluate(this.F[i]); 183 } 184 } 185 } 186 return this; 187 }, 188 189 /** 190 * Initialize the coords array. 191 * 192 * @private 193 * @returns {Object} Reference to the Point3D object 194 */ 195 initCoords: function () { 196 var i; 197 198 if (Type.isFunction(this.F)) { 199 this.coords = [1].concat(Type.evaluate(this.F)); 200 } else { 201 this.coords[0] = 1; 202 for (i = 0; i < 3; i++) { 203 this.coords[i + 1] = Type.evaluate(this.F[i]); 204 } 205 } 206 return this; 207 }, 208 209 /** 210 * Normalize homogeneous coordinates such the the first coordinate (the w-coordinate is equal to 1 or 0)- 211 * 212 * @name normalizeCoords 213 * @memberOf Point3D 214 * @function 215 * @returns {Object} Reference to the Point3D object 216 * @private 217 * @example 218 * p.normalizeCoords(); 219 */ 220 normalizeCoords: function () { 221 if (Math.abs(this.coords[0]) > Mat.eps) { 222 this.coords[1] /= this.coords[0]; 223 this.coords[2] /= this.coords[0]; 224 this.coords[3] /= this.coords[0]; 225 this.coords[0] = 1.0; 226 } 227 return this; 228 }, 229 230 /** 231 * Set the position of a 3D point. 232 * 233 * @name setPosition 234 * @memberOf Point3D 235 * @function 236 * @param {Array} coords 3D coordinates. Either of the form [x,y,z] (Euclidean) or [w,x,y,z] (homogeneous). 237 * @param {Boolean} [noevent] If true, no events are triggered. 238 * @returns {Object} Reference to the Point3D object 239 * 240 * @example 241 * p.setPosition([1, 3, 4]); 242 */ 243 setPosition: function (coords, noevent) { 244 var c = this.coords, 245 oc = this.coords.slice(); // Copy of original values 246 247 if (coords.length === 3) { 248 // Euclidean coordinates 249 c[0] = 1.0; 250 c[1] = coords[0]; 251 c[2] = coords[1]; 252 c[3] = coords[2]; 253 } else { 254 // Homogeneous coordinates (normalized) 255 c[0] = coords[0]; 256 c[1] = coords[1]; 257 c[2] = coords[2]; 258 c[3] = coords[2]; 259 this.normalizeCoords(); 260 } 261 262 // console.log(el.emitter, !noevent, oc[0] !== c[0] || oc[1] !== c[1] || oc[2] !== c[2] || oc[3] !== c[3]); 263 // Not yet working 264 // if (el.emitter && !noevent && 265 // (oc[0] !== c[0] || oc[1] !== c[1] || oc[2] !== c[2] || oc[3] !== c[3])) { 266 // this.triggerEventHandlers(['update3D'], [oc]); 267 // } 268 return this; 269 }, 270 271 update: function (drag) { 272 var c3d, foot; 273 274 // Update is called from two methods: 275 // Once in setToPosition and 276 // once in the subsequent board.update 277 if ( 278 this.element2D.draggable() && 279 Geometry.distance(this._c2d, this.element2D.coords.usrCoords) !== 0 280 ) { 281 if (this.slide) { 282 this.projectCoords2Surface(); 283 } else { 284 if (this.view.isVerticalDrag()) { 285 // Drag the point in its vertical to the xy plane 286 c3d = this.view.project2DTo3DVertical(this.element2D, this.coords); 287 } else { 288 // Drag the point in its xy plane 289 foot = [1, 0, 0, this.coords[3]]; 290 c3d = this.view.project2DTo3DPlane(this.element2D, [1, 0, 0, 1], foot); 291 } 292 if (c3d[0] !== 0) { 293 this.coords = this.view.project3DToCube(c3d); 294 } 295 } 296 } else { 297 this.updateCoords(); 298 // Update 2D point from its 3D view 299 this.element2D.coords.setCoordinates( 300 Const.COORDS_BY_USER, 301 this.view.project3DTo2D([1, this.X(), this.Y(), this.Z()]) 302 ); 303 } 304 this._c2d = this.element2D.coords.usrCoords.slice(); 305 306 return this; 307 }, 308 309 updateRenderer: function () { 310 this.needsUpdate = false; 311 return this; 312 }, 313 314 projectCoords2Surface: function () { 315 var n = 2, // # of variables 316 m = 2, // number of constraints 317 x = [0, 0], 318 // Various Cobyla constants, see Cobyla docs in Cobyja.js 319 rhobeg = 5.0, 320 rhoend = 1.0e-6, 321 iprint = 0, 322 maxfun = 200, 323 surface = this.slide, 324 that = this, 325 r, 326 c3d, 327 c2d, 328 _minFunc; 329 330 if (surface === null) { 331 return; 332 } 333 334 _minFunc = function (n, m, x, con) { 335 var c3d = [ 336 1, 337 surface.X(x[0], x[1]), 338 surface.Y(x[0], x[1]), 339 surface.Z(x[0], x[1]) 340 ], 341 c2d = that.view.project3DTo2D(c3d); 342 343 con[0] = that.element2D.X() - c2d[1]; 344 con[1] = that.element2D.Y() - c2d[2]; 345 346 return con[0] * con[0] + con[1] * con[1]; 347 }; 348 if (Type.exists(this._params)) { 349 x = this._params.slice(); 350 } 351 r = Mat.Nlp.FindMinimum(_minFunc, n, m, x, rhobeg, rhoend, iprint, maxfun); 352 353 c3d = [1, surface.X(x[0], x[1]), surface.Y(x[0], x[1]), surface.Z(x[0], x[1])]; 354 c2d = this.view.project3DTo2D(c3d); 355 this._params = x; 356 this.coords = c3d; 357 this.element2D.coords.setCoordinates(Const.COORDS_BY_USER, c2d); 358 this._c2d = c2d; 359 }, 360 361 // Not yet working 362 __evt__update3D: function (oc) {} 363 } 364 ); 365 366 /** 367 * @class This element is used to provide a constructor for a 3D Point. 368 * @pseudo 369 * @description A Point3D object is defined by 3 coordinates [x,y,z]. 370 * <p> 371 * All numbers can also be provided as functions returning a number. 372 * 373 * @name Point3D 374 * @augments JXG.Point3D 375 * @constructor 376 * @throws {Exception} If the element cannot be constructed with the given parent 377 * objects an exception is thrown. 378 * @param {number,function_number,function_number,function} x,y,z The coordinates are given as x, y, z consisting of numbers of functions. 379 * @param {array,function} F Alternatively, the coordinates can be supplied as 380 * <ul> 381 * <li>array arr=[x,y,z] of length 3 consisting of numbers or 382 * <li>function returning an array [x,y,z] of length 3 of numbers. 383 * </ul> 384 * 385 * @example 386 * var bound = [-5, 5]; 387 * var view = board.create('view3d', 388 * [[-6, -3], [8, 8], 389 * [bound, bound, bound]], 390 * {}); 391 * var p = view.create('point3d', [1, 2, 2], { name:'A', size: 5 }); 392 * var q = view.create('point3d', function() { return [p.X(), p.Y(), p.Z() - 3]; }, { name:'B', size: 5, fixed: true }); 393 * 394 * </pre><div id="JXGb9ee8f9f-3d2b-4f73-8221-4f82c09933f1" class="jxgbox" style="width: 300px; height: 300px;"></div> 395 * <script type="text/javascript"> 396 * (function() { 397 * var board = JXG.JSXGraph.initBoard('JXGb9ee8f9f-3d2b-4f73-8221-4f82c09933f1', 398 * {boundingbox: [-8, 8, 8,-8], axis: false, showcopyright: false, shownavigation: false}); 399 * var bound = [-5, 5]; 400 * var view = board.create('view3d', 401 * [[-6, -3], [8, 8], 402 * [bound, bound, bound]], 403 * {}); 404 * var p = view.create('point3d', [1, 2, 2], { name:'A', size: 5 }); 405 * var q = view.create('point3d', function() { return [p.X(), p.Y(), p.Z() - 3]; }, { name:'B', size: 5 }); 406 * })(); 407 * 408 * </script><pre> 409 * 410 */ 411 JXG.createPoint3D = function (board, parents, attributes) { 412 // parents[0]: view 413 // followed by 414 // parents[1]: function or array 415 // or 416 // parents[1..3]: coordinates 417 418 var view = parents[0], 419 attr, F, slide, c2d, el; 420 421 // If the last element of parents is a 3D object, 422 // the point is a glider on that element. 423 if (parents.length > 2 && Type.exists(parents[parents.length - 1].is3D)) { 424 slide = parents.pop(); 425 } else { 426 slide = null; 427 } 428 429 if (parents.length === 2) { 430 // [view, array|fun] (Array [x, y, z] | function) returning [x, y, z] 431 F = parents[1]; 432 } else if (parents.length === 4) { 433 // [view, x, y, z], (3 numbers | functions) 434 F = parents.slice(1); 435 } else { 436 throw new Error( 437 "JSXGraph: Can't create point3d with parent types '" + 438 typeof parents[0] + 439 "' and '" + 440 typeof parents[1] + 441 "'." + 442 "\nPossible parent types: [[x,y,z]], [x,y,z]" 443 ); 444 // "\nPossible parent types: [[x,y,z]], [x,y,z], [element,transformation]"); // TODO 445 } 446 447 attr = Type.copyAttributes(attributes, board.options, 'point3d'); 448 el = new JXG.Point3D(view, F, slide, attr); 449 el.initCoords(); 450 451 c2d = view.project3DTo2D(el.coords); 452 453 attr = el.setAttr2D(attr); 454 el.element2D = view.create('point', c2d, attr); 455 el.addChild(el.element2D); 456 el.inherits.push(el.element2D); 457 el.element2D.setParents(el); 458 459 el._c2d = el.element2D.coords.usrCoords.slice(); // Store a copy of the coordinates to detect dragging 460 461 return el; 462 }; 463 464 JXG.registerElement("point3d", JXG.createPoint3D); 465