babylon.math.js 102 KB

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  1. var BABYLON;
  2. (function (BABYLON) {
  3. var Color3 = (function () {
  4. function Color3(r, g, b) {
  5. if (r === void 0) { r = 0; }
  6. if (g === void 0) { g = 0; }
  7. if (b === void 0) { b = 0; }
  8. this.r = r;
  9. this.g = g;
  10. this.b = b;
  11. }
  12. Color3.prototype.toString = function () {
  13. return "{R: " + this.r + " G:" + this.g + " B:" + this.b + "}";
  14. };
  15. // Operators
  16. Color3.prototype.toArray = function (array, index) {
  17. if (index === undefined) {
  18. index = 0;
  19. }
  20. array[index] = this.r;
  21. array[index + 1] = this.g;
  22. array[index + 2] = this.b;
  23. return this;
  24. };
  25. Color3.prototype.toColor4 = function (alpha) {
  26. if (alpha === void 0) { alpha = 1; }
  27. return new Color4(this.r, this.g, this.b, alpha);
  28. };
  29. Color3.prototype.asArray = function () {
  30. var result = [];
  31. this.toArray(result, 0);
  32. return result;
  33. };
  34. Color3.prototype.toLuminance = function () {
  35. return this.r * 0.3 + this.g * 0.59 + this.b * 0.11;
  36. };
  37. Color3.prototype.multiply = function (otherColor) {
  38. return new Color3(this.r * otherColor.r, this.g * otherColor.g, this.b * otherColor.b);
  39. };
  40. Color3.prototype.multiplyToRef = function (otherColor, result) {
  41. result.r = this.r * otherColor.r;
  42. result.g = this.g * otherColor.g;
  43. result.b = this.b * otherColor.b;
  44. return this;
  45. };
  46. Color3.prototype.equals = function (otherColor) {
  47. return otherColor && this.r === otherColor.r && this.g === otherColor.g && this.b === otherColor.b;
  48. };
  49. Color3.prototype.scale = function (scale) {
  50. return new Color3(this.r * scale, this.g * scale, this.b * scale);
  51. };
  52. Color3.prototype.scaleToRef = function (scale, result) {
  53. result.r = this.r * scale;
  54. result.g = this.g * scale;
  55. result.b = this.b * scale;
  56. return this;
  57. };
  58. Color3.prototype.add = function (otherColor) {
  59. return new Color3(this.r + otherColor.r, this.g + otherColor.g, this.b + otherColor.b);
  60. };
  61. Color3.prototype.addToRef = function (otherColor, result) {
  62. result.r = this.r + otherColor.r;
  63. result.g = this.g + otherColor.g;
  64. result.b = this.b + otherColor.b;
  65. return this;
  66. };
  67. Color3.prototype.subtract = function (otherColor) {
  68. return new Color3(this.r - otherColor.r, this.g - otherColor.g, this.b - otherColor.b);
  69. };
  70. Color3.prototype.subtractToRef = function (otherColor, result) {
  71. result.r = this.r - otherColor.r;
  72. result.g = this.g - otherColor.g;
  73. result.b = this.b - otherColor.b;
  74. return this;
  75. };
  76. Color3.prototype.clone = function () {
  77. return new Color3(this.r, this.g, this.b);
  78. };
  79. Color3.prototype.copyFrom = function (source) {
  80. this.r = source.r;
  81. this.g = source.g;
  82. this.b = source.b;
  83. return this;
  84. };
  85. Color3.prototype.copyFromFloats = function (r, g, b) {
  86. this.r = r;
  87. this.g = g;
  88. this.b = b;
  89. return this;
  90. };
  91. // Statics
  92. Color3.FromArray = function (array, offset) {
  93. if (offset === void 0) { offset = 0; }
  94. return new Color3(array[offset], array[offset + 1], array[offset + 2]);
  95. };
  96. Color3.FromInts = function (r, g, b) {
  97. return new Color3(r / 255.0, g / 255.0, b / 255.0);
  98. };
  99. Color3.Lerp = function (start, end, amount) {
  100. var r = start.r + ((end.r - start.r) * amount);
  101. var g = start.g + ((end.g - start.g) * amount);
  102. var b = start.b + ((end.b - start.b) * amount);
  103. return new Color3(r, g, b);
  104. };
  105. Color3.Red = function () {
  106. return new Color3(1, 0, 0);
  107. };
  108. Color3.Green = function () {
  109. return new Color3(0, 1, 0);
  110. };
  111. Color3.Blue = function () {
  112. return new Color3(0, 0, 1);
  113. };
  114. Color3.Black = function () {
  115. return new Color3(0, 0, 0);
  116. };
  117. Color3.White = function () {
  118. return new Color3(1, 1, 1);
  119. };
  120. Color3.Purple = function () {
  121. return new Color3(0.5, 0, 0.5);
  122. };
  123. Color3.Magenta = function () {
  124. return new Color3(1, 0, 1);
  125. };
  126. Color3.Yellow = function () {
  127. return new Color3(1, 1, 0);
  128. };
  129. Color3.Gray = function () {
  130. return new Color3(0.5, 0.5, 0.5);
  131. };
  132. return Color3;
  133. })();
  134. BABYLON.Color3 = Color3;
  135. var Color4 = (function () {
  136. function Color4(r, g, b, a) {
  137. this.r = r;
  138. this.g = g;
  139. this.b = b;
  140. this.a = a;
  141. }
  142. // Operators
  143. Color4.prototype.addInPlace = function (right) {
  144. this.r += right.r;
  145. this.g += right.g;
  146. this.b += right.b;
  147. this.a += right.a;
  148. return this;
  149. };
  150. Color4.prototype.asArray = function () {
  151. var result = [];
  152. this.toArray(result, 0);
  153. return result;
  154. };
  155. Color4.prototype.toArray = function (array, index) {
  156. if (index === undefined) {
  157. index = 0;
  158. }
  159. array[index] = this.r;
  160. array[index + 1] = this.g;
  161. array[index + 2] = this.b;
  162. array[index + 3] = this.a;
  163. return this;
  164. };
  165. Color4.prototype.add = function (right) {
  166. return new Color4(this.r + right.r, this.g + right.g, this.b + right.b, this.a + right.a);
  167. };
  168. Color4.prototype.subtract = function (right) {
  169. return new Color4(this.r - right.r, this.g - right.g, this.b - right.b, this.a - right.a);
  170. };
  171. Color4.prototype.subtractToRef = function (right, result) {
  172. result.r = this.r - right.r;
  173. result.g = this.g - right.g;
  174. result.b = this.b - right.b;
  175. result.a = this.a - right.a;
  176. return this;
  177. };
  178. Color4.prototype.scale = function (scale) {
  179. return new Color4(this.r * scale, this.g * scale, this.b * scale, this.a * scale);
  180. };
  181. Color4.prototype.scaleToRef = function (scale, result) {
  182. result.r = this.r * scale;
  183. result.g = this.g * scale;
  184. result.b = this.b * scale;
  185. result.a = this.a * scale;
  186. return this;
  187. };
  188. Color4.prototype.toString = function () {
  189. return "{R: " + this.r + " G:" + this.g + " B:" + this.b + " A:" + this.a + "}";
  190. };
  191. Color4.prototype.clone = function () {
  192. return new Color4(this.r, this.g, this.b, this.a);
  193. };
  194. Color4.prototype.copyFrom = function (source) {
  195. this.r = source.r;
  196. this.g = source.g;
  197. this.b = source.b;
  198. this.a = source.a;
  199. return this;
  200. };
  201. // Statics
  202. Color4.Lerp = function (left, right, amount) {
  203. var result = new Color4(0, 0, 0, 0);
  204. Color4.LerpToRef(left, right, amount, result);
  205. return result;
  206. };
  207. Color4.LerpToRef = function (left, right, amount, result) {
  208. result.r = left.r + (right.r - left.r) * amount;
  209. result.g = left.g + (right.g - left.g) * amount;
  210. result.b = left.b + (right.b - left.b) * amount;
  211. result.a = left.a + (right.a - left.a) * amount;
  212. };
  213. Color4.FromArray = function (array, offset) {
  214. if (offset === void 0) { offset = 0; }
  215. return new Color4(array[offset], array[offset + 1], array[offset + 2], array[offset + 3]);
  216. };
  217. Color4.FromInts = function (r, g, b, a) {
  218. return new Color4(r / 255.0, g / 255.0, b / 255.0, a / 255.0);
  219. };
  220. return Color4;
  221. })();
  222. BABYLON.Color4 = Color4;
  223. var Vector2 = (function () {
  224. function Vector2(x, y) {
  225. this.x = x;
  226. this.y = y;
  227. }
  228. Vector2.prototype.toString = function () {
  229. return "{X: " + this.x + " Y:" + this.y + "}";
  230. };
  231. // Operators
  232. Vector2.prototype.toArray = function (array, index) {
  233. if (index === void 0) { index = 0; }
  234. array[index] = this.x;
  235. array[index + 1] = this.y;
  236. return this;
  237. };
  238. Vector2.prototype.asArray = function () {
  239. var result = [];
  240. this.toArray(result, 0);
  241. return result;
  242. };
  243. Vector2.prototype.copyFrom = function (source) {
  244. this.x = source.x;
  245. this.y = source.y;
  246. return this;
  247. };
  248. Vector2.prototype.copyFromFloats = function (x, y) {
  249. this.x = x;
  250. this.y = y;
  251. return this;
  252. };
  253. Vector2.prototype.add = function (otherVector) {
  254. return new Vector2(this.x + otherVector.x, this.y + otherVector.y);
  255. };
  256. Vector2.prototype.addVector3 = function (otherVector) {
  257. return new Vector2(this.x + otherVector.x, this.y + otherVector.y);
  258. };
  259. Vector2.prototype.subtract = function (otherVector) {
  260. return new Vector2(this.x - otherVector.x, this.y - otherVector.y);
  261. };
  262. Vector2.prototype.subtractInPlace = function (otherVector) {
  263. this.x -= otherVector.x;
  264. this.y -= otherVector.y;
  265. return this;
  266. };
  267. Vector2.prototype.multiplyInPlace = function (otherVector) {
  268. this.x *= otherVector.x;
  269. this.y *= otherVector.y;
  270. return this;
  271. };
  272. Vector2.prototype.multiply = function (otherVector) {
  273. return new Vector2(this.x * otherVector.x, this.y * otherVector.y);
  274. };
  275. Vector2.prototype.multiplyToRef = function (otherVector, result) {
  276. result.x = this.x * otherVector.x;
  277. result.y = this.y * otherVector.y;
  278. return this;
  279. };
  280. Vector2.prototype.multiplyByFloats = function (x, y) {
  281. return new Vector2(this.x * x, this.y * y);
  282. };
  283. Vector2.prototype.divide = function (otherVector) {
  284. return new Vector2(this.x / otherVector.x, this.y / otherVector.y);
  285. };
  286. Vector2.prototype.divideToRef = function (otherVector, result) {
  287. result.x = this.x / otherVector.x;
  288. result.y = this.y / otherVector.y;
  289. return this;
  290. };
  291. Vector2.prototype.negate = function () {
  292. return new Vector2(-this.x, -this.y);
  293. };
  294. Vector2.prototype.scaleInPlace = function (scale) {
  295. this.x *= scale;
  296. this.y *= scale;
  297. return this;
  298. };
  299. Vector2.prototype.scale = function (scale) {
  300. return new Vector2(this.x * scale, this.y * scale);
  301. };
  302. Vector2.prototype.equals = function (otherVector) {
  303. return otherVector && this.x === otherVector.x && this.y === otherVector.y;
  304. };
  305. // Properties
  306. Vector2.prototype.length = function () {
  307. return Math.sqrt(this.x * this.x + this.y * this.y);
  308. };
  309. Vector2.prototype.lengthSquared = function () {
  310. return (this.x * this.x + this.y * this.y);
  311. };
  312. // Methods
  313. Vector2.prototype.normalize = function () {
  314. var len = this.length();
  315. if (len === 0)
  316. return this;
  317. var num = 1.0 / len;
  318. this.x *= num;
  319. this.y *= num;
  320. return this;
  321. };
  322. Vector2.prototype.clone = function () {
  323. return new Vector2(this.x, this.y);
  324. };
  325. // Statics
  326. Vector2.Zero = function () {
  327. return new Vector2(0, 0);
  328. };
  329. Vector2.FromArray = function (array, offset) {
  330. if (offset === void 0) { offset = 0; }
  331. return new Vector2(array[offset], array[offset + 1]);
  332. };
  333. Vector2.FromArrayToRef = function (array, offset, result) {
  334. result.x = array[offset];
  335. result.y = array[offset + 1];
  336. };
  337. Vector2.CatmullRom = function (value1, value2, value3, value4, amount) {
  338. var squared = amount * amount;
  339. var cubed = amount * squared;
  340. var x = 0.5 * ((((2.0 * value2.x) + ((-value1.x + value3.x) * amount)) + (((((2.0 * value1.x) - (5.0 * value2.x)) + (4.0 * value3.x)) - value4.x) * squared)) + ((((-value1.x + (3.0 * value2.x)) - (3.0 * value3.x)) + value4.x) * cubed));
  341. var y = 0.5 * ((((2.0 * value2.y) + ((-value1.y + value3.y) * amount)) + (((((2.0 * value1.y) - (5.0 * value2.y)) + (4.0 * value3.y)) - value4.y) * squared)) + ((((-value1.y + (3.0 * value2.y)) - (3.0 * value3.y)) + value4.y) * cubed));
  342. return new Vector2(x, y);
  343. };
  344. Vector2.Clamp = function (value, min, max) {
  345. var x = value.x;
  346. x = (x > max.x) ? max.x : x;
  347. x = (x < min.x) ? min.x : x;
  348. var y = value.y;
  349. y = (y > max.y) ? max.y : y;
  350. y = (y < min.y) ? min.y : y;
  351. return new Vector2(x, y);
  352. };
  353. Vector2.Hermite = function (value1, tangent1, value2, tangent2, amount) {
  354. var squared = amount * amount;
  355. var cubed = amount * squared;
  356. var part1 = ((2.0 * cubed) - (3.0 * squared)) + 1.0;
  357. var part2 = (-2.0 * cubed) + (3.0 * squared);
  358. var part3 = (cubed - (2.0 * squared)) + amount;
  359. var part4 = cubed - squared;
  360. var x = (((value1.x * part1) + (value2.x * part2)) + (tangent1.x * part3)) + (tangent2.x * part4);
  361. var y = (((value1.y * part1) + (value2.y * part2)) + (tangent1.y * part3)) + (tangent2.y * part4);
  362. return new Vector2(x, y);
  363. };
  364. Vector2.Lerp = function (start, end, amount) {
  365. var x = start.x + ((end.x - start.x) * amount);
  366. var y = start.y + ((end.y - start.y) * amount);
  367. return new Vector2(x, y);
  368. };
  369. Vector2.Dot = function (left, right) {
  370. return left.x * right.x + left.y * right.y;
  371. };
  372. Vector2.Normalize = function (vector) {
  373. var newVector = vector.clone();
  374. newVector.normalize();
  375. return newVector;
  376. };
  377. Vector2.Minimize = function (left, right) {
  378. var x = (left.x < right.x) ? left.x : right.x;
  379. var y = (left.y < right.y) ? left.y : right.y;
  380. return new Vector2(x, y);
  381. };
  382. Vector2.Maximize = function (left, right) {
  383. var x = (left.x > right.x) ? left.x : right.x;
  384. var y = (left.y > right.y) ? left.y : right.y;
  385. return new Vector2(x, y);
  386. };
  387. Vector2.Transform = function (vector, transformation) {
  388. var x = (vector.x * transformation.m[0]) + (vector.y * transformation.m[4]);
  389. var y = (vector.x * transformation.m[1]) + (vector.y * transformation.m[5]);
  390. return new Vector2(x, y);
  391. };
  392. Vector2.Distance = function (value1, value2) {
  393. return Math.sqrt(Vector2.DistanceSquared(value1, value2));
  394. };
  395. Vector2.DistanceSquared = function (value1, value2) {
  396. var x = value1.x - value2.x;
  397. var y = value1.y - value2.y;
  398. return (x * x) + (y * y);
  399. };
  400. return Vector2;
  401. })();
  402. BABYLON.Vector2 = Vector2;
  403. var Vector3 = (function () {
  404. function Vector3(x, y, z) {
  405. this.x = x;
  406. this.y = y;
  407. this.z = z;
  408. }
  409. Vector3.prototype.toString = function () {
  410. return "{X: " + this.x + " Y:" + this.y + " Z:" + this.z + "}";
  411. };
  412. // Operators
  413. Vector3.prototype.asArray = function () {
  414. var result = [];
  415. this.toArray(result, 0);
  416. return result;
  417. };
  418. Vector3.prototype.toArray = function (array, index) {
  419. if (index === void 0) { index = 0; }
  420. array[index] = this.x;
  421. array[index + 1] = this.y;
  422. array[index + 2] = this.z;
  423. return this;
  424. };
  425. Vector3.prototype.toQuaternion = function () {
  426. var result = new Quaternion(0, 0, 0, 1);
  427. var cosxPlusz = Math.cos((this.x + this.z) * 0.5);
  428. var sinxPlusz = Math.sin((this.x + this.z) * 0.5);
  429. var coszMinusx = Math.cos((this.z - this.x) * 0.5);
  430. var sinzMinusx = Math.sin((this.z - this.x) * 0.5);
  431. var cosy = Math.cos(this.y * 0.5);
  432. var siny = Math.sin(this.y * 0.5);
  433. result.x = coszMinusx * siny;
  434. result.y = -sinzMinusx * siny;
  435. result.z = sinxPlusz * cosy;
  436. result.w = cosxPlusz * cosy;
  437. return result;
  438. };
  439. Vector3.prototype.addInPlace = function (otherVector) {
  440. this.x += otherVector.x;
  441. this.y += otherVector.y;
  442. this.z += otherVector.z;
  443. return this;
  444. };
  445. Vector3.prototype.add = function (otherVector) {
  446. return new Vector3(this.x + otherVector.x, this.y + otherVector.y, this.z + otherVector.z);
  447. };
  448. Vector3.prototype.addToRef = function (otherVector, result) {
  449. result.x = this.x + otherVector.x;
  450. result.y = this.y + otherVector.y;
  451. result.z = this.z + otherVector.z;
  452. return this;
  453. };
  454. Vector3.prototype.subtractInPlace = function (otherVector) {
  455. this.x -= otherVector.x;
  456. this.y -= otherVector.y;
  457. this.z -= otherVector.z;
  458. return this;
  459. };
  460. Vector3.prototype.subtract = function (otherVector) {
  461. return new Vector3(this.x - otherVector.x, this.y - otherVector.y, this.z - otherVector.z);
  462. };
  463. Vector3.prototype.subtractToRef = function (otherVector, result) {
  464. result.x = this.x - otherVector.x;
  465. result.y = this.y - otherVector.y;
  466. result.z = this.z - otherVector.z;
  467. return this;
  468. };
  469. Vector3.prototype.subtractFromFloats = function (x, y, z) {
  470. return new Vector3(this.x - x, this.y - y, this.z - z);
  471. };
  472. Vector3.prototype.subtractFromFloatsToRef = function (x, y, z, result) {
  473. result.x = this.x - x;
  474. result.y = this.y - y;
  475. result.z = this.z - z;
  476. return this;
  477. };
  478. Vector3.prototype.negate = function () {
  479. return new Vector3(-this.x, -this.y, -this.z);
  480. };
  481. Vector3.prototype.scaleInPlace = function (scale) {
  482. this.x *= scale;
  483. this.y *= scale;
  484. this.z *= scale;
  485. return this;
  486. };
  487. Vector3.prototype.scale = function (scale) {
  488. return new Vector3(this.x * scale, this.y * scale, this.z * scale);
  489. };
  490. Vector3.prototype.scaleToRef = function (scale, result) {
  491. result.x = this.x * scale;
  492. result.y = this.y * scale;
  493. result.z = this.z * scale;
  494. };
  495. Vector3.prototype.equals = function (otherVector) {
  496. return otherVector && this.x === otherVector.x && this.y === otherVector.y && this.z === otherVector.z;
  497. };
  498. Vector3.prototype.equalsWithEpsilon = function (otherVector) {
  499. return Math.abs(this.x - otherVector.x) < BABYLON.Engine.Epsilon && Math.abs(this.y - otherVector.y) < BABYLON.Engine.Epsilon && Math.abs(this.z - otherVector.z) < BABYLON.Engine.Epsilon;
  500. };
  501. Vector3.prototype.equalsToFloats = function (x, y, z) {
  502. return this.x === x && this.y === y && this.z === z;
  503. };
  504. Vector3.prototype.multiplyInPlace = function (otherVector) {
  505. this.x *= otherVector.x;
  506. this.y *= otherVector.y;
  507. this.z *= otherVector.z;
  508. return this;
  509. };
  510. Vector3.prototype.multiply = function (otherVector) {
  511. return new Vector3(this.x * otherVector.x, this.y * otherVector.y, this.z * otherVector.z);
  512. };
  513. Vector3.prototype.multiplyToRef = function (otherVector, result) {
  514. result.x = this.x * otherVector.x;
  515. result.y = this.y * otherVector.y;
  516. result.z = this.z * otherVector.z;
  517. return this;
  518. };
  519. Vector3.prototype.multiplyByFloats = function (x, y, z) {
  520. return new Vector3(this.x * x, this.y * y, this.z * z);
  521. };
  522. Vector3.prototype.divide = function (otherVector) {
  523. return new Vector3(this.x / otherVector.x, this.y / otherVector.y, this.z / otherVector.z);
  524. };
  525. Vector3.prototype.divideToRef = function (otherVector, result) {
  526. result.x = this.x / otherVector.x;
  527. result.y = this.y / otherVector.y;
  528. result.z = this.z / otherVector.z;
  529. return this;
  530. };
  531. Vector3.prototype.MinimizeInPlace = function (other) {
  532. if (other.x < this.x)
  533. this.x = other.x;
  534. if (other.y < this.y)
  535. this.y = other.y;
  536. if (other.z < this.z)
  537. this.z = other.z;
  538. return this;
  539. };
  540. Vector3.prototype.MaximizeInPlace = function (other) {
  541. if (other.x > this.x)
  542. this.x = other.x;
  543. if (other.y > this.y)
  544. this.y = other.y;
  545. if (other.z > this.z)
  546. this.z = other.z;
  547. return this;
  548. };
  549. // Properties
  550. Vector3.prototype.length = function () {
  551. return Math.sqrt(this.x * this.x + this.y * this.y + this.z * this.z);
  552. };
  553. Vector3.prototype.lengthSquared = function () {
  554. return (this.x * this.x + this.y * this.y + this.z * this.z);
  555. };
  556. // Methods
  557. Vector3.prototype.normalize = function () {
  558. var len = this.length();
  559. if (len === 0)
  560. return this;
  561. var num = 1.0 / len;
  562. this.x *= num;
  563. this.y *= num;
  564. this.z *= num;
  565. return this;
  566. };
  567. Vector3.prototype.clone = function () {
  568. return new Vector3(this.x, this.y, this.z);
  569. };
  570. Vector3.prototype.copyFrom = function (source) {
  571. this.x = source.x;
  572. this.y = source.y;
  573. this.z = source.z;
  574. return this;
  575. };
  576. Vector3.prototype.copyFromFloats = function (x, y, z) {
  577. this.x = x;
  578. this.y = y;
  579. this.z = z;
  580. return this;
  581. };
  582. // Statics
  583. Vector3.FromArray = function (array, offset) {
  584. if (!offset) {
  585. offset = 0;
  586. }
  587. return new Vector3(array[offset], array[offset + 1], array[offset + 2]);
  588. };
  589. Vector3.FromArrayToRef = function (array, offset, result) {
  590. result.x = array[offset];
  591. result.y = array[offset + 1];
  592. result.z = array[offset + 2];
  593. };
  594. Vector3.FromFloatArrayToRef = function (array, offset, result) {
  595. result.x = array[offset];
  596. result.y = array[offset + 1];
  597. result.z = array[offset + 2];
  598. };
  599. Vector3.FromFloatsToRef = function (x, y, z, result) {
  600. result.x = x;
  601. result.y = y;
  602. result.z = z;
  603. };
  604. Vector3.Zero = function () {
  605. return new Vector3(0, 0, 0);
  606. };
  607. Vector3.Up = function () {
  608. return new Vector3(0, 1.0, 0);
  609. };
  610. Vector3.TransformCoordinates = function (vector, transformation) {
  611. var result = Vector3.Zero();
  612. Vector3.TransformCoordinatesToRef(vector, transformation, result);
  613. return result;
  614. };
  615. Vector3.TransformCoordinatesToRef = function (vector, transformation, result) {
  616. var x = (vector.x * transformation.m[0]) + (vector.y * transformation.m[4]) + (vector.z * transformation.m[8]) + transformation.m[12];
  617. var y = (vector.x * transformation.m[1]) + (vector.y * transformation.m[5]) + (vector.z * transformation.m[9]) + transformation.m[13];
  618. var z = (vector.x * transformation.m[2]) + (vector.y * transformation.m[6]) + (vector.z * transformation.m[10]) + transformation.m[14];
  619. var w = (vector.x * transformation.m[3]) + (vector.y * transformation.m[7]) + (vector.z * transformation.m[11]) + transformation.m[15];
  620. result.x = x / w;
  621. result.y = y / w;
  622. result.z = z / w;
  623. };
  624. Vector3.TransformCoordinatesFromFloatsToRef = function (x, y, z, transformation, result) {
  625. var rx = (x * transformation.m[0]) + (y * transformation.m[4]) + (z * transformation.m[8]) + transformation.m[12];
  626. var ry = (x * transformation.m[1]) + (y * transformation.m[5]) + (z * transformation.m[9]) + transformation.m[13];
  627. var rz = (x * transformation.m[2]) + (y * transformation.m[6]) + (z * transformation.m[10]) + transformation.m[14];
  628. var rw = (x * transformation.m[3]) + (y * transformation.m[7]) + (z * transformation.m[11]) + transformation.m[15];
  629. result.x = rx / rw;
  630. result.y = ry / rw;
  631. result.z = rz / rw;
  632. };
  633. Vector3.TransformNormal = function (vector, transformation) {
  634. var result = Vector3.Zero();
  635. Vector3.TransformNormalToRef(vector, transformation, result);
  636. return result;
  637. };
  638. Vector3.TransformNormalToRef = function (vector, transformation, result) {
  639. result.x = (vector.x * transformation.m[0]) + (vector.y * transformation.m[4]) + (vector.z * transformation.m[8]);
  640. result.y = (vector.x * transformation.m[1]) + (vector.y * transformation.m[5]) + (vector.z * transformation.m[9]);
  641. result.z = (vector.x * transformation.m[2]) + (vector.y * transformation.m[6]) + (vector.z * transformation.m[10]);
  642. };
  643. Vector3.TransformNormalFromFloatsToRef = function (x, y, z, transformation, result) {
  644. result.x = (x * transformation.m[0]) + (y * transformation.m[4]) + (z * transformation.m[8]);
  645. result.y = (x * transformation.m[1]) + (y * transformation.m[5]) + (z * transformation.m[9]);
  646. result.z = (x * transformation.m[2]) + (y * transformation.m[6]) + (z * transformation.m[10]);
  647. };
  648. Vector3.CatmullRom = function (value1, value2, value3, value4, amount) {
  649. var squared = amount * amount;
  650. var cubed = amount * squared;
  651. var x = 0.5 * ((((2.0 * value2.x) + ((-value1.x + value3.x) * amount)) + (((((2.0 * value1.x) - (5.0 * value2.x)) + (4.0 * value3.x)) - value4.x) * squared)) + ((((-value1.x + (3.0 * value2.x)) - (3.0 * value3.x)) + value4.x) * cubed));
  652. var y = 0.5 * ((((2.0 * value2.y) + ((-value1.y + value3.y) * amount)) + (((((2.0 * value1.y) - (5.0 * value2.y)) + (4.0 * value3.y)) - value4.y) * squared)) + ((((-value1.y + (3.0 * value2.y)) - (3.0 * value3.y)) + value4.y) * cubed));
  653. var z = 0.5 * ((((2.0 * value2.z) + ((-value1.z + value3.z) * amount)) + (((((2.0 * value1.z) - (5.0 * value2.z)) + (4.0 * value3.z)) - value4.z) * squared)) + ((((-value1.z + (3.0 * value2.z)) - (3.0 * value3.z)) + value4.z) * cubed));
  654. return new Vector3(x, y, z);
  655. };
  656. Vector3.Clamp = function (value, min, max) {
  657. var x = value.x;
  658. x = (x > max.x) ? max.x : x;
  659. x = (x < min.x) ? min.x : x;
  660. var y = value.y;
  661. y = (y > max.y) ? max.y : y;
  662. y = (y < min.y) ? min.y : y;
  663. var z = value.z;
  664. z = (z > max.z) ? max.z : z;
  665. z = (z < min.z) ? min.z : z;
  666. return new Vector3(x, y, z);
  667. };
  668. Vector3.Hermite = function (value1, tangent1, value2, tangent2, amount) {
  669. var squared = amount * amount;
  670. var cubed = amount * squared;
  671. var part1 = ((2.0 * cubed) - (3.0 * squared)) + 1.0;
  672. var part2 = (-2.0 * cubed) + (3.0 * squared);
  673. var part3 = (cubed - (2.0 * squared)) + amount;
  674. var part4 = cubed - squared;
  675. var x = (((value1.x * part1) + (value2.x * part2)) + (tangent1.x * part3)) + (tangent2.x * part4);
  676. var y = (((value1.y * part1) + (value2.y * part2)) + (tangent1.y * part3)) + (tangent2.y * part4);
  677. var z = (((value1.z * part1) + (value2.z * part2)) + (tangent1.z * part3)) + (tangent2.z * part4);
  678. return new Vector3(x, y, z);
  679. };
  680. Vector3.Lerp = function (start, end, amount) {
  681. var x = start.x + ((end.x - start.x) * amount);
  682. var y = start.y + ((end.y - start.y) * amount);
  683. var z = start.z + ((end.z - start.z) * amount);
  684. return new Vector3(x, y, z);
  685. };
  686. Vector3.Dot = function (left, right) {
  687. return (left.x * right.x + left.y * right.y + left.z * right.z);
  688. };
  689. Vector3.Cross = function (left, right) {
  690. var result = Vector3.Zero();
  691. Vector3.CrossToRef(left, right, result);
  692. return result;
  693. };
  694. Vector3.CrossToRef = function (left, right, result) {
  695. result.x = left.y * right.z - left.z * right.y;
  696. result.y = left.z * right.x - left.x * right.z;
  697. result.z = left.x * right.y - left.y * right.x;
  698. };
  699. Vector3.Normalize = function (vector) {
  700. var result = Vector3.Zero();
  701. Vector3.NormalizeToRef(vector, result);
  702. return result;
  703. };
  704. Vector3.NormalizeToRef = function (vector, result) {
  705. result.copyFrom(vector);
  706. result.normalize();
  707. };
  708. Vector3.Project = function (vector, world, transform, viewport) {
  709. var cw = viewport.width;
  710. var ch = viewport.height;
  711. var cx = viewport.x;
  712. var cy = viewport.y;
  713. var viewportMatrix = Matrix.FromValues(cw / 2.0, 0, 0, 0, 0, -ch / 2.0, 0, 0, 0, 0, 1, 0, cx + cw / 2.0, ch / 2.0 + cy, 0, 1);
  714. var finalMatrix = world.multiply(transform).multiply(viewportMatrix);
  715. return Vector3.TransformCoordinates(vector, finalMatrix);
  716. };
  717. Vector3.UnprojectFromTransform = function (source, viewportWidth, viewportHeight, world, transform) {
  718. var matrix = world.multiply(transform);
  719. matrix.invert();
  720. source.x = source.x / viewportWidth * 2 - 1;
  721. source.y = -(source.y / viewportHeight * 2 - 1);
  722. var vector = Vector3.TransformCoordinates(source, matrix);
  723. var num = source.x * matrix.m[3] + source.y * matrix.m[7] + source.z * matrix.m[11] + matrix.m[15];
  724. if (BABYLON.Tools.WithinEpsilon(num, 1.0)) {
  725. vector = vector.scale(1.0 / num);
  726. }
  727. return vector;
  728. };
  729. Vector3.Unproject = function (source, viewportWidth, viewportHeight, world, view, projection) {
  730. var matrix = world.multiply(view).multiply(projection);
  731. matrix.invert();
  732. source.x = source.x / viewportWidth * 2 - 1;
  733. source.y = -(source.y / viewportHeight * 2 - 1);
  734. var vector = Vector3.TransformCoordinates(source, matrix);
  735. var num = source.x * matrix.m[3] + source.y * matrix.m[7] + source.z * matrix.m[11] + matrix.m[15];
  736. if (BABYLON.Tools.WithinEpsilon(num, 1.0)) {
  737. vector = vector.scale(1.0 / num);
  738. }
  739. return vector;
  740. };
  741. Vector3.Minimize = function (left, right) {
  742. var min = left.clone();
  743. min.MinimizeInPlace(right);
  744. return min;
  745. };
  746. Vector3.Maximize = function (left, right) {
  747. var max = left.clone();
  748. max.MaximizeInPlace(right);
  749. return max;
  750. };
  751. Vector3.Distance = function (value1, value2) {
  752. return Math.sqrt(Vector3.DistanceSquared(value1, value2));
  753. };
  754. Vector3.DistanceSquared = function (value1, value2) {
  755. var x = value1.x - value2.x;
  756. var y = value1.y - value2.y;
  757. var z = value1.z - value2.z;
  758. return (x * x) + (y * y) + (z * z);
  759. };
  760. Vector3.Center = function (value1, value2) {
  761. var center = value1.add(value2);
  762. center.scaleInPlace(0.5);
  763. return center;
  764. };
  765. return Vector3;
  766. })();
  767. BABYLON.Vector3 = Vector3;
  768. //Vector4 class created for EulerAngle class conversion to Quaternion
  769. var Vector4 = (function () {
  770. function Vector4(x, y, z, w) {
  771. this.x = x;
  772. this.y = y;
  773. this.z = z;
  774. this.w = w;
  775. }
  776. Vector4.prototype.toString = function () {
  777. return "{X: " + this.x + " Y:" + this.y + " Z:" + this.z + "W:" + this.w + "}";
  778. };
  779. // Operators
  780. Vector4.prototype.asArray = function () {
  781. var result = [];
  782. this.toArray(result, 0);
  783. return result;
  784. };
  785. Vector4.prototype.toArray = function (array, index) {
  786. if (index === undefined) {
  787. index = 0;
  788. }
  789. array[index] = this.x;
  790. array[index + 1] = this.y;
  791. array[index + 2] = this.z;
  792. array[index + 3] = this.w;
  793. return this;
  794. };
  795. Vector4.prototype.addInPlace = function (otherVector) {
  796. this.x += otherVector.x;
  797. this.y += otherVector.y;
  798. this.z += otherVector.z;
  799. this.w += otherVector.w;
  800. return this;
  801. };
  802. Vector4.prototype.add = function (otherVector) {
  803. return new Vector4(this.x + otherVector.x, this.y + otherVector.y, this.z + otherVector.z, this.w + otherVector.w);
  804. };
  805. Vector4.prototype.addToRef = function (otherVector, result) {
  806. result.x = this.x + otherVector.x;
  807. result.y = this.y + otherVector.y;
  808. result.z = this.z + otherVector.z;
  809. result.w = this.w + otherVector.w;
  810. return this;
  811. };
  812. Vector4.prototype.subtractInPlace = function (otherVector) {
  813. this.x -= otherVector.x;
  814. this.y -= otherVector.y;
  815. this.z -= otherVector.z;
  816. this.w -= otherVector.w;
  817. return this;
  818. };
  819. Vector4.prototype.subtract = function (otherVector) {
  820. return new Vector4(this.x - otherVector.x, this.y - otherVector.y, this.z - otherVector.z, this.w - otherVector.w);
  821. };
  822. Vector4.prototype.subtractToRef = function (otherVector, result) {
  823. result.x = this.x - otherVector.x;
  824. result.y = this.y - otherVector.y;
  825. result.z = this.z - otherVector.z;
  826. result.w = this.w - otherVector.w;
  827. return this;
  828. };
  829. Vector4.prototype.subtractFromFloats = function (x, y, z, w) {
  830. return new Vector4(this.x - x, this.y - y, this.z - z, this.w - w);
  831. };
  832. Vector4.prototype.subtractFromFloatsToRef = function (x, y, z, w, result) {
  833. result.x = this.x - x;
  834. result.y = this.y - y;
  835. result.z = this.z - z;
  836. result.w = this.w - w;
  837. return this;
  838. };
  839. Vector4.prototype.negate = function () {
  840. return new Vector4(-this.x, -this.y, -this.z, -this.w);
  841. };
  842. Vector4.prototype.scaleInPlace = function (scale) {
  843. this.x *= scale;
  844. this.y *= scale;
  845. this.z *= scale;
  846. this.w *= scale;
  847. return this;
  848. };
  849. Vector4.prototype.scale = function (scale) {
  850. return new Vector4(this.x * scale, this.y * scale, this.z * scale, this.w * scale);
  851. };
  852. Vector4.prototype.scaleToRef = function (scale, result) {
  853. result.x = this.x * scale;
  854. result.y = this.y * scale;
  855. result.z = this.z * scale;
  856. result.w = this.w * scale;
  857. };
  858. Vector4.prototype.equals = function (otherVector) {
  859. return otherVector && this.x === otherVector.x && this.y === otherVector.y && this.z === otherVector.z && this.w === otherVector.w;
  860. };
  861. Vector4.prototype.equalsWithEpsilon = function (otherVector) {
  862. return Math.abs(this.x - otherVector.x) < BABYLON.Engine.Epsilon && Math.abs(this.y - otherVector.y) < BABYLON.Engine.Epsilon && Math.abs(this.z - otherVector.z) < BABYLON.Engine.Epsilon && Math.abs(this.w - otherVector.w) < BABYLON.Engine.Epsilon;
  863. };
  864. Vector4.prototype.equalsToFloats = function (x, y, z, w) {
  865. return this.x === x && this.y === y && this.z === z && this.w === w;
  866. };
  867. Vector4.prototype.multiplyInPlace = function (otherVector) {
  868. this.x *= otherVector.x;
  869. this.y *= otherVector.y;
  870. this.z *= otherVector.z;
  871. this.w *= otherVector.w;
  872. return this;
  873. };
  874. Vector4.prototype.multiply = function (otherVector) {
  875. return new Vector4(this.x * otherVector.x, this.y * otherVector.y, this.z * otherVector.z, this.w * otherVector.w);
  876. };
  877. Vector4.prototype.multiplyToRef = function (otherVector, result) {
  878. result.x = this.x * otherVector.x;
  879. result.y = this.y * otherVector.y;
  880. result.z = this.z * otherVector.z;
  881. result.w = this.w * otherVector.w;
  882. return this;
  883. };
  884. Vector4.prototype.multiplyByFloats = function (x, y, z, w) {
  885. return new Vector4(this.x * x, this.y * y, this.z * z, this.w * w);
  886. };
  887. Vector4.prototype.divide = function (otherVector) {
  888. return new Vector4(this.x / otherVector.x, this.y / otherVector.y, this.z / otherVector.z, this.w / otherVector.w);
  889. };
  890. Vector4.prototype.divideToRef = function (otherVector, result) {
  891. result.x = this.x / otherVector.x;
  892. result.y = this.y / otherVector.y;
  893. result.z = this.z / otherVector.z;
  894. result.w = this.w / otherVector.w;
  895. return this;
  896. };
  897. Vector4.prototype.MinimizeInPlace = function (other) {
  898. if (other.x < this.x)
  899. this.x = other.x;
  900. if (other.y < this.y)
  901. this.y = other.y;
  902. if (other.z < this.z)
  903. this.z = other.z;
  904. if (other.w < this.w)
  905. this.w = other.w;
  906. return this;
  907. };
  908. Vector4.prototype.MaximizeInPlace = function (other) {
  909. if (other.x > this.x)
  910. this.x = other.x;
  911. if (other.y > this.y)
  912. this.y = other.y;
  913. if (other.z > this.z)
  914. this.z = other.z;
  915. if (other.w > this.w)
  916. this.w = other.w;
  917. return this;
  918. };
  919. // Properties
  920. Vector4.prototype.length = function () {
  921. return Math.sqrt(this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w);
  922. };
  923. Vector4.prototype.lengthSquared = function () {
  924. return (this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w);
  925. };
  926. // Methods
  927. Vector4.prototype.normalize = function () {
  928. var len = this.length();
  929. if (len === 0)
  930. return this;
  931. var num = 1.0 / len;
  932. this.x *= num;
  933. this.y *= num;
  934. this.z *= num;
  935. this.w *= num;
  936. return this;
  937. };
  938. Vector4.prototype.clone = function () {
  939. return new Vector4(this.x, this.y, this.z, this.w);
  940. };
  941. Vector4.prototype.copyFrom = function (source) {
  942. this.x = source.x;
  943. this.y = source.y;
  944. this.z = source.z;
  945. this.w = source.w;
  946. return this;
  947. };
  948. Vector4.prototype.copyFromFloats = function (x, y, z, w) {
  949. this.x = x;
  950. this.y = y;
  951. this.z = z;
  952. this.w = w;
  953. return this;
  954. };
  955. // Statics
  956. Vector4.FromArray = function (array, offset) {
  957. if (!offset) {
  958. offset = 0;
  959. }
  960. return new Vector4(array[offset], array[offset + 1], array[offset + 2], array[offset + 3]);
  961. };
  962. Vector4.FromArrayToRef = function (array, offset, result) {
  963. result.x = array[offset];
  964. result.y = array[offset + 1];
  965. result.z = array[offset + 2];
  966. result.w = array[offset + 3];
  967. };
  968. Vector4.FromFloatArrayToRef = function (array, offset, result) {
  969. result.x = array[offset];
  970. result.y = array[offset + 1];
  971. result.z = array[offset + 2];
  972. result.w = array[offset + 3];
  973. };
  974. Vector4.FromFloatsToRef = function (x, y, z, w, result) {
  975. result.x = x;
  976. result.y = y;
  977. result.z = z;
  978. result.w = w;
  979. };
  980. Vector4.Zero = function () {
  981. return new Vector4(0, 0, 0, 0);
  982. };
  983. Vector4.Normalize = function (vector) {
  984. var result = Vector4.Zero();
  985. Vector4.NormalizeToRef(vector, result);
  986. return result;
  987. };
  988. Vector4.NormalizeToRef = function (vector, result) {
  989. result.copyFrom(vector);
  990. result.normalize();
  991. };
  992. Vector4.Minimize = function (left, right) {
  993. var min = left.clone();
  994. min.MinimizeInPlace(right);
  995. return min;
  996. };
  997. Vector4.Maximize = function (left, right) {
  998. var max = left.clone();
  999. max.MaximizeInPlace(right);
  1000. return max;
  1001. };
  1002. Vector4.Distance = function (value1, value2) {
  1003. return Math.sqrt(Vector4.DistanceSquared(value1, value2));
  1004. };
  1005. Vector4.DistanceSquared = function (value1, value2) {
  1006. var x = value1.x - value2.x;
  1007. var y = value1.y - value2.y;
  1008. var z = value1.z - value2.z;
  1009. var w = value1.w - value2.w;
  1010. return (x * x) + (y * y) + (z * z) + (w * w);
  1011. };
  1012. Vector4.Center = function (value1, value2) {
  1013. var center = value1.add(value2);
  1014. center.scaleInPlace(0.5);
  1015. return center;
  1016. };
  1017. return Vector4;
  1018. })();
  1019. BABYLON.Vector4 = Vector4;
  1020. var Quaternion = (function () {
  1021. function Quaternion(x, y, z, w) {
  1022. if (x === void 0) { x = 0; }
  1023. if (y === void 0) { y = 0; }
  1024. if (z === void 0) { z = 0; }
  1025. if (w === void 0) { w = 1; }
  1026. this.x = x;
  1027. this.y = y;
  1028. this.z = z;
  1029. this.w = w;
  1030. }
  1031. Quaternion.prototype.toString = function () {
  1032. return "{X: " + this.x + " Y:" + this.y + " Z:" + this.z + " W:" + this.w + "}";
  1033. };
  1034. Quaternion.prototype.asArray = function () {
  1035. return [this.x, this.y, this.z, this.w];
  1036. };
  1037. Quaternion.prototype.equals = function (otherQuaternion) {
  1038. return otherQuaternion && this.x === otherQuaternion.x && this.y === otherQuaternion.y && this.z === otherQuaternion.z && this.w === otherQuaternion.w;
  1039. };
  1040. Quaternion.prototype.clone = function () {
  1041. return new Quaternion(this.x, this.y, this.z, this.w);
  1042. };
  1043. Quaternion.prototype.copyFrom = function (other) {
  1044. this.x = other.x;
  1045. this.y = other.y;
  1046. this.z = other.z;
  1047. this.w = other.w;
  1048. return this;
  1049. };
  1050. Quaternion.prototype.copyFromFloats = function (x, y, z, w) {
  1051. this.x = x;
  1052. this.y = y;
  1053. this.z = z;
  1054. this.w = w;
  1055. return this;
  1056. };
  1057. Quaternion.prototype.add = function (other) {
  1058. return new Quaternion(this.x + other.x, this.y + other.y, this.z + other.z, this.w + other.w);
  1059. };
  1060. Quaternion.prototype.subtract = function (other) {
  1061. return new Quaternion(this.x - other.x, this.y - other.y, this.z - other.z, this.w - other.w);
  1062. };
  1063. Quaternion.prototype.scale = function (value) {
  1064. return new Quaternion(this.x * value, this.y * value, this.z * value, this.w * value);
  1065. };
  1066. Quaternion.prototype.multiply = function (q1) {
  1067. var result = new Quaternion(0, 0, 0, 1.0);
  1068. this.multiplyToRef(q1, result);
  1069. return result;
  1070. };
  1071. Quaternion.prototype.multiplyToRef = function (q1, result) {
  1072. result.x = this.x * q1.w + this.y * q1.z - this.z * q1.y + this.w * q1.x;
  1073. result.y = -this.x * q1.z + this.y * q1.w + this.z * q1.x + this.w * q1.y;
  1074. result.z = this.x * q1.y - this.y * q1.x + this.z * q1.w + this.w * q1.z;
  1075. result.w = -this.x * q1.x - this.y * q1.y - this.z * q1.z + this.w * q1.w;
  1076. return this;
  1077. };
  1078. Quaternion.prototype.length = function () {
  1079. return Math.sqrt((this.x * this.x) + (this.y * this.y) + (this.z * this.z) + (this.w * this.w));
  1080. };
  1081. Quaternion.prototype.normalize = function () {
  1082. var length = 1.0 / this.length();
  1083. this.x *= length;
  1084. this.y *= length;
  1085. this.z *= length;
  1086. this.w *= length;
  1087. return this;
  1088. };
  1089. Quaternion.prototype.toEulerAngles = function () {
  1090. var result = Vector3.Zero();
  1091. this.toEulerAnglesToRef(result);
  1092. return result;
  1093. };
  1094. Quaternion.prototype.toEulerAnglesToRef = function (result) {
  1095. //result is an EulerAngles in the in the z-x-z convention
  1096. var qx = this.x;
  1097. var qy = this.y;
  1098. var qz = this.z;
  1099. var qw = this.w;
  1100. var qxy = qx * qy;
  1101. var qxz = qx * qz;
  1102. var qwy = qw * qy;
  1103. var qwz = qw * qz;
  1104. var qwx = qw * qx;
  1105. var qyz = qy * qz;
  1106. var sqx = qx * qx;
  1107. var sqy = qy * qy;
  1108. var determinant = sqx + sqy;
  1109. if (determinant !== 0.000 && determinant !== 1.000) {
  1110. result.x = Math.atan2(qxz + qwy, qwx - qyz);
  1111. result.y = Math.acos(1 - 2 * determinant);
  1112. result.z = Math.atan2(qxz - qwy, qwx + qyz);
  1113. }
  1114. else {
  1115. if (determinant === 0.0) {
  1116. result.x = 0.0;
  1117. result.y = 0.0;
  1118. result.z = Math.atan2(qxy - qwz, 0.5 - sqy - qz * qz); //actually, degeneracy gives us choice with x+z=Math.atan2(qxy-qwz,0.5-sqy-qz*qz)
  1119. }
  1120. else {
  1121. result.x = Math.atan2(qxy - qwz, 0.5 - sqy - qz * qz); //actually, degeneracy gives us choice with x-z=Math.atan2(qxy-qwz,0.5-sqy-qz*qz)
  1122. result.y = Math.PI;
  1123. result.z = 0.0;
  1124. }
  1125. }
  1126. return this;
  1127. };
  1128. Quaternion.prototype.toRotationMatrix = function (result) {
  1129. var xx = this.x * this.x;
  1130. var yy = this.y * this.y;
  1131. var zz = this.z * this.z;
  1132. var xy = this.x * this.y;
  1133. var zw = this.z * this.w;
  1134. var zx = this.z * this.x;
  1135. var yw = this.y * this.w;
  1136. var yz = this.y * this.z;
  1137. var xw = this.x * this.w;
  1138. result.m[0] = 1.0 - (2.0 * (yy + zz));
  1139. result.m[1] = 2.0 * (xy + zw);
  1140. result.m[2] = 2.0 * (zx - yw);
  1141. result.m[3] = 0;
  1142. result.m[4] = 2.0 * (xy - zw);
  1143. result.m[5] = 1.0 - (2.0 * (zz + xx));
  1144. result.m[6] = 2.0 * (yz + xw);
  1145. result.m[7] = 0;
  1146. result.m[8] = 2.0 * (zx + yw);
  1147. result.m[9] = 2.0 * (yz - xw);
  1148. result.m[10] = 1.0 - (2.0 * (yy + xx));
  1149. result.m[11] = 0;
  1150. result.m[12] = 0;
  1151. result.m[13] = 0;
  1152. result.m[14] = 0;
  1153. result.m[15] = 1.0;
  1154. return this;
  1155. };
  1156. Quaternion.prototype.fromRotationMatrix = function (matrix) {
  1157. Quaternion.FromRotationMatrixToRef(matrix, this);
  1158. return this;
  1159. };
  1160. // Statics
  1161. Quaternion.FromRotationMatrix = function (matrix) {
  1162. var result = new Quaternion();
  1163. Quaternion.FromRotationMatrixToRef(matrix, result);
  1164. return result;
  1165. };
  1166. Quaternion.FromRotationMatrixToRef = function (matrix, result) {
  1167. var data = matrix.m;
  1168. var m11 = data[0], m12 = data[4], m13 = data[8];
  1169. var m21 = data[1], m22 = data[5], m23 = data[9];
  1170. var m31 = data[2], m32 = data[6], m33 = data[10];
  1171. var trace = m11 + m22 + m33;
  1172. var s;
  1173. if (trace > 0) {
  1174. s = 0.5 / Math.sqrt(trace + 1.0);
  1175. result.w = 0.25 / s;
  1176. result.x = (m32 - m23) * s;
  1177. result.y = (m13 - m31) * s;
  1178. result.z = (m21 - m12) * s;
  1179. }
  1180. else if (m11 > m22 && m11 > m33) {
  1181. s = 2.0 * Math.sqrt(1.0 + m11 - m22 - m33);
  1182. result.w = (m32 - m23) / s;
  1183. result.x = 0.25 * s;
  1184. result.y = (m12 + m21) / s;
  1185. result.z = (m13 + m31) / s;
  1186. }
  1187. else if (m22 > m33) {
  1188. s = 2.0 * Math.sqrt(1.0 + m22 - m11 - m33);
  1189. result.w = (m13 - m31) / s;
  1190. result.x = (m12 + m21) / s;
  1191. result.y = 0.25 * s;
  1192. result.z = (m23 + m32) / s;
  1193. }
  1194. else {
  1195. s = 2.0 * Math.sqrt(1.0 + m33 - m11 - m22);
  1196. result.w = (m21 - m12) / s;
  1197. result.x = (m13 + m31) / s;
  1198. result.y = (m23 + m32) / s;
  1199. result.z = 0.25 * s;
  1200. }
  1201. };
  1202. Quaternion.Inverse = function (q) {
  1203. return new Quaternion(-q.x, -q.y, -q.z, q.w);
  1204. };
  1205. Quaternion.Identity = function () {
  1206. return new Quaternion(0, 0, 0, 1);
  1207. };
  1208. Quaternion.RotationAxis = function (axis, angle) {
  1209. var result = new Quaternion();
  1210. var sin = Math.sin(angle / 2);
  1211. result.w = Math.cos(angle / 2);
  1212. result.x = axis.x * sin;
  1213. result.y = axis.y * sin;
  1214. result.z = axis.z * sin;
  1215. return result;
  1216. };
  1217. Quaternion.FromArray = function (array, offset) {
  1218. if (!offset) {
  1219. offset = 0;
  1220. }
  1221. return new Quaternion(array[offset], array[offset + 1], array[offset + 2], array[offset + 3]);
  1222. };
  1223. Quaternion.RotationYawPitchRoll = function (yaw, pitch, roll) {
  1224. var result = new Quaternion();
  1225. Quaternion.RotationYawPitchRollToRef(yaw, pitch, roll, result);
  1226. return result;
  1227. };
  1228. Quaternion.RotationYawPitchRollToRef = function (yaw, pitch, roll, result) {
  1229. // Produces a quaternion from Euler angles in the z-y-x orientation (Tait-Bryan angles)
  1230. var halfRoll = roll * 0.5;
  1231. var halfPitch = pitch * 0.5;
  1232. var halfYaw = yaw * 0.5;
  1233. var sinRoll = Math.sin(halfRoll);
  1234. var cosRoll = Math.cos(halfRoll);
  1235. var sinPitch = Math.sin(halfPitch);
  1236. var cosPitch = Math.cos(halfPitch);
  1237. var sinYaw = Math.sin(halfYaw);
  1238. var cosYaw = Math.cos(halfYaw);
  1239. result.x = (cosYaw * sinPitch * cosRoll) + (sinYaw * cosPitch * sinRoll);
  1240. result.y = (sinYaw * cosPitch * cosRoll) - (cosYaw * sinPitch * sinRoll);
  1241. result.z = (cosYaw * cosPitch * sinRoll) - (sinYaw * sinPitch * cosRoll);
  1242. result.w = (cosYaw * cosPitch * cosRoll) + (sinYaw * sinPitch * sinRoll);
  1243. };
  1244. Quaternion.RotationAlphaBetaGamma = function (alpha, beta, gamma) {
  1245. var result = new Quaternion();
  1246. Quaternion.RotationAlphaBetaGammaToRef(alpha, beta, gamma, result);
  1247. return result;
  1248. };
  1249. Quaternion.RotationAlphaBetaGammaToRef = function (alpha, beta, gamma, result) {
  1250. // Produces a quaternion from Euler angles in the z-x-z orientation
  1251. var halfGammaPlusAlpha = (gamma + alpha) * 0.5;
  1252. var halfGammaMinusAlpha = (gamma - alpha) * 0.5;
  1253. var halfBeta = beta * 0.5;
  1254. result.x = Math.cos(halfGammaMinusAlpha) * Math.sin(halfBeta);
  1255. result.y = Math.sin(halfGammaMinusAlpha) * Math.sin(halfBeta);
  1256. result.z = Math.sin(halfGammaPlusAlpha) * Math.cos(halfBeta);
  1257. result.w = Math.cos(halfGammaPlusAlpha) * Math.cos(halfBeta);
  1258. };
  1259. Quaternion.Slerp = function (left, right, amount) {
  1260. var num2;
  1261. var num3;
  1262. var num = amount;
  1263. var num4 = (((left.x * right.x) + (left.y * right.y)) + (left.z * right.z)) + (left.w * right.w);
  1264. var flag = false;
  1265. if (num4 < 0) {
  1266. flag = true;
  1267. num4 = -num4;
  1268. }
  1269. if (num4 > 0.999999) {
  1270. num3 = 1 - num;
  1271. num2 = flag ? -num : num;
  1272. }
  1273. else {
  1274. var num5 = Math.acos(num4);
  1275. var num6 = (1.0 / Math.sin(num5));
  1276. num3 = (Math.sin((1.0 - num) * num5)) * num6;
  1277. num2 = flag ? ((-Math.sin(num * num5)) * num6) : ((Math.sin(num * num5)) * num6);
  1278. }
  1279. return new Quaternion((num3 * left.x) + (num2 * right.x), (num3 * left.y) + (num2 * right.y), (num3 * left.z) + (num2 * right.z), (num3 * left.w) + (num2 * right.w));
  1280. };
  1281. return Quaternion;
  1282. })();
  1283. BABYLON.Quaternion = Quaternion;
  1284. var Matrix = (function () {
  1285. function Matrix() {
  1286. this.m = new Float32Array(16);
  1287. }
  1288. // Properties
  1289. Matrix.prototype.isIdentity = function () {
  1290. if (this.m[0] !== 1.0 || this.m[5] !== 1.0 || this.m[10] !== 1.0 || this.m[15] !== 1.0)
  1291. return false;
  1292. if (this.m[1] !== 0.0 || this.m[2] !== 0.0 || this.m[3] !== 0.0 || this.m[4] !== 0.0 || this.m[6] !== 0.0 || this.m[7] !== 0.0 || this.m[8] !== 0.0 || this.m[9] !== 0.0 || this.m[11] !== 0.0 || this.m[12] !== 0.0 || this.m[13] !== 0.0 || this.m[14] !== 0.0)
  1293. return false;
  1294. return true;
  1295. };
  1296. Matrix.prototype.determinant = function () {
  1297. var temp1 = (this.m[10] * this.m[15]) - (this.m[11] * this.m[14]);
  1298. var temp2 = (this.m[9] * this.m[15]) - (this.m[11] * this.m[13]);
  1299. var temp3 = (this.m[9] * this.m[14]) - (this.m[10] * this.m[13]);
  1300. var temp4 = (this.m[8] * this.m[15]) - (this.m[11] * this.m[12]);
  1301. var temp5 = (this.m[8] * this.m[14]) - (this.m[10] * this.m[12]);
  1302. var temp6 = (this.m[8] * this.m[13]) - (this.m[9] * this.m[12]);
  1303. return ((((this.m[0] * (((this.m[5] * temp1) - (this.m[6] * temp2)) + (this.m[7] * temp3))) - (this.m[1] * (((this.m[4] * temp1) - (this.m[6] * temp4)) + (this.m[7] * temp5)))) + (this.m[2] * (((this.m[4] * temp2) - (this.m[5] * temp4)) + (this.m[7] * temp6)))) - (this.m[3] * (((this.m[4] * temp3) - (this.m[5] * temp5)) + (this.m[6] * temp6))));
  1304. };
  1305. // Methods
  1306. Matrix.prototype.toArray = function () {
  1307. return this.m;
  1308. };
  1309. Matrix.prototype.asArray = function () {
  1310. return this.toArray();
  1311. };
  1312. Matrix.prototype.invert = function () {
  1313. this.invertToRef(this);
  1314. return this;
  1315. };
  1316. Matrix.prototype.invertToRef = function (other) {
  1317. var l1 = this.m[0];
  1318. var l2 = this.m[1];
  1319. var l3 = this.m[2];
  1320. var l4 = this.m[3];
  1321. var l5 = this.m[4];
  1322. var l6 = this.m[5];
  1323. var l7 = this.m[6];
  1324. var l8 = this.m[7];
  1325. var l9 = this.m[8];
  1326. var l10 = this.m[9];
  1327. var l11 = this.m[10];
  1328. var l12 = this.m[11];
  1329. var l13 = this.m[12];
  1330. var l14 = this.m[13];
  1331. var l15 = this.m[14];
  1332. var l16 = this.m[15];
  1333. var l17 = (l11 * l16) - (l12 * l15);
  1334. var l18 = (l10 * l16) - (l12 * l14);
  1335. var l19 = (l10 * l15) - (l11 * l14);
  1336. var l20 = (l9 * l16) - (l12 * l13);
  1337. var l21 = (l9 * l15) - (l11 * l13);
  1338. var l22 = (l9 * l14) - (l10 * l13);
  1339. var l23 = ((l6 * l17) - (l7 * l18)) + (l8 * l19);
  1340. var l24 = -(((l5 * l17) - (l7 * l20)) + (l8 * l21));
  1341. var l25 = ((l5 * l18) - (l6 * l20)) + (l8 * l22);
  1342. var l26 = -(((l5 * l19) - (l6 * l21)) + (l7 * l22));
  1343. var l27 = 1.0 / ((((l1 * l23) + (l2 * l24)) + (l3 * l25)) + (l4 * l26));
  1344. var l28 = (l7 * l16) - (l8 * l15);
  1345. var l29 = (l6 * l16) - (l8 * l14);
  1346. var l30 = (l6 * l15) - (l7 * l14);
  1347. var l31 = (l5 * l16) - (l8 * l13);
  1348. var l32 = (l5 * l15) - (l7 * l13);
  1349. var l33 = (l5 * l14) - (l6 * l13);
  1350. var l34 = (l7 * l12) - (l8 * l11);
  1351. var l35 = (l6 * l12) - (l8 * l10);
  1352. var l36 = (l6 * l11) - (l7 * l10);
  1353. var l37 = (l5 * l12) - (l8 * l9);
  1354. var l38 = (l5 * l11) - (l7 * l9);
  1355. var l39 = (l5 * l10) - (l6 * l9);
  1356. other.m[0] = l23 * l27;
  1357. other.m[4] = l24 * l27;
  1358. other.m[8] = l25 * l27;
  1359. other.m[12] = l26 * l27;
  1360. other.m[1] = -(((l2 * l17) - (l3 * l18)) + (l4 * l19)) * l27;
  1361. other.m[5] = (((l1 * l17) - (l3 * l20)) + (l4 * l21)) * l27;
  1362. other.m[9] = -(((l1 * l18) - (l2 * l20)) + (l4 * l22)) * l27;
  1363. other.m[13] = (((l1 * l19) - (l2 * l21)) + (l3 * l22)) * l27;
  1364. other.m[2] = (((l2 * l28) - (l3 * l29)) + (l4 * l30)) * l27;
  1365. other.m[6] = -(((l1 * l28) - (l3 * l31)) + (l4 * l32)) * l27;
  1366. other.m[10] = (((l1 * l29) - (l2 * l31)) + (l4 * l33)) * l27;
  1367. other.m[14] = -(((l1 * l30) - (l2 * l32)) + (l3 * l33)) * l27;
  1368. other.m[3] = -(((l2 * l34) - (l3 * l35)) + (l4 * l36)) * l27;
  1369. other.m[7] = (((l1 * l34) - (l3 * l37)) + (l4 * l38)) * l27;
  1370. other.m[11] = -(((l1 * l35) - (l2 * l37)) + (l4 * l39)) * l27;
  1371. other.m[15] = (((l1 * l36) - (l2 * l38)) + (l3 * l39)) * l27;
  1372. return this;
  1373. };
  1374. Matrix.prototype.setTranslation = function (vector3) {
  1375. this.m[12] = vector3.x;
  1376. this.m[13] = vector3.y;
  1377. this.m[14] = vector3.z;
  1378. return this;
  1379. };
  1380. Matrix.prototype.multiply = function (other) {
  1381. var result = new Matrix();
  1382. this.multiplyToRef(other, result);
  1383. return result;
  1384. };
  1385. Matrix.prototype.copyFrom = function (other) {
  1386. for (var index = 0; index < 16; index++) {
  1387. this.m[index] = other.m[index];
  1388. }
  1389. return this;
  1390. };
  1391. Matrix.prototype.copyToArray = function (array, offset) {
  1392. if (offset === void 0) { offset = 0; }
  1393. for (var index = 0; index < 16; index++) {
  1394. array[offset + index] = this.m[index];
  1395. }
  1396. return this;
  1397. };
  1398. Matrix.prototype.multiplyToRef = function (other, result) {
  1399. this.multiplyToArray(other, result.m, 0);
  1400. return this;
  1401. };
  1402. Matrix.prototype.multiplyToArray = function (other, result, offset) {
  1403. var tm0 = this.m[0];
  1404. var tm1 = this.m[1];
  1405. var tm2 = this.m[2];
  1406. var tm3 = this.m[3];
  1407. var tm4 = this.m[4];
  1408. var tm5 = this.m[5];
  1409. var tm6 = this.m[6];
  1410. var tm7 = this.m[7];
  1411. var tm8 = this.m[8];
  1412. var tm9 = this.m[9];
  1413. var tm10 = this.m[10];
  1414. var tm11 = this.m[11];
  1415. var tm12 = this.m[12];
  1416. var tm13 = this.m[13];
  1417. var tm14 = this.m[14];
  1418. var tm15 = this.m[15];
  1419. var om0 = other.m[0];
  1420. var om1 = other.m[1];
  1421. var om2 = other.m[2];
  1422. var om3 = other.m[3];
  1423. var om4 = other.m[4];
  1424. var om5 = other.m[5];
  1425. var om6 = other.m[6];
  1426. var om7 = other.m[7];
  1427. var om8 = other.m[8];
  1428. var om9 = other.m[9];
  1429. var om10 = other.m[10];
  1430. var om11 = other.m[11];
  1431. var om12 = other.m[12];
  1432. var om13 = other.m[13];
  1433. var om14 = other.m[14];
  1434. var om15 = other.m[15];
  1435. result[offset] = tm0 * om0 + tm1 * om4 + tm2 * om8 + tm3 * om12;
  1436. result[offset + 1] = tm0 * om1 + tm1 * om5 + tm2 * om9 + tm3 * om13;
  1437. result[offset + 2] = tm0 * om2 + tm1 * om6 + tm2 * om10 + tm3 * om14;
  1438. result[offset + 3] = tm0 * om3 + tm1 * om7 + tm2 * om11 + tm3 * om15;
  1439. result[offset + 4] = tm4 * om0 + tm5 * om4 + tm6 * om8 + tm7 * om12;
  1440. result[offset + 5] = tm4 * om1 + tm5 * om5 + tm6 * om9 + tm7 * om13;
  1441. result[offset + 6] = tm4 * om2 + tm5 * om6 + tm6 * om10 + tm7 * om14;
  1442. result[offset + 7] = tm4 * om3 + tm5 * om7 + tm6 * om11 + tm7 * om15;
  1443. result[offset + 8] = tm8 * om0 + tm9 * om4 + tm10 * om8 + tm11 * om12;
  1444. result[offset + 9] = tm8 * om1 + tm9 * om5 + tm10 * om9 + tm11 * om13;
  1445. result[offset + 10] = tm8 * om2 + tm9 * om6 + tm10 * om10 + tm11 * om14;
  1446. result[offset + 11] = tm8 * om3 + tm9 * om7 + tm10 * om11 + tm11 * om15;
  1447. result[offset + 12] = tm12 * om0 + tm13 * om4 + tm14 * om8 + tm15 * om12;
  1448. result[offset + 13] = tm12 * om1 + tm13 * om5 + tm14 * om9 + tm15 * om13;
  1449. result[offset + 14] = tm12 * om2 + tm13 * om6 + tm14 * om10 + tm15 * om14;
  1450. result[offset + 15] = tm12 * om3 + tm13 * om7 + tm14 * om11 + tm15 * om15;
  1451. return this;
  1452. };
  1453. Matrix.prototype.equals = function (value) {
  1454. return value && (this.m[0] === value.m[0] && this.m[1] === value.m[1] && this.m[2] === value.m[2] && this.m[3] === value.m[3] && this.m[4] === value.m[4] && this.m[5] === value.m[5] && this.m[6] === value.m[6] && this.m[7] === value.m[7] && this.m[8] === value.m[8] && this.m[9] === value.m[9] && this.m[10] === value.m[10] && this.m[11] === value.m[11] && this.m[12] === value.m[12] && this.m[13] === value.m[13] && this.m[14] === value.m[14] && this.m[15] === value.m[15]);
  1455. };
  1456. Matrix.prototype.clone = function () {
  1457. return Matrix.FromValues(this.m[0], this.m[1], this.m[2], this.m[3], this.m[4], this.m[5], this.m[6], this.m[7], this.m[8], this.m[9], this.m[10], this.m[11], this.m[12], this.m[13], this.m[14], this.m[15]);
  1458. };
  1459. Matrix.prototype.decompose = function (scale, rotation, translation) {
  1460. translation.x = this.m[12];
  1461. translation.y = this.m[13];
  1462. translation.z = this.m[14];
  1463. var xs = BABYLON.Tools.Sign(this.m[0] * this.m[1] * this.m[2] * this.m[3]) < 0 ? -1 : 1;
  1464. var ys = BABYLON.Tools.Sign(this.m[4] * this.m[5] * this.m[6] * this.m[7]) < 0 ? -1 : 1;
  1465. var zs = BABYLON.Tools.Sign(this.m[8] * this.m[9] * this.m[10] * this.m[11]) < 0 ? -1 : 1;
  1466. scale.x = xs * Math.sqrt(this.m[0] * this.m[0] + this.m[1] * this.m[1] + this.m[2] * this.m[2]);
  1467. scale.y = ys * Math.sqrt(this.m[4] * this.m[4] + this.m[5] * this.m[5] + this.m[6] * this.m[6]);
  1468. scale.z = zs * Math.sqrt(this.m[8] * this.m[8] + this.m[9] * this.m[9] + this.m[10] * this.m[10]);
  1469. if (scale.x === 0 || scale.y === 0 || scale.z === 0) {
  1470. rotation.x = 0;
  1471. rotation.y = 0;
  1472. rotation.z = 0;
  1473. rotation.w = 1;
  1474. return false;
  1475. }
  1476. var rotationMatrix = Matrix.FromValues(this.m[0] / scale.x, this.m[1] / scale.x, this.m[2] / scale.x, 0, this.m[4] / scale.y, this.m[5] / scale.y, this.m[6] / scale.y, 0, this.m[8] / scale.z, this.m[9] / scale.z, this.m[10] / scale.z, 0, 0, 0, 0, 1);
  1477. Quaternion.FromRotationMatrixToRef(rotationMatrix, rotation);
  1478. return true;
  1479. };
  1480. // Statics
  1481. Matrix.FromArray = function (array, offset) {
  1482. var result = new Matrix();
  1483. if (!offset) {
  1484. offset = 0;
  1485. }
  1486. Matrix.FromArrayToRef(array, offset, result);
  1487. return result;
  1488. };
  1489. Matrix.FromArrayToRef = function (array, offset, result) {
  1490. for (var index = 0; index < 16; index++) {
  1491. result.m[index] = array[index + offset];
  1492. }
  1493. };
  1494. Matrix.FromValuesToRef = function (initialM11, initialM12, initialM13, initialM14, initialM21, initialM22, initialM23, initialM24, initialM31, initialM32, initialM33, initialM34, initialM41, initialM42, initialM43, initialM44, result) {
  1495. result.m[0] = initialM11;
  1496. result.m[1] = initialM12;
  1497. result.m[2] = initialM13;
  1498. result.m[3] = initialM14;
  1499. result.m[4] = initialM21;
  1500. result.m[5] = initialM22;
  1501. result.m[6] = initialM23;
  1502. result.m[7] = initialM24;
  1503. result.m[8] = initialM31;
  1504. result.m[9] = initialM32;
  1505. result.m[10] = initialM33;
  1506. result.m[11] = initialM34;
  1507. result.m[12] = initialM41;
  1508. result.m[13] = initialM42;
  1509. result.m[14] = initialM43;
  1510. result.m[15] = initialM44;
  1511. };
  1512. Matrix.FromValues = function (initialM11, initialM12, initialM13, initialM14, initialM21, initialM22, initialM23, initialM24, initialM31, initialM32, initialM33, initialM34, initialM41, initialM42, initialM43, initialM44) {
  1513. var result = new Matrix();
  1514. result.m[0] = initialM11;
  1515. result.m[1] = initialM12;
  1516. result.m[2] = initialM13;
  1517. result.m[3] = initialM14;
  1518. result.m[4] = initialM21;
  1519. result.m[5] = initialM22;
  1520. result.m[6] = initialM23;
  1521. result.m[7] = initialM24;
  1522. result.m[8] = initialM31;
  1523. result.m[9] = initialM32;
  1524. result.m[10] = initialM33;
  1525. result.m[11] = initialM34;
  1526. result.m[12] = initialM41;
  1527. result.m[13] = initialM42;
  1528. result.m[14] = initialM43;
  1529. result.m[15] = initialM44;
  1530. return result;
  1531. };
  1532. Matrix.Compose = function (scale, rotation, translation) {
  1533. var result = Matrix.FromValues(scale.x, 0, 0, 0, 0, scale.y, 0, 0, 0, 0, scale.z, 0, 0, 0, 0, 1);
  1534. var rotationMatrix = Matrix.Identity();
  1535. rotation.toRotationMatrix(rotationMatrix);
  1536. result = result.multiply(rotationMatrix);
  1537. result.setTranslation(translation);
  1538. return result;
  1539. };
  1540. Matrix.Identity = function () {
  1541. return Matrix.FromValues(1.0, 0, 0, 0, 0, 1.0, 0, 0, 0, 0, 1.0, 0, 0, 0, 0, 1.0);
  1542. };
  1543. Matrix.IdentityToRef = function (result) {
  1544. Matrix.FromValuesToRef(1.0, 0, 0, 0, 0, 1.0, 0, 0, 0, 0, 1.0, 0, 0, 0, 0, 1.0, result);
  1545. };
  1546. Matrix.Zero = function () {
  1547. return Matrix.FromValues(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
  1548. };
  1549. Matrix.RotationX = function (angle) {
  1550. var result = new Matrix();
  1551. Matrix.RotationXToRef(angle, result);
  1552. return result;
  1553. };
  1554. Matrix.Invert = function (source) {
  1555. var result = new Matrix();
  1556. source.invertToRef(result);
  1557. return result;
  1558. };
  1559. Matrix.RotationXToRef = function (angle, result) {
  1560. var s = Math.sin(angle);
  1561. var c = Math.cos(angle);
  1562. result.m[0] = 1.0;
  1563. result.m[15] = 1.0;
  1564. result.m[5] = c;
  1565. result.m[10] = c;
  1566. result.m[9] = -s;
  1567. result.m[6] = s;
  1568. result.m[1] = 0;
  1569. result.m[2] = 0;
  1570. result.m[3] = 0;
  1571. result.m[4] = 0;
  1572. result.m[7] = 0;
  1573. result.m[8] = 0;
  1574. result.m[11] = 0;
  1575. result.m[12] = 0;
  1576. result.m[13] = 0;
  1577. result.m[14] = 0;
  1578. };
  1579. Matrix.RotationY = function (angle) {
  1580. var result = new Matrix();
  1581. Matrix.RotationYToRef(angle, result);
  1582. return result;
  1583. };
  1584. Matrix.RotationYToRef = function (angle, result) {
  1585. var s = Math.sin(angle);
  1586. var c = Math.cos(angle);
  1587. result.m[5] = 1.0;
  1588. result.m[15] = 1.0;
  1589. result.m[0] = c;
  1590. result.m[2] = -s;
  1591. result.m[8] = s;
  1592. result.m[10] = c;
  1593. result.m[1] = 0;
  1594. result.m[3] = 0;
  1595. result.m[4] = 0;
  1596. result.m[6] = 0;
  1597. result.m[7] = 0;
  1598. result.m[9] = 0;
  1599. result.m[11] = 0;
  1600. result.m[12] = 0;
  1601. result.m[13] = 0;
  1602. result.m[14] = 0;
  1603. };
  1604. Matrix.RotationZ = function (angle) {
  1605. var result = new Matrix();
  1606. Matrix.RotationZToRef(angle, result);
  1607. return result;
  1608. };
  1609. Matrix.RotationZToRef = function (angle, result) {
  1610. var s = Math.sin(angle);
  1611. var c = Math.cos(angle);
  1612. result.m[10] = 1.0;
  1613. result.m[15] = 1.0;
  1614. result.m[0] = c;
  1615. result.m[1] = s;
  1616. result.m[4] = -s;
  1617. result.m[5] = c;
  1618. result.m[2] = 0;
  1619. result.m[3] = 0;
  1620. result.m[6] = 0;
  1621. result.m[7] = 0;
  1622. result.m[8] = 0;
  1623. result.m[9] = 0;
  1624. result.m[11] = 0;
  1625. result.m[12] = 0;
  1626. result.m[13] = 0;
  1627. result.m[14] = 0;
  1628. };
  1629. Matrix.RotationAxis = function (axis, angle) {
  1630. var s = Math.sin(-angle);
  1631. var c = Math.cos(-angle);
  1632. var c1 = 1 - c;
  1633. axis.normalize();
  1634. var result = Matrix.Zero();
  1635. result.m[0] = (axis.x * axis.x) * c1 + c;
  1636. result.m[1] = (axis.x * axis.y) * c1 - (axis.z * s);
  1637. result.m[2] = (axis.x * axis.z) * c1 + (axis.y * s);
  1638. result.m[3] = 0.0;
  1639. result.m[4] = (axis.y * axis.x) * c1 + (axis.z * s);
  1640. result.m[5] = (axis.y * axis.y) * c1 + c;
  1641. result.m[6] = (axis.y * axis.z) * c1 - (axis.x * s);
  1642. result.m[7] = 0.0;
  1643. result.m[8] = (axis.z * axis.x) * c1 - (axis.y * s);
  1644. result.m[9] = (axis.z * axis.y) * c1 + (axis.x * s);
  1645. result.m[10] = (axis.z * axis.z) * c1 + c;
  1646. result.m[11] = 0.0;
  1647. result.m[15] = 1.0;
  1648. return result;
  1649. };
  1650. Matrix.RotationYawPitchRoll = function (yaw, pitch, roll) {
  1651. var result = new Matrix();
  1652. Matrix.RotationYawPitchRollToRef(yaw, pitch, roll, result);
  1653. return result;
  1654. };
  1655. Matrix.RotationYawPitchRollToRef = function (yaw, pitch, roll, result) {
  1656. Quaternion.RotationYawPitchRollToRef(yaw, pitch, roll, this._tempQuaternion);
  1657. this._tempQuaternion.toRotationMatrix(result);
  1658. };
  1659. Matrix.Scaling = function (x, y, z) {
  1660. var result = Matrix.Zero();
  1661. Matrix.ScalingToRef(x, y, z, result);
  1662. return result;
  1663. };
  1664. Matrix.ScalingToRef = function (x, y, z, result) {
  1665. result.m[0] = x;
  1666. result.m[1] = 0;
  1667. result.m[2] = 0;
  1668. result.m[3] = 0;
  1669. result.m[4] = 0;
  1670. result.m[5] = y;
  1671. result.m[6] = 0;
  1672. result.m[7] = 0;
  1673. result.m[8] = 0;
  1674. result.m[9] = 0;
  1675. result.m[10] = z;
  1676. result.m[11] = 0;
  1677. result.m[12] = 0;
  1678. result.m[13] = 0;
  1679. result.m[14] = 0;
  1680. result.m[15] = 1.0;
  1681. };
  1682. Matrix.Translation = function (x, y, z) {
  1683. var result = Matrix.Identity();
  1684. Matrix.TranslationToRef(x, y, z, result);
  1685. return result;
  1686. };
  1687. Matrix.TranslationToRef = function (x, y, z, result) {
  1688. Matrix.FromValuesToRef(1.0, 0, 0, 0, 0, 1.0, 0, 0, 0, 0, 1.0, 0, x, y, z, 1.0, result);
  1689. };
  1690. Matrix.LookAtLH = function (eye, target, up) {
  1691. var result = Matrix.Zero();
  1692. Matrix.LookAtLHToRef(eye, target, up, result);
  1693. return result;
  1694. };
  1695. Matrix.LookAtLHToRef = function (eye, target, up, result) {
  1696. // Z axis
  1697. target.subtractToRef(eye, this._zAxis);
  1698. this._zAxis.normalize();
  1699. // X axis
  1700. Vector3.CrossToRef(up, this._zAxis, this._xAxis);
  1701. this._xAxis.normalize();
  1702. // Y axis
  1703. Vector3.CrossToRef(this._zAxis, this._xAxis, this._yAxis);
  1704. this._yAxis.normalize();
  1705. // Eye angles
  1706. var ex = -Vector3.Dot(this._xAxis, eye);
  1707. var ey = -Vector3.Dot(this._yAxis, eye);
  1708. var ez = -Vector3.Dot(this._zAxis, eye);
  1709. return Matrix.FromValuesToRef(this._xAxis.x, this._yAxis.x, this._zAxis.x, 0, this._xAxis.y, this._yAxis.y, this._zAxis.y, 0, this._xAxis.z, this._yAxis.z, this._zAxis.z, 0, ex, ey, ez, 1, result);
  1710. };
  1711. Matrix.OrthoLH = function (width, height, znear, zfar) {
  1712. var hw = 2.0 / width;
  1713. var hh = 2.0 / height;
  1714. var id = 1.0 / (zfar - znear);
  1715. var nid = znear / (znear - zfar);
  1716. return Matrix.FromValues(hw, 0, 0, 0, 0, hh, 0, 0, 0, 0, id, 0, 0, 0, nid, 1);
  1717. };
  1718. Matrix.OrthoOffCenterLH = function (left, right, bottom, top, znear, zfar) {
  1719. var matrix = Matrix.Zero();
  1720. Matrix.OrthoOffCenterLHToRef(left, right, bottom, top, znear, zfar, matrix);
  1721. return matrix;
  1722. };
  1723. Matrix.OrthoOffCenterLHToRef = function (left, right, bottom, top, znear, zfar, result) {
  1724. result.m[0] = 2.0 / (right - left);
  1725. result.m[1] = result.m[2] = result.m[3] = 0;
  1726. result.m[5] = 2.0 / (top - bottom);
  1727. result.m[4] = result.m[6] = result.m[7] = 0;
  1728. result.m[10] = -1.0 / (znear - zfar);
  1729. result.m[8] = result.m[9] = result.m[11] = 0;
  1730. result.m[12] = (left + right) / (left - right);
  1731. result.m[13] = (top + bottom) / (bottom - top);
  1732. result.m[14] = znear / (znear - zfar);
  1733. result.m[15] = 1.0;
  1734. };
  1735. Matrix.PerspectiveLH = function (width, height, znear, zfar) {
  1736. var matrix = Matrix.Zero();
  1737. matrix.m[0] = (2.0 * znear) / width;
  1738. matrix.m[1] = matrix.m[2] = matrix.m[3] = 0.0;
  1739. matrix.m[5] = (2.0 * znear) / height;
  1740. matrix.m[4] = matrix.m[6] = matrix.m[7] = 0.0;
  1741. matrix.m[10] = -zfar / (znear - zfar);
  1742. matrix.m[8] = matrix.m[9] = 0.0;
  1743. matrix.m[11] = 1.0;
  1744. matrix.m[12] = matrix.m[13] = matrix.m[15] = 0.0;
  1745. matrix.m[14] = (znear * zfar) / (znear - zfar);
  1746. return matrix;
  1747. };
  1748. Matrix.PerspectiveFovLH = function (fov, aspect, znear, zfar) {
  1749. var matrix = Matrix.Zero();
  1750. Matrix.PerspectiveFovLHToRef(fov, aspect, znear, zfar, matrix);
  1751. return matrix;
  1752. };
  1753. Matrix.PerspectiveFovLHToRef = function (fov, aspect, znear, zfar, result, fovMode) {
  1754. if (fovMode === void 0) { fovMode = BABYLON.Camera.FOVMODE_VERTICAL_FIXED; }
  1755. var tan = 1.0 / (Math.tan(fov * 0.5));
  1756. var v_fixed = (fovMode === BABYLON.Camera.FOVMODE_VERTICAL_FIXED);
  1757. if (v_fixed) {
  1758. result.m[0] = tan / aspect;
  1759. }
  1760. else {
  1761. result.m[0] = tan;
  1762. }
  1763. result.m[1] = result.m[2] = result.m[3] = 0.0;
  1764. if (v_fixed) {
  1765. result.m[5] = tan;
  1766. }
  1767. else {
  1768. result.m[5] = tan * aspect;
  1769. }
  1770. result.m[4] = result.m[6] = result.m[7] = 0.0;
  1771. result.m[8] = result.m[9] = 0.0;
  1772. result.m[10] = -zfar / (znear - zfar);
  1773. result.m[11] = 1.0;
  1774. result.m[12] = result.m[13] = result.m[15] = 0.0;
  1775. result.m[14] = (znear * zfar) / (znear - zfar);
  1776. };
  1777. Matrix.GetFinalMatrix = function (viewport, world, view, projection, zmin, zmax) {
  1778. var cw = viewport.width;
  1779. var ch = viewport.height;
  1780. var cx = viewport.x;
  1781. var cy = viewport.y;
  1782. var viewportMatrix = Matrix.FromValues(cw / 2.0, 0, 0, 0, 0, -ch / 2.0, 0, 0, 0, 0, zmax - zmin, 0, cx + cw / 2.0, ch / 2.0 + cy, zmin, 1);
  1783. return world.multiply(view).multiply(projection).multiply(viewportMatrix);
  1784. };
  1785. Matrix.Transpose = function (matrix) {
  1786. var result = new Matrix();
  1787. result.m[0] = matrix.m[0];
  1788. result.m[1] = matrix.m[4];
  1789. result.m[2] = matrix.m[8];
  1790. result.m[3] = matrix.m[12];
  1791. result.m[4] = matrix.m[1];
  1792. result.m[5] = matrix.m[5];
  1793. result.m[6] = matrix.m[9];
  1794. result.m[7] = matrix.m[13];
  1795. result.m[8] = matrix.m[2];
  1796. result.m[9] = matrix.m[6];
  1797. result.m[10] = matrix.m[10];
  1798. result.m[11] = matrix.m[14];
  1799. result.m[12] = matrix.m[3];
  1800. result.m[13] = matrix.m[7];
  1801. result.m[14] = matrix.m[11];
  1802. result.m[15] = matrix.m[15];
  1803. return result;
  1804. };
  1805. Matrix.Reflection = function (plane) {
  1806. var matrix = new Matrix();
  1807. Matrix.ReflectionToRef(plane, matrix);
  1808. return matrix;
  1809. };
  1810. Matrix.ReflectionToRef = function (plane, result) {
  1811. plane.normalize();
  1812. var x = plane.normal.x;
  1813. var y = plane.normal.y;
  1814. var z = plane.normal.z;
  1815. var temp = -2 * x;
  1816. var temp2 = -2 * y;
  1817. var temp3 = -2 * z;
  1818. result.m[0] = (temp * x) + 1;
  1819. result.m[1] = temp2 * x;
  1820. result.m[2] = temp3 * x;
  1821. result.m[3] = 0.0;
  1822. result.m[4] = temp * y;
  1823. result.m[5] = (temp2 * y) + 1;
  1824. result.m[6] = temp3 * y;
  1825. result.m[7] = 0.0;
  1826. result.m[8] = temp * z;
  1827. result.m[9] = temp2 * z;
  1828. result.m[10] = (temp3 * z) + 1;
  1829. result.m[11] = 0.0;
  1830. result.m[12] = temp * plane.d;
  1831. result.m[13] = temp2 * plane.d;
  1832. result.m[14] = temp3 * plane.d;
  1833. result.m[15] = 1.0;
  1834. };
  1835. Matrix._tempQuaternion = new Quaternion();
  1836. Matrix._xAxis = Vector3.Zero();
  1837. Matrix._yAxis = Vector3.Zero();
  1838. Matrix._zAxis = Vector3.Zero();
  1839. return Matrix;
  1840. })();
  1841. BABYLON.Matrix = Matrix;
  1842. var Plane = (function () {
  1843. function Plane(a, b, c, d) {
  1844. this.normal = new Vector3(a, b, c);
  1845. this.d = d;
  1846. }
  1847. Plane.prototype.asArray = function () {
  1848. return [this.normal.x, this.normal.y, this.normal.z, this.d];
  1849. };
  1850. // Methods
  1851. Plane.prototype.clone = function () {
  1852. return new Plane(this.normal.x, this.normal.y, this.normal.z, this.d);
  1853. };
  1854. Plane.prototype.normalize = function () {
  1855. var norm = (Math.sqrt((this.normal.x * this.normal.x) + (this.normal.y * this.normal.y) + (this.normal.z * this.normal.z)));
  1856. var magnitude = 0;
  1857. if (norm !== 0) {
  1858. magnitude = 1.0 / norm;
  1859. }
  1860. this.normal.x *= magnitude;
  1861. this.normal.y *= magnitude;
  1862. this.normal.z *= magnitude;
  1863. this.d *= magnitude;
  1864. return this;
  1865. };
  1866. Plane.prototype.transform = function (transformation) {
  1867. var transposedMatrix = Matrix.Transpose(transformation);
  1868. var x = this.normal.x;
  1869. var y = this.normal.y;
  1870. var z = this.normal.z;
  1871. var d = this.d;
  1872. var normalX = (((x * transposedMatrix.m[0]) + (y * transposedMatrix.m[1])) + (z * transposedMatrix.m[2])) + (d * transposedMatrix.m[3]);
  1873. var normalY = (((x * transposedMatrix.m[4]) + (y * transposedMatrix.m[5])) + (z * transposedMatrix.m[6])) + (d * transposedMatrix.m[7]);
  1874. var normalZ = (((x * transposedMatrix.m[8]) + (y * transposedMatrix.m[9])) + (z * transposedMatrix.m[10])) + (d * transposedMatrix.m[11]);
  1875. var finalD = (((x * transposedMatrix.m[12]) + (y * transposedMatrix.m[13])) + (z * transposedMatrix.m[14])) + (d * transposedMatrix.m[15]);
  1876. return new Plane(normalX, normalY, normalZ, finalD);
  1877. };
  1878. Plane.prototype.dotCoordinate = function (point) {
  1879. return ((((this.normal.x * point.x) + (this.normal.y * point.y)) + (this.normal.z * point.z)) + this.d);
  1880. };
  1881. Plane.prototype.copyFromPoints = function (point1, point2, point3) {
  1882. var x1 = point2.x - point1.x;
  1883. var y1 = point2.y - point1.y;
  1884. var z1 = point2.z - point1.z;
  1885. var x2 = point3.x - point1.x;
  1886. var y2 = point3.y - point1.y;
  1887. var z2 = point3.z - point1.z;
  1888. var yz = (y1 * z2) - (z1 * y2);
  1889. var xz = (z1 * x2) - (x1 * z2);
  1890. var xy = (x1 * y2) - (y1 * x2);
  1891. var pyth = (Math.sqrt((yz * yz) + (xz * xz) + (xy * xy)));
  1892. var invPyth;
  1893. if (pyth !== 0) {
  1894. invPyth = 1.0 / pyth;
  1895. }
  1896. else {
  1897. invPyth = 0;
  1898. }
  1899. this.normal.x = yz * invPyth;
  1900. this.normal.y = xz * invPyth;
  1901. this.normal.z = xy * invPyth;
  1902. this.d = -((this.normal.x * point1.x) + (this.normal.y * point1.y) + (this.normal.z * point1.z));
  1903. return this;
  1904. };
  1905. Plane.prototype.isFrontFacingTo = function (direction, epsilon) {
  1906. var dot = Vector3.Dot(this.normal, direction);
  1907. return (dot <= epsilon);
  1908. };
  1909. Plane.prototype.signedDistanceTo = function (point) {
  1910. return Vector3.Dot(point, this.normal) + this.d;
  1911. };
  1912. // Statics
  1913. Plane.FromArray = function (array) {
  1914. return new Plane(array[0], array[1], array[2], array[3]);
  1915. };
  1916. Plane.FromPoints = function (point1, point2, point3) {
  1917. var result = new Plane(0, 0, 0, 0);
  1918. result.copyFromPoints(point1, point2, point3);
  1919. return result;
  1920. };
  1921. Plane.FromPositionAndNormal = function (origin, normal) {
  1922. var result = new Plane(0, 0, 0, 0);
  1923. normal.normalize();
  1924. result.normal = normal;
  1925. result.d = -(normal.x * origin.x + normal.y * origin.y + normal.z * origin.z);
  1926. return result;
  1927. };
  1928. Plane.SignedDistanceToPlaneFromPositionAndNormal = function (origin, normal, point) {
  1929. var d = -(normal.x * origin.x + normal.y * origin.y + normal.z * origin.z);
  1930. return Vector3.Dot(point, normal) + d;
  1931. };
  1932. return Plane;
  1933. })();
  1934. BABYLON.Plane = Plane;
  1935. var Viewport = (function () {
  1936. function Viewport(x, y, width, height) {
  1937. this.x = x;
  1938. this.y = y;
  1939. this.width = width;
  1940. this.height = height;
  1941. }
  1942. Viewport.prototype.toGlobal = function (engine) {
  1943. var width = engine.getRenderWidth();
  1944. var height = engine.getRenderHeight();
  1945. return new Viewport(this.x * width, this.y * height, this.width * width, this.height * height);
  1946. };
  1947. return Viewport;
  1948. })();
  1949. BABYLON.Viewport = Viewport;
  1950. var Frustum = (function () {
  1951. function Frustum() {
  1952. }
  1953. Frustum.GetPlanes = function (transform) {
  1954. var frustumPlanes = [];
  1955. for (var index = 0; index < 6; index++) {
  1956. frustumPlanes.push(new Plane(0, 0, 0, 0));
  1957. }
  1958. Frustum.GetPlanesToRef(transform, frustumPlanes);
  1959. return frustumPlanes;
  1960. };
  1961. Frustum.GetPlanesToRef = function (transform, frustumPlanes) {
  1962. // Near
  1963. frustumPlanes[0].normal.x = transform.m[3] + transform.m[2];
  1964. frustumPlanes[0].normal.y = transform.m[7] + transform.m[6];
  1965. frustumPlanes[0].normal.z = transform.m[10] + transform.m[10];
  1966. frustumPlanes[0].d = transform.m[15] + transform.m[14];
  1967. frustumPlanes[0].normalize();
  1968. // Far
  1969. frustumPlanes[1].normal.x = transform.m[3] - transform.m[2];
  1970. frustumPlanes[1].normal.y = transform.m[7] - transform.m[6];
  1971. frustumPlanes[1].normal.z = transform.m[11] - transform.m[10];
  1972. frustumPlanes[1].d = transform.m[15] - transform.m[14];
  1973. frustumPlanes[1].normalize();
  1974. // Left
  1975. frustumPlanes[2].normal.x = transform.m[3] + transform.m[0];
  1976. frustumPlanes[2].normal.y = transform.m[7] + transform.m[4];
  1977. frustumPlanes[2].normal.z = transform.m[11] + transform.m[8];
  1978. frustumPlanes[2].d = transform.m[15] + transform.m[12];
  1979. frustumPlanes[2].normalize();
  1980. // Right
  1981. frustumPlanes[3].normal.x = transform.m[3] - transform.m[0];
  1982. frustumPlanes[3].normal.y = transform.m[7] - transform.m[4];
  1983. frustumPlanes[3].normal.z = transform.m[11] - transform.m[8];
  1984. frustumPlanes[3].d = transform.m[15] - transform.m[12];
  1985. frustumPlanes[3].normalize();
  1986. // Top
  1987. frustumPlanes[4].normal.x = transform.m[3] - transform.m[1];
  1988. frustumPlanes[4].normal.y = transform.m[7] - transform.m[5];
  1989. frustumPlanes[4].normal.z = transform.m[11] - transform.m[9];
  1990. frustumPlanes[4].d = transform.m[15] - transform.m[13];
  1991. frustumPlanes[4].normalize();
  1992. // Bottom
  1993. frustumPlanes[5].normal.x = transform.m[3] + transform.m[1];
  1994. frustumPlanes[5].normal.y = transform.m[7] + transform.m[5];
  1995. frustumPlanes[5].normal.z = transform.m[11] + transform.m[9];
  1996. frustumPlanes[5].d = transform.m[15] + transform.m[13];
  1997. frustumPlanes[5].normalize();
  1998. };
  1999. return Frustum;
  2000. })();
  2001. BABYLON.Frustum = Frustum;
  2002. var Ray = (function () {
  2003. function Ray(origin, direction, length) {
  2004. if (length === void 0) { length = Number.MAX_VALUE; }
  2005. this.origin = origin;
  2006. this.direction = direction;
  2007. this.length = length;
  2008. }
  2009. // Methods
  2010. Ray.prototype.intersectsBoxMinMax = function (minimum, maximum) {
  2011. var d = 0.0;
  2012. var maxValue = Number.MAX_VALUE;
  2013. if (Math.abs(this.direction.x) < 0.0000001) {
  2014. if (this.origin.x < minimum.x || this.origin.x > maximum.x) {
  2015. return false;
  2016. }
  2017. }
  2018. else {
  2019. var inv = 1.0 / this.direction.x;
  2020. var min = (minimum.x - this.origin.x) * inv;
  2021. var max = (maximum.x - this.origin.x) * inv;
  2022. if (max === -Infinity) {
  2023. max = Infinity;
  2024. }
  2025. if (min > max) {
  2026. var temp = min;
  2027. min = max;
  2028. max = temp;
  2029. }
  2030. d = Math.max(min, d);
  2031. maxValue = Math.min(max, maxValue);
  2032. if (d > maxValue) {
  2033. return false;
  2034. }
  2035. }
  2036. if (Math.abs(this.direction.y) < 0.0000001) {
  2037. if (this.origin.y < minimum.y || this.origin.y > maximum.y) {
  2038. return false;
  2039. }
  2040. }
  2041. else {
  2042. inv = 1.0 / this.direction.y;
  2043. min = (minimum.y - this.origin.y) * inv;
  2044. max = (maximum.y - this.origin.y) * inv;
  2045. if (max === -Infinity) {
  2046. max = Infinity;
  2047. }
  2048. if (min > max) {
  2049. temp = min;
  2050. min = max;
  2051. max = temp;
  2052. }
  2053. d = Math.max(min, d);
  2054. maxValue = Math.min(max, maxValue);
  2055. if (d > maxValue) {
  2056. return false;
  2057. }
  2058. }
  2059. if (Math.abs(this.direction.z) < 0.0000001) {
  2060. if (this.origin.z < minimum.z || this.origin.z > maximum.z) {
  2061. return false;
  2062. }
  2063. }
  2064. else {
  2065. inv = 1.0 / this.direction.z;
  2066. min = (minimum.z - this.origin.z) * inv;
  2067. max = (maximum.z - this.origin.z) * inv;
  2068. if (max === -Infinity) {
  2069. max = Infinity;
  2070. }
  2071. if (min > max) {
  2072. temp = min;
  2073. min = max;
  2074. max = temp;
  2075. }
  2076. d = Math.max(min, d);
  2077. maxValue = Math.min(max, maxValue);
  2078. if (d > maxValue) {
  2079. return false;
  2080. }
  2081. }
  2082. return true;
  2083. };
  2084. Ray.prototype.intersectsBox = function (box) {
  2085. return this.intersectsBoxMinMax(box.minimum, box.maximum);
  2086. };
  2087. Ray.prototype.intersectsSphere = function (sphere) {
  2088. var x = sphere.center.x - this.origin.x;
  2089. var y = sphere.center.y - this.origin.y;
  2090. var z = sphere.center.z - this.origin.z;
  2091. var pyth = (x * x) + (y * y) + (z * z);
  2092. var rr = sphere.radius * sphere.radius;
  2093. if (pyth <= rr) {
  2094. return true;
  2095. }
  2096. var dot = (x * this.direction.x) + (y * this.direction.y) + (z * this.direction.z);
  2097. if (dot < 0.0) {
  2098. return false;
  2099. }
  2100. var temp = pyth - (dot * dot);
  2101. return temp <= rr;
  2102. };
  2103. Ray.prototype.intersectsTriangle = function (vertex0, vertex1, vertex2) {
  2104. if (!this._edge1) {
  2105. this._edge1 = Vector3.Zero();
  2106. this._edge2 = Vector3.Zero();
  2107. this._pvec = Vector3.Zero();
  2108. this._tvec = Vector3.Zero();
  2109. this._qvec = Vector3.Zero();
  2110. }
  2111. vertex1.subtractToRef(vertex0, this._edge1);
  2112. vertex2.subtractToRef(vertex0, this._edge2);
  2113. Vector3.CrossToRef(this.direction, this._edge2, this._pvec);
  2114. var det = Vector3.Dot(this._edge1, this._pvec);
  2115. if (det === 0) {
  2116. return null;
  2117. }
  2118. var invdet = 1 / det;
  2119. this.origin.subtractToRef(vertex0, this._tvec);
  2120. var bu = Vector3.Dot(this._tvec, this._pvec) * invdet;
  2121. if (bu < 0 || bu > 1.0) {
  2122. return null;
  2123. }
  2124. Vector3.CrossToRef(this._tvec, this._edge1, this._qvec);
  2125. var bv = Vector3.Dot(this.direction, this._qvec) * invdet;
  2126. if (bv < 0 || bu + bv > 1.0) {
  2127. return null;
  2128. }
  2129. //check if the distance is longer than the predefined length.
  2130. var distance = Vector3.Dot(this._edge2, this._qvec) * invdet;
  2131. if (distance > this.length) {
  2132. return null;
  2133. }
  2134. return new BABYLON.IntersectionInfo(bu, bv, distance);
  2135. };
  2136. // Statics
  2137. Ray.CreateNew = function (x, y, viewportWidth, viewportHeight, world, view, projection) {
  2138. var start = Vector3.Unproject(new Vector3(x, y, 0), viewportWidth, viewportHeight, world, view, projection);
  2139. var end = Vector3.Unproject(new Vector3(x, y, 1), viewportWidth, viewportHeight, world, view, projection);
  2140. var direction = end.subtract(start);
  2141. direction.normalize();
  2142. return new Ray(start, direction);
  2143. };
  2144. /**
  2145. * Function will create a new transformed ray starting from origin and ending at the end point. Ray's length will be set, and ray will be
  2146. * transformed to the given world matrix.
  2147. * @param origin The origin point
  2148. * @param end The end point
  2149. * @param world a matrix to transform the ray to. Default is the identity matrix.
  2150. */
  2151. Ray.CreateNewFromTo = function (origin, end, world) {
  2152. if (world === void 0) { world = Matrix.Identity(); }
  2153. var direction = end.subtract(origin);
  2154. var length = Math.sqrt((direction.x * direction.x) + (direction.y * direction.y) + (direction.z * direction.z));
  2155. direction.normalize();
  2156. return Ray.Transform(new Ray(origin, direction, length), world);
  2157. };
  2158. Ray.Transform = function (ray, matrix) {
  2159. var newOrigin = Vector3.TransformCoordinates(ray.origin, matrix);
  2160. var newDirection = Vector3.TransformNormal(ray.direction, matrix);
  2161. return new Ray(newOrigin, newDirection, ray.length);
  2162. };
  2163. return Ray;
  2164. })();
  2165. BABYLON.Ray = Ray;
  2166. (function (Space) {
  2167. Space[Space["LOCAL"] = 0] = "LOCAL";
  2168. Space[Space["WORLD"] = 1] = "WORLD";
  2169. })(BABYLON.Space || (BABYLON.Space = {}));
  2170. var Space = BABYLON.Space;
  2171. var Axis = (function () {
  2172. function Axis() {
  2173. }
  2174. Axis.X = new Vector3(1, 0, 0);
  2175. Axis.Y = new Vector3(0, 1, 0);
  2176. Axis.Z = new Vector3(0, 0, 1);
  2177. return Axis;
  2178. })();
  2179. BABYLON.Axis = Axis;
  2180. ;
  2181. var BezierCurve = (function () {
  2182. function BezierCurve() {
  2183. }
  2184. BezierCurve.interpolate = function (t, x1, y1, x2, y2) {
  2185. // Extract X (which is equal to time here)
  2186. var f0 = 1 - 3 * x2 + 3 * x1;
  2187. var f1 = 3 * x2 - 6 * x1;
  2188. var f2 = 3 * x1;
  2189. var refinedT = t;
  2190. for (var i = 0; i < 5; i++) {
  2191. var refinedT2 = refinedT * refinedT;
  2192. var refinedT3 = refinedT2 * refinedT;
  2193. var x = f0 * refinedT3 + f1 * refinedT2 + f2 * refinedT;
  2194. var slope = 1.0 / (3.0 * f0 * refinedT2 + 2.0 * f1 * refinedT + f2);
  2195. refinedT -= (x - t) * slope;
  2196. refinedT = Math.min(1, Math.max(0, refinedT));
  2197. }
  2198. // Resolve cubic bezier for the given x
  2199. return 3 * Math.pow(1 - refinedT, 2) * refinedT * y1 + 3 * (1 - refinedT) * Math.pow(refinedT, 2) * y2 + Math.pow(refinedT, 3);
  2200. };
  2201. return BezierCurve;
  2202. })();
  2203. BABYLON.BezierCurve = BezierCurve;
  2204. (function (Orientation) {
  2205. Orientation[Orientation["CW"] = 0] = "CW";
  2206. Orientation[Orientation["CCW"] = 1] = "CCW";
  2207. })(BABYLON.Orientation || (BABYLON.Orientation = {}));
  2208. var Orientation = BABYLON.Orientation;
  2209. var Angle = (function () {
  2210. function Angle(radians) {
  2211. var _this = this;
  2212. this.degrees = function () { return _this._radians * 180 / Math.PI; };
  2213. this.radians = function () { return _this._radians; };
  2214. this._radians = radians;
  2215. if (this._radians < 0)
  2216. this._radians += (2 * Math.PI);
  2217. }
  2218. Angle.BetweenTwoPoints = function (a, b) {
  2219. var delta = b.subtract(a);
  2220. var theta = Math.atan2(delta.y, delta.x);
  2221. return new Angle(theta);
  2222. };
  2223. Angle.FromRadians = function (radians) {
  2224. return new Angle(radians);
  2225. };
  2226. Angle.FromDegrees = function (degrees) {
  2227. return new Angle(degrees * Math.PI / 180);
  2228. };
  2229. return Angle;
  2230. })();
  2231. BABYLON.Angle = Angle;
  2232. var Arc2 = (function () {
  2233. function Arc2(startPoint, midPoint, endPoint) {
  2234. this.startPoint = startPoint;
  2235. this.midPoint = midPoint;
  2236. this.endPoint = endPoint;
  2237. var temp = Math.pow(midPoint.x, 2) + Math.pow(midPoint.y, 2);
  2238. var startToMid = (Math.pow(startPoint.x, 2) + Math.pow(startPoint.y, 2) - temp) / 2.;
  2239. var midToEnd = (temp - Math.pow(endPoint.x, 2) - Math.pow(endPoint.y, 2)) / 2.;
  2240. var det = (startPoint.x - midPoint.x) * (midPoint.y - endPoint.y) - (midPoint.x - endPoint.x) * (startPoint.y - midPoint.y);
  2241. this.centerPoint = new Vector2((startToMid * (midPoint.y - endPoint.y) - midToEnd * (startPoint.y - midPoint.y)) / det, ((startPoint.x - midPoint.x) * midToEnd - (midPoint.x - endPoint.x) * startToMid) / det);
  2242. this.radius = this.centerPoint.subtract(this.startPoint).length();
  2243. this.startAngle = Angle.BetweenTwoPoints(this.centerPoint, this.startPoint);
  2244. var a1 = this.startAngle.degrees();
  2245. var a2 = Angle.BetweenTwoPoints(this.centerPoint, this.midPoint).degrees();
  2246. var a3 = Angle.BetweenTwoPoints(this.centerPoint, this.endPoint).degrees();
  2247. // angles correction
  2248. if (a2 - a1 > +180.0)
  2249. a2 -= 360.0;
  2250. if (a2 - a1 < -180.0)
  2251. a2 += 360.0;
  2252. if (a3 - a2 > +180.0)
  2253. a3 -= 360.0;
  2254. if (a3 - a2 < -180.0)
  2255. a3 += 360.0;
  2256. this.orientation = (a2 - a1) < 0 ? 0 /* CW */ : 1 /* CCW */;
  2257. this.angle = Angle.FromDegrees(this.orientation === 0 /* CW */ ? a1 - a3 : a3 - a1);
  2258. }
  2259. return Arc2;
  2260. })();
  2261. BABYLON.Arc2 = Arc2;
  2262. var PathCursor = (function () {
  2263. function PathCursor(path) {
  2264. this.path = path;
  2265. this._onchange = new Array();
  2266. this.value = 0;
  2267. this.animations = new Array();
  2268. }
  2269. PathCursor.prototype.getPoint = function () {
  2270. var point = this.path.getPointAtLengthPosition(this.value);
  2271. return new Vector3(point.x, 0, point.y);
  2272. };
  2273. PathCursor.prototype.moveAhead = function (step) {
  2274. if (step === void 0) { step = 0.002; }
  2275. this.move(step);
  2276. return this;
  2277. };
  2278. PathCursor.prototype.moveBack = function (step) {
  2279. if (step === void 0) { step = 0.002; }
  2280. this.move(-step);
  2281. return this;
  2282. };
  2283. PathCursor.prototype.move = function (step) {
  2284. if (Math.abs(step) > 1) {
  2285. throw "step size should be less than 1.";
  2286. }
  2287. this.value += step;
  2288. this.ensureLimits();
  2289. this.raiseOnChange();
  2290. return this;
  2291. };
  2292. PathCursor.prototype.ensureLimits = function () {
  2293. while (this.value > 1) {
  2294. this.value -= 1;
  2295. }
  2296. while (this.value < 0) {
  2297. this.value += 1;
  2298. }
  2299. return this;
  2300. };
  2301. // used by animation engine
  2302. PathCursor.prototype.markAsDirty = function (propertyName) {
  2303. this.ensureLimits();
  2304. this.raiseOnChange();
  2305. return this;
  2306. };
  2307. PathCursor.prototype.raiseOnChange = function () {
  2308. var _this = this;
  2309. this._onchange.forEach(function (f) { return f(_this); });
  2310. return this;
  2311. };
  2312. PathCursor.prototype.onchange = function (f) {
  2313. this._onchange.push(f);
  2314. return this;
  2315. };
  2316. return PathCursor;
  2317. })();
  2318. BABYLON.PathCursor = PathCursor;
  2319. var Path2 = (function () {
  2320. function Path2(x, y) {
  2321. this._points = [];
  2322. this._length = 0;
  2323. this.closed = false;
  2324. this._points.push(new Vector2(x, y));
  2325. }
  2326. Path2.prototype.addLineTo = function (x, y) {
  2327. if (closed) {
  2328. BABYLON.Tools.Error("cannot add lines to closed paths");
  2329. return this;
  2330. }
  2331. var newPoint = new Vector2(x, y);
  2332. var previousPoint = this._points[this._points.length - 1];
  2333. this._points.push(newPoint);
  2334. this._length += newPoint.subtract(previousPoint).length();
  2335. return this;
  2336. };
  2337. Path2.prototype.addArcTo = function (midX, midY, endX, endY, numberOfSegments) {
  2338. if (numberOfSegments === void 0) { numberOfSegments = 36; }
  2339. if (closed) {
  2340. BABYLON.Tools.Error("cannot add arcs to closed paths");
  2341. return this;
  2342. }
  2343. var startPoint = this._points[this._points.length - 1];
  2344. var midPoint = new Vector2(midX, midY);
  2345. var endPoint = new Vector2(endX, endY);
  2346. var arc = new Arc2(startPoint, midPoint, endPoint);
  2347. var increment = arc.angle.radians() / numberOfSegments;
  2348. if (arc.orientation === 0 /* CW */)
  2349. increment *= -1;
  2350. var currentAngle = arc.startAngle.radians() + increment;
  2351. for (var i = 0; i < numberOfSegments; i++) {
  2352. var x = Math.cos(currentAngle) * arc.radius + arc.centerPoint.x;
  2353. var y = Math.sin(currentAngle) * arc.radius + arc.centerPoint.y;
  2354. this.addLineTo(x, y);
  2355. currentAngle += increment;
  2356. }
  2357. return this;
  2358. };
  2359. Path2.prototype.close = function () {
  2360. this.closed = true;
  2361. return this;
  2362. };
  2363. Path2.prototype.length = function () {
  2364. var result = this._length;
  2365. if (!this.closed) {
  2366. var lastPoint = this._points[this._points.length - 1];
  2367. var firstPoint = this._points[0];
  2368. result += (firstPoint.subtract(lastPoint).length());
  2369. }
  2370. return result;
  2371. };
  2372. Path2.prototype.getPoints = function () {
  2373. return this._points;
  2374. };
  2375. Path2.prototype.getPointAtLengthPosition = function (normalizedLengthPosition) {
  2376. if (normalizedLengthPosition < 0 || normalizedLengthPosition > 1) {
  2377. BABYLON.Tools.Error("normalized length position should be between 0 and 1.");
  2378. return Vector2.Zero();
  2379. }
  2380. var lengthPosition = normalizedLengthPosition * this.length();
  2381. var previousOffset = 0;
  2382. for (var i = 0; i < this._points.length; i++) {
  2383. var j = (i + 1) % this._points.length;
  2384. var a = this._points[i];
  2385. var b = this._points[j];
  2386. var bToA = b.subtract(a);
  2387. var nextOffset = (bToA.length() + previousOffset);
  2388. if (lengthPosition >= previousOffset && lengthPosition <= nextOffset) {
  2389. var dir = bToA.normalize();
  2390. var localOffset = lengthPosition - previousOffset;
  2391. return new Vector2(a.x + (dir.x * localOffset), a.y + (dir.y * localOffset));
  2392. }
  2393. previousOffset = nextOffset;
  2394. }
  2395. BABYLON.Tools.Error("internal error");
  2396. return Vector2.Zero();
  2397. };
  2398. Path2.StartingAt = function (x, y) {
  2399. return new Path2(x, y);
  2400. };
  2401. return Path2;
  2402. })();
  2403. BABYLON.Path2 = Path2;
  2404. })(BABYLON || (BABYLON = {}));
  2405. //# sourceMappingURL=babylon.math.js.map