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/** |
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* @fileoverview gl-matrix - High performance matrix and vector operations |
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* @author Brandon Jones |
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* @author Colin MacKenzie IV |
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* @version 2.4.0 |
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*/ |
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|
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/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. |
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|
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Permission is hereby granted, free of charge, to any person obtaining a copy |
|
of this software and associated documentation files (the "Software"), to deal |
|
in the Software without restriction, including without limitation the rights |
|
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
|
copies of the Software, and to permit persons to whom the Software is |
|
furnished to do so, subject to the following conditions: |
|
|
|
The above copyright notice and this permission notice shall be included in |
|
all copies or substantial portions of the Software. |
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
|
THE SOFTWARE. */ |
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(function webpackUniversalModuleDefinition(root, factory) { |
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if(typeof exports === 'object' && typeof module === 'object') |
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module.exports = factory(); |
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else if(typeof define === 'function' && define.amd) |
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define([], factory); |
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else { |
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var a = factory(); |
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for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i]; |
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} |
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})(this, function() { |
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return /******/ (function(modules) { // webpackBootstrap |
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/******/ // The module cache |
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/******/ var installedModules = {}; |
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/******/ |
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/******/ // The require function |
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/******/ function __webpack_require__(moduleId) { |
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/******/ |
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/******/ // Check if module is in cache |
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/******/ if(installedModules[moduleId]) { |
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/******/ return installedModules[moduleId].exports; |
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/******/ var module = installedModules[moduleId] = { |
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/******/ i: moduleId, |
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/******/ l: false, |
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/******/ exports: {} |
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/******/ }; |
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/******/ |
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/******/ // Execute the module function |
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/******/ modules[moduleId].call(module.exports, module, module.exports, __webpack_require__); |
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/******/ |
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/******/ // Flag the module as loaded |
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/******/ module.l = true; |
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/******/ |
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/******/ // Return the exports of the module |
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/******/ return module.exports; |
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/******/ } |
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/******/ |
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/******/ |
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/******/ // expose the modules object (__webpack_modules__) |
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/******/ __webpack_require__.m = modules; |
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/******/ |
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/******/ // expose the module cache |
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/******/ __webpack_require__.c = installedModules; |
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/******/ |
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/******/ // define getter function for harmony exports |
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/******/ __webpack_require__.d = function(exports, name, getter) { |
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/******/ if(!__webpack_require__.o(exports, name)) { |
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/******/ Object.defineProperty(exports, name, { |
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/******/ configurable: false, |
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/******/ enumerable: true, |
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/******/ get: getter |
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/******/ }); |
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/******/ } |
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/******/ }; |
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/******/ |
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/******/ // getDefaultExport function for compatibility with non-harmony modules |
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/******/ __webpack_require__.n = function(module) { |
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/******/ var getter = module && module.__esModule ? |
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/******/ function getDefault() { return module['default']; } : |
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/******/ __webpack_require__.d(getter, 'a', getter); |
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/******/ return getter; |
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/******/ // Object.prototype.hasOwnProperty.call |
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/******/ __webpack_require__.o = function(object, property) { return Object.prototype.hasOwnProperty.call(object, property); }; |
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/******/ |
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/******/ // __webpack_public_path__ |
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/******/ __webpack_require__.p = ""; |
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/******/ |
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/******/ // Load entry module and return exports |
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/******/ return __webpack_require__(__webpack_require__.s = 4); |
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/******/ }) |
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/************************************************************************/ |
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/******/ ([ |
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/* 0 */ |
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/***/ (function(module, exports, __webpack_require__) { |
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"use strict"; |
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Object.defineProperty(exports, "__esModule", { |
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value: true |
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}); |
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exports.setMatrixArrayType = setMatrixArrayType; |
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exports.toRadian = toRadian; |
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exports.equals = equals; |
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/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. |
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|
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Permission is hereby granted, free of charge, to any person obtaining a copy |
|
of this software and associated documentation files (the "Software"), to deal |
|
in the Software without restriction, including without limitation the rights |
|
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
|
copies of the Software, and to permit persons to whom the Software is |
|
furnished to do so, subject to the following conditions: |
|
|
|
The above copyright notice and this permission notice shall be included in |
|
all copies or substantial portions of the Software. |
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
|
THE SOFTWARE. */ |
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/** |
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* Common utilities |
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* @module glMatrix |
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*/ |
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// Configuration Constants |
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var EPSILON = exports.EPSILON = 0.000001; |
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var ARRAY_TYPE = exports.ARRAY_TYPE = typeof Float32Array !== 'undefined' ? Float32Array : Array; |
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var RANDOM = exports.RANDOM = Math.random; |
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/** |
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* Sets the type of array used when creating new vectors and matrices |
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* |
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* @param {Type} type Array type, such as Float32Array or Array |
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*/ |
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function setMatrixArrayType(type) { |
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exports.ARRAY_TYPE = ARRAY_TYPE = type; |
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} |
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var degree = Math.PI / 180; |
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/** |
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* Convert Degree To Radian |
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* |
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* @param {Number} a Angle in Degrees |
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*/ |
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function toRadian(a) { |
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return a * degree; |
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} |
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/** |
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* Tests whether or not the arguments have approximately the same value, within an absolute |
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* or relative tolerance of glMatrix.EPSILON (an absolute tolerance is used for values less |
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* than or equal to 1.0, and a relative tolerance is used for larger values) |
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* |
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* @param {Number} a The first number to test. |
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* @param {Number} b The second number to test. |
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* @returns {Boolean} True if the numbers are approximately equal, false otherwise. |
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*/ |
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function equals(a, b) { |
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return Math.abs(a - b) <= EPSILON * Math.max(1.0, Math.abs(a), Math.abs(b)); |
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} |
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/***/ }), |
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/* 1 */ |
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/***/ (function(module, exports, __webpack_require__) { |
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"use strict"; |
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Object.defineProperty(exports, "__esModule", { |
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value: true |
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}); |
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exports.sub = exports.mul = undefined; |
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exports.create = create; |
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exports.fromMat4 = fromMat4; |
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exports.clone = clone; |
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exports.copy = copy; |
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exports.fromValues = fromValues; |
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exports.set = set; |
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exports.identity = identity; |
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exports.transpose = transpose; |
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exports.invert = invert; |
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exports.adjoint = adjoint; |
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exports.determinant = determinant; |
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exports.multiply = multiply; |
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exports.translate = translate; |
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exports.rotate = rotate; |
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exports.scale = scale; |
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exports.fromTranslation = fromTranslation; |
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exports.fromRotation = fromRotation; |
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exports.fromScaling = fromScaling; |
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exports.fromMat2d = fromMat2d; |
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exports.fromQuat = fromQuat; |
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exports.normalFromMat4 = normalFromMat4; |
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exports.projection = projection; |
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exports.str = str; |
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exports.frob = frob; |
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exports.add = add; |
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exports.subtract = subtract; |
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exports.multiplyScalar = multiplyScalar; |
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exports.multiplyScalarAndAdd = multiplyScalarAndAdd; |
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exports.exactEquals = exactEquals; |
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exports.equals = equals; |
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var _common = __webpack_require__(0); |
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var glMatrix = _interopRequireWildcard(_common); |
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function _interopRequireWildcard(obj) { if (obj && obj.__esModule) { return obj; } else { var newObj = {}; if (obj != null) { for (var key in obj) { if (Object.prototype.hasOwnProperty.call(obj, key)) newObj[key] = obj[key]; } } newObj.default = obj; return newObj; } } |
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/** |
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* 3x3 Matrix |
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* @module mat3 |
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*/ |
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/** |
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* Creates a new identity mat3 |
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* |
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* @returns {mat3} a new 3x3 matrix |
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*/ |
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function create() { |
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var out = new glMatrix.ARRAY_TYPE(9); |
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out[0] = 1; |
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out[1] = 0; |
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out[2] = 0; |
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out[3] = 0; |
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out[4] = 1; |
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out[5] = 0; |
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out[6] = 0; |
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out[7] = 0; |
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out[8] = 1; |
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return out; |
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} |
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/** |
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* Copies the upper-left 3x3 values into the given mat3. |
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* |
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* @param {mat3} out the receiving 3x3 matrix |
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* @param {mat4} a the source 4x4 matrix |
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* @returns {mat3} out |
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*/ |
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/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. |
|
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy |
|
of this software and associated documentation files (the "Software"), to deal |
|
in the Software without restriction, including without limitation the rights |
|
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
|
copies of the Software, and to permit persons to whom the Software is |
|
furnished to do so, subject to the following conditions: |
|
|
|
The above copyright notice and this permission notice shall be included in |
|
all copies or substantial portions of the Software. |
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
|
THE SOFTWARE. */ |
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function fromMat4(out, a) { |
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out[0] = a[0]; |
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out[1] = a[1]; |
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out[2] = a[2]; |
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out[3] = a[4]; |
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out[4] = a[5]; |
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out[5] = a[6]; |
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out[6] = a[8]; |
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out[7] = a[9]; |
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out[8] = a[10]; |
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return out; |
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} |
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/** |
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* Creates a new mat3 initialized with values from an existing matrix |
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* |
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* @param {mat3} a matrix to clone |
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* @returns {mat3} a new 3x3 matrix |
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*/ |
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function clone(a) { |
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var out = new glMatrix.ARRAY_TYPE(9); |
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out[0] = a[0]; |
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out[1] = a[1]; |
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out[2] = a[2]; |
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out[3] = a[3]; |
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out[4] = a[4]; |
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out[5] = a[5]; |
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out[6] = a[6]; |
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out[7] = a[7]; |
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out[8] = a[8]; |
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return out; |
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} |
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/** |
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* Copy the values from one mat3 to another |
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* |
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* @param {mat3} out the receiving matrix |
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* @param {mat3} a the source matrix |
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* @returns {mat3} out |
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*/ |
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function copy(out, a) { |
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out[0] = a[0]; |
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out[1] = a[1]; |
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out[2] = a[2]; |
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out[3] = a[3]; |
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out[4] = a[4]; |
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out[5] = a[5]; |
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out[6] = a[6]; |
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out[7] = a[7]; |
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out[8] = a[8]; |
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return out; |
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} |
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/** |
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* Create a new mat3 with the given values |
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* |
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* @param {Number} m00 Component in column 0, row 0 position (index 0) |
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* @param {Number} m01 Component in column 0, row 1 position (index 1) |
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* @param {Number} m02 Component in column 0, row 2 position (index 2) |
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* @param {Number} m10 Component in column 1, row 0 position (index 3) |
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* @param {Number} m11 Component in column 1, row 1 position (index 4) |
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* @param {Number} m12 Component in column 1, row 2 position (index 5) |
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* @param {Number} m20 Component in column 2, row 0 position (index 6) |
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* @param {Number} m21 Component in column 2, row 1 position (index 7) |
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* @param {Number} m22 Component in column 2, row 2 position (index 8) |
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* @returns {mat3} A new mat3 |
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*/ |
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function fromValues(m00, m01, m02, m10, m11, m12, m20, m21, m22) { |
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var out = new glMatrix.ARRAY_TYPE(9); |
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out[0] = m00; |
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out[1] = m01; |
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out[2] = m02; |
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out[3] = m10; |
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out[4] = m11; |
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out[5] = m12; |
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out[6] = m20; |
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out[7] = m21; |
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out[8] = m22; |
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return out; |
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} |
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|
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/** |
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* Set the components of a mat3 to the given values |
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* |
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* @param {mat3} out the receiving matrix |
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* @param {Number} m00 Component in column 0, row 0 position (index 0) |
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* @param {Number} m01 Component in column 0, row 1 position (index 1) |
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* @param {Number} m02 Component in column 0, row 2 position (index 2) |
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* @param {Number} m10 Component in column 1, row 0 position (index 3) |
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* @param {Number} m11 Component in column 1, row 1 position (index 4) |
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* @param {Number} m12 Component in column 1, row 2 position (index 5) |
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* @param {Number} m20 Component in column 2, row 0 position (index 6) |
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* @param {Number} m21 Component in column 2, row 1 position (index 7) |
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* @param {Number} m22 Component in column 2, row 2 position (index 8) |
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* @returns {mat3} out |
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*/ |
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function set(out, m00, m01, m02, m10, m11, m12, m20, m21, m22) { |
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out[0] = m00; |
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out[1] = m01; |
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out[2] = m02; |
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out[3] = m10; |
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out[4] = m11; |
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out[5] = m12; |
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out[6] = m20; |
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out[7] = m21; |
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out[8] = m22; |
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return out; |
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} |
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/** |
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* Set a mat3 to the identity matrix |
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* |
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* @param {mat3} out the receiving matrix |
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* @returns {mat3} out |
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*/ |
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function identity(out) { |
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out[0] = 1; |
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out[1] = 0; |
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out[2] = 0; |
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out[3] = 0; |
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out[4] = 1; |
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out[5] = 0; |
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out[6] = 0; |
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out[7] = 0; |
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out[8] = 1; |
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return out; |
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} |
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/** |
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* Transpose the values of a mat3 |
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* |
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* @param {mat3} out the receiving matrix |
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* @param {mat3} a the source matrix |
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* @returns {mat3} out |
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*/ |
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function transpose(out, a) { |
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// If we are transposing ourselves we can skip a few steps but have to cache some values |
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if (out === a) { |
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var a01 = a[1], |
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a02 = a[2], |
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a12 = a[5]; |
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out[1] = a[3]; |
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out[2] = a[6]; |
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out[3] = a01; |
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out[5] = a[7]; |
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out[6] = a02; |
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out[7] = a12; |
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} else { |
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out[0] = a[0]; |
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out[1] = a[3]; |
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out[2] = a[6]; |
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out[3] = a[1]; |
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out[4] = a[4]; |
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out[5] = a[7]; |
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out[6] = a[2]; |
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out[7] = a[5]; |
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out[8] = a[8]; |
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} |
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return out; |
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} |
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/** |
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* Inverts a mat3 |
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* |
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* @param {mat3} out the receiving matrix |
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* @param {mat3} a the source matrix |
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* @returns {mat3} out |
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*/ |
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function invert(out, a) { |
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var a00 = a[0], |
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a01 = a[1], |
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a02 = a[2]; |
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var a10 = a[3], |
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a11 = a[4], |
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a12 = a[5]; |
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var a20 = a[6], |
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a21 = a[7], |
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a22 = a[8]; |
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|
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var b01 = a22 * a11 - a12 * a21; |
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var b11 = -a22 * a10 + a12 * a20; |
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var b21 = a21 * a10 - a11 * a20; |
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|
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// Calculate the determinant |
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var det = a00 * b01 + a01 * b11 + a02 * b21; |
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|
|
if (!det) { |
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return null; |
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} |
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det = 1.0 / det; |
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|
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out[0] = b01 * det; |
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out[1] = (-a22 * a01 + a02 * a21) * det; |
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out[2] = (a12 * a01 - a02 * a11) * det; |
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out[3] = b11 * det; |
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out[4] = (a22 * a00 - a02 * a20) * det; |
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out[5] = (-a12 * a00 + a02 * a10) * det; |
|
out[6] = b21 * det; |
|
out[7] = (-a21 * a00 + a01 * a20) * det; |
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out[8] = (a11 * a00 - a01 * a10) * det; |
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return out; |
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} |
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|
|
/** |
|
* Calculates the adjugate of a mat3 |
|
* |
|
* @param {mat3} out the receiving matrix |
|
* @param {mat3} a the source matrix |
|
* @returns {mat3} out |
|
*/ |
|
function adjoint(out, a) { |
|
var a00 = a[0], |
|
a01 = a[1], |
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a02 = a[2]; |
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var a10 = a[3], |
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a11 = a[4], |
|
a12 = a[5]; |
|
var a20 = a[6], |
|
a21 = a[7], |
|
a22 = a[8]; |
|
|
|
out[0] = a11 * a22 - a12 * a21; |
|
out[1] = a02 * a21 - a01 * a22; |
|
out[2] = a01 * a12 - a02 * a11; |
|
out[3] = a12 * a20 - a10 * a22; |
|
out[4] = a00 * a22 - a02 * a20; |
|
out[5] = a02 * a10 - a00 * a12; |
|
out[6] = a10 * a21 - a11 * a20; |
|
out[7] = a01 * a20 - a00 * a21; |
|
out[8] = a00 * a11 - a01 * a10; |
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the determinant of a mat3 |
|
* |
|
* @param {mat3} a the source matrix |
|
* @returns {Number} determinant of a |
|
*/ |
|
function determinant(a) { |
|
var a00 = a[0], |
|
a01 = a[1], |
|
a02 = a[2]; |
|
var a10 = a[3], |
|
a11 = a[4], |
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a12 = a[5]; |
|
var a20 = a[6], |
|
a21 = a[7], |
|
a22 = a[8]; |
|
|
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return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20); |
|
} |
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|
|
/** |
|
* Multiplies two mat3's |
|
* |
|
* @param {mat3} out the receiving matrix |
|
* @param {mat3} a the first operand |
|
* @param {mat3} b the second operand |
|
* @returns {mat3} out |
|
*/ |
|
function multiply(out, a, b) { |
|
var a00 = a[0], |
|
a01 = a[1], |
|
a02 = a[2]; |
|
var a10 = a[3], |
|
a11 = a[4], |
|
a12 = a[5]; |
|
var a20 = a[6], |
|
a21 = a[7], |
|
a22 = a[8]; |
|
|
|
var b00 = b[0], |
|
b01 = b[1], |
|
b02 = b[2]; |
|
var b10 = b[3], |
|
b11 = b[4], |
|
b12 = b[5]; |
|
var b20 = b[6], |
|
b21 = b[7], |
|
b22 = b[8]; |
|
|
|
out[0] = b00 * a00 + b01 * a10 + b02 * a20; |
|
out[1] = b00 * a01 + b01 * a11 + b02 * a21; |
|
out[2] = b00 * a02 + b01 * a12 + b02 * a22; |
|
|
|
out[3] = b10 * a00 + b11 * a10 + b12 * a20; |
|
out[4] = b10 * a01 + b11 * a11 + b12 * a21; |
|
out[5] = b10 * a02 + b11 * a12 + b12 * a22; |
|
|
|
out[6] = b20 * a00 + b21 * a10 + b22 * a20; |
|
out[7] = b20 * a01 + b21 * a11 + b22 * a21; |
|
out[8] = b20 * a02 + b21 * a12 + b22 * a22; |
|
return out; |
|
} |
|
|
|
/** |
|
* Translate a mat3 by the given vector |
|
* |
|
* @param {mat3} out the receiving matrix |
|
* @param {mat3} a the matrix to translate |
|
* @param {vec2} v vector to translate by |
|
* @returns {mat3} out |
|
*/ |
|
function translate(out, a, v) { |
|
var a00 = a[0], |
|
a01 = a[1], |
|
a02 = a[2], |
|
a10 = a[3], |
|
a11 = a[4], |
|
a12 = a[5], |
|
a20 = a[6], |
|
a21 = a[7], |
|
a22 = a[8], |
|
x = v[0], |
|
y = v[1]; |
|
|
|
out[0] = a00; |
|
out[1] = a01; |
|
out[2] = a02; |
|
|
|
out[3] = a10; |
|
out[4] = a11; |
|
out[5] = a12; |
|
|
|
out[6] = x * a00 + y * a10 + a20; |
|
out[7] = x * a01 + y * a11 + a21; |
|
out[8] = x * a02 + y * a12 + a22; |
|
return out; |
|
} |
|
|
|
/** |
|
* Rotates a mat3 by the given angle |
|
* |
|
* @param {mat3} out the receiving matrix |
|
* @param {mat3} a the matrix to rotate |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat3} out |
|
*/ |
|
function rotate(out, a, rad) { |
|
var a00 = a[0], |
|
a01 = a[1], |
|
a02 = a[2], |
|
a10 = a[3], |
|
a11 = a[4], |
|
a12 = a[5], |
|
a20 = a[6], |
|
a21 = a[7], |
|
a22 = a[8], |
|
s = Math.sin(rad), |
|
c = Math.cos(rad); |
|
|
|
out[0] = c * a00 + s * a10; |
|
out[1] = c * a01 + s * a11; |
|
out[2] = c * a02 + s * a12; |
|
|
|
out[3] = c * a10 - s * a00; |
|
out[4] = c * a11 - s * a01; |
|
out[5] = c * a12 - s * a02; |
|
|
|
out[6] = a20; |
|
out[7] = a21; |
|
out[8] = a22; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Scales the mat3 by the dimensions in the given vec2 |
|
* |
|
* @param {mat3} out the receiving matrix |
|
* @param {mat3} a the matrix to rotate |
|
* @param {vec2} v the vec2 to scale the matrix by |
|
* @returns {mat3} out |
|
**/ |
|
function scale(out, a, v) { |
|
var x = v[0], |
|
y = v[1]; |
|
|
|
out[0] = x * a[0]; |
|
out[1] = x * a[1]; |
|
out[2] = x * a[2]; |
|
|
|
out[3] = y * a[3]; |
|
out[4] = y * a[4]; |
|
out[5] = y * a[5]; |
|
|
|
out[6] = a[6]; |
|
out[7] = a[7]; |
|
out[8] = a[8]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a vector translation |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat3.identity(dest); |
|
* mat3.translate(dest, dest, vec); |
|
* |
|
* @param {mat3} out mat3 receiving operation result |
|
* @param {vec2} v Translation vector |
|
* @returns {mat3} out |
|
*/ |
|
function fromTranslation(out, v) { |
|
out[0] = 1; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 0; |
|
out[4] = 1; |
|
out[5] = 0; |
|
out[6] = v[0]; |
|
out[7] = v[1]; |
|
out[8] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a given angle |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat3.identity(dest); |
|
* mat3.rotate(dest, dest, rad); |
|
* |
|
* @param {mat3} out mat3 receiving operation result |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat3} out |
|
*/ |
|
function fromRotation(out, rad) { |
|
var s = Math.sin(rad), |
|
c = Math.cos(rad); |
|
|
|
out[0] = c; |
|
out[1] = s; |
|
out[2] = 0; |
|
|
|
out[3] = -s; |
|
out[4] = c; |
|
out[5] = 0; |
|
|
|
out[6] = 0; |
|
out[7] = 0; |
|
out[8] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a vector scaling |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat3.identity(dest); |
|
* mat3.scale(dest, dest, vec); |
|
* |
|
* @param {mat3} out mat3 receiving operation result |
|
* @param {vec2} v Scaling vector |
|
* @returns {mat3} out |
|
*/ |
|
function fromScaling(out, v) { |
|
out[0] = v[0]; |
|
out[1] = 0; |
|
out[2] = 0; |
|
|
|
out[3] = 0; |
|
out[4] = v[1]; |
|
out[5] = 0; |
|
|
|
out[6] = 0; |
|
out[7] = 0; |
|
out[8] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Copies the values from a mat2d into a mat3 |
|
* |
|
* @param {mat3} out the receiving matrix |
|
* @param {mat2d} a the matrix to copy |
|
* @returns {mat3} out |
|
**/ |
|
function fromMat2d(out, a) { |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
out[2] = 0; |
|
|
|
out[3] = a[2]; |
|
out[4] = a[3]; |
|
out[5] = 0; |
|
|
|
out[6] = a[4]; |
|
out[7] = a[5]; |
|
out[8] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates a 3x3 matrix from the given quaternion |
|
* |
|
* @param {mat3} out mat3 receiving operation result |
|
* @param {quat} q Quaternion to create matrix from |
|
* |
|
* @returns {mat3} out |
|
*/ |
|
function fromQuat(out, q) { |
|
var x = q[0], |
|
y = q[1], |
|
z = q[2], |
|
w = q[3]; |
|
var x2 = x + x; |
|
var y2 = y + y; |
|
var z2 = z + z; |
|
|
|
var xx = x * x2; |
|
var yx = y * x2; |
|
var yy = y * y2; |
|
var zx = z * x2; |
|
var zy = z * y2; |
|
var zz = z * z2; |
|
var wx = w * x2; |
|
var wy = w * y2; |
|
var wz = w * z2; |
|
|
|
out[0] = 1 - yy - zz; |
|
out[3] = yx - wz; |
|
out[6] = zx + wy; |
|
|
|
out[1] = yx + wz; |
|
out[4] = 1 - xx - zz; |
|
out[7] = zy - wx; |
|
|
|
out[2] = zx - wy; |
|
out[5] = zy + wx; |
|
out[8] = 1 - xx - yy; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates a 3x3 normal matrix (transpose inverse) from the 4x4 matrix |
|
* |
|
* @param {mat3} out mat3 receiving operation result |
|
* @param {mat4} a Mat4 to derive the normal matrix from |
|
* |
|
* @returns {mat3} out |
|
*/ |
|
function normalFromMat4(out, a) { |
|
var a00 = a[0], |
|
a01 = a[1], |
|
a02 = a[2], |
|
a03 = a[3]; |
|
var a10 = a[4], |
|
a11 = a[5], |
|
a12 = a[6], |
|
a13 = a[7]; |
|
var a20 = a[8], |
|
a21 = a[9], |
|
a22 = a[10], |
|
a23 = a[11]; |
|
var a30 = a[12], |
|
a31 = a[13], |
|
a32 = a[14], |
|
a33 = a[15]; |
|
|
|
var b00 = a00 * a11 - a01 * a10; |
|
var b01 = a00 * a12 - a02 * a10; |
|
var b02 = a00 * a13 - a03 * a10; |
|
var b03 = a01 * a12 - a02 * a11; |
|
var b04 = a01 * a13 - a03 * a11; |
|
var b05 = a02 * a13 - a03 * a12; |
|
var b06 = a20 * a31 - a21 * a30; |
|
var b07 = a20 * a32 - a22 * a30; |
|
var b08 = a20 * a33 - a23 * a30; |
|
var b09 = a21 * a32 - a22 * a31; |
|
var b10 = a21 * a33 - a23 * a31; |
|
var b11 = a22 * a33 - a23 * a32; |
|
|
|
// Calculate the determinant |
|
var det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06; |
|
|
|
if (!det) { |
|
return null; |
|
} |
|
det = 1.0 / det; |
|
|
|
out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det; |
|
out[1] = (a12 * b08 - a10 * b11 - a13 * b07) * det; |
|
out[2] = (a10 * b10 - a11 * b08 + a13 * b06) * det; |
|
|
|
out[3] = (a02 * b10 - a01 * b11 - a03 * b09) * det; |
|
out[4] = (a00 * b11 - a02 * b08 + a03 * b07) * det; |
|
out[5] = (a01 * b08 - a00 * b10 - a03 * b06) * det; |
|
|
|
out[6] = (a31 * b05 - a32 * b04 + a33 * b03) * det; |
|
out[7] = (a32 * b02 - a30 * b05 - a33 * b01) * det; |
|
out[8] = (a30 * b04 - a31 * b02 + a33 * b00) * det; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Generates a 2D projection matrix with the given bounds |
|
* |
|
* @param {mat3} out mat3 frustum matrix will be written into |
|
* @param {number} width Width of your gl context |
|
* @param {number} height Height of gl context |
|
* @returns {mat3} out |
|
*/ |
|
function projection(out, width, height) { |
|
out[0] = 2 / width; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 0; |
|
out[4] = -2 / height; |
|
out[5] = 0; |
|
out[6] = -1; |
|
out[7] = 1; |
|
out[8] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns a string representation of a mat3 |
|
* |
|
* @param {mat3} a matrix to represent as a string |
|
* @returns {String} string representation of the matrix |
|
*/ |
|
function str(a) { |
|
return 'mat3(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ', ' + a[4] + ', ' + a[5] + ', ' + a[6] + ', ' + a[7] + ', ' + a[8] + ')'; |
|
} |
|
|
|
/** |
|
* Returns Frobenius norm of a mat3 |
|
* |
|
* @param {mat3} a the matrix to calculate Frobenius norm of |
|
* @returns {Number} Frobenius norm |
|
*/ |
|
function frob(a) { |
|
return Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2) + Math.pow(a[4], 2) + Math.pow(a[5], 2) + Math.pow(a[6], 2) + Math.pow(a[7], 2) + Math.pow(a[8], 2)); |
|
} |
|
|
|
/** |
|
* Adds two mat3's |
|
* |
|
* @param {mat3} out the receiving matrix |
|
* @param {mat3} a the first operand |
|
* @param {mat3} b the second operand |
|
* @returns {mat3} out |
|
*/ |
|
function add(out, a, b) { |
|
out[0] = a[0] + b[0]; |
|
out[1] = a[1] + b[1]; |
|
out[2] = a[2] + b[2]; |
|
out[3] = a[3] + b[3]; |
|
out[4] = a[4] + b[4]; |
|
out[5] = a[5] + b[5]; |
|
out[6] = a[6] + b[6]; |
|
out[7] = a[7] + b[7]; |
|
out[8] = a[8] + b[8]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Subtracts matrix b from matrix a |
|
* |
|
* @param {mat3} out the receiving matrix |
|
* @param {mat3} a the first operand |
|
* @param {mat3} b the second operand |
|
* @returns {mat3} out |
|
*/ |
|
function subtract(out, a, b) { |
|
out[0] = a[0] - b[0]; |
|
out[1] = a[1] - b[1]; |
|
out[2] = a[2] - b[2]; |
|
out[3] = a[3] - b[3]; |
|
out[4] = a[4] - b[4]; |
|
out[5] = a[5] - b[5]; |
|
out[6] = a[6] - b[6]; |
|
out[7] = a[7] - b[7]; |
|
out[8] = a[8] - b[8]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Multiply each element of the matrix by a scalar. |
|
* |
|
* @param {mat3} out the receiving matrix |
|
* @param {mat3} a the matrix to scale |
|
* @param {Number} b amount to scale the matrix's elements by |
|
* @returns {mat3} out |
|
*/ |
|
function multiplyScalar(out, a, b) { |
|
out[0] = a[0] * b; |
|
out[1] = a[1] * b; |
|
out[2] = a[2] * b; |
|
out[3] = a[3] * b; |
|
out[4] = a[4] * b; |
|
out[5] = a[5] * b; |
|
out[6] = a[6] * b; |
|
out[7] = a[7] * b; |
|
out[8] = a[8] * b; |
|
return out; |
|
} |
|
|
|
/** |
|
* Adds two mat3's after multiplying each element of the second operand by a scalar value. |
|
* |
|
* @param {mat3} out the receiving vector |
|
* @param {mat3} a the first operand |
|
* @param {mat3} b the second operand |
|
* @param {Number} scale the amount to scale b's elements by before adding |
|
* @returns {mat3} out |
|
*/ |
|
function multiplyScalarAndAdd(out, a, b, scale) { |
|
out[0] = a[0] + b[0] * scale; |
|
out[1] = a[1] + b[1] * scale; |
|
out[2] = a[2] + b[2] * scale; |
|
out[3] = a[3] + b[3] * scale; |
|
out[4] = a[4] + b[4] * scale; |
|
out[5] = a[5] + b[5] * scale; |
|
out[6] = a[6] + b[6] * scale; |
|
out[7] = a[7] + b[7] * scale; |
|
out[8] = a[8] + b[8] * scale; |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===) |
|
* |
|
* @param {mat3} a The first matrix. |
|
* @param {mat3} b The second matrix. |
|
* @returns {Boolean} True if the matrices are equal, false otherwise. |
|
*/ |
|
function exactEquals(a, b) { |
|
return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3] && a[4] === b[4] && a[5] === b[5] && a[6] === b[6] && a[7] === b[7] && a[8] === b[8]; |
|
} |
|
|
|
/** |
|
* Returns whether or not the matrices have approximately the same elements in the same position. |
|
* |
|
* @param {mat3} a The first matrix. |
|
* @param {mat3} b The second matrix. |
|
* @returns {Boolean} True if the matrices are equal, false otherwise. |
|
*/ |
|
function equals(a, b) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3], |
|
a4 = a[4], |
|
a5 = a[5], |
|
a6 = a[6], |
|
a7 = a[7], |
|
a8 = a[8]; |
|
var b0 = b[0], |
|
b1 = b[1], |
|
b2 = b[2], |
|
b3 = b[3], |
|
b4 = b[4], |
|
b5 = b[5], |
|
b6 = b[6], |
|
b7 = b[7], |
|
b8 = b[8]; |
|
return Math.abs(a0 - b0) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)) && Math.abs(a6 - b6) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a6), Math.abs(b6)) && Math.abs(a7 - b7) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a7), Math.abs(b7)) && Math.abs(a8 - b8) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a8), Math.abs(b8)); |
|
} |
|
|
|
/** |
|
* Alias for {@link mat3.multiply} |
|
* @function |
|
*/ |
|
var mul = exports.mul = multiply; |
|
|
|
/** |
|
* Alias for {@link mat3.subtract} |
|
* @function |
|
*/ |
|
var sub = exports.sub = subtract; |
|
|
|
/***/ }), |
|
/* 2 */ |
|
/***/ (function(module, exports, __webpack_require__) { |
|
|
|
"use strict"; |
|
|
|
|
|
Object.defineProperty(exports, "__esModule", { |
|
value: true |
|
}); |
|
exports.forEach = exports.sqrLen = exports.len = exports.sqrDist = exports.dist = exports.div = exports.mul = exports.sub = undefined; |
|
exports.create = create; |
|
exports.clone = clone; |
|
exports.length = length; |
|
exports.fromValues = fromValues; |
|
exports.copy = copy; |
|
exports.set = set; |
|
exports.add = add; |
|
exports.subtract = subtract; |
|
exports.multiply = multiply; |
|
exports.divide = divide; |
|
exports.ceil = ceil; |
|
exports.floor = floor; |
|
exports.min = min; |
|
exports.max = max; |
|
exports.round = round; |
|
exports.scale = scale; |
|
exports.scaleAndAdd = scaleAndAdd; |
|
exports.distance = distance; |
|
exports.squaredDistance = squaredDistance; |
|
exports.squaredLength = squaredLength; |
|
exports.negate = negate; |
|
exports.inverse = inverse; |
|
exports.normalize = normalize; |
|
exports.dot = dot; |
|
exports.cross = cross; |
|
exports.lerp = lerp; |
|
exports.hermite = hermite; |
|
exports.bezier = bezier; |
|
exports.random = random; |
|
exports.transformMat4 = transformMat4; |
|
exports.transformMat3 = transformMat3; |
|
exports.transformQuat = transformQuat; |
|
exports.rotateX = rotateX; |
|
exports.rotateY = rotateY; |
|
exports.rotateZ = rotateZ; |
|
exports.angle = angle; |
|
exports.str = str; |
|
exports.exactEquals = exactEquals; |
|
exports.equals = equals; |
|
|
|
var _common = __webpack_require__(0); |
|
|
|
var glMatrix = _interopRequireWildcard(_common); |
|
|
|
function _interopRequireWildcard(obj) { if (obj && obj.__esModule) { return obj; } else { var newObj = {}; if (obj != null) { for (var key in obj) { if (Object.prototype.hasOwnProperty.call(obj, key)) newObj[key] = obj[key]; } } newObj.default = obj; return newObj; } } |
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|
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/** |
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* 3 Dimensional Vector |
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* @module vec3 |
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*/ |
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|
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/** |
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* Creates a new, empty vec3 |
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* |
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* @returns {vec3} a new 3D vector |
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*/ |
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function create() { |
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var out = new glMatrix.ARRAY_TYPE(3); |
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out[0] = 0; |
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out[1] = 0; |
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out[2] = 0; |
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return out; |
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} |
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|
|
/** |
|
* Creates a new vec3 initialized with values from an existing vector |
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* |
|
* @param {vec3} a vector to clone |
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* @returns {vec3} a new 3D vector |
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*/ |
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/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. |
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|
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Permission is hereby granted, free of charge, to any person obtaining a copy |
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of this software and associated documentation files (the "Software"), to deal |
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in the Software without restriction, including without limitation the rights |
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
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copies of the Software, and to permit persons to whom the Software is |
|
furnished to do so, subject to the following conditions: |
|
|
|
The above copyright notice and this permission notice shall be included in |
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all copies or substantial portions of the Software. |
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|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
|
THE SOFTWARE. */ |
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|
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function clone(a) { |
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var out = new glMatrix.ARRAY_TYPE(3); |
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out[0] = a[0]; |
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out[1] = a[1]; |
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out[2] = a[2]; |
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return out; |
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} |
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|
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/** |
|
* Calculates the length of a vec3 |
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* |
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* @param {vec3} a vector to calculate length of |
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* @returns {Number} length of a |
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*/ |
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function length(a) { |
|
var x = a[0]; |
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var y = a[1]; |
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var z = a[2]; |
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return Math.sqrt(x * x + y * y + z * z); |
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} |
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|
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/** |
|
* Creates a new vec3 initialized with the given values |
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* |
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* @param {Number} x X component |
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* @param {Number} y Y component |
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* @param {Number} z Z component |
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* @returns {vec3} a new 3D vector |
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*/ |
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function fromValues(x, y, z) { |
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var out = new glMatrix.ARRAY_TYPE(3); |
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out[0] = x; |
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out[1] = y; |
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out[2] = z; |
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return out; |
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} |
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|
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/** |
|
* Copy the values from one vec3 to another |
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* |
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* @param {vec3} out the receiving vector |
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* @param {vec3} a the source vector |
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* @returns {vec3} out |
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*/ |
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function copy(out, a) { |
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out[0] = a[0]; |
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out[1] = a[1]; |
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out[2] = a[2]; |
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return out; |
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} |
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|
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/** |
|
* Set the components of a vec3 to the given values |
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* |
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* @param {vec3} out the receiving vector |
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* @param {Number} x X component |
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* @param {Number} y Y component |
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* @param {Number} z Z component |
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* @returns {vec3} out |
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*/ |
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function set(out, x, y, z) { |
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out[0] = x; |
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out[1] = y; |
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out[2] = z; |
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return out; |
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} |
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|
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/** |
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* Adds two vec3's |
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* |
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* @param {vec3} out the receiving vector |
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* @param {vec3} a the first operand |
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* @param {vec3} b the second operand |
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* @returns {vec3} out |
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*/ |
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function add(out, a, b) { |
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out[0] = a[0] + b[0]; |
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out[1] = a[1] + b[1]; |
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out[2] = a[2] + b[2]; |
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return out; |
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} |
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|
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/** |
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* Subtracts vector b from vector a |
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* |
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* @param {vec3} out the receiving vector |
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* @param {vec3} a the first operand |
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* @param {vec3} b the second operand |
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* @returns {vec3} out |
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*/ |
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function subtract(out, a, b) { |
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out[0] = a[0] - b[0]; |
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out[1] = a[1] - b[1]; |
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out[2] = a[2] - b[2]; |
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return out; |
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} |
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|
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/** |
|
* Multiplies two vec3's |
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* |
|
* @param {vec3} out the receiving vector |
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* @param {vec3} a the first operand |
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* @param {vec3} b the second operand |
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* @returns {vec3} out |
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*/ |
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function multiply(out, a, b) { |
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out[0] = a[0] * b[0]; |
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out[1] = a[1] * b[1]; |
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out[2] = a[2] * b[2]; |
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return out; |
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} |
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|
|
/** |
|
* Divides two vec3's |
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* |
|
* @param {vec3} out the receiving vector |
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* @param {vec3} a the first operand |
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* @param {vec3} b the second operand |
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* @returns {vec3} out |
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*/ |
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function divide(out, a, b) { |
|
out[0] = a[0] / b[0]; |
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out[1] = a[1] / b[1]; |
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out[2] = a[2] / b[2]; |
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return out; |
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} |
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|
|
/** |
|
* Math.ceil the components of a vec3 |
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* |
|
* @param {vec3} out the receiving vector |
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* @param {vec3} a vector to ceil |
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* @returns {vec3} out |
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*/ |
|
function ceil(out, a) { |
|
out[0] = Math.ceil(a[0]); |
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out[1] = Math.ceil(a[1]); |
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out[2] = Math.ceil(a[2]); |
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return out; |
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} |
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|
|
/** |
|
* Math.floor the components of a vec3 |
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* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a vector to floor |
|
* @returns {vec3} out |
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*/ |
|
function floor(out, a) { |
|
out[0] = Math.floor(a[0]); |
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out[1] = Math.floor(a[1]); |
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out[2] = Math.floor(a[2]); |
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return out; |
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} |
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|
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/** |
|
* Returns the minimum of two vec3's |
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* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a the first operand |
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* @param {vec3} b the second operand |
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* @returns {vec3} out |
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*/ |
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function min(out, a, b) { |
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out[0] = Math.min(a[0], b[0]); |
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out[1] = Math.min(a[1], b[1]); |
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out[2] = Math.min(a[2], b[2]); |
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return out; |
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} |
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|
|
/** |
|
* Returns the maximum of two vec3's |
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* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a the first operand |
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* @param {vec3} b the second operand |
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* @returns {vec3} out |
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*/ |
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function max(out, a, b) { |
|
out[0] = Math.max(a[0], b[0]); |
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out[1] = Math.max(a[1], b[1]); |
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out[2] = Math.max(a[2], b[2]); |
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return out; |
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} |
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|
|
/** |
|
* Math.round the components of a vec3 |
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* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a vector to round |
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* @returns {vec3} out |
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*/ |
|
function round(out, a) { |
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out[0] = Math.round(a[0]); |
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out[1] = Math.round(a[1]); |
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out[2] = Math.round(a[2]); |
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return out; |
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} |
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|
|
/** |
|
* Scales a vec3 by a scalar number |
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* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a the vector to scale |
|
* @param {Number} b amount to scale the vector by |
|
* @returns {vec3} out |
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*/ |
|
function scale(out, a, b) { |
|
out[0] = a[0] * b; |
|
out[1] = a[1] * b; |
|
out[2] = a[2] * b; |
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return out; |
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} |
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|
|
/** |
|
* Adds two vec3's after scaling the second operand by a scalar value |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a the first operand |
|
* @param {vec3} b the second operand |
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* @param {Number} scale the amount to scale b by before adding |
|
* @returns {vec3} out |
|
*/ |
|
function scaleAndAdd(out, a, b, scale) { |
|
out[0] = a[0] + b[0] * scale; |
|
out[1] = a[1] + b[1] * scale; |
|
out[2] = a[2] + b[2] * scale; |
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return out; |
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} |
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|
|
/** |
|
* Calculates the euclidian distance between two vec3's |
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* |
|
* @param {vec3} a the first operand |
|
* @param {vec3} b the second operand |
|
* @returns {Number} distance between a and b |
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*/ |
|
function distance(a, b) { |
|
var x = b[0] - a[0]; |
|
var y = b[1] - a[1]; |
|
var z = b[2] - a[2]; |
|
return Math.sqrt(x * x + y * y + z * z); |
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} |
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|
|
/** |
|
* Calculates the squared euclidian distance between two vec3's |
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* |
|
* @param {vec3} a the first operand |
|
* @param {vec3} b the second operand |
|
* @returns {Number} squared distance between a and b |
|
*/ |
|
function squaredDistance(a, b) { |
|
var x = b[0] - a[0]; |
|
var y = b[1] - a[1]; |
|
var z = b[2] - a[2]; |
|
return x * x + y * y + z * z; |
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} |
|
|
|
/** |
|
* Calculates the squared length of a vec3 |
|
* |
|
* @param {vec3} a vector to calculate squared length of |
|
* @returns {Number} squared length of a |
|
*/ |
|
function squaredLength(a) { |
|
var x = a[0]; |
|
var y = a[1]; |
|
var z = a[2]; |
|
return x * x + y * y + z * z; |
|
} |
|
|
|
/** |
|
* Negates the components of a vec3 |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a vector to negate |
|
* @returns {vec3} out |
|
*/ |
|
function negate(out, a) { |
|
out[0] = -a[0]; |
|
out[1] = -a[1]; |
|
out[2] = -a[2]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns the inverse of the components of a vec3 |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a vector to invert |
|
* @returns {vec3} out |
|
*/ |
|
function inverse(out, a) { |
|
out[0] = 1.0 / a[0]; |
|
out[1] = 1.0 / a[1]; |
|
out[2] = 1.0 / a[2]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Normalize a vec3 |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a vector to normalize |
|
* @returns {vec3} out |
|
*/ |
|
function normalize(out, a) { |
|
var x = a[0]; |
|
var y = a[1]; |
|
var z = a[2]; |
|
var len = x * x + y * y + z * z; |
|
if (len > 0) { |
|
//TODO: evaluate use of glm_invsqrt here? |
|
len = 1 / Math.sqrt(len); |
|
out[0] = a[0] * len; |
|
out[1] = a[1] * len; |
|
out[2] = a[2] * len; |
|
} |
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the dot product of two vec3's |
|
* |
|
* @param {vec3} a the first operand |
|
* @param {vec3} b the second operand |
|
* @returns {Number} dot product of a and b |
|
*/ |
|
function dot(a, b) { |
|
return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; |
|
} |
|
|
|
/** |
|
* Computes the cross product of two vec3's |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a the first operand |
|
* @param {vec3} b the second operand |
|
* @returns {vec3} out |
|
*/ |
|
function cross(out, a, b) { |
|
var ax = a[0], |
|
ay = a[1], |
|
az = a[2]; |
|
var bx = b[0], |
|
by = b[1], |
|
bz = b[2]; |
|
|
|
out[0] = ay * bz - az * by; |
|
out[1] = az * bx - ax * bz; |
|
out[2] = ax * by - ay * bx; |
|
return out; |
|
} |
|
|
|
/** |
|
* Performs a linear interpolation between two vec3's |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a the first operand |
|
* @param {vec3} b the second operand |
|
* @param {Number} t interpolation amount between the two inputs |
|
* @returns {vec3} out |
|
*/ |
|
function lerp(out, a, b, t) { |
|
var ax = a[0]; |
|
var ay = a[1]; |
|
var az = a[2]; |
|
out[0] = ax + t * (b[0] - ax); |
|
out[1] = ay + t * (b[1] - ay); |
|
out[2] = az + t * (b[2] - az); |
|
return out; |
|
} |
|
|
|
/** |
|
* Performs a hermite interpolation with two control points |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a the first operand |
|
* @param {vec3} b the second operand |
|
* @param {vec3} c the third operand |
|
* @param {vec3} d the fourth operand |
|
* @param {Number} t interpolation amount between the two inputs |
|
* @returns {vec3} out |
|
*/ |
|
function hermite(out, a, b, c, d, t) { |
|
var factorTimes2 = t * t; |
|
var factor1 = factorTimes2 * (2 * t - 3) + 1; |
|
var factor2 = factorTimes2 * (t - 2) + t; |
|
var factor3 = factorTimes2 * (t - 1); |
|
var factor4 = factorTimes2 * (3 - 2 * t); |
|
|
|
out[0] = a[0] * factor1 + b[0] * factor2 + c[0] * factor3 + d[0] * factor4; |
|
out[1] = a[1] * factor1 + b[1] * factor2 + c[1] * factor3 + d[1] * factor4; |
|
out[2] = a[2] * factor1 + b[2] * factor2 + c[2] * factor3 + d[2] * factor4; |
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|
|
return out; |
|
} |
|
|
|
/** |
|
* Performs a bezier interpolation with two control points |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a the first operand |
|
* @param {vec3} b the second operand |
|
* @param {vec3} c the third operand |
|
* @param {vec3} d the fourth operand |
|
* @param {Number} t interpolation amount between the two inputs |
|
* @returns {vec3} out |
|
*/ |
|
function bezier(out, a, b, c, d, t) { |
|
var inverseFactor = 1 - t; |
|
var inverseFactorTimesTwo = inverseFactor * inverseFactor; |
|
var factorTimes2 = t * t; |
|
var factor1 = inverseFactorTimesTwo * inverseFactor; |
|
var factor2 = 3 * t * inverseFactorTimesTwo; |
|
var factor3 = 3 * factorTimes2 * inverseFactor; |
|
var factor4 = factorTimes2 * t; |
|
|
|
out[0] = a[0] * factor1 + b[0] * factor2 + c[0] * factor3 + d[0] * factor4; |
|
out[1] = a[1] * factor1 + b[1] * factor2 + c[1] * factor3 + d[1] * factor4; |
|
out[2] = a[2] * factor1 + b[2] * factor2 + c[2] * factor3 + d[2] * factor4; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Generates a random vector with the given scale |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {Number} [scale] Length of the resulting vector. If ommitted, a unit vector will be returned |
|
* @returns {vec3} out |
|
*/ |
|
function random(out, scale) { |
|
scale = scale || 1.0; |
|
|
|
var r = glMatrix.RANDOM() * 2.0 * Math.PI; |
|
var z = glMatrix.RANDOM() * 2.0 - 1.0; |
|
var zScale = Math.sqrt(1.0 - z * z) * scale; |
|
|
|
out[0] = Math.cos(r) * zScale; |
|
out[1] = Math.sin(r) * zScale; |
|
out[2] = z * scale; |
|
return out; |
|
} |
|
|
|
/** |
|
* Transforms the vec3 with a mat4. |
|
* 4th vector component is implicitly '1' |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a the vector to transform |
|
* @param {mat4} m matrix to transform with |
|
* @returns {vec3} out |
|
*/ |
|
function transformMat4(out, a, m) { |
|
var x = a[0], |
|
y = a[1], |
|
z = a[2]; |
|
var w = m[3] * x + m[7] * y + m[11] * z + m[15]; |
|
w = w || 1.0; |
|
out[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w; |
|
out[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w; |
|
out[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w; |
|
return out; |
|
} |
|
|
|
/** |
|
* Transforms the vec3 with a mat3. |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a the vector to transform |
|
* @param {mat3} m the 3x3 matrix to transform with |
|
* @returns {vec3} out |
|
*/ |
|
function transformMat3(out, a, m) { |
|
var x = a[0], |
|
y = a[1], |
|
z = a[2]; |
|
out[0] = x * m[0] + y * m[3] + z * m[6]; |
|
out[1] = x * m[1] + y * m[4] + z * m[7]; |
|
out[2] = x * m[2] + y * m[5] + z * m[8]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Transforms the vec3 with a quat |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec3} a the vector to transform |
|
* @param {quat} q quaternion to transform with |
|
* @returns {vec3} out |
|
*/ |
|
function transformQuat(out, a, q) { |
|
// benchmarks: http://jsperf.com/quaternion-transform-vec3-implementations |
|
|
|
var x = a[0], |
|
y = a[1], |
|
z = a[2]; |
|
var qx = q[0], |
|
qy = q[1], |
|
qz = q[2], |
|
qw = q[3]; |
|
|
|
// calculate quat * vec |
|
var ix = qw * x + qy * z - qz * y; |
|
var iy = qw * y + qz * x - qx * z; |
|
var iz = qw * z + qx * y - qy * x; |
|
var iw = -qx * x - qy * y - qz * z; |
|
|
|
// calculate result * inverse quat |
|
out[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy; |
|
out[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz; |
|
out[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx; |
|
return out; |
|
} |
|
|
|
/** |
|
* Rotate a 3D vector around the x-axis |
|
* @param {vec3} out The receiving vec3 |
|
* @param {vec3} a The vec3 point to rotate |
|
* @param {vec3} b The origin of the rotation |
|
* @param {Number} c The angle of rotation |
|
* @returns {vec3} out |
|
*/ |
|
function rotateX(out, a, b, c) { |
|
var p = [], |
|
r = []; |
|
//Translate point to the origin |
|
p[0] = a[0] - b[0]; |
|
p[1] = a[1] - b[1]; |
|
p[2] = a[2] - b[2]; |
|
|
|
//perform rotation |
|
r[0] = p[0]; |
|
r[1] = p[1] * Math.cos(c) - p[2] * Math.sin(c); |
|
r[2] = p[1] * Math.sin(c) + p[2] * Math.cos(c); |
|
|
|
//translate to correct position |
|
out[0] = r[0] + b[0]; |
|
out[1] = r[1] + b[1]; |
|
out[2] = r[2] + b[2]; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Rotate a 3D vector around the y-axis |
|
* @param {vec3} out The receiving vec3 |
|
* @param {vec3} a The vec3 point to rotate |
|
* @param {vec3} b The origin of the rotation |
|
* @param {Number} c The angle of rotation |
|
* @returns {vec3} out |
|
*/ |
|
function rotateY(out, a, b, c) { |
|
var p = [], |
|
r = []; |
|
//Translate point to the origin |
|
p[0] = a[0] - b[0]; |
|
p[1] = a[1] - b[1]; |
|
p[2] = a[2] - b[2]; |
|
|
|
//perform rotation |
|
r[0] = p[2] * Math.sin(c) + p[0] * Math.cos(c); |
|
r[1] = p[1]; |
|
r[2] = p[2] * Math.cos(c) - p[0] * Math.sin(c); |
|
|
|
//translate to correct position |
|
out[0] = r[0] + b[0]; |
|
out[1] = r[1] + b[1]; |
|
out[2] = r[2] + b[2]; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Rotate a 3D vector around the z-axis |
|
* @param {vec3} out The receiving vec3 |
|
* @param {vec3} a The vec3 point to rotate |
|
* @param {vec3} b The origin of the rotation |
|
* @param {Number} c The angle of rotation |
|
* @returns {vec3} out |
|
*/ |
|
function rotateZ(out, a, b, c) { |
|
var p = [], |
|
r = []; |
|
//Translate point to the origin |
|
p[0] = a[0] - b[0]; |
|
p[1] = a[1] - b[1]; |
|
p[2] = a[2] - b[2]; |
|
|
|
//perform rotation |
|
r[0] = p[0] * Math.cos(c) - p[1] * Math.sin(c); |
|
r[1] = p[0] * Math.sin(c) + p[1] * Math.cos(c); |
|
r[2] = p[2]; |
|
|
|
//translate to correct position |
|
out[0] = r[0] + b[0]; |
|
out[1] = r[1] + b[1]; |
|
out[2] = r[2] + b[2]; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Get the angle between two 3D vectors |
|
* @param {vec3} a The first operand |
|
* @param {vec3} b The second operand |
|
* @returns {Number} The angle in radians |
|
*/ |
|
function angle(a, b) { |
|
var tempA = fromValues(a[0], a[1], a[2]); |
|
var tempB = fromValues(b[0], b[1], b[2]); |
|
|
|
normalize(tempA, tempA); |
|
normalize(tempB, tempB); |
|
|
|
var cosine = dot(tempA, tempB); |
|
|
|
if (cosine > 1.0) { |
|
return 0; |
|
} else if (cosine < -1.0) { |
|
return Math.PI; |
|
} else { |
|
return Math.acos(cosine); |
|
} |
|
} |
|
|
|
/** |
|
* Returns a string representation of a vector |
|
* |
|
* @param {vec3} a vector to represent as a string |
|
* @returns {String} string representation of the vector |
|
*/ |
|
function str(a) { |
|
return 'vec3(' + a[0] + ', ' + a[1] + ', ' + a[2] + ')'; |
|
} |
|
|
|
/** |
|
* Returns whether or not the vectors have exactly the same elements in the same position (when compared with ===) |
|
* |
|
* @param {vec3} a The first vector. |
|
* @param {vec3} b The second vector. |
|
* @returns {Boolean} True if the vectors are equal, false otherwise. |
|
*/ |
|
function exactEquals(a, b) { |
|
return a[0] === b[0] && a[1] === b[1] && a[2] === b[2]; |
|
} |
|
|
|
/** |
|
* Returns whether or not the vectors have approximately the same elements in the same position. |
|
* |
|
* @param {vec3} a The first vector. |
|
* @param {vec3} b The second vector. |
|
* @returns {Boolean} True if the vectors are equal, false otherwise. |
|
*/ |
|
function equals(a, b) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2]; |
|
var b0 = b[0], |
|
b1 = b[1], |
|
b2 = b[2]; |
|
return Math.abs(a0 - b0) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)); |
|
} |
|
|
|
/** |
|
* Alias for {@link vec3.subtract} |
|
* @function |
|
*/ |
|
var sub = exports.sub = subtract; |
|
|
|
/** |
|
* Alias for {@link vec3.multiply} |
|
* @function |
|
*/ |
|
var mul = exports.mul = multiply; |
|
|
|
/** |
|
* Alias for {@link vec3.divide} |
|
* @function |
|
*/ |
|
var div = exports.div = divide; |
|
|
|
/** |
|
* Alias for {@link vec3.distance} |
|
* @function |
|
*/ |
|
var dist = exports.dist = distance; |
|
|
|
/** |
|
* Alias for {@link vec3.squaredDistance} |
|
* @function |
|
*/ |
|
var sqrDist = exports.sqrDist = squaredDistance; |
|
|
|
/** |
|
* Alias for {@link vec3.length} |
|
* @function |
|
*/ |
|
var len = exports.len = length; |
|
|
|
/** |
|
* Alias for {@link vec3.squaredLength} |
|
* @function |
|
*/ |
|
var sqrLen = exports.sqrLen = squaredLength; |
|
|
|
/** |
|
* Perform some operation over an array of vec3s. |
|
* |
|
* @param {Array} a the array of vectors to iterate over |
|
* @param {Number} stride Number of elements between the start of each vec3. If 0 assumes tightly packed |
|
* @param {Number} offset Number of elements to skip at the beginning of the array |
|
* @param {Number} count Number of vec3s to iterate over. If 0 iterates over entire array |
|
* @param {Function} fn Function to call for each vector in the array |
|
* @param {Object} [arg] additional argument to pass to fn |
|
* @returns {Array} a |
|
* @function |
|
*/ |
|
var forEach = exports.forEach = function () { |
|
var vec = create(); |
|
|
|
return function (a, stride, offset, count, fn, arg) { |
|
var i = void 0, |
|
l = void 0; |
|
if (!stride) { |
|
stride = 3; |
|
} |
|
|
|
if (!offset) { |
|
offset = 0; |
|
} |
|
|
|
if (count) { |
|
l = Math.min(count * stride + offset, a.length); |
|
} else { |
|
l = a.length; |
|
} |
|
|
|
for (i = offset; i < l; i += stride) { |
|
vec[0] = a[i];vec[1] = a[i + 1];vec[2] = a[i + 2]; |
|
fn(vec, vec, arg); |
|
a[i] = vec[0];a[i + 1] = vec[1];a[i + 2] = vec[2]; |
|
} |
|
|
|
return a; |
|
}; |
|
}(); |
|
|
|
/***/ }), |
|
/* 3 */ |
|
/***/ (function(module, exports, __webpack_require__) { |
|
|
|
"use strict"; |
|
|
|
|
|
Object.defineProperty(exports, "__esModule", { |
|
value: true |
|
}); |
|
exports.forEach = exports.sqrLen = exports.len = exports.sqrDist = exports.dist = exports.div = exports.mul = exports.sub = undefined; |
|
exports.create = create; |
|
exports.clone = clone; |
|
exports.fromValues = fromValues; |
|
exports.copy = copy; |
|
exports.set = set; |
|
exports.add = add; |
|
exports.subtract = subtract; |
|
exports.multiply = multiply; |
|
exports.divide = divide; |
|
exports.ceil = ceil; |
|
exports.floor = floor; |
|
exports.min = min; |
|
exports.max = max; |
|
exports.round = round; |
|
exports.scale = scale; |
|
exports.scaleAndAdd = scaleAndAdd; |
|
exports.distance = distance; |
|
exports.squaredDistance = squaredDistance; |
|
exports.length = length; |
|
exports.squaredLength = squaredLength; |
|
exports.negate = negate; |
|
exports.inverse = inverse; |
|
exports.normalize = normalize; |
|
exports.dot = dot; |
|
exports.lerp = lerp; |
|
exports.random = random; |
|
exports.transformMat4 = transformMat4; |
|
exports.transformQuat = transformQuat; |
|
exports.str = str; |
|
exports.exactEquals = exactEquals; |
|
exports.equals = equals; |
|
|
|
var _common = __webpack_require__(0); |
|
|
|
var glMatrix = _interopRequireWildcard(_common); |
|
|
|
function _interopRequireWildcard(obj) { if (obj && obj.__esModule) { return obj; } else { var newObj = {}; if (obj != null) { for (var key in obj) { if (Object.prototype.hasOwnProperty.call(obj, key)) newObj[key] = obj[key]; } } newObj.default = obj; return newObj; } } |
|
|
|
/** |
|
* 4 Dimensional Vector |
|
* @module vec4 |
|
*/ |
|
|
|
/** |
|
* Creates a new, empty vec4 |
|
* |
|
* @returns {vec4} a new 4D vector |
|
*/ |
|
function create() { |
|
var out = new glMatrix.ARRAY_TYPE(4); |
|
out[0] = 0; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 0; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a new vec4 initialized with values from an existing vector |
|
* |
|
* @param {vec4} a vector to clone |
|
* @returns {vec4} a new 4D vector |
|
*/ |
|
/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. |
|
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy |
|
of this software and associated documentation files (the "Software"), to deal |
|
in the Software without restriction, including without limitation the rights |
|
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
|
copies of the Software, and to permit persons to whom the Software is |
|
furnished to do so, subject to the following conditions: |
|
|
|
The above copyright notice and this permission notice shall be included in |
|
all copies or substantial portions of the Software. |
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
|
THE SOFTWARE. */ |
|
|
|
function clone(a) { |
|
var out = new glMatrix.ARRAY_TYPE(4); |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
out[2] = a[2]; |
|
out[3] = a[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a new vec4 initialized with the given values |
|
* |
|
* @param {Number} x X component |
|
* @param {Number} y Y component |
|
* @param {Number} z Z component |
|
* @param {Number} w W component |
|
* @returns {vec4} a new 4D vector |
|
*/ |
|
function fromValues(x, y, z, w) { |
|
var out = new glMatrix.ARRAY_TYPE(4); |
|
out[0] = x; |
|
out[1] = y; |
|
out[2] = z; |
|
out[3] = w; |
|
return out; |
|
} |
|
|
|
/** |
|
* Copy the values from one vec4 to another |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the source vector |
|
* @returns {vec4} out |
|
*/ |
|
function copy(out, a) { |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
out[2] = a[2]; |
|
out[3] = a[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Set the components of a vec4 to the given values |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {Number} x X component |
|
* @param {Number} y Y component |
|
* @param {Number} z Z component |
|
* @param {Number} w W component |
|
* @returns {vec4} out |
|
*/ |
|
function set(out, x, y, z, w) { |
|
out[0] = x; |
|
out[1] = y; |
|
out[2] = z; |
|
out[3] = w; |
|
return out; |
|
} |
|
|
|
/** |
|
* Adds two vec4's |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the first operand |
|
* @param {vec4} b the second operand |
|
* @returns {vec4} out |
|
*/ |
|
function add(out, a, b) { |
|
out[0] = a[0] + b[0]; |
|
out[1] = a[1] + b[1]; |
|
out[2] = a[2] + b[2]; |
|
out[3] = a[3] + b[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Subtracts vector b from vector a |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the first operand |
|
* @param {vec4} b the second operand |
|
* @returns {vec4} out |
|
*/ |
|
function subtract(out, a, b) { |
|
out[0] = a[0] - b[0]; |
|
out[1] = a[1] - b[1]; |
|
out[2] = a[2] - b[2]; |
|
out[3] = a[3] - b[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Multiplies two vec4's |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the first operand |
|
* @param {vec4} b the second operand |
|
* @returns {vec4} out |
|
*/ |
|
function multiply(out, a, b) { |
|
out[0] = a[0] * b[0]; |
|
out[1] = a[1] * b[1]; |
|
out[2] = a[2] * b[2]; |
|
out[3] = a[3] * b[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Divides two vec4's |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the first operand |
|
* @param {vec4} b the second operand |
|
* @returns {vec4} out |
|
*/ |
|
function divide(out, a, b) { |
|
out[0] = a[0] / b[0]; |
|
out[1] = a[1] / b[1]; |
|
out[2] = a[2] / b[2]; |
|
out[3] = a[3] / b[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Math.ceil the components of a vec4 |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a vector to ceil |
|
* @returns {vec4} out |
|
*/ |
|
function ceil(out, a) { |
|
out[0] = Math.ceil(a[0]); |
|
out[1] = Math.ceil(a[1]); |
|
out[2] = Math.ceil(a[2]); |
|
out[3] = Math.ceil(a[3]); |
|
return out; |
|
} |
|
|
|
/** |
|
* Math.floor the components of a vec4 |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a vector to floor |
|
* @returns {vec4} out |
|
*/ |
|
function floor(out, a) { |
|
out[0] = Math.floor(a[0]); |
|
out[1] = Math.floor(a[1]); |
|
out[2] = Math.floor(a[2]); |
|
out[3] = Math.floor(a[3]); |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns the minimum of two vec4's |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the first operand |
|
* @param {vec4} b the second operand |
|
* @returns {vec4} out |
|
*/ |
|
function min(out, a, b) { |
|
out[0] = Math.min(a[0], b[0]); |
|
out[1] = Math.min(a[1], b[1]); |
|
out[2] = Math.min(a[2], b[2]); |
|
out[3] = Math.min(a[3], b[3]); |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns the maximum of two vec4's |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the first operand |
|
* @param {vec4} b the second operand |
|
* @returns {vec4} out |
|
*/ |
|
function max(out, a, b) { |
|
out[0] = Math.max(a[0], b[0]); |
|
out[1] = Math.max(a[1], b[1]); |
|
out[2] = Math.max(a[2], b[2]); |
|
out[3] = Math.max(a[3], b[3]); |
|
return out; |
|
} |
|
|
|
/** |
|
* Math.round the components of a vec4 |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a vector to round |
|
* @returns {vec4} out |
|
*/ |
|
function round(out, a) { |
|
out[0] = Math.round(a[0]); |
|
out[1] = Math.round(a[1]); |
|
out[2] = Math.round(a[2]); |
|
out[3] = Math.round(a[3]); |
|
return out; |
|
} |
|
|
|
/** |
|
* Scales a vec4 by a scalar number |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the vector to scale |
|
* @param {Number} b amount to scale the vector by |
|
* @returns {vec4} out |
|
*/ |
|
function scale(out, a, b) { |
|
out[0] = a[0] * b; |
|
out[1] = a[1] * b; |
|
out[2] = a[2] * b; |
|
out[3] = a[3] * b; |
|
return out; |
|
} |
|
|
|
/** |
|
* Adds two vec4's after scaling the second operand by a scalar value |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the first operand |
|
* @param {vec4} b the second operand |
|
* @param {Number} scale the amount to scale b by before adding |
|
* @returns {vec4} out |
|
*/ |
|
function scaleAndAdd(out, a, b, scale) { |
|
out[0] = a[0] + b[0] * scale; |
|
out[1] = a[1] + b[1] * scale; |
|
out[2] = a[2] + b[2] * scale; |
|
out[3] = a[3] + b[3] * scale; |
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the euclidian distance between two vec4's |
|
* |
|
* @param {vec4} a the first operand |
|
* @param {vec4} b the second operand |
|
* @returns {Number} distance between a and b |
|
*/ |
|
function distance(a, b) { |
|
var x = b[0] - a[0]; |
|
var y = b[1] - a[1]; |
|
var z = b[2] - a[2]; |
|
var w = b[3] - a[3]; |
|
return Math.sqrt(x * x + y * y + z * z + w * w); |
|
} |
|
|
|
/** |
|
* Calculates the squared euclidian distance between two vec4's |
|
* |
|
* @param {vec4} a the first operand |
|
* @param {vec4} b the second operand |
|
* @returns {Number} squared distance between a and b |
|
*/ |
|
function squaredDistance(a, b) { |
|
var x = b[0] - a[0]; |
|
var y = b[1] - a[1]; |
|
var z = b[2] - a[2]; |
|
var w = b[3] - a[3]; |
|
return x * x + y * y + z * z + w * w; |
|
} |
|
|
|
/** |
|
* Calculates the length of a vec4 |
|
* |
|
* @param {vec4} a vector to calculate length of |
|
* @returns {Number} length of a |
|
*/ |
|
function length(a) { |
|
var x = a[0]; |
|
var y = a[1]; |
|
var z = a[2]; |
|
var w = a[3]; |
|
return Math.sqrt(x * x + y * y + z * z + w * w); |
|
} |
|
|
|
/** |
|
* Calculates the squared length of a vec4 |
|
* |
|
* @param {vec4} a vector to calculate squared length of |
|
* @returns {Number} squared length of a |
|
*/ |
|
function squaredLength(a) { |
|
var x = a[0]; |
|
var y = a[1]; |
|
var z = a[2]; |
|
var w = a[3]; |
|
return x * x + y * y + z * z + w * w; |
|
} |
|
|
|
/** |
|
* Negates the components of a vec4 |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a vector to negate |
|
* @returns {vec4} out |
|
*/ |
|
function negate(out, a) { |
|
out[0] = -a[0]; |
|
out[1] = -a[1]; |
|
out[2] = -a[2]; |
|
out[3] = -a[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns the inverse of the components of a vec4 |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a vector to invert |
|
* @returns {vec4} out |
|
*/ |
|
function inverse(out, a) { |
|
out[0] = 1.0 / a[0]; |
|
out[1] = 1.0 / a[1]; |
|
out[2] = 1.0 / a[2]; |
|
out[3] = 1.0 / a[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Normalize a vec4 |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a vector to normalize |
|
* @returns {vec4} out |
|
*/ |
|
function normalize(out, a) { |
|
var x = a[0]; |
|
var y = a[1]; |
|
var z = a[2]; |
|
var w = a[3]; |
|
var len = x * x + y * y + z * z + w * w; |
|
if (len > 0) { |
|
len = 1 / Math.sqrt(len); |
|
out[0] = x * len; |
|
out[1] = y * len; |
|
out[2] = z * len; |
|
out[3] = w * len; |
|
} |
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the dot product of two vec4's |
|
* |
|
* @param {vec4} a the first operand |
|
* @param {vec4} b the second operand |
|
* @returns {Number} dot product of a and b |
|
*/ |
|
function dot(a, b) { |
|
return a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3]; |
|
} |
|
|
|
/** |
|
* Performs a linear interpolation between two vec4's |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the first operand |
|
* @param {vec4} b the second operand |
|
* @param {Number} t interpolation amount between the two inputs |
|
* @returns {vec4} out |
|
*/ |
|
function lerp(out, a, b, t) { |
|
var ax = a[0]; |
|
var ay = a[1]; |
|
var az = a[2]; |
|
var aw = a[3]; |
|
out[0] = ax + t * (b[0] - ax); |
|
out[1] = ay + t * (b[1] - ay); |
|
out[2] = az + t * (b[2] - az); |
|
out[3] = aw + t * (b[3] - aw); |
|
return out; |
|
} |
|
|
|
/** |
|
* Generates a random vector with the given scale |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {Number} [scale] Length of the resulting vector. If ommitted, a unit vector will be returned |
|
* @returns {vec4} out |
|
*/ |
|
function random(out, vectorScale) { |
|
vectorScale = vectorScale || 1.0; |
|
|
|
//TODO: This is a pretty awful way of doing this. Find something better. |
|
out[0] = glMatrix.RANDOM(); |
|
out[1] = glMatrix.RANDOM(); |
|
out[2] = glMatrix.RANDOM(); |
|
out[3] = glMatrix.RANDOM(); |
|
normalize(out, out); |
|
scale(out, out, vectorScale); |
|
return out; |
|
} |
|
|
|
/** |
|
* Transforms the vec4 with a mat4. |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the vector to transform |
|
* @param {mat4} m matrix to transform with |
|
* @returns {vec4} out |
|
*/ |
|
function transformMat4(out, a, m) { |
|
var x = a[0], |
|
y = a[1], |
|
z = a[2], |
|
w = a[3]; |
|
out[0] = m[0] * x + m[4] * y + m[8] * z + m[12] * w; |
|
out[1] = m[1] * x + m[5] * y + m[9] * z + m[13] * w; |
|
out[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w; |
|
out[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w; |
|
return out; |
|
} |
|
|
|
/** |
|
* Transforms the vec4 with a quat |
|
* |
|
* @param {vec4} out the receiving vector |
|
* @param {vec4} a the vector to transform |
|
* @param {quat} q quaternion to transform with |
|
* @returns {vec4} out |
|
*/ |
|
function transformQuat(out, a, q) { |
|
var x = a[0], |
|
y = a[1], |
|
z = a[2]; |
|
var qx = q[0], |
|
qy = q[1], |
|
qz = q[2], |
|
qw = q[3]; |
|
|
|
// calculate quat * vec |
|
var ix = qw * x + qy * z - qz * y; |
|
var iy = qw * y + qz * x - qx * z; |
|
var iz = qw * z + qx * y - qy * x; |
|
var iw = -qx * x - qy * y - qz * z; |
|
|
|
// calculate result * inverse quat |
|
out[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy; |
|
out[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz; |
|
out[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx; |
|
out[3] = a[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns a string representation of a vector |
|
* |
|
* @param {vec4} a vector to represent as a string |
|
* @returns {String} string representation of the vector |
|
*/ |
|
function str(a) { |
|
return 'vec4(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')'; |
|
} |
|
|
|
/** |
|
* Returns whether or not the vectors have exactly the same elements in the same position (when compared with ===) |
|
* |
|
* @param {vec4} a The first vector. |
|
* @param {vec4} b The second vector. |
|
* @returns {Boolean} True if the vectors are equal, false otherwise. |
|
*/ |
|
function exactEquals(a, b) { |
|
return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3]; |
|
} |
|
|
|
/** |
|
* Returns whether or not the vectors have approximately the same elements in the same position. |
|
* |
|
* @param {vec4} a The first vector. |
|
* @param {vec4} b The second vector. |
|
* @returns {Boolean} True if the vectors are equal, false otherwise. |
|
*/ |
|
function equals(a, b) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3]; |
|
var b0 = b[0], |
|
b1 = b[1], |
|
b2 = b[2], |
|
b3 = b[3]; |
|
return Math.abs(a0 - b0) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)); |
|
} |
|
|
|
/** |
|
* Alias for {@link vec4.subtract} |
|
* @function |
|
*/ |
|
var sub = exports.sub = subtract; |
|
|
|
/** |
|
* Alias for {@link vec4.multiply} |
|
* @function |
|
*/ |
|
var mul = exports.mul = multiply; |
|
|
|
/** |
|
* Alias for {@link vec4.divide} |
|
* @function |
|
*/ |
|
var div = exports.div = divide; |
|
|
|
/** |
|
* Alias for {@link vec4.distance} |
|
* @function |
|
*/ |
|
var dist = exports.dist = distance; |
|
|
|
/** |
|
* Alias for {@link vec4.squaredDistance} |
|
* @function |
|
*/ |
|
var sqrDist = exports.sqrDist = squaredDistance; |
|
|
|
/** |
|
* Alias for {@link vec4.length} |
|
* @function |
|
*/ |
|
var len = exports.len = length; |
|
|
|
/** |
|
* Alias for {@link vec4.squaredLength} |
|
* @function |
|
*/ |
|
var sqrLen = exports.sqrLen = squaredLength; |
|
|
|
/** |
|
* Perform some operation over an array of vec4s. |
|
* |
|
* @param {Array} a the array of vectors to iterate over |
|
* @param {Number} stride Number of elements between the start of each vec4. If 0 assumes tightly packed |
|
* @param {Number} offset Number of elements to skip at the beginning of the array |
|
* @param {Number} count Number of vec4s to iterate over. If 0 iterates over entire array |
|
* @param {Function} fn Function to call for each vector in the array |
|
* @param {Object} [arg] additional argument to pass to fn |
|
* @returns {Array} a |
|
* @function |
|
*/ |
|
var forEach = exports.forEach = function () { |
|
var vec = create(); |
|
|
|
return function (a, stride, offset, count, fn, arg) { |
|
var i = void 0, |
|
l = void 0; |
|
if (!stride) { |
|
stride = 4; |
|
} |
|
|
|
if (!offset) { |
|
offset = 0; |
|
} |
|
|
|
if (count) { |
|
l = Math.min(count * stride + offset, a.length); |
|
} else { |
|
l = a.length; |
|
} |
|
|
|
for (i = offset; i < l; i += stride) { |
|
vec[0] = a[i];vec[1] = a[i + 1];vec[2] = a[i + 2];vec[3] = a[i + 3]; |
|
fn(vec, vec, arg); |
|
a[i] = vec[0];a[i + 1] = vec[1];a[i + 2] = vec[2];a[i + 3] = vec[3]; |
|
} |
|
|
|
return a; |
|
}; |
|
}(); |
|
|
|
/***/ }), |
|
/* 4 */ |
|
/***/ (function(module, exports, __webpack_require__) { |
|
|
|
"use strict"; |
|
|
|
|
|
Object.defineProperty(exports, "__esModule", { |
|
value: true |
|
}); |
|
exports.vec4 = exports.vec3 = exports.vec2 = exports.quat = exports.mat4 = exports.mat3 = exports.mat2d = exports.mat2 = exports.glMatrix = undefined; |
|
|
|
var _common = __webpack_require__(0); |
|
|
|
var glMatrix = _interopRequireWildcard(_common); |
|
|
|
var _mat = __webpack_require__(5); |
|
|
|
var mat2 = _interopRequireWildcard(_mat); |
|
|
|
var _mat2d = __webpack_require__(6); |
|
|
|
var mat2d = _interopRequireWildcard(_mat2d); |
|
|
|
var _mat2 = __webpack_require__(1); |
|
|
|
var mat3 = _interopRequireWildcard(_mat2); |
|
|
|
var _mat3 = __webpack_require__(7); |
|
|
|
var mat4 = _interopRequireWildcard(_mat3); |
|
|
|
var _quat = __webpack_require__(8); |
|
|
|
var quat = _interopRequireWildcard(_quat); |
|
|
|
var _vec = __webpack_require__(9); |
|
|
|
var vec2 = _interopRequireWildcard(_vec); |
|
|
|
var _vec2 = __webpack_require__(2); |
|
|
|
var vec3 = _interopRequireWildcard(_vec2); |
|
|
|
var _vec3 = __webpack_require__(3); |
|
|
|
var vec4 = _interopRequireWildcard(_vec3); |
|
|
|
function _interopRequireWildcard(obj) { if (obj && obj.__esModule) { return obj; } else { var newObj = {}; if (obj != null) { for (var key in obj) { if (Object.prototype.hasOwnProperty.call(obj, key)) newObj[key] = obj[key]; } } newObj.default = obj; return newObj; } } |
|
|
|
exports.glMatrix = glMatrix; |
|
exports.mat2 = mat2; |
|
exports.mat2d = mat2d; |
|
exports.mat3 = mat3; |
|
exports.mat4 = mat4; |
|
exports.quat = quat; |
|
exports.vec2 = vec2; |
|
exports.vec3 = vec3; |
|
exports.vec4 = vec4; /** |
|
* @fileoverview gl-matrix - High performance matrix and vector operations |
|
* @author Brandon Jones |
|
* @author Colin MacKenzie IV |
|
* @version 2.4.0 |
|
*/ |
|
|
|
/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. |
|
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy |
|
of this software and associated documentation files (the "Software"), to deal |
|
in the Software without restriction, including without limitation the rights |
|
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
|
copies of the Software, and to permit persons to whom the Software is |
|
furnished to do so, subject to the following conditions: |
|
|
|
The above copyright notice and this permission notice shall be included in |
|
all copies or substantial portions of the Software. |
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
|
THE SOFTWARE. */ |
|
// END HEADER |
|
|
|
/***/ }), |
|
/* 5 */ |
|
/***/ (function(module, exports, __webpack_require__) { |
|
|
|
"use strict"; |
|
|
|
|
|
Object.defineProperty(exports, "__esModule", { |
|
value: true |
|
}); |
|
exports.sub = exports.mul = undefined; |
|
exports.create = create; |
|
exports.clone = clone; |
|
exports.copy = copy; |
|
exports.identity = identity; |
|
exports.fromValues = fromValues; |
|
exports.set = set; |
|
exports.transpose = transpose; |
|
exports.invert = invert; |
|
exports.adjoint = adjoint; |
|
exports.determinant = determinant; |
|
exports.multiply = multiply; |
|
exports.rotate = rotate; |
|
exports.scale = scale; |
|
exports.fromRotation = fromRotation; |
|
exports.fromScaling = fromScaling; |
|
exports.str = str; |
|
exports.frob = frob; |
|
exports.LDU = LDU; |
|
exports.add = add; |
|
exports.subtract = subtract; |
|
exports.exactEquals = exactEquals; |
|
exports.equals = equals; |
|
exports.multiplyScalar = multiplyScalar; |
|
exports.multiplyScalarAndAdd = multiplyScalarAndAdd; |
|
|
|
var _common = __webpack_require__(0); |
|
|
|
var glMatrix = _interopRequireWildcard(_common); |
|
|
|
function _interopRequireWildcard(obj) { if (obj && obj.__esModule) { return obj; } else { var newObj = {}; if (obj != null) { for (var key in obj) { if (Object.prototype.hasOwnProperty.call(obj, key)) newObj[key] = obj[key]; } } newObj.default = obj; return newObj; } } |
|
|
|
/** |
|
* 2x2 Matrix |
|
* @module mat2 |
|
*/ |
|
|
|
/** |
|
* Creates a new identity mat2 |
|
* |
|
* @returns {mat2} a new 2x2 matrix |
|
*/ |
|
function create() { |
|
var out = new glMatrix.ARRAY_TYPE(4); |
|
out[0] = 1; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a new mat2 initialized with values from an existing matrix |
|
* |
|
* @param {mat2} a matrix to clone |
|
* @returns {mat2} a new 2x2 matrix |
|
*/ |
|
/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. |
|
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy |
|
of this software and associated documentation files (the "Software"), to deal |
|
in the Software without restriction, including without limitation the rights |
|
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
|
copies of the Software, and to permit persons to whom the Software is |
|
furnished to do so, subject to the following conditions: |
|
|
|
The above copyright notice and this permission notice shall be included in |
|
all copies or substantial portions of the Software. |
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
|
THE SOFTWARE. */ |
|
|
|
function clone(a) { |
|
var out = new glMatrix.ARRAY_TYPE(4); |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
out[2] = a[2]; |
|
out[3] = a[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Copy the values from one mat2 to another |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @param {mat2} a the source matrix |
|
* @returns {mat2} out |
|
*/ |
|
function copy(out, a) { |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
out[2] = a[2]; |
|
out[3] = a[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Set a mat2 to the identity matrix |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @returns {mat2} out |
|
*/ |
|
function identity(out) { |
|
out[0] = 1; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Create a new mat2 with the given values |
|
* |
|
* @param {Number} m00 Component in column 0, row 0 position (index 0) |
|
* @param {Number} m01 Component in column 0, row 1 position (index 1) |
|
* @param {Number} m10 Component in column 1, row 0 position (index 2) |
|
* @param {Number} m11 Component in column 1, row 1 position (index 3) |
|
* @returns {mat2} out A new 2x2 matrix |
|
*/ |
|
function fromValues(m00, m01, m10, m11) { |
|
var out = new glMatrix.ARRAY_TYPE(4); |
|
out[0] = m00; |
|
out[1] = m01; |
|
out[2] = m10; |
|
out[3] = m11; |
|
return out; |
|
} |
|
|
|
/** |
|
* Set the components of a mat2 to the given values |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @param {Number} m00 Component in column 0, row 0 position (index 0) |
|
* @param {Number} m01 Component in column 0, row 1 position (index 1) |
|
* @param {Number} m10 Component in column 1, row 0 position (index 2) |
|
* @param {Number} m11 Component in column 1, row 1 position (index 3) |
|
* @returns {mat2} out |
|
*/ |
|
function set(out, m00, m01, m10, m11) { |
|
out[0] = m00; |
|
out[1] = m01; |
|
out[2] = m10; |
|
out[3] = m11; |
|
return out; |
|
} |
|
|
|
/** |
|
* Transpose the values of a mat2 |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @param {mat2} a the source matrix |
|
* @returns {mat2} out |
|
*/ |
|
function transpose(out, a) { |
|
// If we are transposing ourselves we can skip a few steps but have to cache |
|
// some values |
|
if (out === a) { |
|
var a1 = a[1]; |
|
out[1] = a[2]; |
|
out[2] = a1; |
|
} else { |
|
out[0] = a[0]; |
|
out[1] = a[2]; |
|
out[2] = a[1]; |
|
out[3] = a[3]; |
|
} |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Inverts a mat2 |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @param {mat2} a the source matrix |
|
* @returns {mat2} out |
|
*/ |
|
function invert(out, a) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3]; |
|
|
|
// Calculate the determinant |
|
var det = a0 * a3 - a2 * a1; |
|
|
|
if (!det) { |
|
return null; |
|
} |
|
det = 1.0 / det; |
|
|
|
out[0] = a3 * det; |
|
out[1] = -a1 * det; |
|
out[2] = -a2 * det; |
|
out[3] = a0 * det; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the adjugate of a mat2 |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @param {mat2} a the source matrix |
|
* @returns {mat2} out |
|
*/ |
|
function adjoint(out, a) { |
|
// Caching this value is nessecary if out == a |
|
var a0 = a[0]; |
|
out[0] = a[3]; |
|
out[1] = -a[1]; |
|
out[2] = -a[2]; |
|
out[3] = a0; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the determinant of a mat2 |
|
* |
|
* @param {mat2} a the source matrix |
|
* @returns {Number} determinant of a |
|
*/ |
|
function determinant(a) { |
|
return a[0] * a[3] - a[2] * a[1]; |
|
} |
|
|
|
/** |
|
* Multiplies two mat2's |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @param {mat2} a the first operand |
|
* @param {mat2} b the second operand |
|
* @returns {mat2} out |
|
*/ |
|
function multiply(out, a, b) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3]; |
|
var b0 = b[0], |
|
b1 = b[1], |
|
b2 = b[2], |
|
b3 = b[3]; |
|
out[0] = a0 * b0 + a2 * b1; |
|
out[1] = a1 * b0 + a3 * b1; |
|
out[2] = a0 * b2 + a2 * b3; |
|
out[3] = a1 * b2 + a3 * b3; |
|
return out; |
|
} |
|
|
|
/** |
|
* Rotates a mat2 by the given angle |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @param {mat2} a the matrix to rotate |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat2} out |
|
*/ |
|
function rotate(out, a, rad) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3]; |
|
var s = Math.sin(rad); |
|
var c = Math.cos(rad); |
|
out[0] = a0 * c + a2 * s; |
|
out[1] = a1 * c + a3 * s; |
|
out[2] = a0 * -s + a2 * c; |
|
out[3] = a1 * -s + a3 * c; |
|
return out; |
|
} |
|
|
|
/** |
|
* Scales the mat2 by the dimensions in the given vec2 |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @param {mat2} a the matrix to rotate |
|
* @param {vec2} v the vec2 to scale the matrix by |
|
* @returns {mat2} out |
|
**/ |
|
function scale(out, a, v) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3]; |
|
var v0 = v[0], |
|
v1 = v[1]; |
|
out[0] = a0 * v0; |
|
out[1] = a1 * v0; |
|
out[2] = a2 * v1; |
|
out[3] = a3 * v1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a given angle |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat2.identity(dest); |
|
* mat2.rotate(dest, dest, rad); |
|
* |
|
* @param {mat2} out mat2 receiving operation result |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat2} out |
|
*/ |
|
function fromRotation(out, rad) { |
|
var s = Math.sin(rad); |
|
var c = Math.cos(rad); |
|
out[0] = c; |
|
out[1] = s; |
|
out[2] = -s; |
|
out[3] = c; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a vector scaling |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat2.identity(dest); |
|
* mat2.scale(dest, dest, vec); |
|
* |
|
* @param {mat2} out mat2 receiving operation result |
|
* @param {vec2} v Scaling vector |
|
* @returns {mat2} out |
|
*/ |
|
function fromScaling(out, v) { |
|
out[0] = v[0]; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = v[1]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns a string representation of a mat2 |
|
* |
|
* @param {mat2} a matrix to represent as a string |
|
* @returns {String} string representation of the matrix |
|
*/ |
|
function str(a) { |
|
return 'mat2(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')'; |
|
} |
|
|
|
/** |
|
* Returns Frobenius norm of a mat2 |
|
* |
|
* @param {mat2} a the matrix to calculate Frobenius norm of |
|
* @returns {Number} Frobenius norm |
|
*/ |
|
function frob(a) { |
|
return Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2)); |
|
} |
|
|
|
/** |
|
* Returns L, D and U matrices (Lower triangular, Diagonal and Upper triangular) by factorizing the input matrix |
|
* @param {mat2} L the lower triangular matrix |
|
* @param {mat2} D the diagonal matrix |
|
* @param {mat2} U the upper triangular matrix |
|
* @param {mat2} a the input matrix to factorize |
|
*/ |
|
|
|
function LDU(L, D, U, a) { |
|
L[2] = a[2] / a[0]; |
|
U[0] = a[0]; |
|
U[1] = a[1]; |
|
U[3] = a[3] - L[2] * U[1]; |
|
return [L, D, U]; |
|
} |
|
|
|
/** |
|
* Adds two mat2's |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @param {mat2} a the first operand |
|
* @param {mat2} b the second operand |
|
* @returns {mat2} out |
|
*/ |
|
function add(out, a, b) { |
|
out[0] = a[0] + b[0]; |
|
out[1] = a[1] + b[1]; |
|
out[2] = a[2] + b[2]; |
|
out[3] = a[3] + b[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Subtracts matrix b from matrix a |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @param {mat2} a the first operand |
|
* @param {mat2} b the second operand |
|
* @returns {mat2} out |
|
*/ |
|
function subtract(out, a, b) { |
|
out[0] = a[0] - b[0]; |
|
out[1] = a[1] - b[1]; |
|
out[2] = a[2] - b[2]; |
|
out[3] = a[3] - b[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===) |
|
* |
|
* @param {mat2} a The first matrix. |
|
* @param {mat2} b The second matrix. |
|
* @returns {Boolean} True if the matrices are equal, false otherwise. |
|
*/ |
|
function exactEquals(a, b) { |
|
return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3]; |
|
} |
|
|
|
/** |
|
* Returns whether or not the matrices have approximately the same elements in the same position. |
|
* |
|
* @param {mat2} a The first matrix. |
|
* @param {mat2} b The second matrix. |
|
* @returns {Boolean} True if the matrices are equal, false otherwise. |
|
*/ |
|
function equals(a, b) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3]; |
|
var b0 = b[0], |
|
b1 = b[1], |
|
b2 = b[2], |
|
b3 = b[3]; |
|
return Math.abs(a0 - b0) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)); |
|
} |
|
|
|
/** |
|
* Multiply each element of the matrix by a scalar. |
|
* |
|
* @param {mat2} out the receiving matrix |
|
* @param {mat2} a the matrix to scale |
|
* @param {Number} b amount to scale the matrix's elements by |
|
* @returns {mat2} out |
|
*/ |
|
function multiplyScalar(out, a, b) { |
|
out[0] = a[0] * b; |
|
out[1] = a[1] * b; |
|
out[2] = a[2] * b; |
|
out[3] = a[3] * b; |
|
return out; |
|
} |
|
|
|
/** |
|
* Adds two mat2's after multiplying each element of the second operand by a scalar value. |
|
* |
|
* @param {mat2} out the receiving vector |
|
* @param {mat2} a the first operand |
|
* @param {mat2} b the second operand |
|
* @param {Number} scale the amount to scale b's elements by before adding |
|
* @returns {mat2} out |
|
*/ |
|
function multiplyScalarAndAdd(out, a, b, scale) { |
|
out[0] = a[0] + b[0] * scale; |
|
out[1] = a[1] + b[1] * scale; |
|
out[2] = a[2] + b[2] * scale; |
|
out[3] = a[3] + b[3] * scale; |
|
return out; |
|
} |
|
|
|
/** |
|
* Alias for {@link mat2.multiply} |
|
* @function |
|
*/ |
|
var mul = exports.mul = multiply; |
|
|
|
/** |
|
* Alias for {@link mat2.subtract} |
|
* @function |
|
*/ |
|
var sub = exports.sub = subtract; |
|
|
|
/***/ }), |
|
/* 6 */ |
|
/***/ (function(module, exports, __webpack_require__) { |
|
|
|
"use strict"; |
|
|
|
|
|
Object.defineProperty(exports, "__esModule", { |
|
value: true |
|
}); |
|
exports.sub = exports.mul = undefined; |
|
exports.create = create; |
|
exports.clone = clone; |
|
exports.copy = copy; |
|
exports.identity = identity; |
|
exports.fromValues = fromValues; |
|
exports.set = set; |
|
exports.invert = invert; |
|
exports.determinant = determinant; |
|
exports.multiply = multiply; |
|
exports.rotate = rotate; |
|
exports.scale = scale; |
|
exports.translate = translate; |
|
exports.fromRotation = fromRotation; |
|
exports.fromScaling = fromScaling; |
|
exports.fromTranslation = fromTranslation; |
|
exports.str = str; |
|
exports.frob = frob; |
|
exports.add = add; |
|
exports.subtract = subtract; |
|
exports.multiplyScalar = multiplyScalar; |
|
exports.multiplyScalarAndAdd = multiplyScalarAndAdd; |
|
exports.exactEquals = exactEquals; |
|
exports.equals = equals; |
|
|
|
var _common = __webpack_require__(0); |
|
|
|
var glMatrix = _interopRequireWildcard(_common); |
|
|
|
function _interopRequireWildcard(obj) { if (obj && obj.__esModule) { return obj; } else { var newObj = {}; if (obj != null) { for (var key in obj) { if (Object.prototype.hasOwnProperty.call(obj, key)) newObj[key] = obj[key]; } } newObj.default = obj; return newObj; } } |
|
|
|
/** |
|
* 2x3 Matrix |
|
* @module mat2d |
|
* |
|
* @description |
|
* A mat2d contains six elements defined as: |
|
* <pre> |
|
* [a, c, tx, |
|
* b, d, ty] |
|
* </pre> |
|
* This is a short form for the 3x3 matrix: |
|
* <pre> |
|
* [a, c, tx, |
|
* b, d, ty, |
|
* 0, 0, 1] |
|
* </pre> |
|
* The last row is ignored so the array is shorter and operations are faster. |
|
*/ |
|
|
|
/** |
|
* Creates a new identity mat2d |
|
* |
|
* @returns {mat2d} a new 2x3 matrix |
|
*/ |
|
function create() { |
|
var out = new glMatrix.ARRAY_TYPE(6); |
|
out[0] = 1; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 1; |
|
out[4] = 0; |
|
out[5] = 0; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a new mat2d initialized with values from an existing matrix |
|
* |
|
* @param {mat2d} a matrix to clone |
|
* @returns {mat2d} a new 2x3 matrix |
|
*/ |
|
/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. |
|
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy |
|
of this software and associated documentation files (the "Software"), to deal |
|
in the Software without restriction, including without limitation the rights |
|
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
|
copies of the Software, and to permit persons to whom the Software is |
|
furnished to do so, subject to the following conditions: |
|
|
|
The above copyright notice and this permission notice shall be included in |
|
all copies or substantial portions of the Software. |
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
|
THE SOFTWARE. */ |
|
|
|
function clone(a) { |
|
var out = new glMatrix.ARRAY_TYPE(6); |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
out[2] = a[2]; |
|
out[3] = a[3]; |
|
out[4] = a[4]; |
|
out[5] = a[5]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Copy the values from one mat2d to another |
|
* |
|
* @param {mat2d} out the receiving matrix |
|
* @param {mat2d} a the source matrix |
|
* @returns {mat2d} out |
|
*/ |
|
function copy(out, a) { |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
out[2] = a[2]; |
|
out[3] = a[3]; |
|
out[4] = a[4]; |
|
out[5] = a[5]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Set a mat2d to the identity matrix |
|
* |
|
* @param {mat2d} out the receiving matrix |
|
* @returns {mat2d} out |
|
*/ |
|
function identity(out) { |
|
out[0] = 1; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 1; |
|
out[4] = 0; |
|
out[5] = 0; |
|
return out; |
|
} |
|
|
|
/** |
|
* Create a new mat2d with the given values |
|
* |
|
* @param {Number} a Component A (index 0) |
|
* @param {Number} b Component B (index 1) |
|
* @param {Number} c Component C (index 2) |
|
* @param {Number} d Component D (index 3) |
|
* @param {Number} tx Component TX (index 4) |
|
* @param {Number} ty Component TY (index 5) |
|
* @returns {mat2d} A new mat2d |
|
*/ |
|
function fromValues(a, b, c, d, tx, ty) { |
|
var out = new glMatrix.ARRAY_TYPE(6); |
|
out[0] = a; |
|
out[1] = b; |
|
out[2] = c; |
|
out[3] = d; |
|
out[4] = tx; |
|
out[5] = ty; |
|
return out; |
|
} |
|
|
|
/** |
|
* Set the components of a mat2d to the given values |
|
* |
|
* @param {mat2d} out the receiving matrix |
|
* @param {Number} a Component A (index 0) |
|
* @param {Number} b Component B (index 1) |
|
* @param {Number} c Component C (index 2) |
|
* @param {Number} d Component D (index 3) |
|
* @param {Number} tx Component TX (index 4) |
|
* @param {Number} ty Component TY (index 5) |
|
* @returns {mat2d} out |
|
*/ |
|
function set(out, a, b, c, d, tx, ty) { |
|
out[0] = a; |
|
out[1] = b; |
|
out[2] = c; |
|
out[3] = d; |
|
out[4] = tx; |
|
out[5] = ty; |
|
return out; |
|
} |
|
|
|
/** |
|
* Inverts a mat2d |
|
* |
|
* @param {mat2d} out the receiving matrix |
|
* @param {mat2d} a the source matrix |
|
* @returns {mat2d} out |
|
*/ |
|
function invert(out, a) { |
|
var aa = a[0], |
|
ab = a[1], |
|
ac = a[2], |
|
ad = a[3]; |
|
var atx = a[4], |
|
aty = a[5]; |
|
|
|
var det = aa * ad - ab * ac; |
|
if (!det) { |
|
return null; |
|
} |
|
det = 1.0 / det; |
|
|
|
out[0] = ad * det; |
|
out[1] = -ab * det; |
|
out[2] = -ac * det; |
|
out[3] = aa * det; |
|
out[4] = (ac * aty - ad * atx) * det; |
|
out[5] = (ab * atx - aa * aty) * det; |
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the determinant of a mat2d |
|
* |
|
* @param {mat2d} a the source matrix |
|
* @returns {Number} determinant of a |
|
*/ |
|
function determinant(a) { |
|
return a[0] * a[3] - a[1] * a[2]; |
|
} |
|
|
|
/** |
|
* Multiplies two mat2d's |
|
* |
|
* @param {mat2d} out the receiving matrix |
|
* @param {mat2d} a the first operand |
|
* @param {mat2d} b the second operand |
|
* @returns {mat2d} out |
|
*/ |
|
function multiply(out, a, b) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3], |
|
a4 = a[4], |
|
a5 = a[5]; |
|
var b0 = b[0], |
|
b1 = b[1], |
|
b2 = b[2], |
|
b3 = b[3], |
|
b4 = b[4], |
|
b5 = b[5]; |
|
out[0] = a0 * b0 + a2 * b1; |
|
out[1] = a1 * b0 + a3 * b1; |
|
out[2] = a0 * b2 + a2 * b3; |
|
out[3] = a1 * b2 + a3 * b3; |
|
out[4] = a0 * b4 + a2 * b5 + a4; |
|
out[5] = a1 * b4 + a3 * b5 + a5; |
|
return out; |
|
} |
|
|
|
/** |
|
* Rotates a mat2d by the given angle |
|
* |
|
* @param {mat2d} out the receiving matrix |
|
* @param {mat2d} a the matrix to rotate |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat2d} out |
|
*/ |
|
function rotate(out, a, rad) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3], |
|
a4 = a[4], |
|
a5 = a[5]; |
|
var s = Math.sin(rad); |
|
var c = Math.cos(rad); |
|
out[0] = a0 * c + a2 * s; |
|
out[1] = a1 * c + a3 * s; |
|
out[2] = a0 * -s + a2 * c; |
|
out[3] = a1 * -s + a3 * c; |
|
out[4] = a4; |
|
out[5] = a5; |
|
return out; |
|
} |
|
|
|
/** |
|
* Scales the mat2d by the dimensions in the given vec2 |
|
* |
|
* @param {mat2d} out the receiving matrix |
|
* @param {mat2d} a the matrix to translate |
|
* @param {vec2} v the vec2 to scale the matrix by |
|
* @returns {mat2d} out |
|
**/ |
|
function scale(out, a, v) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3], |
|
a4 = a[4], |
|
a5 = a[5]; |
|
var v0 = v[0], |
|
v1 = v[1]; |
|
out[0] = a0 * v0; |
|
out[1] = a1 * v0; |
|
out[2] = a2 * v1; |
|
out[3] = a3 * v1; |
|
out[4] = a4; |
|
out[5] = a5; |
|
return out; |
|
} |
|
|
|
/** |
|
* Translates the mat2d by the dimensions in the given vec2 |
|
* |
|
* @param {mat2d} out the receiving matrix |
|
* @param {mat2d} a the matrix to translate |
|
* @param {vec2} v the vec2 to translate the matrix by |
|
* @returns {mat2d} out |
|
**/ |
|
function translate(out, a, v) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3], |
|
a4 = a[4], |
|
a5 = a[5]; |
|
var v0 = v[0], |
|
v1 = v[1]; |
|
out[0] = a0; |
|
out[1] = a1; |
|
out[2] = a2; |
|
out[3] = a3; |
|
out[4] = a0 * v0 + a2 * v1 + a4; |
|
out[5] = a1 * v0 + a3 * v1 + a5; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a given angle |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat2d.identity(dest); |
|
* mat2d.rotate(dest, dest, rad); |
|
* |
|
* @param {mat2d} out mat2d receiving operation result |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat2d} out |
|
*/ |
|
function fromRotation(out, rad) { |
|
var s = Math.sin(rad), |
|
c = Math.cos(rad); |
|
out[0] = c; |
|
out[1] = s; |
|
out[2] = -s; |
|
out[3] = c; |
|
out[4] = 0; |
|
out[5] = 0; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a vector scaling |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat2d.identity(dest); |
|
* mat2d.scale(dest, dest, vec); |
|
* |
|
* @param {mat2d} out mat2d receiving operation result |
|
* @param {vec2} v Scaling vector |
|
* @returns {mat2d} out |
|
*/ |
|
function fromScaling(out, v) { |
|
out[0] = v[0]; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = v[1]; |
|
out[4] = 0; |
|
out[5] = 0; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a vector translation |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat2d.identity(dest); |
|
* mat2d.translate(dest, dest, vec); |
|
* |
|
* @param {mat2d} out mat2d receiving operation result |
|
* @param {vec2} v Translation vector |
|
* @returns {mat2d} out |
|
*/ |
|
function fromTranslation(out, v) { |
|
out[0] = 1; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 1; |
|
out[4] = v[0]; |
|
out[5] = v[1]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns a string representation of a mat2d |
|
* |
|
* @param {mat2d} a matrix to represent as a string |
|
* @returns {String} string representation of the matrix |
|
*/ |
|
function str(a) { |
|
return 'mat2d(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ', ' + a[4] + ', ' + a[5] + ')'; |
|
} |
|
|
|
/** |
|
* Returns Frobenius norm of a mat2d |
|
* |
|
* @param {mat2d} a the matrix to calculate Frobenius norm of |
|
* @returns {Number} Frobenius norm |
|
*/ |
|
function frob(a) { |
|
return Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2) + Math.pow(a[4], 2) + Math.pow(a[5], 2) + 1); |
|
} |
|
|
|
/** |
|
* Adds two mat2d's |
|
* |
|
* @param {mat2d} out the receiving matrix |
|
* @param {mat2d} a the first operand |
|
* @param {mat2d} b the second operand |
|
* @returns {mat2d} out |
|
*/ |
|
function add(out, a, b) { |
|
out[0] = a[0] + b[0]; |
|
out[1] = a[1] + b[1]; |
|
out[2] = a[2] + b[2]; |
|
out[3] = a[3] + b[3]; |
|
out[4] = a[4] + b[4]; |
|
out[5] = a[5] + b[5]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Subtracts matrix b from matrix a |
|
* |
|
* @param {mat2d} out the receiving matrix |
|
* @param {mat2d} a the first operand |
|
* @param {mat2d} b the second operand |
|
* @returns {mat2d} out |
|
*/ |
|
function subtract(out, a, b) { |
|
out[0] = a[0] - b[0]; |
|
out[1] = a[1] - b[1]; |
|
out[2] = a[2] - b[2]; |
|
out[3] = a[3] - b[3]; |
|
out[4] = a[4] - b[4]; |
|
out[5] = a[5] - b[5]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Multiply each element of the matrix by a scalar. |
|
* |
|
* @param {mat2d} out the receiving matrix |
|
* @param {mat2d} a the matrix to scale |
|
* @param {Number} b amount to scale the matrix's elements by |
|
* @returns {mat2d} out |
|
*/ |
|
function multiplyScalar(out, a, b) { |
|
out[0] = a[0] * b; |
|
out[1] = a[1] * b; |
|
out[2] = a[2] * b; |
|
out[3] = a[3] * b; |
|
out[4] = a[4] * b; |
|
out[5] = a[5] * b; |
|
return out; |
|
} |
|
|
|
/** |
|
* Adds two mat2d's after multiplying each element of the second operand by a scalar value. |
|
* |
|
* @param {mat2d} out the receiving vector |
|
* @param {mat2d} a the first operand |
|
* @param {mat2d} b the second operand |
|
* @param {Number} scale the amount to scale b's elements by before adding |
|
* @returns {mat2d} out |
|
*/ |
|
function multiplyScalarAndAdd(out, a, b, scale) { |
|
out[0] = a[0] + b[0] * scale; |
|
out[1] = a[1] + b[1] * scale; |
|
out[2] = a[2] + b[2] * scale; |
|
out[3] = a[3] + b[3] * scale; |
|
out[4] = a[4] + b[4] * scale; |
|
out[5] = a[5] + b[5] * scale; |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===) |
|
* |
|
* @param {mat2d} a The first matrix. |
|
* @param {mat2d} b The second matrix. |
|
* @returns {Boolean} True if the matrices are equal, false otherwise. |
|
*/ |
|
function exactEquals(a, b) { |
|
return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3] && a[4] === b[4] && a[5] === b[5]; |
|
} |
|
|
|
/** |
|
* Returns whether or not the matrices have approximately the same elements in the same position. |
|
* |
|
* @param {mat2d} a The first matrix. |
|
* @param {mat2d} b The second matrix. |
|
* @returns {Boolean} True if the matrices are equal, false otherwise. |
|
*/ |
|
function equals(a, b) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3], |
|
a4 = a[4], |
|
a5 = a[5]; |
|
var b0 = b[0], |
|
b1 = b[1], |
|
b2 = b[2], |
|
b3 = b[3], |
|
b4 = b[4], |
|
b5 = b[5]; |
|
return Math.abs(a0 - b0) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)); |
|
} |
|
|
|
/** |
|
* Alias for {@link mat2d.multiply} |
|
* @function |
|
*/ |
|
var mul = exports.mul = multiply; |
|
|
|
/** |
|
* Alias for {@link mat2d.subtract} |
|
* @function |
|
*/ |
|
var sub = exports.sub = subtract; |
|
|
|
/***/ }), |
|
/* 7 */ |
|
/***/ (function(module, exports, __webpack_require__) { |
|
|
|
"use strict"; |
|
|
|
|
|
Object.defineProperty(exports, "__esModule", { |
|
value: true |
|
}); |
|
exports.sub = exports.mul = undefined; |
|
exports.create = create; |
|
exports.clone = clone; |
|
exports.copy = copy; |
|
exports.fromValues = fromValues; |
|
exports.set = set; |
|
exports.identity = identity; |
|
exports.transpose = transpose; |
|
exports.invert = invert; |
|
exports.adjoint = adjoint; |
|
exports.determinant = determinant; |
|
exports.multiply = multiply; |
|
exports.translate = translate; |
|
exports.scale = scale; |
|
exports.rotate = rotate; |
|
exports.rotateX = rotateX; |
|
exports.rotateY = rotateY; |
|
exports.rotateZ = rotateZ; |
|
exports.fromTranslation = fromTranslation; |
|
exports.fromScaling = fromScaling; |
|
exports.fromRotation = fromRotation; |
|
exports.fromXRotation = fromXRotation; |
|
exports.fromYRotation = fromYRotation; |
|
exports.fromZRotation = fromZRotation; |
|
exports.fromRotationTranslation = fromRotationTranslation; |
|
exports.getTranslation = getTranslation; |
|
exports.getScaling = getScaling; |
|
exports.getRotation = getRotation; |
|
exports.fromRotationTranslationScale = fromRotationTranslationScale; |
|
exports.fromRotationTranslationScaleOrigin = fromRotationTranslationScaleOrigin; |
|
exports.fromQuat = fromQuat; |
|
exports.frustum = frustum; |
|
exports.perspective = perspective; |
|
exports.perspectiveFromFieldOfView = perspectiveFromFieldOfView; |
|
exports.ortho = ortho; |
|
exports.lookAt = lookAt; |
|
exports.targetTo = targetTo; |
|
exports.str = str; |
|
exports.frob = frob; |
|
exports.add = add; |
|
exports.subtract = subtract; |
|
exports.multiplyScalar = multiplyScalar; |
|
exports.multiplyScalarAndAdd = multiplyScalarAndAdd; |
|
exports.exactEquals = exactEquals; |
|
exports.equals = equals; |
|
|
|
var _common = __webpack_require__(0); |
|
|
|
var glMatrix = _interopRequireWildcard(_common); |
|
|
|
function _interopRequireWildcard(obj) { if (obj && obj.__esModule) { return obj; } else { var newObj = {}; if (obj != null) { for (var key in obj) { if (Object.prototype.hasOwnProperty.call(obj, key)) newObj[key] = obj[key]; } } newObj.default = obj; return newObj; } } |
|
|
|
/** |
|
* 4x4 Matrix |
|
* @module mat4 |
|
*/ |
|
|
|
/** |
|
* Creates a new identity mat4 |
|
* |
|
* @returns {mat4} a new 4x4 matrix |
|
*/ |
|
function create() { |
|
var out = new glMatrix.ARRAY_TYPE(16); |
|
out[0] = 1; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 0; |
|
out[4] = 0; |
|
out[5] = 1; |
|
out[6] = 0; |
|
out[7] = 0; |
|
out[8] = 0; |
|
out[9] = 0; |
|
out[10] = 1; |
|
out[11] = 0; |
|
out[12] = 0; |
|
out[13] = 0; |
|
out[14] = 0; |
|
out[15] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a new mat4 initialized with values from an existing matrix |
|
* |
|
* @param {mat4} a matrix to clone |
|
* @returns {mat4} a new 4x4 matrix |
|
*/ |
|
/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. |
|
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy |
|
of this software and associated documentation files (the "Software"), to deal |
|
in the Software without restriction, including without limitation the rights |
|
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
|
copies of the Software, and to permit persons to whom the Software is |
|
furnished to do so, subject to the following conditions: |
|
|
|
The above copyright notice and this permission notice shall be included in |
|
all copies or substantial portions of the Software. |
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
|
THE SOFTWARE. */ |
|
|
|
function clone(a) { |
|
var out = new glMatrix.ARRAY_TYPE(16); |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
out[2] = a[2]; |
|
out[3] = a[3]; |
|
out[4] = a[4]; |
|
out[5] = a[5]; |
|
out[6] = a[6]; |
|
out[7] = a[7]; |
|
out[8] = a[8]; |
|
out[9] = a[9]; |
|
out[10] = a[10]; |
|
out[11] = a[11]; |
|
out[12] = a[12]; |
|
out[13] = a[13]; |
|
out[14] = a[14]; |
|
out[15] = a[15]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Copy the values from one mat4 to another |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the source matrix |
|
* @returns {mat4} out |
|
*/ |
|
function copy(out, a) { |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
out[2] = a[2]; |
|
out[3] = a[3]; |
|
out[4] = a[4]; |
|
out[5] = a[5]; |
|
out[6] = a[6]; |
|
out[7] = a[7]; |
|
out[8] = a[8]; |
|
out[9] = a[9]; |
|
out[10] = a[10]; |
|
out[11] = a[11]; |
|
out[12] = a[12]; |
|
out[13] = a[13]; |
|
out[14] = a[14]; |
|
out[15] = a[15]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Create a new mat4 with the given values |
|
* |
|
* @param {Number} m00 Component in column 0, row 0 position (index 0) |
|
* @param {Number} m01 Component in column 0, row 1 position (index 1) |
|
* @param {Number} m02 Component in column 0, row 2 position (index 2) |
|
* @param {Number} m03 Component in column 0, row 3 position (index 3) |
|
* @param {Number} m10 Component in column 1, row 0 position (index 4) |
|
* @param {Number} m11 Component in column 1, row 1 position (index 5) |
|
* @param {Number} m12 Component in column 1, row 2 position (index 6) |
|
* @param {Number} m13 Component in column 1, row 3 position (index 7) |
|
* @param {Number} m20 Component in column 2, row 0 position (index 8) |
|
* @param {Number} m21 Component in column 2, row 1 position (index 9) |
|
* @param {Number} m22 Component in column 2, row 2 position (index 10) |
|
* @param {Number} m23 Component in column 2, row 3 position (index 11) |
|
* @param {Number} m30 Component in column 3, row 0 position (index 12) |
|
* @param {Number} m31 Component in column 3, row 1 position (index 13) |
|
* @param {Number} m32 Component in column 3, row 2 position (index 14) |
|
* @param {Number} m33 Component in column 3, row 3 position (index 15) |
|
* @returns {mat4} A new mat4 |
|
*/ |
|
function fromValues(m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) { |
|
var out = new glMatrix.ARRAY_TYPE(16); |
|
out[0] = m00; |
|
out[1] = m01; |
|
out[2] = m02; |
|
out[3] = m03; |
|
out[4] = m10; |
|
out[5] = m11; |
|
out[6] = m12; |
|
out[7] = m13; |
|
out[8] = m20; |
|
out[9] = m21; |
|
out[10] = m22; |
|
out[11] = m23; |
|
out[12] = m30; |
|
out[13] = m31; |
|
out[14] = m32; |
|
out[15] = m33; |
|
return out; |
|
} |
|
|
|
/** |
|
* Set the components of a mat4 to the given values |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {Number} m00 Component in column 0, row 0 position (index 0) |
|
* @param {Number} m01 Component in column 0, row 1 position (index 1) |
|
* @param {Number} m02 Component in column 0, row 2 position (index 2) |
|
* @param {Number} m03 Component in column 0, row 3 position (index 3) |
|
* @param {Number} m10 Component in column 1, row 0 position (index 4) |
|
* @param {Number} m11 Component in column 1, row 1 position (index 5) |
|
* @param {Number} m12 Component in column 1, row 2 position (index 6) |
|
* @param {Number} m13 Component in column 1, row 3 position (index 7) |
|
* @param {Number} m20 Component in column 2, row 0 position (index 8) |
|
* @param {Number} m21 Component in column 2, row 1 position (index 9) |
|
* @param {Number} m22 Component in column 2, row 2 position (index 10) |
|
* @param {Number} m23 Component in column 2, row 3 position (index 11) |
|
* @param {Number} m30 Component in column 3, row 0 position (index 12) |
|
* @param {Number} m31 Component in column 3, row 1 position (index 13) |
|
* @param {Number} m32 Component in column 3, row 2 position (index 14) |
|
* @param {Number} m33 Component in column 3, row 3 position (index 15) |
|
* @returns {mat4} out |
|
*/ |
|
function set(out, m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) { |
|
out[0] = m00; |
|
out[1] = m01; |
|
out[2] = m02; |
|
out[3] = m03; |
|
out[4] = m10; |
|
out[5] = m11; |
|
out[6] = m12; |
|
out[7] = m13; |
|
out[8] = m20; |
|
out[9] = m21; |
|
out[10] = m22; |
|
out[11] = m23; |
|
out[12] = m30; |
|
out[13] = m31; |
|
out[14] = m32; |
|
out[15] = m33; |
|
return out; |
|
} |
|
|
|
/** |
|
* Set a mat4 to the identity matrix |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @returns {mat4} out |
|
*/ |
|
function identity(out) { |
|
out[0] = 1; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 0; |
|
out[4] = 0; |
|
out[5] = 1; |
|
out[6] = 0; |
|
out[7] = 0; |
|
out[8] = 0; |
|
out[9] = 0; |
|
out[10] = 1; |
|
out[11] = 0; |
|
out[12] = 0; |
|
out[13] = 0; |
|
out[14] = 0; |
|
out[15] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Transpose the values of a mat4 |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the source matrix |
|
* @returns {mat4} out |
|
*/ |
|
function transpose(out, a) { |
|
// If we are transposing ourselves we can skip a few steps but have to cache some values |
|
if (out === a) { |
|
var a01 = a[1], |
|
a02 = a[2], |
|
a03 = a[3]; |
|
var a12 = a[6], |
|
a13 = a[7]; |
|
var a23 = a[11]; |
|
|
|
out[1] = a[4]; |
|
out[2] = a[8]; |
|
out[3] = a[12]; |
|
out[4] = a01; |
|
out[6] = a[9]; |
|
out[7] = a[13]; |
|
out[8] = a02; |
|
out[9] = a12; |
|
out[11] = a[14]; |
|
out[12] = a03; |
|
out[13] = a13; |
|
out[14] = a23; |
|
} else { |
|
out[0] = a[0]; |
|
out[1] = a[4]; |
|
out[2] = a[8]; |
|
out[3] = a[12]; |
|
out[4] = a[1]; |
|
out[5] = a[5]; |
|
out[6] = a[9]; |
|
out[7] = a[13]; |
|
out[8] = a[2]; |
|
out[9] = a[6]; |
|
out[10] = a[10]; |
|
out[11] = a[14]; |
|
out[12] = a[3]; |
|
out[13] = a[7]; |
|
out[14] = a[11]; |
|
out[15] = a[15]; |
|
} |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Inverts a mat4 |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the source matrix |
|
* @returns {mat4} out |
|
*/ |
|
function invert(out, a) { |
|
var a00 = a[0], |
|
a01 = a[1], |
|
a02 = a[2], |
|
a03 = a[3]; |
|
var a10 = a[4], |
|
a11 = a[5], |
|
a12 = a[6], |
|
a13 = a[7]; |
|
var a20 = a[8], |
|
a21 = a[9], |
|
a22 = a[10], |
|
a23 = a[11]; |
|
var a30 = a[12], |
|
a31 = a[13], |
|
a32 = a[14], |
|
a33 = a[15]; |
|
|
|
var b00 = a00 * a11 - a01 * a10; |
|
var b01 = a00 * a12 - a02 * a10; |
|
var b02 = a00 * a13 - a03 * a10; |
|
var b03 = a01 * a12 - a02 * a11; |
|
var b04 = a01 * a13 - a03 * a11; |
|
var b05 = a02 * a13 - a03 * a12; |
|
var b06 = a20 * a31 - a21 * a30; |
|
var b07 = a20 * a32 - a22 * a30; |
|
var b08 = a20 * a33 - a23 * a30; |
|
var b09 = a21 * a32 - a22 * a31; |
|
var b10 = a21 * a33 - a23 * a31; |
|
var b11 = a22 * a33 - a23 * a32; |
|
|
|
// Calculate the determinant |
|
var det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06; |
|
|
|
if (!det) { |
|
return null; |
|
} |
|
det = 1.0 / det; |
|
|
|
out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det; |
|
out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det; |
|
out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det; |
|
out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det; |
|
out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det; |
|
out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det; |
|
out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det; |
|
out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det; |
|
out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det; |
|
out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det; |
|
out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det; |
|
out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det; |
|
out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det; |
|
out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det; |
|
out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det; |
|
out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the adjugate of a mat4 |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the source matrix |
|
* @returns {mat4} out |
|
*/ |
|
function adjoint(out, a) { |
|
var a00 = a[0], |
|
a01 = a[1], |
|
a02 = a[2], |
|
a03 = a[3]; |
|
var a10 = a[4], |
|
a11 = a[5], |
|
a12 = a[6], |
|
a13 = a[7]; |
|
var a20 = a[8], |
|
a21 = a[9], |
|
a22 = a[10], |
|
a23 = a[11]; |
|
var a30 = a[12], |
|
a31 = a[13], |
|
a32 = a[14], |
|
a33 = a[15]; |
|
|
|
out[0] = a11 * (a22 * a33 - a23 * a32) - a21 * (a12 * a33 - a13 * a32) + a31 * (a12 * a23 - a13 * a22); |
|
out[1] = -(a01 * (a22 * a33 - a23 * a32) - a21 * (a02 * a33 - a03 * a32) + a31 * (a02 * a23 - a03 * a22)); |
|
out[2] = a01 * (a12 * a33 - a13 * a32) - a11 * (a02 * a33 - a03 * a32) + a31 * (a02 * a13 - a03 * a12); |
|
out[3] = -(a01 * (a12 * a23 - a13 * a22) - a11 * (a02 * a23 - a03 * a22) + a21 * (a02 * a13 - a03 * a12)); |
|
out[4] = -(a10 * (a22 * a33 - a23 * a32) - a20 * (a12 * a33 - a13 * a32) + a30 * (a12 * a23 - a13 * a22)); |
|
out[5] = a00 * (a22 * a33 - a23 * a32) - a20 * (a02 * a33 - a03 * a32) + a30 * (a02 * a23 - a03 * a22); |
|
out[6] = -(a00 * (a12 * a33 - a13 * a32) - a10 * (a02 * a33 - a03 * a32) + a30 * (a02 * a13 - a03 * a12)); |
|
out[7] = a00 * (a12 * a23 - a13 * a22) - a10 * (a02 * a23 - a03 * a22) + a20 * (a02 * a13 - a03 * a12); |
|
out[8] = a10 * (a21 * a33 - a23 * a31) - a20 * (a11 * a33 - a13 * a31) + a30 * (a11 * a23 - a13 * a21); |
|
out[9] = -(a00 * (a21 * a33 - a23 * a31) - a20 * (a01 * a33 - a03 * a31) + a30 * (a01 * a23 - a03 * a21)); |
|
out[10] = a00 * (a11 * a33 - a13 * a31) - a10 * (a01 * a33 - a03 * a31) + a30 * (a01 * a13 - a03 * a11); |
|
out[11] = -(a00 * (a11 * a23 - a13 * a21) - a10 * (a01 * a23 - a03 * a21) + a20 * (a01 * a13 - a03 * a11)); |
|
out[12] = -(a10 * (a21 * a32 - a22 * a31) - a20 * (a11 * a32 - a12 * a31) + a30 * (a11 * a22 - a12 * a21)); |
|
out[13] = a00 * (a21 * a32 - a22 * a31) - a20 * (a01 * a32 - a02 * a31) + a30 * (a01 * a22 - a02 * a21); |
|
out[14] = -(a00 * (a11 * a32 - a12 * a31) - a10 * (a01 * a32 - a02 * a31) + a30 * (a01 * a12 - a02 * a11)); |
|
out[15] = a00 * (a11 * a22 - a12 * a21) - a10 * (a01 * a22 - a02 * a21) + a20 * (a01 * a12 - a02 * a11); |
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the determinant of a mat4 |
|
* |
|
* @param {mat4} a the source matrix |
|
* @returns {Number} determinant of a |
|
*/ |
|
function determinant(a) { |
|
var a00 = a[0], |
|
a01 = a[1], |
|
a02 = a[2], |
|
a03 = a[3]; |
|
var a10 = a[4], |
|
a11 = a[5], |
|
a12 = a[6], |
|
a13 = a[7]; |
|
var a20 = a[8], |
|
a21 = a[9], |
|
a22 = a[10], |
|
a23 = a[11]; |
|
var a30 = a[12], |
|
a31 = a[13], |
|
a32 = a[14], |
|
a33 = a[15]; |
|
|
|
var b00 = a00 * a11 - a01 * a10; |
|
var b01 = a00 * a12 - a02 * a10; |
|
var b02 = a00 * a13 - a03 * a10; |
|
var b03 = a01 * a12 - a02 * a11; |
|
var b04 = a01 * a13 - a03 * a11; |
|
var b05 = a02 * a13 - a03 * a12; |
|
var b06 = a20 * a31 - a21 * a30; |
|
var b07 = a20 * a32 - a22 * a30; |
|
var b08 = a20 * a33 - a23 * a30; |
|
var b09 = a21 * a32 - a22 * a31; |
|
var b10 = a21 * a33 - a23 * a31; |
|
var b11 = a22 * a33 - a23 * a32; |
|
|
|
// Calculate the determinant |
|
return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06; |
|
} |
|
|
|
/** |
|
* Multiplies two mat4s |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the first operand |
|
* @param {mat4} b the second operand |
|
* @returns {mat4} out |
|
*/ |
|
function multiply(out, a, b) { |
|
var a00 = a[0], |
|
a01 = a[1], |
|
a02 = a[2], |
|
a03 = a[3]; |
|
var a10 = a[4], |
|
a11 = a[5], |
|
a12 = a[6], |
|
a13 = a[7]; |
|
var a20 = a[8], |
|
a21 = a[9], |
|
a22 = a[10], |
|
a23 = a[11]; |
|
var a30 = a[12], |
|
a31 = a[13], |
|
a32 = a[14], |
|
a33 = a[15]; |
|
|
|
// Cache only the current line of the second matrix |
|
var b0 = b[0], |
|
b1 = b[1], |
|
b2 = b[2], |
|
b3 = b[3]; |
|
out[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30; |
|
out[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31; |
|
out[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32; |
|
out[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33; |
|
|
|
b0 = b[4];b1 = b[5];b2 = b[6];b3 = b[7]; |
|
out[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30; |
|
out[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31; |
|
out[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32; |
|
out[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33; |
|
|
|
b0 = b[8];b1 = b[9];b2 = b[10];b3 = b[11]; |
|
out[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30; |
|
out[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31; |
|
out[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32; |
|
out[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33; |
|
|
|
b0 = b[12];b1 = b[13];b2 = b[14];b3 = b[15]; |
|
out[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30; |
|
out[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31; |
|
out[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32; |
|
out[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33; |
|
return out; |
|
} |
|
|
|
/** |
|
* Translate a mat4 by the given vector |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the matrix to translate |
|
* @param {vec3} v vector to translate by |
|
* @returns {mat4} out |
|
*/ |
|
function translate(out, a, v) { |
|
var x = v[0], |
|
y = v[1], |
|
z = v[2]; |
|
var a00 = void 0, |
|
a01 = void 0, |
|
a02 = void 0, |
|
a03 = void 0; |
|
var a10 = void 0, |
|
a11 = void 0, |
|
a12 = void 0, |
|
a13 = void 0; |
|
var a20 = void 0, |
|
a21 = void 0, |
|
a22 = void 0, |
|
a23 = void 0; |
|
|
|
if (a === out) { |
|
out[12] = a[0] * x + a[4] * y + a[8] * z + a[12]; |
|
out[13] = a[1] * x + a[5] * y + a[9] * z + a[13]; |
|
out[14] = a[2] * x + a[6] * y + a[10] * z + a[14]; |
|
out[15] = a[3] * x + a[7] * y + a[11] * z + a[15]; |
|
} else { |
|
a00 = a[0];a01 = a[1];a02 = a[2];a03 = a[3]; |
|
a10 = a[4];a11 = a[5];a12 = a[6];a13 = a[7]; |
|
a20 = a[8];a21 = a[9];a22 = a[10];a23 = a[11]; |
|
|
|
out[0] = a00;out[1] = a01;out[2] = a02;out[3] = a03; |
|
out[4] = a10;out[5] = a11;out[6] = a12;out[7] = a13; |
|
out[8] = a20;out[9] = a21;out[10] = a22;out[11] = a23; |
|
|
|
out[12] = a00 * x + a10 * y + a20 * z + a[12]; |
|
out[13] = a01 * x + a11 * y + a21 * z + a[13]; |
|
out[14] = a02 * x + a12 * y + a22 * z + a[14]; |
|
out[15] = a03 * x + a13 * y + a23 * z + a[15]; |
|
} |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Scales the mat4 by the dimensions in the given vec3 not using vectorization |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the matrix to scale |
|
* @param {vec3} v the vec3 to scale the matrix by |
|
* @returns {mat4} out |
|
**/ |
|
function scale(out, a, v) { |
|
var x = v[0], |
|
y = v[1], |
|
z = v[2]; |
|
|
|
out[0] = a[0] * x; |
|
out[1] = a[1] * x; |
|
out[2] = a[2] * x; |
|
out[3] = a[3] * x; |
|
out[4] = a[4] * y; |
|
out[5] = a[5] * y; |
|
out[6] = a[6] * y; |
|
out[7] = a[7] * y; |
|
out[8] = a[8] * z; |
|
out[9] = a[9] * z; |
|
out[10] = a[10] * z; |
|
out[11] = a[11] * z; |
|
out[12] = a[12]; |
|
out[13] = a[13]; |
|
out[14] = a[14]; |
|
out[15] = a[15]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Rotates a mat4 by the given angle around the given axis |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the matrix to rotate |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @param {vec3} axis the axis to rotate around |
|
* @returns {mat4} out |
|
*/ |
|
function rotate(out, a, rad, axis) { |
|
var x = axis[0], |
|
y = axis[1], |
|
z = axis[2]; |
|
var len = Math.sqrt(x * x + y * y + z * z); |
|
var s = void 0, |
|
c = void 0, |
|
t = void 0; |
|
var a00 = void 0, |
|
a01 = void 0, |
|
a02 = void 0, |
|
a03 = void 0; |
|
var a10 = void 0, |
|
a11 = void 0, |
|
a12 = void 0, |
|
a13 = void 0; |
|
var a20 = void 0, |
|
a21 = void 0, |
|
a22 = void 0, |
|
a23 = void 0; |
|
var b00 = void 0, |
|
b01 = void 0, |
|
b02 = void 0; |
|
var b10 = void 0, |
|
b11 = void 0, |
|
b12 = void 0; |
|
var b20 = void 0, |
|
b21 = void 0, |
|
b22 = void 0; |
|
|
|
if (Math.abs(len) < glMatrix.EPSILON) { |
|
return null; |
|
} |
|
|
|
len = 1 / len; |
|
x *= len; |
|
y *= len; |
|
z *= len; |
|
|
|
s = Math.sin(rad); |
|
c = Math.cos(rad); |
|
t = 1 - c; |
|
|
|
a00 = a[0];a01 = a[1];a02 = a[2];a03 = a[3]; |
|
a10 = a[4];a11 = a[5];a12 = a[6];a13 = a[7]; |
|
a20 = a[8];a21 = a[9];a22 = a[10];a23 = a[11]; |
|
|
|
// Construct the elements of the rotation matrix |
|
b00 = x * x * t + c;b01 = y * x * t + z * s;b02 = z * x * t - y * s; |
|
b10 = x * y * t - z * s;b11 = y * y * t + c;b12 = z * y * t + x * s; |
|
b20 = x * z * t + y * s;b21 = y * z * t - x * s;b22 = z * z * t + c; |
|
|
|
// Perform rotation-specific matrix multiplication |
|
out[0] = a00 * b00 + a10 * b01 + a20 * b02; |
|
out[1] = a01 * b00 + a11 * b01 + a21 * b02; |
|
out[2] = a02 * b00 + a12 * b01 + a22 * b02; |
|
out[3] = a03 * b00 + a13 * b01 + a23 * b02; |
|
out[4] = a00 * b10 + a10 * b11 + a20 * b12; |
|
out[5] = a01 * b10 + a11 * b11 + a21 * b12; |
|
out[6] = a02 * b10 + a12 * b11 + a22 * b12; |
|
out[7] = a03 * b10 + a13 * b11 + a23 * b12; |
|
out[8] = a00 * b20 + a10 * b21 + a20 * b22; |
|
out[9] = a01 * b20 + a11 * b21 + a21 * b22; |
|
out[10] = a02 * b20 + a12 * b21 + a22 * b22; |
|
out[11] = a03 * b20 + a13 * b21 + a23 * b22; |
|
|
|
if (a !== out) { |
|
// If the source and destination differ, copy the unchanged last row |
|
out[12] = a[12]; |
|
out[13] = a[13]; |
|
out[14] = a[14]; |
|
out[15] = a[15]; |
|
} |
|
return out; |
|
} |
|
|
|
/** |
|
* Rotates a matrix by the given angle around the X axis |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the matrix to rotate |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat4} out |
|
*/ |
|
function rotateX(out, a, rad) { |
|
var s = Math.sin(rad); |
|
var c = Math.cos(rad); |
|
var a10 = a[4]; |
|
var a11 = a[5]; |
|
var a12 = a[6]; |
|
var a13 = a[7]; |
|
var a20 = a[8]; |
|
var a21 = a[9]; |
|
var a22 = a[10]; |
|
var a23 = a[11]; |
|
|
|
if (a !== out) { |
|
// If the source and destination differ, copy the unchanged rows |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
out[2] = a[2]; |
|
out[3] = a[3]; |
|
out[12] = a[12]; |
|
out[13] = a[13]; |
|
out[14] = a[14]; |
|
out[15] = a[15]; |
|
} |
|
|
|
// Perform axis-specific matrix multiplication |
|
out[4] = a10 * c + a20 * s; |
|
out[5] = a11 * c + a21 * s; |
|
out[6] = a12 * c + a22 * s; |
|
out[7] = a13 * c + a23 * s; |
|
out[8] = a20 * c - a10 * s; |
|
out[9] = a21 * c - a11 * s; |
|
out[10] = a22 * c - a12 * s; |
|
out[11] = a23 * c - a13 * s; |
|
return out; |
|
} |
|
|
|
/** |
|
* Rotates a matrix by the given angle around the Y axis |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the matrix to rotate |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat4} out |
|
*/ |
|
function rotateY(out, a, rad) { |
|
var s = Math.sin(rad); |
|
var c = Math.cos(rad); |
|
var a00 = a[0]; |
|
var a01 = a[1]; |
|
var a02 = a[2]; |
|
var a03 = a[3]; |
|
var a20 = a[8]; |
|
var a21 = a[9]; |
|
var a22 = a[10]; |
|
var a23 = a[11]; |
|
|
|
if (a !== out) { |
|
// If the source and destination differ, copy the unchanged rows |
|
out[4] = a[4]; |
|
out[5] = a[5]; |
|
out[6] = a[6]; |
|
out[7] = a[7]; |
|
out[12] = a[12]; |
|
out[13] = a[13]; |
|
out[14] = a[14]; |
|
out[15] = a[15]; |
|
} |
|
|
|
// Perform axis-specific matrix multiplication |
|
out[0] = a00 * c - a20 * s; |
|
out[1] = a01 * c - a21 * s; |
|
out[2] = a02 * c - a22 * s; |
|
out[3] = a03 * c - a23 * s; |
|
out[8] = a00 * s + a20 * c; |
|
out[9] = a01 * s + a21 * c; |
|
out[10] = a02 * s + a22 * c; |
|
out[11] = a03 * s + a23 * c; |
|
return out; |
|
} |
|
|
|
/** |
|
* Rotates a matrix by the given angle around the Z axis |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the matrix to rotate |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat4} out |
|
*/ |
|
function rotateZ(out, a, rad) { |
|
var s = Math.sin(rad); |
|
var c = Math.cos(rad); |
|
var a00 = a[0]; |
|
var a01 = a[1]; |
|
var a02 = a[2]; |
|
var a03 = a[3]; |
|
var a10 = a[4]; |
|
var a11 = a[5]; |
|
var a12 = a[6]; |
|
var a13 = a[7]; |
|
|
|
if (a !== out) { |
|
// If the source and destination differ, copy the unchanged last row |
|
out[8] = a[8]; |
|
out[9] = a[9]; |
|
out[10] = a[10]; |
|
out[11] = a[11]; |
|
out[12] = a[12]; |
|
out[13] = a[13]; |
|
out[14] = a[14]; |
|
out[15] = a[15]; |
|
} |
|
|
|
// Perform axis-specific matrix multiplication |
|
out[0] = a00 * c + a10 * s; |
|
out[1] = a01 * c + a11 * s; |
|
out[2] = a02 * c + a12 * s; |
|
out[3] = a03 * c + a13 * s; |
|
out[4] = a10 * c - a00 * s; |
|
out[5] = a11 * c - a01 * s; |
|
out[6] = a12 * c - a02 * s; |
|
out[7] = a13 * c - a03 * s; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a vector translation |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat4.identity(dest); |
|
* mat4.translate(dest, dest, vec); |
|
* |
|
* @param {mat4} out mat4 receiving operation result |
|
* @param {vec3} v Translation vector |
|
* @returns {mat4} out |
|
*/ |
|
function fromTranslation(out, v) { |
|
out[0] = 1; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 0; |
|
out[4] = 0; |
|
out[5] = 1; |
|
out[6] = 0; |
|
out[7] = 0; |
|
out[8] = 0; |
|
out[9] = 0; |
|
out[10] = 1; |
|
out[11] = 0; |
|
out[12] = v[0]; |
|
out[13] = v[1]; |
|
out[14] = v[2]; |
|
out[15] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a vector scaling |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat4.identity(dest); |
|
* mat4.scale(dest, dest, vec); |
|
* |
|
* @param {mat4} out mat4 receiving operation result |
|
* @param {vec3} v Scaling vector |
|
* @returns {mat4} out |
|
*/ |
|
function fromScaling(out, v) { |
|
out[0] = v[0]; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 0; |
|
out[4] = 0; |
|
out[5] = v[1]; |
|
out[6] = 0; |
|
out[7] = 0; |
|
out[8] = 0; |
|
out[9] = 0; |
|
out[10] = v[2]; |
|
out[11] = 0; |
|
out[12] = 0; |
|
out[13] = 0; |
|
out[14] = 0; |
|
out[15] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a given angle around a given axis |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat4.identity(dest); |
|
* mat4.rotate(dest, dest, rad, axis); |
|
* |
|
* @param {mat4} out mat4 receiving operation result |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @param {vec3} axis the axis to rotate around |
|
* @returns {mat4} out |
|
*/ |
|
function fromRotation(out, rad, axis) { |
|
var x = axis[0], |
|
y = axis[1], |
|
z = axis[2]; |
|
var len = Math.sqrt(x * x + y * y + z * z); |
|
var s = void 0, |
|
c = void 0, |
|
t = void 0; |
|
|
|
if (Math.abs(len) < glMatrix.EPSILON) { |
|
return null; |
|
} |
|
|
|
len = 1 / len; |
|
x *= len; |
|
y *= len; |
|
z *= len; |
|
|
|
s = Math.sin(rad); |
|
c = Math.cos(rad); |
|
t = 1 - c; |
|
|
|
// Perform rotation-specific matrix multiplication |
|
out[0] = x * x * t + c; |
|
out[1] = y * x * t + z * s; |
|
out[2] = z * x * t - y * s; |
|
out[3] = 0; |
|
out[4] = x * y * t - z * s; |
|
out[5] = y * y * t + c; |
|
out[6] = z * y * t + x * s; |
|
out[7] = 0; |
|
out[8] = x * z * t + y * s; |
|
out[9] = y * z * t - x * s; |
|
out[10] = z * z * t + c; |
|
out[11] = 0; |
|
out[12] = 0; |
|
out[13] = 0; |
|
out[14] = 0; |
|
out[15] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from the given angle around the X axis |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat4.identity(dest); |
|
* mat4.rotateX(dest, dest, rad); |
|
* |
|
* @param {mat4} out mat4 receiving operation result |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat4} out |
|
*/ |
|
function fromXRotation(out, rad) { |
|
var s = Math.sin(rad); |
|
var c = Math.cos(rad); |
|
|
|
// Perform axis-specific matrix multiplication |
|
out[0] = 1; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 0; |
|
out[4] = 0; |
|
out[5] = c; |
|
out[6] = s; |
|
out[7] = 0; |
|
out[8] = 0; |
|
out[9] = -s; |
|
out[10] = c; |
|
out[11] = 0; |
|
out[12] = 0; |
|
out[13] = 0; |
|
out[14] = 0; |
|
out[15] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from the given angle around the Y axis |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat4.identity(dest); |
|
* mat4.rotateY(dest, dest, rad); |
|
* |
|
* @param {mat4} out mat4 receiving operation result |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat4} out |
|
*/ |
|
function fromYRotation(out, rad) { |
|
var s = Math.sin(rad); |
|
var c = Math.cos(rad); |
|
|
|
// Perform axis-specific matrix multiplication |
|
out[0] = c; |
|
out[1] = 0; |
|
out[2] = -s; |
|
out[3] = 0; |
|
out[4] = 0; |
|
out[5] = 1; |
|
out[6] = 0; |
|
out[7] = 0; |
|
out[8] = s; |
|
out[9] = 0; |
|
out[10] = c; |
|
out[11] = 0; |
|
out[12] = 0; |
|
out[13] = 0; |
|
out[14] = 0; |
|
out[15] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from the given angle around the Z axis |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat4.identity(dest); |
|
* mat4.rotateZ(dest, dest, rad); |
|
* |
|
* @param {mat4} out mat4 receiving operation result |
|
* @param {Number} rad the angle to rotate the matrix by |
|
* @returns {mat4} out |
|
*/ |
|
function fromZRotation(out, rad) { |
|
var s = Math.sin(rad); |
|
var c = Math.cos(rad); |
|
|
|
// Perform axis-specific matrix multiplication |
|
out[0] = c; |
|
out[1] = s; |
|
out[2] = 0; |
|
out[3] = 0; |
|
out[4] = -s; |
|
out[5] = c; |
|
out[6] = 0; |
|
out[7] = 0; |
|
out[8] = 0; |
|
out[9] = 0; |
|
out[10] = 1; |
|
out[11] = 0; |
|
out[12] = 0; |
|
out[13] = 0; |
|
out[14] = 0; |
|
out[15] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a quaternion rotation and vector translation |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat4.identity(dest); |
|
* mat4.translate(dest, vec); |
|
* let quatMat = mat4.create(); |
|
* quat4.toMat4(quat, quatMat); |
|
* mat4.multiply(dest, quatMat); |
|
* |
|
* @param {mat4} out mat4 receiving operation result |
|
* @param {quat4} q Rotation quaternion |
|
* @param {vec3} v Translation vector |
|
* @returns {mat4} out |
|
*/ |
|
function fromRotationTranslation(out, q, v) { |
|
// Quaternion math |
|
var x = q[0], |
|
y = q[1], |
|
z = q[2], |
|
w = q[3]; |
|
var x2 = x + x; |
|
var y2 = y + y; |
|
var z2 = z + z; |
|
|
|
var xx = x * x2; |
|
var xy = x * y2; |
|
var xz = x * z2; |
|
var yy = y * y2; |
|
var yz = y * z2; |
|
var zz = z * z2; |
|
var wx = w * x2; |
|
var wy = w * y2; |
|
var wz = w * z2; |
|
|
|
out[0] = 1 - (yy + zz); |
|
out[1] = xy + wz; |
|
out[2] = xz - wy; |
|
out[3] = 0; |
|
out[4] = xy - wz; |
|
out[5] = 1 - (xx + zz); |
|
out[6] = yz + wx; |
|
out[7] = 0; |
|
out[8] = xz + wy; |
|
out[9] = yz - wx; |
|
out[10] = 1 - (xx + yy); |
|
out[11] = 0; |
|
out[12] = v[0]; |
|
out[13] = v[1]; |
|
out[14] = v[2]; |
|
out[15] = 1; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Returns the translation vector component of a transformation |
|
* matrix. If a matrix is built with fromRotationTranslation, |
|
* the returned vector will be the same as the translation vector |
|
* originally supplied. |
|
* @param {vec3} out Vector to receive translation component |
|
* @param {mat4} mat Matrix to be decomposed (input) |
|
* @return {vec3} out |
|
*/ |
|
function getTranslation(out, mat) { |
|
out[0] = mat[12]; |
|
out[1] = mat[13]; |
|
out[2] = mat[14]; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Returns the scaling factor component of a transformation |
|
* matrix. If a matrix is built with fromRotationTranslationScale |
|
* with a normalized Quaternion paramter, the returned vector will be |
|
* the same as the scaling vector |
|
* originally supplied. |
|
* @param {vec3} out Vector to receive scaling factor component |
|
* @param {mat4} mat Matrix to be decomposed (input) |
|
* @return {vec3} out |
|
*/ |
|
function getScaling(out, mat) { |
|
var m11 = mat[0]; |
|
var m12 = mat[1]; |
|
var m13 = mat[2]; |
|
var m21 = mat[4]; |
|
var m22 = mat[5]; |
|
var m23 = mat[6]; |
|
var m31 = mat[8]; |
|
var m32 = mat[9]; |
|
var m33 = mat[10]; |
|
|
|
out[0] = Math.sqrt(m11 * m11 + m12 * m12 + m13 * m13); |
|
out[1] = Math.sqrt(m21 * m21 + m22 * m22 + m23 * m23); |
|
out[2] = Math.sqrt(m31 * m31 + m32 * m32 + m33 * m33); |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Returns a quaternion representing the rotational component |
|
* of a transformation matrix. If a matrix is built with |
|
* fromRotationTranslation, the returned quaternion will be the |
|
* same as the quaternion originally supplied. |
|
* @param {quat} out Quaternion to receive the rotation component |
|
* @param {mat4} mat Matrix to be decomposed (input) |
|
* @return {quat} out |
|
*/ |
|
function getRotation(out, mat) { |
|
// Algorithm taken from http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm |
|
var trace = mat[0] + mat[5] + mat[10]; |
|
var S = 0; |
|
|
|
if (trace > 0) { |
|
S = Math.sqrt(trace + 1.0) * 2; |
|
out[3] = 0.25 * S; |
|
out[0] = (mat[6] - mat[9]) / S; |
|
out[1] = (mat[8] - mat[2]) / S; |
|
out[2] = (mat[1] - mat[4]) / S; |
|
} else if (mat[0] > mat[5] & mat[0] > mat[10]) { |
|
S = Math.sqrt(1.0 + mat[0] - mat[5] - mat[10]) * 2; |
|
out[3] = (mat[6] - mat[9]) / S; |
|
out[0] = 0.25 * S; |
|
out[1] = (mat[1] + mat[4]) / S; |
|
out[2] = (mat[8] + mat[2]) / S; |
|
} else if (mat[5] > mat[10]) { |
|
S = Math.sqrt(1.0 + mat[5] - mat[0] - mat[10]) * 2; |
|
out[3] = (mat[8] - mat[2]) / S; |
|
out[0] = (mat[1] + mat[4]) / S; |
|
out[1] = 0.25 * S; |
|
out[2] = (mat[6] + mat[9]) / S; |
|
} else { |
|
S = Math.sqrt(1.0 + mat[10] - mat[0] - mat[5]) * 2; |
|
out[3] = (mat[1] - mat[4]) / S; |
|
out[0] = (mat[8] + mat[2]) / S; |
|
out[1] = (mat[6] + mat[9]) / S; |
|
out[2] = 0.25 * S; |
|
} |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a quaternion rotation, vector translation and vector scale |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat4.identity(dest); |
|
* mat4.translate(dest, vec); |
|
* let quatMat = mat4.create(); |
|
* quat4.toMat4(quat, quatMat); |
|
* mat4.multiply(dest, quatMat); |
|
* mat4.scale(dest, scale) |
|
* |
|
* @param {mat4} out mat4 receiving operation result |
|
* @param {quat4} q Rotation quaternion |
|
* @param {vec3} v Translation vector |
|
* @param {vec3} s Scaling vector |
|
* @returns {mat4} out |
|
*/ |
|
function fromRotationTranslationScale(out, q, v, s) { |
|
// Quaternion math |
|
var x = q[0], |
|
y = q[1], |
|
z = q[2], |
|
w = q[3]; |
|
var x2 = x + x; |
|
var y2 = y + y; |
|
var z2 = z + z; |
|
|
|
var xx = x * x2; |
|
var xy = x * y2; |
|
var xz = x * z2; |
|
var yy = y * y2; |
|
var yz = y * z2; |
|
var zz = z * z2; |
|
var wx = w * x2; |
|
var wy = w * y2; |
|
var wz = w * z2; |
|
var sx = s[0]; |
|
var sy = s[1]; |
|
var sz = s[2]; |
|
|
|
out[0] = (1 - (yy + zz)) * sx; |
|
out[1] = (xy + wz) * sx; |
|
out[2] = (xz - wy) * sx; |
|
out[3] = 0; |
|
out[4] = (xy - wz) * sy; |
|
out[5] = (1 - (xx + zz)) * sy; |
|
out[6] = (yz + wx) * sy; |
|
out[7] = 0; |
|
out[8] = (xz + wy) * sz; |
|
out[9] = (yz - wx) * sz; |
|
out[10] = (1 - (xx + yy)) * sz; |
|
out[11] = 0; |
|
out[12] = v[0]; |
|
out[13] = v[1]; |
|
out[14] = v[2]; |
|
out[15] = 1; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a matrix from a quaternion rotation, vector translation and vector scale, rotating and scaling around the given origin |
|
* This is equivalent to (but much faster than): |
|
* |
|
* mat4.identity(dest); |
|
* mat4.translate(dest, vec); |
|
* mat4.translate(dest, origin); |
|
* let quatMat = mat4.create(); |
|
* quat4.toMat4(quat, quatMat); |
|
* mat4.multiply(dest, quatMat); |
|
* mat4.scale(dest, scale) |
|
* mat4.translate(dest, negativeOrigin); |
|
* |
|
* @param {mat4} out mat4 receiving operation result |
|
* @param {quat4} q Rotation quaternion |
|
* @param {vec3} v Translation vector |
|
* @param {vec3} s Scaling vector |
|
* @param {vec3} o The origin vector around which to scale and rotate |
|
* @returns {mat4} out |
|
*/ |
|
function fromRotationTranslationScaleOrigin(out, q, v, s, o) { |
|
// Quaternion math |
|
var x = q[0], |
|
y = q[1], |
|
z = q[2], |
|
w = q[3]; |
|
var x2 = x + x; |
|
var y2 = y + y; |
|
var z2 = z + z; |
|
|
|
var xx = x * x2; |
|
var xy = x * y2; |
|
var xz = x * z2; |
|
var yy = y * y2; |
|
var yz = y * z2; |
|
var zz = z * z2; |
|
var wx = w * x2; |
|
var wy = w * y2; |
|
var wz = w * z2; |
|
|
|
var sx = s[0]; |
|
var sy = s[1]; |
|
var sz = s[2]; |
|
|
|
var ox = o[0]; |
|
var oy = o[1]; |
|
var oz = o[2]; |
|
|
|
out[0] = (1 - (yy + zz)) * sx; |
|
out[1] = (xy + wz) * sx; |
|
out[2] = (xz - wy) * sx; |
|
out[3] = 0; |
|
out[4] = (xy - wz) * sy; |
|
out[5] = (1 - (xx + zz)) * sy; |
|
out[6] = (yz + wx) * sy; |
|
out[7] = 0; |
|
out[8] = (xz + wy) * sz; |
|
out[9] = (yz - wx) * sz; |
|
out[10] = (1 - (xx + yy)) * sz; |
|
out[11] = 0; |
|
out[12] = v[0] + ox - (out[0] * ox + out[4] * oy + out[8] * oz); |
|
out[13] = v[1] + oy - (out[1] * ox + out[5] * oy + out[9] * oz); |
|
out[14] = v[2] + oz - (out[2] * ox + out[6] * oy + out[10] * oz); |
|
out[15] = 1; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates a 4x4 matrix from the given quaternion |
|
* |
|
* @param {mat4} out mat4 receiving operation result |
|
* @param {quat} q Quaternion to create matrix from |
|
* |
|
* @returns {mat4} out |
|
*/ |
|
function fromQuat(out, q) { |
|
var x = q[0], |
|
y = q[1], |
|
z = q[2], |
|
w = q[3]; |
|
var x2 = x + x; |
|
var y2 = y + y; |
|
var z2 = z + z; |
|
|
|
var xx = x * x2; |
|
var yx = y * x2; |
|
var yy = y * y2; |
|
var zx = z * x2; |
|
var zy = z * y2; |
|
var zz = z * z2; |
|
var wx = w * x2; |
|
var wy = w * y2; |
|
var wz = w * z2; |
|
|
|
out[0] = 1 - yy - zz; |
|
out[1] = yx + wz; |
|
out[2] = zx - wy; |
|
out[3] = 0; |
|
|
|
out[4] = yx - wz; |
|
out[5] = 1 - xx - zz; |
|
out[6] = zy + wx; |
|
out[7] = 0; |
|
|
|
out[8] = zx + wy; |
|
out[9] = zy - wx; |
|
out[10] = 1 - xx - yy; |
|
out[11] = 0; |
|
|
|
out[12] = 0; |
|
out[13] = 0; |
|
out[14] = 0; |
|
out[15] = 1; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Generates a frustum matrix with the given bounds |
|
* |
|
* @param {mat4} out mat4 frustum matrix will be written into |
|
* @param {Number} left Left bound of the frustum |
|
* @param {Number} right Right bound of the frustum |
|
* @param {Number} bottom Bottom bound of the frustum |
|
* @param {Number} top Top bound of the frustum |
|
* @param {Number} near Near bound of the frustum |
|
* @param {Number} far Far bound of the frustum |
|
* @returns {mat4} out |
|
*/ |
|
function frustum(out, left, right, bottom, top, near, far) { |
|
var rl = 1 / (right - left); |
|
var tb = 1 / (top - bottom); |
|
var nf = 1 / (near - far); |
|
out[0] = near * 2 * rl; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 0; |
|
out[4] = 0; |
|
out[5] = near * 2 * tb; |
|
out[6] = 0; |
|
out[7] = 0; |
|
out[8] = (right + left) * rl; |
|
out[9] = (top + bottom) * tb; |
|
out[10] = (far + near) * nf; |
|
out[11] = -1; |
|
out[12] = 0; |
|
out[13] = 0; |
|
out[14] = far * near * 2 * nf; |
|
out[15] = 0; |
|
return out; |
|
} |
|
|
|
/** |
|
* Generates a perspective projection matrix with the given bounds |
|
* |
|
* @param {mat4} out mat4 frustum matrix will be written into |
|
* @param {number} fovy Vertical field of view in radians |
|
* @param {number} aspect Aspect ratio. typically viewport width/height |
|
* @param {number} near Near bound of the frustum |
|
* @param {number} far Far bound of the frustum |
|
* @returns {mat4} out |
|
*/ |
|
function perspective(out, fovy, aspect, near, far) { |
|
var f = 1.0 / Math.tan(fovy / 2); |
|
var nf = 1 / (near - far); |
|
out[0] = f / aspect; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 0; |
|
out[4] = 0; |
|
out[5] = f; |
|
out[6] = 0; |
|
out[7] = 0; |
|
out[8] = 0; |
|
out[9] = 0; |
|
out[10] = (far + near) * nf; |
|
out[11] = -1; |
|
out[12] = 0; |
|
out[13] = 0; |
|
out[14] = 2 * far * near * nf; |
|
out[15] = 0; |
|
return out; |
|
} |
|
|
|
/** |
|
* Generates a perspective projection matrix with the given field of view. |
|
* This is primarily useful for generating projection matrices to be used |
|
* with the still experiemental WebVR API. |
|
* |
|
* @param {mat4} out mat4 frustum matrix will be written into |
|
* @param {Object} fov Object containing the following values: upDegrees, downDegrees, leftDegrees, rightDegrees |
|
* @param {number} near Near bound of the frustum |
|
* @param {number} far Far bound of the frustum |
|
* @returns {mat4} out |
|
*/ |
|
function perspectiveFromFieldOfView(out, fov, near, far) { |
|
var upTan = Math.tan(fov.upDegrees * Math.PI / 180.0); |
|
var downTan = Math.tan(fov.downDegrees * Math.PI / 180.0); |
|
var leftTan = Math.tan(fov.leftDegrees * Math.PI / 180.0); |
|
var rightTan = Math.tan(fov.rightDegrees * Math.PI / 180.0); |
|
var xScale = 2.0 / (leftTan + rightTan); |
|
var yScale = 2.0 / (upTan + downTan); |
|
|
|
out[0] = xScale; |
|
out[1] = 0.0; |
|
out[2] = 0.0; |
|
out[3] = 0.0; |
|
out[4] = 0.0; |
|
out[5] = yScale; |
|
out[6] = 0.0; |
|
out[7] = 0.0; |
|
out[8] = -((leftTan - rightTan) * xScale * 0.5); |
|
out[9] = (upTan - downTan) * yScale * 0.5; |
|
out[10] = far / (near - far); |
|
out[11] = -1.0; |
|
out[12] = 0.0; |
|
out[13] = 0.0; |
|
out[14] = far * near / (near - far); |
|
out[15] = 0.0; |
|
return out; |
|
} |
|
|
|
/** |
|
* Generates a orthogonal projection matrix with the given bounds |
|
* |
|
* @param {mat4} out mat4 frustum matrix will be written into |
|
* @param {number} left Left bound of the frustum |
|
* @param {number} right Right bound of the frustum |
|
* @param {number} bottom Bottom bound of the frustum |
|
* @param {number} top Top bound of the frustum |
|
* @param {number} near Near bound of the frustum |
|
* @param {number} far Far bound of the frustum |
|
* @returns {mat4} out |
|
*/ |
|
function ortho(out, left, right, bottom, top, near, far) { |
|
var lr = 1 / (left - right); |
|
var bt = 1 / (bottom - top); |
|
var nf = 1 / (near - far); |
|
out[0] = -2 * lr; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 0; |
|
out[4] = 0; |
|
out[5] = -2 * bt; |
|
out[6] = 0; |
|
out[7] = 0; |
|
out[8] = 0; |
|
out[9] = 0; |
|
out[10] = 2 * nf; |
|
out[11] = 0; |
|
out[12] = (left + right) * lr; |
|
out[13] = (top + bottom) * bt; |
|
out[14] = (far + near) * nf; |
|
out[15] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Generates a look-at matrix with the given eye position, focal point, and up axis |
|
* |
|
* @param {mat4} out mat4 frustum matrix will be written into |
|
* @param {vec3} eye Position of the viewer |
|
* @param {vec3} center Point the viewer is looking at |
|
* @param {vec3} up vec3 pointing up |
|
* @returns {mat4} out |
|
*/ |
|
function lookAt(out, eye, center, up) { |
|
var x0 = void 0, |
|
x1 = void 0, |
|
x2 = void 0, |
|
y0 = void 0, |
|
y1 = void 0, |
|
y2 = void 0, |
|
z0 = void 0, |
|
z1 = void 0, |
|
z2 = void 0, |
|
len = void 0; |
|
var eyex = eye[0]; |
|
var eyey = eye[1]; |
|
var eyez = eye[2]; |
|
var upx = up[0]; |
|
var upy = up[1]; |
|
var upz = up[2]; |
|
var centerx = center[0]; |
|
var centery = center[1]; |
|
var centerz = center[2]; |
|
|
|
if (Math.abs(eyex - centerx) < glMatrix.EPSILON && Math.abs(eyey - centery) < glMatrix.EPSILON && Math.abs(eyez - centerz) < glMatrix.EPSILON) { |
|
return mat4.identity(out); |
|
} |
|
|
|
z0 = eyex - centerx; |
|
z1 = eyey - centery; |
|
z2 = eyez - centerz; |
|
|
|
len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2); |
|
z0 *= len; |
|
z1 *= len; |
|
z2 *= len; |
|
|
|
x0 = upy * z2 - upz * z1; |
|
x1 = upz * z0 - upx * z2; |
|
x2 = upx * z1 - upy * z0; |
|
len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2); |
|
if (!len) { |
|
x0 = 0; |
|
x1 = 0; |
|
x2 = 0; |
|
} else { |
|
len = 1 / len; |
|
x0 *= len; |
|
x1 *= len; |
|
x2 *= len; |
|
} |
|
|
|
y0 = z1 * x2 - z2 * x1; |
|
y1 = z2 * x0 - z0 * x2; |
|
y2 = z0 * x1 - z1 * x0; |
|
|
|
len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2); |
|
if (!len) { |
|
y0 = 0; |
|
y1 = 0; |
|
y2 = 0; |
|
} else { |
|
len = 1 / len; |
|
y0 *= len; |
|
y1 *= len; |
|
y2 *= len; |
|
} |
|
|
|
out[0] = x0; |
|
out[1] = y0; |
|
out[2] = z0; |
|
out[3] = 0; |
|
out[4] = x1; |
|
out[5] = y1; |
|
out[6] = z1; |
|
out[7] = 0; |
|
out[8] = x2; |
|
out[9] = y2; |
|
out[10] = z2; |
|
out[11] = 0; |
|
out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez); |
|
out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez); |
|
out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez); |
|
out[15] = 1; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Generates a matrix that makes something look at something else. |
|
* |
|
* @param {mat4} out mat4 frustum matrix will be written into |
|
* @param {vec3} eye Position of the viewer |
|
* @param {vec3} center Point the viewer is looking at |
|
* @param {vec3} up vec3 pointing up |
|
* @returns {mat4} out |
|
*/ |
|
function targetTo(out, eye, target, up) { |
|
var eyex = eye[0], |
|
eyey = eye[1], |
|
eyez = eye[2], |
|
upx = up[0], |
|
upy = up[1], |
|
upz = up[2]; |
|
|
|
var z0 = eyex - target[0], |
|
z1 = eyey - target[1], |
|
z2 = eyez - target[2]; |
|
|
|
var len = z0 * z0 + z1 * z1 + z2 * z2; |
|
if (len > 0) { |
|
len = 1 / Math.sqrt(len); |
|
z0 *= len; |
|
z1 *= len; |
|
z2 *= len; |
|
} |
|
|
|
var x0 = upy * z2 - upz * z1, |
|
x1 = upz * z0 - upx * z2, |
|
x2 = upx * z1 - upy * z0; |
|
|
|
out[0] = x0; |
|
out[1] = x1; |
|
out[2] = x2; |
|
out[3] = 0; |
|
out[4] = z1 * x2 - z2 * x1; |
|
out[5] = z2 * x0 - z0 * x2; |
|
out[6] = z0 * x1 - z1 * x0; |
|
out[7] = 0; |
|
out[8] = z0; |
|
out[9] = z1; |
|
out[10] = z2; |
|
out[11] = 0; |
|
out[12] = eyex; |
|
out[13] = eyey; |
|
out[14] = eyez; |
|
out[15] = 1; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Returns a string representation of a mat4 |
|
* |
|
* @param {mat4} a matrix to represent as a string |
|
* @returns {String} string representation of the matrix |
|
*/ |
|
function str(a) { |
|
return 'mat4(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ', ' + a[4] + ', ' + a[5] + ', ' + a[6] + ', ' + a[7] + ', ' + a[8] + ', ' + a[9] + ', ' + a[10] + ', ' + a[11] + ', ' + a[12] + ', ' + a[13] + ', ' + a[14] + ', ' + a[15] + ')'; |
|
} |
|
|
|
/** |
|
* Returns Frobenius norm of a mat4 |
|
* |
|
* @param {mat4} a the matrix to calculate Frobenius norm of |
|
* @returns {Number} Frobenius norm |
|
*/ |
|
function frob(a) { |
|
return Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2) + Math.pow(a[4], 2) + Math.pow(a[5], 2) + Math.pow(a[6], 2) + Math.pow(a[7], 2) + Math.pow(a[8], 2) + Math.pow(a[9], 2) + Math.pow(a[10], 2) + Math.pow(a[11], 2) + Math.pow(a[12], 2) + Math.pow(a[13], 2) + Math.pow(a[14], 2) + Math.pow(a[15], 2)); |
|
} |
|
|
|
/** |
|
* Adds two mat4's |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the first operand |
|
* @param {mat4} b the second operand |
|
* @returns {mat4} out |
|
*/ |
|
function add(out, a, b) { |
|
out[0] = a[0] + b[0]; |
|
out[1] = a[1] + b[1]; |
|
out[2] = a[2] + b[2]; |
|
out[3] = a[3] + b[3]; |
|
out[4] = a[4] + b[4]; |
|
out[5] = a[5] + b[5]; |
|
out[6] = a[6] + b[6]; |
|
out[7] = a[7] + b[7]; |
|
out[8] = a[8] + b[8]; |
|
out[9] = a[9] + b[9]; |
|
out[10] = a[10] + b[10]; |
|
out[11] = a[11] + b[11]; |
|
out[12] = a[12] + b[12]; |
|
out[13] = a[13] + b[13]; |
|
out[14] = a[14] + b[14]; |
|
out[15] = a[15] + b[15]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Subtracts matrix b from matrix a |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the first operand |
|
* @param {mat4} b the second operand |
|
* @returns {mat4} out |
|
*/ |
|
function subtract(out, a, b) { |
|
out[0] = a[0] - b[0]; |
|
out[1] = a[1] - b[1]; |
|
out[2] = a[2] - b[2]; |
|
out[3] = a[3] - b[3]; |
|
out[4] = a[4] - b[4]; |
|
out[5] = a[5] - b[5]; |
|
out[6] = a[6] - b[6]; |
|
out[7] = a[7] - b[7]; |
|
out[8] = a[8] - b[8]; |
|
out[9] = a[9] - b[9]; |
|
out[10] = a[10] - b[10]; |
|
out[11] = a[11] - b[11]; |
|
out[12] = a[12] - b[12]; |
|
out[13] = a[13] - b[13]; |
|
out[14] = a[14] - b[14]; |
|
out[15] = a[15] - b[15]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Multiply each element of the matrix by a scalar. |
|
* |
|
* @param {mat4} out the receiving matrix |
|
* @param {mat4} a the matrix to scale |
|
* @param {Number} b amount to scale the matrix's elements by |
|
* @returns {mat4} out |
|
*/ |
|
function multiplyScalar(out, a, b) { |
|
out[0] = a[0] * b; |
|
out[1] = a[1] * b; |
|
out[2] = a[2] * b; |
|
out[3] = a[3] * b; |
|
out[4] = a[4] * b; |
|
out[5] = a[5] * b; |
|
out[6] = a[6] * b; |
|
out[7] = a[7] * b; |
|
out[8] = a[8] * b; |
|
out[9] = a[9] * b; |
|
out[10] = a[10] * b; |
|
out[11] = a[11] * b; |
|
out[12] = a[12] * b; |
|
out[13] = a[13] * b; |
|
out[14] = a[14] * b; |
|
out[15] = a[15] * b; |
|
return out; |
|
} |
|
|
|
/** |
|
* Adds two mat4's after multiplying each element of the second operand by a scalar value. |
|
* |
|
* @param {mat4} out the receiving vector |
|
* @param {mat4} a the first operand |
|
* @param {mat4} b the second operand |
|
* @param {Number} scale the amount to scale b's elements by before adding |
|
* @returns {mat4} out |
|
*/ |
|
function multiplyScalarAndAdd(out, a, b, scale) { |
|
out[0] = a[0] + b[0] * scale; |
|
out[1] = a[1] + b[1] * scale; |
|
out[2] = a[2] + b[2] * scale; |
|
out[3] = a[3] + b[3] * scale; |
|
out[4] = a[4] + b[4] * scale; |
|
out[5] = a[5] + b[5] * scale; |
|
out[6] = a[6] + b[6] * scale; |
|
out[7] = a[7] + b[7] * scale; |
|
out[8] = a[8] + b[8] * scale; |
|
out[9] = a[9] + b[9] * scale; |
|
out[10] = a[10] + b[10] * scale; |
|
out[11] = a[11] + b[11] * scale; |
|
out[12] = a[12] + b[12] * scale; |
|
out[13] = a[13] + b[13] * scale; |
|
out[14] = a[14] + b[14] * scale; |
|
out[15] = a[15] + b[15] * scale; |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===) |
|
* |
|
* @param {mat4} a The first matrix. |
|
* @param {mat4} b The second matrix. |
|
* @returns {Boolean} True if the matrices are equal, false otherwise. |
|
*/ |
|
function exactEquals(a, b) { |
|
return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3] && a[4] === b[4] && a[5] === b[5] && a[6] === b[6] && a[7] === b[7] && a[8] === b[8] && a[9] === b[9] && a[10] === b[10] && a[11] === b[11] && a[12] === b[12] && a[13] === b[13] && a[14] === b[14] && a[15] === b[15]; |
|
} |
|
|
|
/** |
|
* Returns whether or not the matrices have approximately the same elements in the same position. |
|
* |
|
* @param {mat4} a The first matrix. |
|
* @param {mat4} b The second matrix. |
|
* @returns {Boolean} True if the matrices are equal, false otherwise. |
|
*/ |
|
function equals(a, b) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3]; |
|
var a4 = a[4], |
|
a5 = a[5], |
|
a6 = a[6], |
|
a7 = a[7]; |
|
var a8 = a[8], |
|
a9 = a[9], |
|
a10 = a[10], |
|
a11 = a[11]; |
|
var a12 = a[12], |
|
a13 = a[13], |
|
a14 = a[14], |
|
a15 = a[15]; |
|
|
|
var b0 = b[0], |
|
b1 = b[1], |
|
b2 = b[2], |
|
b3 = b[3]; |
|
var b4 = b[4], |
|
b5 = b[5], |
|
b6 = b[6], |
|
b7 = b[7]; |
|
var b8 = b[8], |
|
b9 = b[9], |
|
b10 = b[10], |
|
b11 = b[11]; |
|
var b12 = b[12], |
|
b13 = b[13], |
|
b14 = b[14], |
|
b15 = b[15]; |
|
|
|
return Math.abs(a0 - b0) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)) && Math.abs(a6 - b6) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a6), Math.abs(b6)) && Math.abs(a7 - b7) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a7), Math.abs(b7)) && Math.abs(a8 - b8) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a8), Math.abs(b8)) && Math.abs(a9 - b9) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a9), Math.abs(b9)) && Math.abs(a10 - b10) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a10), Math.abs(b10)) && Math.abs(a11 - b11) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a11), Math.abs(b11)) && Math.abs(a12 - b12) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a12), Math.abs(b12)) && Math.abs(a13 - b13) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a13), Math.abs(b13)) && Math.abs(a14 - b14) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a14), Math.abs(b14)) && Math.abs(a15 - b15) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a15), Math.abs(b15)); |
|
} |
|
|
|
/** |
|
* Alias for {@link mat4.multiply} |
|
* @function |
|
*/ |
|
var mul = exports.mul = multiply; |
|
|
|
/** |
|
* Alias for {@link mat4.subtract} |
|
* @function |
|
*/ |
|
var sub = exports.sub = subtract; |
|
|
|
/***/ }), |
|
/* 8 */ |
|
/***/ (function(module, exports, __webpack_require__) { |
|
|
|
"use strict"; |
|
|
|
|
|
Object.defineProperty(exports, "__esModule", { |
|
value: true |
|
}); |
|
exports.setAxes = exports.sqlerp = exports.rotationTo = exports.equals = exports.exactEquals = exports.normalize = exports.sqrLen = exports.squaredLength = exports.len = exports.length = exports.lerp = exports.dot = exports.scale = exports.mul = exports.add = exports.set = exports.copy = exports.fromValues = exports.clone = undefined; |
|
exports.create = create; |
|
exports.identity = identity; |
|
exports.setAxisAngle = setAxisAngle; |
|
exports.getAxisAngle = getAxisAngle; |
|
exports.multiply = multiply; |
|
exports.rotateX = rotateX; |
|
exports.rotateY = rotateY; |
|
exports.rotateZ = rotateZ; |
|
exports.calculateW = calculateW; |
|
exports.slerp = slerp; |
|
exports.invert = invert; |
|
exports.conjugate = conjugate; |
|
exports.fromMat3 = fromMat3; |
|
exports.fromEuler = fromEuler; |
|
exports.str = str; |
|
|
|
var _common = __webpack_require__(0); |
|
|
|
var glMatrix = _interopRequireWildcard(_common); |
|
|
|
var _mat = __webpack_require__(1); |
|
|
|
var mat3 = _interopRequireWildcard(_mat); |
|
|
|
var _vec = __webpack_require__(2); |
|
|
|
var vec3 = _interopRequireWildcard(_vec); |
|
|
|
var _vec2 = __webpack_require__(3); |
|
|
|
var vec4 = _interopRequireWildcard(_vec2); |
|
|
|
function _interopRequireWildcard(obj) { if (obj && obj.__esModule) { return obj; } else { var newObj = {}; if (obj != null) { for (var key in obj) { if (Object.prototype.hasOwnProperty.call(obj, key)) newObj[key] = obj[key]; } } newObj.default = obj; return newObj; } } |
|
|
|
/** |
|
* Quaternion |
|
* @module quat |
|
*/ |
|
|
|
/** |
|
* Creates a new identity quat |
|
* |
|
* @returns {quat} a new quaternion |
|
*/ |
|
/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. |
|
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy |
|
of this software and associated documentation files (the "Software"), to deal |
|
in the Software without restriction, including without limitation the rights |
|
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
|
copies of the Software, and to permit persons to whom the Software is |
|
furnished to do so, subject to the following conditions: |
|
|
|
The above copyright notice and this permission notice shall be included in |
|
all copies or substantial portions of the Software. |
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
|
THE SOFTWARE. */ |
|
|
|
function create() { |
|
var out = new glMatrix.ARRAY_TYPE(4); |
|
out[0] = 0; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Set a quat to the identity quaternion |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @returns {quat} out |
|
*/ |
|
function identity(out) { |
|
out[0] = 0; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 1; |
|
return out; |
|
} |
|
|
|
/** |
|
* Sets a quat from the given angle and rotation axis, |
|
* then returns it. |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {vec3} axis the axis around which to rotate |
|
* @param {Number} rad the angle in radians |
|
* @returns {quat} out |
|
**/ |
|
function setAxisAngle(out, axis, rad) { |
|
rad = rad * 0.5; |
|
var s = Math.sin(rad); |
|
out[0] = s * axis[0]; |
|
out[1] = s * axis[1]; |
|
out[2] = s * axis[2]; |
|
out[3] = Math.cos(rad); |
|
return out; |
|
} |
|
|
|
/** |
|
* Gets the rotation axis and angle for a given |
|
* quaternion. If a quaternion is created with |
|
* setAxisAngle, this method will return the same |
|
* values as providied in the original parameter list |
|
* OR functionally equivalent values. |
|
* Example: The quaternion formed by axis [0, 0, 1] and |
|
* angle -90 is the same as the quaternion formed by |
|
* [0, 0, 1] and 270. This method favors the latter. |
|
* @param {vec3} out_axis Vector receiving the axis of rotation |
|
* @param {quat} q Quaternion to be decomposed |
|
* @return {Number} Angle, in radians, of the rotation |
|
*/ |
|
function getAxisAngle(out_axis, q) { |
|
var rad = Math.acos(q[3]) * 2.0; |
|
var s = Math.sin(rad / 2.0); |
|
if (s != 0.0) { |
|
out_axis[0] = q[0] / s; |
|
out_axis[1] = q[1] / s; |
|
out_axis[2] = q[2] / s; |
|
} else { |
|
// If s is zero, return any axis (no rotation - axis does not matter) |
|
out_axis[0] = 1; |
|
out_axis[1] = 0; |
|
out_axis[2] = 0; |
|
} |
|
return rad; |
|
} |
|
|
|
/** |
|
* Multiplies two quat's |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {quat} a the first operand |
|
* @param {quat} b the second operand |
|
* @returns {quat} out |
|
*/ |
|
function multiply(out, a, b) { |
|
var ax = a[0], |
|
ay = a[1], |
|
az = a[2], |
|
aw = a[3]; |
|
var bx = b[0], |
|
by = b[1], |
|
bz = b[2], |
|
bw = b[3]; |
|
|
|
out[0] = ax * bw + aw * bx + ay * bz - az * by; |
|
out[1] = ay * bw + aw * by + az * bx - ax * bz; |
|
out[2] = az * bw + aw * bz + ax * by - ay * bx; |
|
out[3] = aw * bw - ax * bx - ay * by - az * bz; |
|
return out; |
|
} |
|
|
|
/** |
|
* Rotates a quaternion by the given angle about the X axis |
|
* |
|
* @param {quat} out quat receiving operation result |
|
* @param {quat} a quat to rotate |
|
* @param {number} rad angle (in radians) to rotate |
|
* @returns {quat} out |
|
*/ |
|
function rotateX(out, a, rad) { |
|
rad *= 0.5; |
|
|
|
var ax = a[0], |
|
ay = a[1], |
|
az = a[2], |
|
aw = a[3]; |
|
var bx = Math.sin(rad), |
|
bw = Math.cos(rad); |
|
|
|
out[0] = ax * bw + aw * bx; |
|
out[1] = ay * bw + az * bx; |
|
out[2] = az * bw - ay * bx; |
|
out[3] = aw * bw - ax * bx; |
|
return out; |
|
} |
|
|
|
/** |
|
* Rotates a quaternion by the given angle about the Y axis |
|
* |
|
* @param {quat} out quat receiving operation result |
|
* @param {quat} a quat to rotate |
|
* @param {number} rad angle (in radians) to rotate |
|
* @returns {quat} out |
|
*/ |
|
function rotateY(out, a, rad) { |
|
rad *= 0.5; |
|
|
|
var ax = a[0], |
|
ay = a[1], |
|
az = a[2], |
|
aw = a[3]; |
|
var by = Math.sin(rad), |
|
bw = Math.cos(rad); |
|
|
|
out[0] = ax * bw - az * by; |
|
out[1] = ay * bw + aw * by; |
|
out[2] = az * bw + ax * by; |
|
out[3] = aw * bw - ay * by; |
|
return out; |
|
} |
|
|
|
/** |
|
* Rotates a quaternion by the given angle about the Z axis |
|
* |
|
* @param {quat} out quat receiving operation result |
|
* @param {quat} a quat to rotate |
|
* @param {number} rad angle (in radians) to rotate |
|
* @returns {quat} out |
|
*/ |
|
function rotateZ(out, a, rad) { |
|
rad *= 0.5; |
|
|
|
var ax = a[0], |
|
ay = a[1], |
|
az = a[2], |
|
aw = a[3]; |
|
var bz = Math.sin(rad), |
|
bw = Math.cos(rad); |
|
|
|
out[0] = ax * bw + ay * bz; |
|
out[1] = ay * bw - ax * bz; |
|
out[2] = az * bw + aw * bz; |
|
out[3] = aw * bw - az * bz; |
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the W component of a quat from the X, Y, and Z components. |
|
* Assumes that quaternion is 1 unit in length. |
|
* Any existing W component will be ignored. |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {quat} a quat to calculate W component of |
|
* @returns {quat} out |
|
*/ |
|
function calculateW(out, a) { |
|
var x = a[0], |
|
y = a[1], |
|
z = a[2]; |
|
|
|
out[0] = x; |
|
out[1] = y; |
|
out[2] = z; |
|
out[3] = Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z)); |
|
return out; |
|
} |
|
|
|
/** |
|
* Performs a spherical linear interpolation between two quat |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {quat} a the first operand |
|
* @param {quat} b the second operand |
|
* @param {Number} t interpolation amount between the two inputs |
|
* @returns {quat} out |
|
*/ |
|
function slerp(out, a, b, t) { |
|
// benchmarks: |
|
// http://jsperf.com/quaternion-slerp-implementations |
|
var ax = a[0], |
|
ay = a[1], |
|
az = a[2], |
|
aw = a[3]; |
|
var bx = b[0], |
|
by = b[1], |
|
bz = b[2], |
|
bw = b[3]; |
|
|
|
var omega = void 0, |
|
cosom = void 0, |
|
sinom = void 0, |
|
scale0 = void 0, |
|
scale1 = void 0; |
|
|
|
// calc cosine |
|
cosom = ax * bx + ay * by + az * bz + aw * bw; |
|
// adjust signs (if necessary) |
|
if (cosom < 0.0) { |
|
cosom = -cosom; |
|
bx = -bx; |
|
by = -by; |
|
bz = -bz; |
|
bw = -bw; |
|
} |
|
// calculate coefficients |
|
if (1.0 - cosom > 0.000001) { |
|
// standard case (slerp) |
|
omega = Math.acos(cosom); |
|
sinom = Math.sin(omega); |
|
scale0 = Math.sin((1.0 - t) * omega) / sinom; |
|
scale1 = Math.sin(t * omega) / sinom; |
|
} else { |
|
// "from" and "to" quaternions are very close |
|
// ... so we can do a linear interpolation |
|
scale0 = 1.0 - t; |
|
scale1 = t; |
|
} |
|
// calculate final values |
|
out[0] = scale0 * ax + scale1 * bx; |
|
out[1] = scale0 * ay + scale1 * by; |
|
out[2] = scale0 * az + scale1 * bz; |
|
out[3] = scale0 * aw + scale1 * bw; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the inverse of a quat |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {quat} a quat to calculate inverse of |
|
* @returns {quat} out |
|
*/ |
|
function invert(out, a) { |
|
var a0 = a[0], |
|
a1 = a[1], |
|
a2 = a[2], |
|
a3 = a[3]; |
|
var dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3; |
|
var invDot = dot ? 1.0 / dot : 0; |
|
|
|
// TODO: Would be faster to return [0,0,0,0] immediately if dot == 0 |
|
|
|
out[0] = -a0 * invDot; |
|
out[1] = -a1 * invDot; |
|
out[2] = -a2 * invDot; |
|
out[3] = a3 * invDot; |
|
return out; |
|
} |
|
|
|
/** |
|
* Calculates the conjugate of a quat |
|
* If the quaternion is normalized, this function is faster than quat.inverse and produces the same result. |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {quat} a quat to calculate conjugate of |
|
* @returns {quat} out |
|
*/ |
|
function conjugate(out, a) { |
|
out[0] = -a[0]; |
|
out[1] = -a[1]; |
|
out[2] = -a[2]; |
|
out[3] = a[3]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a quaternion from the given 3x3 rotation matrix. |
|
* |
|
* NOTE: The resultant quaternion is not normalized, so you should be sure |
|
* to renormalize the quaternion yourself where necessary. |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {mat3} m rotation matrix |
|
* @returns {quat} out |
|
* @function |
|
*/ |
|
function fromMat3(out, m) { |
|
// Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes |
|
// article "Quaternion Calculus and Fast Animation". |
|
var fTrace = m[0] + m[4] + m[8]; |
|
var fRoot = void 0; |
|
|
|
if (fTrace > 0.0) { |
|
// |w| > 1/2, may as well choose w > 1/2 |
|
fRoot = Math.sqrt(fTrace + 1.0); // 2w |
|
out[3] = 0.5 * fRoot; |
|
fRoot = 0.5 / fRoot; // 1/(4w) |
|
out[0] = (m[5] - m[7]) * fRoot; |
|
out[1] = (m[6] - m[2]) * fRoot; |
|
out[2] = (m[1] - m[3]) * fRoot; |
|
} else { |
|
// |w| <= 1/2 |
|
var i = 0; |
|
if (m[4] > m[0]) i = 1; |
|
if (m[8] > m[i * 3 + i]) i = 2; |
|
var j = (i + 1) % 3; |
|
var k = (i + 2) % 3; |
|
|
|
fRoot = Math.sqrt(m[i * 3 + i] - m[j * 3 + j] - m[k * 3 + k] + 1.0); |
|
out[i] = 0.5 * fRoot; |
|
fRoot = 0.5 / fRoot; |
|
out[3] = (m[j * 3 + k] - m[k * 3 + j]) * fRoot; |
|
out[j] = (m[j * 3 + i] + m[i * 3 + j]) * fRoot; |
|
out[k] = (m[k * 3 + i] + m[i * 3 + k]) * fRoot; |
|
} |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a quaternion from the given euler angle x, y, z. |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {x} Angle to rotate around X axis in degrees. |
|
* @param {y} Angle to rotate around Y axis in degrees. |
|
* @param {z} Angle to rotate around Z axis in degrees. |
|
* @returns {quat} out |
|
* @function |
|
*/ |
|
function fromEuler(out, x, y, z) { |
|
var halfToRad = 0.5 * Math.PI / 180.0; |
|
x *= halfToRad; |
|
y *= halfToRad; |
|
z *= halfToRad; |
|
|
|
var sx = Math.sin(x); |
|
var cx = Math.cos(x); |
|
var sy = Math.sin(y); |
|
var cy = Math.cos(y); |
|
var sz = Math.sin(z); |
|
var cz = Math.cos(z); |
|
|
|
out[0] = sx * cy * cz - cx * sy * sz; |
|
out[1] = cx * sy * cz + sx * cy * sz; |
|
out[2] = cx * cy * sz - sx * sy * cz; |
|
out[3] = cx * cy * cz + sx * sy * sz; |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Returns a string representation of a quatenion |
|
* |
|
* @param {quat} a vector to represent as a string |
|
* @returns {String} string representation of the vector |
|
*/ |
|
function str(a) { |
|
return 'quat(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')'; |
|
} |
|
|
|
/** |
|
* Creates a new quat initialized with values from an existing quaternion |
|
* |
|
* @param {quat} a quaternion to clone |
|
* @returns {quat} a new quaternion |
|
* @function |
|
*/ |
|
var clone = exports.clone = vec4.clone; |
|
|
|
/** |
|
* Creates a new quat initialized with the given values |
|
* |
|
* @param {Number} x X component |
|
* @param {Number} y Y component |
|
* @param {Number} z Z component |
|
* @param {Number} w W component |
|
* @returns {quat} a new quaternion |
|
* @function |
|
*/ |
|
var fromValues = exports.fromValues = vec4.fromValues; |
|
|
|
/** |
|
* Copy the values from one quat to another |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {quat} a the source quaternion |
|
* @returns {quat} out |
|
* @function |
|
*/ |
|
var copy = exports.copy = vec4.copy; |
|
|
|
/** |
|
* Set the components of a quat to the given values |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {Number} x X component |
|
* @param {Number} y Y component |
|
* @param {Number} z Z component |
|
* @param {Number} w W component |
|
* @returns {quat} out |
|
* @function |
|
*/ |
|
var set = exports.set = vec4.set; |
|
|
|
/** |
|
* Adds two quat's |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {quat} a the first operand |
|
* @param {quat} b the second operand |
|
* @returns {quat} out |
|
* @function |
|
*/ |
|
var add = exports.add = vec4.add; |
|
|
|
/** |
|
* Alias for {@link quat.multiply} |
|
* @function |
|
*/ |
|
var mul = exports.mul = multiply; |
|
|
|
/** |
|
* Scales a quat by a scalar number |
|
* |
|
* @param {quat} out the receiving vector |
|
* @param {quat} a the vector to scale |
|
* @param {Number} b amount to scale the vector by |
|
* @returns {quat} out |
|
* @function |
|
*/ |
|
var scale = exports.scale = vec4.scale; |
|
|
|
/** |
|
* Calculates the dot product of two quat's |
|
* |
|
* @param {quat} a the first operand |
|
* @param {quat} b the second operand |
|
* @returns {Number} dot product of a and b |
|
* @function |
|
*/ |
|
var dot = exports.dot = vec4.dot; |
|
|
|
/** |
|
* Performs a linear interpolation between two quat's |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {quat} a the first operand |
|
* @param {quat} b the second operand |
|
* @param {Number} t interpolation amount between the two inputs |
|
* @returns {quat} out |
|
* @function |
|
*/ |
|
var lerp = exports.lerp = vec4.lerp; |
|
|
|
/** |
|
* Calculates the length of a quat |
|
* |
|
* @param {quat} a vector to calculate length of |
|
* @returns {Number} length of a |
|
*/ |
|
var length = exports.length = vec4.length; |
|
|
|
/** |
|
* Alias for {@link quat.length} |
|
* @function |
|
*/ |
|
var len = exports.len = length; |
|
|
|
/** |
|
* Calculates the squared length of a quat |
|
* |
|
* @param {quat} a vector to calculate squared length of |
|
* @returns {Number} squared length of a |
|
* @function |
|
*/ |
|
var squaredLength = exports.squaredLength = vec4.squaredLength; |
|
|
|
/** |
|
* Alias for {@link quat.squaredLength} |
|
* @function |
|
*/ |
|
var sqrLen = exports.sqrLen = squaredLength; |
|
|
|
/** |
|
* Normalize a quat |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {quat} a quaternion to normalize |
|
* @returns {quat} out |
|
* @function |
|
*/ |
|
var normalize = exports.normalize = vec4.normalize; |
|
|
|
/** |
|
* Returns whether or not the quaternions have exactly the same elements in the same position (when compared with ===) |
|
* |
|
* @param {quat} a The first quaternion. |
|
* @param {quat} b The second quaternion. |
|
* @returns {Boolean} True if the vectors are equal, false otherwise. |
|
*/ |
|
var exactEquals = exports.exactEquals = vec4.exactEquals; |
|
|
|
/** |
|
* Returns whether or not the quaternions have approximately the same elements in the same position. |
|
* |
|
* @param {quat} a The first vector. |
|
* @param {quat} b The second vector. |
|
* @returns {Boolean} True if the vectors are equal, false otherwise. |
|
*/ |
|
var equals = exports.equals = vec4.equals; |
|
|
|
/** |
|
* Sets a quaternion to represent the shortest rotation from one |
|
* vector to another. |
|
* |
|
* Both vectors are assumed to be unit length. |
|
* |
|
* @param {quat} out the receiving quaternion. |
|
* @param {vec3} a the initial vector |
|
* @param {vec3} b the destination vector |
|
* @returns {quat} out |
|
*/ |
|
var rotationTo = exports.rotationTo = function () { |
|
var tmpvec3 = vec3.create(); |
|
var xUnitVec3 = vec3.fromValues(1, 0, 0); |
|
var yUnitVec3 = vec3.fromValues(0, 1, 0); |
|
|
|
return function (out, a, b) { |
|
var dot = vec3.dot(a, b); |
|
if (dot < -0.999999) { |
|
vec3.cross(tmpvec3, xUnitVec3, a); |
|
if (vec3.len(tmpvec3) < 0.000001) vec3.cross(tmpvec3, yUnitVec3, a); |
|
vec3.normalize(tmpvec3, tmpvec3); |
|
setAxisAngle(out, tmpvec3, Math.PI); |
|
return out; |
|
} else if (dot > 0.999999) { |
|
out[0] = 0; |
|
out[1] = 0; |
|
out[2] = 0; |
|
out[3] = 1; |
|
return out; |
|
} else { |
|
vec3.cross(tmpvec3, a, b); |
|
out[0] = tmpvec3[0]; |
|
out[1] = tmpvec3[1]; |
|
out[2] = tmpvec3[2]; |
|
out[3] = 1 + dot; |
|
return normalize(out, out); |
|
} |
|
}; |
|
}(); |
|
|
|
/** |
|
* Performs a spherical linear interpolation with two control points |
|
* |
|
* @param {quat} out the receiving quaternion |
|
* @param {quat} a the first operand |
|
* @param {quat} b the second operand |
|
* @param {quat} c the third operand |
|
* @param {quat} d the fourth operand |
|
* @param {Number} t interpolation amount |
|
* @returns {quat} out |
|
*/ |
|
var sqlerp = exports.sqlerp = function () { |
|
var temp1 = create(); |
|
var temp2 = create(); |
|
|
|
return function (out, a, b, c, d, t) { |
|
slerp(temp1, a, d, t); |
|
slerp(temp2, b, c, t); |
|
slerp(out, temp1, temp2, 2 * t * (1 - t)); |
|
|
|
return out; |
|
}; |
|
}(); |
|
|
|
/** |
|
* Sets the specified quaternion with values corresponding to the given |
|
* axes. Each axis is a vec3 and is expected to be unit length and |
|
* perpendicular to all other specified axes. |
|
* |
|
* @param {vec3} view the vector representing the viewing direction |
|
* @param {vec3} right the vector representing the local "right" direction |
|
* @param {vec3} up the vector representing the local "up" direction |
|
* @returns {quat} out |
|
*/ |
|
var setAxes = exports.setAxes = function () { |
|
var matr = mat3.create(); |
|
|
|
return function (out, view, right, up) { |
|
matr[0] = right[0]; |
|
matr[3] = right[1]; |
|
matr[6] = right[2]; |
|
|
|
matr[1] = up[0]; |
|
matr[4] = up[1]; |
|
matr[7] = up[2]; |
|
|
|
matr[2] = -view[0]; |
|
matr[5] = -view[1]; |
|
matr[8] = -view[2]; |
|
|
|
return normalize(out, fromMat3(out, matr)); |
|
}; |
|
}(); |
|
|
|
/***/ }), |
|
/* 9 */ |
|
/***/ (function(module, exports, __webpack_require__) { |
|
|
|
"use strict"; |
|
|
|
|
|
Object.defineProperty(exports, "__esModule", { |
|
value: true |
|
}); |
|
exports.forEach = exports.sqrLen = exports.sqrDist = exports.dist = exports.div = exports.mul = exports.sub = exports.len = undefined; |
|
exports.create = create; |
|
exports.clone = clone; |
|
exports.fromValues = fromValues; |
|
exports.copy = copy; |
|
exports.set = set; |
|
exports.add = add; |
|
exports.subtract = subtract; |
|
exports.multiply = multiply; |
|
exports.divide = divide; |
|
exports.ceil = ceil; |
|
exports.floor = floor; |
|
exports.min = min; |
|
exports.max = max; |
|
exports.round = round; |
|
exports.scale = scale; |
|
exports.scaleAndAdd = scaleAndAdd; |
|
exports.distance = distance; |
|
exports.squaredDistance = squaredDistance; |
|
exports.length = length; |
|
exports.squaredLength = squaredLength; |
|
exports.negate = negate; |
|
exports.inverse = inverse; |
|
exports.normalize = normalize; |
|
exports.dot = dot; |
|
exports.cross = cross; |
|
exports.lerp = lerp; |
|
exports.random = random; |
|
exports.transformMat2 = transformMat2; |
|
exports.transformMat2d = transformMat2d; |
|
exports.transformMat3 = transformMat3; |
|
exports.transformMat4 = transformMat4; |
|
exports.str = str; |
|
exports.exactEquals = exactEquals; |
|
exports.equals = equals; |
|
|
|
var _common = __webpack_require__(0); |
|
|
|
var glMatrix = _interopRequireWildcard(_common); |
|
|
|
function _interopRequireWildcard(obj) { if (obj && obj.__esModule) { return obj; } else { var newObj = {}; if (obj != null) { for (var key in obj) { if (Object.prototype.hasOwnProperty.call(obj, key)) newObj[key] = obj[key]; } } newObj.default = obj; return newObj; } } |
|
|
|
/** |
|
* 2 Dimensional Vector |
|
* @module vec2 |
|
*/ |
|
|
|
/** |
|
* Creates a new, empty vec2 |
|
* |
|
* @returns {vec2} a new 2D vector |
|
*/ |
|
function create() { |
|
var out = new glMatrix.ARRAY_TYPE(2); |
|
out[0] = 0; |
|
out[1] = 0; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a new vec2 initialized with values from an existing vector |
|
* |
|
* @param {vec2} a vector to clone |
|
* @returns {vec2} a new 2D vector |
|
*/ |
|
/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. |
|
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy |
|
of this software and associated documentation files (the "Software"), to deal |
|
in the Software without restriction, including without limitation the rights |
|
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
|
copies of the Software, and to permit persons to whom the Software is |
|
furnished to do so, subject to the following conditions: |
|
|
|
The above copyright notice and this permission notice shall be included in |
|
all copies or substantial portions of the Software. |
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
|
THE SOFTWARE. */ |
|
|
|
function clone(a) { |
|
var out = new glMatrix.ARRAY_TYPE(2); |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Creates a new vec2 initialized with the given values |
|
* |
|
* @param {Number} x X component |
|
* @param {Number} y Y component |
|
* @returns {vec2} a new 2D vector |
|
*/ |
|
function fromValues(x, y) { |
|
var out = new glMatrix.ARRAY_TYPE(2); |
|
out[0] = x; |
|
out[1] = y; |
|
return out; |
|
} |
|
|
|
/** |
|
* Copy the values from one vec2 to another |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the source vector |
|
* @returns {vec2} out |
|
*/ |
|
function copy(out, a) { |
|
out[0] = a[0]; |
|
out[1] = a[1]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Set the components of a vec2 to the given values |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {Number} x X component |
|
* @param {Number} y Y component |
|
* @returns {vec2} out |
|
*/ |
|
function set(out, x, y) { |
|
out[0] = x; |
|
out[1] = y; |
|
return out; |
|
} |
|
|
|
/** |
|
* Adds two vec2's |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @returns {vec2} out |
|
*/ |
|
function add(out, a, b) { |
|
out[0] = a[0] + b[0]; |
|
out[1] = a[1] + b[1]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Subtracts vector b from vector a |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @returns {vec2} out |
|
*/ |
|
function subtract(out, a, b) { |
|
out[0] = a[0] - b[0]; |
|
out[1] = a[1] - b[1]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Multiplies two vec2's |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @returns {vec2} out |
|
*/ |
|
function multiply(out, a, b) { |
|
out[0] = a[0] * b[0]; |
|
out[1] = a[1] * b[1]; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Divides two vec2's |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @returns {vec2} out |
|
*/ |
|
function divide(out, a, b) { |
|
out[0] = a[0] / b[0]; |
|
out[1] = a[1] / b[1]; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Math.ceil the components of a vec2 |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a vector to ceil |
|
* @returns {vec2} out |
|
*/ |
|
function ceil(out, a) { |
|
out[0] = Math.ceil(a[0]); |
|
out[1] = Math.ceil(a[1]); |
|
return out; |
|
}; |
|
|
|
/** |
|
* Math.floor the components of a vec2 |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a vector to floor |
|
* @returns {vec2} out |
|
*/ |
|
function floor(out, a) { |
|
out[0] = Math.floor(a[0]); |
|
out[1] = Math.floor(a[1]); |
|
return out; |
|
}; |
|
|
|
/** |
|
* Returns the minimum of two vec2's |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @returns {vec2} out |
|
*/ |
|
function min(out, a, b) { |
|
out[0] = Math.min(a[0], b[0]); |
|
out[1] = Math.min(a[1], b[1]); |
|
return out; |
|
}; |
|
|
|
/** |
|
* Returns the maximum of two vec2's |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @returns {vec2} out |
|
*/ |
|
function max(out, a, b) { |
|
out[0] = Math.max(a[0], b[0]); |
|
out[1] = Math.max(a[1], b[1]); |
|
return out; |
|
}; |
|
|
|
/** |
|
* Math.round the components of a vec2 |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a vector to round |
|
* @returns {vec2} out |
|
*/ |
|
function round(out, a) { |
|
out[0] = Math.round(a[0]); |
|
out[1] = Math.round(a[1]); |
|
return out; |
|
}; |
|
|
|
/** |
|
* Scales a vec2 by a scalar number |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the vector to scale |
|
* @param {Number} b amount to scale the vector by |
|
* @returns {vec2} out |
|
*/ |
|
function scale(out, a, b) { |
|
out[0] = a[0] * b; |
|
out[1] = a[1] * b; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Adds two vec2's after scaling the second operand by a scalar value |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @param {Number} scale the amount to scale b by before adding |
|
* @returns {vec2} out |
|
*/ |
|
function scaleAndAdd(out, a, b, scale) { |
|
out[0] = a[0] + b[0] * scale; |
|
out[1] = a[1] + b[1] * scale; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Calculates the euclidian distance between two vec2's |
|
* |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @returns {Number} distance between a and b |
|
*/ |
|
function distance(a, b) { |
|
var x = b[0] - a[0], |
|
y = b[1] - a[1]; |
|
return Math.sqrt(x * x + y * y); |
|
}; |
|
|
|
/** |
|
* Calculates the squared euclidian distance between two vec2's |
|
* |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @returns {Number} squared distance between a and b |
|
*/ |
|
function squaredDistance(a, b) { |
|
var x = b[0] - a[0], |
|
y = b[1] - a[1]; |
|
return x * x + y * y; |
|
}; |
|
|
|
/** |
|
* Calculates the length of a vec2 |
|
* |
|
* @param {vec2} a vector to calculate length of |
|
* @returns {Number} length of a |
|
*/ |
|
function length(a) { |
|
var x = a[0], |
|
y = a[1]; |
|
return Math.sqrt(x * x + y * y); |
|
}; |
|
|
|
/** |
|
* Calculates the squared length of a vec2 |
|
* |
|
* @param {vec2} a vector to calculate squared length of |
|
* @returns {Number} squared length of a |
|
*/ |
|
function squaredLength(a) { |
|
var x = a[0], |
|
y = a[1]; |
|
return x * x + y * y; |
|
}; |
|
|
|
/** |
|
* Negates the components of a vec2 |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a vector to negate |
|
* @returns {vec2} out |
|
*/ |
|
function negate(out, a) { |
|
out[0] = -a[0]; |
|
out[1] = -a[1]; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Returns the inverse of the components of a vec2 |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a vector to invert |
|
* @returns {vec2} out |
|
*/ |
|
function inverse(out, a) { |
|
out[0] = 1.0 / a[0]; |
|
out[1] = 1.0 / a[1]; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Normalize a vec2 |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a vector to normalize |
|
* @returns {vec2} out |
|
*/ |
|
function normalize(out, a) { |
|
var x = a[0], |
|
y = a[1]; |
|
var len = x * x + y * y; |
|
if (len > 0) { |
|
//TODO: evaluate use of glm_invsqrt here? |
|
len = 1 / Math.sqrt(len); |
|
out[0] = a[0] * len; |
|
out[1] = a[1] * len; |
|
} |
|
return out; |
|
}; |
|
|
|
/** |
|
* Calculates the dot product of two vec2's |
|
* |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @returns {Number} dot product of a and b |
|
*/ |
|
function dot(a, b) { |
|
return a[0] * b[0] + a[1] * b[1]; |
|
}; |
|
|
|
/** |
|
* Computes the cross product of two vec2's |
|
* Note that the cross product must by definition produce a 3D vector |
|
* |
|
* @param {vec3} out the receiving vector |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @returns {vec3} out |
|
*/ |
|
function cross(out, a, b) { |
|
var z = a[0] * b[1] - a[1] * b[0]; |
|
out[0] = out[1] = 0; |
|
out[2] = z; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Performs a linear interpolation between two vec2's |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the first operand |
|
* @param {vec2} b the second operand |
|
* @param {Number} t interpolation amount between the two inputs |
|
* @returns {vec2} out |
|
*/ |
|
function lerp(out, a, b, t) { |
|
var ax = a[0], |
|
ay = a[1]; |
|
out[0] = ax + t * (b[0] - ax); |
|
out[1] = ay + t * (b[1] - ay); |
|
return out; |
|
}; |
|
|
|
/** |
|
* Generates a random vector with the given scale |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {Number} [scale] Length of the resulting vector. If ommitted, a unit vector will be returned |
|
* @returns {vec2} out |
|
*/ |
|
function random(out, scale) { |
|
scale = scale || 1.0; |
|
var r = glMatrix.RANDOM() * 2.0 * Math.PI; |
|
out[0] = Math.cos(r) * scale; |
|
out[1] = Math.sin(r) * scale; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Transforms the vec2 with a mat2 |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the vector to transform |
|
* @param {mat2} m matrix to transform with |
|
* @returns {vec2} out |
|
*/ |
|
function transformMat2(out, a, m) { |
|
var x = a[0], |
|
y = a[1]; |
|
out[0] = m[0] * x + m[2] * y; |
|
out[1] = m[1] * x + m[3] * y; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Transforms the vec2 with a mat2d |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the vector to transform |
|
* @param {mat2d} m matrix to transform with |
|
* @returns {vec2} out |
|
*/ |
|
function transformMat2d(out, a, m) { |
|
var x = a[0], |
|
y = a[1]; |
|
out[0] = m[0] * x + m[2] * y + m[4]; |
|
out[1] = m[1] * x + m[3] * y + m[5]; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Transforms the vec2 with a mat3 |
|
* 3rd vector component is implicitly '1' |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the vector to transform |
|
* @param {mat3} m matrix to transform with |
|
* @returns {vec2} out |
|
*/ |
|
function transformMat3(out, a, m) { |
|
var x = a[0], |
|
y = a[1]; |
|
out[0] = m[0] * x + m[3] * y + m[6]; |
|
out[1] = m[1] * x + m[4] * y + m[7]; |
|
return out; |
|
}; |
|
|
|
/** |
|
* Transforms the vec2 with a mat4 |
|
* 3rd vector component is implicitly '0' |
|
* 4th vector component is implicitly '1' |
|
* |
|
* @param {vec2} out the receiving vector |
|
* @param {vec2} a the vector to transform |
|
* @param {mat4} m matrix to transform with |
|
* @returns {vec2} out |
|
*/ |
|
function transformMat4(out, a, m) { |
|
var x = a[0]; |
|
var y = a[1]; |
|
out[0] = m[0] * x + m[4] * y + m[12]; |
|
out[1] = m[1] * x + m[5] * y + m[13]; |
|
return out; |
|
} |
|
|
|
/** |
|
* Returns a string representation of a vector |
|
* |
|
* @param {vec2} a vector to represent as a string |
|
* @returns {String} string representation of the vector |
|
*/ |
|
function str(a) { |
|
return 'vec2(' + a[0] + ', ' + a[1] + ')'; |
|
} |
|
|
|
/** |
|
* Returns whether or not the vectors exactly have the same elements in the same position (when compared with ===) |
|
* |
|
* @param {vec2} a The first vector. |
|
* @param {vec2} b The second vector. |
|
* @returns {Boolean} True if the vectors are equal, false otherwise. |
|
*/ |
|
function exactEquals(a, b) { |
|
return a[0] === b[0] && a[1] === b[1]; |
|
} |
|
|
|
/** |
|
* Returns whether or not the vectors have approximately the same elements in the same position. |
|
* |
|
* @param {vec2} a The first vector. |
|
* @param {vec2} b The second vector. |
|
* @returns {Boolean} True if the vectors are equal, false otherwise. |
|
*/ |
|
function equals(a, b) { |
|
var a0 = a[0], |
|
a1 = a[1]; |
|
var b0 = b[0], |
|
b1 = b[1]; |
|
return Math.abs(a0 - b0) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)); |
|
} |
|
|
|
/** |
|
* Alias for {@link vec2.length} |
|
* @function |
|
*/ |
|
var len = exports.len = length; |
|
|
|
/** |
|
* Alias for {@link vec2.subtract} |
|
* @function |
|
*/ |
|
var sub = exports.sub = subtract; |
|
|
|
/** |
|
* Alias for {@link vec2.multiply} |
|
* @function |
|
*/ |
|
var mul = exports.mul = multiply; |
|
|
|
/** |
|
* Alias for {@link vec2.divide} |
|
* @function |
|
*/ |
|
var div = exports.div = divide; |
|
|
|
/** |
|
* Alias for {@link vec2.distance} |
|
* @function |
|
*/ |
|
var dist = exports.dist = distance; |
|
|
|
/** |
|
* Alias for {@link vec2.squaredDistance} |
|
* @function |
|
*/ |
|
var sqrDist = exports.sqrDist = squaredDistance; |
|
|
|
/** |
|
* Alias for {@link vec2.squaredLength} |
|
* @function |
|
*/ |
|
var sqrLen = exports.sqrLen = squaredLength; |
|
|
|
/** |
|
* Perform some operation over an array of vec2s. |
|
* |
|
* @param {Array} a the array of vectors to iterate over |
|
* @param {Number} stride Number of elements between the start of each vec2. If 0 assumes tightly packed |
|
* @param {Number} offset Number of elements to skip at the beginning of the array |
|
* @param {Number} count Number of vec2s to iterate over. If 0 iterates over entire array |
|
* @param {Function} fn Function to call for each vector in the array |
|
* @param {Object} [arg] additional argument to pass to fn |
|
* @returns {Array} a |
|
* @function |
|
*/ |
|
var forEach = exports.forEach = function () { |
|
var vec = create(); |
|
|
|
return function (a, stride, offset, count, fn, arg) { |
|
var i = void 0, |
|
l = void 0; |
|
if (!stride) { |
|
stride = 2; |
|
} |
|
|
|
if (!offset) { |
|
offset = 0; |
|
} |
|
|
|
if (count) { |
|
l = Math.min(count * stride + offset, a.length); |
|
} else { |
|
l = a.length; |
|
} |
|
|
|
for (i = offset; i < l; i += stride) { |
|
vec[0] = a[i];vec[1] = a[i + 1]; |
|
fn(vec, vec, arg); |
|
a[i] = vec[0];a[i + 1] = vec[1]; |
|
} |
|
|
|
return a; |
|
}; |
|
}(); |
|
|
|
/***/ }) |
|
/******/ ]); |
|
}); |