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author | Karl Berry <karl@freefriends.org> | 2021-02-25 19:22:25 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2021-02-25 19:22:25 +0000 |
commit | ad547a6b5986815fda458221149728d9d9ab1d87 (patch) | |
tree | 16296910eb3eca724371474ea9aea3994dc69614 /Build/source/utils/asymptote/gl-matrix-2.4.0-pruned/dist/gl-matrix.js | |
parent | 947b43de3dd21d58ccc2ffadefc4441ea1c2a813 (diff) |
restore Build,TODO from r57911
git-svn-id: svn://tug.org/texlive/trunk@57915 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Build/source/utils/asymptote/gl-matrix-2.4.0-pruned/dist/gl-matrix.js')
-rw-r--r-- | Build/source/utils/asymptote/gl-matrix-2.4.0-pruned/dist/gl-matrix.js | 2907 |
1 files changed, 2907 insertions, 0 deletions
diff --git a/Build/source/utils/asymptote/gl-matrix-2.4.0-pruned/dist/gl-matrix.js b/Build/source/utils/asymptote/gl-matrix-2.4.0-pruned/dist/gl-matrix.js new file mode 100644 index 00000000000..7a0f61547af --- /dev/null +++ b/Build/source/utils/asymptote/gl-matrix-2.4.0-pruned/dist/gl-matrix.js @@ -0,0 +1,2907 @@ +/** + * @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. */ + +(function webpackUniversalModuleDefinition(root, factory) { + if(typeof exports === 'object' && typeof module === 'object') + module.exports = factory(); + else if(typeof define === 'function' && define.amd) + define([], factory); + else { + var a = factory(); + for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i]; + } +})(typeof self !== 'undefined' ? self : this, function() { +return /******/ (function(modules) { // webpackBootstrap +/******/ // The module cache +/******/ var installedModules = {}; +/******/ +/******/ // The require function +/******/ function __webpack_require__(moduleId) { +/******/ +/******/ // Check if module is in cache +/******/ if(installedModules[moduleId]) { +/******/ return installedModules[moduleId].exports; +/******/ } +/******/ // Create a new module (and put it into the cache) +/******/ var module = installedModules[moduleId] = { +/******/ i: moduleId, +/******/ l: false, +/******/ exports: {} +/******/ }; +/******/ +/******/ // Execute the module function +/******/ modules[moduleId].call(module.exports, module, module.exports, __webpack_require__); +/******/ +/******/ // Flag the module as loaded +/******/ module.l = true; +/******/ +/******/ // Return the exports of the module +/******/ return module.exports; +/******/ } +/******/ +/******/ +/******/ // expose the modules object (__webpack_modules__) +/******/ __webpack_require__.m = modules; +/******/ +/******/ // expose the module cache +/******/ __webpack_require__.c = installedModules; +/******/ +/******/ // define getter function for harmony exports +/******/ __webpack_require__.d = function(exports, name, getter) { +/******/ if(!__webpack_require__.o(exports, name)) { +/******/ Object.defineProperty(exports, name, { +/******/ configurable: false, +/******/ enumerable: true, +/******/ get: getter +/******/ }); +/******/ } +/******/ }; +/******/ +/******/ // getDefaultExport function for compatibility with non-harmony modules +/******/ __webpack_require__.n = function(module) { +/******/ var getter = module && module.__esModule ? +/******/ function getDefault() { return module['default']; } : +/******/ function getModuleExports() { return module; }; +/******/ __webpack_require__.d(getter, 'a', getter); +/******/ return getter; +/******/ }; +/******/ +/******/ // Object.prototype.hasOwnProperty.call +/******/ __webpack_require__.o = function(object, property) { return Object.prototype.hasOwnProperty.call(object, property); }; +/******/ +/******/ // __webpack_public_path__ +/******/ __webpack_require__.p = ""; +/******/ +/******/ // Load entry module and return exports +/******/ return __webpack_require__(__webpack_require__.s = 1); +/******/ }) +/************************************************************************/ +/******/ ([ +/* 0 */ +/***/ (function(module, exports, __webpack_require__) { + +"use strict"; + + +Object.defineProperty(exports, "__esModule", { + value: true +}); +exports.setMatrixArrayType = setMatrixArrayType; +exports.toRadian = toRadian; +exports.equals = equals; +/* 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. */ + +/** + * Common utilities + * @module glMatrix + */ + +// Configuration Constants +var EPSILON = exports.EPSILON = 0.000001; +var ARRAY_TYPE = exports.ARRAY_TYPE = typeof Float32Array !== 'undefined' ? Float32Array : Array; +var RANDOM = exports.RANDOM = Math.random; + +/** + * Sets the type of array used when creating new vectors and matrices + * + * @param {Type} type Array type, such as Float32Array or Array + */ +function setMatrixArrayType(type) { + exports.ARRAY_TYPE = ARRAY_TYPE = type; +} + +var degree = Math.PI / 180; + +/** + * Convert Degree To Radian + * + * @param {Number} a Angle in Degrees + */ +function toRadian(a) { + return a * degree; +} + +/** + * Tests whether or not the arguments have approximately the same value, within an absolute + * or relative tolerance of glMatrix.EPSILON (an absolute tolerance is used for values less + * than or equal to 1.0, and a relative tolerance is used for larger values) + * + * @param {Number} a The first number to test. + * @param {Number} b The second number to test. + * @returns {Boolean} True if the numbers are approximately equal, false otherwise. + */ +function equals(a, b) { + return Math.abs(a - b) <= EPSILON * Math.max(1.0, Math.abs(a), Math.abs(b)); +} + +/***/ }), +/* 1 */ +/***/ (function(module, exports, __webpack_require__) { + +"use strict"; + + +Object.defineProperty(exports, "__esModule", { + value: true +}); +exports.mat4 = exports.mat3 = undefined; + +var _mat = __webpack_require__(2); + +var mat3 = _interopRequireWildcard(_mat); + +var _mat2 = __webpack_require__(3); + +var mat4 = _interopRequireWildcard(_mat2); + +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; } } + +/** + * @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 + +exports.mat3 = mat3; +exports.mat4 = mat4; + +/***/ }), +/* 2 */ +/***/ (function(module, exports, __webpack_require__) { + +"use strict"; + + +Object.defineProperty(exports, "__esModule", { + value: true +}); +exports.create = create; +exports.fromMat4 = fromMat4; +exports.invert = invert; + +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; } } + +/** + * 3x3 Matrix + * @module mat3 + */ + +/** + * Creates a new identity mat3 + * + * @returns {mat3} a new 3x3 matrix + */ +function create() { + var out = new glMatrix.ARRAY_TYPE(9); + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; + out[4] = 1; + out[5] = 0; + out[6] = 0; + out[7] = 0; + out[8] = 1; + return out; +} + +/** + * Copies the upper-left 3x3 values into the given mat3. + * + * @param {mat3} out the receiving 3x3 matrix + * @param {mat4} a the source 4x4 matrix + * @returns {mat3} out + */ +/* 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 fromMat4(out, a) { + out[0] = a[0]; + out[1] = a[1]; + out[2] = a[2]; + out[3] = a[4]; + out[4] = a[5]; + out[5] = a[6]; + out[6] = a[8]; + out[7] = a[9]; + out[8] = a[10]; + return out; +} + +/** + * Creates a new mat3 initialized with values from an existing matrix + * + * @param {mat3} a matrix to clone + * @returns {mat3} a new 3x3 matrix + */ +function clone(a) { + var out = new glMatrix.ARRAY_TYPE(9); + 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]; + return out; +} + +/** + * Copy the values from one mat3 to another + * + * @param {mat3} out the receiving matrix + * @param {mat3} a the source matrix + * @returns {mat3} 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]; + return out; +} + +/** + * Create a new mat3 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} m10 Component in column 1, row 0 position (index 3) + * @param {Number} m11 Component in column 1, row 1 position (index 4) + * @param {Number} m12 Component in column 1, row 2 position (index 5) + * @param {Number} m20 Component in column 2, row 0 position (index 6) + * @param {Number} m21 Component in column 2, row 1 position (index 7) + * @param {Number} m22 Component in column 2, row 2 position (index 8) + * @returns {mat3} A new mat3 + */ +function fromValues(m00, m01, m02, m10, m11, m12, m20, m21, m22) { + var out = new glMatrix.ARRAY_TYPE(9); + out[0] = m00; + out[1] = m01; + out[2] = m02; + out[3] = m10; + out[4] = m11; + out[5] = m12; + out[6] = m20; + out[7] = m21; + out[8] = m22; + return out; +} + +/** + * Set the components of a mat3 to the given values + * + * @param {mat3} 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} m10 Component in column 1, row 0 position (index 3) + * @param {Number} m11 Component in column 1, row 1 position (index 4) + * @param {Number} m12 Component in column 1, row 2 position (index 5) + * @param {Number} m20 Component in column 2, row 0 position (index 6) + * @param {Number} m21 Component in column 2, row 1 position (index 7) + * @param {Number} m22 Component in column 2, row 2 position (index 8) + * @returns {mat3} out + */ +function set(out, m00, m01, m02, m10, m11, m12, m20, m21, m22) { + out[0] = m00; + out[1] = m01; + out[2] = m02; + out[3] = m10; + out[4] = m11; + out[5] = m12; + out[6] = m20; + out[7] = m21; + out[8] = m22; + return out; +} + +/** + * Set a mat3 to the identity matrix + * + * @param {mat3} out the receiving matrix + * @returns {mat3} out + */ +function identity(out) { + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; + out[4] = 1; + out[5] = 0; + out[6] = 0; + out[7] = 0; + out[8] = 1; + return out; +} + +/** + * Transpose the values of a mat3 + * + * @param {mat3} out the receiving matrix + * @param {mat3} a the source matrix + * @returns {mat3} 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], + a12 = a[5]; + out[1] = a[3]; + out[2] = a[6]; + out[3] = a01; + out[5] = a[7]; + out[6] = a02; + out[7] = a12; + } else { + out[0] = a[0]; + out[1] = a[3]; + out[2] = a[6]; + out[3] = a[1]; + out[4] = a[4]; + out[5] = a[7]; + out[6] = a[2]; + out[7] = a[5]; + out[8] = a[8]; + } + + return out; +} + +/** + * Inverts a mat3 + * + * @param {mat3} out the receiving matrix + * @param {mat3} a the source matrix + * @returns {mat3} out + */ +function invert(out, a) { + 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 b01 = a22 * a11 - a12 * a21; + var b11 = -a22 * a10 + a12 * a20; + var b21 = a21 * a10 - a11 * a20; + + // Calculate the determinant + var det = a00 * b01 + a01 * b11 + a02 * b21; + + if (!det) { + return null; + } + det = 1.0 / det; + + out[0] = b01 * det; + out[1] = (-a22 * a01 + a02 * a21) * det; + out[2] = (a12 * a01 - a02 * a11) * det; + out[3] = b11 * det; + out[4] = (a22 * a00 - a02 * a20) * det; + out[5] = (-a12 * a00 + a02 * a10) * det; + out[6] = b21 * det; + out[7] = (-a21 * a00 + a01 * a20) * det; + out[8] = (a11 * a00 - a01 * a10) * det; + return out; +} + +/** + * 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], + a02 = a[2]; + var a10 = a[3], + 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], + a12 = a[5]; + var a20 = a[6], + a21 = a[7], + a22 = a[8]; + + return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20); +} + +/** + * 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 = multiply; + +/** + * Alias for {@link mat3.subtract} + * @function + */ +var sub = subtract; + +/***/ }), +/* 3 */ +/***/ (function(module, exports, __webpack_require__) { + +"use strict"; + + +Object.defineProperty(exports, "__esModule", { + value: true +}); +exports.create = create; +exports.identity = identity; +exports.invert = invert; +exports.multiply = multiply; +exports.translate = translate; +exports.rotate = rotate; +exports.fromTranslation = fromTranslation; +exports.fromRotation = fromRotation; +exports.frustum = frustum; +exports.ortho = ortho; + +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 = multiply; + +/** + * Alias for {@link mat4.subtract} + * @function + */ +var sub = subtract; + +/***/ }) +/******/ ]); +});
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