From 3042ffc241420bf389ce255ddd04f27467bb4410 Mon Sep 17 00:00:00 2001 From: Brulijam Date: Thu, 30 Nov 2023 10:08:48 +0100 Subject: [PATCH] =?UTF-8?q?Prepared=20Abgabe=204=20and=20=C3=9Cbung?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Abgabe_4/lightTODOs/common/gl-matrix.js | 5555 ++++++++++++++ Abgabe_4/lightTODOs/common/initShaders.js | 46 + Abgabe_4/lightTODOs/common/objects3D.js | 1847 +++++ Abgabe_4/lightTODOs/index.html | 77 + Abgabe_4/lightTODOs/main.js | 205 + index.html | 2 + Übung_30112023/Insel/common/glMatrix.js | 7861 ++++++++++++++++++++ Übung_30112023/Insel/common/initShaders.js | 46 + Übung_30112023/Insel/common/objects3D.js | 437 ++ Übung_30112023/Insel/index.html | 69 + Übung_30112023/Insel/main.js | 534 ++ Übung_30112023/uebung-woche7.pdf | Bin 0 -> 561678 bytes 12 files changed, 16679 insertions(+) create mode 100644 Abgabe_4/lightTODOs/common/gl-matrix.js create mode 100644 Abgabe_4/lightTODOs/common/initShaders.js create mode 100644 Abgabe_4/lightTODOs/common/objects3D.js create mode 100644 Abgabe_4/lightTODOs/index.html create mode 100644 Abgabe_4/lightTODOs/main.js create mode 100644 Übung_30112023/Insel/common/glMatrix.js create mode 100644 Übung_30112023/Insel/common/initShaders.js create mode 100644 Übung_30112023/Insel/common/objects3D.js create mode 100644 Übung_30112023/Insel/index.html create mode 100644 Übung_30112023/Insel/main.js create mode 100644 Übung_30112023/uebung-woche7.pdf diff --git a/Abgabe_4/lightTODOs/common/gl-matrix.js b/Abgabe_4/lightTODOs/common/gl-matrix.js new file mode 100644 index 0000000..5e7dfaa --- /dev/null +++ b/Abgabe_4/lightTODOs/common/gl-matrix.js @@ -0,0 +1,5555 @@ +/** + * @fileoverview gl-matrix - High performance matrix and vector operations + * @author Brandon Jones + * @author Colin MacKenzie IV + * @version 2.3.2 + */ + +/* 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]; + } +})(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] = { +/******/ exports: {}, +/******/ id: moduleId, +/******/ loaded: false +/******/ }; + +/******/ // Execute the module function +/******/ modules[moduleId].call(module.exports, module, module.exports, __webpack_require__); + +/******/ // Flag the module as loaded +/******/ module.loaded = 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; + +/******/ // __webpack_public_path__ +/******/ __webpack_require__.p = ""; + +/******/ // Load entry module and return exports +/******/ return __webpack_require__(0); +/******/ }) +/************************************************************************/ +/******/ ([ +/* 0 */ +/***/ function(module, exports, __webpack_require__) { + + /** + * @fileoverview gl-matrix - High performance matrix and vector operations + * @author Brandon Jones + * @author Colin MacKenzie IV + * @version 2.3.2 + */ + + /* 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.glMatrix = __webpack_require__(1); + exports.mat2 = __webpack_require__(2); + exports.mat2d = __webpack_require__(3); + exports.mat3 = __webpack_require__(4); + exports.mat4 = __webpack_require__(5); + exports.quat = __webpack_require__(6); + exports.vec2 = __webpack_require__(9); + exports.vec3 = __webpack_require__(7); + exports.vec4 = __webpack_require__(8); + +/***/ }, +/* 1 */ +/***/ function(module, exports) { + + /* 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. */ + + /** + * @class Common utilities + * @name glMatrix + */ + var glMatrix = {}; + + // Configuration Constants + glMatrix.EPSILON = 0.000001; + glMatrix.ARRAY_TYPE = (typeof Float32Array !== 'undefined') ? Float32Array : Array; + glMatrix.RANDOM = Math.random; + glMatrix.ENABLE_SIMD = false; + + // Capability detection + glMatrix.SIMD_AVAILABLE = (glMatrix.ARRAY_TYPE === Float32Array) && ('SIMD' in this); + glMatrix.USE_SIMD = glMatrix.ENABLE_SIMD && glMatrix.SIMD_AVAILABLE; + + /** + * Sets the type of array used when creating new vectors and matrices + * + * @param {Type} type Array type, such as Float32Array or Array + */ + glMatrix.setMatrixArrayType = function(type) { + glMatrix.ARRAY_TYPE = type; + } + + var degree = Math.PI / 180; + + /** + * Convert Degree To Radian + * + * @param {Number} Angle in Degrees + */ + glMatrix.toRadian = function(a){ + return a * degree; + } + + module.exports = glMatrix; + + +/***/ }, +/* 2 */ +/***/ function(module, exports, __webpack_require__) { + + /* 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. */ + + var glMatrix = __webpack_require__(1); + + /** + * @class 2x2 Matrix + * @name mat2 + */ + var mat2 = {}; + + /** + * Creates a new identity mat2 + * + * @returns {mat2} a new 2x2 matrix + */ + mat2.create = function() { + 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 + */ + mat2.clone = function(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 + */ + mat2.copy = function(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 + */ + mat2.identity = function(out) { + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 1; + return out; + }; + + /** + * Transpose the values of a mat2 + * + * @param {mat2} out the receiving matrix + * @param {mat2} a the source matrix + * @returns {mat2} out + */ + mat2.transpose = function(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 + */ + mat2.invert = function(out, a) { + var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], + + // Calculate the determinant + 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 + */ + mat2.adjoint = function(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 + */ + mat2.determinant = function (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 + */ + mat2.multiply = function (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; + }; + + /** + * Alias for {@link mat2.multiply} + * @function + */ + mat2.mul = mat2.multiply; + + /** + * 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 + */ + mat2.rotate = function (out, a, rad) { + var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], + s = Math.sin(rad), + 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 + **/ + mat2.scale = function(out, a, v) { + var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], + 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 + */ + mat2.fromRotation = function(out, rad) { + var s = Math.sin(rad), + 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 + */ + mat2.fromScaling = function(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} mat matrix to represent as a string + * @returns {String} string representation of the matrix + */ + mat2.str = function (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 + */ + mat2.frob = function (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 + */ + + mat2.LDU = function (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]; + }; + + + module.exports = mat2; + + +/***/ }, +/* 3 */ +/***/ function(module, exports, __webpack_require__) { + + /* 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. */ + + var glMatrix = __webpack_require__(1); + + /** + * @class 2x3 Matrix + * @name mat2d + * + * @description + * A mat2d contains six elements defined as: + * 
+	 * [a, c, tx,
+	 *  b, d, ty]
+	 *
+ * This is a short form for the 3x3 matrix: + * 
+	 * [a, c, tx,
+	 *  b, d, ty,
+	 *  0, 0, 1]
+	 *
+ * The last row is ignored so the array is shorter and operations are faster. + */ + var mat2d = {}; + + /** + * Creates a new identity mat2d + * + * @returns {mat2d} a new 2x3 matrix + */ + mat2d.create = function() { + 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 + */ + mat2d.clone = function(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 + */ + mat2d.copy = function(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 + */ + mat2d.identity = function(out) { + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 1; + out[4] = 0; + out[5] = 0; + return out; + }; + + /** + * Inverts a mat2d + * + * @param {mat2d} out the receiving matrix + * @param {mat2d} a the source matrix + * @returns {mat2d} out + */ + mat2d.invert = function(out, a) { + var aa = a[0], ab = a[1], ac = a[2], ad = a[3], + 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 + */ + mat2d.determinant = function (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 + */ + mat2d.multiply = function (out, a, b) { + var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5], + 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; + }; + + /** + * Alias for {@link mat2d.multiply} + * @function + */ + mat2d.mul = mat2d.multiply; + + /** + * 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 + */ + mat2d.rotate = function (out, a, rad) { + var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5], + s = Math.sin(rad), + 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 + **/ + mat2d.scale = function(out, a, v) { + var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5], + 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 + **/ + mat2d.translate = function(out, a, v) { + var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5], + 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 + */ + mat2d.fromRotation = function(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 + */ + mat2d.fromScaling = function(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 + */ + mat2d.fromTranslation = function(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 + */ + mat2d.str = function (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 + */ + mat2d.frob = function (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)) + }; + + module.exports = mat2d; + + +/***/ }, +/* 4 */ +/***/ function(module, exports, __webpack_require__) { + + /* 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. */ + + var glMatrix = __webpack_require__(1); + + /** + * @class 3x3 Matrix + * @name mat3 + */ + var mat3 = {}; + + /** + * Creates a new identity mat3 + * + * @returns {mat3} a new 3x3 matrix + */ + mat3.create = function() { + 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 + */ + mat3.fromMat4 = function(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 + */ + mat3.clone = function(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 + */ + mat3.copy = function(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; + }; + + /** + * Set a mat3 to the identity matrix + * + * @param {mat3} out the receiving matrix + * @returns {mat3} out + */ + mat3.identity = function(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 + */ + mat3.transpose = function(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 + */ + mat3.invert = function(out, a) { + 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], + + b01 = a22 * a11 - a12 * a21, + b11 = -a22 * a10 + a12 * a20, + b21 = a21 * a10 - a11 * a20, + + // Calculate the determinant + 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 + */ + mat3.adjoint = function(out, a) { + 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]; + + 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 + */ + mat3.determinant = function (a) { + 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]; + + 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 + */ + mat3.multiply = function (out, a, b) { + 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], + + b00 = b[0], b01 = b[1], b02 = b[2], + b10 = b[3], b11 = b[4], b12 = b[5], + 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; + }; + + /** + * Alias for {@link mat3.multiply} + * @function + */ + mat3.mul = mat3.multiply; + + /** + * 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 + */ + mat3.translate = function(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 + */ + mat3.rotate = function (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 + **/ + mat3.scale = function(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 + */ + mat3.fromTranslation = function(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 + */ + mat3.fromRotation = function(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 + */ + mat3.fromScaling = function(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 + **/ + mat3.fromMat2d = function(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 + */ + mat3.fromQuat = function (out, q) { + var x = q[0], y = q[1], z = q[2], w = q[3], + x2 = x + x, + y2 = y + y, + z2 = z + z, + + xx = x * x2, + yx = y * x2, + yy = y * y2, + zx = z * x2, + zy = z * y2, + zz = z * z2, + wx = w * x2, + wy = w * y2, + 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 + */ + mat3.normalFromMat4 = function (out, a) { + var 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], + a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15], + + b00 = a00 * a11 - a01 * a10, + b01 = a00 * a12 - a02 * a10, + b02 = a00 * a13 - a03 * a10, + b03 = a01 * a12 - a02 * a11, + b04 = a01 * a13 - a03 * a11, + b05 = a02 * a13 - a03 * a12, + b06 = a20 * a31 - a21 * a30, + b07 = a20 * a32 - a22 * a30, + b08 = a20 * a33 - a23 * a30, + b09 = a21 * a32 - a22 * a31, + b10 = a21 * a33 - a23 * a31, + b11 = a22 * a33 - a23 * a32, + + // Calculate the determinant + 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; + }; + + /** + * Returns a string representation of a mat3 + * + * @param {mat3} mat matrix to represent as a string + * @returns {String} string representation of the matrix + */ + mat3.str = function (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 + */ + mat3.frob = function (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))) + }; + + + module.exports = mat3; + + +/***/ }, +/* 5 */ +/***/ function(module, exports, __webpack_require__) { + + /* 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. */ + + var glMatrix = __webpack_require__(1); + + /** + * @class 4x4 Matrix + * @name mat4 + */ + var mat4 = { + scalar: {}, + SIMD: {}, + }; + + /** + * Creates a new identity mat4 + * + * @returns {mat4} a new 4x4 matrix + */ + mat4.create = function() { + 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 + */ + mat4.clone = function(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 + */ + mat4.copy = function(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; + }; + + /** + * Set a mat4 to the identity matrix + * + * @param {mat4} out the receiving matrix + * @returns {mat4} out + */ + mat4.identity = function(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 not using SIMD + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the source matrix + * @returns {mat4} out + */ + mat4.scalar.transpose = function(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], + a12 = a[6], a13 = a[7], + 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; + }; + + /** + * Transpose the values of a mat4 using SIMD + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the source matrix + * @returns {mat4} out + */ + mat4.SIMD.transpose = function(out, a) { + var a0, a1, a2, a3, + tmp01, tmp23, + out0, out1, out2, out3; + + a0 = SIMD.Float32x4.load(a, 0); + a1 = SIMD.Float32x4.load(a, 4); + a2 = SIMD.Float32x4.load(a, 8); + a3 = SIMD.Float32x4.load(a, 12); + + tmp01 = SIMD.Float32x4.shuffle(a0, a1, 0, 1, 4, 5); + tmp23 = SIMD.Float32x4.shuffle(a2, a3, 0, 1, 4, 5); + out0 = SIMD.Float32x4.shuffle(tmp01, tmp23, 0, 2, 4, 6); + out1 = SIMD.Float32x4.shuffle(tmp01, tmp23, 1, 3, 5, 7); + SIMD.Float32x4.store(out, 0, out0); + SIMD.Float32x4.store(out, 4, out1); + + tmp01 = SIMD.Float32x4.shuffle(a0, a1, 2, 3, 6, 7); + tmp23 = SIMD.Float32x4.shuffle(a2, a3, 2, 3, 6, 7); + out2 = SIMD.Float32x4.shuffle(tmp01, tmp23, 0, 2, 4, 6); + out3 = SIMD.Float32x4.shuffle(tmp01, tmp23, 1, 3, 5, 7); + SIMD.Float32x4.store(out, 8, out2); + SIMD.Float32x4.store(out, 12, out3); + + return out; + }; + + /** + * Transpse a mat4 using SIMD if available and enabled + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the source matrix + * @returns {mat4} out + */ + mat4.transpose = glMatrix.USE_SIMD ? mat4.SIMD.transpose : mat4.scalar.transpose; + + /** + * Inverts a mat4 not using SIMD + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the source matrix + * @returns {mat4} out + */ + mat4.scalar.invert = function(out, a) { + var 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], + a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15], + + b00 = a00 * a11 - a01 * a10, + b01 = a00 * a12 - a02 * a10, + b02 = a00 * a13 - a03 * a10, + b03 = a01 * a12 - a02 * a11, + b04 = a01 * a13 - a03 * a11, + b05 = a02 * a13 - a03 * a12, + b06 = a20 * a31 - a21 * a30, + b07 = a20 * a32 - a22 * a30, + b08 = a20 * a33 - a23 * a30, + b09 = a21 * a32 - a22 * a31, + b10 = a21 * a33 - a23 * a31, + b11 = a22 * a33 - a23 * a32, + + // Calculate the determinant + 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; + }; + + /** + * Inverts a mat4 using SIMD + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the source matrix + * @returns {mat4} out + */ + mat4.SIMD.invert = function(out, a) { + var row0, row1, row2, row3, + tmp1, + minor0, minor1, minor2, minor3, + det, + a0 = SIMD.Float32x4.load(a, 0), + a1 = SIMD.Float32x4.load(a, 4), + a2 = SIMD.Float32x4.load(a, 8), + a3 = SIMD.Float32x4.load(a, 12); + + // Compute matrix adjugate + tmp1 = SIMD.Float32x4.shuffle(a0, a1, 0, 1, 4, 5); + row1 = SIMD.Float32x4.shuffle(a2, a3, 0, 1, 4, 5); + row0 = SIMD.Float32x4.shuffle(tmp1, row1, 0, 2, 4, 6); + row1 = SIMD.Float32x4.shuffle(row1, tmp1, 1, 3, 5, 7); + tmp1 = SIMD.Float32x4.shuffle(a0, a1, 2, 3, 6, 7); + row3 = SIMD.Float32x4.shuffle(a2, a3, 2, 3, 6, 7); + row2 = SIMD.Float32x4.shuffle(tmp1, row3, 0, 2, 4, 6); + row3 = SIMD.Float32x4.shuffle(row3, tmp1, 1, 3, 5, 7); + + tmp1 = SIMD.Float32x4.mul(row2, row3); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + minor0 = SIMD.Float32x4.mul(row1, tmp1); + minor1 = SIMD.Float32x4.mul(row0, tmp1); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor0 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row1, tmp1), minor0); + minor1 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor1); + minor1 = SIMD.Float32x4.swizzle(minor1, 2, 3, 0, 1); + + tmp1 = SIMD.Float32x4.mul(row1, row2); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + minor0 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor0); + minor3 = SIMD.Float32x4.mul(row0, tmp1); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor0 = SIMD.Float32x4.sub(minor0, SIMD.Float32x4.mul(row3, tmp1)); + minor3 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor3); + minor3 = SIMD.Float32x4.swizzle(minor3, 2, 3, 0, 1); + + tmp1 = SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(row1, 2, 3, 0, 1), row3); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + row2 = SIMD.Float32x4.swizzle(row2, 2, 3, 0, 1); + minor0 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row2, tmp1), minor0); + minor2 = SIMD.Float32x4.mul(row0, tmp1); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor0 = SIMD.Float32x4.sub(minor0, SIMD.Float32x4.mul(row2, tmp1)); + minor2 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor2); + minor2 = SIMD.Float32x4.swizzle(minor2, 2, 3, 0, 1); + + tmp1 = SIMD.Float32x4.mul(row0, row1); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + minor2 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor2); + minor3 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row2, tmp1), minor3); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor2 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row3, tmp1), minor2); + minor3 = SIMD.Float32x4.sub(minor3, SIMD.Float32x4.mul(row2, tmp1)); + + tmp1 = SIMD.Float32x4.mul(row0, row3); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + minor1 = SIMD.Float32x4.sub(minor1, SIMD.Float32x4.mul(row2, tmp1)); + minor2 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row1, tmp1), minor2); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor1 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row2, tmp1), minor1); + minor2 = SIMD.Float32x4.sub(minor2, SIMD.Float32x4.mul(row1, tmp1)); + + tmp1 = SIMD.Float32x4.mul(row0, row2); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + minor1 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor1); + minor3 = SIMD.Float32x4.sub(minor3, SIMD.Float32x4.mul(row1, tmp1)); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor1 = SIMD.Float32x4.sub(minor1, SIMD.Float32x4.mul(row3, tmp1)); + minor3 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row1, tmp1), minor3); + + // Compute matrix determinant + det = SIMD.Float32x4.mul(row0, minor0); + det = SIMD.Float32x4.add(SIMD.Float32x4.swizzle(det, 2, 3, 0, 1), det); + det = SIMD.Float32x4.add(SIMD.Float32x4.swizzle(det, 1, 0, 3, 2), det); + tmp1 = SIMD.Float32x4.reciprocalApproximation(det); + det = SIMD.Float32x4.sub( + SIMD.Float32x4.add(tmp1, tmp1), + SIMD.Float32x4.mul(det, SIMD.Float32x4.mul(tmp1, tmp1))); + det = SIMD.Float32x4.swizzle(det, 0, 0, 0, 0); + if (!det) { + return null; + } + + // Compute matrix inverse + SIMD.Float32x4.store(out, 0, SIMD.Float32x4.mul(det, minor0)); + SIMD.Float32x4.store(out, 4, SIMD.Float32x4.mul(det, minor1)); + SIMD.Float32x4.store(out, 8, SIMD.Float32x4.mul(det, minor2)); + SIMD.Float32x4.store(out, 12, SIMD.Float32x4.mul(det, minor3)); + return out; + } + + /** + * Inverts a mat4 using SIMD if available and enabled + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the source matrix + * @returns {mat4} out + */ + mat4.invert = glMatrix.USE_SIMD ? mat4.SIMD.invert : mat4.scalar.invert; + + /** + * Calculates the adjugate of a mat4 not using SIMD + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the source matrix + * @returns {mat4} out + */ + mat4.scalar.adjoint = function(out, a) { + var 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], + 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 adjugate of a mat4 using SIMD + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the source matrix + * @returns {mat4} out + */ + mat4.SIMD.adjoint = function(out, a) { + var a0, a1, a2, a3; + var row0, row1, row2, row3; + var tmp1; + var minor0, minor1, minor2, minor3; + + var a0 = SIMD.Float32x4.load(a, 0); + var a1 = SIMD.Float32x4.load(a, 4); + var a2 = SIMD.Float32x4.load(a, 8); + var a3 = SIMD.Float32x4.load(a, 12); + + // Transpose the source matrix. Sort of. Not a true transpose operation + tmp1 = SIMD.Float32x4.shuffle(a0, a1, 0, 1, 4, 5); + row1 = SIMD.Float32x4.shuffle(a2, a3, 0, 1, 4, 5); + row0 = SIMD.Float32x4.shuffle(tmp1, row1, 0, 2, 4, 6); + row1 = SIMD.Float32x4.shuffle(row1, tmp1, 1, 3, 5, 7); + + tmp1 = SIMD.Float32x4.shuffle(a0, a1, 2, 3, 6, 7); + row3 = SIMD.Float32x4.shuffle(a2, a3, 2, 3, 6, 7); + row2 = SIMD.Float32x4.shuffle(tmp1, row3, 0, 2, 4, 6); + row3 = SIMD.Float32x4.shuffle(row3, tmp1, 1, 3, 5, 7); + + tmp1 = SIMD.Float32x4.mul(row2, row3); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + minor0 = SIMD.Float32x4.mul(row1, tmp1); + minor1 = SIMD.Float32x4.mul(row0, tmp1); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor0 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row1, tmp1), minor0); + minor1 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor1); + minor1 = SIMD.Float32x4.swizzle(minor1, 2, 3, 0, 1); + + tmp1 = SIMD.Float32x4.mul(row1, row2); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + minor0 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor0); + minor3 = SIMD.Float32x4.mul(row0, tmp1); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor0 = SIMD.Float32x4.sub(minor0, SIMD.Float32x4.mul(row3, tmp1)); + minor3 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor3); + minor3 = SIMD.Float32x4.swizzle(minor3, 2, 3, 0, 1); + + tmp1 = SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(row1, 2, 3, 0, 1), row3); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + row2 = SIMD.Float32x4.swizzle(row2, 2, 3, 0, 1); + minor0 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row2, tmp1), minor0); + minor2 = SIMD.Float32x4.mul(row0, tmp1); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor0 = SIMD.Float32x4.sub(minor0, SIMD.Float32x4.mul(row2, tmp1)); + minor2 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor2); + minor2 = SIMD.Float32x4.swizzle(minor2, 2, 3, 0, 1); + + tmp1 = SIMD.Float32x4.mul(row0, row1); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + minor2 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor2); + minor3 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row2, tmp1), minor3); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor2 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row3, tmp1), minor2); + minor3 = SIMD.Float32x4.sub(minor3, SIMD.Float32x4.mul(row2, tmp1)); + + tmp1 = SIMD.Float32x4.mul(row0, row3); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + minor1 = SIMD.Float32x4.sub(minor1, SIMD.Float32x4.mul(row2, tmp1)); + minor2 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row1, tmp1), minor2); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor1 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row2, tmp1), minor1); + minor2 = SIMD.Float32x4.sub(minor2, SIMD.Float32x4.mul(row1, tmp1)); + + tmp1 = SIMD.Float32x4.mul(row0, row2); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2); + minor1 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor1); + minor3 = SIMD.Float32x4.sub(minor3, SIMD.Float32x4.mul(row1, tmp1)); + tmp1 = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1); + minor1 = SIMD.Float32x4.sub(minor1, SIMD.Float32x4.mul(row3, tmp1)); + minor3 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row1, tmp1), minor3); + + SIMD.Float32x4.store(out, 0, minor0); + SIMD.Float32x4.store(out, 4, minor1); + SIMD.Float32x4.store(out, 8, minor2); + SIMD.Float32x4.store(out, 12, minor3); + return out; + }; + + /** + * Calculates the adjugate of a mat4 using SIMD if available and enabled + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the source matrix + * @returns {mat4} out + */ + mat4.adjoint = glMatrix.USE_SIMD ? mat4.SIMD.adjoint : mat4.scalar.adjoint; + + /** + * Calculates the determinant of a mat4 + * + * @param {mat4} a the source matrix + * @returns {Number} determinant of a + */ + mat4.determinant = function (a) { + var 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], + a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15], + + b00 = a00 * a11 - a01 * a10, + b01 = a00 * a12 - a02 * a10, + b02 = a00 * a13 - a03 * a10, + b03 = a01 * a12 - a02 * a11, + b04 = a01 * a13 - a03 * a11, + b05 = a02 * a13 - a03 * a12, + b06 = a20 * a31 - a21 * a30, + b07 = a20 * a32 - a22 * a30, + b08 = a20 * a33 - a23 * a30, + b09 = a21 * a32 - a22 * a31, + b10 = a21 * a33 - a23 * a31, + b11 = a22 * a33 - a23 * a32; + + // Calculate the determinant + return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06; + }; + + /** + * Multiplies two mat4's explicitly using SIMD + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the first operand, must be a Float32Array + * @param {mat4} b the second operand, must be a Float32Array + * @returns {mat4} out + */ + mat4.SIMD.multiply = function (out, a, b) { + var a0 = SIMD.Float32x4.load(a, 0); + var a1 = SIMD.Float32x4.load(a, 4); + var a2 = SIMD.Float32x4.load(a, 8); + var a3 = SIMD.Float32x4.load(a, 12); + + var b0 = SIMD.Float32x4.load(b, 0); + var out0 = SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b0, 0, 0, 0, 0), a0), + SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b0, 1, 1, 1, 1), a1), + SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b0, 2, 2, 2, 2), a2), + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b0, 3, 3, 3, 3), a3)))); + SIMD.Float32x4.store(out, 0, out0); + + var b1 = SIMD.Float32x4.load(b, 4); + var out1 = SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b1, 0, 0, 0, 0), a0), + SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b1, 1, 1, 1, 1), a1), + SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b1, 2, 2, 2, 2), a2), + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b1, 3, 3, 3, 3), a3)))); + SIMD.Float32x4.store(out, 4, out1); + + var b2 = SIMD.Float32x4.load(b, 8); + var out2 = SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b2, 0, 0, 0, 0), a0), + SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b2, 1, 1, 1, 1), a1), + SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b2, 2, 2, 2, 2), a2), + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b2, 3, 3, 3, 3), a3)))); + SIMD.Float32x4.store(out, 8, out2); + + var b3 = SIMD.Float32x4.load(b, 12); + var out3 = SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b3, 0, 0, 0, 0), a0), + SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b3, 1, 1, 1, 1), a1), + SIMD.Float32x4.add( + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b3, 2, 2, 2, 2), a2), + SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b3, 3, 3, 3, 3), a3)))); + SIMD.Float32x4.store(out, 12, out3); + + return out; + }; + + /** + * Multiplies two mat4's explicitly not using SIMD + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the first operand + * @param {mat4} b the second operand + * @returns {mat4} out + */ + mat4.scalar.multiply = function (out, a, b) { + var 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], + 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; + }; + + /** + * Multiplies two mat4's using SIMD if available and enabled + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the first operand + * @param {mat4} b the second operand + * @returns {mat4} out + */ + mat4.multiply = glMatrix.USE_SIMD ? mat4.SIMD.multiply : mat4.scalar.multiply; + + /** + * Alias for {@link mat4.multiply} + * @function + */ + mat4.mul = mat4.multiply; + + /** + * Translate a mat4 by the given vector not using SIMD + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the matrix to translate + * @param {vec3} v vector to translate by + * @returns {mat4} out + */ + mat4.scalar.translate = function (out, a, v) { + var x = v[0], y = v[1], z = v[2], + a00, a01, a02, a03, + a10, a11, a12, a13, + a20, a21, a22, a23; + + 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; + }; + + /** + * Translates a mat4 by the given vector using SIMD + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the matrix to translate + * @param {vec3} v vector to translate by + * @returns {mat4} out + */ + mat4.SIMD.translate = function (out, a, v) { + var a0 = SIMD.Float32x4.load(a, 0), + a1 = SIMD.Float32x4.load(a, 4), + a2 = SIMD.Float32x4.load(a, 8), + a3 = SIMD.Float32x4.load(a, 12), + vec = SIMD.Float32x4(v[0], v[1], v[2] , 0); + + if (a !== out) { + 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]; + } + + a0 = SIMD.Float32x4.mul(a0, SIMD.Float32x4.swizzle(vec, 0, 0, 0, 0)); + a1 = SIMD.Float32x4.mul(a1, SIMD.Float32x4.swizzle(vec, 1, 1, 1, 1)); + a2 = SIMD.Float32x4.mul(a2, SIMD.Float32x4.swizzle(vec, 2, 2, 2, 2)); + + var t0 = SIMD.Float32x4.add(a0, SIMD.Float32x4.add(a1, SIMD.Float32x4.add(a2, a3))); + SIMD.Float32x4.store(out, 12, t0); + + return out; + }; + + /** + * Translates a mat4 by the given vector using SIMD if available and enabled + * + * @param {mat4} out the receiving matrix + * @param {mat4} a the matrix to translate + * @param {vec3} v vector to translate by + * @returns {mat4} out + */ + mat4.translate = glMatrix.USE_SIMD ? mat4.SIMD.translate : mat4.scalar.translate; + + /** + * 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 + **/ + mat4.scalar.scale = function(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; + }; + + /** + * Scales the mat4 by the dimensions in the given vec3 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 + **/ + mat4.SIMD.scale = function(out, a, v) { + var a0, a1, a2; + var vec = SIMD.Float32x4(v[0], v[1], v[2], 0); + + a0 = SIMD.Float32x4.load(a, 0); + SIMD.Float32x4.store( + out, 0, SIMD.Float32x4.mul(a0, SIMD.Float32x4.swizzle(vec, 0, 0, 0, 0))); + + a1 = SIMD.Float32x4.load(a, 4); + SIMD.Float32x4.store( + out, 4, SIMD.Float32x4.mul(a1, SIMD.Float32x4.swizzle(vec, 1, 1, 1, 1))); + + a2 = SIMD.Float32x4.load(a, 8); + SIMD.Float32x4.store( + out, 8, SIMD.Float32x4.mul(a2, SIMD.Float32x4.swizzle(vec, 2, 2, 2, 2))); + + out[12] = a[12]; + out[13] = a[13]; + out[14] = a[14]; + out[15] = a[15]; + return out; + }; + + /** + * Scales the mat4 by the dimensions in the given vec3 using SIMD if available and enabled + * + * @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 + */ + mat4.scale = glMatrix.USE_SIMD ? mat4.SIMD.scale : mat4.scalar.scale; + + /** + * 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 + */ + mat4.rotate = function (out, a, rad, axis) { + var x = axis[0], y = axis[1], z = axis[2], + len = Math.sqrt(x * x + y * y + z * z), + s, c, t, + a00, a01, a02, a03, + a10, a11, a12, a13, + a20, a21, a22, a23, + b00, b01, b02, + b10, b11, b12, + b20, b21, b22; + + 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 not using SIMD + * + * @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 + */ + mat4.scalar.rotateX = function (out, a, rad) { + var s = Math.sin(rad), + c = Math.cos(rad), + a10 = a[4], + a11 = a[5], + a12 = a[6], + a13 = a[7], + a20 = a[8], + a21 = a[9], + a22 = a[10], + 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 X axis using SIMD + * + * @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 + */ + mat4.SIMD.rotateX = function (out, a, rad) { + var s = SIMD.Float32x4.splat(Math.sin(rad)), + c = SIMD.Float32x4.splat(Math.cos(rad)); + + 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 + var a_1 = SIMD.Float32x4.load(a, 4); + var a_2 = SIMD.Float32x4.load(a, 8); + SIMD.Float32x4.store(out, 4, + SIMD.Float32x4.add(SIMD.Float32x4.mul(a_1, c), SIMD.Float32x4.mul(a_2, s))); + SIMD.Float32x4.store(out, 8, + SIMD.Float32x4.sub(SIMD.Float32x4.mul(a_2, c), SIMD.Float32x4.mul(a_1, s))); + return out; + }; + + /** + * Rotates a matrix by the given angle around the X axis using SIMD if availabe and enabled + * + * @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 + */ + mat4.rotateX = glMatrix.USE_SIMD ? mat4.SIMD.rotateX : mat4.scalar.rotateX; + + /** + * Rotates a matrix by the given angle around the Y axis not using SIMD + * + * @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 + */ + mat4.scalar.rotateY = function (out, a, rad) { + var s = Math.sin(rad), + c = Math.cos(rad), + a00 = a[0], + a01 = a[1], + a02 = a[2], + a03 = a[3], + a20 = a[8], + a21 = a[9], + a22 = a[10], + 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 Y axis using SIMD + * + * @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 + */ + mat4.SIMD.rotateY = function (out, a, rad) { + var s = SIMD.Float32x4.splat(Math.sin(rad)), + c = SIMD.Float32x4.splat(Math.cos(rad)); + + 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 + var a_0 = SIMD.Float32x4.load(a, 0); + var a_2 = SIMD.Float32x4.load(a, 8); + SIMD.Float32x4.store(out, 0, + SIMD.Float32x4.sub(SIMD.Float32x4.mul(a_0, c), SIMD.Float32x4.mul(a_2, s))); + SIMD.Float32x4.store(out, 8, + SIMD.Float32x4.add(SIMD.Float32x4.mul(a_0, s), SIMD.Float32x4.mul(a_2, c))); + return out; + }; + + /** + * Rotates a matrix by the given angle around the Y axis if SIMD available and enabled + * + * @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 + */ + mat4.rotateY = glMatrix.USE_SIMD ? mat4.SIMD.rotateY : mat4.scalar.rotateY; + + /** + * Rotates a matrix by the given angle around the Z axis not using SIMD + * + * @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 + */ + mat4.scalar.rotateZ = function (out, a, rad) { + var s = Math.sin(rad), + c = Math.cos(rad), + a00 = a[0], + a01 = a[1], + a02 = a[2], + a03 = a[3], + a10 = a[4], + a11 = a[5], + a12 = a[6], + 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; + }; + + /** + * Rotates a matrix by the given angle around the Z axis using SIMD + * + * @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 + */ + mat4.SIMD.rotateZ = function (out, a, rad) { + var s = SIMD.Float32x4.splat(Math.sin(rad)), + c = SIMD.Float32x4.splat(Math.cos(rad)); + + 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 + var a_0 = SIMD.Float32x4.load(a, 0); + var a_1 = SIMD.Float32x4.load(a, 4); + SIMD.Float32x4.store(out, 0, + SIMD.Float32x4.add(SIMD.Float32x4.mul(a_0, c), SIMD.Float32x4.mul(a_1, s))); + SIMD.Float32x4.store(out, 4, + SIMD.Float32x4.sub(SIMD.Float32x4.mul(a_1, c), SIMD.Float32x4.mul(a_0, s))); + return out; + }; + + /** + * Rotates a matrix by the given angle around the Z axis if SIMD available and enabled + * + * @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 + */ + mat4.rotateZ = glMatrix.USE_SIMD ? mat4.SIMD.rotateZ : mat4.scalar.rotateZ; + + /** + * 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 + */ + mat4.fromTranslation = function(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 + */ + mat4.fromScaling = function(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 + */ + mat4.fromRotation = function(out, rad, axis) { + var x = axis[0], y = axis[1], z = axis[2], + len = Math.sqrt(x * x + y * y + z * z), + s, c, t; + + 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 + */ + mat4.fromXRotation = function(out, rad) { + var s = Math.sin(rad), + 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 + */ + mat4.fromYRotation = function(out, rad) { + var s = Math.sin(rad), + 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 + */ + mat4.fromZRotation = function(out, rad) { + var s = Math.sin(rad), + 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); + * var 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 + */ + mat4.fromRotationTranslation = function (out, q, v) { + // Quaternion math + var x = q[0], y = q[1], z = q[2], w = q[3], + x2 = x + x, + y2 = y + y, + z2 = z + z, + + xx = x * x2, + xy = x * y2, + xz = x * z2, + yy = y * y2, + yz = y * z2, + zz = z * z2, + wx = w * x2, + wy = w * y2, + 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; + }; + + /** + * 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); + * var 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 + */ + mat4.fromRotationTranslationScale = function (out, q, v, s) { + // Quaternion math + var x = q[0], y = q[1], z = q[2], w = q[3], + x2 = x + x, + y2 = y + y, + z2 = z + z, + + xx = x * x2, + xy = x * y2, + xz = x * z2, + yy = y * y2, + yz = y * z2, + zz = z * z2, + wx = w * x2, + wy = w * y2, + wz = w * z2, + sx = s[0], + sy = s[1], + 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); + * var 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 + */ + mat4.fromRotationTranslationScaleOrigin = function (out, q, v, s, o) { + // Quaternion math + var x = q[0], y = q[1], z = q[2], w = q[3], + x2 = x + x, + y2 = y + y, + z2 = z + z, + + xx = x * x2, + xy = x * y2, + xz = x * z2, + yy = y * y2, + yz = y * z2, + zz = z * z2, + wx = w * x2, + wy = w * y2, + wz = w * z2, + + sx = s[0], + sy = s[1], + sz = s[2], + + ox = o[0], + oy = o[1], + 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; + }; + + mat4.fromQuat = function (out, q) { + var x = q[0], y = q[1], z = q[2], w = q[3], + x2 = x + x, + y2 = y + y, + z2 = z + z, + + xx = x * x2, + yx = y * x2, + yy = y * y2, + zx = z * x2, + zy = z * y2, + zz = z * z2, + wx = w * x2, + wy = w * y2, + 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 + */ + mat4.frustum = function (out, left, right, bottom, top, near, far) { + var rl = 1 / (right - left), + tb = 1 / (top - bottom), + 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 + */ + mat4.perspective = function (out, fovy, aspect, near, far) { + var f = 1.0 / Math.tan(fovy / 2), + 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 {number} 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 + */ + mat4.perspectiveFromFieldOfView = function (out, fov, near, far) { + var upTan = Math.tan(fov.upDegrees * Math.PI/180.0), + downTan = Math.tan(fov.downDegrees * Math.PI/180.0), + leftTan = Math.tan(fov.leftDegrees * Math.PI/180.0), + rightTan = Math.tan(fov.rightDegrees * Math.PI/180.0), + xScale = 2.0 / (leftTan + rightTan), + 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 + */ + mat4.ortho = function (out, left, right, bottom, top, near, far) { + var lr = 1 / (left - right), + bt = 1 / (bottom - top), + 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 + */ + mat4.lookAt = function (out, eye, center, up) { + var x0, x1, x2, y0, y1, y2, z0, z1, z2, len, + eyex = eye[0], + eyey = eye[1], + eyez = eye[2], + upx = up[0], + upy = up[1], + upz = up[2], + centerx = center[0], + centery = center[1], + 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; + }; + + /** + * Returns a string representation of a mat4 + * + * @param {mat4} mat matrix to represent as a string + * @returns {String} string representation of the matrix + */ + mat4.str = function (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 + */ + mat4.frob = function (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) )) + }; + + + module.exports = mat4; + + +/***/ }, +/* 6 */ +/***/ function(module, exports, __webpack_require__) { + + /* 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. */ + + var glMatrix = __webpack_require__(1); + var mat3 = __webpack_require__(4); + var vec3 = __webpack_require__(7); + var vec4 = __webpack_require__(8); + + /** + * @class Quaternion + * @name quat + */ + var quat = {}; + + /** + * Creates a new identity quat + * + * @returns {quat} a new quaternion + */ + quat.create = function() { + var out = new glMatrix.ARRAY_TYPE(4); + out[0] = 0; + out[1] = 0; + out[2] = 0; + out[3] = 1; + return out; + }; + + /** + * 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 + */ + quat.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.length(tmpvec3) < 0.000001) + vec3.cross(tmpvec3, yUnitVec3, a); + vec3.normalize(tmpvec3, tmpvec3); + quat.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 quat.normalize(out, 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 + */ + quat.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 quat.normalize(out, quat.fromMat3(out, matr)); + }; + })(); + + /** + * Creates a new quat initialized with values from an existing quaternion + * + * @param {quat} a quaternion to clone + * @returns {quat} a new quaternion + * @function + */ + quat.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 + */ + quat.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 + */ + quat.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 + */ + quat.set = vec4.set; + + /** + * Set a quat to the identity quaternion + * + * @param {quat} out the receiving quaternion + * @returns {quat} out + */ + quat.identity = function(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 + **/ + quat.setAxisAngle = function(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; + }; + + /** + * 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 + */ + quat.add = vec4.add; + + /** + * 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 + */ + quat.multiply = function(out, a, b) { + var ax = a[0], ay = a[1], az = a[2], aw = a[3], + 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; + }; + + /** + * Alias for {@link quat.multiply} + * @function + */ + quat.mul = quat.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 + */ + quat.scale = vec4.scale; + + /** + * 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 + */ + quat.rotateX = function (out, a, rad) { + rad *= 0.5; + + var ax = a[0], ay = a[1], az = a[2], aw = a[3], + 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 + */ + quat.rotateY = function (out, a, rad) { + rad *= 0.5; + + var ax = a[0], ay = a[1], az = a[2], aw = a[3], + 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 + */ + quat.rotateZ = function (out, a, rad) { + rad *= 0.5; + + var ax = a[0], ay = a[1], az = a[2], aw = a[3], + 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 + */ + quat.calculateW = function (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; + }; + + /** + * 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 + */ + quat.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 + */ + quat.lerp = vec4.lerp; + + /** + * 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 + */ + quat.slerp = function (out, a, b, t) { + // benchmarks: + // http://jsperf.com/quaternion-slerp-implementations + + var ax = a[0], ay = a[1], az = a[2], aw = a[3], + bx = b[0], by = b[1], bz = b[2], bw = b[3]; + + var omega, cosom, sinom, scale0, scale1; + + // 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; + }; + + /** + * 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 + */ + quat.sqlerp = (function () { + var temp1 = quat.create(); + var temp2 = quat.create(); + + return function (out, a, b, c, d, t) { + quat.slerp(temp1, a, d, t); + quat.slerp(temp2, b, c, t); + quat.slerp(out, temp1, temp2, 2 * t * (1 - t)); + + 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 + */ + quat.invert = function(out, a) { + var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], + dot = a0*a0 + a1*a1 + a2*a2 + a3*a3, + 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 + */ + quat.conjugate = function (out, a) { + out[0] = -a[0]; + out[1] = -a[1]; + out[2] = -a[2]; + out[3] = a[3]; + return out; + }; + + /** + * Calculates the length of a quat + * + * @param {quat} a vector to calculate length of + * @returns {Number} length of a + * @function + */ + quat.length = vec4.length; + + /** + * Alias for {@link quat.length} + * @function + */ + quat.len = quat.length; + + /** + * Calculates the squared length of a quat + * + * @param {quat} a vector to calculate squared length of + * @returns {Number} squared length of a + * @function + */ + quat.squaredLength = vec4.squaredLength; + + /** + * Alias for {@link quat.squaredLength} + * @function + */ + quat.sqrLen = quat.squaredLength; + + /** + * Normalize a quat + * + * @param {quat} out the receiving quaternion + * @param {quat} a quaternion to normalize + * @returns {quat} out + * @function + */ + quat.normalize = vec4.normalize; + + /** + * 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 + */ + quat.fromMat3 = function(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; + + 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; + }; + + /** + * Returns a string representation of a quatenion + * + * @param {quat} vec vector to represent as a string + * @returns {String} string representation of the vector + */ + quat.str = function (a) { + return 'quat(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')'; + }; + + module.exports = quat; + + +/***/ }, +/* 7 */ +/***/ function(module, exports, __webpack_require__) { + + /* 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. */ + + var glMatrix = __webpack_require__(1); + + /** + * @class 3 Dimensional Vector + * @name vec3 + */ + var vec3 = {}; + + /** + * Creates a new, empty vec3 + * + * @returns {vec3} a new 3D vector + */ + vec3.create = function() { + var out = new glMatrix.ARRAY_TYPE(3); + out[0] = 0; + out[1] = 0; + out[2] = 0; + return out; + }; + + /** + * Creates a new vec3 initialized with values from an existing vector + * + * @param {vec3} a vector to clone + * @returns {vec3} a new 3D vector + */ + vec3.clone = function(a) { + var out = new glMatrix.ARRAY_TYPE(3); + out[0] = a[0]; + out[1] = a[1]; + out[2] = a[2]; + return out; + }; + + /** + * Creates a new vec3 initialized with the given values + * + * @param {Number} x X component + * @param {Number} y Y component + * @param {Number} z Z component + * @returns {vec3} a new 3D vector + */ + vec3.fromValues = function(x, y, z) { + var out = new glMatrix.ARRAY_TYPE(3); + out[0] = x; + out[1] = y; + out[2] = z; + return out; + }; + + /** + * Copy the values from one vec3 to another + * + * @param {vec3} out the receiving vector + * @param {vec3} a the source vector + * @returns {vec3} out + */ + vec3.copy = function(out, a) { + out[0] = a[0]; + out[1] = a[1]; + out[2] = a[2]; + return out; + }; + + /** + * Set the components of a vec3 to the given values + * + * @param {vec3} out the receiving vector + * @param {Number} x X component + * @param {Number} y Y component + * @param {Number} z Z component + * @returns {vec3} out + */ + vec3.set = function(out, x, y, z) { + out[0] = x; + out[1] = y; + out[2] = z; + return out; + }; + + /** + * Adds two vec3's + * + * @param {vec3} out the receiving vector + * @param {vec3} a the first operand + * @param {vec3} b the second operand + * @returns {vec3} out + */ + vec3.add = function(out, a, b) { + out[0] = a[0] + b[0]; + out[1] = a[1] + b[1]; + out[2] = a[2] + b[2]; + return out; + }; + + /** + * Subtracts vector b from vector a + * + * @param {vec3} out the receiving vector + * @param {vec3} a the first operand + * @param {vec3} b the second operand + * @returns {vec3} out + */ + vec3.subtract = function(out, a, b) { + out[0] = a[0] - b[0]; + out[1] = a[1] - b[1]; + out[2] = a[2] - b[2]; + return out; + }; + + /** + * Alias for {@link vec3.subtract} + * @function + */ + vec3.sub = vec3.subtract; + + /** + * Multiplies two vec3's + * + * @param {vec3} out the receiving vector + * @param {vec3} a the first operand + * @param {vec3} b the second operand + * @returns {vec3} out + */ + vec3.multiply = function(out, a, b) { + out[0] = a[0] * b[0]; + out[1] = a[1] * b[1]; + out[2] = a[2] * b[2]; + return out; + }; + + /** + * Alias for {@link vec3.multiply} + * @function + */ + vec3.mul = vec3.multiply; + + /** + * Divides two vec3's + * + * @param {vec3} out the receiving vector + * @param {vec3} a the first operand + * @param {vec3} b the second operand + * @returns {vec3} out + */ + vec3.divide = function(out, a, b) { + out[0] = a[0] / b[0]; + out[1] = a[1] / b[1]; + out[2] = a[2] / b[2]; + return out; + }; + + /** + * Alias for {@link vec3.divide} + * @function + */ + vec3.div = vec3.divide; + + /** + * Returns the minimum 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 + */ + vec3.min = function(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]); + return out; + }; + + /** + * Returns the maximum 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 + */ + vec3.max = function(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]); + return out; + }; + + /** + * Scales a vec3 by a scalar number + * + * @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 + */ + vec3.scale = function(out, a, b) { + out[0] = a[0] * b; + out[1] = a[1] * b; + out[2] = a[2] * b; + return out; + }; + + /** + * 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 + * @param {Number} scale the amount to scale b by before adding + * @returns {vec3} out + */ + vec3.scaleAndAdd = function(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); + return out; + }; + + /** + * Calculates the euclidian distance between two vec3's + * + * @param {vec3} a the first operand + * @param {vec3} b the second operand + * @returns {Number} distance between a and b + */ + vec3.distance = function(a, b) { + var x = b[0] - a[0], + y = b[1] - a[1], + z = b[2] - a[2]; + return Math.sqrt(x*x + y*y + z*z); + }; + + /** + * Alias for {@link vec3.distance} + * @function + */ + vec3.dist = vec3.distance; + + /** + * Calculates the squared euclidian distance between two vec3's + * + * @param {vec3} a the first operand + * @param {vec3} b the second operand + * @returns {Number} squared distance between a and b + */ + vec3.squaredDistance = function(a, b) { + var x = b[0] - a[0], + y = b[1] - a[1], + z = b[2] - a[2]; + return x*x + y*y + z*z; + }; + + /** + * Alias for {@link vec3.squaredDistance} + * @function + */ + vec3.sqrDist = vec3.squaredDistance; + + /** + * Calculates the length of a vec3 + * + * @param {vec3} a vector to calculate length of + * @returns {Number} length of a + */ + vec3.length = function (a) { + var x = a[0], + y = a[1], + z = a[2]; + return Math.sqrt(x*x + y*y + z*z); + }; + + /** + * Alias for {@link vec3.length} + * @function + */ + vec3.len = vec3.length; + + /** + * Calculates the squared length of a vec3 + * + * @param {vec3} a vector to calculate squared length of + * @returns {Number} squared length of a + */ + vec3.squaredLength = function (a) { + var x = a[0], + y = a[1], + z = a[2]; + return x*x + y*y + z*z; + }; + + /** + * Alias for {@link vec3.squaredLength} + * @function + */ + vec3.sqrLen = vec3.squaredLength; + + /** + * Negates the components of a vec3 + * + * @param {vec3} out the receiving vector + * @param {vec3} a vector to negate + * @returns {vec3} out + */ + vec3.negate = function(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 + */ + vec3.inverse = function(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 + */ + vec3.normalize = function(out, a) { + var x = a[0], + y = a[1], + 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 + */ + vec3.dot = function (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 + */ + vec3.cross = function(out, a, b) { + var ax = a[0], ay = a[1], az = a[2], + 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 + */ + vec3.lerp = function (out, a, b, t) { + var ax = a[0], + ay = a[1], + 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 + */ + vec3.hermite = function (out, a, b, c, d, t) { + var factorTimes2 = t * t, + factor1 = factorTimes2 * (2 * t - 3) + 1, + factor2 = factorTimes2 * (t - 2) + t, + factor3 = factorTimes2 * (t - 1), + 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; + + 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 + */ + vec3.bezier = function (out, a, b, c, d, t) { + var inverseFactor = 1 - t, + inverseFactorTimesTwo = inverseFactor * inverseFactor, + factorTimes2 = t * t, + factor1 = inverseFactorTimesTwo * inverseFactor, + factor2 = 3 * t * inverseFactorTimesTwo, + factor3 = 3 * factorTimes2 * inverseFactor, + 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 + */ + vec3.random = function (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 + */ + vec3.transformMat4 = function(out, a, m) { + var x = a[0], y = a[1], z = a[2], + 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 {mat4} m the 3x3 matrix to transform with + * @returns {vec3} out + */ + vec3.transformMat3 = function(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 + */ + vec3.transformQuat = function(out, a, q) { + // benchmarks: http://jsperf.com/quaternion-transform-vec3-implementations + + var x = a[0], y = a[1], z = a[2], + qx = q[0], qy = q[1], qz = q[2], qw = q[3], + + // calculate quat * vec + ix = qw * x + qy * z - qz * y, + iy = qw * y + qz * x - qx * z, + iz = qw * z + qx * y - qy * x, + 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 + */ + vec3.rotateX = function(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 + */ + vec3.rotateY = function(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 + */ + vec3.rotateZ = function(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; + }; + + /** + * 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 + */ + vec3.forEach = (function() { + var vec = vec3.create(); + + return function(a, stride, offset, count, fn, arg) { + var i, l; + 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; + }; + })(); + + /** + * 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 + */ + vec3.angle = function(a, b) { + + var tempA = vec3.fromValues(a[0], a[1], a[2]); + var tempB = vec3.fromValues(b[0], b[1], b[2]); + + vec3.normalize(tempA, tempA); + vec3.normalize(tempB, tempB); + + var cosine = vec3.dot(tempA, tempB); + + if(cosine > 1.0){ + return 0; + } else { + return Math.acos(cosine); + } + }; + + /** + * Returns a string representation of a vector + * + * @param {vec3} vec vector to represent as a string + * @returns {String} string representation of the vector + */ + vec3.str = function (a) { + return 'vec3(' + a[0] + ', ' + a[1] + ', ' + a[2] + ')'; + }; + + module.exports = vec3; + + +/***/ }, +/* 8 */ +/***/ function(module, exports, __webpack_require__) { + + /* 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. */ + + var glMatrix = __webpack_require__(1); + + /** + * @class 4 Dimensional Vector + * @name vec4 + */ + var vec4 = {}; + + /** + * Creates a new, empty vec4 + * + * @returns {vec4} a new 4D vector + */ + vec4.create = function() { + 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 + */ + vec4.clone = function(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 + */ + vec4.fromValues = function(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 + */ + vec4.copy = function(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 + */ + vec4.set = function(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 + */ + vec4.add = function(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 + */ + vec4.subtract = function(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; + }; + + /** + * Alias for {@link vec4.subtract} + * @function + */ + vec4.sub = vec4.subtract; + + /** + * 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 + */ + vec4.multiply = function(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; + }; + + /** + * Alias for {@link vec4.multiply} + * @function + */ + vec4.mul = vec4.multiply; + + /** + * 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 + */ + vec4.divide = function(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; + }; + + /** + * Alias for {@link vec4.divide} + * @function + */ + vec4.div = vec4.divide; + + /** + * 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 + */ + vec4.min = function(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 + */ + vec4.max = function(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; + }; + + /** + * 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 + */ + vec4.scale = function(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 + */ + vec4.scaleAndAdd = function(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 + */ + vec4.distance = function(a, b) { + var x = b[0] - a[0], + y = b[1] - a[1], + z = b[2] - a[2], + w = b[3] - a[3]; + return Math.sqrt(x*x + y*y + z*z + w*w); + }; + + /** + * Alias for {@link vec4.distance} + * @function + */ + vec4.dist = vec4.distance; + + /** + * 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 + */ + vec4.squaredDistance = function(a, b) { + var x = b[0] - a[0], + y = b[1] - a[1], + z = b[2] - a[2], + w = b[3] - a[3]; + return x*x + y*y + z*z + w*w; + }; + + /** + * Alias for {@link vec4.squaredDistance} + * @function + */ + vec4.sqrDist = vec4.squaredDistance; + + /** + * Calculates the length of a vec4 + * + * @param {vec4} a vector to calculate length of + * @returns {Number} length of a + */ + vec4.length = function (a) { + var x = a[0], + y = a[1], + z = a[2], + w = a[3]; + return Math.sqrt(x*x + y*y + z*z + w*w); + }; + + /** + * Alias for {@link vec4.length} + * @function + */ + vec4.len = vec4.length; + + /** + * Calculates the squared length of a vec4 + * + * @param {vec4} a vector to calculate squared length of + * @returns {Number} squared length of a + */ + vec4.squaredLength = function (a) { + var x = a[0], + y = a[1], + z = a[2], + w = a[3]; + return x*x + y*y + z*z + w*w; + }; + + /** + * Alias for {@link vec4.squaredLength} + * @function + */ + vec4.sqrLen = vec4.squaredLength; + + /** + * Negates the components of a vec4 + * + * @param {vec4} out the receiving vector + * @param {vec4} a vector to negate + * @returns {vec4} out + */ + vec4.negate = function(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 + */ + vec4.inverse = function(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 + */ + vec4.normalize = function(out, a) { + var x = a[0], + y = a[1], + z = a[2], + 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 + */ + vec4.dot = function (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 + */ + vec4.lerp = function (out, a, b, t) { + var ax = a[0], + ay = a[1], + az = a[2], + 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 + */ + vec4.random = function (out, scale) { + scale = scale || 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(); + vec4.normalize(out, out); + vec4.scale(out, out, scale); + 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 + */ + vec4.transformMat4 = function(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 + */ + vec4.transformQuat = function(out, a, q) { + var x = a[0], y = a[1], z = a[2], + qx = q[0], qy = q[1], qz = q[2], qw = q[3], + + // calculate quat * vec + ix = qw * x + qy * z - qz * y, + iy = qw * y + qz * x - qx * z, + iz = qw * z + qx * y - qy * x, + 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; + }; + + /** + * 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 + */ + vec4.forEach = (function() { + var vec = vec4.create(); + + return function(a, stride, offset, count, fn, arg) { + var i, l; + 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; + }; + })(); + + /** + * Returns a string representation of a vector + * + * @param {vec4} vec vector to represent as a string + * @returns {String} string representation of the vector + */ + vec4.str = function (a) { + return 'vec4(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')'; + }; + + module.exports = vec4; + + +/***/ }, +/* 9 */ +/***/ function(module, exports, __webpack_require__) { + + /* 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. */ + + var glMatrix = __webpack_require__(1); + + /** + * @class 2 Dimensional Vector + * @name vec2 + */ + var vec2 = {}; + + /** + * Creates a new, empty vec2 + * + * @returns {vec2} a new 2D vector + */ + vec2.create = function() { + 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 + */ + vec2.clone = function(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 + */ + vec2.fromValues = function(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 + */ + vec2.copy = function(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 + */ + vec2.set = function(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 + */ + vec2.add = function(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 + */ + vec2.subtract = function(out, a, b) { + out[0] = a[0] - b[0]; + out[1] = a[1] - b[1]; + return out; + }; + + /** + * Alias for {@link vec2.subtract} + * @function + */ + vec2.sub = vec2.subtract; + + /** + * 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 + */ + vec2.multiply = function(out, a, b) { + out[0] = a[0] * b[0]; + out[1] = a[1] * b[1]; + return out; + }; + + /** + * Alias for {@link vec2.multiply} + * @function + */ + vec2.mul = vec2.multiply; + + /** + * 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 + */ + vec2.divide = function(out, a, b) { + out[0] = a[0] / b[0]; + out[1] = a[1] / b[1]; + return out; + }; + + /** + * Alias for {@link vec2.divide} + * @function + */ + vec2.div = vec2.divide; + + /** + * 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 + */ + vec2.min = function(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 + */ + vec2.max = function(out, a, b) { + out[0] = Math.max(a[0], b[0]); + out[1] = Math.max(a[1], b[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 + */ + vec2.scale = function(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 + */ + vec2.scaleAndAdd = function(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 + */ + vec2.distance = function(a, b) { + var x = b[0] - a[0], + y = b[1] - a[1]; + return Math.sqrt(x*x + y*y); + }; + + /** + * Alias for {@link vec2.distance} + * @function + */ + vec2.dist = vec2.distance; + + /** + * 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 + */ + vec2.squaredDistance = function(a, b) { + var x = b[0] - a[0], + y = b[1] - a[1]; + return x*x + y*y; + }; + + /** + * Alias for {@link vec2.squaredDistance} + * @function + */ + vec2.sqrDist = vec2.squaredDistance; + + /** + * Calculates the length of a vec2 + * + * @param {vec2} a vector to calculate length of + * @returns {Number} length of a + */ + vec2.length = function (a) { + var x = a[0], + y = a[1]; + return Math.sqrt(x*x + y*y); + }; + + /** + * Alias for {@link vec2.length} + * @function + */ + vec2.len = vec2.length; + + /** + * Calculates the squared length of a vec2 + * + * @param {vec2} a vector to calculate squared length of + * @returns {Number} squared length of a + */ + vec2.squaredLength = function (a) { + var x = a[0], + y = a[1]; + return x*x + y*y; + }; + + /** + * Alias for {@link vec2.squaredLength} + * @function + */ + vec2.sqrLen = vec2.squaredLength; + + /** + * Negates the components of a vec2 + * + * @param {vec2} out the receiving vector + * @param {vec2} a vector to negate + * @returns {vec2} out + */ + vec2.negate = function(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 + */ + vec2.inverse = function(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 + */ + vec2.normalize = function(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 + */ + vec2.dot = function (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 + */ + vec2.cross = function(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 + */ + vec2.lerp = function (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 + */ + vec2.random = function (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 + */ + vec2.transformMat2 = function(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 + */ + vec2.transformMat2d = function(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 + */ + vec2.transformMat3 = function(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 + */ + vec2.transformMat4 = function(out, a, m) { + var x = a[0], + 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; + }; + + /** + * 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 + */ + vec2.forEach = (function() { + var vec = vec2.create(); + + return function(a, stride, offset, count, fn, arg) { + var i, l; + 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; + }; + })(); + + /** + * Returns a string representation of a vector + * + * @param {vec2} vec vector to represent as a string + * @returns {String} string representation of the vector + */ + vec2.str = function (a) { + return 'vec2(' + a[0] + ', ' + a[1] + ')'; + }; + + module.exports = vec2; + + +/***/ } +/******/ ]) +}); +; \ No newline at end of file diff --git a/Abgabe_4/lightTODOs/common/initShaders.js b/Abgabe_4/lightTODOs/common/initShaders.js new file mode 100644 index 0000000..95a6657 --- /dev/null +++ b/Abgabe_4/lightTODOs/common/initShaders.js @@ -0,0 +1,46 @@ +// +// initShaders.js +// + +function initShaders( gl, vertexShaderId, fragmentShaderId ) +{ + const compileShader = ( gl, gl_shaderType, shaderSource ) => { + // Create the shader + shader = gl.createShader( gl_shaderType ); + + // Set the shader source code + gl.shaderSource( shader, shaderSource ); + + // Compile the shader to make it readable for the GPU + gl.compileShader( shader ); + var success = gl.getShaderParameter(shader, gl.COMPILE_STATUS); + + if (!success) { + // Something went wrong during compilation; get the error + throw "could not compile shader:" + gl.getShaderInfoLog(shader); + } + else { + return shader; + } + } + + /* + * Setup shader program + */ + vShaderSource = document.querySelector( '#' + vertexShaderId ).text; + fShaderSource = document.querySelector( '#' + fragmentShaderId ).text; + + vertexShader = compileShader( gl, gl.VERTEX_SHADER, vShaderSource ); + fragmentShader = compileShader( gl, gl.FRAGMENT_SHADER, fShaderSource ); + + // Build the program + const program = gl.createProgram(); + + // Attach shaders to it + gl.attachShader( program, vertexShader ); + gl.attachShader( program, fragmentShader ); + + gl.linkProgram( program ); + + return program; +} \ No newline at end of file diff --git a/Abgabe_4/lightTODOs/common/objects3D.js b/Abgabe_4/lightTODOs/common/objects3D.js new file mode 100644 index 0000000..4085950 --- /dev/null +++ b/Abgabe_4/lightTODOs/common/objects3D.js @@ -0,0 +1,1847 @@ +class Object3D { + + // DONE: Füge Default-Materialkoeffizienten hinzu + constructor(ka = [0.5, 0.5, 0.5], kd = [0.5, 0.5, 0.5], ks = [0.5, 0.5, 0.5]) { + + this.posVBO = gl.createBuffer(); + // DONE: Kein colorVBO mehr! (Farben werden über Materialkoeffizienten bestimmt) + this.indexVBO = gl.createBuffer(); + + this.positions = []; + this.indices = []; + + // DONE: Lege objektspezifische Materialkoeffizienten an + this.ka = ka; + this.kd = kd; + this.ks = ks; + this.specularExponent = 4.0; + + this.position = [0, 0, 0]; + this.orientation = [0, 0, 0]; + this.scale = [1, 1, 1]; + this.modelMatrix; + this.SetModelMatrix(); + } + + InitBuffers() { + + gl.bindBuffer(gl.ARRAY_BUFFER, this.posVBO); + gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(this.positions), gl.STATIC_DRAW); + + gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, this.indexVBO); + gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, new Uint16Array(this.indices), gl.STATIC_DRAW); + } + + SetModelMatrix (position = this.position, orientation = this.orientation, scale = this.scale) { + + this.position = position; + this.orientation = [orientation[0] * Math.PI / 180, orientation[1] * Math.PI / 180, orientation[2] * Math.PI / 180]; // Convert the orientation to RAD + this.scale = scale; + + this.modelMatrix = mat4.create(); + mat4.translate(this.modelMatrix, this.modelMatrix, position); + mat4.rotate(this.modelMatrix, this.modelMatrix, this.orientation[0], [1, 0, 0]); + mat4.rotate(this.modelMatrix, this.modelMatrix, this.orientation[1], [0, 1, 0]); + mat4.rotate(this.modelMatrix, this.modelMatrix, this.orientation[2], [0, 0, 1]); + mat4.scale(this.modelMatrix, this.modelMatrix, scale); + } + + UpdateUniforms () { + + gl.uniformMatrix4fv(modelMatrixLoc, false, this.modelMatrix); + + // DONE: Übergebe Materialkoeffizienten des Objektes an den Shader + gl.uniform3fv(kaLoc, this.ka); + gl.uniform3fv(kdLoc, this.kd); + gl.uniform3fv(ksLoc, this.ks); + gl.uniform1f(specularExponentLoc, this.specularExponent); + } + + Render() { + + // Link data in VBO to shader variables + gl.bindBuffer(gl.ARRAY_BUFFER, this.posVBO); + gl.enableVertexAttribArray(posLoc); + gl.enableVertexAttribArray(normalLoc); + // DONE: Passe Stride-Wert an (vorletzter Parameter) + // -> Vertex-Position und -Normale werden abwechselnd gespeichert + gl.vertexAttribPointer(posLoc, 3, gl.FLOAT, false, 2 * 3 * 4, 0); + gl.vertexAttribPointer(normalLoc, 3, gl.FLOAT, false, 2 * 3 * 4, 3 * 4); + + this.UpdateUniforms(); + + // Render + gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, this.indexVBO); + gl.drawElements(gl.TRIANGLES, this.indices.length, gl.UNSIGNED_SHORT, 0); + } +} + + +class Island extends Object3D { + + constructor() { + + // DONE: Setze Material für Insel + super([0.4, 0.2, 0.0], [0.6, 0.3, 0.0], [0.7, 0.7, 0.7]); + + // DONE: Füge zu jedem Vertex Normale hinzu (bei PLY-Export in Blender) + this.positions = [ + -0.344503,-0.106899,-2.313329,-0.011310,-0.533934,-0.845450, + 0.254658,0.065420,-2.430170,-0.011310,-0.533934,-0.845450, + 0.506020,-0.293147,-2.207084,-0.011310,-0.533934,-0.845450, + 1.415955,0.064912,-1.957500,0.432419,-0.749451,-0.501335, + 1.489208,-0.318759,-1.320762,0.432419,-0.749451,-0.501335, + 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8.0, 0, 1, 0, // index 8 + -2.4, 0.0, 6.0, 0, 1, 0, // index 9 + 0.1, 0.0, 6.0, 0, 1, 0, // index 10 + -3.0, 0.0, 4.0, 0, 1, 0, // index 11 + 0.0, 0.0, 4.0, 0, 1, 0, // index 12 + -2.4, 0.0, 2.0, 0, 1, 0, // index 13 + 1.1, 0.0, 2.0, 0, 1, 0, // index 14 + 0.0, 0.0, 0.0, 0, 1, 0, // index 15 + 4.0, 0.0, 0.0, 0, 1, 0, // index 16 + 0.0, -7.0, 0.0, 0, 0, 1, // index 17 -> additional for waterfall + 4.0, -6.0, 0.0, 0, 0, 1 // index 18 -> additional for waterfall + ]; + + this.indices = [ + 0, 1, 2, + 1, 2, 3, + 2, 3, 4, + 3, 4, 5, + 4, 5, 6, + 5, 6, 7, + 6, 7, 8, + 7, 8, 9, + 8, 9, 10, + 9, 10, 11, + 10, 11, 12, + 11, 12, 13, + 12, 13, 14, + 13, 14, 15, + 14, 15, 16, + 15, 16, 17, // additional for waterfall + 16, 17, 18 // additional for waterfall + ]; + + this.InitBuffers(); + } +} + + +class Tree extends Object3D { + + constructor() { + + // DONE: Setze Material für Baum + super([0.2, 0.5, 0.0], [0.4, 0.8, 0.2], [0.6, 0.9, 0.2]); + + // DONE: Füge zu jedem Vertex Normale hinzu (bei PLY-Export in Blender) + this.positions = [ + -0.056969,0.301313,0.059775,-0.999612,-0.027868,0.000000, + -0.056969,0.301313,-0.040876,-0.999612,-0.027868,0.000000, + -0.055153,0.236174,-0.050744,-0.999612,-0.027868,0.000000, + -0.055153,0.236174,-0.050744,0.000000,0.000000,0.000000, + -0.055153,0.236174,-0.050744,0.000000,0.000000,0.000000, + 0.045498,0.236174,-0.050744,0.000000,0.000000,0.000000, + 0.045498,0.236174,-0.050744,0.385482,-0.922715,0.000000, + 0.183358,0.293767,-0.010892,0.385482,-0.922715,0.000000, + 0.183358,0.293767,0.016715,0.385482,-0.922715,0.000000, + -0.056969,0.301313,0.059775,0.000000,-0.149788,0.988718, + -0.055153,0.236174,0.049907,0.000000,-0.149788,0.988718, + 0.045498,0.236174,0.049907,0.000000,-0.149788,0.988718, + -0.055153,0.236174,0.049907,0.000000,-0.000000,1.000000, + -0.055153,0.051740,0.049907,0.000000,-0.000000,1.000000, + 0.045498,0.051740,0.049907,0.000000,-0.000000,1.000000, + 0.043682,0.301313,0.059775,0.000000,-0.616587,0.787287, + 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51,52,53, + 54,55,56, + 57,58,59, + 60,61,62, + 63,64,65, + 66,67,68, + 69,70,71, + 72,73,74, + 75,76,77, + 78,79,80, + 81,82,83, + 84,85,86, + 87,88,89, + 90,91,92, + 93,94,95, + 96,97,98, + 99,100,101, + 102,103,104, + 105,106,107, + 108,109,110, + 111,112,113, + 114,115,116, + 117,118,119, + 120,121,122, + 123,124,125, + 126,127,128, + 129,130,131, + 132,133,134, + 135,136,137, + 138,139,140, + 141,142,143, + 144,145,146, + 147,148,149, + 150,151,152, + 153,154,155, + 156,157,158, + 159,160,161, + 162,163,164, + 165,166,167, + 168,169,170, + 171,172,173, + 174,175,176, + 177,178,179, + 180,181,182, + 183,184,185, + 186,187,188, + 189,190,191, + 192,193,194, + 195,196,197, + 198,199,200, + 201,202,203, + 204,205,206, + 207,208,209, + 210,211,212, + 213,214,215, + 216,217,218, + 219,220,221, + 222,223,224, + 225,226,227, + 228,229,230, + 231,232,233, + 234,235,236, + 237,238,239 + ]; + + this.InitBuffers(); + } +} \ No newline at end of file diff --git a/Abgabe_4/lightTODOs/index.html b/Abgabe_4/lightTODOs/index.html new file mode 100644 index 0000000..41c0afa --- /dev/null +++ b/Abgabe_4/lightTODOs/index.html @@ -0,0 +1,77 @@ + + + + + WebGL Example + + + + + + + + +

Lorem Ipsum

+ + + If you see this, your browser doesn't support WebGL. + + + + + diff --git a/Abgabe_4/lightTODOs/main.js b/Abgabe_4/lightTODOs/main.js new file mode 100644 index 0000000..da369b7 --- /dev/null +++ b/Abgabe_4/lightTODOs/main.js @@ -0,0 +1,205 @@ +let gl; +let program; + +let objects = []; + +let posLoc; + +// DONE: Deklariere benötigte Locations von Shadervariablen als globale Variablen +let normalLoc, + lightPositionLoc, + IaLoc, + IdLoc, + IsLoc, + kaLoc, + kdLoc, + ksLoc, + specularExponentLoc; + +let modelMatrixLoc; + +let viewMatrixLoc, + viewMatrix; + +let eye, + target, + up; + +let keyPressed = { + KeyW: false, + KeyA: false, + KeyS: false, + KeyD: false +}; + +const speed = 0.005; + + +function main() { + + // Get canvas and setup WebGL context + const canvas = document.getElementById("gl-canvas"); + gl = canvas.getContext('webgl2'); + + // Configure viewport + gl.viewport(0,0,canvas.width,canvas.height); + gl.clearColor(0.75,0.8,1.0,1.0); + + gl.enable(gl.DEPTH_TEST); + + // Init shader program via additional function and bind it + program = initShaders(gl, "vertex-shader", "fragment-shader"); + gl.useProgram(program); + + // Get locations of shader variables + posLoc = gl.getAttribLocation(program, "vPosition"); + modelMatrixLoc = gl.getUniformLocation(program, "modelMatrix"); + viewMatrixLoc = gl.getUniformLocation(program, "viewMatrix"); + + // DONE: Fülle globale Variablen mit Speicherlocations für Materialkoeffizienten und Lichtintensitäten + normalLoc = gl.getAttribLocation(program, "vNormal"); + lightPositionLoc = gl.getUniformLocation(program, "lightPosition"); + IaLoc = gl.getUniformLocation(program, "Ia"); + IdLoc = gl.getUniformLocation(program, "Id"); + IsLoc = gl.getUniformLocation(program, "Is"); + kaLoc = gl.getUniformLocation(program, "ka"); + kdLoc = gl.getUniformLocation(program, "kd"); + ksLoc = gl.getUniformLocation(program, "ks"); + specularExponentLoc = gl.getUniformLocation(program, "specExp"); + + eye = vec3.fromValues(0.0, 0.3, 4.0); + target = vec3.fromValues(0.0, 0.3, 0.0); + up = vec3.fromValues(0.0, 1.0, 0.0); + + viewMatrix = mat4.create(); + mat4.lookAt(viewMatrix, eye, target, up); + + gl.uniformMatrix4fv(viewMatrixLoc, false, viewMatrix); + + // DONE: Setze Position und Intensitäten der Lichtquelle als Uniform-Variablen + gl.uniform3fv(lightPositionLoc, [1.0, 2.0, 1.0]); + gl.uniform3fv(IaLoc, [0.3, 0.3, 0.3]); + gl.uniform3fv(IdLoc, [0.8, 0.8, 0.8]); + gl.uniform3fv(IsLoc, [0.7, 0.7, 0.7]); + + document.addEventListener("keydown", keydown); + document.addEventListener("keyup", keyup); + document.addEventListener("mousemove", changeView); + + canvas.onmousedown = function() { + canvas.requestPointerLock(); + } + + // Create object instances + let island = new Island(); + objects.push(island); + + let tree1 = new Tree(); + tree1.SetModelMatrix([1.3, 0, 0.6], [0, 45, 0], [0.3, 0.3, 0.3]); + objects.push(tree1); + + let tree2 = new Tree(); + tree2.SetModelMatrix([0.9, 0, 0.3], [0, 33, 0], [0.45, 0.45, 0.45]); + objects.push(tree2); + + let tree3 = new Tree(); + tree3.SetModelMatrix([0.45, 0, 0.75], [0, 0, 0], [0.4, 0.4, 0.4]); + objects.push(tree3); + + let tree4 = new Tree(); + tree4.SetModelMatrix([-1.1, 0, 0.5], [0, 222, 0], [0.42, 0.42, 0.42]); + objects.push(tree4); + + let tree5 = new Tree(); + tree5.SetModelMatrix([-0.65, 0, 0.7], [0, 79, 0], [0.32, 0.32, 0.32]); + objects.push(tree5); + + let cloud1 = new Cloud(); + cloud1.SetModelMatrix([-0.4, 1, -0.9], [0, 0, 0], [0.32, 0.32, 0.32]); + objects.push(cloud1); + + let cloud2 = new Cloud(); + cloud2.SetModelMatrix([0, 1.4, -1.6], [0, -90, 0], [0.2, 0.2, 0.2]); + objects.push(cloud2); + + let cloud3 = new Cloud(); + cloud3.SetModelMatrix([0.7, 0.9, -0.8], [0, 100, 0], [0.25, 0.25, 0.25]); + objects.push(cloud3); + + let river = new River(); + river.SetModelMatrix([0, 0.04, 1.8], [0, 185, 0], [0.11, 0.11, 0.11]); + objects.push(river); + + gameLoop(); +}; + +function update() +{ + let look = vec3.create(); + vec3.sub(look, target, eye); + vec3.scale(look, look, speed); + + if(keyPressed.KeyW) { + eye[0] += look[0]; + eye[2] += look[2]; + target[0] += look[0]; + target[2] += look[2]; + } + if(keyPressed.KeyS) { + eye[0] -= look[0]; + eye[2] -= look[2]; + target[0] -= look[0]; + target[2] -= look[2]; + } + if(keyPressed.KeyA) { + eye[0] += look[2]; + eye[2] -= look[0]; + target[0] += look[2]; + target[2] -= look[0]; + } + if(keyPressed.KeyD) { + eye[0] -= look[2]; + eye[2] += look[0]; + target[0] -= look[2]; + target[2] += look[0]; + } + mat4.lookAt(viewMatrix, eye, target, up); + gl.uniformMatrix4fv(viewMatrixLoc, false, viewMatrix); +} + +function render() { + + // Only clear once + gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT); + + // Call render function of each scene object + for(let object of objects) { + object.Render(); + }; +} + +function gameLoop() +{ + update(); + render(); + requestAnimationFrame(gameLoop); +} + +function keydown(e) +{ + keyPressed[e.code] = true; +} + +function keyup(e) +{ + keyPressed[e.code] = false; +} + +function changeView(e) +{ + vec3.rotateY(target, target, eye, -e.movementX * speed); + mat4.lookAt(viewMatrix, eye, target, up); + gl.uniformMatrix4fv(viewMatrixLoc, false, viewMatrix); +} + +main(); diff --git a/index.html b/index.html index d036eeb..b39da18 100644 --- a/index.html +++ b/index.html @@ -6,8 +6,10 @@ Übung_23112023/
+Übung_30112023/
Abgabe_3/
+Abgabe_4/
diff --git a/Übung_30112023/Insel/common/glMatrix.js b/Übung_30112023/Insel/common/glMatrix.js new file mode 100644 index 0000000..0799c59 --- /dev/null +++ b/Übung_30112023/Insel/common/glMatrix.js @@ -0,0 +1,7861 @@ + +/*! +@fileoverview gl-matrix - High performance matrix and vector operations +@author Brandon Jones +@author Colin MacKenzie IV +@version 3.4.0 + +Copyright (c) 2015-2021, 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 (global, factory) { + typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) : + typeof define === 'function' && define.amd ? define(['exports'], factory) : + (global = typeof globalThis !== 'undefined' ? globalThis : global || self, factory(global.glMatrix = {})); + })(this, (function (exports) { 'use strict'; + + /** + * Common utilities + * @module glMatrix + */ + // Configuration Constants + var EPSILON = 0.000001; + var ARRAY_TYPE = typeof Float32Array !== "undefined" ? Float32Array : Array; + var RANDOM = Math.random; + var ANGLE_ORDER = "zyx"; + /** + * Sets the type of array used when creating new vectors and matrices + * + * @param {Float32ArrayConstructor | ArrayConstructor} type Array type, such as Float32Array or Array + */ + + function setMatrixArrayType(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$9(a, b) { + return Math.abs(a - b) <= EPSILON * Math.max(1.0, Math.abs(a), Math.abs(b)); + } + if (!Math.hypot) Math.hypot = function () { + var y = 0, + i = arguments.length; + + while (i--) { + y += arguments[i] * arguments[i]; + } + + return Math.sqrt(y); + }; + + var common = /*#__PURE__*/Object.freeze({ + __proto__: null, + EPSILON: EPSILON, + get ARRAY_TYPE () { return ARRAY_TYPE; }, + RANDOM: RANDOM, + ANGLE_ORDER: ANGLE_ORDER, + setMatrixArrayType: setMatrixArrayType, + toRadian: toRadian, + equals: equals$9 + }); + + /** + * 2x2 Matrix + * @module mat2 + */ + + /** + * Creates a new identity mat2 + * + * @returns {mat2} a new 2x2 matrix + */ + + function create$8() { + var out = new ARRAY_TYPE(4); + + if (ARRAY_TYPE != Float32Array) { + out[1] = 0; + out[2] = 0; + } + + out[0] = 1; + out[3] = 1; + return out; + } + /** + * Creates a new mat2 initialized with values from an existing matrix + * + * @param {ReadonlyMat2} a matrix to clone + * @returns {mat2} a new 2x2 matrix + */ + + function clone$8(a) { + var out = new 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 {ReadonlyMat2} a the source matrix + * @returns {mat2} out + */ + + function copy$8(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$5(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$8(m00, m01, m10, m11) { + var out = new 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$8(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 {ReadonlyMat2} a the source matrix + * @returns {mat2} out + */ + + function transpose$2(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 {ReadonlyMat2} a the source matrix + * @returns {mat2} out + */ + + function invert$5(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 {ReadonlyMat2} a the source matrix + * @returns {mat2} out + */ + + function adjoint$2(out, a) { + // Caching this value is necessary 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 {ReadonlyMat2} a the source matrix + * @returns {Number} determinant of a + */ + + function determinant$3(a) { + return a[0] * a[3] - a[2] * a[1]; + } + /** + * Multiplies two mat2's + * + * @param {mat2} out the receiving matrix + * @param {ReadonlyMat2} a the first operand + * @param {ReadonlyMat2} b the second operand + * @returns {mat2} out + */ + + function multiply$8(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 {ReadonlyMat2} a the matrix to rotate + * @param {Number} rad the angle to rotate the matrix by + * @returns {mat2} out + */ + + function rotate$4(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 {ReadonlyMat2} a the matrix to rotate + * @param {ReadonlyVec2} v the vec2 to scale the matrix by + * @returns {mat2} out + **/ + + function scale$8(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$4(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 {ReadonlyVec2} v Scaling vector + * @returns {mat2} out + */ + + function fromScaling$3(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 {ReadonlyMat2} a matrix to represent as a string + * @returns {String} string representation of the matrix + */ + + function str$8(a) { + return "mat2(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ")"; + } + /** + * Returns Frobenius norm of a mat2 + * + * @param {ReadonlyMat2} a the matrix to calculate Frobenius norm of + * @returns {Number} Frobenius norm + */ + + function frob$3(a) { + return Math.hypot(a[0], a[1], a[2], a[3]); + } + /** + * Returns L, D and U matrices (Lower triangular, Diagonal and Upper triangular) by factorizing the input matrix + * @param {ReadonlyMat2} L the lower triangular matrix + * @param {ReadonlyMat2} D the diagonal matrix + * @param {ReadonlyMat2} U the upper triangular matrix + * @param {ReadonlyMat2} 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 {ReadonlyMat2} a the first operand + * @param {ReadonlyMat2} b the second operand + * @returns {mat2} out + */ + + function add$8(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 {ReadonlyMat2} a the first operand + * @param {ReadonlyMat2} b the second operand + * @returns {mat2} out + */ + + function subtract$6(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 {ReadonlyMat2} a The first matrix. + * @param {ReadonlyMat2} b The second matrix. + * @returns {Boolean} True if the matrices are equal, false otherwise. + */ + + function exactEquals$8(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 {ReadonlyMat2} a The first matrix. + * @param {ReadonlyMat2} b The second matrix. + * @returns {Boolean} True if the matrices are equal, false otherwise. + */ + + function equals$8(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) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= 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 {ReadonlyMat2} a the matrix to scale + * @param {Number} b amount to scale the matrix's elements by + * @returns {mat2} out + */ + + function multiplyScalar$3(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 {ReadonlyMat2} a the first operand + * @param {ReadonlyMat2} b the second operand + * @param {Number} scale the amount to scale b's elements by before adding + * @returns {mat2} out + */ + + function multiplyScalarAndAdd$3(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$8 = multiply$8; + /** + * Alias for {@link mat2.subtract} + * @function + */ + + var sub$6 = subtract$6; + + var mat2 = /*#__PURE__*/Object.freeze({ + __proto__: null, + create: create$8, + clone: clone$8, + copy: copy$8, + identity: identity$5, + fromValues: fromValues$8, + set: set$8, + transpose: transpose$2, + invert: invert$5, + adjoint: adjoint$2, + determinant: determinant$3, + multiply: multiply$8, + rotate: rotate$4, + scale: scale$8, + fromRotation: fromRotation$4, + fromScaling: fromScaling$3, + str: str$8, + frob: frob$3, + LDU: LDU, + add: add$8, + subtract: subtract$6, + exactEquals: exactEquals$8, + equals: equals$8, + multiplyScalar: multiplyScalar$3, + multiplyScalarAndAdd: multiplyScalarAndAdd$3, + mul: mul$8, + sub: sub$6 + }); + + /** + * 2x3 Matrix + * @module mat2d + * @description + * A mat2d contains six elements defined as: + * 
+     * [a, b,
+     *  c, d,
+     *  tx, ty]
+     *
+ * This is a short form for the 3x3 matrix: + * 
+     * [a, b, 0,
+     *  c, d, 0,
+     *  tx, ty, 1]
+     *
+ * The last column is ignored so the array is shorter and operations are faster. + */ + + /** + * Creates a new identity mat2d + * + * @returns {mat2d} a new 2x3 matrix + */ + + function create$7() { + var out = new ARRAY_TYPE(6); + + if (ARRAY_TYPE != Float32Array) { + out[1] = 0; + out[2] = 0; + out[4] = 0; + out[5] = 0; + } + + out[0] = 1; + out[3] = 1; + return out; + } + /** + * Creates a new mat2d initialized with values from an existing matrix + * + * @param {ReadonlyMat2d} a matrix to clone + * @returns {mat2d} a new 2x3 matrix + */ + + function clone$7(a) { + var out = new 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 {ReadonlyMat2d} a the source matrix + * @returns {mat2d} out + */ + + function copy$7(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$4(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$7(a, b, c, d, tx, ty) { + var out = new 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$7(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 {ReadonlyMat2d} a the source matrix + * @returns {mat2d} out + */ + + function invert$4(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 {ReadonlyMat2d} a the source matrix + * @returns {Number} determinant of a + */ + + function determinant$2(a) { + return a[0] * a[3] - a[1] * a[2]; + } + /** + * Multiplies two mat2d's + * + * @param {mat2d} out the receiving matrix + * @param {ReadonlyMat2d} a the first operand + * @param {ReadonlyMat2d} b the second operand + * @returns {mat2d} out + */ + + function multiply$7(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 {ReadonlyMat2d} a the matrix to rotate + * @param {Number} rad the angle to rotate the matrix by + * @returns {mat2d} out + */ + + function rotate$3(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 {ReadonlyMat2d} a the matrix to translate + * @param {ReadonlyVec2} v the vec2 to scale the matrix by + * @returns {mat2d} out + **/ + + function scale$7(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 {ReadonlyMat2d} a the matrix to translate + * @param {ReadonlyVec2} v the vec2 to translate the matrix by + * @returns {mat2d} out + **/ + + function translate$3(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$3(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 {ReadonlyVec2} v Scaling vector + * @returns {mat2d} out + */ + + function fromScaling$2(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 {ReadonlyVec2} v Translation vector + * @returns {mat2d} out + */ + + function fromTranslation$3(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 {ReadonlyMat2d} a matrix to represent as a string + * @returns {String} string representation of the matrix + */ + + function str$7(a) { + return "mat2d(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ", " + a[4] + ", " + a[5] + ")"; + } + /** + * Returns Frobenius norm of a mat2d + * + * @param {ReadonlyMat2d} a the matrix to calculate Frobenius norm of + * @returns {Number} Frobenius norm + */ + + function frob$2(a) { + return Math.hypot(a[0], a[1], a[2], a[3], a[4], a[5], 1); + } + /** + * Adds two mat2d's + * + * @param {mat2d} out the receiving matrix + * @param {ReadonlyMat2d} a the first operand + * @param {ReadonlyMat2d} b the second operand + * @returns {mat2d} out + */ + + function add$7(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 {ReadonlyMat2d} a the first operand + * @param {ReadonlyMat2d} b the second operand + * @returns {mat2d} out + */ + + function subtract$5(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 {ReadonlyMat2d} a the matrix to scale + * @param {Number} b amount to scale the matrix's elements by + * @returns {mat2d} out + */ + + function multiplyScalar$2(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 {ReadonlyMat2d} a the first operand + * @param {ReadonlyMat2d} b the second operand + * @param {Number} scale the amount to scale b's elements by before adding + * @returns {mat2d} out + */ + + function multiplyScalarAndAdd$2(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 {ReadonlyMat2d} a The first matrix. + * @param {ReadonlyMat2d} b The second matrix. + * @returns {Boolean} True if the matrices are equal, false otherwise. + */ + + function exactEquals$7(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 {ReadonlyMat2d} a The first matrix. + * @param {ReadonlyMat2d} b The second matrix. + * @returns {Boolean} True if the matrices are equal, false otherwise. + */ + + function equals$7(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) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)); + } + /** + * Alias for {@link mat2d.multiply} + * @function + */ + + var mul$7 = multiply$7; + /** + * Alias for {@link mat2d.subtract} + * @function + */ + + var sub$5 = subtract$5; + + var mat2d = /*#__PURE__*/Object.freeze({ + __proto__: null, + create: create$7, + clone: clone$7, + copy: copy$7, + identity: identity$4, + fromValues: fromValues$7, + set: set$7, + invert: invert$4, + determinant: determinant$2, + multiply: multiply$7, + rotate: rotate$3, + scale: scale$7, + translate: translate$3, + fromRotation: fromRotation$3, + fromScaling: fromScaling$2, + fromTranslation: fromTranslation$3, + str: str$7, + frob: frob$2, + add: add$7, + subtract: subtract$5, + multiplyScalar: multiplyScalar$2, + multiplyScalarAndAdd: multiplyScalarAndAdd$2, + exactEquals: exactEquals$7, + equals: equals$7, + mul: mul$7, + sub: sub$5 + }); + + /** + * 3x3 Matrix + * @module mat3 + */ + + /** + * Creates a new identity mat3 + * + * @returns {mat3} a new 3x3 matrix + */ + + function create$6() { + var out = new ARRAY_TYPE(9); + + if (ARRAY_TYPE != Float32Array) { + out[1] = 0; + out[2] = 0; + out[3] = 0; + out[5] = 0; + out[6] = 0; + out[7] = 0; + } + + out[0] = 1; + out[4] = 1; + out[8] = 1; + return out; + } + /** + * Copies the upper-left 3x3 values into the given mat3. + * + * @param {mat3} out the receiving 3x3 matrix + * @param {ReadonlyMat4} a the source 4x4 matrix + * @returns {mat3} out + */ + + function fromMat4$1(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 {ReadonlyMat3} a matrix to clone + * @returns {mat3} a new 3x3 matrix + */ + + function clone$6(a) { + var out = new 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 {ReadonlyMat3} a the source matrix + * @returns {mat3} out + */ + + function copy$6(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$6(m00, m01, m02, m10, m11, m12, m20, m21, m22) { + var out = new 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$6(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$3(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 {ReadonlyMat3} a the source matrix + * @returns {mat3} out + */ + + function transpose$1(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 {ReadonlyMat3} a the source matrix + * @returns {mat3} out + */ + + function invert$3(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 {ReadonlyMat3} a the source matrix + * @returns {mat3} out + */ + + function adjoint$1(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 {ReadonlyMat3} a the source matrix + * @returns {Number} determinant of a + */ + + function determinant$1(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 {ReadonlyMat3} a the first operand + * @param {ReadonlyMat3} b the second operand + * @returns {mat3} out + */ + + function multiply$6(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 {ReadonlyMat3} a the matrix to translate + * @param {ReadonlyVec2} v vector to translate by + * @returns {mat3} out + */ + + function translate$2(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 {ReadonlyMat3} a the matrix to rotate + * @param {Number} rad the angle to rotate the matrix by + * @returns {mat3} out + */ + + function rotate$2(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 {ReadonlyMat3} a the matrix to rotate + * @param {ReadonlyVec2} v the vec2 to scale the matrix by + * @returns {mat3} out + **/ + + function scale$6(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 {ReadonlyVec2} v Translation vector + * @returns {mat3} out + */ + + function fromTranslation$2(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$2(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 {ReadonlyVec2} v Scaling vector + * @returns {mat3} out + */ + + function fromScaling$1(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 {ReadonlyMat2d} 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 {ReadonlyQuat} q Quaternion to create matrix from + * + * @returns {mat3} out + */ + + function fromQuat$1(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 {ReadonlyMat4} 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 {ReadonlyMat3} a matrix to represent as a string + * @returns {String} string representation of the matrix + */ + + function str$6(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 {ReadonlyMat3} a the matrix to calculate Frobenius norm of + * @returns {Number} Frobenius norm + */ + + function frob$1(a) { + return Math.hypot(a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8]); + } + /** + * Adds two mat3's + * + * @param {mat3} out the receiving matrix + * @param {ReadonlyMat3} a the first operand + * @param {ReadonlyMat3} b the second operand + * @returns {mat3} out + */ + + function add$6(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 {ReadonlyMat3} a the first operand + * @param {ReadonlyMat3} b the second operand + * @returns {mat3} out + */ + + function subtract$4(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 {ReadonlyMat3} a the matrix to scale + * @param {Number} b amount to scale the matrix's elements by + * @returns {mat3} out + */ + + function multiplyScalar$1(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 {ReadonlyMat3} a the first operand + * @param {ReadonlyMat3} b the second operand + * @param {Number} scale the amount to scale b's elements by before adding + * @returns {mat3} out + */ + + function multiplyScalarAndAdd$1(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 {ReadonlyMat3} a The first matrix. + * @param {ReadonlyMat3} b The second matrix. + * @returns {Boolean} True if the matrices are equal, false otherwise. + */ + + function exactEquals$6(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 {ReadonlyMat3} a The first matrix. + * @param {ReadonlyMat3} b The second matrix. + * @returns {Boolean} True if the matrices are equal, false otherwise. + */ + + function equals$6(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) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)) && Math.abs(a6 - b6) <= EPSILON * Math.max(1.0, Math.abs(a6), Math.abs(b6)) && Math.abs(a7 - b7) <= EPSILON * Math.max(1.0, Math.abs(a7), Math.abs(b7)) && Math.abs(a8 - b8) <= EPSILON * Math.max(1.0, Math.abs(a8), Math.abs(b8)); + } + /** + * Alias for {@link mat3.multiply} + * @function + */ + + var mul$6 = multiply$6; + /** + * Alias for {@link mat3.subtract} + * @function + */ + + var sub$4 = subtract$4; + + var mat3 = /*#__PURE__*/Object.freeze({ + __proto__: null, + create: create$6, + fromMat4: fromMat4$1, + clone: clone$6, + copy: copy$6, + fromValues: fromValues$6, + set: set$6, + identity: identity$3, + transpose: transpose$1, + invert: invert$3, + adjoint: adjoint$1, + determinant: determinant$1, + multiply: multiply$6, + translate: translate$2, + rotate: rotate$2, + scale: scale$6, + fromTranslation: fromTranslation$2, + fromRotation: fromRotation$2, + fromScaling: fromScaling$1, + fromMat2d: fromMat2d, + fromQuat: fromQuat$1, + normalFromMat4: normalFromMat4, + projection: projection, + str: str$6, + frob: frob$1, + add: add$6, + subtract: subtract$4, + multiplyScalar: multiplyScalar$1, + multiplyScalarAndAdd: multiplyScalarAndAdd$1, + exactEquals: exactEquals$6, + equals: equals$6, + mul: mul$6, + sub: sub$4 + }); + + /** + * 4x4 Matrix
Format: column-major, when typed out it looks like row-major
The matrices are being post multiplied. + * @module mat4 + */ + + /** + * Creates a new identity mat4 + * + * @returns {mat4} a new 4x4 matrix + */ + + function create$5() { + var out = new ARRAY_TYPE(16); + + if (ARRAY_TYPE != Float32Array) { + out[1] = 0; + out[2] = 0; + out[3] = 0; + out[4] = 0; + out[6] = 0; + out[7] = 0; + out[8] = 0; + out[9] = 0; + out[11] = 0; + out[12] = 0; + out[13] = 0; + out[14] = 0; + } + + out[0] = 1; + out[5] = 1; + out[10] = 1; + out[15] = 1; + return out; + } + /** + * Creates a new mat4 initialized with values from an existing matrix + * + * @param {ReadonlyMat4} a matrix to clone + * @returns {mat4} a new 4x4 matrix + */ + + function clone$5(a) { + var out = new 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 {ReadonlyMat4} a the source matrix + * @returns {mat4} out + */ + + function copy$5(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$5(m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) { + var out = new 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$5(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$2(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 {ReadonlyMat4} 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 {ReadonlyMat4} a the source matrix + * @returns {mat4} out + */ + + function invert$2(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 {ReadonlyMat4} 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]; + 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; + out[0] = a11 * b11 - a12 * b10 + a13 * b09; + out[1] = a02 * b10 - a01 * b11 - a03 * b09; + out[2] = a31 * b05 - a32 * b04 + a33 * b03; + out[3] = a22 * b04 - a21 * b05 - a23 * b03; + out[4] = a12 * b08 - a10 * b11 - a13 * b07; + out[5] = a00 * b11 - a02 * b08 + a03 * b07; + out[6] = a32 * b02 - a30 * b05 - a33 * b01; + out[7] = a20 * b05 - a22 * b02 + a23 * b01; + out[8] = a10 * b10 - a11 * b08 + a13 * b06; + out[9] = a01 * b08 - a00 * b10 - a03 * b06; + out[10] = a30 * b04 - a31 * b02 + a33 * b00; + out[11] = a21 * b02 - a20 * b04 - a23 * b00; + out[12] = a11 * b07 - a10 * b09 - a12 * b06; + out[13] = a00 * b09 - a01 * b07 + a02 * b06; + out[14] = a31 * b01 - a30 * b03 - a32 * b00; + out[15] = a20 * b03 - a21 * b01 + a22 * b00; + return out; + } + /** + * Calculates the determinant of a mat4 + * + * @param {ReadonlyMat4} 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 b0 = a00 * a11 - a01 * a10; + var b1 = a00 * a12 - a02 * a10; + var b2 = a01 * a12 - a02 * a11; + var b3 = a20 * a31 - a21 * a30; + var b4 = a20 * a32 - a22 * a30; + var b5 = a21 * a32 - a22 * a31; + var b6 = a00 * b5 - a01 * b4 + a02 * b3; + var b7 = a10 * b5 - a11 * b4 + a12 * b3; + var b8 = a20 * b2 - a21 * b1 + a22 * b0; + var b9 = a30 * b2 - a31 * b1 + a32 * b0; // Calculate the determinant + + return a13 * b6 - a03 * b7 + a33 * b8 - a23 * b9; + } + /** + * Multiplies two mat4s + * + * @param {mat4} out the receiving matrix + * @param {ReadonlyMat4} a the first operand + * @param {ReadonlyMat4} b the second operand + * @returns {mat4} out + */ + + function multiply$5(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 {ReadonlyMat4} a the matrix to translate + * @param {ReadonlyVec3} v vector to translate by + * @returns {mat4} out + */ + + function translate$1(out, a, v) { + var x = v[0], + y = v[1], + z = v[2]; + var a00, a01, a02, a03; + var a10, a11, a12, a13; + var a20, a21, a22, a23; + + 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 {ReadonlyMat4} a the matrix to scale + * @param {ReadonlyVec3} v the vec3 to scale the matrix by + * @returns {mat4} out + **/ + + function scale$5(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 {ReadonlyMat4} a the matrix to rotate + * @param {Number} rad the angle to rotate the matrix by + * @param {ReadonlyVec3} axis the axis to rotate around + * @returns {mat4} out + */ + + function rotate$1(out, a, rad, axis) { + var x = axis[0], + y = axis[1], + z = axis[2]; + var len = Math.hypot(x, y, z); + var s, c, t; + var a00, a01, a02, a03; + var a10, a11, a12, a13; + var a20, a21, a22, a23; + var b00, b01, b02; + var b10, b11, b12; + var b20, b21, b22; + + if (len < 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 {ReadonlyMat4} a the matrix to rotate + * @param {Number} rad the angle to rotate the matrix by + * @returns {mat4} out + */ + + function rotateX$3(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 {ReadonlyMat4} a the matrix to rotate + * @param {Number} rad the angle to rotate the matrix by + * @returns {mat4} out + */ + + function rotateY$3(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 {ReadonlyMat4} a the matrix to rotate + * @param {Number} rad the angle to rotate the matrix by + * @returns {mat4} out + */ + + function rotateZ$3(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 {ReadonlyVec3} v Translation vector + * @returns {mat4} out + */ + + function fromTranslation$1(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 {ReadonlyVec3} 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 {ReadonlyVec3} axis the axis to rotate around + * @returns {mat4} out + */ + + function fromRotation$1(out, rad, axis) { + var x = axis[0], + y = axis[1], + z = axis[2]; + var len = Math.hypot(x, y, z); + var s, c, t; + + if (len < 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 {ReadonlyVec3} v Translation vector + * @returns {mat4} out + */ + + function fromRotationTranslation$1(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; + } + /** + * Creates a new mat4 from a dual quat. + * + * @param {mat4} out Matrix + * @param {ReadonlyQuat2} a Dual Quaternion + * @returns {mat4} mat4 receiving operation result + */ + + function fromQuat2(out, a) { + var translation = new ARRAY_TYPE(3); + var bx = -a[0], + by = -a[1], + bz = -a[2], + bw = a[3], + ax = a[4], + ay = a[5], + az = a[6], + aw = a[7]; + var magnitude = bx * bx + by * by + bz * bz + bw * bw; //Only scale if it makes sense + + if (magnitude > 0) { + translation[0] = (ax * bw + aw * bx + ay * bz - az * by) * 2 / magnitude; + translation[1] = (ay * bw + aw * by + az * bx - ax * bz) * 2 / magnitude; + translation[2] = (az * bw + aw * bz + ax * by - ay * bx) * 2 / magnitude; + } else { + translation[0] = (ax * bw + aw * bx + ay * bz - az * by) * 2; + translation[1] = (ay * bw + aw * by + az * bx - ax * bz) * 2; + translation[2] = (az * bw + aw * bz + ax * by - ay * bx) * 2; + } + + fromRotationTranslation$1(out, a, translation); + 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 {ReadonlyMat4} mat Matrix to be decomposed (input) + * @return {vec3} out + */ + + function getTranslation$1(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 {ReadonlyMat4} 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.hypot(m11, m12, m13); + out[1] = Math.hypot(m21, m22, m23); + out[2] = Math.hypot(m31, m32, 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 {ReadonlyMat4} mat Matrix to be decomposed (input) + * @return {quat} out + */ + + function getRotation(out, mat) { + var scaling = new ARRAY_TYPE(3); + getScaling(scaling, mat); + var is1 = 1 / scaling[0]; + var is2 = 1 / scaling[1]; + var is3 = 1 / scaling[2]; + var sm11 = mat[0] * is1; + var sm12 = mat[1] * is2; + var sm13 = mat[2] * is3; + var sm21 = mat[4] * is1; + var sm22 = mat[5] * is2; + var sm23 = mat[6] * is3; + var sm31 = mat[8] * is1; + var sm32 = mat[9] * is2; + var sm33 = mat[10] * is3; + var trace = sm11 + sm22 + sm33; + var S = 0; + + if (trace > 0) { + S = Math.sqrt(trace + 1.0) * 2; + out[3] = 0.25 * S; + out[0] = (sm23 - sm32) / S; + out[1] = (sm31 - sm13) / S; + out[2] = (sm12 - sm21) / S; + } else if (sm11 > sm22 && sm11 > sm33) { + S = Math.sqrt(1.0 + sm11 - sm22 - sm33) * 2; + out[3] = (sm23 - sm32) / S; + out[0] = 0.25 * S; + out[1] = (sm12 + sm21) / S; + out[2] = (sm31 + sm13) / S; + } else if (sm22 > sm33) { + S = Math.sqrt(1.0 + sm22 - sm11 - sm33) * 2; + out[3] = (sm31 - sm13) / S; + out[0] = (sm12 + sm21) / S; + out[1] = 0.25 * S; + out[2] = (sm23 + sm32) / S; + } else { + S = Math.sqrt(1.0 + sm33 - sm11 - sm22) * 2; + out[3] = (sm12 - sm21) / S; + out[0] = (sm31 + sm13) / S; + out[1] = (sm23 + sm32) / S; + out[2] = 0.25 * S; + } + + return out; + } + /** + * Decomposes a transformation matrix into its rotation, translation + * and scale components. Returns only the rotation component + * @param {quat} out_r Quaternion to receive the rotation component + * @param {vec3} out_t Vector to receive the translation vector + * @param {vec3} out_s Vector to receive the scaling factor + * @param {ReadonlyMat4} mat Matrix to be decomposed (input) + * @returns {quat} out_r + */ + + function decompose(out_r, out_t, out_s, mat) { + out_t[0] = mat[12]; + out_t[1] = mat[13]; + out_t[2] = mat[14]; + 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_s[0] = Math.hypot(m11, m12, m13); + out_s[1] = Math.hypot(m21, m22, m23); + out_s[2] = Math.hypot(m31, m32, m33); + var is1 = 1 / out_s[0]; + var is2 = 1 / out_s[1]; + var is3 = 1 / out_s[2]; + var sm11 = m11 * is1; + var sm12 = m12 * is2; + var sm13 = m13 * is3; + var sm21 = m21 * is1; + var sm22 = m22 * is2; + var sm23 = m23 * is3; + var sm31 = m31 * is1; + var sm32 = m32 * is2; + var sm33 = m33 * is3; + var trace = sm11 + sm22 + sm33; + var S = 0; + + if (trace > 0) { + S = Math.sqrt(trace + 1.0) * 2; + out_r[3] = 0.25 * S; + out_r[0] = (sm23 - sm32) / S; + out_r[1] = (sm31 - sm13) / S; + out_r[2] = (sm12 - sm21) / S; + } else if (sm11 > sm22 && sm11 > sm33) { + S = Math.sqrt(1.0 + sm11 - sm22 - sm33) * 2; + out_r[3] = (sm23 - sm32) / S; + out_r[0] = 0.25 * S; + out_r[1] = (sm12 + sm21) / S; + out_r[2] = (sm31 + sm13) / S; + } else if (sm22 > sm33) { + S = Math.sqrt(1.0 + sm22 - sm11 - sm33) * 2; + out_r[3] = (sm31 - sm13) / S; + out_r[0] = (sm12 + sm21) / S; + out_r[1] = 0.25 * S; + out_r[2] = (sm23 + sm32) / S; + } else { + S = Math.sqrt(1.0 + sm33 - sm11 - sm22) * 2; + out_r[3] = (sm12 - sm21) / S; + out_r[0] = (sm31 + sm13) / S; + out_r[1] = (sm23 + sm32) / S; + out_r[2] = 0.25 * S; + } + + return out_r; + } + /** + * 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 {ReadonlyVec3} v Translation vector + * @param {ReadonlyVec3} 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 {ReadonlyVec3} v Translation vector + * @param {ReadonlyVec3} s Scaling vector + * @param {ReadonlyVec3} 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]; + var out0 = (1 - (yy + zz)) * sx; + var out1 = (xy + wz) * sx; + var out2 = (xz - wy) * sx; + var out4 = (xy - wz) * sy; + var out5 = (1 - (xx + zz)) * sy; + var out6 = (yz + wx) * sy; + var out8 = (xz + wy) * sz; + var out9 = (yz - wx) * sz; + var out10 = (1 - (xx + yy)) * sz; + out[0] = out0; + out[1] = out1; + out[2] = out2; + out[3] = 0; + out[4] = out4; + out[5] = out5; + out[6] = out6; + out[7] = 0; + out[8] = out8; + out[9] = out9; + out[10] = out10; + out[11] = 0; + out[12] = v[0] + ox - (out0 * ox + out4 * oy + out8 * oz); + out[13] = v[1] + oy - (out1 * ox + out5 * oy + out9 * oz); + out[14] = v[2] + oz - (out2 * ox + out6 * oy + out10 * oz); + out[15] = 1; + return out; + } + /** + * Calculates a 4x4 matrix from the given quaternion + * + * @param {mat4} out mat4 receiving operation result + * @param {ReadonlyQuat} 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. + * The near/far clip planes correspond to a normalized device coordinate Z range of [-1, 1], + * which matches WebGL/OpenGL's clip volume. + * Passing null/undefined/no value for far will generate infinite projection matrix. + * + * @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, can be null or Infinity + * @returns {mat4} out + */ + + function perspectiveNO(out, fovy, aspect, near, far) { + var f = 1.0 / Math.tan(fovy / 2); + 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[11] = -1; + out[12] = 0; + out[13] = 0; + out[15] = 0; + + if (far != null && far !== Infinity) { + var nf = 1 / (near - far); + out[10] = (far + near) * nf; + out[14] = 2 * far * near * nf; + } else { + out[10] = -1; + out[14] = -2 * near; + } + + return out; + } + /** + * Alias for {@link mat4.perspectiveNO} + * @function + */ + + var perspective = perspectiveNO; + /** + * Generates a perspective projection matrix suitable for WebGPU with the given bounds. + * The near/far clip planes correspond to a normalized device coordinate Z range of [0, 1], + * which matches WebGPU/Vulkan/DirectX/Metal's clip volume. + * Passing null/undefined/no value for far will generate infinite projection matrix. + * + * @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, can be null or Infinity + * @returns {mat4} out + */ + + function perspectiveZO(out, fovy, aspect, near, far) { + var f = 1.0 / Math.tan(fovy / 2); + 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[11] = -1; + out[12] = 0; + out[13] = 0; + out[15] = 0; + + if (far != null && far !== Infinity) { + var nf = 1 / (near - far); + out[10] = far * nf; + out[14] = far * near * nf; + } else { + out[10] = -1; + out[14] = -near; + } + + 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. + * The near/far clip planes correspond to a normalized device coordinate Z range of [-1, 1], + * which matches WebGL/OpenGL's clip volume. + * + * @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 orthoNO(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; + } + /** + * Alias for {@link mat4.orthoNO} + * @function + */ + + var ortho = orthoNO; + /** + * Generates a orthogonal projection matrix with the given bounds. + * The near/far clip planes correspond to a normalized device coordinate Z range of [0, 1], + * which matches WebGPU/Vulkan/DirectX/Metal's clip volume. + * + * @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 orthoZO(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] = nf; + out[11] = 0; + out[12] = (left + right) * lr; + out[13] = (top + bottom) * bt; + out[14] = near * nf; + out[15] = 1; + return out; + } + /** + * Generates a look-at matrix with the given eye position, focal point, and up axis. + * If you want a matrix that actually makes an object look at another object, you should use targetTo instead. + * + * @param {mat4} out mat4 frustum matrix will be written into + * @param {ReadonlyVec3} eye Position of the viewer + * @param {ReadonlyVec3} center Point the viewer is looking at + * @param {ReadonlyVec3} up vec3 pointing up + * @returns {mat4} out + */ + + function lookAt(out, eye, center, up) { + var x0, x1, x2, y0, y1, y2, z0, z1, z2, len; + 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) < EPSILON && Math.abs(eyey - centery) < EPSILON && Math.abs(eyez - centerz) < EPSILON) { + return identity$2(out); + } + + z0 = eyex - centerx; + z1 = eyey - centery; + z2 = eyez - centerz; + len = 1 / Math.hypot(z0, z1, z2); + z0 *= len; + z1 *= len; + z2 *= len; + x0 = upy * z2 - upz * z1; + x1 = upz * z0 - upx * z2; + x2 = upx * z1 - upy * z0; + len = Math.hypot(x0, x1, 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.hypot(y0, y1, 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 {ReadonlyVec3} eye Position of the viewer + * @param {ReadonlyVec3} center Point the viewer is looking at + * @param {ReadonlyVec3} 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; + len = x0 * x0 + x1 * x1 + x2 * x2; + + if (len > 0) { + len = 1 / Math.sqrt(len); + x0 *= len; + x1 *= len; + x2 *= len; + } + + 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 {ReadonlyMat4} a matrix to represent as a string + * @returns {String} string representation of the matrix + */ + + function str$5(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 {ReadonlyMat4} a the matrix to calculate Frobenius norm of + * @returns {Number} Frobenius norm + */ + + function frob(a) { + return Math.hypot(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]); + } + /** + * Adds two mat4's + * + * @param {mat4} out the receiving matrix + * @param {ReadonlyMat4} a the first operand + * @param {ReadonlyMat4} b the second operand + * @returns {mat4} out + */ + + function add$5(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 {ReadonlyMat4} a the first operand + * @param {ReadonlyMat4} b the second operand + * @returns {mat4} out + */ + + function subtract$3(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 {ReadonlyMat4} 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 {ReadonlyMat4} a the first operand + * @param {ReadonlyMat4} 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 {ReadonlyMat4} a The first matrix. + * @param {ReadonlyMat4} b The second matrix. + * @returns {Boolean} True if the matrices are equal, false otherwise. + */ + + function exactEquals$5(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 {ReadonlyMat4} a The first matrix. + * @param {ReadonlyMat4} b The second matrix. + * @returns {Boolean} True if the matrices are equal, false otherwise. + */ + + function equals$5(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) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)) && Math.abs(a6 - b6) <= EPSILON * Math.max(1.0, Math.abs(a6), Math.abs(b6)) && Math.abs(a7 - b7) <= EPSILON * Math.max(1.0, Math.abs(a7), Math.abs(b7)) && Math.abs(a8 - b8) <= EPSILON * Math.max(1.0, Math.abs(a8), Math.abs(b8)) && Math.abs(a9 - b9) <= EPSILON * Math.max(1.0, Math.abs(a9), Math.abs(b9)) && Math.abs(a10 - b10) <= EPSILON * Math.max(1.0, Math.abs(a10), Math.abs(b10)) && Math.abs(a11 - b11) <= EPSILON * Math.max(1.0, Math.abs(a11), Math.abs(b11)) && Math.abs(a12 - b12) <= EPSILON * Math.max(1.0, Math.abs(a12), Math.abs(b12)) && Math.abs(a13 - b13) <= EPSILON * Math.max(1.0, Math.abs(a13), Math.abs(b13)) && Math.abs(a14 - b14) <= EPSILON * Math.max(1.0, Math.abs(a14), Math.abs(b14)) && Math.abs(a15 - b15) <= EPSILON * Math.max(1.0, Math.abs(a15), Math.abs(b15)); + } + /** + * Alias for {@link mat4.multiply} + * @function + */ + + var mul$5 = multiply$5; + /** + * Alias for {@link mat4.subtract} + * @function + */ + + var sub$3 = subtract$3; + + var mat4 = /*#__PURE__*/Object.freeze({ + __proto__: null, + create: create$5, + clone: clone$5, + copy: copy$5, + fromValues: fromValues$5, + set: set$5, + identity: identity$2, + transpose: transpose, + invert: invert$2, + adjoint: adjoint, + determinant: determinant, + multiply: multiply$5, + translate: translate$1, + scale: scale$5, + rotate: rotate$1, + rotateX: rotateX$3, + rotateY: rotateY$3, + rotateZ: rotateZ$3, + fromTranslation: fromTranslation$1, + fromScaling: fromScaling, + fromRotation: fromRotation$1, + fromXRotation: fromXRotation, + fromYRotation: fromYRotation, + fromZRotation: fromZRotation, + fromRotationTranslation: fromRotationTranslation$1, + fromQuat2: fromQuat2, + getTranslation: getTranslation$1, + getScaling: getScaling, + getRotation: getRotation, + decompose: decompose, + fromRotationTranslationScale: fromRotationTranslationScale, + fromRotationTranslationScaleOrigin: fromRotationTranslationScaleOrigin, + fromQuat: fromQuat, + frustum: frustum, + perspectiveNO: perspectiveNO, + perspective: perspective, + perspectiveZO: perspectiveZO, + perspectiveFromFieldOfView: perspectiveFromFieldOfView, + orthoNO: orthoNO, + ortho: ortho, + orthoZO: orthoZO, + lookAt: lookAt, + targetTo: targetTo, + str: str$5, + frob: frob, + add: add$5, + subtract: subtract$3, + multiplyScalar: multiplyScalar, + multiplyScalarAndAdd: multiplyScalarAndAdd, + exactEquals: exactEquals$5, + equals: equals$5, + mul: mul$5, + sub: sub$3 + }); + + /** + * 3 Dimensional Vector + * @module vec3 + */ + + /** + * Creates a new, empty vec3 + * + * @returns {vec3} a new 3D vector + */ + + function create$4() { + var out = new ARRAY_TYPE(3); + + if (ARRAY_TYPE != Float32Array) { + out[0] = 0; + out[1] = 0; + out[2] = 0; + } + + return out; + } + /** + * Creates a new vec3 initialized with values from an existing vector + * + * @param {ReadonlyVec3} a vector to clone + * @returns {vec3} a new 3D vector + */ + + function clone$4(a) { + var out = new ARRAY_TYPE(3); + out[0] = a[0]; + out[1] = a[1]; + out[2] = a[2]; + return out; + } + /** + * Calculates the length of a vec3 + * + * @param {ReadonlyVec3} a vector to calculate length of + * @returns {Number} length of a + */ + + function length$4(a) { + var x = a[0]; + var y = a[1]; + var z = a[2]; + return Math.hypot(x, y, z); + } + /** + * Creates a new vec3 initialized with the given values + * + * @param {Number} x X component + * @param {Number} y Y component + * @param {Number} z Z component + * @returns {vec3} a new 3D vector + */ + + function fromValues$4(x, y, z) { + var out = new ARRAY_TYPE(3); + out[0] = x; + out[1] = y; + out[2] = z; + return out; + } + /** + * Copy the values from one vec3 to another + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the source vector + * @returns {vec3} out + */ + + function copy$4(out, a) { + out[0] = a[0]; + out[1] = a[1]; + out[2] = a[2]; + return out; + } + /** + * Set the components of a vec3 to the given values + * + * @param {vec3} out the receiving vector + * @param {Number} x X component + * @param {Number} y Y component + * @param {Number} z Z component + * @returns {vec3} out + */ + + function set$4(out, x, y, z) { + out[0] = x; + out[1] = y; + out[2] = z; + return out; + } + /** + * Adds two vec3's + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @returns {vec3} out + */ + + function add$4(out, a, b) { + out[0] = a[0] + b[0]; + out[1] = a[1] + b[1]; + out[2] = a[2] + b[2]; + return out; + } + /** + * Subtracts vector b from vector a + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @returns {vec3} out + */ + + function subtract$2(out, a, b) { + out[0] = a[0] - b[0]; + out[1] = a[1] - b[1]; + out[2] = a[2] - b[2]; + return out; + } + /** + * Multiplies two vec3's + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @returns {vec3} out + */ + + function multiply$4(out, a, b) { + out[0] = a[0] * b[0]; + out[1] = a[1] * b[1]; + out[2] = a[2] * b[2]; + return out; + } + /** + * Divides two vec3's + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @returns {vec3} out + */ + + function divide$2(out, a, b) { + out[0] = a[0] / b[0]; + out[1] = a[1] / b[1]; + out[2] = a[2] / b[2]; + return out; + } + /** + * Math.ceil the components of a vec3 + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a vector to ceil + * @returns {vec3} out + */ + + function ceil$2(out, a) { + out[0] = Math.ceil(a[0]); + out[1] = Math.ceil(a[1]); + out[2] = Math.ceil(a[2]); + return out; + } + /** + * Math.floor the components of a vec3 + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a vector to floor + * @returns {vec3} out + */ + + function floor$2(out, a) { + out[0] = Math.floor(a[0]); + out[1] = Math.floor(a[1]); + out[2] = Math.floor(a[2]); + return out; + } + /** + * Returns the minimum of two vec3's + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @returns {vec3} out + */ + + function min$2(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]); + return out; + } + /** + * Returns the maximum of two vec3's + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @returns {vec3} out + */ + + function max$2(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]); + return out; + } + /** + * Math.round the components of a vec3 + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a vector to round + * @returns {vec3} out + */ + + function round$2(out, a) { + out[0] = Math.round(a[0]); + out[1] = Math.round(a[1]); + out[2] = Math.round(a[2]); + return out; + } + /** + * Scales a vec3 by a scalar number + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the vector to scale + * @param {Number} b amount to scale the vector by + * @returns {vec3} out + */ + + function scale$4(out, a, b) { + out[0] = a[0] * b; + out[1] = a[1] * b; + out[2] = a[2] * b; + return out; + } + /** + * Adds two vec3's after scaling the second operand by a scalar value + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @param {Number} scale the amount to scale b by before adding + * @returns {vec3} out + */ + + function scaleAndAdd$2(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; + return out; + } + /** + * Calculates the euclidian distance between two vec3's + * + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @returns {Number} distance between a and b + */ + + function distance$2(a, b) { + var x = b[0] - a[0]; + var y = b[1] - a[1]; + var z = b[2] - a[2]; + return Math.hypot(x, y, z); + } + /** + * Calculates the squared euclidian distance between two vec3's + * + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @returns {Number} squared distance between a and b + */ + + function squaredDistance$2(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; + } + /** + * Calculates the squared length of a vec3 + * + * @param {ReadonlyVec3} a vector to calculate squared length of + * @returns {Number} squared length of a + */ + + function squaredLength$4(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 {ReadonlyVec3} a vector to negate + * @returns {vec3} out + */ + + function negate$2(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 {ReadonlyVec3} a vector to invert + * @returns {vec3} out + */ + + function inverse$2(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 {ReadonlyVec3} a vector to normalize + * @returns {vec3} out + */ + + function normalize$4(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 {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @returns {Number} dot product of a and b + */ + + function dot$4(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 {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @returns {vec3} out + */ + + function cross$2(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 {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @param {Number} t interpolation amount, in the range [0-1], between the two inputs + * @returns {vec3} out + */ + + function lerp$4(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 spherical linear interpolation between two vec3's + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @param {Number} t interpolation amount, in the range [0-1], between the two inputs + * @returns {vec3} out + */ + + function slerp$1(out, a, b, t) { + var angle = Math.acos(Math.min(Math.max(dot$4(a, b), -1), 1)); + var sinTotal = Math.sin(angle); + var ratioA = Math.sin((1 - t) * angle) / sinTotal; + var ratioB = Math.sin(t * angle) / sinTotal; + out[0] = ratioA * a[0] + ratioB * b[0]; + out[1] = ratioA * a[1] + ratioB * b[1]; + out[2] = ratioA * a[2] + ratioB * b[2]; + return out; + } + /** + * Performs a hermite interpolation with two control points + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @param {ReadonlyVec3} c the third operand + * @param {ReadonlyVec3} d the fourth operand + * @param {Number} t interpolation amount, in the range [0-1], 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; + return out; + } + /** + * Performs a bezier interpolation with two control points + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the first operand + * @param {ReadonlyVec3} b the second operand + * @param {ReadonlyVec3} c the third operand + * @param {ReadonlyVec3} d the fourth operand + * @param {Number} t interpolation amount, in the range [0-1], 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 omitted, a unit vector will be returned + * @returns {vec3} out + */ + + function random$3(out, scale) { + scale = scale === undefined ? 1.0 : scale; + var r = RANDOM() * 2.0 * Math.PI; + var z = 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 {ReadonlyVec3} a the vector to transform + * @param {ReadonlyMat4} m matrix to transform with + * @returns {vec3} out + */ + + function transformMat4$2(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 {ReadonlyVec3} a the vector to transform + * @param {ReadonlyMat3} m the 3x3 matrix to transform with + * @returns {vec3} out + */ + + function transformMat3$1(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 + * Can also be used for dual quaternions. (Multiply it with the real part) + * + * @param {vec3} out the receiving vector + * @param {ReadonlyVec3} a the vector to transform + * @param {ReadonlyQuat} q quaternion to transform with + * @returns {vec3} out + */ + + function transformQuat$1(out, a, q) { + // benchmarks: https://jsperf.com/quaternion-transform-vec3-implementations-fixed + var qx = q[0], + qy = q[1], + qz = q[2], + qw = q[3]; + var x = a[0], + y = a[1], + z = a[2]; // var qvec = [qx, qy, qz]; + // var uv = vec3.cross([], qvec, a); + + var uvx = qy * z - qz * y, + uvy = qz * x - qx * z, + uvz = qx * y - qy * x; // var uuv = vec3.cross([], qvec, uv); + + var uuvx = qy * uvz - qz * uvy, + uuvy = qz * uvx - qx * uvz, + uuvz = qx * uvy - qy * uvx; // vec3.scale(uv, uv, 2 * w); + + var w2 = qw * 2; + uvx *= w2; + uvy *= w2; + uvz *= w2; // vec3.scale(uuv, uuv, 2); + + uuvx *= 2; + uuvy *= 2; + uuvz *= 2; // return vec3.add(out, a, vec3.add(out, uv, uuv)); + + out[0] = x + uvx + uuvx; + out[1] = y + uvy + uuvy; + out[2] = z + uvz + uuvz; + return out; + } + /** + * Rotate a 3D vector around the x-axis + * @param {vec3} out The receiving vec3 + * @param {ReadonlyVec3} a The vec3 point to rotate + * @param {ReadonlyVec3} b The origin of the rotation + * @param {Number} rad The angle of rotation in radians + * @returns {vec3} out + */ + + function rotateX$2(out, a, b, rad) { + 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(rad) - p[2] * Math.sin(rad); + r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad); //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 {ReadonlyVec3} a The vec3 point to rotate + * @param {ReadonlyVec3} b The origin of the rotation + * @param {Number} rad The angle of rotation in radians + * @returns {vec3} out + */ + + function rotateY$2(out, a, b, rad) { + 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(rad) + p[0] * Math.cos(rad); + r[1] = p[1]; + r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad); //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 {ReadonlyVec3} a The vec3 point to rotate + * @param {ReadonlyVec3} b The origin of the rotation + * @param {Number} rad The angle of rotation in radians + * @returns {vec3} out + */ + + function rotateZ$2(out, a, b, rad) { + 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(rad) - p[1] * Math.sin(rad); + r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad); + 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 {ReadonlyVec3} a The first operand + * @param {ReadonlyVec3} b The second operand + * @returns {Number} The angle in radians + */ + + function angle$1(a, b) { + var ax = a[0], + ay = a[1], + az = a[2], + bx = b[0], + by = b[1], + bz = b[2], + mag = Math.sqrt((ax * ax + ay * ay + az * az) * (bx * bx + by * by + bz * bz)), + cosine = mag && dot$4(a, b) / mag; + return Math.acos(Math.min(Math.max(cosine, -1), 1)); + } + /** + * Set the components of a vec3 to zero + * + * @param {vec3} out the receiving vector + * @returns {vec3} out + */ + + function zero$2(out) { + out[0] = 0.0; + out[1] = 0.0; + out[2] = 0.0; + return out; + } + /** + * Returns a string representation of a vector + * + * @param {ReadonlyVec3} a vector to represent as a string + * @returns {String} string representation of the vector + */ + + function str$4(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 {ReadonlyVec3} a The first vector. + * @param {ReadonlyVec3} b The second vector. + * @returns {Boolean} True if the vectors are equal, false otherwise. + */ + + function exactEquals$4(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 {ReadonlyVec3} a The first vector. + * @param {ReadonlyVec3} b The second vector. + * @returns {Boolean} True if the vectors are equal, false otherwise. + */ + + function equals$4(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) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)); + } + /** + * Alias for {@link vec3.subtract} + * @function + */ + + var sub$2 = subtract$2; + /** + * Alias for {@link vec3.multiply} + * @function + */ + + var mul$4 = multiply$4; + /** + * Alias for {@link vec3.divide} + * @function + */ + + var div$2 = divide$2; + /** + * Alias for {@link vec3.distance} + * @function + */ + + var dist$2 = distance$2; + /** + * Alias for {@link vec3.squaredDistance} + * @function + */ + + var sqrDist$2 = squaredDistance$2; + /** + * Alias for {@link vec3.length} + * @function + */ + + var len$4 = length$4; + /** + * Alias for {@link vec3.squaredLength} + * @function + */ + + var sqrLen$4 = squaredLength$4; + /** + * 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$2 = function () { + var vec = create$4(); + return function (a, stride, offset, count, fn, arg) { + var i, l; + + 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; + }; + }(); + + var vec3 = /*#__PURE__*/Object.freeze({ + __proto__: null, + create: create$4, + clone: clone$4, + length: length$4, + fromValues: fromValues$4, + copy: copy$4, + set: set$4, + add: add$4, + subtract: subtract$2, + multiply: multiply$4, + divide: divide$2, + ceil: ceil$2, + floor: floor$2, + min: min$2, + max: max$2, + round: round$2, + scale: scale$4, + scaleAndAdd: scaleAndAdd$2, + distance: distance$2, + squaredDistance: squaredDistance$2, + squaredLength: squaredLength$4, + negate: negate$2, + inverse: inverse$2, + normalize: normalize$4, + dot: dot$4, + cross: cross$2, + lerp: lerp$4, + slerp: slerp$1, + hermite: hermite, + bezier: bezier, + random: random$3, + transformMat4: transformMat4$2, + transformMat3: transformMat3$1, + transformQuat: transformQuat$1, + rotateX: rotateX$2, + rotateY: rotateY$2, + rotateZ: rotateZ$2, + angle: angle$1, + zero: zero$2, + str: str$4, + exactEquals: exactEquals$4, + equals: equals$4, + sub: sub$2, + mul: mul$4, + div: div$2, + dist: dist$2, + sqrDist: sqrDist$2, + len: len$4, + sqrLen: sqrLen$4, + forEach: forEach$2 + }); + + /** + * 4 Dimensional Vector + * @module vec4 + */ + + /** + * Creates a new, empty vec4 + * + * @returns {vec4} a new 4D vector + */ + + function create$3() { + var out = new ARRAY_TYPE(4); + + if (ARRAY_TYPE != Float32Array) { + 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 {ReadonlyVec4} a vector to clone + * @returns {vec4} a new 4D vector + */ + + function clone$3(a) { + var out = new 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$3(x, y, z, w) { + var out = new 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 {ReadonlyVec4} a the source vector + * @returns {vec4} out + */ + + function copy$3(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$3(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 {ReadonlyVec4} a the first operand + * @param {ReadonlyVec4} b the second operand + * @returns {vec4} out + */ + + function add$3(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 {ReadonlyVec4} a the first operand + * @param {ReadonlyVec4} b the second operand + * @returns {vec4} out + */ + + function subtract$1(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 {ReadonlyVec4} a the first operand + * @param {ReadonlyVec4} b the second operand + * @returns {vec4} out + */ + + function multiply$3(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 {ReadonlyVec4} a the first operand + * @param {ReadonlyVec4} b the second operand + * @returns {vec4} out + */ + + function divide$1(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 {ReadonlyVec4} a vector to ceil + * @returns {vec4} out + */ + + function ceil$1(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 {ReadonlyVec4} a vector to floor + * @returns {vec4} out + */ + + function floor$1(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 {ReadonlyVec4} a the first operand + * @param {ReadonlyVec4} b the second operand + * @returns {vec4} out + */ + + function min$1(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 {ReadonlyVec4} a the first operand + * @param {ReadonlyVec4} b the second operand + * @returns {vec4} out + */ + + function max$1(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 {ReadonlyVec4} a vector to round + * @returns {vec4} out + */ + + function round$1(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 {ReadonlyVec4} a the vector to scale + * @param {Number} b amount to scale the vector by + * @returns {vec4} out + */ + + function scale$3(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 {ReadonlyVec4} a the first operand + * @param {ReadonlyVec4} b the second operand + * @param {Number} scale the amount to scale b by before adding + * @returns {vec4} out + */ + + function scaleAndAdd$1(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 {ReadonlyVec4} a the first operand + * @param {ReadonlyVec4} b the second operand + * @returns {Number} distance between a and b + */ + + function distance$1(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.hypot(x, y, z, w); + } + /** + * Calculates the squared euclidian distance between two vec4's + * + * @param {ReadonlyVec4} a the first operand + * @param {ReadonlyVec4} b the second operand + * @returns {Number} squared distance between a and b + */ + + function squaredDistance$1(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 {ReadonlyVec4} a vector to calculate length of + * @returns {Number} length of a + */ + + function length$3(a) { + var x = a[0]; + var y = a[1]; + var z = a[2]; + var w = a[3]; + return Math.hypot(x, y, z, w); + } + /** + * Calculates the squared length of a vec4 + * + * @param {ReadonlyVec4} a vector to calculate squared length of + * @returns {Number} squared length of a + */ + + function squaredLength$3(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 {ReadonlyVec4} a vector to negate + * @returns {vec4} out + */ + + function negate$1(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 {ReadonlyVec4} a vector to invert + * @returns {vec4} out + */ + + function inverse$1(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 {ReadonlyVec4} a vector to normalize + * @returns {vec4} out + */ + + function normalize$3(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 {ReadonlyVec4} a the first operand + * @param {ReadonlyVec4} b the second operand + * @returns {Number} dot product of a and b + */ + + function dot$3(a, b) { + return a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3]; + } + /** + * Returns the cross-product of three vectors in a 4-dimensional space + * + * @param {ReadonlyVec4} result the receiving vector + * @param {ReadonlyVec4} U the first vector + * @param {ReadonlyVec4} V the second vector + * @param {ReadonlyVec4} W the third vector + * @returns {vec4} result + */ + + function cross$1(out, u, v, w) { + var A = v[0] * w[1] - v[1] * w[0], + B = v[0] * w[2] - v[2] * w[0], + C = v[0] * w[3] - v[3] * w[0], + D = v[1] * w[2] - v[2] * w[1], + E = v[1] * w[3] - v[3] * w[1], + F = v[2] * w[3] - v[3] * w[2]; + var G = u[0]; + var H = u[1]; + var I = u[2]; + var J = u[3]; + out[0] = H * F - I * E + J * D; + out[1] = -(G * F) + I * C - J * B; + out[2] = G * E - H * C + J * A; + out[3] = -(G * D) + H * B - I * A; + return out; + } + /** + * Performs a linear interpolation between two vec4's + * + * @param {vec4} out the receiving vector + * @param {ReadonlyVec4} a the first operand + * @param {ReadonlyVec4} b the second operand + * @param {Number} t interpolation amount, in the range [0-1], between the two inputs + * @returns {vec4} out + */ + + function lerp$3(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 omitted, a unit vector will be returned + * @returns {vec4} out + */ + + function random$2(out, scale) { + scale = scale === undefined ? 1.0 : scale; // Marsaglia, George. Choosing a Point from the Surface of a + // Sphere. Ann. Math. Statist. 43 (1972), no. 2, 645--646. + // http://projecteuclid.org/euclid.aoms/1177692644; + + var v1, v2, v3, v4; + var s1, s2; + + do { + v1 = RANDOM() * 2 - 1; + v2 = RANDOM() * 2 - 1; + s1 = v1 * v1 + v2 * v2; + } while (s1 >= 1); + + do { + v3 = RANDOM() * 2 - 1; + v4 = RANDOM() * 2 - 1; + s2 = v3 * v3 + v4 * v4; + } while (s2 >= 1); + + var d = Math.sqrt((1 - s1) / s2); + out[0] = scale * v1; + out[1] = scale * v2; + out[2] = scale * v3 * d; + out[3] = scale * v4 * d; + return out; + } + /** + * Transforms the vec4 with a mat4. + * + * @param {vec4} out the receiving vector + * @param {ReadonlyVec4} a the vector to transform + * @param {ReadonlyMat4} m matrix to transform with + * @returns {vec4} out + */ + + function transformMat4$1(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 {ReadonlyVec4} a the vector to transform + * @param {ReadonlyQuat} 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; + } + /** + * Set the components of a vec4 to zero + * + * @param {vec4} out the receiving vector + * @returns {vec4} out + */ + + function zero$1(out) { + out[0] = 0.0; + out[1] = 0.0; + out[2] = 0.0; + out[3] = 0.0; + return out; + } + /** + * Returns a string representation of a vector + * + * @param {ReadonlyVec4} a vector to represent as a string + * @returns {String} string representation of the vector + */ + + function str$3(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 {ReadonlyVec4} a The first vector. + * @param {ReadonlyVec4} b The second vector. + * @returns {Boolean} True if the vectors are equal, false otherwise. + */ + + function exactEquals$3(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 {ReadonlyVec4} a The first vector. + * @param {ReadonlyVec4} b The second vector. + * @returns {Boolean} True if the vectors are equal, false otherwise. + */ + + function equals$3(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) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)); + } + /** + * Alias for {@link vec4.subtract} + * @function + */ + + var sub$1 = subtract$1; + /** + * Alias for {@link vec4.multiply} + * @function + */ + + var mul$3 = multiply$3; + /** + * Alias for {@link vec4.divide} + * @function + */ + + var div$1 = divide$1; + /** + * Alias for {@link vec4.distance} + * @function + */ + + var dist$1 = distance$1; + /** + * Alias for {@link vec4.squaredDistance} + * @function + */ + + var sqrDist$1 = squaredDistance$1; + /** + * Alias for {@link vec4.length} + * @function + */ + + var len$3 = length$3; + /** + * Alias for {@link vec4.squaredLength} + * @function + */ + + var sqrLen$3 = squaredLength$3; + /** + * 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$1 = function () { + var vec = create$3(); + return function (a, stride, offset, count, fn, arg) { + var i, l; + + 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; + }; + }(); + + var vec4 = /*#__PURE__*/Object.freeze({ + __proto__: null, + create: create$3, + clone: clone$3, + fromValues: fromValues$3, + copy: copy$3, + set: set$3, + add: add$3, + subtract: subtract$1, + multiply: multiply$3, + divide: divide$1, + ceil: ceil$1, + floor: floor$1, + min: min$1, + max: max$1, + round: round$1, + scale: scale$3, + scaleAndAdd: scaleAndAdd$1, + distance: distance$1, + squaredDistance: squaredDistance$1, + length: length$3, + squaredLength: squaredLength$3, + negate: negate$1, + inverse: inverse$1, + normalize: normalize$3, + dot: dot$3, + cross: cross$1, + lerp: lerp$3, + random: random$2, + transformMat4: transformMat4$1, + transformQuat: transformQuat, + zero: zero$1, + str: str$3, + exactEquals: exactEquals$3, + equals: equals$3, + sub: sub$1, + mul: mul$3, + div: div$1, + dist: dist$1, + sqrDist: sqrDist$1, + len: len$3, + sqrLen: sqrLen$3, + forEach: forEach$1 + }); + + /** + * Quaternion in the format XYZW + * @module quat + */ + + /** + * Creates a new identity quat + * + * @returns {quat} a new quaternion + */ + + function create$2() { + var out = new ARRAY_TYPE(4); + + if (ARRAY_TYPE != Float32Array) { + 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$1(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 {ReadonlyVec3} 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 {ReadonlyQuat} 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 > EPSILON) { + 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; + } + /** + * Gets the angular distance between two unit quaternions + * + * @param {ReadonlyQuat} a Origin unit quaternion + * @param {ReadonlyQuat} b Destination unit quaternion + * @return {Number} Angle, in radians, between the two quaternions + */ + + function getAngle(a, b) { + var dotproduct = dot$2(a, b); + return Math.acos(2 * dotproduct * dotproduct - 1); + } + /** + * Multiplies two quat's + * + * @param {quat} out the receiving quaternion + * @param {ReadonlyQuat} a the first operand + * @param {ReadonlyQuat} b the second operand + * @returns {quat} out + */ + + function multiply$2(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 {ReadonlyQuat} a quat to rotate + * @param {number} rad angle (in radians) to rotate + * @returns {quat} out + */ + + function rotateX$1(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 {ReadonlyQuat} a quat to rotate + * @param {number} rad angle (in radians) to rotate + * @returns {quat} out + */ + + function rotateY$1(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 {ReadonlyQuat} a quat to rotate + * @param {number} rad angle (in radians) to rotate + * @returns {quat} out + */ + + function rotateZ$1(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 {ReadonlyQuat} 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; + } + /** + * Calculate the exponential of a unit quaternion. + * + * @param {quat} out the receiving quaternion + * @param {ReadonlyQuat} a quat to calculate the exponential of + * @returns {quat} out + */ + + function exp(out, a) { + var x = a[0], + y = a[1], + z = a[2], + w = a[3]; + var r = Math.sqrt(x * x + y * y + z * z); + var et = Math.exp(w); + var s = r > 0 ? et * Math.sin(r) / r : 0; + out[0] = x * s; + out[1] = y * s; + out[2] = z * s; + out[3] = et * Math.cos(r); + return out; + } + /** + * Calculate the natural logarithm of a unit quaternion. + * + * @param {quat} out the receiving quaternion + * @param {ReadonlyQuat} a quat to calculate the exponential of + * @returns {quat} out + */ + + function ln(out, a) { + var x = a[0], + y = a[1], + z = a[2], + w = a[3]; + var r = Math.sqrt(x * x + y * y + z * z); + var t = r > 0 ? Math.atan2(r, w) / r : 0; + out[0] = x * t; + out[1] = y * t; + out[2] = z * t; + out[3] = 0.5 * Math.log(x * x + y * y + z * z + w * w); + return out; + } + /** + * Calculate the scalar power of a unit quaternion. + * + * @param {quat} out the receiving quaternion + * @param {ReadonlyQuat} a quat to calculate the exponential of + * @param {Number} b amount to scale the quaternion by + * @returns {quat} out + */ + + function pow(out, a, b) { + ln(out, a); + scale$2(out, out, b); + exp(out, out); + return out; + } + /** + * Performs a spherical linear interpolation between two quat + * + * @param {quat} out the receiving quaternion + * @param {ReadonlyQuat} a the first operand + * @param {ReadonlyQuat} b the second operand + * @param {Number} t interpolation amount, in the range [0-1], 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, cosom, sinom, scale0, scale1; // 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 > EPSILON) { + // 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; + } + /** + * Generates a random unit quaternion + * + * @param {quat} out the receiving quaternion + * @returns {quat} out + */ + + function random$1(out) { + // Implementation of http://planning.cs.uiuc.edu/node198.html + // TODO: Calling random 3 times is probably not the fastest solution + var u1 = RANDOM(); + var u2 = RANDOM(); + var u3 = RANDOM(); + var sqrt1MinusU1 = Math.sqrt(1 - u1); + var sqrtU1 = Math.sqrt(u1); + out[0] = sqrt1MinusU1 * Math.sin(2.0 * Math.PI * u2); + out[1] = sqrt1MinusU1 * Math.cos(2.0 * Math.PI * u2); + out[2] = sqrtU1 * Math.sin(2.0 * Math.PI * u3); + out[3] = sqrtU1 * Math.cos(2.0 * Math.PI * u3); + return out; + } + /** + * Calculates the inverse of a quat + * + * @param {quat} out the receiving quaternion + * @param {ReadonlyQuat} a quat to calculate inverse of + * @returns {quat} out + */ + + function invert$1(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 {ReadonlyQuat} a quat to calculate conjugate of + * @returns {quat} out + */ + + function conjugate$1(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 {ReadonlyMat3} 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; + + 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 using the provided intrinsic order for the conversion. + * + * @param {quat} out the receiving quaternion + * @param {x} x Angle to rotate around X axis in degrees. + * @param {y} y Angle to rotate around Y axis in degrees. + * @param {z} z Angle to rotate around Z axis in degrees. + * @param {'zyx'|'xyz'|'yxz'|'yzx'|'zxy'|'zyx'} order Intrinsic order for conversion, default is zyx. + * @returns {quat} out + * @function + */ + + function fromEuler(out, x, y, z) { + var order = arguments.length > 4 && arguments[4] !== undefined ? arguments[4] : ANGLE_ORDER; + var halfToRad = Math.PI / 360; + x *= halfToRad; + z *= halfToRad; + y *= 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); + + switch (order) { + case "xyz": + 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; + break; + + case "xzy": + 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; + break; + + case "yxz": + 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; + break; + + case "yzx": + 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; + break; + + case "zxy": + 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; + break; + + case "zyx": + 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; + break; + + default: + throw new Error('Unknown angle order ' + order); + } + + return out; + } + /** + * Returns a string representation of a quaternion + * + * @param {ReadonlyQuat} a vector to represent as a string + * @returns {String} string representation of the vector + */ + + function str$2(a) { + return "quat(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ")"; + } + /** + * Creates a new quat initialized with values from an existing quaternion + * + * @param {ReadonlyQuat} a quaternion to clone + * @returns {quat} a new quaternion + * @function + */ + + var clone$2 = clone$3; + /** + * 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$2 = fromValues$3; + /** + * Copy the values from one quat to another + * + * @param {quat} out the receiving quaternion + * @param {ReadonlyQuat} a the source quaternion + * @returns {quat} out + * @function + */ + + var copy$2 = copy$3; + /** + * 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$2 = set$3; + /** + * Adds two quat's + * + * @param {quat} out the receiving quaternion + * @param {ReadonlyQuat} a the first operand + * @param {ReadonlyQuat} b the second operand + * @returns {quat} out + * @function + */ + + var add$2 = add$3; + /** + * Alias for {@link quat.multiply} + * @function + */ + + var mul$2 = multiply$2; + /** + * Scales a quat by a scalar number + * + * @param {quat} out the receiving vector + * @param {ReadonlyQuat} a the vector to scale + * @param {Number} b amount to scale the vector by + * @returns {quat} out + * @function + */ + + var scale$2 = scale$3; + /** + * Calculates the dot product of two quat's + * + * @param {ReadonlyQuat} a the first operand + * @param {ReadonlyQuat} b the second operand + * @returns {Number} dot product of a and b + * @function + */ + + var dot$2 = dot$3; + /** + * Performs a linear interpolation between two quat's + * + * @param {quat} out the receiving quaternion + * @param {ReadonlyQuat} a the first operand + * @param {ReadonlyQuat} b the second operand + * @param {Number} t interpolation amount, in the range [0-1], between the two inputs + * @returns {quat} out + * @function + */ + + var lerp$2 = lerp$3; + /** + * Calculates the length of a quat + * + * @param {ReadonlyQuat} a vector to calculate length of + * @returns {Number} length of a + */ + + var length$2 = length$3; + /** + * Alias for {@link quat.length} + * @function + */ + + var len$2 = length$2; + /** + * Calculates the squared length of a quat + * + * @param {ReadonlyQuat} a vector to calculate squared length of + * @returns {Number} squared length of a + * @function + */ + + var squaredLength$2 = squaredLength$3; + /** + * Alias for {@link quat.squaredLength} + * @function + */ + + var sqrLen$2 = squaredLength$2; + /** + * Normalize a quat + * + * @param {quat} out the receiving quaternion + * @param {ReadonlyQuat} a quaternion to normalize + * @returns {quat} out + * @function + */ + + var normalize$2 = normalize$3; + /** + * Returns whether or not the quaternions have exactly the same elements in the same position (when compared with ===) + * + * @param {ReadonlyQuat} a The first quaternion. + * @param {ReadonlyQuat} b The second quaternion. + * @returns {Boolean} True if the vectors are equal, false otherwise. + */ + + var exactEquals$2 = exactEquals$3; + /** + * Returns whether or not the quaternions point approximately to the same direction. + * + * Both quaternions are assumed to be unit length. + * + * @param {ReadonlyQuat} a The first unit quaternion. + * @param {ReadonlyQuat} b The second unit quaternion. + * @returns {Boolean} True if the quaternions are equal, false otherwise. + */ + + function equals$2(a, b) { + return Math.abs(dot$3(a, b)) >= 1 - EPSILON; + } + /** + * 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 {ReadonlyVec3} a the initial vector + * @param {ReadonlyVec3} b the destination vector + * @returns {quat} out + */ + + var rotationTo = function () { + var tmpvec3 = create$4(); + var xUnitVec3 = fromValues$4(1, 0, 0); + var yUnitVec3 = fromValues$4(0, 1, 0); + return function (out, a, b) { + var dot = dot$4(a, b); + + if (dot < -0.999999) { + cross$2(tmpvec3, xUnitVec3, a); + if (len$4(tmpvec3) < 0.000001) cross$2(tmpvec3, yUnitVec3, a); + normalize$4(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 { + cross$2(tmpvec3, a, b); + out[0] = tmpvec3[0]; + out[1] = tmpvec3[1]; + out[2] = tmpvec3[2]; + out[3] = 1 + dot; + return normalize$2(out, out); + } + }; + }(); + /** + * Performs a spherical linear interpolation with two control points + * + * @param {quat} out the receiving quaternion + * @param {ReadonlyQuat} a the first operand + * @param {ReadonlyQuat} b the second operand + * @param {ReadonlyQuat} c the third operand + * @param {ReadonlyQuat} d the fourth operand + * @param {Number} t interpolation amount, in the range [0-1], between the two inputs + * @returns {quat} out + */ + + var sqlerp = function () { + var temp1 = create$2(); + var temp2 = create$2(); + 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 {ReadonlyVec3} view the vector representing the viewing direction + * @param {ReadonlyVec3} right the vector representing the local "right" direction + * @param {ReadonlyVec3} up the vector representing the local "up" direction + * @returns {quat} out + */ + + var setAxes = function () { + var matr = create$6(); + 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$2(out, fromMat3(out, matr)); + }; + }(); + + var quat = /*#__PURE__*/Object.freeze({ + __proto__: null, + create: create$2, + identity: identity$1, + setAxisAngle: setAxisAngle, + getAxisAngle: getAxisAngle, + getAngle: getAngle, + multiply: multiply$2, + rotateX: rotateX$1, + rotateY: rotateY$1, + rotateZ: rotateZ$1, + calculateW: calculateW, + exp: exp, + ln: ln, + pow: pow, + slerp: slerp, + random: random$1, + invert: invert$1, + conjugate: conjugate$1, + fromMat3: fromMat3, + fromEuler: fromEuler, + str: str$2, + clone: clone$2, + fromValues: fromValues$2, + copy: copy$2, + set: set$2, + add: add$2, + mul: mul$2, + scale: scale$2, + dot: dot$2, + lerp: lerp$2, + length: length$2, + len: len$2, + squaredLength: squaredLength$2, + sqrLen: sqrLen$2, + normalize: normalize$2, + exactEquals: exactEquals$2, + equals: equals$2, + rotationTo: rotationTo, + sqlerp: sqlerp, + setAxes: setAxes + }); + + /** + * Dual Quaternion
+ * Format: [real, dual]
+ * Quaternion format: XYZW
+ * Make sure to have normalized dual quaternions, otherwise the functions may not work as intended.
+ * @module quat2 + */ + + /** + * Creates a new identity dual quat + * + * @returns {quat2} a new dual quaternion [real -> rotation, dual -> translation] + */ + + function create$1() { + var dq = new ARRAY_TYPE(8); + + if (ARRAY_TYPE != Float32Array) { + dq[0] = 0; + dq[1] = 0; + dq[2] = 0; + dq[4] = 0; + dq[5] = 0; + dq[6] = 0; + dq[7] = 0; + } + + dq[3] = 1; + return dq; + } + /** + * Creates a new quat initialized with values from an existing quaternion + * + * @param {ReadonlyQuat2} a dual quaternion to clone + * @returns {quat2} new dual quaternion + * @function + */ + + function clone$1(a) { + var dq = new ARRAY_TYPE(8); + dq[0] = a[0]; + dq[1] = a[1]; + dq[2] = a[2]; + dq[3] = a[3]; + dq[4] = a[4]; + dq[5] = a[5]; + dq[6] = a[6]; + dq[7] = a[7]; + return dq; + } + /** + * Creates a new dual quat initialized with the given values + * + * @param {Number} x1 X component + * @param {Number} y1 Y component + * @param {Number} z1 Z component + * @param {Number} w1 W component + * @param {Number} x2 X component + * @param {Number} y2 Y component + * @param {Number} z2 Z component + * @param {Number} w2 W component + * @returns {quat2} new dual quaternion + * @function + */ + + function fromValues$1(x1, y1, z1, w1, x2, y2, z2, w2) { + var dq = new ARRAY_TYPE(8); + dq[0] = x1; + dq[1] = y1; + dq[2] = z1; + dq[3] = w1; + dq[4] = x2; + dq[5] = y2; + dq[6] = z2; + dq[7] = w2; + return dq; + } + /** + * Creates a new dual quat from the given values (quat and translation) + * + * @param {Number} x1 X component + * @param {Number} y1 Y component + * @param {Number} z1 Z component + * @param {Number} w1 W component + * @param {Number} x2 X component (translation) + * @param {Number} y2 Y component (translation) + * @param {Number} z2 Z component (translation) + * @returns {quat2} new dual quaternion + * @function + */ + + function fromRotationTranslationValues(x1, y1, z1, w1, x2, y2, z2) { + var dq = new ARRAY_TYPE(8); + dq[0] = x1; + dq[1] = y1; + dq[2] = z1; + dq[3] = w1; + var ax = x2 * 0.5, + ay = y2 * 0.5, + az = z2 * 0.5; + dq[4] = ax * w1 + ay * z1 - az * y1; + dq[5] = ay * w1 + az * x1 - ax * z1; + dq[6] = az * w1 + ax * y1 - ay * x1; + dq[7] = -ax * x1 - ay * y1 - az * z1; + return dq; + } + /** + * Creates a dual quat from a quaternion and a translation + * + * @param {ReadonlyQuat2} dual quaternion receiving operation result + * @param {ReadonlyQuat} q a normalized quaternion + * @param {ReadonlyVec3} t translation vector + * @returns {quat2} dual quaternion receiving operation result + * @function + */ + + function fromRotationTranslation(out, q, t) { + var ax = t[0] * 0.5, + ay = t[1] * 0.5, + az = t[2] * 0.5, + bx = q[0], + by = q[1], + bz = q[2], + bw = q[3]; + out[0] = bx; + out[1] = by; + out[2] = bz; + out[3] = bw; + out[4] = ax * bw + ay * bz - az * by; + out[5] = ay * bw + az * bx - ax * bz; + out[6] = az * bw + ax * by - ay * bx; + out[7] = -ax * bx - ay * by - az * bz; + return out; + } + /** + * Creates a dual quat from a translation + * + * @param {ReadonlyQuat2} dual quaternion receiving operation result + * @param {ReadonlyVec3} t translation vector + * @returns {quat2} dual quaternion receiving operation result + * @function + */ + + function fromTranslation(out, t) { + out[0] = 0; + out[1] = 0; + out[2] = 0; + out[3] = 1; + out[4] = t[0] * 0.5; + out[5] = t[1] * 0.5; + out[6] = t[2] * 0.5; + out[7] = 0; + return out; + } + /** + * Creates a dual quat from a quaternion + * + * @param {ReadonlyQuat2} dual quaternion receiving operation result + * @param {ReadonlyQuat} q the quaternion + * @returns {quat2} dual quaternion receiving operation result + * @function + */ + + function fromRotation(out, q) { + out[0] = q[0]; + out[1] = q[1]; + out[2] = q[2]; + out[3] = q[3]; + out[4] = 0; + out[5] = 0; + out[6] = 0; + out[7] = 0; + return out; + } + /** + * Creates a new dual quat from a matrix (4x4) + * + * @param {quat2} out the dual quaternion + * @param {ReadonlyMat4} a the matrix + * @returns {quat2} dual quat receiving operation result + * @function + */ + + function fromMat4(out, a) { + //TODO Optimize this + var outer = create$2(); + getRotation(outer, a); + var t = new ARRAY_TYPE(3); + getTranslation$1(t, a); + fromRotationTranslation(out, outer, t); + return out; + } + /** + * Copy the values from one dual quat to another + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat2} a the source dual quaternion + * @returns {quat2} out + * @function + */ + + function copy$1(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]; + return out; + } + /** + * Set a dual quat to the identity dual quaternion + * + * @param {quat2} out the receiving quaternion + * @returns {quat2} out + */ + + function identity(out) { + out[0] = 0; + out[1] = 0; + out[2] = 0; + out[3] = 1; + out[4] = 0; + out[5] = 0; + out[6] = 0; + out[7] = 0; + return out; + } + /** + * Set the components of a dual quat to the given values + * + * @param {quat2} out the receiving quaternion + * @param {Number} x1 X component + * @param {Number} y1 Y component + * @param {Number} z1 Z component + * @param {Number} w1 W component + * @param {Number} x2 X component + * @param {Number} y2 Y component + * @param {Number} z2 Z component + * @param {Number} w2 W component + * @returns {quat2} out + * @function + */ + + function set$1(out, x1, y1, z1, w1, x2, y2, z2, w2) { + out[0] = x1; + out[1] = y1; + out[2] = z1; + out[3] = w1; + out[4] = x2; + out[5] = y2; + out[6] = z2; + out[7] = w2; + return out; + } + /** + * Gets the real part of a dual quat + * @param {quat} out real part + * @param {ReadonlyQuat2} a Dual Quaternion + * @return {quat} real part + */ + + var getReal = copy$2; + /** + * Gets the dual part of a dual quat + * @param {quat} out dual part + * @param {ReadonlyQuat2} a Dual Quaternion + * @return {quat} dual part + */ + + function getDual(out, a) { + out[0] = a[4]; + out[1] = a[5]; + out[2] = a[6]; + out[3] = a[7]; + return out; + } + /** + * Set the real component of a dual quat to the given quaternion + * + * @param {quat2} out the receiving quaternion + * @param {ReadonlyQuat} q a quaternion representing the real part + * @returns {quat2} out + * @function + */ + + var setReal = copy$2; + /** + * Set the dual component of a dual quat to the given quaternion + * + * @param {quat2} out the receiving quaternion + * @param {ReadonlyQuat} q a quaternion representing the dual part + * @returns {quat2} out + * @function + */ + + function setDual(out, q) { + out[4] = q[0]; + out[5] = q[1]; + out[6] = q[2]; + out[7] = q[3]; + return out; + } + /** + * Gets the translation of a normalized dual quat + * @param {vec3} out translation + * @param {ReadonlyQuat2} a Dual Quaternion to be decomposed + * @return {vec3} translation + */ + + function getTranslation(out, a) { + var ax = a[4], + ay = a[5], + az = a[6], + aw = a[7], + bx = -a[0], + by = -a[1], + bz = -a[2], + bw = a[3]; + out[0] = (ax * bw + aw * bx + ay * bz - az * by) * 2; + out[1] = (ay * bw + aw * by + az * bx - ax * bz) * 2; + out[2] = (az * bw + aw * bz + ax * by - ay * bx) * 2; + return out; + } + /** + * Translates a dual quat by the given vector + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat2} a the dual quaternion to translate + * @param {ReadonlyVec3} v vector to translate by + * @returns {quat2} out + */ + + function translate(out, a, v) { + var ax1 = a[0], + ay1 = a[1], + az1 = a[2], + aw1 = a[3], + bx1 = v[0] * 0.5, + by1 = v[1] * 0.5, + bz1 = v[2] * 0.5, + ax2 = a[4], + ay2 = a[5], + az2 = a[6], + aw2 = a[7]; + out[0] = ax1; + out[1] = ay1; + out[2] = az1; + out[3] = aw1; + out[4] = aw1 * bx1 + ay1 * bz1 - az1 * by1 + ax2; + out[5] = aw1 * by1 + az1 * bx1 - ax1 * bz1 + ay2; + out[6] = aw1 * bz1 + ax1 * by1 - ay1 * bx1 + az2; + out[7] = -ax1 * bx1 - ay1 * by1 - az1 * bz1 + aw2; + return out; + } + /** + * Rotates a dual quat around the X axis + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat2} a the dual quaternion to rotate + * @param {number} rad how far should the rotation be + * @returns {quat2} out + */ + + function rotateX(out, a, rad) { + var bx = -a[0], + by = -a[1], + bz = -a[2], + bw = a[3], + ax = a[4], + ay = a[5], + az = a[6], + aw = a[7], + ax1 = ax * bw + aw * bx + ay * bz - az * by, + ay1 = ay * bw + aw * by + az * bx - ax * bz, + az1 = az * bw + aw * bz + ax * by - ay * bx, + aw1 = aw * bw - ax * bx - ay * by - az * bz; + rotateX$1(out, a, rad); + bx = out[0]; + by = out[1]; + bz = out[2]; + bw = out[3]; + out[4] = ax1 * bw + aw1 * bx + ay1 * bz - az1 * by; + out[5] = ay1 * bw + aw1 * by + az1 * bx - ax1 * bz; + out[6] = az1 * bw + aw1 * bz + ax1 * by - ay1 * bx; + out[7] = aw1 * bw - ax1 * bx - ay1 * by - az1 * bz; + return out; + } + /** + * Rotates a dual quat around the Y axis + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat2} a the dual quaternion to rotate + * @param {number} rad how far should the rotation be + * @returns {quat2} out + */ + + function rotateY(out, a, rad) { + var bx = -a[0], + by = -a[1], + bz = -a[2], + bw = a[3], + ax = a[4], + ay = a[5], + az = a[6], + aw = a[7], + ax1 = ax * bw + aw * bx + ay * bz - az * by, + ay1 = ay * bw + aw * by + az * bx - ax * bz, + az1 = az * bw + aw * bz + ax * by - ay * bx, + aw1 = aw * bw - ax * bx - ay * by - az * bz; + rotateY$1(out, a, rad); + bx = out[0]; + by = out[1]; + bz = out[2]; + bw = out[3]; + out[4] = ax1 * bw + aw1 * bx + ay1 * bz - az1 * by; + out[5] = ay1 * bw + aw1 * by + az1 * bx - ax1 * bz; + out[6] = az1 * bw + aw1 * bz + ax1 * by - ay1 * bx; + out[7] = aw1 * bw - ax1 * bx - ay1 * by - az1 * bz; + return out; + } + /** + * Rotates a dual quat around the Z axis + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat2} a the dual quaternion to rotate + * @param {number} rad how far should the rotation be + * @returns {quat2} out + */ + + function rotateZ(out, a, rad) { + var bx = -a[0], + by = -a[1], + bz = -a[2], + bw = a[3], + ax = a[4], + ay = a[5], + az = a[6], + aw = a[7], + ax1 = ax * bw + aw * bx + ay * bz - az * by, + ay1 = ay * bw + aw * by + az * bx - ax * bz, + az1 = az * bw + aw * bz + ax * by - ay * bx, + aw1 = aw * bw - ax * bx - ay * by - az * bz; + rotateZ$1(out, a, rad); + bx = out[0]; + by = out[1]; + bz = out[2]; + bw = out[3]; + out[4] = ax1 * bw + aw1 * bx + ay1 * bz - az1 * by; + out[5] = ay1 * bw + aw1 * by + az1 * bx - ax1 * bz; + out[6] = az1 * bw + aw1 * bz + ax1 * by - ay1 * bx; + out[7] = aw1 * bw - ax1 * bx - ay1 * by - az1 * bz; + return out; + } + /** + * Rotates a dual quat by a given quaternion (a * q) + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat2} a the dual quaternion to rotate + * @param {ReadonlyQuat} q quaternion to rotate by + * @returns {quat2} out + */ + + function rotateByQuatAppend(out, a, q) { + var qx = q[0], + qy = q[1], + qz = q[2], + qw = q[3], + ax = a[0], + ay = a[1], + az = a[2], + aw = a[3]; + out[0] = ax * qw + aw * qx + ay * qz - az * qy; + out[1] = ay * qw + aw * qy + az * qx - ax * qz; + out[2] = az * qw + aw * qz + ax * qy - ay * qx; + out[3] = aw * qw - ax * qx - ay * qy - az * qz; + ax = a[4]; + ay = a[5]; + az = a[6]; + aw = a[7]; + out[4] = ax * qw + aw * qx + ay * qz - az * qy; + out[5] = ay * qw + aw * qy + az * qx - ax * qz; + out[6] = az * qw + aw * qz + ax * qy - ay * qx; + out[7] = aw * qw - ax * qx - ay * qy - az * qz; + return out; + } + /** + * Rotates a dual quat by a given quaternion (q * a) + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat} q quaternion to rotate by + * @param {ReadonlyQuat2} a the dual quaternion to rotate + * @returns {quat2} out + */ + + function rotateByQuatPrepend(out, q, a) { + var qx = q[0], + qy = q[1], + qz = q[2], + qw = q[3], + bx = a[0], + by = a[1], + bz = a[2], + bw = a[3]; + out[0] = qx * bw + qw * bx + qy * bz - qz * by; + out[1] = qy * bw + qw * by + qz * bx - qx * bz; + out[2] = qz * bw + qw * bz + qx * by - qy * bx; + out[3] = qw * bw - qx * bx - qy * by - qz * bz; + bx = a[4]; + by = a[5]; + bz = a[6]; + bw = a[7]; + out[4] = qx * bw + qw * bx + qy * bz - qz * by; + out[5] = qy * bw + qw * by + qz * bx - qx * bz; + out[6] = qz * bw + qw * bz + qx * by - qy * bx; + out[7] = qw * bw - qx * bx - qy * by - qz * bz; + return out; + } + /** + * Rotates a dual quat around a given axis. Does the normalisation automatically + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat2} a the dual quaternion to rotate + * @param {ReadonlyVec3} axis the axis to rotate around + * @param {Number} rad how far the rotation should be + * @returns {quat2} out + */ + + function rotateAroundAxis(out, a, axis, rad) { + //Special case for rad = 0 + if (Math.abs(rad) < EPSILON) { + return copy$1(out, a); + } + + var axisLength = Math.hypot(axis[0], axis[1], axis[2]); + rad = rad * 0.5; + var s = Math.sin(rad); + var bx = s * axis[0] / axisLength; + var by = s * axis[1] / axisLength; + var bz = s * axis[2] / axisLength; + var bw = Math.cos(rad); + var ax1 = a[0], + ay1 = a[1], + az1 = a[2], + aw1 = a[3]; + out[0] = ax1 * bw + aw1 * bx + ay1 * bz - az1 * by; + out[1] = ay1 * bw + aw1 * by + az1 * bx - ax1 * bz; + out[2] = az1 * bw + aw1 * bz + ax1 * by - ay1 * bx; + out[3] = aw1 * bw - ax1 * bx - ay1 * by - az1 * bz; + var ax = a[4], + ay = a[5], + az = a[6], + aw = a[7]; + out[4] = ax * bw + aw * bx + ay * bz - az * by; + out[5] = ay * bw + aw * by + az * bx - ax * bz; + out[6] = az * bw + aw * bz + ax * by - ay * bx; + out[7] = aw * bw - ax * bx - ay * by - az * bz; + return out; + } + /** + * Adds two dual quat's + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat2} a the first operand + * @param {ReadonlyQuat2} b the second operand + * @returns {quat2} out + * @function + */ + + function add$1(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]; + return out; + } + /** + * Multiplies two dual quat's + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat2} a the first operand + * @param {ReadonlyQuat2} b the second operand + * @returns {quat2} out + */ + + function multiply$1(out, a, b) { + var ax0 = a[0], + ay0 = a[1], + az0 = a[2], + aw0 = a[3], + bx1 = b[4], + by1 = b[5], + bz1 = b[6], + bw1 = b[7], + ax1 = a[4], + ay1 = a[5], + az1 = a[6], + aw1 = a[7], + bx0 = b[0], + by0 = b[1], + bz0 = b[2], + bw0 = b[3]; + out[0] = ax0 * bw0 + aw0 * bx0 + ay0 * bz0 - az0 * by0; + out[1] = ay0 * bw0 + aw0 * by0 + az0 * bx0 - ax0 * bz0; + out[2] = az0 * bw0 + aw0 * bz0 + ax0 * by0 - ay0 * bx0; + out[3] = aw0 * bw0 - ax0 * bx0 - ay0 * by0 - az0 * bz0; + out[4] = ax0 * bw1 + aw0 * bx1 + ay0 * bz1 - az0 * by1 + ax1 * bw0 + aw1 * bx0 + ay1 * bz0 - az1 * by0; + out[5] = ay0 * bw1 + aw0 * by1 + az0 * bx1 - ax0 * bz1 + ay1 * bw0 + aw1 * by0 + az1 * bx0 - ax1 * bz0; + out[6] = az0 * bw1 + aw0 * bz1 + ax0 * by1 - ay0 * bx1 + az1 * bw0 + aw1 * bz0 + ax1 * by0 - ay1 * bx0; + out[7] = aw0 * bw1 - ax0 * bx1 - ay0 * by1 - az0 * bz1 + aw1 * bw0 - ax1 * bx0 - ay1 * by0 - az1 * bz0; + return out; + } + /** + * Alias for {@link quat2.multiply} + * @function + */ + + var mul$1 = multiply$1; + /** + * Scales a dual quat by a scalar number + * + * @param {quat2} out the receiving dual quat + * @param {ReadonlyQuat2} a the dual quat to scale + * @param {Number} b amount to scale the dual quat by + * @returns {quat2} out + * @function + */ + + function scale$1(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; + return out; + } + /** + * Calculates the dot product of two dual quat's (The dot product of the real parts) + * + * @param {ReadonlyQuat2} a the first operand + * @param {ReadonlyQuat2} b the second operand + * @returns {Number} dot product of a and b + * @function + */ + + var dot$1 = dot$2; + /** + * Performs a linear interpolation between two dual quats's + * NOTE: The resulting dual quaternions won't always be normalized (The error is most noticeable when t = 0.5) + * + * @param {quat2} out the receiving dual quat + * @param {ReadonlyQuat2} a the first operand + * @param {ReadonlyQuat2} b the second operand + * @param {Number} t interpolation amount, in the range [0-1], between the two inputs + * @returns {quat2} out + */ + + function lerp$1(out, a, b, t) { + var mt = 1 - t; + if (dot$1(a, b) < 0) t = -t; + out[0] = a[0] * mt + b[0] * t; + out[1] = a[1] * mt + b[1] * t; + out[2] = a[2] * mt + b[2] * t; + out[3] = a[3] * mt + b[3] * t; + out[4] = a[4] * mt + b[4] * t; + out[5] = a[5] * mt + b[5] * t; + out[6] = a[6] * mt + b[6] * t; + out[7] = a[7] * mt + b[7] * t; + return out; + } + /** + * Calculates the inverse of a dual quat. If they are normalized, conjugate is cheaper + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat2} a dual quat to calculate inverse of + * @returns {quat2} out + */ + + function invert(out, a) { + var sqlen = squaredLength$1(a); + out[0] = -a[0] / sqlen; + out[1] = -a[1] / sqlen; + out[2] = -a[2] / sqlen; + out[3] = a[3] / sqlen; + out[4] = -a[4] / sqlen; + out[5] = -a[5] / sqlen; + out[6] = -a[6] / sqlen; + out[7] = a[7] / sqlen; + return out; + } + /** + * Calculates the conjugate of a dual quat + * If the dual quaternion is normalized, this function is faster than quat2.inverse and produces the same result. + * + * @param {quat2} out the receiving quaternion + * @param {ReadonlyQuat2} a quat to calculate conjugate of + * @returns {quat2} out + */ + + function conjugate(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]; + return out; + } + /** + * Calculates the length of a dual quat + * + * @param {ReadonlyQuat2} a dual quat to calculate length of + * @returns {Number} length of a + * @function + */ + + var length$1 = length$2; + /** + * Alias for {@link quat2.length} + * @function + */ + + var len$1 = length$1; + /** + * Calculates the squared length of a dual quat + * + * @param {ReadonlyQuat2} a dual quat to calculate squared length of + * @returns {Number} squared length of a + * @function + */ + + var squaredLength$1 = squaredLength$2; + /** + * Alias for {@link quat2.squaredLength} + * @function + */ + + var sqrLen$1 = squaredLength$1; + /** + * Normalize a dual quat + * + * @param {quat2} out the receiving dual quaternion + * @param {ReadonlyQuat2} a dual quaternion to normalize + * @returns {quat2} out + * @function + */ + + function normalize$1(out, a) { + var magnitude = squaredLength$1(a); + + if (magnitude > 0) { + magnitude = Math.sqrt(magnitude); + var a0 = a[0] / magnitude; + var a1 = a[1] / magnitude; + var a2 = a[2] / magnitude; + var a3 = a[3] / magnitude; + var b0 = a[4]; + var b1 = a[5]; + var b2 = a[6]; + var b3 = a[7]; + var a_dot_b = a0 * b0 + a1 * b1 + a2 * b2 + a3 * b3; + out[0] = a0; + out[1] = a1; + out[2] = a2; + out[3] = a3; + out[4] = (b0 - a0 * a_dot_b) / magnitude; + out[5] = (b1 - a1 * a_dot_b) / magnitude; + out[6] = (b2 - a2 * a_dot_b) / magnitude; + out[7] = (b3 - a3 * a_dot_b) / magnitude; + } + + return out; + } + /** + * Returns a string representation of a dual quaternion + * + * @param {ReadonlyQuat2} a dual quaternion to represent as a string + * @returns {String} string representation of the dual quat + */ + + function str$1(a) { + return "quat2(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ", " + a[4] + ", " + a[5] + ", " + a[6] + ", " + a[7] + ")"; + } + /** + * Returns whether or not the dual quaternions have exactly the same elements in the same position (when compared with ===) + * + * @param {ReadonlyQuat2} a the first dual quaternion. + * @param {ReadonlyQuat2} b the second dual quaternion. + * @returns {Boolean} true if the dual quaternions are equal, false otherwise. + */ + + function exactEquals$1(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]; + } + /** + * Returns whether or not the dual quaternions have approximately the same elements in the same position. + * + * @param {ReadonlyQuat2} a the first dual quat. + * @param {ReadonlyQuat2} b the second dual quat. + * @returns {Boolean} true if the dual quats are equal, false otherwise. + */ + + function equals$1(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]; + 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]; + return Math.abs(a0 - b0) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)) && Math.abs(a6 - b6) <= EPSILON * Math.max(1.0, Math.abs(a6), Math.abs(b6)) && Math.abs(a7 - b7) <= EPSILON * Math.max(1.0, Math.abs(a7), Math.abs(b7)); + } + + var quat2 = /*#__PURE__*/Object.freeze({ + __proto__: null, + create: create$1, + clone: clone$1, + fromValues: fromValues$1, + fromRotationTranslationValues: fromRotationTranslationValues, + fromRotationTranslation: fromRotationTranslation, + fromTranslation: fromTranslation, + fromRotation: fromRotation, + fromMat4: fromMat4, + copy: copy$1, + identity: identity, + set: set$1, + getReal: getReal, + getDual: getDual, + setReal: setReal, + setDual: setDual, + getTranslation: getTranslation, + translate: translate, + rotateX: rotateX, + rotateY: rotateY, + rotateZ: rotateZ, + rotateByQuatAppend: rotateByQuatAppend, + rotateByQuatPrepend: rotateByQuatPrepend, + rotateAroundAxis: rotateAroundAxis, + add: add$1, + multiply: multiply$1, + mul: mul$1, + scale: scale$1, + dot: dot$1, + lerp: lerp$1, + invert: invert, + conjugate: conjugate, + length: length$1, + len: len$1, + squaredLength: squaredLength$1, + sqrLen: sqrLen$1, + normalize: normalize$1, + str: str$1, + exactEquals: exactEquals$1, + equals: equals$1 + }); + + /** + * 2 Dimensional Vector + * @module vec2 + */ + + /** + * Creates a new, empty vec2 + * + * @returns {vec2} a new 2D vector + */ + + function create() { + var out = new ARRAY_TYPE(2); + + if (ARRAY_TYPE != Float32Array) { + out[0] = 0; + out[1] = 0; + } + + return out; + } + /** + * Creates a new vec2 initialized with values from an existing vector + * + * @param {ReadonlyVec2} a vector to clone + * @returns {vec2} a new 2D vector + */ + + function clone(a) { + var out = new 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 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 {ReadonlyVec2} 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 {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} 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 {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} 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 {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} 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 {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} 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 {ReadonlyVec2} 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 {ReadonlyVec2} 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 {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} 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 {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} 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 {ReadonlyVec2} 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 {ReadonlyVec2} 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 {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} 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 {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} 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.hypot(x, y); + } + /** + * Calculates the squared euclidian distance between two vec2's + * + * @param {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} 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 {ReadonlyVec2} a vector to calculate length of + * @returns {Number} length of a + */ + + function length(a) { + var x = a[0], + y = a[1]; + return Math.hypot(x, y); + } + /** + * Calculates the squared length of a vec2 + * + * @param {ReadonlyVec2} 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 {ReadonlyVec2} 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 {ReadonlyVec2} 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 {ReadonlyVec2} 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 {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} 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 {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} 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 {ReadonlyVec2} a the first operand + * @param {ReadonlyVec2} b the second operand + * @param {Number} t interpolation amount, in the range [0-1], 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 omitted, a unit vector will be returned + * @returns {vec2} out + */ + + function random(out, scale) { + scale = scale === undefined ? 1.0 : scale; + var r = 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 {ReadonlyVec2} a the vector to transform + * @param {ReadonlyMat2} 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 {ReadonlyVec2} a the vector to transform + * @param {ReadonlyMat2d} 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 {ReadonlyVec2} a the vector to transform + * @param {ReadonlyMat3} 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 {ReadonlyVec2} a the vector to transform + * @param {ReadonlyMat4} 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; + } + /** + * Rotate a 2D vector + * @param {vec2} out The receiving vec2 + * @param {ReadonlyVec2} a The vec2 point to rotate + * @param {ReadonlyVec2} b The origin of the rotation + * @param {Number} rad The angle of rotation in radians + * @returns {vec2} out + */ + + function rotate(out, a, b, rad) { + //Translate point to the origin + var p0 = a[0] - b[0], + p1 = a[1] - b[1], + sinC = Math.sin(rad), + cosC = Math.cos(rad); //perform rotation and translate to correct position + + out[0] = p0 * cosC - p1 * sinC + b[0]; + out[1] = p0 * sinC + p1 * cosC + b[1]; + return out; + } + /** + * Get the angle between two 2D vectors + * @param {ReadonlyVec2} a The first operand + * @param {ReadonlyVec2} b The second operand + * @returns {Number} The angle in radians + */ + + function angle(a, b) { + var x1 = a[0], + y1 = a[1], + x2 = b[0], + y2 = b[1], + // mag is the product of the magnitudes of a and b + mag = Math.sqrt((x1 * x1 + y1 * y1) * (x2 * x2 + y2 * y2)), + // mag &&.. short circuits if mag == 0 + cosine = mag && (x1 * x2 + y1 * y2) / mag; // Math.min(Math.max(cosine, -1), 1) clamps the cosine between -1 and 1 + + return Math.acos(Math.min(Math.max(cosine, -1), 1)); + } + /** + * Set the components of a vec2 to zero + * + * @param {vec2} out the receiving vector + * @returns {vec2} out + */ + + function zero(out) { + out[0] = 0.0; + out[1] = 0.0; + return out; + } + /** + * Returns a string representation of a vector + * + * @param {ReadonlyVec2} 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 {ReadonlyVec2} a The first vector. + * @param {ReadonlyVec2} 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 {ReadonlyVec2} a The first vector. + * @param {ReadonlyVec2} 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) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)); + } + /** + * Alias for {@link vec2.length} + * @function + */ + + var len = length; + /** + * Alias for {@link vec2.subtract} + * @function + */ + + var sub = subtract; + /** + * Alias for {@link vec2.multiply} + * @function + */ + + var mul = multiply; + /** + * Alias for {@link vec2.divide} + * @function + */ + + var div = divide; + /** + * Alias for {@link vec2.distance} + * @function + */ + + var dist = distance; + /** + * Alias for {@link vec2.squaredDistance} + * @function + */ + + var sqrDist = squaredDistance; + /** + * Alias for {@link vec2.squaredLength} + * @function + */ + + var 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 = function () { + var vec = create(); + return function (a, stride, offset, count, fn, arg) { + var i, l; + + 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; + }; + }(); + + var vec2 = /*#__PURE__*/Object.freeze({ + __proto__: null, + create: create, + clone: clone, + fromValues: fromValues, + copy: copy, + set: set, + add: add, + subtract: subtract, + multiply: multiply, + divide: divide, + ceil: ceil, + floor: floor, + min: min, + max: max, + round: round, + scale: scale, + scaleAndAdd: scaleAndAdd, + distance: distance, + squaredDistance: squaredDistance, + length: length, + squaredLength: squaredLength, + negate: negate, + inverse: inverse, + normalize: normalize, + dot: dot, + cross: cross, + lerp: lerp, + random: random, + transformMat2: transformMat2, + transformMat2d: transformMat2d, + transformMat3: transformMat3, + transformMat4: transformMat4, + rotate: rotate, + angle: angle, + zero: zero, + str: str, + exactEquals: exactEquals, + equals: equals, + len: len, + sub: sub, + mul: mul, + div: div, + dist: dist, + sqrDist: sqrDist, + sqrLen: sqrLen, + forEach: forEach + }); + + exports.glMatrix = common; + exports.mat2 = mat2; + exports.mat2d = mat2d; + exports.mat3 = mat3; + exports.mat4 = mat4; + exports.quat = quat; + exports.quat2 = quat2; + exports.vec2 = vec2; + exports.vec3 = vec3; + exports.vec4 = vec4; + + Object.defineProperty(exports, '__esModule', { value: true }); + + })); + \ No newline at end of file diff --git a/Übung_30112023/Insel/common/initShaders.js b/Übung_30112023/Insel/common/initShaders.js new file mode 100644 index 0000000..95a6657 --- /dev/null +++ b/Übung_30112023/Insel/common/initShaders.js @@ -0,0 +1,46 @@ +// +// initShaders.js +// + +function initShaders( gl, vertexShaderId, fragmentShaderId ) +{ + const compileShader = ( gl, gl_shaderType, shaderSource ) => { + // Create the shader + shader = gl.createShader( gl_shaderType ); + + // Set the shader source code + gl.shaderSource( shader, shaderSource ); + + // Compile the shader to make it readable for the GPU + gl.compileShader( shader ); + var success = gl.getShaderParameter(shader, gl.COMPILE_STATUS); + + if (!success) { + // Something went wrong during compilation; get the error + throw "could not compile shader:" + gl.getShaderInfoLog(shader); + } + else { + return shader; + } + } + + /* + * Setup shader program + */ + vShaderSource = document.querySelector( '#' + vertexShaderId ).text; + fShaderSource = document.querySelector( '#' + fragmentShaderId ).text; + + vertexShader = compileShader( gl, gl.VERTEX_SHADER, vShaderSource ); + fragmentShader = compileShader( gl, gl.FRAGMENT_SHADER, fShaderSource ); + + // Build the program + const program = gl.createProgram(); + + // Attach shaders to it + gl.attachShader( program, vertexShader ); + gl.attachShader( program, fragmentShader ); + + gl.linkProgram( program ); + + return program; +} \ No newline at end of file diff --git a/Übung_30112023/Insel/common/objects3D.js b/Übung_30112023/Insel/common/objects3D.js new file mode 100644 index 0000000..fe8ed0e --- /dev/null +++ b/Übung_30112023/Insel/common/objects3D.js @@ -0,0 +1,437 @@ +class Object3D +{ + constructor() + { + this.posVBO = gl.createBuffer(); + this.colorVBO = gl.createBuffer(); + this.indexVBO = gl.createBuffer(); + } + + initBuffers() + { + // Create VBO for positions and activate it + gl.bindBuffer(gl.ARRAY_BUFFER, this.posVBO); + + // Fill VBO with positions + gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(this.positions), gl.STATIC_DRAW); + + // Create VBO for colors and activate it + gl.bindBuffer(gl.ARRAY_BUFFER, this.colorVBO); + + // Fill VBO with colors + gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(this.colors), gl.STATIC_DRAW); + + // Create VBO for indices and activate it + gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, this.indexVBO); + + // Fill VBO with indices + gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, new Uint16Array(this.indices), gl.STATIC_DRAW); + } + + render() + { + + // Link data in VBO to shader variables + gl.bindBuffer(gl.ARRAY_BUFFER, this.posVBO); + gl.enableVertexAttribArray(posLoc); + gl.vertexAttribPointer(posLoc, 3, gl.FLOAT, false, 0, 0); + + // Link data in VBO to shader variables + gl.bindBuffer(gl.ARRAY_BUFFER, this.colorVBO); + gl.enableVertexAttribArray(colorLoc); + gl.vertexAttribPointer(colorLoc, 4, gl.FLOAT, false, 0, 0); + + // Render + gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, this.indexVBO); + gl.drawElements(gl.TRIANGLES, this.indices.length, gl.UNSIGNED_SHORT, 0); + } +} + + + +class Cube extends Object3D +{ + constructor() + { + super(); + + this.positions = + [ + -1 , -1 , -1 , // index 0 + -1 , -1 , 1 , // index 1 + -1 , 1 , -1 , // index 2 + -1 , 1 , 1 , // index 3 + 1 , -1 , -1 , // index 4 + 1 , -1 , 1 , // index 5 + 1 , 1 , -1 , // index 6 + 1 , 1 , 1 // index 7 + ]; + + this.indices = + [ + 1 , 7 , 3 , 1 , 5 , 7 , // Front + 5 , 6 , 7 , 5 , 4 , 6 , // Right + 4 , 2 , 0 , 4 , 6 , 2 , // Back + 0 , 3 , 2 , 0 , 1 , 3 , // Left + 0 , 5 , 1 , 0 , 4 , 5 , // Bottom + 3 , 6 , 2 , 3 , 7 , 6 // Top + ]; + + this.colors = + [ + 0 , 0 , 0 , 1 , // index 0 + 1 , 0 , 0 , 1 , // index 1 + 0 , 1 , 0 , 1 , // index 2 + 0 , 0 , 1 , 1 , // index 3 + 1 , 1 , 0 , 1 , // index 4 + 1 , 0 , 1 , 1 , // index 5 + 0 , 1 , 1 , 1 , // index 6 + 1 , 1 , 1 , 1 // index 7 + ]; + + this.initBuffers(); + } +} + +class Insel extends Object3D +{ + constructor() + { + super(); + + this.positions = + [ + -0.344503,-0.106899,-2.313329, + 0.254658,0.065420,-2.430170, + 0.506020,-0.293147,-2.207084, + 1.415955,0.064912,-1.957500, + 1.489208,-0.318759,-1.320762, + 1.685851,0.084184,-1.268915, + 2.014675,-0.126122,-0.782958, + 0.957233,-1.089151,-0.905606, + 0.454708,-1.256676,-0.897711, + 0.810208,-0.709404,-1.141590, + 0.739686,-1.249709,-0.541415, + 0.231851,-1.904112,-0.621845, + 0.052641,-1.633897,-0.758536, + -0.020753,-0.743329,-1.377161, + 1.364762,-0.324582,0.647285, + 2.074500,0.090083,0.068582, + 1.608835,0.037777,0.559365, + 1.955554,-0.191974,0.132568, + 1.393132,0.037777,1.383312, + 1.210661,-0.322174,1.134609, + 0.514977,-0.286422,1.576757, + 0.507135,-1.581211,0.348922, + 0.342563,-2.052501,-0.027325, + 0.620568,-1.491335,-0.146730, + 0.745909,-0.723539,0.485115, + 0.089439,-1.345612,0.360167, + 1.089500,-0.770651,-0.314462, + -0.123718,-0.298339,1.611730, + -0.930959,0.037777,1.550149, + -0.866234,-0.291222,1.300128, + -0.414258,0.037777,1.808618, + -1.444312,-0.282136,0.794076, + -1.591571,0.097928,0.827036, + -1.839477,-0.177971,0.145553, + -0.936850,-0.751093,-0.176985, + -0.611777,-1.317411,-0.262516, + -0.326162,-1.310280,0.225784, + 0.289486,-0.743127,0.679448, + 0.020776,-1.770522,0.330532, + -1.675519,-0.336500,-0.606829, + -1.607249,0.010755,-1.680275, + -0.625318,-0.725192,-1.039731, + -2.011082,0.043485,-0.744422, + -1.247727,0.059337,-1.332687, + -0.934732,-0.314137,-1.943344, + -0.184171,-0.491687,-2.096484, + -0.707720,0.065178,-2.205832, + -0.350659,-1.373304,-0.758204, + -0.299529,-2.155551,-0.308846, + -0.086080,-2.478361,-0.004677, + 0.091215,-2.267556,0.130842, + -0.260030,-2.240649,0.060849, + -0.470828,-1.954876,0.024811, + -0.278168,0.037777,-0.209083, + -0.914878,0.210568,-1.267986, + -0.862298,0.231412,-0.781910, + -0.302799,0.520691,-1.301783, + -1.068480,0.101026,-0.360536, + -1.736910,0.103204,0.106553, + 0.236277,0.037777,0.701510, + 0.656348,0.037777,-0.098120, + 0.501631,0.037777,1.688231, + 1.034499,0.275328,-1.269756, + 0.471459,0.267036,-1.698558, + 0.637660,0.376390,-1.207861, + 0.812177,0.491673,-0.567514, + 1.244986,0.398908,-0.324291, + 1.002755,0.639249,-0.717163, + 1.381545,0.288786,-0.765328, + 1.348978,0.284964,-1.076072, + -0.505260,0.213488,-1.704558, + -0.221831,0.306144,-1.838428, + -0.274246,0.065420,-2.359878, + 2.054775,0.091828,-0.677912, + -0.148262,0.773865,-0.947432, + 0.101020,0.922236,-0.839739, + 0.312442,0.779166,-1.109731, + -0.262315,0.721321,-1.533752, + -0.404757,0.197895,-0.782219, + 0.568488,0.537125,-0.913448, + 0.115069,0.760356,-1.450921, + -0.061115,0.654189,-0.643377, + 0.205810,0.801703,-0.757537, + 0.344937,0.262088,-0.492076, + 0.077232,0.934717,-1.202342, + -0.102879,0.422805,-0.489015, + -0.269697,0.566033,-0.874217, + -0.186512,0.743264,-1.152426 + ]; + + this.indices = + [ + 0,1,2, + 3,4,2, + 5,6,4, + 7,8,9, + 8,10,11, + 9,12,13, + 14,15,16, + 14,6,17, + 6,15,17, + 14,18,19, + 18,20,19, + 21,22,23, + 24,25,21, + 24,23,26, + 27,28,29, + 20,30,27, + 28,31,29, + 32,33,31, + 34,35,36, + 36,25,37, + 36,38,25, + 39,40,41, + 40,42,43, + 33,42,39, + 40,44,41, + 44,0,45, + 40,46,44, + 46,0,44, + 41,12,47, + 47,12,48, + 41,35,34, + 48,35,47, + 48,11,49, + 11,50,49, + 50,51,49, + 50,52,51, + 51,48,49, + 53,32,28, + 54,55,56, + 57,58,32, + 59,16,60, + 28,59,53, + 59,61,18, + 62,63,64, + 65,66,67, + 68,5,69, + 70,43,54, + 63,1,71, + 71,72,46, + 13,45,2, + 9,4,7, + 4,26,7, + 26,14,24, + 26,6,14, + 19,37,24, + 37,29,36, + 29,34,36, + 44,13,41, + 2,1,3, + 2,45,0, + 0,72,1, + 9,2,4, + 3,5,4, + 5,73,6, + 7,10,8, + 7,26,10, + 9,8,12, + 8,11,12, + 14,17,15, + 6,73,15, + 14,16,18, + 18,61,20, + 24,21,23, + 21,38,22, + 24,37,25, + 21,25,38, + 26,23,10, + 23,22,10, + 27,30,28, + 20,61,30, + 28,32,31, + 32,58,33, + 36,35,52, + 74,75,76, + 36,52,38, + 40,39,42, + 33,58,42, + 40,43,46, + 46,72,0, + 41,13,12, + 41,47,35, + 48,52,35, + 48,12,11, + 11,22,50, + 11,10,22, + 50,38,52, + 22,38,50, + 48,51,52, + 53,57,32, + 43,42,57, + 57,42,58, + 59,18,16, + 28,30,59, + 59,30,61, + 5,62,69, + 60,16,15, + 66,73,68, + 71,70,77, + 63,3,1, + 71,1,72, + 13,2,9, + 4,6,26, + 14,19,24, + 19,20,37, + 37,27,29, + 37,20,27, + 29,31,34, + 31,33,34, + 34,39,41, + 34,33,39, + 44,45,13, + 55,78,56, + 59,60,53, + 79,60,65, + 77,56,80, + 81,82,75, + 82,76,75, + 60,76,83, + 76,80,84, + 53,83,85, + 86,74,87, + 64,76,79, + 74,84,87, + 53,60,83, + 78,85,86, + 67,64,79, + 67,79,65, + 67,66,68, + 67,69,62, + 67,68,69, + 60,66,65, + 67,62,64, + 62,3,63, + 68,73,5, + 5,3,62, + 66,15,73, + 79,76,60, + 64,63,76, + 60,15,66, + 76,82,83, + 85,82,81, + 85,83,82, + 74,85,81, + 56,78,86, + 56,87,84, + 56,86,87, + 56,84,80, + 71,80,63, + 53,55,57, + 56,77,70, + 56,70,54, + 43,55,54, + 70,46,43, + 71,46,70, + 76,63,80, + 86,85,74, + 74,76,84, + 78,53,85, + 71,77,80, + 53,78,55, + 43,57,55, + 74,81,75 + ]; + + this.colors = []; + for(var i = 0; i < this.positions.length; i += 3) + { + this.colors.push(0.5, 0.5, 0.5, 1); + } + + this.initBuffers(); + } +} + +class River extends Object3D +{ + constructor() + { + super(); + + this.positions = + [ + 0.0, 0.0, 14.0, // index 0 + 0.75, 0.0, 12.5, // index 1 + 1.25, 0.0, 12.5, // index 2 + 1.0, 0.0, 11.0, // index 3 + 2.0, 0.0, 11.0, // index 4 + 0.75, 0.0, 9.5, // index 5 + 2.25, 0.0, 9.5, // index 6 + 0.0, 0.0, 8.0, // index 7 + 2.0, 0.0, 8.0, // index 8 + -2.25, 0.0, 6.1875, // index 9 + 0.25, 0.0, 6.1875, // index 10 + -3.0, 0.0, 4.0, // index 11 + 0.0, 0.0, 4.0, // index 12 + -2.25, 0.0, 1.8125, // index 13 + 1.25, 0.0, 1.8125, // index 14 + 0.0, 0.0, 0.0, // index 15 + 4.0, 0.0, 0.0, // index 16 + 0.0, -7.0, 0.0, // index 17 -> additional for waterfall + 4.0, -6.0, 0.0 // index 18 -> additional for waterfall + ]; + + this.indices = + [ + 0, 1, 2, + 1, 2, 3, + 2, 3, 4, + 3, 4, 5, + 4, 5, 6, + 5, 6, 7, + 6, 7, 8, + 7, 8, 9, + 8, 9, 10, + 9, 10, 11, + 10, 11, 12, + 11, 12, 13, + 12, 13, 14, + 13, 14, 15, + 14, 15, 16, + 15, 16, 17, // additional for waterfall + 16, 17, 18 // additional for waterfall + ]; + + this.colors = []; + for(var i = 0; i < this.positions.length; i += 3) { + this.colors.push(0.2, 0.2, 0.8, 1); + } + + this.initBuffers(); + } +} \ No newline at end of file diff --git a/Übung_30112023/Insel/index.html b/Übung_30112023/Insel/index.html new file mode 100644 index 0000000..71f233c --- /dev/null +++ b/Übung_30112023/Insel/index.html @@ -0,0 +1,69 @@ + + + + + WebGL Example + + + + + + + + +

Lorem Ipsum

+ + + If you see this, your browser doesn't support WebGL. + + + + + + diff --git a/Übung_30112023/Insel/main.js b/Übung_30112023/Insel/main.js new file mode 100644 index 0000000..e4a5ce8 --- /dev/null +++ b/Übung_30112023/Insel/main.js @@ -0,0 +1,534 @@ +let gl; +let program; +let positions1, + positions2, + colors1, + colors2, + indices1, + indices2; +let posVBO1, + posVBO2, + colorVBO1, + colorVBO2, + indexVBO1, + indexVBO2; +let posLoc, + colorLoc; +let objects = []; +let lastTimestamp; +const {mat4, mat3, vec3} = glMatrix; + +function main() { + + // Get canvas and setup WebGL context + const canvas = document.getElementById("gl-canvas"); + gl = canvas.getContext('webgl2'); + + // Configure viewport + gl.viewport(0,0,canvas.width,canvas.height); + gl.clearColor(1.0,1.0,1.0,1.0); + + gl.enable(gl.DEPTH_TEST); + + // Init shader program via additional function and bind it + program = initShaders(gl, "vertex-shader", "fragment-shader"); + gl.useProgram(program); + + // Get locations of shader variables + posLoc = gl.getAttribLocation(program, "vPosition"); + colorLoc = gl.getAttribLocation(program, "vColor"); + + const moveLoc = gl.getUniformLocation(program, "moveDown"); + + transformMatrix = [ + 1, 0, 0, 0, + 0, 1, 0, -0.2, + 0, 0, 1, 0, + 0, 0, 0, 1, + ]; + + gl.uniformMatrix4fv(moveLoc, false, transformMatrix) + + const viewLoc = gl.getUniformLocation(program, "viewMatrix"); + + /* + viewMatrix = [ + 0.1767766922712326, -0.0589255653321743, -0.013334667310118675, 0, + 0, 0.2357022613286972, -0.006667333655059338, 0, + -0.1767766922712326, -0.0589255653321743, -0.013334667310118675, 0, + 0, 0, -0.8801880478858948, 1 + ]; + */ + + viewMatrix = mat4.create(); + projectionMatrix = mat4.create(); + modelViewProjection = mat4.create(); + mat4.perspective(projectionMatrix, 90.0, 1.0, 0.0001, 1000.0); + + gl.uniformMatrix4fv(viewLoc, false, viewMatrix); + + + // Only clear once + gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT); + + objects.push(new Insel()); + objects.push(new River()); + + //initListener(); + + window.requestAnimationFrame(render); +}; + + +function initListener() +{ + document.body.addEventListener('mousemove', printMouseMovement); + document.body.addEventListener('keydown', printKeyPress); +} + +function printMouseMovement(e) +{ + console.log('mousemoved'); +} + +function printKeyPress(e) +{ + console.log(e.which); +} + + +function render(timestamp) +{ + if(lastTimestamp == undefined) + { + lastTimestamp = timestamp; + } + + const elapsed = timestamp - lastTimestamp; + + let p = [3 * Math.sin(0.001 * timestamp), 1, 3 * Math.cos(0.001 * timestamp)]; + mat4.lookAt(viewMatrix, p, [0, 0, 0], [0, 1, 0]); + + mat4.multiply(modelViewProjection, projectionMatrix, viewMatrix); + viewLoc = gl.getUniformLocation(program, "viewMatrix"); + gl.uniformMatrix4fv(viewLoc, false, modelViewProjection); + + for (var i = 0; i < objects.length; i++) + { + objects[i].render(); + } + + window.requestAnimationFrame(render); +} + +function init1() { + + // Specify geometry + positions1 = [ + -0.344503,-0.106899,-2.313329, + 0.254658,0.065420,-2.430170, + 0.506020,-0.293147,-2.207084, + 1.415955,0.064912,-1.957500, + 1.489208,-0.318759,-1.320762, + 1.685851,0.084184,-1.268915, + 2.014675,-0.126122,-0.782958, + 0.957233,-1.089151,-0.905606, + 0.454708,-1.256676,-0.897711, + 0.810208,-0.709404,-1.141590, + 0.739686,-1.249709,-0.541415, + 0.231851,-1.904112,-0.621845, + 0.052641,-1.633897,-0.758536, + -0.020753,-0.743329,-1.377161, + 1.364762,-0.324582,0.647285, + 2.074500,0.090083,0.068582, + 1.608835,0.037777,0.559365, + 1.955554,-0.191974,0.132568, + 1.393132,0.037777,1.383312, + 1.210661,-0.322174,1.134609, + 0.514977,-0.286422,1.576757, + 0.507135,-1.581211,0.348922, + 0.342563,-2.052501,-0.027325, + 0.620568,-1.491335,-0.146730, + 0.745909,-0.723539,0.485115, + 0.089439,-1.345612,0.360167, + 1.089500,-0.770651,-0.314462, + -0.123718,-0.298339,1.611730, + -0.930959,0.037777,1.550149, + -0.866234,-0.291222,1.300128, + -0.414258,0.037777,1.808618, + -1.444312,-0.282136,0.794076, + -1.591571,0.097928,0.827036, + -1.839477,-0.177971,0.145553, + -0.936850,-0.751093,-0.176985, + -0.611777,-1.317411,-0.262516, + -0.326162,-1.310280,0.225784, + 0.289486,-0.743127,0.679448, + 0.020776,-1.770522,0.330532, + -1.675519,-0.336500,-0.606829, + -1.607249,0.010755,-1.680275, + -0.625318,-0.725192,-1.039731, + -2.011082,0.043485,-0.744422, + -1.247727,0.059337,-1.332687, + -0.934732,-0.314137,-1.943344, + -0.184171,-0.491687,-2.096484, + -0.707720,0.065178,-2.205832, + -0.350659,-1.373304,-0.758204, + -0.299529,-2.155551,-0.308846, + -0.086080,-2.478361,-0.004677, + 0.091215,-2.267556,0.130842, + -0.260030,-2.240649,0.060849, + -0.470828,-1.954876,0.024811, + -0.278168,0.037777,-0.209083, + -0.914878,0.210568,-1.267986, + -0.862298,0.231412,-0.781910, + -0.302799,0.520691,-1.301783, + -1.068480,0.101026,-0.360536, + -1.736910,0.103204,0.106553, + 0.236277,0.037777,0.701510, + 0.656348,0.037777,-0.098120, + 0.501631,0.037777,1.688231, + 1.034499,0.275328,-1.269756, + 0.471459,0.267036,-1.698558, + 0.637660,0.376390,-1.207861, + 0.812177,0.491673,-0.567514, + 1.244986,0.398908,-0.324291, + 1.002755,0.639249,-0.717163, + 1.381545,0.288786,-0.765328, + 1.348978,0.284964,-1.076072, + -0.505260,0.213488,-1.704558, + -0.221831,0.306144,-1.838428, + -0.274246,0.065420,-2.359878, + 2.054775,0.091828,-0.677912, + -0.148262,0.773865,-0.947432, + 0.101020,0.922236,-0.839739, + 0.312442,0.779166,-1.109731, + -0.262315,0.721321,-1.533752, + -0.404757,0.197895,-0.782219, + 0.568488,0.537125,-0.913448, + 0.115069,0.760356,-1.450921, + -0.061115,0.654189,-0.643377, + 0.205810,0.801703,-0.757537, + 0.344937,0.262088,-0.492076, + 0.077232,0.934717,-1.202342, + -0.102879,0.422805,-0.489015, + -0.269697,0.566033,-0.874217, + -0.186512,0.743264,-1.152426 + ]; + + indices1 = [ + 0,1,2, + 3,4,2, + 5,6,4, + 7,8,9, + 8,10,11, + 9,12,13, + 14,15,16, + 14,6,17, + 6,15,17, + 14,18,19, + 18,20,19, + 21,22,23, + 24,25,21, + 24,23,26, + 27,28,29, + 20,30,27, + 28,31,29, + 32,33,31, + 34,35,36, + 36,25,37, + 36,38,25, + 39,40,41, + 40,42,43, + 33,42,39, + 40,44,41, + 44,0,45, + 40,46,44, + 46,0,44, + 41,12,47, + 47,12,48, + 41,35,34, + 48,35,47, + 48,11,49, + 11,50,49, + 50,51,49, + 50,52,51, + 51,48,49, + 53,32,28, + 54,55,56, + 57,58,32, + 59,16,60, + 28,59,53, + 59,61,18, + 62,63,64, + 65,66,67, + 68,5,69, + 70,43,54, + 63,1,71, + 71,72,46, + 13,45,2, + 9,4,7, + 4,26,7, + 26,14,24, + 26,6,14, + 19,37,24, + 37,29,36, + 29,34,36, + 44,13,41, + 2,1,3, + 2,45,0, + 0,72,1, + 9,2,4, + 3,5,4, + 5,73,6, + 7,10,8, + 7,26,10, + 9,8,12, + 8,11,12, + 14,17,15, + 6,73,15, + 14,16,18, + 18,61,20, + 24,21,23, + 21,38,22, + 24,37,25, + 21,25,38, + 26,23,10, + 23,22,10, + 27,30,28, + 20,61,30, + 28,32,31, + 32,58,33, + 36,35,52, + 74,75,76, + 36,52,38, + 40,39,42, + 33,58,42, + 40,43,46, + 46,72,0, + 41,13,12, + 41,47,35, + 48,52,35, + 48,12,11, + 11,22,50, + 11,10,22, + 50,38,52, + 22,38,50, + 48,51,52, + 53,57,32, + 43,42,57, + 57,42,58, + 59,18,16, + 28,30,59, + 59,30,61, + 5,62,69, + 60,16,15, + 66,73,68, + 71,70,77, + 63,3,1, + 71,1,72, + 13,2,9, + 4,6,26, + 14,19,24, + 19,20,37, + 37,27,29, + 37,20,27, + 29,31,34, + 31,33,34, + 34,39,41, + 34,33,39, + 44,45,13, + 55,78,56, + 59,60,53, + 79,60,65, + 77,56,80, + 81,82,75, + 82,76,75, + 60,76,83, + 76,80,84, + 53,83,85, + 86,74,87, + 64,76,79, + 74,84,87, + 53,60,83, + 78,85,86, + 67,64,79, + 67,79,65, + 67,66,68, + 67,69,62, + 67,68,69, + 60,66,65, + 67,62,64, + 62,3,63, + 68,73,5, + 5,3,62, + 66,15,73, + 79,76,60, + 64,63,76, + 60,15,66, + 76,82,83, + 85,82,81, + 85,83,82, + 74,85,81, + 56,78,86, + 56,87,84, + 56,86,87, + 56,84,80, + 71,80,63, + 53,55,57, + 56,77,70, + 56,70,54, + 43,55,54, + 70,46,43, + 71,46,70, + 76,63,80, + 86,85,74, + 74,76,84, + 78,53,85, + 71,77,80, + 53,78,55, + 43,57,55, + 74,81,75 + ]; + + colors1 = []; + for(var i = 0; i < positions1.length; i += 3) { + colors1.push(0.5, 0.5, 0.5, 1); + } + + initBuffers1(); +} + +function initBuffers1() { + + // Create VBO for positions and activate it + posVBO1 = gl.createBuffer(); + gl.bindBuffer(gl.ARRAY_BUFFER, posVBO1); + + // Fill VBO with positions + gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(positions1), gl.STATIC_DRAW); + + // Create VBO for colors and activate it + colorVBO1 = gl.createBuffer(); + gl.bindBuffer(gl.ARRAY_BUFFER, colorVBO1); + + // Fill VBO with colors + gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(colors1), gl.STATIC_DRAW); + + // Create VBO for indices and activate it + indexVBO1 = gl.createBuffer(); + gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, indexVBO1); + + // Fill VBO with indices + gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, new Uint16Array(indices1), gl.STATIC_DRAW); +} + +function render1() { + + // Link data in VBO to shader variables + gl.bindBuffer(gl.ARRAY_BUFFER, posVBO1); + gl.enableVertexAttribArray(posLoc); + gl.vertexAttribPointer(posLoc, 3, gl.FLOAT, false, 0, 0); + + // Link data in VBO to shader variables + gl.bindBuffer(gl.ARRAY_BUFFER, colorVBO1); + gl.enableVertexAttribArray(colorLoc); + gl.vertexAttribPointer(colorLoc, 4, gl.FLOAT, false, 0, 0); + + // Render + gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, indexVBO1); + gl.drawElements(gl.TRIANGLES, indices1.length, gl.UNSIGNED_SHORT, 0); +} + +function init2() { + + // Specify geometry + positions2 = [ + 0.0, 0.0, 14.0, // index 0 + 0.75, 0.0, 12.5, // index 1 + 1.25, 0.0, 12.5, // index 2 + 1.0, 0.0, 11.0, // index 3 + 2.0, 0.0, 11.0, // index 4 + 0.75, 0.0, 9.5, // index 5 + 2.25, 0.0, 9.5, // index 6 + 0.0, 0.0, 8.0, // index 7 + 2.0, 0.0, 8.0, // index 8 + -2.25, 0.0, 6.1875, // index 9 + 0.25, 0.0, 6.1875, // index 10 + -3.0, 0.0, 4.0, // index 11 + 0.0, 0.0, 4.0, // index 12 + -2.25, 0.0, 1.8125, // index 13 + 1.25, 0.0, 1.8125, // index 14 + 0.0, 0.0, 0.0, // index 15 + 4.0, 0.0, 0.0, // index 16 + 0.0, -7.0, 0.0, // index 17 -> additional for waterfall + 4.0, -6.0, 0.0 // index 18 -> additional for waterfall + ]; + + indices2 = [ + 0, 1, 2, + 1, 2, 3, + 2, 3, 4, + 3, 4, 5, + 4, 5, 6, + 5, 6, 7, + 6, 7, 8, + 7, 8, 9, + 8, 9, 10, + 9, 10, 11, + 10, 11, 12, + 11, 12, 13, + 12, 13, 14, + 13, 14, 15, + 14, 15, 16, + 15, 16, 17, // additional for waterfall + 16, 17, 18 // additional for waterfall + ]; + + colors2 = []; + for(var i = 0; i < positions2.length; i += 3) { + colors2.push(0.2, 0.2, 0.8, 1); + } + + initBuffers2(); +} + +function initBuffers2() { + // Create VBO for positions and activate it + posVBO2 = gl.createBuffer(); + gl.bindBuffer(gl.ARRAY_BUFFER, posVBO2); + + // Fill VBO with positions + gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(positions2), gl.STATIC_DRAW); + + // Create VBO for colors and activate it + colorVBO2 = gl.createBuffer(); + gl.bindBuffer(gl.ARRAY_BUFFER, colorVBO2); + + // Fill VBO with colors + gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(colors2), gl.STATIC_DRAW); + + // Create VBO for indices and activate it + indexVBO2 = gl.createBuffer(); + gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, indexVBO2); + + // Fill VBO with indices + gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, new Uint16Array(indices2), gl.STATIC_DRAW); +} + +function render2() { + // Link data in VBO to shader variables + gl.bindBuffer(gl.ARRAY_BUFFER, posVBO2); + gl.enableVertexAttribArray(posLoc); + gl.vertexAttribPointer(posLoc, 3, gl.FLOAT, false, 0, 0); + + // Link data in VBO to shader variables + gl.bindBuffer(gl.ARRAY_BUFFER, colorVBO2); + gl.enableVertexAttribArray(colorLoc); + gl.vertexAttribPointer(colorLoc, 4, gl.FLOAT, false, 0, 0); + + // Render + gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, indexVBO2); + gl.drawElements(gl.TRIANGLES, indices2.length, gl.UNSIGNED_SHORT, 0); +} + +main(); diff --git a/Übung_30112023/uebung-woche7.pdf b/Übung_30112023/uebung-woche7.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b0fc5bb207746d02d9c1235dff4a0c63fd514cdc GIT binary patch literal 561678 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