166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved. 266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 366a37686207944273ced825e0e8b6b6375f8c3deJamie GennisRedistribution and use in source and binary forms, with or without modification, 466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennisare permitted provided that the following conditions are met: 566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Redistributions of source code must retain the above copyright notice, this 766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis list of conditions and the following disclaimer. 866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Redistributions in binary form must reproduce the above copyright notice, 966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis this list of conditions and the following disclaimer in the documentation 1066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis and/or other materials provided with the distribution. 1166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 1266a37686207944273ced825e0e8b6b6375f8c3deJamie GennisTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND 1366a37686207944273ced825e0e8b6b6375f8c3deJamie GennisANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED 1466a37686207944273ced825e0e8b6b6375f8c3deJamie GennisWARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE 1566a37686207944273ced825e0e8b6b6375f8c3deJamie GennisDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR 1666a37686207944273ced825e0e8b6b6375f8c3deJamie GennisANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES 1766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 1866a37686207944273ced825e0e8b6b6375f8c3deJamie GennisLOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON 1966a37686207944273ced825e0e8b6b6375f8c3deJamie GennisANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 2066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 2166a37686207944273ced825e0e8b6b6375f8c3deJamie GennisSOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ 2266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 2366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 2466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @class 3x3 Matrix 2566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @name mat3 2666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 2766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennisvar mat3 = {}; 2866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 2966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 3066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Creates a new identity mat3 3166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 3266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} a new 3x3 matrix 3366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 3466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.create = function() { 3566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis var out = new GLMAT_ARRAY_TYPE(9); 3666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = 1; 3766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = 0; 3866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = 0; 3966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = 0; 4066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = 1; 4166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = 0; 4266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = 0; 4366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = 0; 4466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = 1; 4566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 4666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 4766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 4866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 4966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Copies the upper-left 3x3 values into the given mat3. 5066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 5166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} out the receiving 3x3 matrix 5266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat4} a the source 4x4 matrix 5366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} out 5466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 5566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.fromMat4 = function(out, a) { 5666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = a[0]; 5766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = a[1]; 5866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = a[2]; 5966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = a[4]; 6066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = a[5]; 6166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = a[6]; 6266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = a[8]; 6366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = a[9]; 6466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = a[10]; 6566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 6666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 6766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 6866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 6966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Creates a new mat3 initialized with values from an existing matrix 7066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 7166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} a matrix to clone 7266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} a new 3x3 matrix 7366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 7466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.clone = function(a) { 7566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis var out = new GLMAT_ARRAY_TYPE(9); 7666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = a[0]; 7766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = a[1]; 7866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = a[2]; 7966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = a[3]; 8066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = a[4]; 8166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = a[5]; 8266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = a[6]; 8366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = a[7]; 8466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = a[8]; 8566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 8666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 8766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 8866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 8966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Copy the values from one mat3 to another 9066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 9166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} out the receiving matrix 9266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} a the source matrix 9366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} out 9466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 9566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.copy = function(out, a) { 9666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = a[0]; 9766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = a[1]; 9866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = a[2]; 9966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = a[3]; 10066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = a[4]; 10166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = a[5]; 10266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = a[6]; 10366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = a[7]; 10466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = a[8]; 10566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 10666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 10766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 10866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 10966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Set a mat3 to the identity matrix 11066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 11166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} out the receiving matrix 11266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} out 11366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 11466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.identity = function(out) { 11566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = 1; 11666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = 0; 11766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = 0; 11866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = 0; 11966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = 1; 12066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = 0; 12166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = 0; 12266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = 0; 12366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = 1; 12466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 12566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 12666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 12766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 12866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Transpose the values of a mat3 12966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 13066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} out the receiving matrix 13166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} a the source matrix 13266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} out 13366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 13466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.transpose = function(out, a) { 13566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis // If we are transposing ourselves we can skip a few steps but have to cache some values 13666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis if (out === a) { 13766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis var a01 = a[1], a02 = a[2], a12 = a[5]; 13866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = a[3]; 13966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = a[6]; 14066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = a01; 14166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = a[7]; 14266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = a02; 14366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = a12; 14466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis } else { 14566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = a[0]; 14666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = a[3]; 14766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = a[6]; 14866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = a[1]; 14966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = a[4]; 15066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = a[7]; 15166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = a[2]; 15266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = a[5]; 15366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = a[8]; 15466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis } 15566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 15666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 15766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 15866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 15966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 16066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Inverts a mat3 16166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 16266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} out the receiving matrix 16366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} a the source matrix 16466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} out 16566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 16666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.invert = function(out, a) { 16766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis var a00 = a[0], a01 = a[1], a02 = a[2], 16866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a10 = a[3], a11 = a[4], a12 = a[5], 16966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a20 = a[6], a21 = a[7], a22 = a[8], 17066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 17166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis b01 = a22 * a11 - a12 * a21, 17266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis b11 = -a22 * a10 + a12 * a20, 17366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis b21 = a21 * a10 - a11 * a20, 17466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 17566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis // Calculate the determinant 17666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis det = a00 * b01 + a01 * b11 + a02 * b21; 17766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 17866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis if (!det) { 17966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return null; 18066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis } 18166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis det = 1.0 / det; 18266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 18366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = b01 * det; 18466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = (-a22 * a01 + a02 * a21) * det; 18566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = (a12 * a01 - a02 * a11) * det; 18666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = b11 * det; 18766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = (a22 * a00 - a02 * a20) * det; 18866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = (-a12 * a00 + a02 * a10) * det; 18966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = b21 * det; 19066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = (-a21 * a00 + a01 * a20) * det; 19166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = (a11 * a00 - a01 * a10) * det; 19266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 19366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 19466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 19566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 19666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Calculates the adjugate of a mat3 19766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 19866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} out the receiving matrix 19966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} a the source matrix 20066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} out 20166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 20266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.adjoint = function(out, a) { 20366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis var a00 = a[0], a01 = a[1], a02 = a[2], 20466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a10 = a[3], a11 = a[4], a12 = a[5], 20566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a20 = a[6], a21 = a[7], a22 = a[8]; 20666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 20766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = (a11 * a22 - a12 * a21); 20866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = (a02 * a21 - a01 * a22); 20966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = (a01 * a12 - a02 * a11); 21066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = (a12 * a20 - a10 * a22); 21166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = (a00 * a22 - a02 * a20); 21266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = (a02 * a10 - a00 * a12); 21366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = (a10 * a21 - a11 * a20); 21466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = (a01 * a20 - a00 * a21); 21566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = (a00 * a11 - a01 * a10); 21666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 21766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 21866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 21966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 22066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Calculates the determinant of a mat3 22166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 22266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} a the source matrix 22366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {Number} determinant of a 22466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 22566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.determinant = function (a) { 22666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis var a00 = a[0], a01 = a[1], a02 = a[2], 22766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a10 = a[3], a11 = a[4], a12 = a[5], 22866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a20 = a[6], a21 = a[7], a22 = a[8]; 22966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 23066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20); 23166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 23266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 23366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 23466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Multiplies two mat3's 23566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 23666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} out the receiving matrix 23766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} a the first operand 23866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} b the second operand 23966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} out 24066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 24166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.multiply = function (out, a, b) { 24266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis var a00 = a[0], a01 = a[1], a02 = a[2], 24366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a10 = a[3], a11 = a[4], a12 = a[5], 24466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a20 = a[6], a21 = a[7], a22 = a[8], 24566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 24666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis b00 = b[0], b01 = b[1], b02 = b[2], 24766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis b10 = b[3], b11 = b[4], b12 = b[5], 24866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis b20 = b[6], b21 = b[7], b22 = b[8]; 24966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 25066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = b00 * a00 + b01 * a10 + b02 * a20; 25166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = b00 * a01 + b01 * a11 + b02 * a21; 25266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = b00 * a02 + b01 * a12 + b02 * a22; 25366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 25466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = b10 * a00 + b11 * a10 + b12 * a20; 25566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = b10 * a01 + b11 * a11 + b12 * a21; 25666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = b10 * a02 + b11 * a12 + b12 * a22; 25766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 25866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = b20 * a00 + b21 * a10 + b22 * a20; 25966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = b20 * a01 + b21 * a11 + b22 * a21; 26066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = b20 * a02 + b21 * a12 + b22 * a22; 26166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 26266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 26366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 26466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 26566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Alias for {@link mat3.multiply} 26666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @function 26766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 26866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.mul = mat3.multiply; 26966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 27066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 27166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Translate a mat3 by the given vector 27266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 27366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} out the receiving matrix 27466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} a the matrix to translate 27566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {vec2} v vector to translate by 27666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} out 27766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 27866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.translate = function(out, a, v) { 27966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis var a00 = a[0], a01 = a[1], a02 = a[2], 28066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a10 = a[3], a11 = a[4], a12 = a[5], 28166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a20 = a[6], a21 = a[7], a22 = a[8], 28266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis x = v[0], y = v[1]; 28366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 28466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = a00; 28566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = a01; 28666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = a02; 28766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 28866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = a10; 28966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = a11; 29066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = a12; 29166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 29266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = x * a00 + y * a10 + a20; 29366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = x * a01 + y * a11 + a21; 29466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = x * a02 + y * a12 + a22; 29566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 29666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 29766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 29866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 29966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Rotates a mat3 by the given angle 30066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 30166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} out the receiving matrix 30266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} a the matrix to rotate 30366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {Number} rad the angle to rotate the matrix by 30466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} out 30566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 30666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.rotate = function (out, a, rad) { 30766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis var a00 = a[0], a01 = a[1], a02 = a[2], 30866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a10 = a[3], a11 = a[4], a12 = a[5], 30966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a20 = a[6], a21 = a[7], a22 = a[8], 31066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 31166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis s = Math.sin(rad), 31266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis c = Math.cos(rad); 31366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 31466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = c * a00 + s * a10; 31566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = c * a01 + s * a11; 31666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = c * a02 + s * a12; 31766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 31866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = c * a10 - s * a00; 31966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = c * a11 - s * a01; 32066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = c * a12 - s * a02; 32166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 32266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = a20; 32366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = a21; 32466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = a22; 32566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 32666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 32766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 32866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 32966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Scales the mat3 by the dimensions in the given vec2 33066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 33166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} out the receiving matrix 33266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} a the matrix to rotate 33366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {vec2} v the vec2 to scale the matrix by 33466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} out 33566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis **/ 33666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.scale = function(out, a, v) { 33766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis var x = v[0], y = v[2]; 33866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 33966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = x * a[0]; 34066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = x * a[1]; 34166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = x * a[2]; 34266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 34366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = y * a[3]; 34466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = y * a[4]; 34566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = y * a[5]; 34666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 34766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = a[6]; 34866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = a[7]; 34966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = a[8]; 35066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 35166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 35266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 35366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 35466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Copies the values from a mat2d into a mat3 35566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 35666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} out the receiving matrix 35766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} a the matrix to rotate 35866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {vec2} v the vec2 to scale the matrix by 35966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {mat3} out 36066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis **/ 36166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.fromMat2d = function(out, a) { 36266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = a[0]; 36366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = a[1]; 36466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = 0; 36566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 36666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = a[2]; 36766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = a[3]; 36866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = 0; 36966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 37066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = a[4]; 37166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = a[5]; 37266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = 1; 37366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 37466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 37566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 37666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 37766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis* Calculates a 3x3 matrix from the given quaternion 37866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis* 37966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis* @param {mat3} out mat3 receiving operation result 38066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis* @param {quat} q Quaternion to create matrix from 38166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis* 38266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis* @returns {mat3} out 38366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis*/ 38466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.fromQuat = function (out, q) { 38566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis var x = q[0], y = q[1], z = q[2], w = q[3], 38666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis x2 = x + x, 38766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis y2 = y + y, 38866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis z2 = z + z, 38966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 39066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis xx = x * x2, 39166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis xy = x * y2, 39266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis xz = x * z2, 39366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis yy = y * y2, 39466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis yz = y * z2, 39566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis zz = z * z2, 39666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis wx = w * x2, 39766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis wy = w * y2, 39866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis wz = w * z2; 39966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 40066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[0] = 1 - (yy + zz); 40166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[1] = xy + wz; 40266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[2] = xz - wy; 40366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 40466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[3] = xy - wz; 40566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[4] = 1 - (xx + zz); 40666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[5] = yz + wx; 40766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 40866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[6] = xz + wy; 40966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[7] = yz - wx; 41066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis out[8] = 1 - (xx + yy); 41166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 41266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return out; 41366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 41466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 41566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis/** 41666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * Returns a string representation of a mat3 41766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * 41866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @param {mat3} mat matrix to represent as a string 41966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis * @returns {String} string representation of the matrix 42066a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis */ 42166a37686207944273ced825e0e8b6b6375f8c3deJamie Gennismat3.str = function (a) { 42266a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis return 'mat3(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + 42366a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a[3] + ', ' + a[4] + ', ' + a[5] + ', ' + 42466a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis a[6] + ', ' + a[7] + ', ' + a[8] + ')'; 42566a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis}; 42666a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis 42766a37686207944273ced825e0e8b6b6375f8c3deJamie Gennisif(typeof(exports) !== 'undefined') { 42866a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis exports.mat3 = mat3; 42966a37686207944273ced825e0e8b6b6375f8c3deJamie Gennis} 430