1 /* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV. 2 3 Permission is hereby granted, free of charge, to any person obtaining a copy 4 of this software and associated documentation files (the "Software"), to deal 5 in the Software without restriction, including without limitation the rights 6 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 7 copies of the Software, and to permit persons to whom the Software is 8 furnished to do so, subject to the following conditions: 9 10 The above copyright notice and this permission notice shall be included in 11 all copies or substantial portions of the Software. 12 13 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 14 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 15 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 16 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 17 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 18 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 19 THE SOFTWARE. */ 20 21 var glMatrix = require("./common.js"); 22 23 /** 24 * @class 2x2 Matrix 25 * @name mat2 26 */ 27 var mat2 = {}; 28 29 /** 30 * Creates a new identity mat2 31 * 32 * @returns {mat2} a new 2x2 matrix 33 */ 34 mat2.create = function() { 35 var out = new glMatrix.ARRAY_TYPE(4); 36 out[0] = 1; 37 out[1] = 0; 38 out[2] = 0; 39 out[3] = 1; 40 return out; 41 }; 42 43 /** 44 * Creates a new mat2 initialized with values from an existing matrix 45 * 46 * @param {mat2} a matrix to clone 47 * @returns {mat2} a new 2x2 matrix 48 */ 49 mat2.clone = function(a) { 50 var out = new glMatrix.ARRAY_TYPE(4); 51 out[0] = a[0]; 52 out[1] = a[1]; 53 out[2] = a[2]; 54 out[3] = a[3]; 55 return out; 56 }; 57 58 /** 59 * Copy the values from one mat2 to another 60 * 61 * @param {mat2} out the receiving matrix 62 * @param {mat2} a the source matrix 63 * @returns {mat2} out 64 */ 65 mat2.copy = function(out, a) { 66 out[0] = a[0]; 67 out[1] = a[1]; 68 out[2] = a[2]; 69 out[3] = a[3]; 70 return out; 71 }; 72 73 /** 74 * Set a mat2 to the identity matrix 75 * 76 * @param {mat2} out the receiving matrix 77 * @returns {mat2} out 78 */ 79 mat2.identity = function(out) { 80 out[0] = 1; 81 out[1] = 0; 82 out[2] = 0; 83 out[3] = 1; 84 return out; 85 }; 86 87 /** 88 * Transpose the values of a mat2 89 * 90 * @param {mat2} out the receiving matrix 91 * @param {mat2} a the source matrix 92 * @returns {mat2} out 93 */ 94 mat2.transpose = function(out, a) { 95 // If we are transposing ourselves we can skip a few steps but have to cache some values 96 if (out === a) { 97 var a1 = a[1]; 98 out[1] = a[2]; 99 out[2] = a1; 100 } else { 101 out[0] = a[0]; 102 out[1] = a[2]; 103 out[2] = a[1]; 104 out[3] = a[3]; 105 } 106 107 return out; 108 }; 109 110 /** 111 * Inverts a mat2 112 * 113 * @param {mat2} out the receiving matrix 114 * @param {mat2} a the source matrix 115 * @returns {mat2} out 116 */ 117 mat2.invert = function(out, a) { 118 var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], 119 120 // Calculate the determinant 121 det = a0 * a3 - a2 * a1; 122 123 if (!det) { 124 return null; 125 } 126 det = 1.0 / det; 127 128 out[0] = a3 * det; 129 out[1] = -a1 * det; 130 out[2] = -a2 * det; 131 out[3] = a0 * det; 132 133 return out; 134 }; 135 136 /** 137 * Calculates the adjugate of a mat2 138 * 139 * @param {mat2} out the receiving matrix 140 * @param {mat2} a the source matrix 141 * @returns {mat2} out 142 */ 143 mat2.adjoint = function(out, a) { 144 // Caching this value is nessecary if out == a 145 var a0 = a[0]; 146 out[0] = a[3]; 147 out[1] = -a[1]; 148 out[2] = -a[2]; 149 out[3] = a0; 150 151 return out; 152 }; 153 154 /** 155 * Calculates the determinant of a mat2 156 * 157 * @param {mat2} a the source matrix 158 * @returns {Number} determinant of a 159 */ 160 mat2.determinant = function (a) { 161 return a[0] * a[3] - a[2] * a[1]; 162 }; 163 164 /** 165 * Multiplies two mat2's 166 * 167 * @param {mat2} out the receiving matrix 168 * @param {mat2} a the first operand 169 * @param {mat2} b the second operand 170 * @returns {mat2} out 171 */ 172 mat2.multiply = function (out, a, b) { 173 var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3]; 174 var b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3]; 175 out[0] = a0 * b0 + a2 * b1; 176 out[1] = a1 * b0 + a3 * b1; 177 out[2] = a0 * b2 + a2 * b3; 178 out[3] = a1 * b2 + a3 * b3; 179 return out; 180 }; 181 182 /** 183 * Alias for {@link mat2.multiply} 184 * @function 185 */ 186 mat2.mul = mat2.multiply; 187 188 /** 189 * Rotates a mat2 by the given angle 190 * 191 * @param {mat2} out the receiving matrix 192 * @param {mat2} a the matrix to rotate 193 * @param {Number} rad the angle to rotate the matrix by 194 * @returns {mat2} out 195 */ 196 mat2.rotate = function (out, a, rad) { 197 var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], 198 s = Math.sin(rad), 199 c = Math.cos(rad); 200 out[0] = a0 * c + a2 * s; 201 out[1] = a1 * c + a3 * s; 202 out[2] = a0 * -s + a2 * c; 203 out[3] = a1 * -s + a3 * c; 204 return out; 205 }; 206 207 /** 208 * Scales the mat2 by the dimensions in the given vec2 209 * 210 * @param {mat2} out the receiving matrix 211 * @param {mat2} a the matrix to rotate 212 * @param {vec2} v the vec2 to scale the matrix by 213 * @returns {mat2} out 214 **/ 215 mat2.scale = function(out, a, v) { 216 var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], 217 v0 = v[0], v1 = v[1]; 218 out[0] = a0 * v0; 219 out[1] = a1 * v0; 220 out[2] = a2 * v1; 221 out[3] = a3 * v1; 222 return out; 223 }; 224 225 /** 226 * Creates a matrix from a given angle 227 * This is equivalent to (but much faster than): 228 * 229 * mat2.identity(dest); 230 * mat2.rotate(dest, dest, rad); 231 * 232 * @param {mat2} out mat2 receiving operation result 233 * @param {Number} rad the angle to rotate the matrix by 234 * @returns {mat2} out 235 */ 236 mat2.fromRotation = function(out, rad) { 237 var s = Math.sin(rad), 238 c = Math.cos(rad); 239 out[0] = c; 240 out[1] = s; 241 out[2] = -s; 242 out[3] = c; 243 return out; 244 } 245 246 /** 247 * Creates a matrix from a vector scaling 248 * This is equivalent to (but much faster than): 249 * 250 * mat2.identity(dest); 251 * mat2.scale(dest, dest, vec); 252 * 253 * @param {mat2} out mat2 receiving operation result 254 * @param {vec2} v Scaling vector 255 * @returns {mat2} out 256 */ 257 mat2.fromScaling = function(out, v) { 258 out[0] = v[0]; 259 out[1] = 0; 260 out[2] = 0; 261 out[3] = v[1]; 262 return out; 263 } 264 265 /** 266 * Returns a string representation of a mat2 267 * 268 * @param {mat2} mat matrix to represent as a string 269 * @returns {String} string representation of the matrix 270 */ 271 mat2.str = function (a) { 272 return 'mat2(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')'; 273 }; 274 275 /** 276 * Returns Frobenius norm of a mat2 277 * 278 * @param {mat2} a the matrix to calculate Frobenius norm of 279 * @returns {Number} Frobenius norm 280 */ 281 mat2.frob = function (a) { 282 return(Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2))) 283 }; 284 285 /** 286 * Returns L, D and U matrices (Lower triangular, Diagonal and Upper triangular) by factorizing the input matrix 287 * @param {mat2} L the lower triangular matrix 288 * @param {mat2} D the diagonal matrix 289 * @param {mat2} U the upper triangular matrix 290 * @param {mat2} a the input matrix to factorize 291 */ 292 293 mat2.LDU = function (L, D, U, a) { 294 L[2] = a[2]/a[0]; 295 U[0] = a[0]; 296 U[1] = a[1]; 297 U[3] = a[3] - L[2] * U[1]; 298 return [L, D, U]; 299 }; 300 301 302 module.exports = mat2; 303
