1 module gfm.math.matrix; 2 3 import std.math, 4 std.typetuple, 5 std.traits, 6 std.string, 7 std.typecons, 8 std.conv; 9 10 import gfm.math.vector, 11 gfm.math.shapes, 12 gfm.math.quaternion; 13 14 /// Generic non-resizeable matrix with R rows and C columns. 15 /// Intended for 3D use (size 3x3 and 4x4). 16 /// Important: <b>Matrices here are in row-major order whereas OpenGL is column-major.</b> 17 /// Params: 18 /// T = type of elements 19 /// R = number of rows 20 /// C = number of columns 21 align(1) struct Matrix(T, size_t R, size_t C) 22 { 23 align(1): 24 public 25 { 26 static assert(R >= 1u && C >= 1u); 27 28 alias Vector!(T, C) row_t; 29 alias Vector!(T, R) column_t; 30 31 enum bool isSquare = (R == C); 32 33 // fields definition 34 union 35 { 36 T[C*R] v; // all elements 37 row_t[R] rows; // all rows 38 T[C][R] c; // components 39 } 40 41 this(U...)(U values) pure nothrow 42 { 43 static if ((U.length == C*R) && allSatisfy!(isTConvertible, U)) 44 { 45 // construct with components 46 foreach(int i, x; values) 47 v[i] = x; 48 } 49 else static if ((U.length == 1) && (isAssignable!(U[0])) && (!is(U[0] : Matrix))) 50 { 51 // construct with assignment 52 opAssign!(U[0])(values[0]); 53 } 54 else static assert(false, "cannot create a matrix from given arguments"); 55 } 56 57 /// Construct a matrix from columns. 58 static Matrix fromColumns(column_t[] columns) pure nothrow 59 { 60 assert(columns.length == C); 61 Matrix res; 62 for (size_t i = 0; i < R; ++i) 63 for (size_t j = 0; j < C; ++j) 64 { 65 res.c[i][j] = columns[j][i]; 66 } 67 return res; 68 } 69 70 /// Construct a matrix from rows. 71 static Matrix fromRows(row_t[] rows) pure nothrow 72 { 73 assert(rows.length == R); 74 Matrix res; 75 res.rows[] = rows[]; 76 return res; 77 } 78 79 /// Construct matrix with a scalar. 80 this(U)(T x) 81 { 82 for (size_t i = 0; i < _N; ++i) 83 v[i] = x; 84 } 85 86 /// Assign with a samey matrice. 87 ref Matrix opAssign(U : Matrix)(U x) pure nothrow 88 { 89 for (size_t i = 0; i < R * C; ++i) 90 v[i] = x.v[i]; 91 return this; 92 } 93 94 /// Assign from other small matrices (same size, compatible type). 95 ref Matrix opAssign(U)(U x) pure nothrow 96 if (is(typeof(U._isMatrix)) 97 && is(U._T : _T) 98 && (!is(U: Matrix)) 99 && (U._R == R) && (U._C == C)) 100 { 101 for (size_t i = 0; i < R * C; ++i) 102 v[i] = x.v[i]; 103 return this; 104 } 105 106 /// Assign with a static array of size R * C. 107 ref Matrix opAssign(U)(U x) pure nothrow 108 if ((isStaticArray!U) 109 && is(typeof(x[0]) : T) 110 && (U.length == R * C)) 111 { 112 for (size_t i = 0; i < R * C; ++i) 113 v[i] = x[i]; 114 return this; 115 } 116 117 /// Assign with a dynamic array of size R * C. 118 ref Matrix opAssign(U)(U x) pure nothrow 119 if ((isDynamicArray!U) 120 && is(typeof(x[0]) : T)) 121 { 122 assert(x.length == R * C); 123 for (size_t i = 0; i < R * C; ++i) 124 v[i] = x[i]; 125 return this; 126 } 127 128 /// Return a pointer to content. 129 T* ptr() pure nothrow @property 130 { 131 return v.ptr; 132 } 133 134 /// Returns: column j as a vector. 135 column_t column(size_t j) pure const nothrow 136 { 137 column_t res = void; 138 for (size_t i = 0; i < R; ++i) 139 res.v[i] = c[i][j]; 140 return res; 141 } 142 143 /// Returns: row i as a vector. 144 row_t row(size_t i) pure const nothrow 145 { 146 return rows[i]; 147 } 148 149 /// Covnerts to pretty string. 150 string toString() const nothrow 151 { 152 try 153 return format("%s", v); 154 catch (Exception e) 155 assert(false); // should not happen since format is right 156 } 157 158 /// Matrix * vector multiplication. 159 column_t opBinary(string op)(row_t x) pure const nothrow if (op == "*") 160 { 161 column_t res = void; 162 for (size_t i = 0; i < R; ++i) 163 { 164 T sum = 0; 165 for (size_t j = 0; j < C; ++j) 166 { 167 sum += c[i][j] * x.v[j]; 168 } 169 res.v[i] = sum; 170 } 171 return res; 172 } 173 174 /// Matrix * matrix multiplication. 175 auto opBinary(string op, U)(U x) pure const nothrow 176 if (is(typeof(U._isMatrix)) && (U._R == C) && (op == "*")) 177 { 178 Matrix!(T, R, U._C) result = void; 179 180 for (size_t i = 0; i < R; ++i) 181 { 182 for (size_t j = 0; j < U._C; ++j) 183 { 184 T sum = 0; 185 for (size_t k = 0; k < C; ++k) 186 sum += c[i][k] * x.c[k][j]; 187 result.c[i][j] = sum; 188 } 189 } 190 return result; 191 } 192 193 ref Matrix opOpAssign(string op, U)(U operand) pure nothrow if (isConvertible!U) 194 { 195 Matrix conv = operand; 196 return opOpAssign!op(conv); 197 } 198 199 /// Cast to other matrix types. 200 /// If the size are different, the result matrix is truncated 201 /// and/or filled with identity coefficients. 202 U opCast(U)() pure nothrow const if (is(typeof(U._isMatrix))) 203 { 204 U res = U.identity(); 205 enum minR = R < U._R ? R : U._R; 206 enum minC = C < U._C ? C : U._C; 207 for (size_t i = 0; i < minR; ++i) 208 for (size_t j = 0; j < minC; ++j) 209 { 210 res.c[i][j] = cast(U._T)(c[i][j]); 211 } 212 return res; 213 } 214 215 bool opEquals(U)(U other) pure const nothrow if (is(U : Matrix)) 216 { 217 for (size_t i = 0; i < R * C; ++i) 218 if (v[i] != other.v[i]) 219 return false; 220 return true; 221 } 222 223 bool opEquals(U)(U other) pure const nothrow 224 if ((isAssignable!U) && (!is(U: Matrix))) 225 { 226 Matrix conv = other; 227 return opEquals(conv); 228 } 229 230 // +matrix, -matrix, ~matrix, !matrix 231 Matrix opUnary(string op)() pure const nothrow if (op == "+" || op == "-" || op == "~" || op == "!") 232 { 233 Matrix res = void; 234 for (size_t i = 0; i < N; ++i) 235 mixin("res.v[i] = " ~ op ~ "v[i];"); 236 return res; 237 } 238 239 /// Convert 3x3 rotation matrix to quaternion. 240 /// See_also: 3D Math Primer for Graphics and Game Development. 241 U opCast(U)() pure const nothrow if (is(typeof(U._isQuaternion)) 242 && is(U._T : _T) 243 && (_R == 3) && (_C == 3)) 244 { 245 T fourXSquaredMinus1 = c[0][0] - c[1][1] - c[2][2]; 246 T fourYSquaredMinus1 = c[1][1] - c[0][0] - c[2][2]; 247 T fourZSquaredMinus1 = c[2][2] - c[0][0] - c[1][1]; 248 T fourWSquaredMinus1 = c[0][0] + c[1][1] + c[2][2]; 249 250 int biggestIndex = 0; 251 T fourBiggestSquaredMinus1 = fourWSquaredMinus1; 252 253 if(fourXSquaredMinus1 > fourBiggestSquaredMinus1) 254 { 255 fourBiggestSquaredMinus1 = fourXSquaredMinus1; 256 biggestIndex = 1; 257 } 258 259 if(fourYSquaredMinus1 > fourBiggestSquaredMinus1) 260 { 261 fourBiggestSquaredMinus1 = fourYSquaredMinus1; 262 biggestIndex = 2; 263 } 264 265 if(fourZSquaredMinus1 > fourBiggestSquaredMinus1) 266 { 267 fourBiggestSquaredMinus1 = fourZSquaredMinus1; 268 biggestIndex = 3; 269 } 270 271 T biggestVal = sqrt(fourBiggestSquaredMinus1 + 1) / 2; 272 T mult = 1 / (biggestVal * 4); 273 274 U quat; 275 switch(biggestIndex) 276 { 277 case 1: 278 quat.w = (c[1][2] - c[2][1]) * mult; 279 quat.x = biggestVal; 280 quat.y = (c[0][1] + c[1][0]) * mult; 281 quat.z = (c[2][0] + c[0][2]) * mult; 282 break; 283 284 case 2: 285 quat.w = (c[2][0] - c[0][2]) * mult; 286 quat.x = (c[0][1] + c[1][0]) * mult; 287 quat.y = biggestVal; 288 quat.z = (c[1][2] + c[2][1]) * mult; 289 break; 290 291 case 3: 292 quat.w = (c[0][1] - c[1][0]) * mult; 293 quat.x = (c[2][0] + c[0][2]) * mult; 294 quat.y = (c[1][2] + c[2][1]) * mult; 295 quat.z = biggestVal; 296 break; 297 298 default: // biggestIndex == 0 299 quat.w = biggestVal; 300 quat.x = (c[1][2] - c[2][1]) * mult; 301 quat.y = (c[2][0] - c[0][2]) * mult; 302 quat.z = (c[0][1] - c[1][0]) * mult; 303 break; 304 } 305 306 return quat; 307 } 308 309 /// Converts a 4x4 rotation matrix to quaternion. 310 U opCast(U)() pure const nothrow if (is(typeof(U._isQuaternion)) 311 && is(U._T : _T) 312 && (_R == 4) && (_C == 4)) 313 { 314 auto m3 = cast(mat3!T)(this); 315 return cast(U)(m3); 316 } 317 318 /// Matrix inversion is provided for 2x2, 3x3 and 4x4 floating point matrices. 319 320 static if (isSquare && isFloatingPoint!T && R == 2) 321 { 322 /// Returns: inverse of matrix. 323 Matrix inverse() pure const nothrow 324 { 325 T invDet = 1 / (c[0][0] * c[1][1] - c[0][1] * c[1][0]); 326 return Matrix( c[1][1] * invDet, -c[0][1] * invDet, 327 -c[1][0] * invDet, c[0][0] * invDet); 328 } 329 } 330 331 static if (isSquare && isFloatingPoint!T && R == 3) 332 { 333 /// Returns: inverse of matrix. 334 Matrix inverse() pure const nothrow 335 { 336 T det = c[0][0] * (c[1][1] * c[2][2] - c[2][1] * c[1][2]) 337 - c[0][1] * (c[1][0] * c[2][2] - c[1][2] * c[2][0]) 338 + c[0][2] * (c[1][0] * c[2][1] - c[1][1] * c[2][0]); 339 T invDet = 1 / det; 340 341 Matrix res = void; 342 res.c[0][0] = (c[1][1] * c[2][2] - c[2][1] * c[1][2]) * invDet; 343 res.c[0][1] = -(c[0][1] * c[2][2] - c[0][2] * c[2][1]) * invDet; 344 res.c[0][2] = (c[0][1] * c[1][2] - c[0][2] * c[1][1]) * invDet; 345 res.c[1][0] = -(c[1][0] * c[2][2] - c[1][2] * c[2][0]) * invDet; 346 res.c[1][1] = (c[0][0] * c[2][2] - c[0][2] * c[2][0]) * invDet; 347 res.c[1][2] = -(c[0][0] * c[1][2] - c[1][0] * c[0][2]) * invDet; 348 res.c[2][0] = (c[1][0] * c[2][1] - c[2][0] * c[1][1]) * invDet; 349 res.c[2][1] = -(c[0][0] * c[2][1] - c[2][0] * c[0][1]) * invDet; 350 res.c[2][2] = (c[0][0] * c[1][1] - c[1][0] * c[0][1]) * invDet; 351 return res; 352 } 353 } 354 355 static if (isSquare && isFloatingPoint!T && R == 4) 356 { 357 /// Returns: inverse of matrix. 358 Matrix inverse() pure const nothrow 359 { 360 T det2_01_01 = c[0][0] * c[1][1] - c[0][1] * c[1][0]; 361 T det2_01_02 = c[0][0] * c[1][2] - c[0][2] * c[1][0]; 362 T det2_01_03 = c[0][0] * c[1][3] - c[0][3] * c[1][0]; 363 T det2_01_12 = c[0][1] * c[1][2] - c[0][2] * c[1][1]; 364 T det2_01_13 = c[0][1] * c[1][3] - c[0][3] * c[1][1]; 365 T det2_01_23 = c[0][2] * c[1][3] - c[0][3] * c[1][2]; 366 367 T det3_201_012 = c[2][0] * det2_01_12 - c[2][1] * det2_01_02 + c[2][2] * det2_01_01; 368 T det3_201_013 = c[2][0] * det2_01_13 - c[2][1] * det2_01_03 + c[2][3] * det2_01_01; 369 T det3_201_023 = c[2][0] * det2_01_23 - c[2][2] * det2_01_03 + c[2][3] * det2_01_02; 370 T det3_201_123 = c[2][1] * det2_01_23 - c[2][2] * det2_01_13 + c[2][3] * det2_01_12; 371 372 T det = - det3_201_123 * c[3][0] + det3_201_023 * c[3][1] - det3_201_013 * c[3][2] + det3_201_012 * c[3][3]; 373 T invDet = 1 / det; 374 375 T det2_03_01 = c[0][0] * c[3][1] - c[0][1] * c[3][0]; 376 T det2_03_02 = c[0][0] * c[3][2] - c[0][2] * c[3][0]; 377 T det2_03_03 = c[0][0] * c[3][3] - c[0][3] * c[3][0]; 378 T det2_03_12 = c[0][1] * c[3][2] - c[0][2] * c[3][1]; 379 T det2_03_13 = c[0][1] * c[3][3] - c[0][3] * c[3][1]; 380 T det2_03_23 = c[0][2] * c[3][3] - c[0][3] * c[3][2]; 381 T det2_13_01 = c[1][0] * c[3][1] - c[1][1] * c[3][0]; 382 T det2_13_02 = c[1][0] * c[3][2] - c[1][2] * c[3][0]; 383 T det2_13_03 = c[1][0] * c[3][3] - c[1][3] * c[3][0]; 384 T det2_13_12 = c[1][1] * c[3][2] - c[1][2] * c[3][1]; 385 T det2_13_13 = c[1][1] * c[3][3] - c[1][3] * c[3][1]; 386 T det2_13_23 = c[1][2] * c[3][3] - c[1][3] * c[3][2]; 387 388 T det3_203_012 = c[2][0] * det2_03_12 - c[2][1] * det2_03_02 + c[2][2] * det2_03_01; 389 T det3_203_013 = c[2][0] * det2_03_13 - c[2][1] * det2_03_03 + c[2][3] * det2_03_01; 390 T det3_203_023 = c[2][0] * det2_03_23 - c[2][2] * det2_03_03 + c[2][3] * det2_03_02; 391 T det3_203_123 = c[2][1] * det2_03_23 - c[2][2] * det2_03_13 + c[2][3] * det2_03_12; 392 393 T det3_213_012 = c[2][0] * det2_13_12 - c[2][1] * det2_13_02 + c[2][2] * det2_13_01; 394 T det3_213_013 = c[2][0] * det2_13_13 - c[2][1] * det2_13_03 + c[2][3] * det2_13_01; 395 T det3_213_023 = c[2][0] * det2_13_23 - c[2][2] * det2_13_03 + c[2][3] * det2_13_02; 396 T det3_213_123 = c[2][1] * det2_13_23 - c[2][2] * det2_13_13 + c[2][3] * det2_13_12; 397 398 T det3_301_012 = c[3][0] * det2_01_12 - c[3][1] * det2_01_02 + c[3][2] * det2_01_01; 399 T det3_301_013 = c[3][0] * det2_01_13 - c[3][1] * det2_01_03 + c[3][3] * det2_01_01; 400 T det3_301_023 = c[3][0] * det2_01_23 - c[3][2] * det2_01_03 + c[3][3] * det2_01_02; 401 T det3_301_123 = c[3][1] * det2_01_23 - c[3][2] * det2_01_13 + c[3][3] * det2_01_12; 402 403 Matrix res = void; 404 res.c[0][0] = - det3_213_123 * invDet; 405 res.c[1][0] = + det3_213_023 * invDet; 406 res.c[2][0] = - det3_213_013 * invDet; 407 res.c[3][0] = + det3_213_012 * invDet; 408 409 res.c[0][1] = + det3_203_123 * invDet; 410 res.c[1][1] = - det3_203_023 * invDet; 411 res.c[2][1] = + det3_203_013 * invDet; 412 res.c[3][1] = - det3_203_012 * invDet; 413 414 res.c[0][2] = + det3_301_123 * invDet; 415 res.c[1][2] = - det3_301_023 * invDet; 416 res.c[2][2] = + det3_301_013 * invDet; 417 res.c[3][2] = - det3_301_012 * invDet; 418 419 res.c[0][3] = - det3_201_123 * invDet; 420 res.c[1][3] = + det3_201_023 * invDet; 421 res.c[2][3] = - det3_201_013 * invDet; 422 res.c[3][3] = + det3_201_012 * invDet; 423 return res; 424 } 425 } 426 427 /// Returns: transposed matrice. 428 Matrix!(T, C, R) transposed() pure const nothrow 429 { 430 Matrix!(T, C, R) res; 431 for (size_t i = 0; i < C; ++i) 432 for (size_t j = 0; j < R; ++j) 433 res.c[i][j] = c[j][i]; 434 return res; 435 } 436 437 static if (isSquare && R > 1) 438 { 439 /// In-place translate by (v, 1) 440 void translate(Vector!(T, R-1) v) pure nothrow 441 { 442 for (size_t i = 0; i < R; ++i) 443 { 444 T dot = 0; 445 for (size_t j = 0; j + 1 < C; ++j) 446 dot += v.v[j] * c[i][j]; 447 448 c[i][C-1] += dot; 449 } 450 } 451 452 /// Make a translation matrix. 453 static Matrix translation(Vector!(T, R-1) v) pure nothrow 454 { 455 Matrix res = identity(); 456 for (size_t i = 0; i + 1 < R; ++i) 457 res.c[i][C-1] += v.v[i]; 458 return res; 459 } 460 461 /// In-place matrix scaling. 462 void scale(Vector!(T, R-1) v) pure nothrow 463 { 464 for (size_t i = 0; i < R; ++i) 465 for (size_t j = 0; j + 1 < C; ++j) 466 c[i][j] *= v.v[j]; 467 } 468 469 /// Make a scaling matrix. 470 static Matrix scaling(Vector!(T, R-1) v) pure nothrow 471 { 472 Matrix res = identity(); 473 for (size_t i = 0; i + 1 < R; ++i) 474 res.c[i][i] = v.v[i]; 475 return res; 476 } 477 } 478 479 // rotations are implemented for 3x3 and 4x4 matrices. 480 static if (isSquare && (R == 3 || R == 4) && isFloatingPoint!T) 481 { 482 public static Matrix rotateAxis(size_t i, size_t j)(T angle) pure nothrow 483 { 484 Matrix res = identity(); 485 const T cosa = cos(angle); 486 const T sina = sin(angle); 487 res.c[i][i] = cosa; 488 res.c[i][j] = -sina; 489 res.c[j][i] = sina; 490 res.c[j][j] = cosa; 491 return res; 492 } 493 494 /// Returns: rotation matrix along axis X 495 alias rotateAxis!(1, 2) rotateX; 496 497 /// Returns: rotation matrix along axis Y 498 alias rotateAxis!(2, 0) rotateY; 499 500 /// Returns: rotation matrix along axis Z 501 alias rotateAxis!(0, 1) rotateZ; 502 503 /// Similar to the glRotate matrix, however the angle is expressed in radians 504 /// See_also: $(LINK http://www.cs.rutgers.edu/~decarlo/428/gl_man/rotate.html) 505 static Matrix rotation(T angle, vec3!T axis) pure nothrow 506 { 507 Matrix res = identity(); 508 const T c = cos(angle); 509 const oneMinusC = 1 - c; 510 const T s = sin(angle); 511 axis = axis.normalized(); 512 T x = axis.x, 513 y = axis.y, 514 z = axis.z; 515 T xy = x * y, 516 yz = y * z, 517 xz = x * z; 518 519 res.c[0][0] = x * x * oneMinusC + c; 520 res.c[0][1] = x * y * oneMinusC - z * s; 521 res.c[0][2] = x * z * oneMinusC + y * s; 522 res.c[1][0] = y * x * oneMinusC + z * s; 523 res.c[1][1] = y * y * oneMinusC + c; 524 res.c[1][2] = y * z * oneMinusC - x * s; 525 res.c[2][0] = z * x * oneMinusC - y * s; 526 res.c[2][1] = z * y * oneMinusC + x * s; 527 res.c[2][2] = z * z * oneMinusC + c; 528 return res; 529 } 530 } 531 532 // 4x4 specific transformations for 3D usage 533 static if (isSquare && R == 4 && isFloatingPoint!T) 534 { 535 /// Returns: orthographic projection. 536 static Matrix orthographic(T left, T right, T bottom, T top, T near, T far) pure nothrow 537 { 538 T dx = right - left, 539 dy = top - bottom, 540 dz = far - near; 541 542 T tx = -(right + left) / dx; 543 T ty = -(top + bottom) / dy; 544 T tz = -(far + near) / dz; 545 546 return Matrix(2 / dx, 0, 0, tx, 547 0, 2 / dy, 0, ty, 548 0, 0, 2 / dz, tz, 549 0, 0, 0, 1); 550 } 551 552 /// Returns: perspective projection. 553 static Matrix perspective(T FOVInRadians, T aspect, T zNear, T zFar) pure nothrow 554 { 555 T f = 1 / tan(FOVInRadians / 2); 556 T d = 1 / (zNear - zFar); 557 558 return Matrix(f / aspect, 0, 0, 0, 559 0, f, 0, 0, 560 0, 0, (zFar + zNear) * d, 2 * d * zFar * zNear, 561 0, 0, -1, 0); 562 } 563 564 /// Returns: "lookAt" projection. 565 /// Thanks to vuaru for corrections. 566 static Matrix lookAt(vec3!T eye, vec3!T target, vec3!T up) pure nothrow 567 { 568 vec3!T Z = (eye - target).normalized(); 569 vec3!T X = cross(-up, Z).normalized(); 570 vec3!T Y = cross(Z, -X); 571 572 return Matrix(-X.x, -X.y, -X.z, dot(X, eye), 573 Y.x, Y.y, Y.z, -dot(Y, eye), 574 Z.x, Z.y, Z.z, -dot(Z, eye), 575 0, 0, 0, 1); 576 } 577 578 /// Extract frustum from a 4x4 matrice. 579 Frustum!T frustum() pure const nothrow 580 { 581 auto left = Plane!T(row(3) + row(0)); 582 auto right = Plane!T(row(3) - row(0)); 583 auto top = Plane!T(row(3) - row(1)); 584 auto bottom = Plane!T(row(3) + row(1)); 585 auto near = Plane!T(row(3) + row(2)); 586 auto far = Plane!T(row(3) - row(2)); 587 return Frustum!T(left, right, top, bottom, near, far); 588 } 589 590 } 591 } 592 593 private 594 { 595 alias T _T; 596 enum _R = R; 597 enum _C = C; 598 enum bool _isMatrix = true; 599 600 template isAssignable(T) 601 { 602 enum bool isAssignable = 603 is(typeof( 604 { 605 T x; 606 Matrix m = x; 607 }())); 608 } 609 610 template isTConvertible(U) 611 { 612 enum bool isTConvertible = is(U : T); 613 } 614 615 template isRowConvertible(U) 616 { 617 enum bool isRowConvertible = is(U : row_t); 618 } 619 620 template isColumnConvertible(U) 621 { 622 enum bool isColumnConvertible = is(U : column_t); 623 } 624 } 625 626 public 627 { 628 /// Returns: an identity matrice. 629 /// Note: the identity matrix, while only meaningful for square matrices, 630 /// is also defined for non-square ones. 631 static Matrix identity() pure nothrow 632 { 633 Matrix res = void; 634 for (size_t i = 0; i < R; ++i) 635 for (size_t j = 0; j < C; ++j) 636 res.c[i][j] = (i == j) ? 1 : 0; 637 return res; 638 } 639 640 /// Returns: a constant matrice. 641 static Matrix constant(U)(U x) pure nothrow 642 { 643 Matrix res = void; 644 645 for (size_t i = 0; i < R * C; ++i) 646 res.v[i] = cast(T)x; 647 return res; 648 } 649 } 650 } 651 652 // GLSL is a big inspiration here 653 // we defines types with more or less the same names 654 template mat2x2(T) { alias Matrix!(T, 2u, 2u) mat2x2; } 655 template mat3x3(T) { alias Matrix!(T, 3u, 3u) mat3x3; } 656 template mat4x4(T) { alias Matrix!(T, 4u, 4u) mat4x4; } 657 658 // WARNING: in GLSL, first number is _columns_, second is rows 659 // It is the opposite here: first number is rows, second is columns 660 // With this convention mat2x3 * mat3x4 -> mat2x4. 661 template mat2x3(T) { alias Matrix!(T, 2u, 3u) mat2x3; } 662 template mat2x4(T) { alias Matrix!(T, 2u, 4u) mat2x4; } 663 template mat3x2(T) { alias Matrix!(T, 3u, 2u) mat3x2; } 664 template mat3x4(T) { alias Matrix!(T, 3u, 4u) mat3x4; } 665 template mat4x2(T) { alias Matrix!(T, 4u, 2u) mat4x2; } 666 template mat4x3(T) { alias Matrix!(T, 4u, 3u) mat4x3; } 667 668 alias mat2x2 mat2; 669 alias mat3x3 mat3; // shorter names for most common matrices 670 alias mat4x4 mat4; 671 672 private string definePostfixAliases(string type) 673 { 674 return "alias " ~ type ~ "!byte " ~ type ~ "b;\n" 675 ~ "alias " ~ type ~ "!ubyte " ~ type ~ "ub;\n" 676 ~ "alias " ~ type ~ "!short " ~ type ~ "s;\n" 677 ~ "alias " ~ type ~ "!ushort " ~ type ~ "us;\n" 678 ~ "alias " ~ type ~ "!int " ~ type ~ "i;\n" 679 ~ "alias " ~ type ~ "!uint " ~ type ~ "ui;\n" 680 ~ "alias " ~ type ~ "!long " ~ type ~ "l;\n" 681 ~ "alias " ~ type ~ "!ulong " ~ type ~ "ul;\n" 682 ~ "alias " ~ type ~ "!float " ~ type ~ "f;\n" 683 ~ "alias " ~ type ~ "!double " ~ type ~ "d;\n" 684 ~ "alias " ~ type ~ "!real " ~ type ~ "L;\n"; 685 } 686 687 // define a lot of type names 688 mixin(definePostfixAliases("mat2")); 689 mixin(definePostfixAliases("mat3")); 690 mixin(definePostfixAliases("mat4")); 691 mixin(definePostfixAliases("mat2x2")); 692 mixin(definePostfixAliases("mat2x3")); 693 mixin(definePostfixAliases("mat2x4")); 694 mixin(definePostfixAliases("mat3x2")); 695 mixin(definePostfixAliases("mat3x3")); 696 mixin(definePostfixAliases("mat3x4")); 697 mixin(definePostfixAliases("mat4x2")); 698 mixin(definePostfixAliases("mat4x3")); 699 mixin(definePostfixAliases("mat4x4")); 700 701 unittest 702 { 703 mat2i x = mat2i(0, 1, 704 2, 3); 705 assert(x.c[0][0] == 0 && x.c[0][1] == 1 && x.c[1][0] == 2 && x.c[1][1] == 3); 706 707 vec2i[2] cols = [vec2i(0, 2), vec2i(1, 3)]; 708 mat2i y = mat2i.fromColumns(cols[]); 709 assert(y.c[0][0] == 0 && y.c[0][1] == 1 && y.c[1][0] == 2 && y.c[1][1] == 3); 710 y = mat2i.fromRows(cols[]); 711 assert(y.c[0][0] == 0 && y.c[1][0] == 1 && y.c[0][1] == 2 && y.c[1][1] == 3); 712 y = y.transposed(); 713 714 assert(x == y); 715 x = [0, 1, 2, 3]; 716 assert(x == y); 717 718 719 mat2i z = x * y; 720 assert(z == mat2i([2, 3, 6, 11])); 721 vec2i vz = z * vec2i(2, -1); 722 assert(vz == vec2i(1, 1)); 723 724 mat2f a = z; 725 mat2f w = [4, 5, 6, 7]; 726 z = cast(mat2i)w; 727 assert(w == z); 728 729 { 730 mat2x3f A; 731 mat3x4f B; 732 mat2x4f C = A * B; 733 } 734 }