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 struct Matrix(T, int R, int C) 22 { 23 public 24 { 25 static assert(R >= 1 && C >= 1); 26 27 alias Vector!(T, C) row_t; 28 alias Vector!(T, R) column_t; 29 30 enum bool isSquare = (R == C); 31 32 // fields definition 33 union 34 { 35 T[C*R] v; // all elements 36 row_t[R] rows; // all rows 37 T[C][R] c; // components 38 } 39 40 @nogc this(U...)(U values) pure nothrow 41 { 42 static if ((U.length == C*R) && allSatisfy!(isTAssignable, U)) 43 { 44 // construct with components 45 foreach(int i, x; values) 46 v[i] = x; 47 } 48 else static if ((U.length == 1) && (isAssignable!(U[0])) && (!is(U[0] : Matrix))) 49 { 50 // construct with assignment 51 opAssign!(U[0])(values[0]); 52 } 53 else static assert(false, "cannot create a matrix from given arguments"); 54 } 55 56 /// Construct a matrix from columns. 57 @nogc static Matrix fromColumns(column_t[] columns) pure nothrow 58 { 59 assert(columns.length == C); 60 Matrix res; 61 for (int i = 0; i < R; ++i) 62 for (int j = 0; j < C; ++j) 63 { 64 res.c[i][j] = columns[j][i]; 65 } 66 return res; 67 } 68 69 /// Construct a matrix from rows. 70 @nogc static Matrix fromRows(row_t[] rows) pure nothrow 71 { 72 assert(rows.length == R); 73 Matrix res; 74 res.rows[] = rows[]; 75 return res; 76 } 77 78 /// Construct matrix with a scalar. 79 @nogc this(U)(T x) pure nothrow 80 { 81 for (int i = 0; i < _N; ++i) 82 v[i] = x; 83 } 84 85 /// Assign with a samey matrice. 86 @nogc ref Matrix opAssign(U : Matrix)(U x) pure nothrow 87 { 88 for (int i = 0; i < R * C; ++i) 89 v[i] = x.v[i]; 90 return this; 91 } 92 93 /// Assign from other small matrices (same size, compatible type). 94 @nogc ref Matrix opAssign(U)(U x) pure nothrow 95 if (isMatrixInstantiation!U 96 && is(U._T : _T) 97 && (!is(U: Matrix)) 98 && (U._R == R) && (U._C == C)) 99 { 100 for (int i = 0; i < R * C; ++i) 101 v[i] = x.v[i]; 102 return this; 103 } 104 105 /// Assign with a static array of size R * C. 106 @nogc ref Matrix opAssign(U)(U x) pure nothrow 107 if ((isStaticArray!U) 108 && is(typeof(x[0]) : T) 109 && (U.length == R * C)) 110 { 111 for (int i = 0; i < R * C; ++i) 112 v[i] = x[i]; 113 return this; 114 } 115 116 /// Assign with a dynamic array of size R * C. 117 @nogc ref Matrix opAssign(U)(U x) pure nothrow 118 if ((isDynamicArray!U) 119 && is(typeof(x[0]) : T)) 120 { 121 assert(x.length == R * C); 122 for (int i = 0; i < R * C; ++i) 123 v[i] = x[i]; 124 return this; 125 } 126 127 /// Return a pointer to content. 128 @nogc inout(T)* ptr() pure inout nothrow @property 129 { 130 return v.ptr; 131 } 132 133 /// Returns: column j as a vector. 134 @nogc column_t column(int j) pure const nothrow 135 { 136 column_t res = void; 137 for (int i = 0; i < R; ++i) 138 res.v[i] = c[i][j]; 139 return res; 140 } 141 142 /// Returns: row i as a vector. 143 @nogc row_t row(int i) pure const nothrow 144 { 145 return rows[i]; 146 } 147 148 /// Covnerts to pretty string. 149 string toString() const nothrow 150 { 151 try 152 return format("%s", v); 153 catch (Exception e) 154 assert(false); // should not happen since format is right 155 } 156 157 /// Matrix * vector multiplication. 158 @nogc column_t opBinary(string op)(row_t x) pure const nothrow if (op == "*") 159 { 160 column_t res = void; 161 for (int i = 0; i < R; ++i) 162 { 163 T sum = 0; 164 for (int j = 0; j < C; ++j) 165 { 166 sum += c[i][j] * x.v[j]; 167 } 168 res.v[i] = sum; 169 } 170 return res; 171 } 172 173 /// Matrix * matrix multiplication. 174 @nogc auto opBinary(string op, U)(U x) pure const nothrow 175 if (isMatrixInstantiation!U && (U._R == C) && (op == "*")) 176 { 177 Matrix!(T, R, U._C) result = void; 178 179 for (int i = 0; i < R; ++i) 180 { 181 for (int j = 0; j < U._C; ++j) 182 { 183 T sum = 0; 184 for (int k = 0; k < C; ++k) 185 sum += c[i][k] * x.c[k][j]; 186 result.c[i][j] = sum; 187 } 188 } 189 return result; 190 } 191 192 /// Matrix add and substraction. 193 @nogc Matrix opBinary(string op, U)(U other) pure const nothrow 194 if (is(U : Matrix) && (op == "+" || op == "-")) 195 { 196 Matrix result = void; 197 198 for (int i = 0; i < R; ++i) 199 { 200 for (int j = 0; j < C; ++j) 201 { 202 mixin("result.c[i][j] = c[i][j] " ~ op ~ " other.c[i][j];"); 203 } 204 } 205 return result; 206 } 207 208 /// Assignment operator with another samey matrix. 209 @nogc ref Matrix opOpAssign(string op, U)(U operand) pure nothrow if (is(U : Matrix)) 210 { 211 mixin("Matrix result = this " ~ op ~ " operand;"); 212 return opAssign!Matrix(result); 213 } 214 215 /// Assignment operator with another samey matrix. 216 @nogc ref Matrix opOpAssign(string op, U)(U operand) pure nothrow if (isConvertible!U) 217 { 218 Matrix conv = operand; 219 return opOpAssign!op(conv); 220 } 221 222 /// Cast to other matrix types. 223 /// If the size are different, the resulting matrix is truncated 224 /// and/or filled with identity coefficients. 225 @nogc U opCast(U)() pure const nothrow if (isMatrixInstantiation!U) 226 { 227 U res = U.identity(); 228 enum minR = R < U._R ? R : U._R; 229 enum minC = C < U._C ? C : U._C; 230 for (int i = 0; i < minR; ++i) 231 for (int j = 0; j < minC; ++j) 232 { 233 res.c[i][j] = cast(U._T)(c[i][j]); 234 } 235 return res; 236 } 237 238 @nogc bool opEquals(U)(U other) pure const nothrow if (is(U : Matrix)) 239 { 240 for (int i = 0; i < R * C; ++i) 241 if (v[i] != other.v[i]) 242 return false; 243 return true; 244 } 245 246 @nogc bool opEquals(U)(U other) pure const nothrow 247 if ((isAssignable!U) && (!is(U: Matrix))) 248 { 249 Matrix conv = other; 250 return opEquals(conv); 251 } 252 253 // +matrix, -matrix, ~matrix, !matrix 254 @nogc Matrix opUnary(string op)() pure const nothrow if (op == "+" || op == "-" || op == "~" || op == "!") 255 { 256 Matrix res = void; 257 for (int i = 0; i < N; ++i) 258 mixin("res.v[i] = " ~ op ~ "v[i];"); 259 return res; 260 } 261 262 /// Convert 3x3 rotation matrix to quaternion. 263 /// See_also: 3D Math Primer for Graphics and Game Development. 264 @nogc U opCast(U)() pure const nothrow if (isQuaternionInstantiation!U 265 && is(U._T : _T) 266 && (_R == 3) && (_C == 3)) 267 { 268 T fourXSquaredMinus1 = c[0][0] - c[1][1] - c[2][2]; 269 T fourYSquaredMinus1 = c[1][1] - c[0][0] - c[2][2]; 270 T fourZSquaredMinus1 = c[2][2] - c[0][0] - c[1][1]; 271 T fourWSquaredMinus1 = c[0][0] + c[1][1] + c[2][2]; 272 273 int biggestIndex = 0; 274 T fourBiggestSquaredMinus1 = fourWSquaredMinus1; 275 276 if(fourXSquaredMinus1 > fourBiggestSquaredMinus1) 277 { 278 fourBiggestSquaredMinus1 = fourXSquaredMinus1; 279 biggestIndex = 1; 280 } 281 282 if(fourYSquaredMinus1 > fourBiggestSquaredMinus1) 283 { 284 fourBiggestSquaredMinus1 = fourYSquaredMinus1; 285 biggestIndex = 2; 286 } 287 288 if(fourZSquaredMinus1 > fourBiggestSquaredMinus1) 289 { 290 fourBiggestSquaredMinus1 = fourZSquaredMinus1; 291 biggestIndex = 3; 292 } 293 294 T biggestVal = sqrt(fourBiggestSquaredMinus1 + 1) / 2; 295 T mult = 1 / (biggestVal * 4); 296 297 U quat; 298 switch(biggestIndex) 299 { 300 case 1: 301 quat.w = (c[1][2] - c[2][1]) * mult; 302 quat.x = biggestVal; 303 quat.y = (c[0][1] + c[1][0]) * mult; 304 quat.z = (c[2][0] + c[0][2]) * mult; 305 break; 306 307 case 2: 308 quat.w = (c[2][0] - c[0][2]) * mult; 309 quat.x = (c[0][1] + c[1][0]) * mult; 310 quat.y = biggestVal; 311 quat.z = (c[1][2] + c[2][1]) * mult; 312 break; 313 314 case 3: 315 quat.w = (c[0][1] - c[1][0]) * mult; 316 quat.x = (c[2][0] + c[0][2]) * mult; 317 quat.y = (c[1][2] + c[2][1]) * mult; 318 quat.z = biggestVal; 319 break; 320 321 default: // biggestIndex == 0 322 quat.w = biggestVal; 323 quat.x = (c[1][2] - c[2][1]) * mult; 324 quat.y = (c[2][0] - c[0][2]) * mult; 325 quat.z = (c[0][1] - c[1][0]) * mult; 326 break; 327 } 328 329 return quat; 330 } 331 332 /// Converts a 4x4 rotation matrix to quaternion. 333 @nogc U opCast(U)() pure const nothrow if (isQuaternionInstantiation!U 334 && is(U._T : _T) 335 && (_R == 4) && (_C == 4)) 336 { 337 auto m3 = cast(mat3!T)(this); 338 return cast(U)(m3); 339 } 340 341 /// Matrix inversion is provided for 2x2, 3x3 and 4x4 floating point matrices. 342 343 static if (isSquare && isFloatingPoint!T && R == 2) 344 { 345 /// Returns: inverse of matrix. 346 @nogc Matrix inverse() pure const nothrow 347 { 348 T invDet = 1 / (c[0][0] * c[1][1] - c[0][1] * c[1][0]); 349 return Matrix( c[1][1] * invDet, -c[0][1] * invDet, 350 -c[1][0] * invDet, c[0][0] * invDet); 351 } 352 } 353 354 static if (isSquare && isFloatingPoint!T && R == 3) 355 { 356 /// Returns: inverse of matrix. 357 @nogc Matrix inverse() pure const nothrow 358 { 359 T det = c[0][0] * (c[1][1] * c[2][2] - c[2][1] * c[1][2]) 360 - c[0][1] * (c[1][0] * c[2][2] - c[1][2] * c[2][0]) 361 + c[0][2] * (c[1][0] * c[2][1] - c[1][1] * c[2][0]); 362 T invDet = 1 / det; 363 364 Matrix res = void; 365 res.c[0][0] = (c[1][1] * c[2][2] - c[2][1] * c[1][2]) * invDet; 366 res.c[0][1] = -(c[0][1] * c[2][2] - c[0][2] * c[2][1]) * invDet; 367 res.c[0][2] = (c[0][1] * c[1][2] - c[0][2] * c[1][1]) * invDet; 368 res.c[1][0] = -(c[1][0] * c[2][2] - c[1][2] * c[2][0]) * invDet; 369 res.c[1][1] = (c[0][0] * c[2][2] - c[0][2] * c[2][0]) * invDet; 370 res.c[1][2] = -(c[0][0] * c[1][2] - c[1][0] * c[0][2]) * invDet; 371 res.c[2][0] = (c[1][0] * c[2][1] - c[2][0] * c[1][1]) * invDet; 372 res.c[2][1] = -(c[0][0] * c[2][1] - c[2][0] * c[0][1]) * invDet; 373 res.c[2][2] = (c[0][0] * c[1][1] - c[1][0] * c[0][1]) * invDet; 374 return res; 375 } 376 } 377 378 static if (isSquare && isFloatingPoint!T && R == 4) 379 { 380 /// Returns: inverse of matrix. 381 @nogc Matrix inverse() pure const nothrow 382 { 383 T det2_01_01 = c[0][0] * c[1][1] - c[0][1] * c[1][0]; 384 T det2_01_02 = c[0][0] * c[1][2] - c[0][2] * c[1][0]; 385 T det2_01_03 = c[0][0] * c[1][3] - c[0][3] * c[1][0]; 386 T det2_01_12 = c[0][1] * c[1][2] - c[0][2] * c[1][1]; 387 T det2_01_13 = c[0][1] * c[1][3] - c[0][3] * c[1][1]; 388 T det2_01_23 = c[0][2] * c[1][3] - c[0][3] * c[1][2]; 389 390 T det3_201_012 = c[2][0] * det2_01_12 - c[2][1] * det2_01_02 + c[2][2] * det2_01_01; 391 T det3_201_013 = c[2][0] * det2_01_13 - c[2][1] * det2_01_03 + c[2][3] * det2_01_01; 392 T det3_201_023 = c[2][0] * det2_01_23 - c[2][2] * det2_01_03 + c[2][3] * det2_01_02; 393 T det3_201_123 = c[2][1] * det2_01_23 - c[2][2] * det2_01_13 + c[2][3] * det2_01_12; 394 395 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]; 396 T invDet = 1 / det; 397 398 T det2_03_01 = c[0][0] * c[3][1] - c[0][1] * c[3][0]; 399 T det2_03_02 = c[0][0] * c[3][2] - c[0][2] * c[3][0]; 400 T det2_03_03 = c[0][0] * c[3][3] - c[0][3] * c[3][0]; 401 T det2_03_12 = c[0][1] * c[3][2] - c[0][2] * c[3][1]; 402 T det2_03_13 = c[0][1] * c[3][3] - c[0][3] * c[3][1]; 403 T det2_03_23 = c[0][2] * c[3][3] - c[0][3] * c[3][2]; 404 T det2_13_01 = c[1][0] * c[3][1] - c[1][1] * c[3][0]; 405 T det2_13_02 = c[1][0] * c[3][2] - c[1][2] * c[3][0]; 406 T det2_13_03 = c[1][0] * c[3][3] - c[1][3] * c[3][0]; 407 T det2_13_12 = c[1][1] * c[3][2] - c[1][2] * c[3][1]; 408 T det2_13_13 = c[1][1] * c[3][3] - c[1][3] * c[3][1]; 409 T det2_13_23 = c[1][2] * c[3][3] - c[1][3] * c[3][2]; 410 411 T det3_203_012 = c[2][0] * det2_03_12 - c[2][1] * det2_03_02 + c[2][2] * det2_03_01; 412 T det3_203_013 = c[2][0] * det2_03_13 - c[2][1] * det2_03_03 + c[2][3] * det2_03_01; 413 T det3_203_023 = c[2][0] * det2_03_23 - c[2][2] * det2_03_03 + c[2][3] * det2_03_02; 414 T det3_203_123 = c[2][1] * det2_03_23 - c[2][2] * det2_03_13 + c[2][3] * det2_03_12; 415 416 T det3_213_012 = c[2][0] * det2_13_12 - c[2][1] * det2_13_02 + c[2][2] * det2_13_01; 417 T det3_213_013 = c[2][0] * det2_13_13 - c[2][1] * det2_13_03 + c[2][3] * det2_13_01; 418 T det3_213_023 = c[2][0] * det2_13_23 - c[2][2] * det2_13_03 + c[2][3] * det2_13_02; 419 T det3_213_123 = c[2][1] * det2_13_23 - c[2][2] * det2_13_13 + c[2][3] * det2_13_12; 420 421 T det3_301_012 = c[3][0] * det2_01_12 - c[3][1] * det2_01_02 + c[3][2] * det2_01_01; 422 T det3_301_013 = c[3][0] * det2_01_13 - c[3][1] * det2_01_03 + c[3][3] * det2_01_01; 423 T det3_301_023 = c[3][0] * det2_01_23 - c[3][2] * det2_01_03 + c[3][3] * det2_01_02; 424 T det3_301_123 = c[3][1] * det2_01_23 - c[3][2] * det2_01_13 + c[3][3] * det2_01_12; 425 426 Matrix res = void; 427 res.c[0][0] = - det3_213_123 * invDet; 428 res.c[1][0] = + det3_213_023 * invDet; 429 res.c[2][0] = - det3_213_013 * invDet; 430 res.c[3][0] = + det3_213_012 * invDet; 431 432 res.c[0][1] = + det3_203_123 * invDet; 433 res.c[1][1] = - det3_203_023 * invDet; 434 res.c[2][1] = + det3_203_013 * invDet; 435 res.c[3][1] = - det3_203_012 * invDet; 436 437 res.c[0][2] = + det3_301_123 * invDet; 438 res.c[1][2] = - det3_301_023 * invDet; 439 res.c[2][2] = + det3_301_013 * invDet; 440 res.c[3][2] = - det3_301_012 * invDet; 441 442 res.c[0][3] = - det3_201_123 * invDet; 443 res.c[1][3] = + det3_201_023 * invDet; 444 res.c[2][3] = - det3_201_013 * invDet; 445 res.c[3][3] = + det3_201_012 * invDet; 446 return res; 447 } 448 } 449 450 /// Returns: transposed matrice. 451 @nogc Matrix!(T, C, R) transposed() pure const nothrow 452 { 453 Matrix!(T, C, R) res; 454 for (int i = 0; i < C; ++i) 455 for (int j = 0; j < R; ++j) 456 res.c[i][j] = c[j][i]; 457 return res; 458 } 459 460 static if (isSquare && R > 1) 461 { 462 /// In-place translate by (v, 1) 463 @nogc void translate(Vector!(T, R-1) v) pure nothrow 464 { 465 for (int i = 0; i < R; ++i) 466 { 467 T dot = 0; 468 for (int j = 0; j + 1 < C; ++j) 469 dot += v.v[j] * c[i][j]; 470 471 c[i][C-1] += dot; 472 } 473 } 474 475 /// Make a translation matrix. 476 @nogc static Matrix translation(Vector!(T, R-1) v) pure nothrow 477 { 478 Matrix res = identity(); 479 for (int i = 0; i + 1 < R; ++i) 480 res.c[i][C-1] += v.v[i]; 481 return res; 482 } 483 484 /// In-place matrix scaling. 485 void scale(Vector!(T, R-1) v) pure nothrow 486 { 487 for (int i = 0; i < R; ++i) 488 for (int j = 0; j + 1 < C; ++j) 489 c[i][j] *= v.v[j]; 490 } 491 492 /// Make a scaling matrix. 493 @nogc static Matrix scaling(Vector!(T, R-1) v) pure nothrow 494 { 495 Matrix res = identity(); 496 for (int i = 0; i + 1 < R; ++i) 497 res.c[i][i] = v.v[i]; 498 return res; 499 } 500 } 501 502 // rotations are implemented for 3x3 and 4x4 matrices. 503 static if (isSquare && (R == 3 || R == 4) && isFloatingPoint!T) 504 { 505 @nogc public static Matrix rotateAxis(int i, int j)(T angle) pure nothrow 506 { 507 Matrix res = identity(); 508 const T cosa = cos(angle); 509 const T sina = sin(angle); 510 res.c[i][i] = cosa; 511 res.c[i][j] = -sina; 512 res.c[j][i] = sina; 513 res.c[j][j] = cosa; 514 return res; 515 } 516 517 /// Returns: rotation matrix along axis X 518 alias rotateAxis!(1, 2) rotateX; 519 520 /// Returns: rotation matrix along axis Y 521 alias rotateAxis!(2, 0) rotateY; 522 523 /// Returns: rotation matrix along axis Z 524 alias rotateAxis!(0, 1) rotateZ; 525 526 /// Similar to the glRotate matrix, however the angle is expressed in radians 527 /// See_also: $(LINK http://www.cs.rutgers.edu/~decarlo/428/gl_man/rotate.html) 528 @nogc static Matrix rotation(T angle, vec3!T axis) pure nothrow 529 { 530 Matrix res = identity(); 531 const T c = cos(angle); 532 const oneMinusC = 1 - c; 533 const T s = sin(angle); 534 axis = axis.normalized(); 535 T x = axis.x, 536 y = axis.y, 537 z = axis.z; 538 T xy = x * y, 539 yz = y * z, 540 xz = x * z; 541 542 res.c[0][0] = x * x * oneMinusC + c; 543 res.c[0][1] = x * y * oneMinusC - z * s; 544 res.c[0][2] = x * z * oneMinusC + y * s; 545 res.c[1][0] = y * x * oneMinusC + z * s; 546 res.c[1][1] = y * y * oneMinusC + c; 547 res.c[1][2] = y * z * oneMinusC - x * s; 548 res.c[2][0] = z * x * oneMinusC - y * s; 549 res.c[2][1] = z * y * oneMinusC + x * s; 550 res.c[2][2] = z * z * oneMinusC + c; 551 return res; 552 } 553 } 554 555 // 4x4 specific transformations for 3D usage 556 static if (isSquare && R == 4 && isFloatingPoint!T) 557 { 558 /// Returns: orthographic projection. 559 @nogc static Matrix orthographic(T left, T right, T bottom, T top, T near, T far) pure nothrow 560 { 561 T dx = right - left, 562 dy = top - bottom, 563 dz = far - near; 564 565 T tx = -(right + left) / dx; 566 T ty = -(top + bottom) / dy; 567 T tz = -(far + near) / dz; 568 569 return Matrix(2 / dx, 0, 0, tx, 570 0, 2 / dy, 0, ty, 571 0, 0, -2 / dz, tz, 572 0, 0, 0, 1); 573 } 574 575 /// Returns: perspective projection. 576 @nogc static Matrix perspective(T FOVInRadians, T aspect, T zNear, T zFar) pure nothrow 577 { 578 T f = 1 / tan(FOVInRadians / 2); 579 T d = 1 / (zNear - zFar); 580 581 return Matrix(f / aspect, 0, 0, 0, 582 0, f, 0, 0, 583 0, 0, (zFar + zNear) * d, 2 * d * zFar * zNear, 584 0, 0, -1, 0); 585 } 586 587 /// Returns: "lookAt" projection. 588 /// Thanks to vuaru for corrections. 589 @nogc static Matrix lookAt(vec3!T eye, vec3!T target, vec3!T up) pure nothrow 590 { 591 vec3!T Z = (eye - target).normalized(); 592 vec3!T X = cross(-up, Z).normalized(); 593 vec3!T Y = cross(Z, -X); 594 595 return Matrix(-X.x, -X.y, -X.z, dot(X, eye), 596 Y.x, Y.y, Y.z, -dot(Y, eye), 597 Z.x, Z.y, Z.z, -dot(Z, eye), 598 0, 0, 0, 1); 599 } 600 601 /// Extract frustum from a 4x4 matrice. 602 @nogc Frustum!T frustum() pure const nothrow 603 { 604 auto left = Plane!T(row(3) + row(0)); 605 auto right = Plane!T(row(3) - row(0)); 606 auto top = Plane!T(row(3) - row(1)); 607 auto bottom = Plane!T(row(3) + row(1)); 608 auto near = Plane!T(row(3) + row(2)); 609 auto far = Plane!T(row(3) - row(2)); 610 return Frustum!T(left, right, top, bottom, near, far); 611 } 612 613 } 614 } 615 616 package 617 { 618 alias T _T; 619 enum _R = R; 620 enum _C = C; 621 } 622 623 private 624 { 625 template isAssignable(T) 626 { 627 enum bool isAssignable = std.traits.isAssignable!(Matrix, T); 628 } 629 630 template isConvertible(T) 631 { 632 enum bool isConvertible = (!is(T : Matrix)) && isAssignable!T; 633 } 634 635 template isTAssignable(U) 636 { 637 enum bool isTAssignable = std.traits.isAssignable!(T, U); 638 } 639 640 template isRowConvertible(U) 641 { 642 enum bool isRowConvertible = is(U : row_t); 643 } 644 645 template isColumnConvertible(U) 646 { 647 enum bool isColumnConvertible = is(U : column_t); 648 } 649 } 650 651 public 652 { 653 /// Returns: an identity matrice. 654 /// Note: the identity matrix, while only meaningful for square matrices, 655 /// is also defined for non-square ones. 656 @nogc static Matrix identity() pure nothrow 657 { 658 Matrix res = void; 659 for (int i = 0; i < R; ++i) 660 for (int j = 0; j < C; ++j) 661 res.c[i][j] = (i == j) ? 1 : 0; 662 return res; 663 } 664 665 /// Returns: a constant matrice. 666 @nogc static Matrix constant(U)(U x) pure nothrow 667 { 668 Matrix res = void; 669 670 for (int i = 0; i < R * C; ++i) 671 res.v[i] = cast(T)x; 672 return res; 673 } 674 } 675 } 676 677 template isMatrixInstantiation(U) 678 { 679 private static void isMatrix(T, int R, int C)(Matrix!(T, R, C) x) 680 { 681 } 682 683 enum bool isMatrixInstantiation = is(typeof(isMatrix(U.init))); 684 } 685 686 // GLSL is a big inspiration here 687 // we defines types with more or less the same names 688 template mat2x2(T) { alias Matrix!(T, 2, 2) mat2x2; } 689 template mat3x3(T) { alias Matrix!(T, 3, 3) mat3x3; } 690 template mat4x4(T) { alias Matrix!(T, 4, 4) mat4x4; } 691 692 // WARNING: in GLSL, first number is _columns_, second is rows 693 // It is the opposite here: first number is rows, second is columns 694 // With this convention mat2x3 * mat3x4 -> mat2x4. 695 template mat2x3(T) { alias Matrix!(T, 2, 3) mat2x3; } 696 template mat2x4(T) { alias Matrix!(T, 2, 4) mat2x4; } 697 template mat3x2(T) { alias Matrix!(T, 3, 2) mat3x2; } 698 template mat3x4(T) { alias Matrix!(T, 3, 4) mat3x4; } 699 template mat4x2(T) { alias Matrix!(T, 4, 2) mat4x2; } 700 template mat4x3(T) { alias Matrix!(T, 4, 3) mat4x3; } 701 702 alias mat2x2 mat2; 703 alias mat3x3 mat3; // shorter names for most common matrices 704 alias mat4x4 mat4; 705 706 private string definePostfixAliases(string type) 707 { 708 return "alias " ~ type ~ "!byte " ~ type ~ "b;" 709 ~ "alias " ~ type ~ "!short " ~ type ~ "s;" 710 ~ "alias " ~ type ~ "!int " ~ type ~ "i;" 711 ~ "alias " ~ type ~ "!long " ~ type ~ "l;" 712 ~ "alias " ~ type ~ "!float " ~ type ~ "f;" 713 ~ "alias " ~ type ~ "!double " ~ type ~ "d;"; 714 } 715 716 // define a lot of type names 717 mixin(definePostfixAliases("mat2")); 718 mixin(definePostfixAliases("mat3")); 719 mixin(definePostfixAliases("mat4")); 720 mixin(definePostfixAliases("mat2x2")); 721 mixin(definePostfixAliases("mat2x3")); 722 mixin(definePostfixAliases("mat2x4")); 723 mixin(definePostfixAliases("mat3x2")); 724 mixin(definePostfixAliases("mat3x3")); 725 mixin(definePostfixAliases("mat3x4")); 726 mixin(definePostfixAliases("mat4x2")); 727 mixin(definePostfixAliases("mat4x3")); 728 mixin(definePostfixAliases("mat4x4")); 729 730 unittest 731 { 732 mat2i x = mat2i(0, 1, 733 2, 3); 734 assert(x.c[0][0] == 0 && x.c[0][1] == 1 && x.c[1][0] == 2 && x.c[1][1] == 3); 735 736 vec2i[2] cols = [vec2i(0, 2), vec2i(1, 3)]; 737 mat2i y = mat2i.fromColumns(cols[]); 738 assert(y.c[0][0] == 0 && y.c[0][1] == 1 && y.c[1][0] == 2 && y.c[1][1] == 3); 739 y = mat2i.fromRows(cols[]); 740 assert(y.c[0][0] == 0 && y.c[1][0] == 1 && y.c[0][1] == 2 && y.c[1][1] == 3); 741 y = y.transposed(); 742 743 assert(x == y); 744 x = [0, 1, 2, 3]; 745 assert(x == y); 746 747 mat2i z = x * y; 748 assert(z == mat2i([2, 3, 6, 11])); 749 vec2i vz = z * vec2i(2, -1); 750 assert(vz == vec2i(1, 1)); 751 752 mat2f a = z; 753 mat2d ad = a; 754 ad += a; 755 mat2f w = [4, 5, 6, 7]; 756 z = cast(mat2i)w; 757 assert(w == z); 758 759 { 760 mat2x3f A; 761 mat3x4f B; 762 mat2x4f C = A * B; 763 } 764 }