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 1x1, 2x2, 3x3 and 4x4 floating point matrices. 342 343 static if (isSquare && isFloatingPoint!T && R == 1) 344 { 345 /// Returns: inverse of matrix. 346 @nogc Matrix inverse() pure const nothrow 347 { 348 return Matrix( 1 / c[0][0]); 349 } 350 } 351 352 static if (isSquare && isFloatingPoint!T && R == 2) 353 { 354 /// Returns: inverse of matrix. 355 @nogc Matrix inverse() pure const nothrow 356 { 357 T invDet = 1 / (c[0][0] * c[1][1] - c[0][1] * c[1][0]); 358 return Matrix( c[1][1] * invDet, -c[0][1] * invDet, 359 -c[1][0] * invDet, c[0][0] * invDet); 360 } 361 } 362 363 static if (isSquare && isFloatingPoint!T && R == 3) 364 { 365 /// Returns: inverse of matrix. 366 @nogc Matrix inverse() pure const nothrow 367 { 368 T det = c[0][0] * (c[1][1] * c[2][2] - c[2][1] * c[1][2]) 369 - c[0][1] * (c[1][0] * c[2][2] - c[1][2] * c[2][0]) 370 + c[0][2] * (c[1][0] * c[2][1] - c[1][1] * c[2][0]); 371 T invDet = 1 / det; 372 373 Matrix res = void; 374 res.c[0][0] = (c[1][1] * c[2][2] - c[2][1] * c[1][2]) * invDet; 375 res.c[0][1] = -(c[0][1] * c[2][2] - c[0][2] * c[2][1]) * invDet; 376 res.c[0][2] = (c[0][1] * c[1][2] - c[0][2] * c[1][1]) * invDet; 377 res.c[1][0] = -(c[1][0] * c[2][2] - c[1][2] * c[2][0]) * invDet; 378 res.c[1][1] = (c[0][0] * c[2][2] - c[0][2] * c[2][0]) * invDet; 379 res.c[1][2] = -(c[0][0] * c[1][2] - c[1][0] * c[0][2]) * invDet; 380 res.c[2][0] = (c[1][0] * c[2][1] - c[2][0] * c[1][1]) * invDet; 381 res.c[2][1] = -(c[0][0] * c[2][1] - c[2][0] * c[0][1]) * invDet; 382 res.c[2][2] = (c[0][0] * c[1][1] - c[1][0] * c[0][1]) * invDet; 383 return res; 384 } 385 } 386 387 static if (isSquare && isFloatingPoint!T && R == 4) 388 { 389 /// Returns: inverse of matrix. 390 @nogc Matrix inverse() pure const nothrow 391 { 392 T det2_01_01 = c[0][0] * c[1][1] - c[0][1] * c[1][0]; 393 T det2_01_02 = c[0][0] * c[1][2] - c[0][2] * c[1][0]; 394 T det2_01_03 = c[0][0] * c[1][3] - c[0][3] * c[1][0]; 395 T det2_01_12 = c[0][1] * c[1][2] - c[0][2] * c[1][1]; 396 T det2_01_13 = c[0][1] * c[1][3] - c[0][3] * c[1][1]; 397 T det2_01_23 = c[0][2] * c[1][3] - c[0][3] * c[1][2]; 398 399 T det3_201_012 = c[2][0] * det2_01_12 - c[2][1] * det2_01_02 + c[2][2] * det2_01_01; 400 T det3_201_013 = c[2][0] * det2_01_13 - c[2][1] * det2_01_03 + c[2][3] * det2_01_01; 401 T det3_201_023 = c[2][0] * det2_01_23 - c[2][2] * det2_01_03 + c[2][3] * det2_01_02; 402 T det3_201_123 = c[2][1] * det2_01_23 - c[2][2] * det2_01_13 + c[2][3] * det2_01_12; 403 404 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]; 405 T invDet = 1 / det; 406 407 T det2_03_01 = c[0][0] * c[3][1] - c[0][1] * c[3][0]; 408 T det2_03_02 = c[0][0] * c[3][2] - c[0][2] * c[3][0]; 409 T det2_03_03 = c[0][0] * c[3][3] - c[0][3] * c[3][0]; 410 T det2_03_12 = c[0][1] * c[3][2] - c[0][2] * c[3][1]; 411 T det2_03_13 = c[0][1] * c[3][3] - c[0][3] * c[3][1]; 412 T det2_03_23 = c[0][2] * c[3][3] - c[0][3] * c[3][2]; 413 T det2_13_01 = c[1][0] * c[3][1] - c[1][1] * c[3][0]; 414 T det2_13_02 = c[1][0] * c[3][2] - c[1][2] * c[3][0]; 415 T det2_13_03 = c[1][0] * c[3][3] - c[1][3] * c[3][0]; 416 T det2_13_12 = c[1][1] * c[3][2] - c[1][2] * c[3][1]; 417 T det2_13_13 = c[1][1] * c[3][3] - c[1][3] * c[3][1]; 418 T det2_13_23 = c[1][2] * c[3][3] - c[1][3] * c[3][2]; 419 420 T det3_203_012 = c[2][0] * det2_03_12 - c[2][1] * det2_03_02 + c[2][2] * det2_03_01; 421 T det3_203_013 = c[2][0] * det2_03_13 - c[2][1] * det2_03_03 + c[2][3] * det2_03_01; 422 T det3_203_023 = c[2][0] * det2_03_23 - c[2][2] * det2_03_03 + c[2][3] * det2_03_02; 423 T det3_203_123 = c[2][1] * det2_03_23 - c[2][2] * det2_03_13 + c[2][3] * det2_03_12; 424 425 T det3_213_012 = c[2][0] * det2_13_12 - c[2][1] * det2_13_02 + c[2][2] * det2_13_01; 426 T det3_213_013 = c[2][0] * det2_13_13 - c[2][1] * det2_13_03 + c[2][3] * det2_13_01; 427 T det3_213_023 = c[2][0] * det2_13_23 - c[2][2] * det2_13_03 + c[2][3] * det2_13_02; 428 T det3_213_123 = c[2][1] * det2_13_23 - c[2][2] * det2_13_13 + c[2][3] * det2_13_12; 429 430 T det3_301_012 = c[3][0] * det2_01_12 - c[3][1] * det2_01_02 + c[3][2] * det2_01_01; 431 T det3_301_013 = c[3][0] * det2_01_13 - c[3][1] * det2_01_03 + c[3][3] * det2_01_01; 432 T det3_301_023 = c[3][0] * det2_01_23 - c[3][2] * det2_01_03 + c[3][3] * det2_01_02; 433 T det3_301_123 = c[3][1] * det2_01_23 - c[3][2] * det2_01_13 + c[3][3] * det2_01_12; 434 435 Matrix res = void; 436 res.c[0][0] = - det3_213_123 * invDet; 437 res.c[1][0] = + det3_213_023 * invDet; 438 res.c[2][0] = - det3_213_013 * invDet; 439 res.c[3][0] = + det3_213_012 * invDet; 440 441 res.c[0][1] = + det3_203_123 * invDet; 442 res.c[1][1] = - det3_203_023 * invDet; 443 res.c[2][1] = + det3_203_013 * invDet; 444 res.c[3][1] = - det3_203_012 * invDet; 445 446 res.c[0][2] = + det3_301_123 * invDet; 447 res.c[1][2] = - det3_301_023 * invDet; 448 res.c[2][2] = + det3_301_013 * invDet; 449 res.c[3][2] = - det3_301_012 * invDet; 450 451 res.c[0][3] = - det3_201_123 * invDet; 452 res.c[1][3] = + det3_201_023 * invDet; 453 res.c[2][3] = - det3_201_013 * invDet; 454 res.c[3][3] = + det3_201_012 * invDet; 455 return res; 456 } 457 } 458 459 /// Returns: transposed matrice. 460 @nogc Matrix!(T, C, R) transposed() pure const nothrow 461 { 462 Matrix!(T, C, R) res; 463 for (int i = 0; i < C; ++i) 464 for (int j = 0; j < R; ++j) 465 res.c[i][j] = c[j][i]; 466 return res; 467 } 468 469 static if (isSquare && R > 1) 470 { 471 /// In-place translate by (v, 1) 472 @nogc void translate(Vector!(T, R-1) v) pure nothrow 473 { 474 for (int i = 0; i < R; ++i) 475 { 476 T dot = 0; 477 for (int j = 0; j + 1 < C; ++j) 478 dot += v.v[j] * c[i][j]; 479 480 c[i][C-1] += dot; 481 } 482 } 483 484 /// Make a translation matrix. 485 @nogc static Matrix translation(Vector!(T, R-1) v) pure nothrow 486 { 487 Matrix res = identity(); 488 for (int i = 0; i + 1 < R; ++i) 489 res.c[i][C-1] += v.v[i]; 490 return res; 491 } 492 493 /// In-place matrix scaling. 494 void scale(Vector!(T, R-1) v) pure nothrow 495 { 496 for (int i = 0; i < R; ++i) 497 for (int j = 0; j + 1 < C; ++j) 498 c[i][j] *= v.v[j]; 499 } 500 501 /// Make a scaling matrix. 502 @nogc static Matrix scaling(Vector!(T, R-1) v) pure nothrow 503 { 504 Matrix res = identity(); 505 for (int i = 0; i + 1 < R; ++i) 506 res.c[i][i] = v.v[i]; 507 return res; 508 } 509 } 510 511 // rotations are implemented for 3x3 and 4x4 matrices. 512 static if (isSquare && (R == 3 || R == 4) && isFloatingPoint!T) 513 { 514 @nogc public static Matrix rotateAxis(int i, int j)(T angle) pure nothrow 515 { 516 Matrix res = identity(); 517 const T cosa = cos(angle); 518 const T sina = sin(angle); 519 res.c[i][i] = cosa; 520 res.c[i][j] = -sina; 521 res.c[j][i] = sina; 522 res.c[j][j] = cosa; 523 return res; 524 } 525 526 /// Returns: rotation matrix along axis X 527 alias rotateAxis!(1, 2) rotateX; 528 529 /// Returns: rotation matrix along axis Y 530 alias rotateAxis!(2, 0) rotateY; 531 532 /// Returns: rotation matrix along axis Z 533 alias rotateAxis!(0, 1) rotateZ; 534 535 /// Similar to the glRotate matrix, however the angle is expressed in radians 536 /// See_also: $(LINK http://www.cs.rutgers.edu/~decarlo/428/gl_man/rotate.html) 537 @nogc static Matrix rotation(T angle, vec3!T axis) pure nothrow 538 { 539 Matrix res = identity(); 540 const T c = cos(angle); 541 const oneMinusC = 1 - c; 542 const T s = sin(angle); 543 axis = axis.normalized(); 544 T x = axis.x, 545 y = axis.y, 546 z = axis.z; 547 T xy = x * y, 548 yz = y * z, 549 xz = x * z; 550 551 res.c[0][0] = x * x * oneMinusC + c; 552 res.c[0][1] = x * y * oneMinusC - z * s; 553 res.c[0][2] = x * z * oneMinusC + y * s; 554 res.c[1][0] = y * x * oneMinusC + z * s; 555 res.c[1][1] = y * y * oneMinusC + c; 556 res.c[1][2] = y * z * oneMinusC - x * s; 557 res.c[2][0] = z * x * oneMinusC - y * s; 558 res.c[2][1] = z * y * oneMinusC + x * s; 559 res.c[2][2] = z * z * oneMinusC + c; 560 return res; 561 } 562 } 563 564 // 4x4 specific transformations for 3D usage 565 static if (isSquare && R == 4 && isFloatingPoint!T) 566 { 567 /// Returns: orthographic projection. 568 @nogc static Matrix orthographic(T left, T right, T bottom, T top, T near, T far) pure nothrow 569 { 570 T dx = right - left, 571 dy = top - bottom, 572 dz = far - near; 573 574 T tx = -(right + left) / dx; 575 T ty = -(top + bottom) / dy; 576 T tz = -(far + near) / dz; 577 578 return Matrix(2 / dx, 0, 0, tx, 579 0, 2 / dy, 0, ty, 580 0, 0, -2 / dz, tz, 581 0, 0, 0, 1); 582 } 583 584 /// Returns: perspective projection. 585 @nogc static Matrix perspective(T FOVInRadians, T aspect, T zNear, T zFar) pure nothrow 586 { 587 T f = 1 / tan(FOVInRadians / 2); 588 T d = 1 / (zNear - zFar); 589 590 return Matrix(f / aspect, 0, 0, 0, 591 0, f, 0, 0, 592 0, 0, (zFar + zNear) * d, 2 * d * zFar * zNear, 593 0, 0, -1, 0); 594 } 595 596 /// Returns: "lookAt" projection. 597 /// Thanks to vuaru for corrections. 598 @nogc static Matrix lookAt(vec3!T eye, vec3!T target, vec3!T up) pure nothrow 599 { 600 vec3!T Z = (eye - target).normalized(); 601 vec3!T X = cross(-up, Z).normalized(); 602 vec3!T Y = cross(Z, -X); 603 604 return Matrix(-X.x, -X.y, -X.z, dot(X, eye), 605 Y.x, Y.y, Y.z, -dot(Y, eye), 606 Z.x, Z.y, Z.z, -dot(Z, eye), 607 0, 0, 0, 1); 608 } 609 610 /// Extract frustum from a 4x4 matrice. 611 @nogc Frustum!T frustum() pure const nothrow 612 { 613 auto left = Plane!T(row(3) + row(0)); 614 auto right = Plane!T(row(3) - row(0)); 615 auto top = Plane!T(row(3) - row(1)); 616 auto bottom = Plane!T(row(3) + row(1)); 617 auto near = Plane!T(row(3) + row(2)); 618 auto far = Plane!T(row(3) - row(2)); 619 return Frustum!T(left, right, top, bottom, near, far); 620 } 621 622 } 623 } 624 625 package 626 { 627 alias T _T; 628 enum _R = R; 629 enum _C = C; 630 } 631 632 private 633 { 634 template isAssignable(T) 635 { 636 enum bool isAssignable = std.traits.isAssignable!(Matrix, T); 637 } 638 639 template isConvertible(T) 640 { 641 enum bool isConvertible = (!is(T : Matrix)) && isAssignable!T; 642 } 643 644 template isTAssignable(U) 645 { 646 enum bool isTAssignable = std.traits.isAssignable!(T, U); 647 } 648 649 template isRowConvertible(U) 650 { 651 enum bool isRowConvertible = is(U : row_t); 652 } 653 654 template isColumnConvertible(U) 655 { 656 enum bool isColumnConvertible = is(U : column_t); 657 } 658 } 659 660 public 661 { 662 /// Returns: an identity matrice. 663 /// Note: the identity matrix, while only meaningful for square matrices, 664 /// is also defined for non-square ones. 665 @nogc static Matrix identity() pure nothrow 666 { 667 Matrix res = void; 668 for (int i = 0; i < R; ++i) 669 for (int j = 0; j < C; ++j) 670 res.c[i][j] = (i == j) ? 1 : 0; 671 return res; 672 } 673 674 /// Returns: a constant matrice. 675 @nogc static Matrix constant(U)(U x) pure nothrow 676 { 677 Matrix res = void; 678 679 for (int i = 0; i < R * C; ++i) 680 res.v[i] = cast(T)x; 681 return res; 682 } 683 } 684 } 685 686 template isMatrixInstantiation(U) 687 { 688 private static void isMatrix(T, int R, int C)(Matrix!(T, R, C) x) 689 { 690 } 691 692 enum bool isMatrixInstantiation = is(typeof(isMatrix(U.init))); 693 } 694 695 // GLSL is a big inspiration here 696 // we defines types with more or less the same names 697 template mat2x2(T) { alias Matrix!(T, 2, 2) mat2x2; } 698 template mat3x3(T) { alias Matrix!(T, 3, 3) mat3x3; } 699 template mat4x4(T) { alias Matrix!(T, 4, 4) mat4x4; } 700 701 // WARNING: in GLSL, first number is _columns_, second is rows 702 // It is the opposite here: first number is rows, second is columns 703 // With this convention mat2x3 * mat3x4 -> mat2x4. 704 template mat2x3(T) { alias Matrix!(T, 2, 3) mat2x3; } 705 template mat2x4(T) { alias Matrix!(T, 2, 4) mat2x4; } 706 template mat3x2(T) { alias Matrix!(T, 3, 2) mat3x2; } 707 template mat3x4(T) { alias Matrix!(T, 3, 4) mat3x4; } 708 template mat4x2(T) { alias Matrix!(T, 4, 2) mat4x2; } 709 template mat4x3(T) { alias Matrix!(T, 4, 3) mat4x3; } 710 711 alias mat2x2 mat2; 712 alias mat3x3 mat3; // shorter names for most common matrices 713 alias mat4x4 mat4; 714 715 // Define a lot of type names 716 // Most useful are probably mat4f and mat4d 717 718 alias mat2!byte mat2b; 719 alias mat2!short mat2s; 720 alias mat2!int mat2i; 721 alias mat2!long mat2l; 722 alias mat2!float mat2f; 723 alias mat2!double mat2d; 724 725 alias mat3!byte mat3b; 726 alias mat3!short mat3s; 727 alias mat3!int mat3i; 728 alias mat3!long mat3l; 729 alias mat3!float mat3f; 730 alias mat3!double mat3d; 731 732 alias mat4!byte mat4b; 733 alias mat4!short mat4s; 734 alias mat4!int mat4i; 735 alias mat4!long mat4l; 736 alias mat4!float mat4f; 737 alias mat4!double mat4d; 738 739 alias mat2x2!byte mat2x2b; 740 alias mat2x2!short mat2x2s; 741 alias mat2x2!int mat2x2i; 742 alias mat2x2!long mat2x2l; 743 alias mat2x2!float mat2x2f; 744 alias mat2x2!double mat2x2d; 745 746 alias mat2x3!byte mat2x3b; 747 alias mat2x3!short mat2x3s; 748 alias mat2x3!int mat2x3i; 749 alias mat2x3!long mat2x3l; 750 alias mat2x3!float mat2x3f; 751 alias mat2x3!double mat2x3d; 752 753 alias mat2x4!byte mat2x4b; 754 alias mat2x4!short mat2x4s; 755 alias mat2x4!int mat2x4i; 756 alias mat2x4!long mat2x4l; 757 alias mat2x4!float mat2x4f; 758 alias mat2x4!double mat2x4d; 759 760 alias mat3x2!byte mat3x2b; 761 alias mat3x2!short mat3x2s; 762 alias mat3x2!int mat3x2i; 763 alias mat3x2!long mat3x2l; 764 alias mat3x2!float mat3x2f; 765 alias mat3x2!double mat3x2d; 766 767 alias mat3x3!byte mat3x3b; 768 alias mat3x3!short mat3x3s; 769 alias mat3x3!int mat3x3i; 770 alias mat3x3!long mat3x3l; 771 alias mat3x3!float mat3x3f; 772 alias mat3x3!double mat3x3d; 773 774 alias mat3x4!byte mat3x4b; 775 alias mat3x4!short mat3x4s; 776 alias mat3x4!int mat3x4i; 777 alias mat3x4!long mat3x4l; 778 alias mat3x4!float mat3x4f; 779 alias mat3x4!double mat3x4d; 780 781 alias mat4x2!byte mat4x2b; 782 alias mat4x2!short mat4x2s; 783 alias mat4x2!int mat4x2i; 784 alias mat4x2!long mat4x2l; 785 alias mat4x2!float mat4x2f; 786 alias mat4x2!double mat4x2d; 787 788 alias mat4x3!byte mat4x3b; 789 alias mat4x3!short mat4x3s; 790 alias mat4x3!int mat4x3i; 791 alias mat4x3!long mat4x3l; 792 alias mat4x3!float mat4x3f; 793 alias mat4x3!double mat4x3d; 794 795 alias mat4x4!byte mat4x4b; 796 alias mat4x4!short mat4x4s; 797 alias mat4x4!int mat4x4i; 798 alias mat4x4!long mat4x4l; 799 alias mat4x4!float mat4x4f; 800 alias mat4x4!double mat4x4d; 801 802 unittest 803 { 804 mat2i x = mat2i(0, 1, 805 2, 3); 806 assert(x.c[0][0] == 0 && x.c[0][1] == 1 && x.c[1][0] == 2 && x.c[1][1] == 3); 807 808 vec2i[2] cols = [vec2i(0, 2), vec2i(1, 3)]; 809 mat2i y = mat2i.fromColumns(cols[]); 810 assert(y.c[0][0] == 0 && y.c[0][1] == 1 && y.c[1][0] == 2 && y.c[1][1] == 3); 811 y = mat2i.fromRows(cols[]); 812 assert(y.c[0][0] == 0 && y.c[1][0] == 1 && y.c[0][1] == 2 && y.c[1][1] == 3); 813 y = y.transposed(); 814 815 assert(x == y); 816 x = [0, 1, 2, 3]; 817 assert(x == y); 818 819 mat2i z = x * y; 820 assert(z == mat2i([2, 3, 6, 11])); 821 vec2i vz = z * vec2i(2, -1); 822 assert(vz == vec2i(1, 1)); 823 824 mat2f a = z; 825 mat2d ad = a; 826 ad += a; 827 mat2f w = [4, 5, 6, 7]; 828 z = cast(mat2i)w; 829 assert(w == z); 830 831 { 832 mat2x3f A; 833 mat3x4f B; 834 mat2x4f C = A * B; 835 } 836 }