1 #ifndef GIM_LINEAR_H_INCLUDED 2 #define GIM_LINEAR_H_INCLUDED 3 4 /*! \file gim_linear_math.h 5 *\author Francisco Leon Najera 6 Type Independant Vector and matrix operations. 7 */ 8 /* 9 ----------------------------------------------------------------------------- 10 This source file is part of GIMPACT Library. 11 12 For the latest info, see http://gimpact.sourceforge.net/ 13 14 Copyright (c) 2006 Francisco Leon Najera. C.C. 80087371. 15 email: projectileman (at) yahoo.com 16 17 This library is free software; you can redistribute it and/or 18 modify it under the terms of EITHER: 19 (1) The GNU Lesser General Public License as published by the Free 20 Software Foundation; either version 2.1 of the License, or (at 21 your option) any later version. The text of the GNU Lesser 22 General Public License is included with this library in the 23 file GIMPACT-LICENSE-LGPL.TXT. 24 (2) The BSD-style license that is included with this library in 25 the file GIMPACT-LICENSE-BSD.TXT. 26 (3) The zlib/libpng license that is included with this library in 27 the file GIMPACT-LICENSE-ZLIB.TXT. 28 29 This library is distributed in the hope that it will be useful, 30 but WITHOUT ANY WARRANTY; without even the implied warranty of 31 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files 32 GIMPACT-LICENSE-LGPL.TXT, GIMPACT-LICENSE-ZLIB.TXT and GIMPACT-LICENSE-BSD.TXT for more details. 33 34 ----------------------------------------------------------------------------- 35 */ 36 37 38 #include "gim_math.h" 39 #include "gim_geom_types.h" 40 41 42 43 44 //! Zero out a 2D vector 45 #define VEC_ZERO_2(a) \ 46 { \ 47 (a)[0] = (a)[1] = 0.0f; \ 48 }\ 49 50 51 //! Zero out a 3D vector 52 #define VEC_ZERO(a) \ 53 { \ 54 (a)[0] = (a)[1] = (a)[2] = 0.0f; \ 55 }\ 56 57 58 /// Zero out a 4D vector 59 #define VEC_ZERO_4(a) \ 60 { \ 61 (a)[0] = (a)[1] = (a)[2] = (a)[3] = 0.0f; \ 62 }\ 63 64 65 /// Vector copy 66 #define VEC_COPY_2(b,a) \ 67 { \ 68 (b)[0] = (a)[0]; \ 69 (b)[1] = (a)[1]; \ 70 }\ 71 72 73 /// Copy 3D vector 74 #define VEC_COPY(b,a) \ 75 { \ 76 (b)[0] = (a)[0]; \ 77 (b)[1] = (a)[1]; \ 78 (b)[2] = (a)[2]; \ 79 }\ 80 81 82 /// Copy 4D vector 83 #define VEC_COPY_4(b,a) \ 84 { \ 85 (b)[0] = (a)[0]; \ 86 (b)[1] = (a)[1]; \ 87 (b)[2] = (a)[2]; \ 88 (b)[3] = (a)[3]; \ 89 }\ 90 91 /// VECTOR SWAP 92 #define VEC_SWAP(b,a) \ 93 { \ 94 GIM_SWAP_NUMBERS((b)[0],(a)[0]);\ 95 GIM_SWAP_NUMBERS((b)[1],(a)[1]);\ 96 GIM_SWAP_NUMBERS((b)[2],(a)[2]);\ 97 }\ 98 99 /// Vector difference 100 #define VEC_DIFF_2(v21,v2,v1) \ 101 { \ 102 (v21)[0] = (v2)[0] - (v1)[0]; \ 103 (v21)[1] = (v2)[1] - (v1)[1]; \ 104 }\ 105 106 107 /// Vector difference 108 #define VEC_DIFF(v21,v2,v1) \ 109 { \ 110 (v21)[0] = (v2)[0] - (v1)[0]; \ 111 (v21)[1] = (v2)[1] - (v1)[1]; \ 112 (v21)[2] = (v2)[2] - (v1)[2]; \ 113 }\ 114 115 116 /// Vector difference 117 #define VEC_DIFF_4(v21,v2,v1) \ 118 { \ 119 (v21)[0] = (v2)[0] - (v1)[0]; \ 120 (v21)[1] = (v2)[1] - (v1)[1]; \ 121 (v21)[2] = (v2)[2] - (v1)[2]; \ 122 (v21)[3] = (v2)[3] - (v1)[3]; \ 123 }\ 124 125 126 /// Vector sum 127 #define VEC_SUM_2(v21,v2,v1) \ 128 { \ 129 (v21)[0] = (v2)[0] + (v1)[0]; \ 130 (v21)[1] = (v2)[1] + (v1)[1]; \ 131 }\ 132 133 134 /// Vector sum 135 #define VEC_SUM(v21,v2,v1) \ 136 { \ 137 (v21)[0] = (v2)[0] + (v1)[0]; \ 138 (v21)[1] = (v2)[1] + (v1)[1]; \ 139 (v21)[2] = (v2)[2] + (v1)[2]; \ 140 }\ 141 142 143 /// Vector sum 144 #define VEC_SUM_4(v21,v2,v1) \ 145 { \ 146 (v21)[0] = (v2)[0] + (v1)[0]; \ 147 (v21)[1] = (v2)[1] + (v1)[1]; \ 148 (v21)[2] = (v2)[2] + (v1)[2]; \ 149 (v21)[3] = (v2)[3] + (v1)[3]; \ 150 }\ 151 152 153 /// scalar times vector 154 #define VEC_SCALE_2(c,a,b) \ 155 { \ 156 (c)[0] = (a)*(b)[0]; \ 157 (c)[1] = (a)*(b)[1]; \ 158 }\ 159 160 161 /// scalar times vector 162 #define VEC_SCALE(c,a,b) \ 163 { \ 164 (c)[0] = (a)*(b)[0]; \ 165 (c)[1] = (a)*(b)[1]; \ 166 (c)[2] = (a)*(b)[2]; \ 167 }\ 168 169 170 /// scalar times vector 171 #define VEC_SCALE_4(c,a,b) \ 172 { \ 173 (c)[0] = (a)*(b)[0]; \ 174 (c)[1] = (a)*(b)[1]; \ 175 (c)[2] = (a)*(b)[2]; \ 176 (c)[3] = (a)*(b)[3]; \ 177 }\ 178 179 180 /// accumulate scaled vector 181 #define VEC_ACCUM_2(c,a,b) \ 182 { \ 183 (c)[0] += (a)*(b)[0]; \ 184 (c)[1] += (a)*(b)[1]; \ 185 }\ 186 187 188 /// accumulate scaled vector 189 #define VEC_ACCUM(c,a,b) \ 190 { \ 191 (c)[0] += (a)*(b)[0]; \ 192 (c)[1] += (a)*(b)[1]; \ 193 (c)[2] += (a)*(b)[2]; \ 194 }\ 195 196 197 /// accumulate scaled vector 198 #define VEC_ACCUM_4(c,a,b) \ 199 { \ 200 (c)[0] += (a)*(b)[0]; \ 201 (c)[1] += (a)*(b)[1]; \ 202 (c)[2] += (a)*(b)[2]; \ 203 (c)[3] += (a)*(b)[3]; \ 204 }\ 205 206 207 /// Vector dot product 208 #define VEC_DOT_2(a,b) ((a)[0]*(b)[0] + (a)[1]*(b)[1]) 209 210 211 /// Vector dot product 212 #define VEC_DOT(a,b) ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2]) 213 214 /// Vector dot product 215 #define VEC_DOT_4(a,b) ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2] + (a)[3]*(b)[3]) 216 217 /// vector impact parameter (squared) 218 #define VEC_IMPACT_SQ(bsq,direction,position) {\ 219 GREAL _llel_ = VEC_DOT(direction, position);\ 220 bsq = VEC_DOT(position, position) - _llel_*_llel_;\ 221 }\ 222 223 224 /// vector impact parameter 225 #define VEC_IMPACT(bsq,direction,position) {\ 226 VEC_IMPACT_SQ(bsq,direction,position); \ 227 GIM_SQRT(bsq,bsq); \ 228 }\ 229 230 /// Vector length 231 #define VEC_LENGTH_2(a,l)\ 232 {\ 233 GREAL _pp = VEC_DOT_2(a,a);\ 234 GIM_SQRT(_pp,l);\ 235 }\ 236 237 238 /// Vector length 239 #define VEC_LENGTH(a,l)\ 240 {\ 241 GREAL _pp = VEC_DOT(a,a);\ 242 GIM_SQRT(_pp,l);\ 243 }\ 244 245 246 /// Vector length 247 #define VEC_LENGTH_4(a,l)\ 248 {\ 249 GREAL _pp = VEC_DOT_4(a,a);\ 250 GIM_SQRT(_pp,l);\ 251 }\ 252 253 /// Vector inv length 254 #define VEC_INV_LENGTH_2(a,l)\ 255 {\ 256 GREAL _pp = VEC_DOT_2(a,a);\ 257 GIM_INV_SQRT(_pp,l);\ 258 }\ 259 260 261 /// Vector inv length 262 #define VEC_INV_LENGTH(a,l)\ 263 {\ 264 GREAL _pp = VEC_DOT(a,a);\ 265 GIM_INV_SQRT(_pp,l);\ 266 }\ 267 268 269 /// Vector inv length 270 #define VEC_INV_LENGTH_4(a,l)\ 271 {\ 272 GREAL _pp = VEC_DOT_4(a,a);\ 273 GIM_INV_SQRT(_pp,l);\ 274 }\ 275 276 277 278 /// distance between two points 279 #define VEC_DISTANCE(_len,_va,_vb) {\ 280 vec3f _tmp_; \ 281 VEC_DIFF(_tmp_, _vb, _va); \ 282 VEC_LENGTH(_tmp_,_len); \ 283 }\ 284 285 286 /// Vector length 287 #define VEC_CONJUGATE_LENGTH(a,l)\ 288 {\ 289 GREAL _pp = 1.0 - a[0]*a[0] - a[1]*a[1] - a[2]*a[2];\ 290 GIM_SQRT(_pp,l);\ 291 }\ 292 293 294 /// Vector length 295 #define VEC_NORMALIZE(a) { \ 296 GREAL len;\ 297 VEC_INV_LENGTH(a,len); \ 298 if(len<G_REAL_INFINITY)\ 299 {\ 300 a[0] *= len; \ 301 a[1] *= len; \ 302 a[2] *= len; \ 303 } \ 304 }\ 305 306 /// Set Vector size 307 #define VEC_RENORMALIZE(a,newlen) { \ 308 GREAL len;\ 309 VEC_INV_LENGTH(a,len); \ 310 if(len<G_REAL_INFINITY)\ 311 {\ 312 len *= newlen;\ 313 a[0] *= len; \ 314 a[1] *= len; \ 315 a[2] *= len; \ 316 } \ 317 }\ 318 319 /// Vector cross 320 #define VEC_CROSS(c,a,b) \ 321 { \ 322 c[0] = (a)[1] * (b)[2] - (a)[2] * (b)[1]; \ 323 c[1] = (a)[2] * (b)[0] - (a)[0] * (b)[2]; \ 324 c[2] = (a)[0] * (b)[1] - (a)[1] * (b)[0]; \ 325 }\ 326 327 328 /*! Vector perp -- assumes that n is of unit length 329 * accepts vector v, subtracts out any component parallel to n */ 330 #define VEC_PERPENDICULAR(vp,v,n) \ 331 { \ 332 GREAL dot = VEC_DOT(v, n); \ 333 vp[0] = (v)[0] - dot*(n)[0]; \ 334 vp[1] = (v)[1] - dot*(n)[1]; \ 335 vp[2] = (v)[2] - dot*(n)[2]; \ 336 }\ 337 338 339 /*! Vector parallel -- assumes that n is of unit length */ 340 #define VEC_PARALLEL(vp,v,n) \ 341 { \ 342 GREAL dot = VEC_DOT(v, n); \ 343 vp[0] = (dot) * (n)[0]; \ 344 vp[1] = (dot) * (n)[1]; \ 345 vp[2] = (dot) * (n)[2]; \ 346 }\ 347 348 /*! Same as Vector parallel -- n can have any length 349 * accepts vector v, subtracts out any component perpendicular to n */ 350 #define VEC_PROJECT(vp,v,n) \ 351 { \ 352 GREAL scalar = VEC_DOT(v, n); \ 353 scalar/= VEC_DOT(n, n); \ 354 vp[0] = (scalar) * (n)[0]; \ 355 vp[1] = (scalar) * (n)[1]; \ 356 vp[2] = (scalar) * (n)[2]; \ 357 }\ 358 359 360 /*! accepts vector v*/ 361 #define VEC_UNPROJECT(vp,v,n) \ 362 { \ 363 GREAL scalar = VEC_DOT(v, n); \ 364 scalar = VEC_DOT(n, n)/scalar; \ 365 vp[0] = (scalar) * (n)[0]; \ 366 vp[1] = (scalar) * (n)[1]; \ 367 vp[2] = (scalar) * (n)[2]; \ 368 }\ 369 370 371 /*! Vector reflection -- assumes n is of unit length 372 Takes vector v, reflects it against reflector n, and returns vr */ 373 #define VEC_REFLECT(vr,v,n) \ 374 { \ 375 GREAL dot = VEC_DOT(v, n); \ 376 vr[0] = (v)[0] - 2.0 * (dot) * (n)[0]; \ 377 vr[1] = (v)[1] - 2.0 * (dot) * (n)[1]; \ 378 vr[2] = (v)[2] - 2.0 * (dot) * (n)[2]; \ 379 }\ 380 381 382 /*! Vector blending 383 Takes two vectors a, b, blends them together with two scalars */ 384 #define VEC_BLEND_AB(vr,sa,a,sb,b) \ 385 { \ 386 vr[0] = (sa) * (a)[0] + (sb) * (b)[0]; \ 387 vr[1] = (sa) * (a)[1] + (sb) * (b)[1]; \ 388 vr[2] = (sa) * (a)[2] + (sb) * (b)[2]; \ 389 }\ 390 391 /*! Vector blending 392 Takes two vectors a, b, blends them together with s <=1 */ 393 #define VEC_BLEND(vr,a,b,s) VEC_BLEND_AB(vr,(1-s),a,s,b) 394 395 #define VEC_SET3(a,b,op,c) a[0]=b[0] op c[0]; a[1]=b[1] op c[1]; a[2]=b[2] op c[2]; 396 397 //! Finds the bigger cartesian coordinate from a vector 398 #define VEC_MAYOR_COORD(vec, maxc)\ 399 {\ 400 GREAL A[] = {fabs(vec[0]),fabs(vec[1]),fabs(vec[2])};\ 401 maxc = A[0]>A[1]?(A[0]>A[2]?0:2):(A[1]>A[2]?1:2);\ 402 }\ 403 404 //! Finds the 2 smallest cartesian coordinates from a vector 405 #define VEC_MINOR_AXES(vec, i0, i1)\ 406 {\ 407 VEC_MAYOR_COORD(vec,i0);\ 408 i0 = (i0+1)%3;\ 409 i1 = (i0+1)%3;\ 410 }\ 411 412 413 414 415 #define VEC_EQUAL(v1,v2) (v1[0]==v2[0]&&v1[1]==v2[1]&&v1[2]==v2[2]) 416 417 #define VEC_NEAR_EQUAL(v1,v2) (GIM_NEAR_EQUAL(v1[0],v2[0])&&GIM_NEAR_EQUAL(v1[1],v2[1])&&GIM_NEAR_EQUAL(v1[2],v2[2])) 418 419 420 /// Vector cross 421 #define X_AXIS_CROSS_VEC(dst,src)\ 422 { \ 423 dst[0] = 0.0f; \ 424 dst[1] = -src[2]; \ 425 dst[2] = src[1]; \ 426 }\ 427 428 #define Y_AXIS_CROSS_VEC(dst,src)\ 429 { \ 430 dst[0] = src[2]; \ 431 dst[1] = 0.0f; \ 432 dst[2] = -src[0]; \ 433 }\ 434 435 #define Z_AXIS_CROSS_VEC(dst,src)\ 436 { \ 437 dst[0] = -src[1]; \ 438 dst[1] = src[0]; \ 439 dst[2] = 0.0f; \ 440 }\ 441 442 443 444 445 446 447 /// initialize matrix 448 #define IDENTIFY_MATRIX_3X3(m) \ 449 { \ 450 m[0][0] = 1.0; \ 451 m[0][1] = 0.0; \ 452 m[0][2] = 0.0; \ 453 \ 454 m[1][0] = 0.0; \ 455 m[1][1] = 1.0; \ 456 m[1][2] = 0.0; \ 457 \ 458 m[2][0] = 0.0; \ 459 m[2][1] = 0.0; \ 460 m[2][2] = 1.0; \ 461 }\ 462 463 /*! initialize matrix */ 464 #define IDENTIFY_MATRIX_4X4(m) \ 465 { \ 466 m[0][0] = 1.0; \ 467 m[0][1] = 0.0; \ 468 m[0][2] = 0.0; \ 469 m[0][3] = 0.0; \ 470 \ 471 m[1][0] = 0.0; \ 472 m[1][1] = 1.0; \ 473 m[1][2] = 0.0; \ 474 m[1][3] = 0.0; \ 475 \ 476 m[2][0] = 0.0; \ 477 m[2][1] = 0.0; \ 478 m[2][2] = 1.0; \ 479 m[2][3] = 0.0; \ 480 \ 481 m[3][0] = 0.0; \ 482 m[3][1] = 0.0; \ 483 m[3][2] = 0.0; \ 484 m[3][3] = 1.0; \ 485 }\ 486 487 /*! initialize matrix */ 488 #define ZERO_MATRIX_4X4(m) \ 489 { \ 490 m[0][0] = 0.0; \ 491 m[0][1] = 0.0; \ 492 m[0][2] = 0.0; \ 493 m[0][3] = 0.0; \ 494 \ 495 m[1][0] = 0.0; \ 496 m[1][1] = 0.0; \ 497 m[1][2] = 0.0; \ 498 m[1][3] = 0.0; \ 499 \ 500 m[2][0] = 0.0; \ 501 m[2][1] = 0.0; \ 502 m[2][2] = 0.0; \ 503 m[2][3] = 0.0; \ 504 \ 505 m[3][0] = 0.0; \ 506 m[3][1] = 0.0; \ 507 m[3][2] = 0.0; \ 508 m[3][3] = 0.0; \ 509 }\ 510 511 /*! matrix rotation X */ 512 #define ROTX_CS(m,cosine,sine) \ 513 { \ 514 /* rotation about the x-axis */ \ 515 \ 516 m[0][0] = 1.0; \ 517 m[0][1] = 0.0; \ 518 m[0][2] = 0.0; \ 519 m[0][3] = 0.0; \ 520 \ 521 m[1][0] = 0.0; \ 522 m[1][1] = (cosine); \ 523 m[1][2] = (sine); \ 524 m[1][3] = 0.0; \ 525 \ 526 m[2][0] = 0.0; \ 527 m[2][1] = -(sine); \ 528 m[2][2] = (cosine); \ 529 m[2][3] = 0.0; \ 530 \ 531 m[3][0] = 0.0; \ 532 m[3][1] = 0.0; \ 533 m[3][2] = 0.0; \ 534 m[3][3] = 1.0; \ 535 }\ 536 537 /*! matrix rotation Y */ 538 #define ROTY_CS(m,cosine,sine) \ 539 { \ 540 /* rotation about the y-axis */ \ 541 \ 542 m[0][0] = (cosine); \ 543 m[0][1] = 0.0; \ 544 m[0][2] = -(sine); \ 545 m[0][3] = 0.0; \ 546 \ 547 m[1][0] = 0.0; \ 548 m[1][1] = 1.0; \ 549 m[1][2] = 0.0; \ 550 m[1][3] = 0.0; \ 551 \ 552 m[2][0] = (sine); \ 553 m[2][1] = 0.0; \ 554 m[2][2] = (cosine); \ 555 m[2][3] = 0.0; \ 556 \ 557 m[3][0] = 0.0; \ 558 m[3][1] = 0.0; \ 559 m[3][2] = 0.0; \ 560 m[3][3] = 1.0; \ 561 }\ 562 563 /*! matrix rotation Z */ 564 #define ROTZ_CS(m,cosine,sine) \ 565 { \ 566 /* rotation about the z-axis */ \ 567 \ 568 m[0][0] = (cosine); \ 569 m[0][1] = (sine); \ 570 m[0][2] = 0.0; \ 571 m[0][3] = 0.0; \ 572 \ 573 m[1][0] = -(sine); \ 574 m[1][1] = (cosine); \ 575 m[1][2] = 0.0; \ 576 m[1][3] = 0.0; \ 577 \ 578 m[2][0] = 0.0; \ 579 m[2][1] = 0.0; \ 580 m[2][2] = 1.0; \ 581 m[2][3] = 0.0; \ 582 \ 583 m[3][0] = 0.0; \ 584 m[3][1] = 0.0; \ 585 m[3][2] = 0.0; \ 586 m[3][3] = 1.0; \ 587 }\ 588 589 /*! matrix copy */ 590 #define COPY_MATRIX_2X2(b,a) \ 591 { \ 592 b[0][0] = a[0][0]; \ 593 b[0][1] = a[0][1]; \ 594 \ 595 b[1][0] = a[1][0]; \ 596 b[1][1] = a[1][1]; \ 597 \ 598 }\ 599 600 601 /*! matrix copy */ 602 #define COPY_MATRIX_2X3(b,a) \ 603 { \ 604 b[0][0] = a[0][0]; \ 605 b[0][1] = a[0][1]; \ 606 b[0][2] = a[0][2]; \ 607 \ 608 b[1][0] = a[1][0]; \ 609 b[1][1] = a[1][1]; \ 610 b[1][2] = a[1][2]; \ 611 }\ 612 613 614 /*! matrix copy */ 615 #define COPY_MATRIX_3X3(b,a) \ 616 { \ 617 b[0][0] = a[0][0]; \ 618 b[0][1] = a[0][1]; \ 619 b[0][2] = a[0][2]; \ 620 \ 621 b[1][0] = a[1][0]; \ 622 b[1][1] = a[1][1]; \ 623 b[1][2] = a[1][2]; \ 624 \ 625 b[2][0] = a[2][0]; \ 626 b[2][1] = a[2][1]; \ 627 b[2][2] = a[2][2]; \ 628 }\ 629 630 631 /*! matrix copy */ 632 #define COPY_MATRIX_4X4(b,a) \ 633 { \ 634 b[0][0] = a[0][0]; \ 635 b[0][1] = a[0][1]; \ 636 b[0][2] = a[0][2]; \ 637 b[0][3] = a[0][3]; \ 638 \ 639 b[1][0] = a[1][0]; \ 640 b[1][1] = a[1][1]; \ 641 b[1][2] = a[1][2]; \ 642 b[1][3] = a[1][3]; \ 643 \ 644 b[2][0] = a[2][0]; \ 645 b[2][1] = a[2][1]; \ 646 b[2][2] = a[2][2]; \ 647 b[2][3] = a[2][3]; \ 648 \ 649 b[3][0] = a[3][0]; \ 650 b[3][1] = a[3][1]; \ 651 b[3][2] = a[3][2]; \ 652 b[3][3] = a[3][3]; \ 653 }\ 654 655 656 /*! matrix transpose */ 657 #define TRANSPOSE_MATRIX_2X2(b,a) \ 658 { \ 659 b[0][0] = a[0][0]; \ 660 b[0][1] = a[1][0]; \ 661 \ 662 b[1][0] = a[0][1]; \ 663 b[1][1] = a[1][1]; \ 664 }\ 665 666 667 /*! matrix transpose */ 668 #define TRANSPOSE_MATRIX_3X3(b,a) \ 669 { \ 670 b[0][0] = a[0][0]; \ 671 b[0][1] = a[1][0]; \ 672 b[0][2] = a[2][0]; \ 673 \ 674 b[1][0] = a[0][1]; \ 675 b[1][1] = a[1][1]; \ 676 b[1][2] = a[2][1]; \ 677 \ 678 b[2][0] = a[0][2]; \ 679 b[2][1] = a[1][2]; \ 680 b[2][2] = a[2][2]; \ 681 }\ 682 683 684 /*! matrix transpose */ 685 #define TRANSPOSE_MATRIX_4X4(b,a) \ 686 { \ 687 b[0][0] = a[0][0]; \ 688 b[0][1] = a[1][0]; \ 689 b[0][2] = a[2][0]; \ 690 b[0][3] = a[3][0]; \ 691 \ 692 b[1][0] = a[0][1]; \ 693 b[1][1] = a[1][1]; \ 694 b[1][2] = a[2][1]; \ 695 b[1][3] = a[3][1]; \ 696 \ 697 b[2][0] = a[0][2]; \ 698 b[2][1] = a[1][2]; \ 699 b[2][2] = a[2][2]; \ 700 b[2][3] = a[3][2]; \ 701 \ 702 b[3][0] = a[0][3]; \ 703 b[3][1] = a[1][3]; \ 704 b[3][2] = a[2][3]; \ 705 b[3][3] = a[3][3]; \ 706 }\ 707 708 709 /*! multiply matrix by scalar */ 710 #define SCALE_MATRIX_2X2(b,s,a) \ 711 { \ 712 b[0][0] = (s) * a[0][0]; \ 713 b[0][1] = (s) * a[0][1]; \ 714 \ 715 b[1][0] = (s) * a[1][0]; \ 716 b[1][1] = (s) * a[1][1]; \ 717 }\ 718 719 720 /*! multiply matrix by scalar */ 721 #define SCALE_MATRIX_3X3(b,s,a) \ 722 { \ 723 b[0][0] = (s) * a[0][0]; \ 724 b[0][1] = (s) * a[0][1]; \ 725 b[0][2] = (s) * a[0][2]; \ 726 \ 727 b[1][0] = (s) * a[1][0]; \ 728 b[1][1] = (s) * a[1][1]; \ 729 b[1][2] = (s) * a[1][2]; \ 730 \ 731 b[2][0] = (s) * a[2][0]; \ 732 b[2][1] = (s) * a[2][1]; \ 733 b[2][2] = (s) * a[2][2]; \ 734 }\ 735 736 737 /*! multiply matrix by scalar */ 738 #define SCALE_MATRIX_4X4(b,s,a) \ 739 { \ 740 b[0][0] = (s) * a[0][0]; \ 741 b[0][1] = (s) * a[0][1]; \ 742 b[0][2] = (s) * a[0][2]; \ 743 b[0][3] = (s) * a[0][3]; \ 744 \ 745 b[1][0] = (s) * a[1][0]; \ 746 b[1][1] = (s) * a[1][1]; \ 747 b[1][2] = (s) * a[1][2]; \ 748 b[1][3] = (s) * a[1][3]; \ 749 \ 750 b[2][0] = (s) * a[2][0]; \ 751 b[2][1] = (s) * a[2][1]; \ 752 b[2][2] = (s) * a[2][2]; \ 753 b[2][3] = (s) * a[2][3]; \ 754 \ 755 b[3][0] = s * a[3][0]; \ 756 b[3][1] = s * a[3][1]; \ 757 b[3][2] = s * a[3][2]; \ 758 b[3][3] = s * a[3][3]; \ 759 }\ 760 761 762 /*! multiply matrix by scalar */ 763 #define SCALE_VEC_MATRIX_2X2(b,svec,a) \ 764 { \ 765 b[0][0] = svec[0] * a[0][0]; \ 766 b[1][0] = svec[0] * a[1][0]; \ 767 \ 768 b[0][1] = svec[1] * a[0][1]; \ 769 b[1][1] = svec[1] * a[1][1]; \ 770 }\ 771 772 773 /*! multiply matrix by scalar. Each columns is scaled by each scalar vector component */ 774 #define SCALE_VEC_MATRIX_3X3(b,svec,a) \ 775 { \ 776 b[0][0] = svec[0] * a[0][0]; \ 777 b[1][0] = svec[0] * a[1][0]; \ 778 b[2][0] = svec[0] * a[2][0]; \ 779 \ 780 b[0][1] = svec[1] * a[0][1]; \ 781 b[1][1] = svec[1] * a[1][1]; \ 782 b[2][1] = svec[1] * a[2][1]; \ 783 \ 784 b[0][2] = svec[2] * a[0][2]; \ 785 b[1][2] = svec[2] * a[1][2]; \ 786 b[2][2] = svec[2] * a[2][2]; \ 787 }\ 788 789 790 /*! multiply matrix by scalar */ 791 #define SCALE_VEC_MATRIX_4X4(b,svec,a) \ 792 { \ 793 b[0][0] = svec[0] * a[0][0]; \ 794 b[1][0] = svec[0] * a[1][0]; \ 795 b[2][0] = svec[0] * a[2][0]; \ 796 b[3][0] = svec[0] * a[3][0]; \ 797 \ 798 b[0][1] = svec[1] * a[0][1]; \ 799 b[1][1] = svec[1] * a[1][1]; \ 800 b[2][1] = svec[1] * a[2][1]; \ 801 b[3][1] = svec[1] * a[3][1]; \ 802 \ 803 b[0][2] = svec[2] * a[0][2]; \ 804 b[1][2] = svec[2] * a[1][2]; \ 805 b[2][2] = svec[2] * a[2][2]; \ 806 b[3][2] = svec[2] * a[3][2]; \ 807 \ 808 b[0][3] = svec[3] * a[0][3]; \ 809 b[1][3] = svec[3] * a[1][3]; \ 810 b[2][3] = svec[3] * a[2][3]; \ 811 b[3][3] = svec[3] * a[3][3]; \ 812 }\ 813 814 815 /*! multiply matrix by scalar */ 816 #define ACCUM_SCALE_MATRIX_2X2(b,s,a) \ 817 { \ 818 b[0][0] += (s) * a[0][0]; \ 819 b[0][1] += (s) * a[0][1]; \ 820 \ 821 b[1][0] += (s) * a[1][0]; \ 822 b[1][1] += (s) * a[1][1]; \ 823 }\ 824 825 826 /*! multiply matrix by scalar */ 827 #define ACCUM_SCALE_MATRIX_3X3(b,s,a) \ 828 { \ 829 b[0][0] += (s) * a[0][0]; \ 830 b[0][1] += (s) * a[0][1]; \ 831 b[0][2] += (s) * a[0][2]; \ 832 \ 833 b[1][0] += (s) * a[1][0]; \ 834 b[1][1] += (s) * a[1][1]; \ 835 b[1][2] += (s) * a[1][2]; \ 836 \ 837 b[2][0] += (s) * a[2][0]; \ 838 b[2][1] += (s) * a[2][1]; \ 839 b[2][2] += (s) * a[2][2]; \ 840 }\ 841 842 843 /*! multiply matrix by scalar */ 844 #define ACCUM_SCALE_MATRIX_4X4(b,s,a) \ 845 { \ 846 b[0][0] += (s) * a[0][0]; \ 847 b[0][1] += (s) * a[0][1]; \ 848 b[0][2] += (s) * a[0][2]; \ 849 b[0][3] += (s) * a[0][3]; \ 850 \ 851 b[1][0] += (s) * a[1][0]; \ 852 b[1][1] += (s) * a[1][1]; \ 853 b[1][2] += (s) * a[1][2]; \ 854 b[1][3] += (s) * a[1][3]; \ 855 \ 856 b[2][0] += (s) * a[2][0]; \ 857 b[2][1] += (s) * a[2][1]; \ 858 b[2][2] += (s) * a[2][2]; \ 859 b[2][3] += (s) * a[2][3]; \ 860 \ 861 b[3][0] += (s) * a[3][0]; \ 862 b[3][1] += (s) * a[3][1]; \ 863 b[3][2] += (s) * a[3][2]; \ 864 b[3][3] += (s) * a[3][3]; \ 865 }\ 866 867 /*! matrix product */ 868 /*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/ 869 #define MATRIX_PRODUCT_2X2(c,a,b) \ 870 { \ 871 c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]; \ 872 c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]; \ 873 \ 874 c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]; \ 875 c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]; \ 876 \ 877 }\ 878 879 /*! matrix product */ 880 /*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/ 881 #define MATRIX_PRODUCT_3X3(c,a,b) \ 882 { \ 883 c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]+a[0][2]*b[2][0]; \ 884 c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]+a[0][2]*b[2][1]; \ 885 c[0][2] = a[0][0]*b[0][2]+a[0][1]*b[1][2]+a[0][2]*b[2][2]; \ 886 \ 887 c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]+a[1][2]*b[2][0]; \ 888 c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]+a[1][2]*b[2][1]; \ 889 c[1][2] = a[1][0]*b[0][2]+a[1][1]*b[1][2]+a[1][2]*b[2][2]; \ 890 \ 891 c[2][0] = a[2][0]*b[0][0]+a[2][1]*b[1][0]+a[2][2]*b[2][0]; \ 892 c[2][1] = a[2][0]*b[0][1]+a[2][1]*b[1][1]+a[2][2]*b[2][1]; \ 893 c[2][2] = a[2][0]*b[0][2]+a[2][1]*b[1][2]+a[2][2]*b[2][2]; \ 894 }\ 895 896 897 /*! matrix product */ 898 /*! c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];*/ 899 #define MATRIX_PRODUCT_4X4(c,a,b) \ 900 { \ 901 c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]+a[0][2]*b[2][0]+a[0][3]*b[3][0];\ 902 c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]+a[0][2]*b[2][1]+a[0][3]*b[3][1];\ 903 c[0][2] = a[0][0]*b[0][2]+a[0][1]*b[1][2]+a[0][2]*b[2][2]+a[0][3]*b[3][2];\ 904 c[0][3] = a[0][0]*b[0][3]+a[0][1]*b[1][3]+a[0][2]*b[2][3]+a[0][3]*b[3][3];\ 905 \ 906 c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]+a[1][2]*b[2][0]+a[1][3]*b[3][0];\ 907 c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]+a[1][2]*b[2][1]+a[1][3]*b[3][1];\ 908 c[1][2] = a[1][0]*b[0][2]+a[1][1]*b[1][2]+a[1][2]*b[2][2]+a[1][3]*b[3][2];\ 909 c[1][3] = a[1][0]*b[0][3]+a[1][1]*b[1][3]+a[1][2]*b[2][3]+a[1][3]*b[3][3];\ 910 \ 911 c[2][0] = a[2][0]*b[0][0]+a[2][1]*b[1][0]+a[2][2]*b[2][0]+a[2][3]*b[3][0];\ 912 c[2][1] = a[2][0]*b[0][1]+a[2][1]*b[1][1]+a[2][2]*b[2][1]+a[2][3]*b[3][1];\ 913 c[2][2] = a[2][0]*b[0][2]+a[2][1]*b[1][2]+a[2][2]*b[2][2]+a[2][3]*b[3][2];\ 914 c[2][3] = a[2][0]*b[0][3]+a[2][1]*b[1][3]+a[2][2]*b[2][3]+a[2][3]*b[3][3];\ 915 \ 916 c[3][0] = a[3][0]*b[0][0]+a[3][1]*b[1][0]+a[3][2]*b[2][0]+a[3][3]*b[3][0];\ 917 c[3][1] = a[3][0]*b[0][1]+a[3][1]*b[1][1]+a[3][2]*b[2][1]+a[3][3]*b[3][1];\ 918 c[3][2] = a[3][0]*b[0][2]+a[3][1]*b[1][2]+a[3][2]*b[2][2]+a[3][3]*b[3][2];\ 919 c[3][3] = a[3][0]*b[0][3]+a[3][1]*b[1][3]+a[3][2]*b[2][3]+a[3][3]*b[3][3];\ 920 }\ 921 922 923 /*! matrix times vector */ 924 #define MAT_DOT_VEC_2X2(p,m,v) \ 925 { \ 926 p[0] = m[0][0]*v[0] + m[0][1]*v[1]; \ 927 p[1] = m[1][0]*v[0] + m[1][1]*v[1]; \ 928 }\ 929 930 931 /*! matrix times vector */ 932 #define MAT_DOT_VEC_3X3(p,m,v) \ 933 { \ 934 p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2]; \ 935 p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2]; \ 936 p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2]; \ 937 }\ 938 939 940 /*! matrix times vector 941 v is a vec4f 942 */ 943 #define MAT_DOT_VEC_4X4(p,m,v) \ 944 { \ 945 p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2] + m[0][3]*v[3]; \ 946 p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2] + m[1][3]*v[3]; \ 947 p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2] + m[2][3]*v[3]; \ 948 p[3] = m[3][0]*v[0] + m[3][1]*v[1] + m[3][2]*v[2] + m[3][3]*v[3]; \ 949 }\ 950 951 /*! matrix times vector 952 v is a vec3f 953 and m is a mat4f<br> 954 Last column is added as the position 955 */ 956 #define MAT_DOT_VEC_3X4(p,m,v) \ 957 { \ 958 p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2] + m[0][3]; \ 959 p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2] + m[1][3]; \ 960 p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2] + m[2][3]; \ 961 }\ 962 963 964 /*! vector transpose times matrix */ 965 /*! p[j] = v[0]*m[0][j] + v[1]*m[1][j] + v[2]*m[2][j]; */ 966 #define VEC_DOT_MAT_3X3(p,v,m) \ 967 { \ 968 p[0] = v[0]*m[0][0] + v[1]*m[1][0] + v[2]*m[2][0]; \ 969 p[1] = v[0]*m[0][1] + v[1]*m[1][1] + v[2]*m[2][1]; \ 970 p[2] = v[0]*m[0][2] + v[1]*m[1][2] + v[2]*m[2][2]; \ 971 }\ 972 973 974 /*! affine matrix times vector */ 975 /** The matrix is assumed to be an affine matrix, with last two 976 * entries representing a translation */ 977 #define MAT_DOT_VEC_2X3(p,m,v) \ 978 { \ 979 p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]; \ 980 p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]; \ 981 }\ 982 983 //! Transform a plane 984 #define MAT_TRANSFORM_PLANE_4X4(pout,m,plane)\ 985 { \ 986 pout[0] = m[0][0]*plane[0] + m[0][1]*plane[1] + m[0][2]*plane[2];\ 987 pout[1] = m[1][0]*plane[0] + m[1][1]*plane[1] + m[1][2]*plane[2];\ 988 pout[2] = m[2][0]*plane[0] + m[2][1]*plane[1] + m[2][2]*plane[2];\ 989 pout[3] = m[0][3]*pout[0] + m[1][3]*pout[1] + m[2][3]*pout[2] + plane[3];\ 990 }\ 991 992 993 994 /** inverse transpose of matrix times vector 995 * 996 * This macro computes inverse transpose of matrix m, 997 * and multiplies vector v into it, to yeild vector p 998 * 999 * DANGER !!! Do Not use this on normal vectors!!! 1000 * It will leave normals the wrong length !!! 1001 * See macro below for use on normals. 1002 */ 1003 #define INV_TRANSP_MAT_DOT_VEC_2X2(p,m,v) \ 1004 { \ 1005 GREAL det; \ 1006 \ 1007 det = m[0][0]*m[1][1] - m[0][1]*m[1][0]; \ 1008 p[0] = m[1][1]*v[0] - m[1][0]*v[1]; \ 1009 p[1] = - m[0][1]*v[0] + m[0][0]*v[1]; \ 1010 \ 1011 /* if matrix not singular, and not orthonormal, then renormalize */ \ 1012 if ((det!=1.0f) && (det != 0.0f)) { \ 1013 det = 1.0f / det; \ 1014 p[0] *= det; \ 1015 p[1] *= det; \ 1016 } \ 1017 }\ 1018 1019 1020 /** transform normal vector by inverse transpose of matrix 1021 * and then renormalize the vector 1022 * 1023 * This macro computes inverse transpose of matrix m, 1024 * and multiplies vector v into it, to yeild vector p 1025 * Vector p is then normalized. 1026 */ 1027 #define NORM_XFORM_2X2(p,m,v) \ 1028 { \ 1029 GREAL len; \ 1030 \ 1031 /* do nothing if off-diagonals are zero and diagonals are \ 1032 * equal */ \ 1033 if ((m[0][1] != 0.0) || (m[1][0] != 0.0) || (m[0][0] != m[1][1])) { \ 1034 p[0] = m[1][1]*v[0] - m[1][0]*v[1]; \ 1035 p[1] = - m[0][1]*v[0] + m[0][0]*v[1]; \ 1036 \ 1037 len = p[0]*p[0] + p[1]*p[1]; \ 1038 GIM_INV_SQRT(len,len); \ 1039 p[0] *= len; \ 1040 p[1] *= len; \ 1041 } else { \ 1042 VEC_COPY_2 (p, v); \ 1043 } \ 1044 }\ 1045 1046 1047 /** outer product of vector times vector transpose 1048 * 1049 * The outer product of vector v and vector transpose t yeilds 1050 * dyadic matrix m. 1051 */ 1052 #define OUTER_PRODUCT_2X2(m,v,t) \ 1053 { \ 1054 m[0][0] = v[0] * t[0]; \ 1055 m[0][1] = v[0] * t[1]; \ 1056 \ 1057 m[1][0] = v[1] * t[0]; \ 1058 m[1][1] = v[1] * t[1]; \ 1059 }\ 1060 1061 1062 /** outer product of vector times vector transpose 1063 * 1064 * The outer product of vector v and vector transpose t yeilds 1065 * dyadic matrix m. 1066 */ 1067 #define OUTER_PRODUCT_3X3(m,v,t) \ 1068 { \ 1069 m[0][0] = v[0] * t[0]; \ 1070 m[0][1] = v[0] * t[1]; \ 1071 m[0][2] = v[0] * t[2]; \ 1072 \ 1073 m[1][0] = v[1] * t[0]; \ 1074 m[1][1] = v[1] * t[1]; \ 1075 m[1][2] = v[1] * t[2]; \ 1076 \ 1077 m[2][0] = v[2] * t[0]; \ 1078 m[2][1] = v[2] * t[1]; \ 1079 m[2][2] = v[2] * t[2]; \ 1080 }\ 1081 1082 1083 /** outer product of vector times vector transpose 1084 * 1085 * The outer product of vector v and vector transpose t yeilds 1086 * dyadic matrix m. 1087 */ 1088 #define OUTER_PRODUCT_4X4(m,v,t) \ 1089 { \ 1090 m[0][0] = v[0] * t[0]; \ 1091 m[0][1] = v[0] * t[1]; \ 1092 m[0][2] = v[0] * t[2]; \ 1093 m[0][3] = v[0] * t[3]; \ 1094 \ 1095 m[1][0] = v[1] * t[0]; \ 1096 m[1][1] = v[1] * t[1]; \ 1097 m[1][2] = v[1] * t[2]; \ 1098 m[1][3] = v[1] * t[3]; \ 1099 \ 1100 m[2][0] = v[2] * t[0]; \ 1101 m[2][1] = v[2] * t[1]; \ 1102 m[2][2] = v[2] * t[2]; \ 1103 m[2][3] = v[2] * t[3]; \ 1104 \ 1105 m[3][0] = v[3] * t[0]; \ 1106 m[3][1] = v[3] * t[1]; \ 1107 m[3][2] = v[3] * t[2]; \ 1108 m[3][3] = v[3] * t[3]; \ 1109 }\ 1110 1111 1112 /** outer product of vector times vector transpose 1113 * 1114 * The outer product of vector v and vector transpose t yeilds 1115 * dyadic matrix m. 1116 */ 1117 #define ACCUM_OUTER_PRODUCT_2X2(m,v,t) \ 1118 { \ 1119 m[0][0] += v[0] * t[0]; \ 1120 m[0][1] += v[0] * t[1]; \ 1121 \ 1122 m[1][0] += v[1] * t[0]; \ 1123 m[1][1] += v[1] * t[1]; \ 1124 }\ 1125 1126 1127 /** outer product of vector times vector transpose 1128 * 1129 * The outer product of vector v and vector transpose t yeilds 1130 * dyadic matrix m. 1131 */ 1132 #define ACCUM_OUTER_PRODUCT_3X3(m,v,t) \ 1133 { \ 1134 m[0][0] += v[0] * t[0]; \ 1135 m[0][1] += v[0] * t[1]; \ 1136 m[0][2] += v[0] * t[2]; \ 1137 \ 1138 m[1][0] += v[1] * t[0]; \ 1139 m[1][1] += v[1] * t[1]; \ 1140 m[1][2] += v[1] * t[2]; \ 1141 \ 1142 m[2][0] += v[2] * t[0]; \ 1143 m[2][1] += v[2] * t[1]; \ 1144 m[2][2] += v[2] * t[2]; \ 1145 }\ 1146 1147 1148 /** outer product of vector times vector transpose 1149 * 1150 * The outer product of vector v and vector transpose t yeilds 1151 * dyadic matrix m. 1152 */ 1153 #define ACCUM_OUTER_PRODUCT_4X4(m,v,t) \ 1154 { \ 1155 m[0][0] += v[0] * t[0]; \ 1156 m[0][1] += v[0] * t[1]; \ 1157 m[0][2] += v[0] * t[2]; \ 1158 m[0][3] += v[0] * t[3]; \ 1159 \ 1160 m[1][0] += v[1] * t[0]; \ 1161 m[1][1] += v[1] * t[1]; \ 1162 m[1][2] += v[1] * t[2]; \ 1163 m[1][3] += v[1] * t[3]; \ 1164 \ 1165 m[2][0] += v[2] * t[0]; \ 1166 m[2][1] += v[2] * t[1]; \ 1167 m[2][2] += v[2] * t[2]; \ 1168 m[2][3] += v[2] * t[3]; \ 1169 \ 1170 m[3][0] += v[3] * t[0]; \ 1171 m[3][1] += v[3] * t[1]; \ 1172 m[3][2] += v[3] * t[2]; \ 1173 m[3][3] += v[3] * t[3]; \ 1174 }\ 1175 1176 1177 /** determinant of matrix 1178 * 1179 * Computes determinant of matrix m, returning d 1180 */ 1181 #define DETERMINANT_2X2(d,m) \ 1182 { \ 1183 d = m[0][0] * m[1][1] - m[0][1] * m[1][0]; \ 1184 }\ 1185 1186 1187 /** determinant of matrix 1188 * 1189 * Computes determinant of matrix m, returning d 1190 */ 1191 #define DETERMINANT_3X3(d,m) \ 1192 { \ 1193 d = m[0][0] * (m[1][1]*m[2][2] - m[1][2] * m[2][1]); \ 1194 d -= m[0][1] * (m[1][0]*m[2][2] - m[1][2] * m[2][0]); \ 1195 d += m[0][2] * (m[1][0]*m[2][1] - m[1][1] * m[2][0]); \ 1196 }\ 1197 1198 1199 /** i,j,th cofactor of a 4x4 matrix 1200 * 1201 */ 1202 #define COFACTOR_4X4_IJ(fac,m,i,j) \ 1203 { \ 1204 GUINT __ii[4], __jj[4], __k; \ 1205 \ 1206 for (__k=0; __k<i; __k++) __ii[__k] = __k; \ 1207 for (__k=i; __k<3; __k++) __ii[__k] = __k+1; \ 1208 for (__k=0; __k<j; __k++) __jj[__k] = __k; \ 1209 for (__k=j; __k<3; __k++) __jj[__k] = __k+1; \ 1210 \ 1211 (fac) = m[__ii[0]][__jj[0]] * (m[__ii[1]][__jj[1]]*m[__ii[2]][__jj[2]] \ 1212 - m[__ii[1]][__jj[2]]*m[__ii[2]][__jj[1]]); \ 1213 (fac) -= m[__ii[0]][__jj[1]] * (m[__ii[1]][__jj[0]]*m[__ii[2]][__jj[2]] \ 1214 - m[__ii[1]][__jj[2]]*m[__ii[2]][__jj[0]]);\ 1215 (fac) += m[__ii[0]][__jj[2]] * (m[__ii[1]][__jj[0]]*m[__ii[2]][__jj[1]] \ 1216 - m[__ii[1]][__jj[1]]*m[__ii[2]][__jj[0]]);\ 1217 \ 1218 __k = i+j; \ 1219 if ( __k != (__k/2)*2) { \ 1220 (fac) = -(fac); \ 1221 } \ 1222 }\ 1223 1224 1225 /** determinant of matrix 1226 * 1227 * Computes determinant of matrix m, returning d 1228 */ 1229 #define DETERMINANT_4X4(d,m) \ 1230 { \ 1231 GREAL cofac; \ 1232 COFACTOR_4X4_IJ (cofac, m, 0, 0); \ 1233 d = m[0][0] * cofac; \ 1234 COFACTOR_4X4_IJ (cofac, m, 0, 1); \ 1235 d += m[0][1] * cofac; \ 1236 COFACTOR_4X4_IJ (cofac, m, 0, 2); \ 1237 d += m[0][2] * cofac; \ 1238 COFACTOR_4X4_IJ (cofac, m, 0, 3); \ 1239 d += m[0][3] * cofac; \ 1240 }\ 1241 1242 1243 /** cofactor of matrix 1244 * 1245 * Computes cofactor of matrix m, returning a 1246 */ 1247 #define COFACTOR_2X2(a,m) \ 1248 { \ 1249 a[0][0] = (m)[1][1]; \ 1250 a[0][1] = - (m)[1][0]; \ 1251 a[1][0] = - (m)[0][1]; \ 1252 a[1][1] = (m)[0][0]; \ 1253 }\ 1254 1255 1256 /** cofactor of matrix 1257 * 1258 * Computes cofactor of matrix m, returning a 1259 */ 1260 #define COFACTOR_3X3(a,m) \ 1261 { \ 1262 a[0][0] = m[1][1]*m[2][2] - m[1][2]*m[2][1]; \ 1263 a[0][1] = - (m[1][0]*m[2][2] - m[2][0]*m[1][2]); \ 1264 a[0][2] = m[1][0]*m[2][1] - m[1][1]*m[2][0]; \ 1265 a[1][0] = - (m[0][1]*m[2][2] - m[0][2]*m[2][1]); \ 1266 a[1][1] = m[0][0]*m[2][2] - m[0][2]*m[2][0]; \ 1267 a[1][2] = - (m[0][0]*m[2][1] - m[0][1]*m[2][0]); \ 1268 a[2][0] = m[0][1]*m[1][2] - m[0][2]*m[1][1]; \ 1269 a[2][1] = - (m[0][0]*m[1][2] - m[0][2]*m[1][0]); \ 1270 a[2][2] = m[0][0]*m[1][1] - m[0][1]*m[1][0]); \ 1271 }\ 1272 1273 1274 /** cofactor of matrix 1275 * 1276 * Computes cofactor of matrix m, returning a 1277 */ 1278 #define COFACTOR_4X4(a,m) \ 1279 { \ 1280 int i,j; \ 1281 \ 1282 for (i=0; i<4; i++) { \ 1283 for (j=0; j<4; j++) { \ 1284 COFACTOR_4X4_IJ (a[i][j], m, i, j); \ 1285 } \ 1286 } \ 1287 }\ 1288 1289 1290 /** adjoint of matrix 1291 * 1292 * Computes adjoint of matrix m, returning a 1293 * (Note that adjoint is just the transpose of the cofactor matrix) 1294 */ 1295 #define ADJOINT_2X2(a,m) \ 1296 { \ 1297 a[0][0] = (m)[1][1]; \ 1298 a[1][0] = - (m)[1][0]; \ 1299 a[0][1] = - (m)[0][1]; \ 1300 a[1][1] = (m)[0][0]; \ 1301 }\ 1302 1303 1304 /** adjoint of matrix 1305 * 1306 * Computes adjoint of matrix m, returning a 1307 * (Note that adjoint is just the transpose of the cofactor matrix) 1308 */ 1309 #define ADJOINT_3X3(a,m) \ 1310 { \ 1311 a[0][0] = m[1][1]*m[2][2] - m[1][2]*m[2][1]; \ 1312 a[1][0] = - (m[1][0]*m[2][2] - m[2][0]*m[1][2]); \ 1313 a[2][0] = m[1][0]*m[2][1] - m[1][1]*m[2][0]; \ 1314 a[0][1] = - (m[0][1]*m[2][2] - m[0][2]*m[2][1]); \ 1315 a[1][1] = m[0][0]*m[2][2] - m[0][2]*m[2][0]; \ 1316 a[2][1] = - (m[0][0]*m[2][1] - m[0][1]*m[2][0]); \ 1317 a[0][2] = m[0][1]*m[1][2] - m[0][2]*m[1][1]; \ 1318 a[1][2] = - (m[0][0]*m[1][2] - m[0][2]*m[1][0]); \ 1319 a[2][2] = m[0][0]*m[1][1] - m[0][1]*m[1][0]); \ 1320 }\ 1321 1322 1323 /** adjoint of matrix 1324 * 1325 * Computes adjoint of matrix m, returning a 1326 * (Note that adjoint is just the transpose of the cofactor matrix) 1327 */ 1328 #define ADJOINT_4X4(a,m) \ 1329 { \ 1330 char _i_,_j_; \ 1331 \ 1332 for (_i_=0; _i_<4; _i_++) { \ 1333 for (_j_=0; _j_<4; _j_++) { \ 1334 COFACTOR_4X4_IJ (a[_j_][_i_], m, _i_, _j_); \ 1335 } \ 1336 } \ 1337 }\ 1338 1339 1340 /** compute adjoint of matrix and scale 1341 * 1342 * Computes adjoint of matrix m, scales it by s, returning a 1343 */ 1344 #define SCALE_ADJOINT_2X2(a,s,m) \ 1345 { \ 1346 a[0][0] = (s) * m[1][1]; \ 1347 a[1][0] = - (s) * m[1][0]; \ 1348 a[0][1] = - (s) * m[0][1]; \ 1349 a[1][1] = (s) * m[0][0]; \ 1350 }\ 1351 1352 1353 /** compute adjoint of matrix and scale 1354 * 1355 * Computes adjoint of matrix m, scales it by s, returning a 1356 */ 1357 #define SCALE_ADJOINT_3X3(a,s,m) \ 1358 { \ 1359 a[0][0] = (s) * (m[1][1] * m[2][2] - m[1][2] * m[2][1]); \ 1360 a[1][0] = (s) * (m[1][2] * m[2][0] - m[1][0] * m[2][2]); \ 1361 a[2][0] = (s) * (m[1][0] * m[2][1] - m[1][1] * m[2][0]); \ 1362 \ 1363 a[0][1] = (s) * (m[0][2] * m[2][1] - m[0][1] * m[2][2]); \ 1364 a[1][1] = (s) * (m[0][0] * m[2][2] - m[0][2] * m[2][0]); \ 1365 a[2][1] = (s) * (m[0][1] * m[2][0] - m[0][0] * m[2][1]); \ 1366 \ 1367 a[0][2] = (s) * (m[0][1] * m[1][2] - m[0][2] * m[1][1]); \ 1368 a[1][2] = (s) * (m[0][2] * m[1][0] - m[0][0] * m[1][2]); \ 1369 a[2][2] = (s) * (m[0][0] * m[1][1] - m[0][1] * m[1][0]); \ 1370 }\ 1371 1372 1373 /** compute adjoint of matrix and scale 1374 * 1375 * Computes adjoint of matrix m, scales it by s, returning a 1376 */ 1377 #define SCALE_ADJOINT_4X4(a,s,m) \ 1378 { \ 1379 char _i_,_j_; \ 1380 for (_i_=0; _i_<4; _i_++) { \ 1381 for (_j_=0; _j_<4; _j_++) { \ 1382 COFACTOR_4X4_IJ (a[_j_][_i_], m, _i_, _j_); \ 1383 a[_j_][_i_] *= s; \ 1384 } \ 1385 } \ 1386 }\ 1387 1388 /** inverse of matrix 1389 * 1390 * Compute inverse of matrix a, returning determinant m and 1391 * inverse b 1392 */ 1393 #define INVERT_2X2(b,det,a) \ 1394 { \ 1395 GREAL _tmp_; \ 1396 DETERMINANT_2X2 (det, a); \ 1397 _tmp_ = 1.0 / (det); \ 1398 SCALE_ADJOINT_2X2 (b, _tmp_, a); \ 1399 }\ 1400 1401 1402 /** inverse of matrix 1403 * 1404 * Compute inverse of matrix a, returning determinant m and 1405 * inverse b 1406 */ 1407 #define INVERT_3X3(b,det,a) \ 1408 { \ 1409 GREAL _tmp_; \ 1410 DETERMINANT_3X3 (det, a); \ 1411 _tmp_ = 1.0 / (det); \ 1412 SCALE_ADJOINT_3X3 (b, _tmp_, a); \ 1413 }\ 1414 1415 1416 /** inverse of matrix 1417 * 1418 * Compute inverse of matrix a, returning determinant m and 1419 * inverse b 1420 */ 1421 #define INVERT_4X4(b,det,a) \ 1422 { \ 1423 GREAL _tmp_; \ 1424 DETERMINANT_4X4 (det, a); \ 1425 _tmp_ = 1.0 / (det); \ 1426 SCALE_ADJOINT_4X4 (b, _tmp_, a); \ 1427 }\ 1428 1429 //! Get the triple(3) row of a transform matrix 1430 #define MAT_GET_ROW(mat,vec3,rowindex)\ 1431 {\ 1432 vec3[0] = mat[rowindex][0];\ 1433 vec3[1] = mat[rowindex][1];\ 1434 vec3[2] = mat[rowindex][2]; \ 1435 }\ 1436 1437 //! Get the tuple(2) row of a transform matrix 1438 #define MAT_GET_ROW2(mat,vec2,rowindex)\ 1439 {\ 1440 vec2[0] = mat[rowindex][0];\ 1441 vec2[1] = mat[rowindex][1];\ 1442 }\ 1443 1444 1445 //! Get the quad (4) row of a transform matrix 1446 #define MAT_GET_ROW4(mat,vec4,rowindex)\ 1447 {\ 1448 vec4[0] = mat[rowindex][0];\ 1449 vec4[1] = mat[rowindex][1];\ 1450 vec4[2] = mat[rowindex][2];\ 1451 vec4[3] = mat[rowindex][3];\ 1452 }\ 1453 1454 //! Get the triple(3) col of a transform matrix 1455 #define MAT_GET_COL(mat,vec3,colindex)\ 1456 {\ 1457 vec3[0] = mat[0][colindex];\ 1458 vec3[1] = mat[1][colindex];\ 1459 vec3[2] = mat[2][colindex]; \ 1460 }\ 1461 1462 //! Get the tuple(2) col of a transform matrix 1463 #define MAT_GET_COL2(mat,vec2,colindex)\ 1464 {\ 1465 vec2[0] = mat[0][colindex];\ 1466 vec2[1] = mat[1][colindex];\ 1467 }\ 1468 1469 1470 //! Get the quad (4) col of a transform matrix 1471 #define MAT_GET_COL4(mat,vec4,colindex)\ 1472 {\ 1473 vec4[0] = mat[0][colindex];\ 1474 vec4[1] = mat[1][colindex];\ 1475 vec4[2] = mat[2][colindex];\ 1476 vec4[3] = mat[3][colindex];\ 1477 }\ 1478 1479 //! Get the triple(3) col of a transform matrix 1480 #define MAT_GET_X(mat,vec3)\ 1481 {\ 1482 MAT_GET_COL(mat,vec3,0);\ 1483 }\ 1484 1485 //! Get the triple(3) col of a transform matrix 1486 #define MAT_GET_Y(mat,vec3)\ 1487 {\ 1488 MAT_GET_COL(mat,vec3,1);\ 1489 }\ 1490 1491 //! Get the triple(3) col of a transform matrix 1492 #define MAT_GET_Z(mat,vec3)\ 1493 {\ 1494 MAT_GET_COL(mat,vec3,2);\ 1495 }\ 1496 1497 1498 //! Get the triple(3) col of a transform matrix 1499 #define MAT_SET_X(mat,vec3)\ 1500 {\ 1501 mat[0][0] = vec3[0];\ 1502 mat[1][0] = vec3[1];\ 1503 mat[2][0] = vec3[2];\ 1504 }\ 1505 1506 //! Get the triple(3) col of a transform matrix 1507 #define MAT_SET_Y(mat,vec3)\ 1508 {\ 1509 mat[0][1] = vec3[0];\ 1510 mat[1][1] = vec3[1];\ 1511 mat[2][1] = vec3[2];\ 1512 }\ 1513 1514 //! Get the triple(3) col of a transform matrix 1515 #define MAT_SET_Z(mat,vec3)\ 1516 {\ 1517 mat[0][2] = vec3[0];\ 1518 mat[1][2] = vec3[1];\ 1519 mat[2][2] = vec3[2];\ 1520 }\ 1521 1522 1523 //! Get the triple(3) col of a transform matrix 1524 #define MAT_GET_TRANSLATION(mat,vec3)\ 1525 {\ 1526 vec3[0] = mat[0][3];\ 1527 vec3[1] = mat[1][3];\ 1528 vec3[2] = mat[2][3]; \ 1529 }\ 1530 1531 //! Set the triple(3) col of a transform matrix 1532 #define MAT_SET_TRANSLATION(mat,vec3)\ 1533 {\ 1534 mat[0][3] = vec3[0];\ 1535 mat[1][3] = vec3[1];\ 1536 mat[2][3] = vec3[2]; \ 1537 }\ 1538 1539 1540 1541 //! Returns the dot product between a vec3f and the row of a matrix 1542 #define MAT_DOT_ROW(mat,vec3,rowindex) (vec3[0]*mat[rowindex][0] + vec3[1]*mat[rowindex][1] + vec3[2]*mat[rowindex][2]) 1543 1544 //! Returns the dot product between a vec2f and the row of a matrix 1545 #define MAT_DOT_ROW2(mat,vec2,rowindex) (vec2[0]*mat[rowindex][0] + vec2[1]*mat[rowindex][1]) 1546 1547 //! Returns the dot product between a vec4f and the row of a matrix 1548 #define MAT_DOT_ROW4(mat,vec4,rowindex) (vec4[0]*mat[rowindex][0] + vec4[1]*mat[rowindex][1] + vec4[2]*mat[rowindex][2] + vec4[3]*mat[rowindex][3]) 1549 1550 1551 //! Returns the dot product between a vec3f and the col of a matrix 1552 #define MAT_DOT_COL(mat,vec3,colindex) (vec3[0]*mat[0][colindex] + vec3[1]*mat[1][colindex] + vec3[2]*mat[2][colindex]) 1553 1554 //! Returns the dot product between a vec2f and the col of a matrix 1555 #define MAT_DOT_COL2(mat,vec2,colindex) (vec2[0]*mat[0][colindex] + vec2[1]*mat[1][colindex]) 1556 1557 //! Returns the dot product between a vec4f and the col of a matrix 1558 #define MAT_DOT_COL4(mat,vec4,colindex) (vec4[0]*mat[0][colindex] + vec4[1]*mat[1][colindex] + vec4[2]*mat[2][colindex] + vec4[3]*mat[3][colindex]) 1559 1560 /*!Transpose matrix times vector 1561 v is a vec3f 1562 and m is a mat4f<br> 1563 */ 1564 #define INV_MAT_DOT_VEC_3X3(p,m,v) \ 1565 { \ 1566 p[0] = MAT_DOT_COL(m,v,0); \ 1567 p[1] = MAT_DOT_COL(m,v,1); \ 1568 p[2] = MAT_DOT_COL(m,v,2); \ 1569 }\ 1570 1571 1572 1573 #endif // GIM_VECTOR_H_INCLUDED 1574
