m_matrix.c revision aa2069586d434dd0487b0daa2b583efe801a0d51
1/* 2 * Mesa 3-D graphics library 3 * Version: 6.3 4 * 5 * Copyright (C) 1999-2005 Brian Paul All Rights Reserved. 6 * 7 * Permission is hereby granted, free of charge, to any person obtaining a 8 * copy of this software and associated documentation files (the "Software"), 9 * to deal in the Software without restriction, including without limitation 10 * the rights to use, copy, modify, merge, publish, distribute, sublicense, 11 * and/or sell copies of the Software, and to permit persons to whom the 12 * Software is furnished to do so, subject to the following conditions: 13 * 14 * The above copyright notice and this permission notice shall be included 15 * in all copies or substantial portions of the Software. 16 * 17 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 18 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 19 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 20 * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN 21 * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN 22 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 23 */ 24 25 26/** 27 * \file m_matrix.c 28 * Matrix operations. 29 * 30 * \note 31 * -# 4x4 transformation matrices are stored in memory in column major order. 32 * -# Points/vertices are to be thought of as column vectors. 33 * -# Transformation of a point p by a matrix M is: p' = M * p 34 */ 35 36 37#include "glheader.h" 38#include "imports.h" 39#include "macros.h" 40#include "imports.h" 41 42#include "m_matrix.h" 43 44 45/** 46 * \defgroup MatFlags MAT_FLAG_XXX-flags 47 * 48 * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags 49 * It would be nice to make all these flags private to m_matrix.c 50 */ 51/*@{*/ 52#define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag. 53 * (Not actually used - the identity 54 * matrix is identified by the absense 55 * of all other flags.) 56 */ 57#define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */ 58#define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */ 59#define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */ 60#define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */ 61#define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */ 62#define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */ 63#define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */ 64#define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */ 65#define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */ 66#define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */ 67#define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */ 68 69/** angle preserving matrix flags mask */ 70#define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \ 71 MAT_FLAG_TRANSLATION | \ 72 MAT_FLAG_UNIFORM_SCALE) 73 74/** geometry related matrix flags mask */ 75#define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \ 76 MAT_FLAG_ROTATION | \ 77 MAT_FLAG_TRANSLATION | \ 78 MAT_FLAG_UNIFORM_SCALE | \ 79 MAT_FLAG_GENERAL_SCALE | \ 80 MAT_FLAG_GENERAL_3D | \ 81 MAT_FLAG_PERSPECTIVE | \ 82 MAT_FLAG_SINGULAR) 83 84/** length preserving matrix flags mask */ 85#define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \ 86 MAT_FLAG_TRANSLATION) 87 88 89/** 3D (non-perspective) matrix flags mask */ 90#define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \ 91 MAT_FLAG_TRANSLATION | \ 92 MAT_FLAG_UNIFORM_SCALE | \ 93 MAT_FLAG_GENERAL_SCALE | \ 94 MAT_FLAG_GENERAL_3D) 95 96/** dirty matrix flags mask */ 97#define MAT_DIRTY (MAT_DIRTY_TYPE | \ 98 MAT_DIRTY_FLAGS | \ 99 MAT_DIRTY_INVERSE) 100 101/*@}*/ 102 103 104/** 105 * Test geometry related matrix flags. 106 * 107 * \param mat a pointer to a GLmatrix structure. 108 * \param a flags mask. 109 * 110 * \returns non-zero if all geometry related matrix flags are contained within 111 * the mask, or zero otherwise. 112 */ 113#define TEST_MAT_FLAGS(mat, a) \ 114 ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0) 115 116 117 118/** 119 * Names of the corresponding GLmatrixtype values. 120 */ 121static const char *types[] = { 122 "MATRIX_GENERAL", 123 "MATRIX_IDENTITY", 124 "MATRIX_3D_NO_ROT", 125 "MATRIX_PERSPECTIVE", 126 "MATRIX_2D", 127 "MATRIX_2D_NO_ROT", 128 "MATRIX_3D" 129}; 130 131 132/** 133 * Identity matrix. 134 */ 135static GLfloat Identity[16] = { 136 1.0, 0.0, 0.0, 0.0, 137 0.0, 1.0, 0.0, 0.0, 138 0.0, 0.0, 1.0, 0.0, 139 0.0, 0.0, 0.0, 1.0 140}; 141 142 143 144/**********************************************************************/ 145/** \name Matrix multiplication */ 146/*@{*/ 147 148#define A(row,col) a[(col<<2)+row] 149#define B(row,col) b[(col<<2)+row] 150#define P(row,col) product[(col<<2)+row] 151 152/** 153 * Perform a full 4x4 matrix multiplication. 154 * 155 * \param a matrix. 156 * \param b matrix. 157 * \param product will receive the product of \p a and \p b. 158 * 159 * \warning Is assumed that \p product != \p b. \p product == \p a is allowed. 160 * 161 * \note KW: 4*16 = 64 multiplications 162 * 163 * \author This \c matmul was contributed by Thomas Malik 164 */ 165static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b ) 166{ 167 GLint i; 168 for (i = 0; i < 4; i++) { 169 const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); 170 P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0); 171 P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1); 172 P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2); 173 P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3); 174 } 175} 176 177/** 178 * Multiply two matrices known to occupy only the top three rows, such 179 * as typical model matrices, and orthogonal matrices. 180 * 181 * \param a matrix. 182 * \param b matrix. 183 * \param product will receive the product of \p a and \p b. 184 */ 185static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b ) 186{ 187 GLint i; 188 for (i = 0; i < 3; i++) { 189 const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); 190 P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0); 191 P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1); 192 P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2); 193 P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3; 194 } 195 P(3,0) = 0; 196 P(3,1) = 0; 197 P(3,2) = 0; 198 P(3,3) = 1; 199} 200 201#undef A 202#undef B 203#undef P 204 205/** 206 * Multiply a matrix by an array of floats with known properties. 207 * 208 * \param mat pointer to a GLmatrix structure containing the left multiplication 209 * matrix, and that will receive the product result. 210 * \param m right multiplication matrix array. 211 * \param flags flags of the matrix \p m. 212 * 213 * Joins both flags and marks the type and inverse as dirty. Calls matmul34() 214 * if both matrices are 3D, or matmul4() otherwise. 215 */ 216static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags ) 217{ 218 mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE); 219 220 if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) 221 matmul34( mat->m, mat->m, m ); 222 else 223 matmul4( mat->m, mat->m, m ); 224} 225 226/** 227 * Matrix multiplication. 228 * 229 * \param dest destination matrix. 230 * \param a left matrix. 231 * \param b right matrix. 232 * 233 * Joins both flags and marks the type and inverse as dirty. Calls matmul34() 234 * if both matrices are 3D, or matmul4() otherwise. 235 */ 236void 237_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b ) 238{ 239 dest->flags = (a->flags | 240 b->flags | 241 MAT_DIRTY_TYPE | 242 MAT_DIRTY_INVERSE); 243 244 if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D)) 245 matmul34( dest->m, a->m, b->m ); 246 else 247 matmul4( dest->m, a->m, b->m ); 248} 249 250/** 251 * Matrix multiplication. 252 * 253 * \param dest left and destination matrix. 254 * \param m right matrix array. 255 * 256 * Marks the matrix flags with general flag, and type and inverse dirty flags. 257 * Calls matmul4() for the multiplication. 258 */ 259void 260_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m ) 261{ 262 dest->flags |= (MAT_FLAG_GENERAL | 263 MAT_DIRTY_TYPE | 264 MAT_DIRTY_INVERSE | 265 MAT_DIRTY_FLAGS); 266 267 matmul4( dest->m, dest->m, m ); 268} 269 270/*@}*/ 271 272 273/**********************************************************************/ 274/** \name Matrix output */ 275/*@{*/ 276 277/** 278 * Print a matrix array. 279 * 280 * \param m matrix array. 281 * 282 * Called by _math_matrix_print() to print a matrix or its inverse. 283 */ 284static void print_matrix_floats( const GLfloat m[16] ) 285{ 286 int i; 287 for (i=0;i<4;i++) { 288 _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] ); 289 } 290} 291 292/** 293 * Dumps the contents of a GLmatrix structure. 294 * 295 * \param m pointer to the GLmatrix structure. 296 */ 297void 298_math_matrix_print( const GLmatrix *m ) 299{ 300 _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags); 301 print_matrix_floats(m->m); 302 _mesa_debug(NULL, "Inverse: \n"); 303 if (m->inv) { 304 GLfloat prod[16]; 305 print_matrix_floats(m->inv); 306 matmul4(prod, m->m, m->inv); 307 _mesa_debug(NULL, "Mat * Inverse:\n"); 308 print_matrix_floats(prod); 309 } 310 else { 311 _mesa_debug(NULL, " - not available\n"); 312 } 313} 314 315/*@}*/ 316 317 318/** 319 * References an element of 4x4 matrix. 320 * 321 * \param m matrix array. 322 * \param c column of the desired element. 323 * \param r row of the desired element. 324 * 325 * \return value of the desired element. 326 * 327 * Calculate the linear storage index of the element and references it. 328 */ 329#define MAT(m,r,c) (m)[(c)*4+(r)] 330 331 332/**********************************************************************/ 333/** \name Matrix inversion */ 334/*@{*/ 335 336/** 337 * Swaps the values of two floating pointer variables. 338 * 339 * Used by invert_matrix_general() to swap the row pointers. 340 */ 341#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; } 342 343/** 344 * Compute inverse of 4x4 transformation matrix. 345 * 346 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 347 * stored in the GLmatrix::inv attribute. 348 * 349 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 350 * 351 * \author 352 * Code contributed by Jacques Leroy jle@star.be 353 * 354 * Calculates the inverse matrix by performing the gaussian matrix reduction 355 * with partial pivoting followed by back/substitution with the loops manually 356 * unrolled. 357 */ 358static GLboolean invert_matrix_general( GLmatrix *mat ) 359{ 360 const GLfloat *m = mat->m; 361 GLfloat *out = mat->inv; 362 GLfloat wtmp[4][8]; 363 GLfloat m0, m1, m2, m3, s; 364 GLfloat *r0, *r1, *r2, *r3; 365 366 r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3]; 367 368 r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1), 369 r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3), 370 r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0, 371 372 r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1), 373 r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3), 374 r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0, 375 376 r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1), 377 r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3), 378 r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0, 379 380 r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1), 381 r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3), 382 r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0; 383 384 /* choose pivot - or die */ 385 if (fabs(r3[0])>fabs(r2[0])) SWAP_ROWS(r3, r2); 386 if (fabs(r2[0])>fabs(r1[0])) SWAP_ROWS(r2, r1); 387 if (fabs(r1[0])>fabs(r0[0])) SWAP_ROWS(r1, r0); 388 if (0.0 == r0[0]) return GL_FALSE; 389 390 /* eliminate first variable */ 391 m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0]; 392 s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s; 393 s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s; 394 s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s; 395 s = r0[4]; 396 if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; } 397 s = r0[5]; 398 if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; } 399 s = r0[6]; 400 if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; } 401 s = r0[7]; 402 if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; } 403 404 /* choose pivot - or die */ 405 if (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2); 406 if (fabs(r2[1])>fabs(r1[1])) SWAP_ROWS(r2, r1); 407 if (0.0 == r1[1]) return GL_FALSE; 408 409 /* eliminate second variable */ 410 m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1]; 411 r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2]; 412 r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3]; 413 s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; } 414 s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; } 415 s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; } 416 s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; } 417 418 /* choose pivot - or die */ 419 if (fabs(r3[2])>fabs(r2[2])) SWAP_ROWS(r3, r2); 420 if (0.0 == r2[2]) return GL_FALSE; 421 422 /* eliminate third variable */ 423 m3 = r3[2]/r2[2]; 424 r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4], 425 r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], 426 r3[7] -= m3 * r2[7]; 427 428 /* last check */ 429 if (0.0 == r3[3]) return GL_FALSE; 430 431 s = 1.0F/r3[3]; /* now back substitute row 3 */ 432 r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s; 433 434 m2 = r2[3]; /* now back substitute row 2 */ 435 s = 1.0F/r2[2]; 436 r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2), 437 r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2); 438 m1 = r1[3]; 439 r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1, 440 r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1; 441 m0 = r0[3]; 442 r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0, 443 r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0; 444 445 m1 = r1[2]; /* now back substitute row 1 */ 446 s = 1.0F/r1[1]; 447 r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1), 448 r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1); 449 m0 = r0[2]; 450 r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0, 451 r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0; 452 453 m0 = r0[1]; /* now back substitute row 0 */ 454 s = 1.0F/r0[0]; 455 r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0), 456 r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0); 457 458 MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5], 459 MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7], 460 MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5], 461 MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7], 462 MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5], 463 MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7], 464 MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5], 465 MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7]; 466 467 return GL_TRUE; 468} 469#undef SWAP_ROWS 470 471/** 472 * Compute inverse of a general 3d transformation matrix. 473 * 474 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 475 * stored in the GLmatrix::inv attribute. 476 * 477 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 478 * 479 * \author Adapted from graphics gems II. 480 * 481 * Calculates the inverse of the upper left by first calculating its 482 * determinant and multiplying it to the symmetric adjust matrix of each 483 * element. Finally deals with the translation part by transforming the 484 * original translation vector using by the calculated submatrix inverse. 485 */ 486static GLboolean invert_matrix_3d_general( GLmatrix *mat ) 487{ 488 const GLfloat *in = mat->m; 489 GLfloat *out = mat->inv; 490 GLfloat pos, neg, t; 491 GLfloat det; 492 493 /* Calculate the determinant of upper left 3x3 submatrix and 494 * determine if the matrix is singular. 495 */ 496 pos = neg = 0.0; 497 t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2); 498 if (t >= 0.0) pos += t; else neg += t; 499 500 t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2); 501 if (t >= 0.0) pos += t; else neg += t; 502 503 t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2); 504 if (t >= 0.0) pos += t; else neg += t; 505 506 t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2); 507 if (t >= 0.0) pos += t; else neg += t; 508 509 t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2); 510 if (t >= 0.0) pos += t; else neg += t; 511 512 t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2); 513 if (t >= 0.0) pos += t; else neg += t; 514 515 det = pos + neg; 516 517 if (det*det < 1e-25) 518 return GL_FALSE; 519 520 det = 1.0F / det; 521 MAT(out,0,0) = ( (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det); 522 MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det); 523 MAT(out,0,2) = ( (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det); 524 MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det); 525 MAT(out,1,1) = ( (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det); 526 MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det); 527 MAT(out,2,0) = ( (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det); 528 MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det); 529 MAT(out,2,2) = ( (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det); 530 531 /* Do the translation part */ 532 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + 533 MAT(in,1,3) * MAT(out,0,1) + 534 MAT(in,2,3) * MAT(out,0,2) ); 535 MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + 536 MAT(in,1,3) * MAT(out,1,1) + 537 MAT(in,2,3) * MAT(out,1,2) ); 538 MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + 539 MAT(in,1,3) * MAT(out,2,1) + 540 MAT(in,2,3) * MAT(out,2,2) ); 541 542 return GL_TRUE; 543} 544 545/** 546 * Compute inverse of a 3d transformation matrix. 547 * 548 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 549 * stored in the GLmatrix::inv attribute. 550 * 551 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 552 * 553 * If the matrix is not an angle preserving matrix then calls 554 * invert_matrix_3d_general for the actual calculation. Otherwise calculates 555 * the inverse matrix analyzing and inverting each of the scaling, rotation and 556 * translation parts. 557 */ 558static GLboolean invert_matrix_3d( GLmatrix *mat ) 559{ 560 const GLfloat *in = mat->m; 561 GLfloat *out = mat->inv; 562 563 if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) { 564 return invert_matrix_3d_general( mat ); 565 } 566 567 if (mat->flags & MAT_FLAG_UNIFORM_SCALE) { 568 GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) + 569 MAT(in,0,1) * MAT(in,0,1) + 570 MAT(in,0,2) * MAT(in,0,2)); 571 572 if (scale == 0.0) 573 return GL_FALSE; 574 575 scale = 1.0F / scale; 576 577 /* Transpose and scale the 3 by 3 upper-left submatrix. */ 578 MAT(out,0,0) = scale * MAT(in,0,0); 579 MAT(out,1,0) = scale * MAT(in,0,1); 580 MAT(out,2,0) = scale * MAT(in,0,2); 581 MAT(out,0,1) = scale * MAT(in,1,0); 582 MAT(out,1,1) = scale * MAT(in,1,1); 583 MAT(out,2,1) = scale * MAT(in,1,2); 584 MAT(out,0,2) = scale * MAT(in,2,0); 585 MAT(out,1,2) = scale * MAT(in,2,1); 586 MAT(out,2,2) = scale * MAT(in,2,2); 587 } 588 else if (mat->flags & MAT_FLAG_ROTATION) { 589 /* Transpose the 3 by 3 upper-left submatrix. */ 590 MAT(out,0,0) = MAT(in,0,0); 591 MAT(out,1,0) = MAT(in,0,1); 592 MAT(out,2,0) = MAT(in,0,2); 593 MAT(out,0,1) = MAT(in,1,0); 594 MAT(out,1,1) = MAT(in,1,1); 595 MAT(out,2,1) = MAT(in,1,2); 596 MAT(out,0,2) = MAT(in,2,0); 597 MAT(out,1,2) = MAT(in,2,1); 598 MAT(out,2,2) = MAT(in,2,2); 599 } 600 else { 601 /* pure translation */ 602 MEMCPY( out, Identity, sizeof(Identity) ); 603 MAT(out,0,3) = - MAT(in,0,3); 604 MAT(out,1,3) = - MAT(in,1,3); 605 MAT(out,2,3) = - MAT(in,2,3); 606 return GL_TRUE; 607 } 608 609 if (mat->flags & MAT_FLAG_TRANSLATION) { 610 /* Do the translation part */ 611 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + 612 MAT(in,1,3) * MAT(out,0,1) + 613 MAT(in,2,3) * MAT(out,0,2) ); 614 MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + 615 MAT(in,1,3) * MAT(out,1,1) + 616 MAT(in,2,3) * MAT(out,1,2) ); 617 MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + 618 MAT(in,1,3) * MAT(out,2,1) + 619 MAT(in,2,3) * MAT(out,2,2) ); 620 } 621 else { 622 MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0; 623 } 624 625 return GL_TRUE; 626} 627 628/** 629 * Compute inverse of an identity transformation matrix. 630 * 631 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 632 * stored in the GLmatrix::inv attribute. 633 * 634 * \return always GL_TRUE. 635 * 636 * Simply copies Identity into GLmatrix::inv. 637 */ 638static GLboolean invert_matrix_identity( GLmatrix *mat ) 639{ 640 MEMCPY( mat->inv, Identity, sizeof(Identity) ); 641 return GL_TRUE; 642} 643 644/** 645 * Compute inverse of a no-rotation 3d transformation matrix. 646 * 647 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 648 * stored in the GLmatrix::inv attribute. 649 * 650 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 651 * 652 * Calculates the 653 */ 654static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat ) 655{ 656 const GLfloat *in = mat->m; 657 GLfloat *out = mat->inv; 658 659 if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 ) 660 return GL_FALSE; 661 662 MEMCPY( out, Identity, 16 * sizeof(GLfloat) ); 663 MAT(out,0,0) = 1.0F / MAT(in,0,0); 664 MAT(out,1,1) = 1.0F / MAT(in,1,1); 665 MAT(out,2,2) = 1.0F / MAT(in,2,2); 666 667 if (mat->flags & MAT_FLAG_TRANSLATION) { 668 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); 669 MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); 670 MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2)); 671 } 672 673 return GL_TRUE; 674} 675 676/** 677 * Compute inverse of a no-rotation 2d transformation matrix. 678 * 679 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 680 * stored in the GLmatrix::inv attribute. 681 * 682 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 683 * 684 * Calculates the inverse matrix by applying the inverse scaling and 685 * translation to the identity matrix. 686 */ 687static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat ) 688{ 689 const GLfloat *in = mat->m; 690 GLfloat *out = mat->inv; 691 692 if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0) 693 return GL_FALSE; 694 695 MEMCPY( out, Identity, 16 * sizeof(GLfloat) ); 696 MAT(out,0,0) = 1.0F / MAT(in,0,0); 697 MAT(out,1,1) = 1.0F / MAT(in,1,1); 698 699 if (mat->flags & MAT_FLAG_TRANSLATION) { 700 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); 701 MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); 702 } 703 704 return GL_TRUE; 705} 706 707#if 0 708/* broken */ 709static GLboolean invert_matrix_perspective( GLmatrix *mat ) 710{ 711 const GLfloat *in = mat->m; 712 GLfloat *out = mat->inv; 713 714 if (MAT(in,2,3) == 0) 715 return GL_FALSE; 716 717 MEMCPY( out, Identity, 16 * sizeof(GLfloat) ); 718 719 MAT(out,0,0) = 1.0F / MAT(in,0,0); 720 MAT(out,1,1) = 1.0F / MAT(in,1,1); 721 722 MAT(out,0,3) = MAT(in,0,2); 723 MAT(out,1,3) = MAT(in,1,2); 724 725 MAT(out,2,2) = 0; 726 MAT(out,2,3) = -1; 727 728 MAT(out,3,2) = 1.0F / MAT(in,2,3); 729 MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2); 730 731 return GL_TRUE; 732} 733#endif 734 735/** 736 * Matrix inversion function pointer type. 737 */ 738typedef GLboolean (*inv_mat_func)( GLmatrix *mat ); 739 740/** 741 * Table of the matrix inversion functions according to the matrix type. 742 */ 743static inv_mat_func inv_mat_tab[7] = { 744 invert_matrix_general, 745 invert_matrix_identity, 746 invert_matrix_3d_no_rot, 747#if 0 748 /* Don't use this function for now - it fails when the projection matrix 749 * is premultiplied by a translation (ala Chromium's tilesort SPU). 750 */ 751 invert_matrix_perspective, 752#else 753 invert_matrix_general, 754#endif 755 invert_matrix_3d, /* lazy! */ 756 invert_matrix_2d_no_rot, 757 invert_matrix_3d 758}; 759 760/** 761 * Compute inverse of a transformation matrix. 762 * 763 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 764 * stored in the GLmatrix::inv attribute. 765 * 766 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 767 * 768 * Calls the matrix inversion function in inv_mat_tab corresponding to the 769 * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag, 770 * and copies the identity matrix into GLmatrix::inv. 771 */ 772static GLboolean matrix_invert( GLmatrix *mat ) 773{ 774 if (inv_mat_tab[mat->type](mat)) { 775 mat->flags &= ~MAT_FLAG_SINGULAR; 776 return GL_TRUE; 777 } else { 778 mat->flags |= MAT_FLAG_SINGULAR; 779 MEMCPY( mat->inv, Identity, sizeof(Identity) ); 780 return GL_FALSE; 781 } 782} 783 784/*@}*/ 785 786 787/**********************************************************************/ 788/** \name Matrix generation */ 789/*@{*/ 790 791/** 792 * Generate a 4x4 transformation matrix from glRotate parameters, and 793 * post-multiply the input matrix by it. 794 * 795 * \author 796 * This function was contributed by Erich Boleyn (erich@uruk.org). 797 * Optimizations contributed by Rudolf Opalla (rudi@khm.de). 798 */ 799void 800_math_matrix_rotate( GLmatrix *mat, 801 GLfloat angle, GLfloat x, GLfloat y, GLfloat z ) 802{ 803 GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c; 804 GLfloat m[16]; 805 GLboolean optimized; 806 807 s = (GLfloat) _mesa_sin( angle * DEG2RAD ); 808 c = (GLfloat) _mesa_cos( angle * DEG2RAD ); 809 810 MEMCPY(m, Identity, sizeof(GLfloat)*16); 811 optimized = GL_FALSE; 812 813#define M(row,col) m[col*4+row] 814 815 if (x == 0.0F) { 816 if (y == 0.0F) { 817 if (z != 0.0F) { 818 optimized = GL_TRUE; 819 /* rotate only around z-axis */ 820 M(0,0) = c; 821 M(1,1) = c; 822 if (z < 0.0F) { 823 M(0,1) = s; 824 M(1,0) = -s; 825 } 826 else { 827 M(0,1) = -s; 828 M(1,0) = s; 829 } 830 } 831 } 832 else if (z == 0.0F) { 833 optimized = GL_TRUE; 834 /* rotate only around y-axis */ 835 M(0,0) = c; 836 M(2,2) = c; 837 if (y < 0.0F) { 838 M(0,2) = -s; 839 M(2,0) = s; 840 } 841 else { 842 M(0,2) = s; 843 M(2,0) = -s; 844 } 845 } 846 } 847 else if (y == 0.0F) { 848 if (z == 0.0F) { 849 optimized = GL_TRUE; 850 /* rotate only around x-axis */ 851 M(1,1) = c; 852 M(2,2) = c; 853 if (x < 0.0F) { 854 M(1,2) = s; 855 M(2,1) = -s; 856 } 857 else { 858 M(1,2) = -s; 859 M(2,1) = s; 860 } 861 } 862 } 863 864 if (!optimized) { 865 const GLfloat mag = SQRTF(x * x + y * y + z * z); 866 867 if (mag <= 1.0e-4) { 868 /* no rotation, leave mat as-is */ 869 return; 870 } 871 872 x /= mag; 873 y /= mag; 874 z /= mag; 875 876 877 /* 878 * Arbitrary axis rotation matrix. 879 * 880 * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied 881 * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation 882 * (which is about the X-axis), and the two composite transforms 883 * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary 884 * from the arbitrary axis to the X-axis then back. They are 885 * all elementary rotations. 886 * 887 * Rz' is a rotation about the Z-axis, to bring the axis vector 888 * into the x-z plane. Then Ry' is applied, rotating about the 889 * Y-axis to bring the axis vector parallel with the X-axis. The 890 * rotation about the X-axis is then performed. Ry and Rz are 891 * simply the respective inverse transforms to bring the arbitrary 892 * axis back to it's original orientation. The first transforms 893 * Rz' and Ry' are considered inverses, since the data from the 894 * arbitrary axis gives you info on how to get to it, not how 895 * to get away from it, and an inverse must be applied. 896 * 897 * The basic calculation used is to recognize that the arbitrary 898 * axis vector (x, y, z), since it is of unit length, actually 899 * represents the sines and cosines of the angles to rotate the 900 * X-axis to the same orientation, with theta being the angle about 901 * Z and phi the angle about Y (in the order described above) 902 * as follows: 903 * 904 * cos ( theta ) = x / sqrt ( 1 - z^2 ) 905 * sin ( theta ) = y / sqrt ( 1 - z^2 ) 906 * 907 * cos ( phi ) = sqrt ( 1 - z^2 ) 908 * sin ( phi ) = z 909 * 910 * Note that cos ( phi ) can further be inserted to the above 911 * formulas: 912 * 913 * cos ( theta ) = x / cos ( phi ) 914 * sin ( theta ) = y / sin ( phi ) 915 * 916 * ...etc. Because of those relations and the standard trigonometric 917 * relations, it is pssible to reduce the transforms down to what 918 * is used below. It may be that any primary axis chosen will give the 919 * same results (modulo a sign convention) using thie method. 920 * 921 * Particularly nice is to notice that all divisions that might 922 * have caused trouble when parallel to certain planes or 923 * axis go away with care paid to reducing the expressions. 924 * After checking, it does perform correctly under all cases, since 925 * in all the cases of division where the denominator would have 926 * been zero, the numerator would have been zero as well, giving 927 * the expected result. 928 */ 929 930 xx = x * x; 931 yy = y * y; 932 zz = z * z; 933 xy = x * y; 934 yz = y * z; 935 zx = z * x; 936 xs = x * s; 937 ys = y * s; 938 zs = z * s; 939 one_c = 1.0F - c; 940 941 /* We already hold the identity-matrix so we can skip some statements */ 942 M(0,0) = (one_c * xx) + c; 943 M(0,1) = (one_c * xy) - zs; 944 M(0,2) = (one_c * zx) + ys; 945/* M(0,3) = 0.0F; */ 946 947 M(1,0) = (one_c * xy) + zs; 948 M(1,1) = (one_c * yy) + c; 949 M(1,2) = (one_c * yz) - xs; 950/* M(1,3) = 0.0F; */ 951 952 M(2,0) = (one_c * zx) - ys; 953 M(2,1) = (one_c * yz) + xs; 954 M(2,2) = (one_c * zz) + c; 955/* M(2,3) = 0.0F; */ 956 957/* 958 M(3,0) = 0.0F; 959 M(3,1) = 0.0F; 960 M(3,2) = 0.0F; 961 M(3,3) = 1.0F; 962*/ 963 } 964#undef M 965 966 matrix_multf( mat, m, MAT_FLAG_ROTATION ); 967} 968 969/** 970 * Apply a perspective projection matrix. 971 * 972 * \param mat matrix to apply the projection. 973 * \param left left clipping plane coordinate. 974 * \param right right clipping plane coordinate. 975 * \param bottom bottom clipping plane coordinate. 976 * \param top top clipping plane coordinate. 977 * \param nearval distance to the near clipping plane. 978 * \param farval distance to the far clipping plane. 979 * 980 * Creates the projection matrix and multiplies it with \p mat, marking the 981 * MAT_FLAG_PERSPECTIVE flag. 982 */ 983void 984_math_matrix_frustum( GLmatrix *mat, 985 GLfloat left, GLfloat right, 986 GLfloat bottom, GLfloat top, 987 GLfloat nearval, GLfloat farval ) 988{ 989 GLfloat x, y, a, b, c, d; 990 GLfloat m[16]; 991 992 x = (2.0F*nearval) / (right-left); 993 y = (2.0F*nearval) / (top-bottom); 994 a = (right+left) / (right-left); 995 b = (top+bottom) / (top-bottom); 996 c = -(farval+nearval) / ( farval-nearval); 997 d = -(2.0F*farval*nearval) / (farval-nearval); /* error? */ 998 999#define M(row,col) m[col*4+row] 1000 M(0,0) = x; M(0,1) = 0.0F; M(0,2) = a; M(0,3) = 0.0F; 1001 M(1,0) = 0.0F; M(1,1) = y; M(1,2) = b; M(1,3) = 0.0F; 1002 M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = c; M(2,3) = d; 1003 M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = -1.0F; M(3,3) = 0.0F; 1004#undef M 1005 1006 matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE ); 1007} 1008 1009/** 1010 * Apply an orthographic projection matrix. 1011 * 1012 * \param mat matrix to apply the projection. 1013 * \param left left clipping plane coordinate. 1014 * \param right right clipping plane coordinate. 1015 * \param bottom bottom clipping plane coordinate. 1016 * \param top top clipping plane coordinate. 1017 * \param nearval distance to the near clipping plane. 1018 * \param farval distance to the far clipping plane. 1019 * 1020 * Creates the projection matrix and multiplies it with \p mat, marking the 1021 * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags. 1022 */ 1023void 1024_math_matrix_ortho( GLmatrix *mat, 1025 GLfloat left, GLfloat right, 1026 GLfloat bottom, GLfloat top, 1027 GLfloat nearval, GLfloat farval ) 1028{ 1029 GLfloat m[16]; 1030 1031#define M(row,col) m[col*4+row] 1032 M(0,0) = 2.0F / (right-left); 1033 M(0,1) = 0.0F; 1034 M(0,2) = 0.0F; 1035 M(0,3) = -(right+left) / (right-left); 1036 1037 M(1,0) = 0.0F; 1038 M(1,1) = 2.0F / (top-bottom); 1039 M(1,2) = 0.0F; 1040 M(1,3) = -(top+bottom) / (top-bottom); 1041 1042 M(2,0) = 0.0F; 1043 M(2,1) = 0.0F; 1044 M(2,2) = -2.0F / (farval-nearval); 1045 M(2,3) = -(farval+nearval) / (farval-nearval); 1046 1047 M(3,0) = 0.0F; 1048 M(3,1) = 0.0F; 1049 M(3,2) = 0.0F; 1050 M(3,3) = 1.0F; 1051#undef M 1052 1053 matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION)); 1054} 1055 1056/** 1057 * Multiply a matrix with a general scaling matrix. 1058 * 1059 * \param mat matrix. 1060 * \param x x axis scale factor. 1061 * \param y y axis scale factor. 1062 * \param z z axis scale factor. 1063 * 1064 * Multiplies in-place the elements of \p mat by the scale factors. Checks if 1065 * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE 1066 * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and 1067 * MAT_DIRTY_INVERSE dirty flags. 1068 */ 1069void 1070_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) 1071{ 1072 GLfloat *m = mat->m; 1073 m[0] *= x; m[4] *= y; m[8] *= z; 1074 m[1] *= x; m[5] *= y; m[9] *= z; 1075 m[2] *= x; m[6] *= y; m[10] *= z; 1076 m[3] *= x; m[7] *= y; m[11] *= z; 1077 1078 if (fabs(x - y) < 1e-8 && fabs(x - z) < 1e-8) 1079 mat->flags |= MAT_FLAG_UNIFORM_SCALE; 1080 else 1081 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1082 1083 mat->flags |= (MAT_DIRTY_TYPE | 1084 MAT_DIRTY_INVERSE); 1085} 1086 1087/** 1088 * Multiply a matrix with a translation matrix. 1089 * 1090 * \param mat matrix. 1091 * \param x translation vector x coordinate. 1092 * \param y translation vector y coordinate. 1093 * \param z translation vector z coordinate. 1094 * 1095 * Adds the translation coordinates to the elements of \p mat in-place. Marks 1096 * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE 1097 * dirty flags. 1098 */ 1099void 1100_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) 1101{ 1102 GLfloat *m = mat->m; 1103 m[12] = m[0] * x + m[4] * y + m[8] * z + m[12]; 1104 m[13] = m[1] * x + m[5] * y + m[9] * z + m[13]; 1105 m[14] = m[2] * x + m[6] * y + m[10] * z + m[14]; 1106 m[15] = m[3] * x + m[7] * y + m[11] * z + m[15]; 1107 1108 mat->flags |= (MAT_FLAG_TRANSLATION | 1109 MAT_DIRTY_TYPE | 1110 MAT_DIRTY_INVERSE); 1111} 1112 1113 1114/** 1115 * Set matrix to do viewport and depthrange mapping. 1116 * Transforms Normalized Device Coords to window/Z values. 1117 */ 1118void 1119_math_matrix_viewport(GLmatrix *m, GLint x, GLint y, GLint width, GLint height, 1120 GLfloat zNear, GLfloat zFar, GLfloat depthMax) 1121{ 1122 m->m[MAT_SX] = (GLfloat) width / 2.0F; 1123 m->m[MAT_TX] = m->m[MAT_SX] + x; 1124 m->m[MAT_SY] = (GLfloat) height / 2.0F; 1125 m->m[MAT_TY] = m->m[MAT_SY] + y; 1126 m->m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0F); 1127 m->m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0F + zNear); 1128 m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION; 1129 m->type = MATRIX_3D_NO_ROT; 1130} 1131 1132 1133/** 1134 * Set a matrix to the identity matrix. 1135 * 1136 * \param mat matrix. 1137 * 1138 * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL. 1139 * Sets the matrix type to identity, and clear the dirty flags. 1140 */ 1141void 1142_math_matrix_set_identity( GLmatrix *mat ) 1143{ 1144 MEMCPY( mat->m, Identity, 16*sizeof(GLfloat) ); 1145 1146 if (mat->inv) 1147 MEMCPY( mat->inv, Identity, 16*sizeof(GLfloat) ); 1148 1149 mat->type = MATRIX_IDENTITY; 1150 mat->flags &= ~(MAT_DIRTY_FLAGS| 1151 MAT_DIRTY_TYPE| 1152 MAT_DIRTY_INVERSE); 1153} 1154 1155/*@}*/ 1156 1157 1158/**********************************************************************/ 1159/** \name Matrix analysis */ 1160/*@{*/ 1161 1162#define ZERO(x) (1<<x) 1163#define ONE(x) (1<<(x+16)) 1164 1165#define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14)) 1166#define MASK_NO_2D_SCALE ( ONE(0) | ONE(5)) 1167 1168#define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\ 1169 ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\ 1170 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1171 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1172 1173#define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \ 1174 ZERO(1) | ZERO(9) | \ 1175 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1176 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1177 1178#define MASK_2D ( ZERO(8) | \ 1179 ZERO(9) | \ 1180 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1181 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1182 1183 1184#define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \ 1185 ZERO(1) | ZERO(9) | \ 1186 ZERO(2) | ZERO(6) | \ 1187 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1188 1189#define MASK_3D ( \ 1190 \ 1191 \ 1192 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1193 1194 1195#define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\ 1196 ZERO(1) | ZERO(13) |\ 1197 ZERO(2) | ZERO(6) | \ 1198 ZERO(3) | ZERO(7) | ZERO(15) ) 1199 1200#define SQ(x) ((x)*(x)) 1201 1202/** 1203 * Determine type and flags from scratch. 1204 * 1205 * \param mat matrix. 1206 * 1207 * This is expensive enough to only want to do it once. 1208 */ 1209static void analyse_from_scratch( GLmatrix *mat ) 1210{ 1211 const GLfloat *m = mat->m; 1212 GLuint mask = 0; 1213 GLuint i; 1214 1215 for (i = 0 ; i < 16 ; i++) { 1216 if (m[i] == 0.0) mask |= (1<<i); 1217 } 1218 1219 if (m[0] == 1.0F) mask |= (1<<16); 1220 if (m[5] == 1.0F) mask |= (1<<21); 1221 if (m[10] == 1.0F) mask |= (1<<26); 1222 if (m[15] == 1.0F) mask |= (1<<31); 1223 1224 mat->flags &= ~MAT_FLAGS_GEOMETRY; 1225 1226 /* Check for translation - no-one really cares 1227 */ 1228 if ((mask & MASK_NO_TRX) != MASK_NO_TRX) 1229 mat->flags |= MAT_FLAG_TRANSLATION; 1230 1231 /* Do the real work 1232 */ 1233 if (mask == (GLuint) MASK_IDENTITY) { 1234 mat->type = MATRIX_IDENTITY; 1235 } 1236 else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) { 1237 mat->type = MATRIX_2D_NO_ROT; 1238 1239 if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE) 1240 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1241 } 1242 else if ((mask & MASK_2D) == (GLuint) MASK_2D) { 1243 GLfloat mm = DOT2(m, m); 1244 GLfloat m4m4 = DOT2(m+4,m+4); 1245 GLfloat mm4 = DOT2(m,m+4); 1246 1247 mat->type = MATRIX_2D; 1248 1249 /* Check for scale */ 1250 if (SQ(mm-1) > SQ(1e-6) || 1251 SQ(m4m4-1) > SQ(1e-6)) 1252 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1253 1254 /* Check for rotation */ 1255 if (SQ(mm4) > SQ(1e-6)) 1256 mat->flags |= MAT_FLAG_GENERAL_3D; 1257 else 1258 mat->flags |= MAT_FLAG_ROTATION; 1259 1260 } 1261 else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) { 1262 mat->type = MATRIX_3D_NO_ROT; 1263 1264 /* Check for scale */ 1265 if (SQ(m[0]-m[5]) < SQ(1e-6) && 1266 SQ(m[0]-m[10]) < SQ(1e-6)) { 1267 if (SQ(m[0]-1.0) > SQ(1e-6)) { 1268 mat->flags |= MAT_FLAG_UNIFORM_SCALE; 1269 } 1270 } 1271 else { 1272 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1273 } 1274 } 1275 else if ((mask & MASK_3D) == (GLuint) MASK_3D) { 1276 GLfloat c1 = DOT3(m,m); 1277 GLfloat c2 = DOT3(m+4,m+4); 1278 GLfloat c3 = DOT3(m+8,m+8); 1279 GLfloat d1 = DOT3(m, m+4); 1280 GLfloat cp[3]; 1281 1282 mat->type = MATRIX_3D; 1283 1284 /* Check for scale */ 1285 if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) { 1286 if (SQ(c1-1.0) > SQ(1e-6)) 1287 mat->flags |= MAT_FLAG_UNIFORM_SCALE; 1288 /* else no scale at all */ 1289 } 1290 else { 1291 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1292 } 1293 1294 /* Check for rotation */ 1295 if (SQ(d1) < SQ(1e-6)) { 1296 CROSS3( cp, m, m+4 ); 1297 SUB_3V( cp, cp, (m+8) ); 1298 if (LEN_SQUARED_3FV(cp) < SQ(1e-6)) 1299 mat->flags |= MAT_FLAG_ROTATION; 1300 else 1301 mat->flags |= MAT_FLAG_GENERAL_3D; 1302 } 1303 else { 1304 mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */ 1305 } 1306 } 1307 else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) { 1308 mat->type = MATRIX_PERSPECTIVE; 1309 mat->flags |= MAT_FLAG_GENERAL; 1310 } 1311 else { 1312 mat->type = MATRIX_GENERAL; 1313 mat->flags |= MAT_FLAG_GENERAL; 1314 } 1315} 1316 1317/** 1318 * Analyze a matrix given that its flags are accurate. 1319 * 1320 * This is the more common operation, hopefully. 1321 */ 1322static void analyse_from_flags( GLmatrix *mat ) 1323{ 1324 const GLfloat *m = mat->m; 1325 1326 if (TEST_MAT_FLAGS(mat, 0)) { 1327 mat->type = MATRIX_IDENTITY; 1328 } 1329 else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION | 1330 MAT_FLAG_UNIFORM_SCALE | 1331 MAT_FLAG_GENERAL_SCALE))) { 1332 if ( m[10]==1.0F && m[14]==0.0F ) { 1333 mat->type = MATRIX_2D_NO_ROT; 1334 } 1335 else { 1336 mat->type = MATRIX_3D_NO_ROT; 1337 } 1338 } 1339 else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) { 1340 if ( m[ 8]==0.0F 1341 && m[ 9]==0.0F 1342 && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) { 1343 mat->type = MATRIX_2D; 1344 } 1345 else { 1346 mat->type = MATRIX_3D; 1347 } 1348 } 1349 else if ( m[4]==0.0F && m[12]==0.0F 1350 && m[1]==0.0F && m[13]==0.0F 1351 && m[2]==0.0F && m[6]==0.0F 1352 && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) { 1353 mat->type = MATRIX_PERSPECTIVE; 1354 } 1355 else { 1356 mat->type = MATRIX_GENERAL; 1357 } 1358} 1359 1360/** 1361 * Analyze and update a matrix. 1362 * 1363 * \param mat matrix. 1364 * 1365 * If the matrix type is dirty then calls either analyse_from_scratch() or 1366 * analyse_from_flags() to determine its type, according to whether the flags 1367 * are dirty or not, respectively. If the matrix has an inverse and it's dirty 1368 * then calls matrix_invert(). Finally clears the dirty flags. 1369 */ 1370void 1371_math_matrix_analyse( GLmatrix *mat ) 1372{ 1373 if (mat->flags & MAT_DIRTY_TYPE) { 1374 if (mat->flags & MAT_DIRTY_FLAGS) 1375 analyse_from_scratch( mat ); 1376 else 1377 analyse_from_flags( mat ); 1378 } 1379 1380 if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) { 1381 matrix_invert( mat ); 1382 } 1383 1384 mat->flags &= ~(MAT_DIRTY_FLAGS| 1385 MAT_DIRTY_TYPE| 1386 MAT_DIRTY_INVERSE); 1387} 1388 1389/*@}*/ 1390 1391 1392/** 1393 * Test if the given matrix preserves vector lengths. 1394 */ 1395GLboolean 1396_math_matrix_is_length_preserving( const GLmatrix *m ) 1397{ 1398 return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING); 1399} 1400 1401 1402/** 1403 * Test if the given matrix does any rotation. 1404 * (or perhaps if the upper-left 3x3 is non-identity) 1405 */ 1406GLboolean 1407_math_matrix_has_rotation( const GLmatrix *m ) 1408{ 1409 if (m->flags & (MAT_FLAG_GENERAL | 1410 MAT_FLAG_ROTATION | 1411 MAT_FLAG_GENERAL_3D | 1412 MAT_FLAG_PERSPECTIVE)) 1413 return GL_TRUE; 1414 else 1415 return GL_FALSE; 1416} 1417 1418 1419GLboolean 1420_math_matrix_is_general_scale( const GLmatrix *m ) 1421{ 1422 return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE; 1423} 1424 1425 1426GLboolean 1427_math_matrix_is_dirty( const GLmatrix *m ) 1428{ 1429 return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE; 1430} 1431 1432 1433/**********************************************************************/ 1434/** \name Matrix setup */ 1435/*@{*/ 1436 1437/** 1438 * Copy a matrix. 1439 * 1440 * \param to destination matrix. 1441 * \param from source matrix. 1442 * 1443 * Copies all fields in GLmatrix, creating an inverse array if necessary. 1444 */ 1445void 1446_math_matrix_copy( GLmatrix *to, const GLmatrix *from ) 1447{ 1448 MEMCPY( to->m, from->m, sizeof(Identity) ); 1449 to->flags = from->flags; 1450 to->type = from->type; 1451 1452 if (to->inv != 0) { 1453 if (from->inv == 0) { 1454 matrix_invert( to ); 1455 } 1456 else { 1457 MEMCPY(to->inv, from->inv, sizeof(GLfloat)*16); 1458 } 1459 } 1460} 1461 1462/** 1463 * Loads a matrix array into GLmatrix. 1464 * 1465 * \param m matrix array. 1466 * \param mat matrix. 1467 * 1468 * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY 1469 * flags. 1470 */ 1471void 1472_math_matrix_loadf( GLmatrix *mat, const GLfloat *m ) 1473{ 1474 MEMCPY( mat->m, m, 16*sizeof(GLfloat) ); 1475 mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY); 1476} 1477 1478/** 1479 * Matrix constructor. 1480 * 1481 * \param m matrix. 1482 * 1483 * Initialize the GLmatrix fields. 1484 */ 1485void 1486_math_matrix_ctr( GLmatrix *m ) 1487{ 1488 m->m = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 ); 1489 if (m->m) 1490 MEMCPY( m->m, Identity, sizeof(Identity) ); 1491 m->inv = NULL; 1492 m->type = MATRIX_IDENTITY; 1493 m->flags = 0; 1494} 1495 1496/** 1497 * Matrix destructor. 1498 * 1499 * \param m matrix. 1500 * 1501 * Frees the data in a GLmatrix. 1502 */ 1503void 1504_math_matrix_dtr( GLmatrix *m ) 1505{ 1506 if (m->m) { 1507 ALIGN_FREE( m->m ); 1508 m->m = NULL; 1509 } 1510 if (m->inv) { 1511 ALIGN_FREE( m->inv ); 1512 m->inv = NULL; 1513 } 1514} 1515 1516/** 1517 * Allocate a matrix inverse. 1518 * 1519 * \param m matrix. 1520 * 1521 * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity. 1522 */ 1523void 1524_math_matrix_alloc_inv( GLmatrix *m ) 1525{ 1526 if (!m->inv) { 1527 m->inv = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 ); 1528 if (m->inv) 1529 MEMCPY( m->inv, Identity, 16 * sizeof(GLfloat) ); 1530 } 1531} 1532 1533/*@}*/ 1534 1535 1536/**********************************************************************/ 1537/** \name Matrix transpose */ 1538/*@{*/ 1539 1540/** 1541 * Transpose a GLfloat matrix. 1542 * 1543 * \param to destination array. 1544 * \param from source array. 1545 */ 1546void 1547_math_transposef( GLfloat to[16], const GLfloat from[16] ) 1548{ 1549 to[0] = from[0]; 1550 to[1] = from[4]; 1551 to[2] = from[8]; 1552 to[3] = from[12]; 1553 to[4] = from[1]; 1554 to[5] = from[5]; 1555 to[6] = from[9]; 1556 to[7] = from[13]; 1557 to[8] = from[2]; 1558 to[9] = from[6]; 1559 to[10] = from[10]; 1560 to[11] = from[14]; 1561 to[12] = from[3]; 1562 to[13] = from[7]; 1563 to[14] = from[11]; 1564 to[15] = from[15]; 1565} 1566 1567/** 1568 * Transpose a GLdouble matrix. 1569 * 1570 * \param to destination array. 1571 * \param from source array. 1572 */ 1573void 1574_math_transposed( GLdouble to[16], const GLdouble from[16] ) 1575{ 1576 to[0] = from[0]; 1577 to[1] = from[4]; 1578 to[2] = from[8]; 1579 to[3] = from[12]; 1580 to[4] = from[1]; 1581 to[5] = from[5]; 1582 to[6] = from[9]; 1583 to[7] = from[13]; 1584 to[8] = from[2]; 1585 to[9] = from[6]; 1586 to[10] = from[10]; 1587 to[11] = from[14]; 1588 to[12] = from[3]; 1589 to[13] = from[7]; 1590 to[14] = from[11]; 1591 to[15] = from[15]; 1592} 1593 1594/** 1595 * Transpose a GLdouble matrix and convert to GLfloat. 1596 * 1597 * \param to destination array. 1598 * \param from source array. 1599 */ 1600void 1601_math_transposefd( GLfloat to[16], const GLdouble from[16] ) 1602{ 1603 to[0] = (GLfloat) from[0]; 1604 to[1] = (GLfloat) from[4]; 1605 to[2] = (GLfloat) from[8]; 1606 to[3] = (GLfloat) from[12]; 1607 to[4] = (GLfloat) from[1]; 1608 to[5] = (GLfloat) from[5]; 1609 to[6] = (GLfloat) from[9]; 1610 to[7] = (GLfloat) from[13]; 1611 to[8] = (GLfloat) from[2]; 1612 to[9] = (GLfloat) from[6]; 1613 to[10] = (GLfloat) from[10]; 1614 to[11] = (GLfloat) from[14]; 1615 to[12] = (GLfloat) from[3]; 1616 to[13] = (GLfloat) from[7]; 1617 to[14] = (GLfloat) from[11]; 1618 to[15] = (GLfloat) from[15]; 1619} 1620 1621/*@}*/ 1622 1623