m_matrix.c revision 50db8129152f3d5ea8db13d55f82673d53bf1b8f
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 "main/glheader.h" 38#include "main/imports.h" 39#include "main/macros.h" 40 41#include "m_matrix.h" 42 43 44/** 45 * \defgroup MatFlags MAT_FLAG_XXX-flags 46 * 47 * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags 48 * It would be nice to make all these flags private to m_matrix.c 49 */ 50/*@{*/ 51#define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag. 52 * (Not actually used - the identity 53 * matrix is identified by the absense 54 * of all other flags.) 55 */ 56#define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */ 57#define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */ 58#define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */ 59#define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */ 60#define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */ 61#define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */ 62#define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */ 63#define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */ 64#define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */ 65#define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */ 66#define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */ 67 68/** angle preserving matrix flags mask */ 69#define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \ 70 MAT_FLAG_TRANSLATION | \ 71 MAT_FLAG_UNIFORM_SCALE) 72 73/** geometry related matrix flags mask */ 74#define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \ 75 MAT_FLAG_ROTATION | \ 76 MAT_FLAG_TRANSLATION | \ 77 MAT_FLAG_UNIFORM_SCALE | \ 78 MAT_FLAG_GENERAL_SCALE | \ 79 MAT_FLAG_GENERAL_3D | \ 80 MAT_FLAG_PERSPECTIVE | \ 81 MAT_FLAG_SINGULAR) 82 83/** length preserving matrix flags mask */ 84#define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \ 85 MAT_FLAG_TRANSLATION) 86 87 88/** 3D (non-perspective) matrix flags mask */ 89#define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \ 90 MAT_FLAG_TRANSLATION | \ 91 MAT_FLAG_UNIFORM_SCALE | \ 92 MAT_FLAG_GENERAL_SCALE | \ 93 MAT_FLAG_GENERAL_3D) 94 95/** dirty matrix flags mask */ 96#define MAT_DIRTY (MAT_DIRTY_TYPE | \ 97 MAT_DIRTY_FLAGS | \ 98 MAT_DIRTY_INVERSE) 99 100/*@}*/ 101 102 103/** 104 * Test geometry related matrix flags. 105 * 106 * \param mat a pointer to a GLmatrix structure. 107 * \param a flags mask. 108 * 109 * \returns non-zero if all geometry related matrix flags are contained within 110 * the mask, or zero otherwise. 111 */ 112#define TEST_MAT_FLAGS(mat, a) \ 113 ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0) 114 115 116 117/** 118 * Names of the corresponding GLmatrixtype values. 119 */ 120static const char *types[] = { 121 "MATRIX_GENERAL", 122 "MATRIX_IDENTITY", 123 "MATRIX_3D_NO_ROT", 124 "MATRIX_PERSPECTIVE", 125 "MATRIX_2D", 126 "MATRIX_2D_NO_ROT", 127 "MATRIX_3D" 128}; 129 130 131/** 132 * Identity matrix. 133 */ 134static GLfloat Identity[16] = { 135 1.0, 0.0, 0.0, 0.0, 136 0.0, 1.0, 0.0, 0.0, 137 0.0, 0.0, 1.0, 0.0, 138 0.0, 0.0, 0.0, 1.0 139}; 140 141 142 143/**********************************************************************/ 144/** \name Matrix multiplication */ 145/*@{*/ 146 147#define A(row,col) a[(col<<2)+row] 148#define B(row,col) b[(col<<2)+row] 149#define P(row,col) product[(col<<2)+row] 150 151/** 152 * Perform a full 4x4 matrix multiplication. 153 * 154 * \param a matrix. 155 * \param b matrix. 156 * \param product will receive the product of \p a and \p b. 157 * 158 * \warning Is assumed that \p product != \p b. \p product == \p a is allowed. 159 * 160 * \note KW: 4*16 = 64 multiplications 161 * 162 * \author This \c matmul was contributed by Thomas Malik 163 */ 164static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b ) 165{ 166 GLint i; 167 for (i = 0; i < 4; i++) { 168 const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); 169 P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0); 170 P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1); 171 P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2); 172 P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3); 173 } 174} 175 176/** 177 * Multiply two matrices known to occupy only the top three rows, such 178 * as typical model matrices, and orthogonal matrices. 179 * 180 * \param a matrix. 181 * \param b matrix. 182 * \param product will receive the product of \p a and \p b. 183 */ 184static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b ) 185{ 186 GLint i; 187 for (i = 0; i < 3; i++) { 188 const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); 189 P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0); 190 P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1); 191 P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2); 192 P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3; 193 } 194 P(3,0) = 0; 195 P(3,1) = 0; 196 P(3,2) = 0; 197 P(3,3) = 1; 198} 199 200#undef A 201#undef B 202#undef P 203 204/** 205 * Multiply a matrix by an array of floats with known properties. 206 * 207 * \param mat pointer to a GLmatrix structure containing the left multiplication 208 * matrix, and that will receive the product result. 209 * \param m right multiplication matrix array. 210 * \param flags flags of the matrix \p m. 211 * 212 * Joins both flags and marks the type and inverse as dirty. Calls matmul34() 213 * if both matrices are 3D, or matmul4() otherwise. 214 */ 215static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags ) 216{ 217 mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE); 218 219 if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) 220 matmul34( mat->m, mat->m, m ); 221 else 222 matmul4( mat->m, mat->m, m ); 223} 224 225/** 226 * Matrix multiplication. 227 * 228 * \param dest destination matrix. 229 * \param a left matrix. 230 * \param b right matrix. 231 * 232 * Joins both flags and marks the type and inverse as dirty. Calls matmul34() 233 * if both matrices are 3D, or matmul4() otherwise. 234 */ 235void 236_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b ) 237{ 238 dest->flags = (a->flags | 239 b->flags | 240 MAT_DIRTY_TYPE | 241 MAT_DIRTY_INVERSE); 242 243 if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D)) 244 matmul34( dest->m, a->m, b->m ); 245 else 246 matmul4( dest->m, a->m, b->m ); 247} 248 249/** 250 * Matrix multiplication. 251 * 252 * \param dest left and destination matrix. 253 * \param m right matrix array. 254 * 255 * Marks the matrix flags with general flag, and type and inverse dirty flags. 256 * Calls matmul4() for the multiplication. 257 */ 258void 259_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m ) 260{ 261 dest->flags |= (MAT_FLAG_GENERAL | 262 MAT_DIRTY_TYPE | 263 MAT_DIRTY_INVERSE | 264 MAT_DIRTY_FLAGS); 265 266 matmul4( dest->m, dest->m, m ); 267} 268 269/*@}*/ 270 271 272/**********************************************************************/ 273/** \name Matrix output */ 274/*@{*/ 275 276/** 277 * Print a matrix array. 278 * 279 * \param m matrix array. 280 * 281 * Called by _math_matrix_print() to print a matrix or its inverse. 282 */ 283static void print_matrix_floats( const GLfloat m[16] ) 284{ 285 int i; 286 for (i=0;i<4;i++) { 287 _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] ); 288 } 289} 290 291/** 292 * Dumps the contents of a GLmatrix structure. 293 * 294 * \param m pointer to the GLmatrix structure. 295 */ 296void 297_math_matrix_print( const GLmatrix *m ) 298{ 299 _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags); 300 print_matrix_floats(m->m); 301 _mesa_debug(NULL, "Inverse: \n"); 302 if (m->inv) { 303 GLfloat prod[16]; 304 print_matrix_floats(m->inv); 305 matmul4(prod, m->m, m->inv); 306 _mesa_debug(NULL, "Mat * Inverse:\n"); 307 print_matrix_floats(prod); 308 } 309 else { 310 _mesa_debug(NULL, " - not available\n"); 311 } 312} 313 314/*@}*/ 315 316 317/** 318 * References an element of 4x4 matrix. 319 * 320 * \param m matrix array. 321 * \param c column of the desired element. 322 * \param r row of the desired element. 323 * 324 * \return value of the desired element. 325 * 326 * Calculate the linear storage index of the element and references it. 327 */ 328#define MAT(m,r,c) (m)[(c)*4+(r)] 329 330 331/**********************************************************************/ 332/** \name Matrix inversion */ 333/*@{*/ 334 335/** 336 * Swaps the values of two floating pointer variables. 337 * 338 * Used by invert_matrix_general() to swap the row pointers. 339 */ 340#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; } 341 342/** 343 * Compute inverse of 4x4 transformation matrix. 344 * 345 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 346 * stored in the GLmatrix::inv attribute. 347 * 348 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 349 * 350 * \author 351 * Code contributed by Jacques Leroy jle@star.be 352 * 353 * Calculates the inverse matrix by performing the gaussian matrix reduction 354 * with partial pivoting followed by back/substitution with the loops manually 355 * unrolled. 356 */ 357static GLboolean invert_matrix_general( GLmatrix *mat ) 358{ 359 const GLfloat *m = mat->m; 360 GLfloat *out = mat->inv; 361 GLfloat wtmp[4][8]; 362 GLfloat m0, m1, m2, m3, s; 363 GLfloat *r0, *r1, *r2, *r3; 364 365 r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3]; 366 367 r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1), 368 r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3), 369 r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0, 370 371 r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1), 372 r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3), 373 r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0, 374 375 r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1), 376 r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3), 377 r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0, 378 379 r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1), 380 r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3), 381 r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0; 382 383 /* choose pivot - or die */ 384 if (FABSF(r3[0])>FABSF(r2[0])) SWAP_ROWS(r3, r2); 385 if (FABSF(r2[0])>FABSF(r1[0])) SWAP_ROWS(r2, r1); 386 if (FABSF(r1[0])>FABSF(r0[0])) SWAP_ROWS(r1, r0); 387 if (0.0 == r0[0]) return GL_FALSE; 388 389 /* eliminate first variable */ 390 m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0]; 391 s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s; 392 s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s; 393 s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s; 394 s = r0[4]; 395 if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; } 396 s = r0[5]; 397 if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; } 398 s = r0[6]; 399 if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; } 400 s = r0[7]; 401 if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; } 402 403 /* choose pivot - or die */ 404 if (FABSF(r3[1])>FABSF(r2[1])) SWAP_ROWS(r3, r2); 405 if (FABSF(r2[1])>FABSF(r1[1])) SWAP_ROWS(r2, r1); 406 if (0.0 == r1[1]) return GL_FALSE; 407 408 /* eliminate second variable */ 409 m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1]; 410 r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2]; 411 r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3]; 412 s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; } 413 s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; } 414 s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; } 415 s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; } 416 417 /* choose pivot - or die */ 418 if (FABSF(r3[2])>FABSF(r2[2])) SWAP_ROWS(r3, r2); 419 if (0.0 == r2[2]) return GL_FALSE; 420 421 /* eliminate third variable */ 422 m3 = r3[2]/r2[2]; 423 r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4], 424 r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], 425 r3[7] -= m3 * r2[7]; 426 427 /* last check */ 428 if (0.0 == r3[3]) return GL_FALSE; 429 430 s = 1.0F/r3[3]; /* now back substitute row 3 */ 431 r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s; 432 433 m2 = r2[3]; /* now back substitute row 2 */ 434 s = 1.0F/r2[2]; 435 r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2), 436 r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2); 437 m1 = r1[3]; 438 r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1, 439 r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1; 440 m0 = r0[3]; 441 r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0, 442 r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0; 443 444 m1 = r1[2]; /* now back substitute row 1 */ 445 s = 1.0F/r1[1]; 446 r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1), 447 r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1); 448 m0 = r0[2]; 449 r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0, 450 r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0; 451 452 m0 = r0[1]; /* now back substitute row 0 */ 453 s = 1.0F/r0[0]; 454 r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0), 455 r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0); 456 457 MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5], 458 MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7], 459 MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5], 460 MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7], 461 MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5], 462 MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7], 463 MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5], 464 MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7]; 465 466 return GL_TRUE; 467} 468#undef SWAP_ROWS 469 470/** 471 * Compute inverse of a general 3d transformation matrix. 472 * 473 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 474 * stored in the GLmatrix::inv attribute. 475 * 476 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 477 * 478 * \author Adapted from graphics gems II. 479 * 480 * Calculates the inverse of the upper left by first calculating its 481 * determinant and multiplying it to the symmetric adjust matrix of each 482 * element. Finally deals with the translation part by transforming the 483 * original translation vector using by the calculated submatrix inverse. 484 */ 485static GLboolean invert_matrix_3d_general( GLmatrix *mat ) 486{ 487 const GLfloat *in = mat->m; 488 GLfloat *out = mat->inv; 489 GLfloat pos, neg, t; 490 GLfloat det; 491 492 /* Calculate the determinant of upper left 3x3 submatrix and 493 * determine if the matrix is singular. 494 */ 495 pos = neg = 0.0; 496 t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2); 497 if (t >= 0.0) pos += t; else neg += t; 498 499 t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2); 500 if (t >= 0.0) pos += t; else neg += t; 501 502 t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2); 503 if (t >= 0.0) pos += t; else neg += t; 504 505 t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2); 506 if (t >= 0.0) pos += t; else neg += t; 507 508 t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2); 509 if (t >= 0.0) pos += t; else neg += t; 510 511 t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2); 512 if (t >= 0.0) pos += t; else neg += t; 513 514 det = pos + neg; 515 516 if (FABSF(det) < 1e-25) 517 return GL_FALSE; 518 519 det = 1.0F / det; 520 MAT(out,0,0) = ( (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det); 521 MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det); 522 MAT(out,0,2) = ( (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det); 523 MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det); 524 MAT(out,1,1) = ( (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det); 525 MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det); 526 MAT(out,2,0) = ( (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det); 527 MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det); 528 MAT(out,2,2) = ( (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det); 529 530 /* Do the translation part */ 531 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + 532 MAT(in,1,3) * MAT(out,0,1) + 533 MAT(in,2,3) * MAT(out,0,2) ); 534 MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + 535 MAT(in,1,3) * MAT(out,1,1) + 536 MAT(in,2,3) * MAT(out,1,2) ); 537 MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + 538 MAT(in,1,3) * MAT(out,2,1) + 539 MAT(in,2,3) * MAT(out,2,2) ); 540 541 return GL_TRUE; 542} 543 544/** 545 * Compute inverse of a 3d transformation matrix. 546 * 547 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 548 * stored in the GLmatrix::inv attribute. 549 * 550 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 551 * 552 * If the matrix is not an angle preserving matrix then calls 553 * invert_matrix_3d_general for the actual calculation. Otherwise calculates 554 * the inverse matrix analyzing and inverting each of the scaling, rotation and 555 * translation parts. 556 */ 557static GLboolean invert_matrix_3d( GLmatrix *mat ) 558{ 559 const GLfloat *in = mat->m; 560 GLfloat *out = mat->inv; 561 562 if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) { 563 return invert_matrix_3d_general( mat ); 564 } 565 566 if (mat->flags & MAT_FLAG_UNIFORM_SCALE) { 567 GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) + 568 MAT(in,0,1) * MAT(in,0,1) + 569 MAT(in,0,2) * MAT(in,0,2)); 570 571 if (scale == 0.0) 572 return GL_FALSE; 573 574 scale = 1.0F / scale; 575 576 /* Transpose and scale the 3 by 3 upper-left submatrix. */ 577 MAT(out,0,0) = scale * MAT(in,0,0); 578 MAT(out,1,0) = scale * MAT(in,0,1); 579 MAT(out,2,0) = scale * MAT(in,0,2); 580 MAT(out,0,1) = scale * MAT(in,1,0); 581 MAT(out,1,1) = scale * MAT(in,1,1); 582 MAT(out,2,1) = scale * MAT(in,1,2); 583 MAT(out,0,2) = scale * MAT(in,2,0); 584 MAT(out,1,2) = scale * MAT(in,2,1); 585 MAT(out,2,2) = scale * MAT(in,2,2); 586 } 587 else if (mat->flags & MAT_FLAG_ROTATION) { 588 /* Transpose the 3 by 3 upper-left submatrix. */ 589 MAT(out,0,0) = MAT(in,0,0); 590 MAT(out,1,0) = MAT(in,0,1); 591 MAT(out,2,0) = MAT(in,0,2); 592 MAT(out,0,1) = MAT(in,1,0); 593 MAT(out,1,1) = MAT(in,1,1); 594 MAT(out,2,1) = MAT(in,1,2); 595 MAT(out,0,2) = MAT(in,2,0); 596 MAT(out,1,2) = MAT(in,2,1); 597 MAT(out,2,2) = MAT(in,2,2); 598 } 599 else { 600 /* pure translation */ 601 memcpy( out, Identity, sizeof(Identity) ); 602 MAT(out,0,3) = - MAT(in,0,3); 603 MAT(out,1,3) = - MAT(in,1,3); 604 MAT(out,2,3) = - MAT(in,2,3); 605 return GL_TRUE; 606 } 607 608 if (mat->flags & MAT_FLAG_TRANSLATION) { 609 /* Do the translation part */ 610 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + 611 MAT(in,1,3) * MAT(out,0,1) + 612 MAT(in,2,3) * MAT(out,0,2) ); 613 MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + 614 MAT(in,1,3) * MAT(out,1,1) + 615 MAT(in,2,3) * MAT(out,1,2) ); 616 MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + 617 MAT(in,1,3) * MAT(out,2,1) + 618 MAT(in,2,3) * MAT(out,2,2) ); 619 } 620 else { 621 MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0; 622 } 623 624 return GL_TRUE; 625} 626 627/** 628 * Compute inverse of an identity transformation matrix. 629 * 630 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 631 * stored in the GLmatrix::inv attribute. 632 * 633 * \return always GL_TRUE. 634 * 635 * Simply copies Identity into GLmatrix::inv. 636 */ 637static GLboolean invert_matrix_identity( GLmatrix *mat ) 638{ 639 memcpy( mat->inv, Identity, sizeof(Identity) ); 640 return GL_TRUE; 641} 642 643/** 644 * Compute inverse of a no-rotation 3d transformation matrix. 645 * 646 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 647 * stored in the GLmatrix::inv attribute. 648 * 649 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 650 * 651 * Calculates the 652 */ 653static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat ) 654{ 655 const GLfloat *in = mat->m; 656 GLfloat *out = mat->inv; 657 658 if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 ) 659 return GL_FALSE; 660 661 memcpy( out, Identity, 16 * sizeof(GLfloat) ); 662 MAT(out,0,0) = 1.0F / MAT(in,0,0); 663 MAT(out,1,1) = 1.0F / MAT(in,1,1); 664 MAT(out,2,2) = 1.0F / MAT(in,2,2); 665 666 if (mat->flags & MAT_FLAG_TRANSLATION) { 667 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); 668 MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); 669 MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2)); 670 } 671 672 return GL_TRUE; 673} 674 675/** 676 * Compute inverse of a no-rotation 2d transformation matrix. 677 * 678 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 679 * stored in the GLmatrix::inv attribute. 680 * 681 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 682 * 683 * Calculates the inverse matrix by applying the inverse scaling and 684 * translation to the identity matrix. 685 */ 686static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat ) 687{ 688 const GLfloat *in = mat->m; 689 GLfloat *out = mat->inv; 690 691 if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0) 692 return GL_FALSE; 693 694 memcpy( out, Identity, 16 * sizeof(GLfloat) ); 695 MAT(out,0,0) = 1.0F / MAT(in,0,0); 696 MAT(out,1,1) = 1.0F / MAT(in,1,1); 697 698 if (mat->flags & MAT_FLAG_TRANSLATION) { 699 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); 700 MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); 701 } 702 703 return GL_TRUE; 704} 705 706#if 0 707/* broken */ 708static GLboolean invert_matrix_perspective( GLmatrix *mat ) 709{ 710 const GLfloat *in = mat->m; 711 GLfloat *out = mat->inv; 712 713 if (MAT(in,2,3) == 0) 714 return GL_FALSE; 715 716 memcpy( out, Identity, 16 * sizeof(GLfloat) ); 717 718 MAT(out,0,0) = 1.0F / MAT(in,0,0); 719 MAT(out,1,1) = 1.0F / MAT(in,1,1); 720 721 MAT(out,0,3) = MAT(in,0,2); 722 MAT(out,1,3) = MAT(in,1,2); 723 724 MAT(out,2,2) = 0; 725 MAT(out,2,3) = -1; 726 727 MAT(out,3,2) = 1.0F / MAT(in,2,3); 728 MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2); 729 730 return GL_TRUE; 731} 732#endif 733 734/** 735 * Matrix inversion function pointer type. 736 */ 737typedef GLboolean (*inv_mat_func)( GLmatrix *mat ); 738 739/** 740 * Table of the matrix inversion functions according to the matrix type. 741 */ 742static inv_mat_func inv_mat_tab[7] = { 743 invert_matrix_general, 744 invert_matrix_identity, 745 invert_matrix_3d_no_rot, 746#if 0 747 /* Don't use this function for now - it fails when the projection matrix 748 * is premultiplied by a translation (ala Chromium's tilesort SPU). 749 */ 750 invert_matrix_perspective, 751#else 752 invert_matrix_general, 753#endif 754 invert_matrix_3d, /* lazy! */ 755 invert_matrix_2d_no_rot, 756 invert_matrix_3d 757}; 758 759/** 760 * Compute inverse of a transformation matrix. 761 * 762 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 763 * stored in the GLmatrix::inv attribute. 764 * 765 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 766 * 767 * Calls the matrix inversion function in inv_mat_tab corresponding to the 768 * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag, 769 * and copies the identity matrix into GLmatrix::inv. 770 */ 771static GLboolean matrix_invert( GLmatrix *mat ) 772{ 773 if (inv_mat_tab[mat->type](mat)) { 774 mat->flags &= ~MAT_FLAG_SINGULAR; 775 return GL_TRUE; 776 } else { 777 mat->flags |= MAT_FLAG_SINGULAR; 778 memcpy( mat->inv, Identity, sizeof(Identity) ); 779 return GL_FALSE; 780 } 781} 782 783/*@}*/ 784 785 786/**********************************************************************/ 787/** \name Matrix generation */ 788/*@{*/ 789 790/** 791 * Generate a 4x4 transformation matrix from glRotate parameters, and 792 * post-multiply the input matrix by it. 793 * 794 * \author 795 * This function was contributed by Erich Boleyn (erich@uruk.org). 796 * Optimizations contributed by Rudolf Opalla (rudi@khm.de). 797 */ 798void 799_math_matrix_rotate( GLmatrix *mat, 800 GLfloat angle, GLfloat x, GLfloat y, GLfloat z ) 801{ 802 GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c; 803 GLfloat m[16]; 804 GLboolean optimized; 805 806 s = (GLfloat) sin( angle * DEG2RAD ); 807 c = (GLfloat) cos( angle * DEG2RAD ); 808 809 memcpy(m, Identity, sizeof(GLfloat)*16); 810 optimized = GL_FALSE; 811 812#define M(row,col) m[col*4+row] 813 814 if (x == 0.0F) { 815 if (y == 0.0F) { 816 if (z != 0.0F) { 817 optimized = GL_TRUE; 818 /* rotate only around z-axis */ 819 M(0,0) = c; 820 M(1,1) = c; 821 if (z < 0.0F) { 822 M(0,1) = s; 823 M(1,0) = -s; 824 } 825 else { 826 M(0,1) = -s; 827 M(1,0) = s; 828 } 829 } 830 } 831 else if (z == 0.0F) { 832 optimized = GL_TRUE; 833 /* rotate only around y-axis */ 834 M(0,0) = c; 835 M(2,2) = c; 836 if (y < 0.0F) { 837 M(0,2) = -s; 838 M(2,0) = s; 839 } 840 else { 841 M(0,2) = s; 842 M(2,0) = -s; 843 } 844 } 845 } 846 else if (y == 0.0F) { 847 if (z == 0.0F) { 848 optimized = GL_TRUE; 849 /* rotate only around x-axis */ 850 M(1,1) = c; 851 M(2,2) = c; 852 if (x < 0.0F) { 853 M(1,2) = s; 854 M(2,1) = -s; 855 } 856 else { 857 M(1,2) = -s; 858 M(2,1) = s; 859 } 860 } 861 } 862 863 if (!optimized) { 864 const GLfloat mag = SQRTF(x * x + y * y + z * z); 865 866 if (mag <= 1.0e-4) { 867 /* no rotation, leave mat as-is */ 868 return; 869 } 870 871 x /= mag; 872 y /= mag; 873 z /= mag; 874 875 876 /* 877 * Arbitrary axis rotation matrix. 878 * 879 * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied 880 * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation 881 * (which is about the X-axis), and the two composite transforms 882 * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary 883 * from the arbitrary axis to the X-axis then back. They are 884 * all elementary rotations. 885 * 886 * Rz' is a rotation about the Z-axis, to bring the axis vector 887 * into the x-z plane. Then Ry' is applied, rotating about the 888 * Y-axis to bring the axis vector parallel with the X-axis. The 889 * rotation about the X-axis is then performed. Ry and Rz are 890 * simply the respective inverse transforms to bring the arbitrary 891 * axis back to its original orientation. The first transforms 892 * Rz' and Ry' are considered inverses, since the data from the 893 * arbitrary axis gives you info on how to get to it, not how 894 * to get away from it, and an inverse must be applied. 895 * 896 * The basic calculation used is to recognize that the arbitrary 897 * axis vector (x, y, z), since it is of unit length, actually 898 * represents the sines and cosines of the angles to rotate the 899 * X-axis to the same orientation, with theta being the angle about 900 * Z and phi the angle about Y (in the order described above) 901 * as follows: 902 * 903 * cos ( theta ) = x / sqrt ( 1 - z^2 ) 904 * sin ( theta ) = y / sqrt ( 1 - z^2 ) 905 * 906 * cos ( phi ) = sqrt ( 1 - z^2 ) 907 * sin ( phi ) = z 908 * 909 * Note that cos ( phi ) can further be inserted to the above 910 * formulas: 911 * 912 * cos ( theta ) = x / cos ( phi ) 913 * sin ( theta ) = y / sin ( phi ) 914 * 915 * ...etc. Because of those relations and the standard trigonometric 916 * relations, it is pssible to reduce the transforms down to what 917 * is used below. It may be that any primary axis chosen will give the 918 * same results (modulo a sign convention) using thie method. 919 * 920 * Particularly nice is to notice that all divisions that might 921 * have caused trouble when parallel to certain planes or 922 * axis go away with care paid to reducing the expressions. 923 * After checking, it does perform correctly under all cases, since 924 * in all the cases of division where the denominator would have 925 * been zero, the numerator would have been zero as well, giving 926 * the expected result. 927 */ 928 929 xx = x * x; 930 yy = y * y; 931 zz = z * z; 932 xy = x * y; 933 yz = y * z; 934 zx = z * x; 935 xs = x * s; 936 ys = y * s; 937 zs = z * s; 938 one_c = 1.0F - c; 939 940 /* We already hold the identity-matrix so we can skip some statements */ 941 M(0,0) = (one_c * xx) + c; 942 M(0,1) = (one_c * xy) - zs; 943 M(0,2) = (one_c * zx) + ys; 944/* M(0,3) = 0.0F; */ 945 946 M(1,0) = (one_c * xy) + zs; 947 M(1,1) = (one_c * yy) + c; 948 M(1,2) = (one_c * yz) - xs; 949/* M(1,3) = 0.0F; */ 950 951 M(2,0) = (one_c * zx) - ys; 952 M(2,1) = (one_c * yz) + xs; 953 M(2,2) = (one_c * zz) + c; 954/* M(2,3) = 0.0F; */ 955 956/* 957 M(3,0) = 0.0F; 958 M(3,1) = 0.0F; 959 M(3,2) = 0.0F; 960 M(3,3) = 1.0F; 961*/ 962 } 963#undef M 964 965 matrix_multf( mat, m, MAT_FLAG_ROTATION ); 966} 967 968/** 969 * Apply a perspective projection matrix. 970 * 971 * \param mat matrix to apply the projection. 972 * \param left left clipping plane coordinate. 973 * \param right right clipping plane coordinate. 974 * \param bottom bottom clipping plane coordinate. 975 * \param top top clipping plane coordinate. 976 * \param nearval distance to the near clipping plane. 977 * \param farval distance to the far clipping plane. 978 * 979 * Creates the projection matrix and multiplies it with \p mat, marking the 980 * MAT_FLAG_PERSPECTIVE flag. 981 */ 982void 983_math_matrix_frustum( GLmatrix *mat, 984 GLfloat left, GLfloat right, 985 GLfloat bottom, GLfloat top, 986 GLfloat nearval, GLfloat farval ) 987{ 988 GLfloat x, y, a, b, c, d; 989 GLfloat m[16]; 990 991 x = (2.0F*nearval) / (right-left); 992 y = (2.0F*nearval) / (top-bottom); 993 a = (right+left) / (right-left); 994 b = (top+bottom) / (top-bottom); 995 c = -(farval+nearval) / ( farval-nearval); 996 d = -(2.0F*farval*nearval) / (farval-nearval); /* error? */ 997 998#define M(row,col) m[col*4+row] 999 M(0,0) = x; M(0,1) = 0.0F; M(0,2) = a; M(0,3) = 0.0F; 1000 M(1,0) = 0.0F; M(1,1) = y; M(1,2) = b; M(1,3) = 0.0F; 1001 M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = c; M(2,3) = d; 1002 M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = -1.0F; M(3,3) = 0.0F; 1003#undef M 1004 1005 matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE ); 1006} 1007 1008/** 1009 * Apply an orthographic projection matrix. 1010 * 1011 * \param mat matrix to apply the projection. 1012 * \param left left clipping plane coordinate. 1013 * \param right right clipping plane coordinate. 1014 * \param bottom bottom clipping plane coordinate. 1015 * \param top top clipping plane coordinate. 1016 * \param nearval distance to the near clipping plane. 1017 * \param farval distance to the far clipping plane. 1018 * 1019 * Creates the projection matrix and multiplies it with \p mat, marking the 1020 * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags. 1021 */ 1022void 1023_math_matrix_ortho( GLmatrix *mat, 1024 GLfloat left, GLfloat right, 1025 GLfloat bottom, GLfloat top, 1026 GLfloat nearval, GLfloat farval ) 1027{ 1028 GLfloat m[16]; 1029 1030#define M(row,col) m[col*4+row] 1031 M(0,0) = 2.0F / (right-left); 1032 M(0,1) = 0.0F; 1033 M(0,2) = 0.0F; 1034 M(0,3) = -(right+left) / (right-left); 1035 1036 M(1,0) = 0.0F; 1037 M(1,1) = 2.0F / (top-bottom); 1038 M(1,2) = 0.0F; 1039 M(1,3) = -(top+bottom) / (top-bottom); 1040 1041 M(2,0) = 0.0F; 1042 M(2,1) = 0.0F; 1043 M(2,2) = -2.0F / (farval-nearval); 1044 M(2,3) = -(farval+nearval) / (farval-nearval); 1045 1046 M(3,0) = 0.0F; 1047 M(3,1) = 0.0F; 1048 M(3,2) = 0.0F; 1049 M(3,3) = 1.0F; 1050#undef M 1051 1052 matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION)); 1053} 1054 1055/** 1056 * Multiply a matrix with a general scaling matrix. 1057 * 1058 * \param mat matrix. 1059 * \param x x axis scale factor. 1060 * \param y y axis scale factor. 1061 * \param z z axis scale factor. 1062 * 1063 * Multiplies in-place the elements of \p mat by the scale factors. Checks if 1064 * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE 1065 * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and 1066 * MAT_DIRTY_INVERSE dirty flags. 1067 */ 1068void 1069_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) 1070{ 1071 GLfloat *m = mat->m; 1072 m[0] *= x; m[4] *= y; m[8] *= z; 1073 m[1] *= x; m[5] *= y; m[9] *= z; 1074 m[2] *= x; m[6] *= y; m[10] *= z; 1075 m[3] *= x; m[7] *= y; m[11] *= z; 1076 1077 if (FABSF(x - y) < 1e-8 && FABSF(x - z) < 1e-8) 1078 mat->flags |= MAT_FLAG_UNIFORM_SCALE; 1079 else 1080 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1081 1082 mat->flags |= (MAT_DIRTY_TYPE | 1083 MAT_DIRTY_INVERSE); 1084} 1085 1086/** 1087 * Multiply a matrix with a translation matrix. 1088 * 1089 * \param mat matrix. 1090 * \param x translation vector x coordinate. 1091 * \param y translation vector y coordinate. 1092 * \param z translation vector z coordinate. 1093 * 1094 * Adds the translation coordinates to the elements of \p mat in-place. Marks 1095 * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE 1096 * dirty flags. 1097 */ 1098void 1099_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) 1100{ 1101 GLfloat *m = mat->m; 1102 m[12] = m[0] * x + m[4] * y + m[8] * z + m[12]; 1103 m[13] = m[1] * x + m[5] * y + m[9] * z + m[13]; 1104 m[14] = m[2] * x + m[6] * y + m[10] * z + m[14]; 1105 m[15] = m[3] * x + m[7] * y + m[11] * z + m[15]; 1106 1107 mat->flags |= (MAT_FLAG_TRANSLATION | 1108 MAT_DIRTY_TYPE | 1109 MAT_DIRTY_INVERSE); 1110} 1111 1112 1113/** 1114 * Set matrix to do viewport and depthrange mapping. 1115 * Transforms Normalized Device Coords to window/Z values. 1116 */ 1117void 1118_math_matrix_viewport(GLmatrix *m, GLint x, GLint y, GLint width, GLint height, 1119 GLfloat zNear, GLfloat zFar, GLfloat depthMax) 1120{ 1121 m->m[MAT_SX] = (GLfloat) width / 2.0F; 1122 m->m[MAT_TX] = m->m[MAT_SX] + x; 1123 m->m[MAT_SY] = (GLfloat) height / 2.0F; 1124 m->m[MAT_TY] = m->m[MAT_SY] + y; 1125 m->m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0F); 1126 m->m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0F + zNear); 1127 m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION; 1128 m->type = MATRIX_3D_NO_ROT; 1129} 1130 1131 1132/** 1133 * Set a matrix to the identity matrix. 1134 * 1135 * \param mat matrix. 1136 * 1137 * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL. 1138 * Sets the matrix type to identity, and clear the dirty flags. 1139 */ 1140void 1141_math_matrix_set_identity( GLmatrix *mat ) 1142{ 1143 memcpy( mat->m, Identity, 16*sizeof(GLfloat) ); 1144 1145 if (mat->inv) 1146 memcpy( mat->inv, Identity, 16*sizeof(GLfloat) ); 1147 1148 mat->type = MATRIX_IDENTITY; 1149 mat->flags &= ~(MAT_DIRTY_FLAGS| 1150 MAT_DIRTY_TYPE| 1151 MAT_DIRTY_INVERSE); 1152} 1153 1154/*@}*/ 1155 1156 1157/**********************************************************************/ 1158/** \name Matrix analysis */ 1159/*@{*/ 1160 1161#define ZERO(x) (1<<x) 1162#define ONE(x) (1<<(x+16)) 1163 1164#define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14)) 1165#define MASK_NO_2D_SCALE ( ONE(0) | ONE(5)) 1166 1167#define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\ 1168 ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\ 1169 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1170 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1171 1172#define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \ 1173 ZERO(1) | ZERO(9) | \ 1174 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1175 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1176 1177#define MASK_2D ( ZERO(8) | \ 1178 ZERO(9) | \ 1179 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1180 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1181 1182 1183#define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \ 1184 ZERO(1) | ZERO(9) | \ 1185 ZERO(2) | ZERO(6) | \ 1186 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1187 1188#define MASK_3D ( \ 1189 \ 1190 \ 1191 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1192 1193 1194#define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\ 1195 ZERO(1) | ZERO(13) |\ 1196 ZERO(2) | ZERO(6) | \ 1197 ZERO(3) | ZERO(7) | ZERO(15) ) 1198 1199#define SQ(x) ((x)*(x)) 1200 1201/** 1202 * Determine type and flags from scratch. 1203 * 1204 * \param mat matrix. 1205 * 1206 * This is expensive enough to only want to do it once. 1207 */ 1208static void analyse_from_scratch( GLmatrix *mat ) 1209{ 1210 const GLfloat *m = mat->m; 1211 GLuint mask = 0; 1212 GLuint i; 1213 1214 for (i = 0 ; i < 16 ; i++) { 1215 if (m[i] == 0.0) mask |= (1<<i); 1216 } 1217 1218 if (m[0] == 1.0F) mask |= (1<<16); 1219 if (m[5] == 1.0F) mask |= (1<<21); 1220 if (m[10] == 1.0F) mask |= (1<<26); 1221 if (m[15] == 1.0F) mask |= (1<<31); 1222 1223 mat->flags &= ~MAT_FLAGS_GEOMETRY; 1224 1225 /* Check for translation - no-one really cares 1226 */ 1227 if ((mask & MASK_NO_TRX) != MASK_NO_TRX) 1228 mat->flags |= MAT_FLAG_TRANSLATION; 1229 1230 /* Do the real work 1231 */ 1232 if (mask == (GLuint) MASK_IDENTITY) { 1233 mat->type = MATRIX_IDENTITY; 1234 } 1235 else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) { 1236 mat->type = MATRIX_2D_NO_ROT; 1237 1238 if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE) 1239 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1240 } 1241 else if ((mask & MASK_2D) == (GLuint) MASK_2D) { 1242 GLfloat mm = DOT2(m, m); 1243 GLfloat m4m4 = DOT2(m+4,m+4); 1244 GLfloat mm4 = DOT2(m,m+4); 1245 1246 mat->type = MATRIX_2D; 1247 1248 /* Check for scale */ 1249 if (SQ(mm-1) > SQ(1e-6) || 1250 SQ(m4m4-1) > SQ(1e-6)) 1251 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1252 1253 /* Check for rotation */ 1254 if (SQ(mm4) > SQ(1e-6)) 1255 mat->flags |= MAT_FLAG_GENERAL_3D; 1256 else 1257 mat->flags |= MAT_FLAG_ROTATION; 1258 1259 } 1260 else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) { 1261 mat->type = MATRIX_3D_NO_ROT; 1262 1263 /* Check for scale */ 1264 if (SQ(m[0]-m[5]) < SQ(1e-6) && 1265 SQ(m[0]-m[10]) < SQ(1e-6)) { 1266 if (SQ(m[0]-1.0) > SQ(1e-6)) { 1267 mat->flags |= MAT_FLAG_UNIFORM_SCALE; 1268 } 1269 } 1270 else { 1271 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1272 } 1273 } 1274 else if ((mask & MASK_3D) == (GLuint) MASK_3D) { 1275 GLfloat c1 = DOT3(m,m); 1276 GLfloat c2 = DOT3(m+4,m+4); 1277 GLfloat c3 = DOT3(m+8,m+8); 1278 GLfloat d1 = DOT3(m, m+4); 1279 GLfloat cp[3]; 1280 1281 mat->type = MATRIX_3D; 1282 1283 /* Check for scale */ 1284 if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) { 1285 if (SQ(c1-1.0) > SQ(1e-6)) 1286 mat->flags |= MAT_FLAG_UNIFORM_SCALE; 1287 /* else no scale at all */ 1288 } 1289 else { 1290 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1291 } 1292 1293 /* Check for rotation */ 1294 if (SQ(d1) < SQ(1e-6)) { 1295 CROSS3( cp, m, m+4 ); 1296 SUB_3V( cp, cp, (m+8) ); 1297 if (LEN_SQUARED_3FV(cp) < SQ(1e-6)) 1298 mat->flags |= MAT_FLAG_ROTATION; 1299 else 1300 mat->flags |= MAT_FLAG_GENERAL_3D; 1301 } 1302 else { 1303 mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */ 1304 } 1305 } 1306 else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) { 1307 mat->type = MATRIX_PERSPECTIVE; 1308 mat->flags |= MAT_FLAG_GENERAL; 1309 } 1310 else { 1311 mat->type = MATRIX_GENERAL; 1312 mat->flags |= MAT_FLAG_GENERAL; 1313 } 1314} 1315 1316/** 1317 * Analyze a matrix given that its flags are accurate. 1318 * 1319 * This is the more common operation, hopefully. 1320 */ 1321static void analyse_from_flags( GLmatrix *mat ) 1322{ 1323 const GLfloat *m = mat->m; 1324 1325 if (TEST_MAT_FLAGS(mat, 0)) { 1326 mat->type = MATRIX_IDENTITY; 1327 } 1328 else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION | 1329 MAT_FLAG_UNIFORM_SCALE | 1330 MAT_FLAG_GENERAL_SCALE))) { 1331 if ( m[10]==1.0F && m[14]==0.0F ) { 1332 mat->type = MATRIX_2D_NO_ROT; 1333 } 1334 else { 1335 mat->type = MATRIX_3D_NO_ROT; 1336 } 1337 } 1338 else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) { 1339 if ( m[ 8]==0.0F 1340 && m[ 9]==0.0F 1341 && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) { 1342 mat->type = MATRIX_2D; 1343 } 1344 else { 1345 mat->type = MATRIX_3D; 1346 } 1347 } 1348 else if ( m[4]==0.0F && m[12]==0.0F 1349 && m[1]==0.0F && m[13]==0.0F 1350 && m[2]==0.0F && m[6]==0.0F 1351 && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) { 1352 mat->type = MATRIX_PERSPECTIVE; 1353 } 1354 else { 1355 mat->type = MATRIX_GENERAL; 1356 } 1357} 1358 1359/** 1360 * Analyze and update a matrix. 1361 * 1362 * \param mat matrix. 1363 * 1364 * If the matrix type is dirty then calls either analyse_from_scratch() or 1365 * analyse_from_flags() to determine its type, according to whether the flags 1366 * are dirty or not, respectively. If the matrix has an inverse and it's dirty 1367 * then calls matrix_invert(). Finally clears the dirty flags. 1368 */ 1369void 1370_math_matrix_analyse( GLmatrix *mat ) 1371{ 1372 if (mat->flags & MAT_DIRTY_TYPE) { 1373 if (mat->flags & MAT_DIRTY_FLAGS) 1374 analyse_from_scratch( mat ); 1375 else 1376 analyse_from_flags( mat ); 1377 } 1378 1379 if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) { 1380 matrix_invert( mat ); 1381 mat->flags &= ~MAT_DIRTY_INVERSE; 1382 } 1383 1384 mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE); 1385} 1386 1387/*@}*/ 1388 1389 1390/** 1391 * Test if the given matrix preserves vector lengths. 1392 */ 1393GLboolean 1394_math_matrix_is_length_preserving( const GLmatrix *m ) 1395{ 1396 return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING); 1397} 1398 1399 1400/** 1401 * Test if the given matrix does any rotation. 1402 * (or perhaps if the upper-left 3x3 is non-identity) 1403 */ 1404GLboolean 1405_math_matrix_has_rotation( const GLmatrix *m ) 1406{ 1407 if (m->flags & (MAT_FLAG_GENERAL | 1408 MAT_FLAG_ROTATION | 1409 MAT_FLAG_GENERAL_3D | 1410 MAT_FLAG_PERSPECTIVE)) 1411 return GL_TRUE; 1412 else 1413 return GL_FALSE; 1414} 1415 1416 1417GLboolean 1418_math_matrix_is_general_scale( const GLmatrix *m ) 1419{ 1420 return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE; 1421} 1422 1423 1424GLboolean 1425_math_matrix_is_dirty( const GLmatrix *m ) 1426{ 1427 return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE; 1428} 1429 1430 1431/**********************************************************************/ 1432/** \name Matrix setup */ 1433/*@{*/ 1434 1435/** 1436 * Copy a matrix. 1437 * 1438 * \param to destination matrix. 1439 * \param from source matrix. 1440 * 1441 * Copies all fields in GLmatrix, creating an inverse array if necessary. 1442 */ 1443void 1444_math_matrix_copy( GLmatrix *to, const GLmatrix *from ) 1445{ 1446 memcpy( to->m, from->m, sizeof(Identity) ); 1447 to->flags = from->flags; 1448 to->type = from->type; 1449 1450 if (to->inv != 0) { 1451 if (from->inv == 0) { 1452 matrix_invert( to ); 1453 } 1454 else { 1455 memcpy(to->inv, from->inv, sizeof(GLfloat)*16); 1456 } 1457 } 1458} 1459 1460/** 1461 * Loads a matrix array into GLmatrix. 1462 * 1463 * \param m matrix array. 1464 * \param mat matrix. 1465 * 1466 * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY 1467 * flags. 1468 */ 1469void 1470_math_matrix_loadf( GLmatrix *mat, const GLfloat *m ) 1471{ 1472 memcpy( mat->m, m, 16*sizeof(GLfloat) ); 1473 mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY); 1474} 1475 1476/** 1477 * Matrix constructor. 1478 * 1479 * \param m matrix. 1480 * 1481 * Initialize the GLmatrix fields. 1482 */ 1483void 1484_math_matrix_ctr( GLmatrix *m ) 1485{ 1486 m->m = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 ); 1487 if (m->m) 1488 memcpy( m->m, Identity, sizeof(Identity) ); 1489 m->inv = NULL; 1490 m->type = MATRIX_IDENTITY; 1491 m->flags = 0; 1492} 1493 1494/** 1495 * Matrix destructor. 1496 * 1497 * \param m matrix. 1498 * 1499 * Frees the data in a GLmatrix. 1500 */ 1501void 1502_math_matrix_dtr( GLmatrix *m ) 1503{ 1504 if (m->m) { 1505 _mesa_align_free( m->m ); 1506 m->m = NULL; 1507 } 1508 if (m->inv) { 1509 _mesa_align_free( m->inv ); 1510 m->inv = NULL; 1511 } 1512} 1513 1514/** 1515 * Allocate a matrix inverse. 1516 * 1517 * \param m matrix. 1518 * 1519 * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity. 1520 */ 1521void 1522_math_matrix_alloc_inv( GLmatrix *m ) 1523{ 1524 if (!m->inv) { 1525 m->inv = (GLfloat *) _mesa_align_malloc( 16 * sizeof(GLfloat), 16 ); 1526 if (m->inv) 1527 memcpy( m->inv, Identity, 16 * sizeof(GLfloat) ); 1528 } 1529} 1530 1531/*@}*/ 1532 1533 1534/**********************************************************************/ 1535/** \name Matrix transpose */ 1536/*@{*/ 1537 1538/** 1539 * Transpose a GLfloat matrix. 1540 * 1541 * \param to destination array. 1542 * \param from source array. 1543 */ 1544void 1545_math_transposef( GLfloat to[16], const GLfloat from[16] ) 1546{ 1547 to[0] = from[0]; 1548 to[1] = from[4]; 1549 to[2] = from[8]; 1550 to[3] = from[12]; 1551 to[4] = from[1]; 1552 to[5] = from[5]; 1553 to[6] = from[9]; 1554 to[7] = from[13]; 1555 to[8] = from[2]; 1556 to[9] = from[6]; 1557 to[10] = from[10]; 1558 to[11] = from[14]; 1559 to[12] = from[3]; 1560 to[13] = from[7]; 1561 to[14] = from[11]; 1562 to[15] = from[15]; 1563} 1564 1565/** 1566 * Transpose a GLdouble matrix. 1567 * 1568 * \param to destination array. 1569 * \param from source array. 1570 */ 1571void 1572_math_transposed( GLdouble to[16], const GLdouble from[16] ) 1573{ 1574 to[0] = from[0]; 1575 to[1] = from[4]; 1576 to[2] = from[8]; 1577 to[3] = from[12]; 1578 to[4] = from[1]; 1579 to[5] = from[5]; 1580 to[6] = from[9]; 1581 to[7] = from[13]; 1582 to[8] = from[2]; 1583 to[9] = from[6]; 1584 to[10] = from[10]; 1585 to[11] = from[14]; 1586 to[12] = from[3]; 1587 to[13] = from[7]; 1588 to[14] = from[11]; 1589 to[15] = from[15]; 1590} 1591 1592/** 1593 * Transpose a GLdouble matrix and convert to GLfloat. 1594 * 1595 * \param to destination array. 1596 * \param from source array. 1597 */ 1598void 1599_math_transposefd( GLfloat to[16], const GLdouble from[16] ) 1600{ 1601 to[0] = (GLfloat) from[0]; 1602 to[1] = (GLfloat) from[4]; 1603 to[2] = (GLfloat) from[8]; 1604 to[3] = (GLfloat) from[12]; 1605 to[4] = (GLfloat) from[1]; 1606 to[5] = (GLfloat) from[5]; 1607 to[6] = (GLfloat) from[9]; 1608 to[7] = (GLfloat) from[13]; 1609 to[8] = (GLfloat) from[2]; 1610 to[9] = (GLfloat) from[6]; 1611 to[10] = (GLfloat) from[10]; 1612 to[11] = (GLfloat) from[14]; 1613 to[12] = (GLfloat) from[3]; 1614 to[13] = (GLfloat) from[7]; 1615 to[14] = (GLfloat) from[11]; 1616 to[15] = (GLfloat) from[15]; 1617} 1618 1619/*@}*/ 1620 1621 1622/** 1623 * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This 1624 * function is used for transforming clipping plane equations and spotlight 1625 * directions. 1626 * Mathematically, u = v * m. 1627 * Input: v - input vector 1628 * m - transformation matrix 1629 * Output: u - transformed vector 1630 */ 1631void 1632_mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] ) 1633{ 1634 const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3]; 1635#define M(row,col) m[row + col*4] 1636 u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0); 1637 u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1); 1638 u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2); 1639 u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3); 1640#undef M 1641} 1642