m_matrix.c revision 6dc85575000127630489b407c50a4b3ea87c9acb
1/** 2 * \file m_matrix.c 3 * Matrix operations. 4 * 5 * \note 6 * -# 4x4 transformation matrices are stored in memory in column major order. 7 * -# Points/vertices are to be thought of as column vectors. 8 * -# Transformation of a point p by a matrix M is: p' = M * p 9 */ 10 11/* 12 * Mesa 3-D graphics library 13 * Version: 5.1 14 * 15 * Copyright (C) 1999-2003 Brian Paul All Rights Reserved. 16 * 17 * Permission is hereby granted, free of charge, to any person obtaining a 18 * copy of this software and associated documentation files (the "Software"), 19 * to deal in the Software without restriction, including without limitation 20 * the rights to use, copy, modify, merge, publish, distribute, sublicense, 21 * and/or sell copies of the Software, and to permit persons to whom the 22 * Software is furnished to do so, subject to the following conditions: 23 * 24 * The above copyright notice and this permission notice shall be included 25 * in all copies or substantial portions of the Software. 26 * 27 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 28 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 29 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 30 * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN 31 * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN 32 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 33 */ 34 35 36#include "glheader.h" 37#include "imports.h" 38#include "macros.h" 39#include "imports.h" 40 41#include "m_matrix.h" 42 43 44/** 45 * Names of the corresponding GLmatrixtype values. 46 */ 47static const char *types[] = { 48 "MATRIX_GENERAL", 49 "MATRIX_IDENTITY", 50 "MATRIX_3D_NO_ROT", 51 "MATRIX_PERSPECTIVE", 52 "MATRIX_2D", 53 "MATRIX_2D_NO_ROT", 54 "MATRIX_3D" 55}; 56 57 58/** 59 * Identity matrix. 60 */ 61static GLfloat Identity[16] = { 62 1.0, 0.0, 0.0, 0.0, 63 0.0, 1.0, 0.0, 0.0, 64 0.0, 0.0, 1.0, 0.0, 65 0.0, 0.0, 0.0, 1.0 66}; 67 68 69 70/**********************************************************************/ 71/** \name Matrix multiplication */ 72/*@{*/ 73 74#define A(row,col) a[(col<<2)+row] 75#define B(row,col) b[(col<<2)+row] 76#define P(row,col) product[(col<<2)+row] 77 78/** 79 * Perform a full 4x4 matrix multiplication. 80 * 81 * \param a matrix. 82 * \param b matrix. 83 * \param product will receive the product of \p a and \p b. 84 * 85 * \warning Is assumed that \p product != \p b. \p product == \p a is allowed. 86 * 87 * \note KW: 4*16 = 64 multiplications 88 * 89 * \author This \c matmul was contributed by Thomas Malik 90 */ 91static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b ) 92{ 93 GLint i; 94 for (i = 0; i < 4; i++) { 95 const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); 96 P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0); 97 P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1); 98 P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2); 99 P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3); 100 } 101} 102 103/** 104 * Multiply two matrices known to occupy only the top three rows, such 105 * as typical model matrices, and orthogonal matrices. 106 * 107 * \param a matrix. 108 * \param b matrix. 109 * \param product will receive the product of \p a and \p b. 110 */ 111static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b ) 112{ 113 GLint i; 114 for (i = 0; i < 3; i++) { 115 const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); 116 P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0); 117 P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1); 118 P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2); 119 P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3; 120 } 121 P(3,0) = 0; 122 P(3,1) = 0; 123 P(3,2) = 0; 124 P(3,3) = 1; 125} 126 127#undef A 128#undef B 129#undef P 130 131/** 132 * Multiply a matrix by an array of floats with known properties. 133 * 134 * \param mat pointer to a GLmatrix structure containing the left multiplication 135 * matrix, and that will receive the product result. 136 * \param m right multiplication matrix array. 137 * \param flags flags of the matrix \p m. 138 * 139 * Joins both flags and marks the type and inverse as dirty. Calls matmul34() 140 * if both matrices are 3D, or matmul4() otherwise. 141 */ 142static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags ) 143{ 144 mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE); 145 146 if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) 147 matmul34( mat->m, mat->m, m ); 148 else 149 matmul4( mat->m, mat->m, m ); 150} 151 152/** 153 * Matrix multiplication. 154 * 155 * \param dest destination matrix. 156 * \param a left matrix. 157 * \param b right matrix. 158 * 159 * Joins both flags and marks the type and inverse as dirty. Calls matmul34() 160 * if both matrices are 3D, or matmul4() otherwise. 161 */ 162void 163_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b ) 164{ 165 dest->flags = (a->flags | 166 b->flags | 167 MAT_DIRTY_TYPE | 168 MAT_DIRTY_INVERSE); 169 170 if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D)) 171 matmul34( dest->m, a->m, b->m ); 172 else 173 matmul4( dest->m, a->m, b->m ); 174} 175 176/** 177 * Matrix multiplication. 178 * 179 * \param dest left and destination matrix. 180 * \param m right matrix array. 181 * 182 * Marks the matrix flags with general flag, and type and inverse dirty flags. 183 * Calls matmul4() for the multiplication. 184 */ 185void 186_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m ) 187{ 188 dest->flags |= (MAT_FLAG_GENERAL | 189 MAT_DIRTY_TYPE | 190 MAT_DIRTY_INVERSE); 191 192 matmul4( dest->m, dest->m, m ); 193} 194 195/*@}*/ 196 197 198/**********************************************************************/ 199/** \name Matrix output */ 200/*@{*/ 201 202/** 203 * Print a matrix array. 204 * 205 * \param m matrix array. 206 * 207 * Called by _math_matrix_print() to print a matrix or its inverse. 208 */ 209static void print_matrix_floats( const GLfloat m[16] ) 210{ 211 int i; 212 for (i=0;i<4;i++) { 213 _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] ); 214 } 215} 216 217/** 218 * Dumps the contents of a GLmatrix structure. 219 * 220 * \param m pointer to the GLmatrix structure. 221 */ 222void 223_math_matrix_print( const GLmatrix *m ) 224{ 225 _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags); 226 print_matrix_floats(m->m); 227 _mesa_debug(NULL, "Inverse: \n"); 228 if (m->inv) { 229 GLfloat prod[16]; 230 print_matrix_floats(m->inv); 231 matmul4(prod, m->m, m->inv); 232 _mesa_debug(NULL, "Mat * Inverse:\n"); 233 print_matrix_floats(prod); 234 } 235 else { 236 _mesa_debug(NULL, " - not available\n"); 237 } 238} 239 240/*@}*/ 241 242 243/** 244 * References an element of 4x4 matrix. 245 * 246 * \param m matrix array. 247 * \param c column of the desired element. 248 * \param r row of the desired element. 249 * 250 * \return value of the desired element. 251 * 252 * Calculate the linear storage index of the element and references it. 253 */ 254#define MAT(m,r,c) (m)[(c)*4+(r)] 255 256 257/**********************************************************************/ 258/** \name Matrix inversion */ 259/*@{*/ 260 261/** 262 * Swaps the values of two floating pointer variables. 263 * 264 * Used by invert_matrix_general() to swap the row pointers. 265 */ 266#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; } 267 268/** 269 * Compute inverse of 4x4 transformation matrix. 270 * 271 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 272 * stored in the GLmatrix::inv attribute. 273 * 274 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 275 * 276 * \author 277 * Code contributed by Jacques Leroy jle@star.be 278 * 279 * Calculates the inverse matrix by performing the gaussian matrix reduction 280 * with partial pivoting followed by back/substitution with the loops manually 281 * unrolled. 282 */ 283static GLboolean invert_matrix_general( GLmatrix *mat ) 284{ 285 const GLfloat *m = mat->m; 286 GLfloat *out = mat->inv; 287 GLfloat wtmp[4][8]; 288 GLfloat m0, m1, m2, m3, s; 289 GLfloat *r0, *r1, *r2, *r3; 290 291 r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3]; 292 293 r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1), 294 r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3), 295 r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0, 296 297 r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1), 298 r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3), 299 r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0, 300 301 r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1), 302 r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3), 303 r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0, 304 305 r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1), 306 r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3), 307 r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0; 308 309 /* choose pivot - or die */ 310 if (fabs(r3[0])>fabs(r2[0])) SWAP_ROWS(r3, r2); 311 if (fabs(r2[0])>fabs(r1[0])) SWAP_ROWS(r2, r1); 312 if (fabs(r1[0])>fabs(r0[0])) SWAP_ROWS(r1, r0); 313 if (0.0 == r0[0]) return GL_FALSE; 314 315 /* eliminate first variable */ 316 m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0]; 317 s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s; 318 s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s; 319 s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s; 320 s = r0[4]; 321 if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; } 322 s = r0[5]; 323 if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; } 324 s = r0[6]; 325 if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; } 326 s = r0[7]; 327 if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; } 328 329 /* choose pivot - or die */ 330 if (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2); 331 if (fabs(r2[1])>fabs(r1[1])) SWAP_ROWS(r2, r1); 332 if (0.0 == r1[1]) return GL_FALSE; 333 334 /* eliminate second variable */ 335 m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1]; 336 r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2]; 337 r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3]; 338 s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; } 339 s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; } 340 s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; } 341 s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; } 342 343 /* choose pivot - or die */ 344 if (fabs(r3[2])>fabs(r2[2])) SWAP_ROWS(r3, r2); 345 if (0.0 == r2[2]) return GL_FALSE; 346 347 /* eliminate third variable */ 348 m3 = r3[2]/r2[2]; 349 r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4], 350 r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], 351 r3[7] -= m3 * r2[7]; 352 353 /* last check */ 354 if (0.0 == r3[3]) return GL_FALSE; 355 356 s = 1.0F/r3[3]; /* now back substitute row 3 */ 357 r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s; 358 359 m2 = r2[3]; /* now back substitute row 2 */ 360 s = 1.0F/r2[2]; 361 r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2), 362 r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2); 363 m1 = r1[3]; 364 r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1, 365 r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1; 366 m0 = r0[3]; 367 r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0, 368 r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0; 369 370 m1 = r1[2]; /* now back substitute row 1 */ 371 s = 1.0F/r1[1]; 372 r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1), 373 r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1); 374 m0 = r0[2]; 375 r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0, 376 r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0; 377 378 m0 = r0[1]; /* now back substitute row 0 */ 379 s = 1.0F/r0[0]; 380 r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0), 381 r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0); 382 383 MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5], 384 MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7], 385 MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5], 386 MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7], 387 MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5], 388 MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7], 389 MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5], 390 MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7]; 391 392 return GL_TRUE; 393} 394#undef SWAP_ROWS 395 396/** 397 * Compute inverse of a general 3d transformation matrix. 398 * 399 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 400 * stored in the GLmatrix::inv attribute. 401 * 402 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 403 * 404 * \author Adapted from graphics gems II. 405 * 406 * Calculates the inverse of the upper left by first calculating its 407 * determinant and multiplying it to the symmetric adjust matrix of each 408 * element. Finally deals with the translation part by transforming the 409 * original translation vector using by the calculated submatrix inverse. 410 */ 411static GLboolean invert_matrix_3d_general( GLmatrix *mat ) 412{ 413 const GLfloat *in = mat->m; 414 GLfloat *out = mat->inv; 415 GLfloat pos, neg, t; 416 GLfloat det; 417 418 /* Calculate the determinant of upper left 3x3 submatrix and 419 * determine if the matrix is singular. 420 */ 421 pos = neg = 0.0; 422 t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2); 423 if (t >= 0.0) pos += t; else neg += t; 424 425 t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2); 426 if (t >= 0.0) pos += t; else neg += t; 427 428 t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2); 429 if (t >= 0.0) pos += t; else neg += t; 430 431 t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2); 432 if (t >= 0.0) pos += t; else neg += t; 433 434 t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2); 435 if (t >= 0.0) pos += t; else neg += t; 436 437 t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2); 438 if (t >= 0.0) pos += t; else neg += t; 439 440 det = pos + neg; 441 442 if (det*det < 1e-25) 443 return GL_FALSE; 444 445 det = 1.0F / det; 446 MAT(out,0,0) = ( (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det); 447 MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det); 448 MAT(out,0,2) = ( (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det); 449 MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det); 450 MAT(out,1,1) = ( (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det); 451 MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det); 452 MAT(out,2,0) = ( (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det); 453 MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det); 454 MAT(out,2,2) = ( (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det); 455 456 /* Do the translation part */ 457 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + 458 MAT(in,1,3) * MAT(out,0,1) + 459 MAT(in,2,3) * MAT(out,0,2) ); 460 MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + 461 MAT(in,1,3) * MAT(out,1,1) + 462 MAT(in,2,3) * MAT(out,1,2) ); 463 MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + 464 MAT(in,1,3) * MAT(out,2,1) + 465 MAT(in,2,3) * MAT(out,2,2) ); 466 467 return GL_TRUE; 468} 469 470/** 471 * Compute inverse of a 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 * If the matrix is not an angle preserving matrix then calls 479 * invert_matrix_3d_general for the actual calculation. Otherwise calculates 480 * the inverse matrix analyzing and inverting each of the scaling, rotation and 481 * translation parts. 482 */ 483static GLboolean invert_matrix_3d( GLmatrix *mat ) 484{ 485 const GLfloat *in = mat->m; 486 GLfloat *out = mat->inv; 487 488 if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) { 489 return invert_matrix_3d_general( mat ); 490 } 491 492 if (mat->flags & MAT_FLAG_UNIFORM_SCALE) { 493 GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) + 494 MAT(in,0,1) * MAT(in,0,1) + 495 MAT(in,0,2) * MAT(in,0,2)); 496 497 if (scale == 0.0) 498 return GL_FALSE; 499 500 scale = 1.0F / scale; 501 502 /* Transpose and scale the 3 by 3 upper-left submatrix. */ 503 MAT(out,0,0) = scale * MAT(in,0,0); 504 MAT(out,1,0) = scale * MAT(in,0,1); 505 MAT(out,2,0) = scale * MAT(in,0,2); 506 MAT(out,0,1) = scale * MAT(in,1,0); 507 MAT(out,1,1) = scale * MAT(in,1,1); 508 MAT(out,2,1) = scale * MAT(in,1,2); 509 MAT(out,0,2) = scale * MAT(in,2,0); 510 MAT(out,1,2) = scale * MAT(in,2,1); 511 MAT(out,2,2) = scale * MAT(in,2,2); 512 } 513 else if (mat->flags & MAT_FLAG_ROTATION) { 514 /* Transpose the 3 by 3 upper-left submatrix. */ 515 MAT(out,0,0) = MAT(in,0,0); 516 MAT(out,1,0) = MAT(in,0,1); 517 MAT(out,2,0) = MAT(in,0,2); 518 MAT(out,0,1) = MAT(in,1,0); 519 MAT(out,1,1) = MAT(in,1,1); 520 MAT(out,2,1) = MAT(in,1,2); 521 MAT(out,0,2) = MAT(in,2,0); 522 MAT(out,1,2) = MAT(in,2,1); 523 MAT(out,2,2) = MAT(in,2,2); 524 } 525 else { 526 /* pure translation */ 527 MEMCPY( out, Identity, sizeof(Identity) ); 528 MAT(out,0,3) = - MAT(in,0,3); 529 MAT(out,1,3) = - MAT(in,1,3); 530 MAT(out,2,3) = - MAT(in,2,3); 531 return GL_TRUE; 532 } 533 534 if (mat->flags & MAT_FLAG_TRANSLATION) { 535 /* Do the translation part */ 536 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) + 537 MAT(in,1,3) * MAT(out,0,1) + 538 MAT(in,2,3) * MAT(out,0,2) ); 539 MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) + 540 MAT(in,1,3) * MAT(out,1,1) + 541 MAT(in,2,3) * MAT(out,1,2) ); 542 MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) + 543 MAT(in,1,3) * MAT(out,2,1) + 544 MAT(in,2,3) * MAT(out,2,2) ); 545 } 546 else { 547 MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0; 548 } 549 550 return GL_TRUE; 551} 552 553/** 554 * Compute inverse of an identity transformation matrix. 555 * 556 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 557 * stored in the GLmatrix::inv attribute. 558 * 559 * \return always GL_TRUE. 560 * 561 * Simply copies Identity into GLmatrix::inv. 562 */ 563static GLboolean invert_matrix_identity( GLmatrix *mat ) 564{ 565 MEMCPY( mat->inv, Identity, sizeof(Identity) ); 566 return GL_TRUE; 567} 568 569/** 570 * Compute inverse of a no-rotation 3d transformation matrix. 571 * 572 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 573 * stored in the GLmatrix::inv attribute. 574 * 575 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 576 * 577 * Calculates the 578 */ 579static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat ) 580{ 581 const GLfloat *in = mat->m; 582 GLfloat *out = mat->inv; 583 584 if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 ) 585 return GL_FALSE; 586 587 MEMCPY( out, Identity, 16 * sizeof(GLfloat) ); 588 MAT(out,0,0) = 1.0F / MAT(in,0,0); 589 MAT(out,1,1) = 1.0F / MAT(in,1,1); 590 MAT(out,2,2) = 1.0F / MAT(in,2,2); 591 592 if (mat->flags & MAT_FLAG_TRANSLATION) { 593 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); 594 MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); 595 MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2)); 596 } 597 598 return GL_TRUE; 599} 600 601/** 602 * Compute inverse of a no-rotation 2d transformation matrix. 603 * 604 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 605 * stored in the GLmatrix::inv attribute. 606 * 607 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 608 * 609 * Calculates the inverse matrix by applying the inverse scaling and 610 * translation to the identity matrix. 611 */ 612static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat ) 613{ 614 const GLfloat *in = mat->m; 615 GLfloat *out = mat->inv; 616 617 if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0) 618 return GL_FALSE; 619 620 MEMCPY( out, Identity, 16 * sizeof(GLfloat) ); 621 MAT(out,0,0) = 1.0F / MAT(in,0,0); 622 MAT(out,1,1) = 1.0F / MAT(in,1,1); 623 624 if (mat->flags & MAT_FLAG_TRANSLATION) { 625 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0)); 626 MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1)); 627 } 628 629 return GL_TRUE; 630} 631 632#if 0 633/* broken */ 634static GLboolean invert_matrix_perspective( GLmatrix *mat ) 635{ 636 const GLfloat *in = mat->m; 637 GLfloat *out = mat->inv; 638 639 if (MAT(in,2,3) == 0) 640 return GL_FALSE; 641 642 MEMCPY( out, Identity, 16 * sizeof(GLfloat) ); 643 644 MAT(out,0,0) = 1.0F / MAT(in,0,0); 645 MAT(out,1,1) = 1.0F / MAT(in,1,1); 646 647 MAT(out,0,3) = MAT(in,0,2); 648 MAT(out,1,3) = MAT(in,1,2); 649 650 MAT(out,2,2) = 0; 651 MAT(out,2,3) = -1; 652 653 MAT(out,3,2) = 1.0F / MAT(in,2,3); 654 MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2); 655 656 return GL_TRUE; 657} 658#endif 659 660/** 661 * Matrix inversion function pointer type. 662 */ 663typedef GLboolean (*inv_mat_func)( GLmatrix *mat ); 664 665/** 666 * Table of the matrix inversion functions according to the matrix type. 667 */ 668static inv_mat_func inv_mat_tab[7] = { 669 invert_matrix_general, 670 invert_matrix_identity, 671 invert_matrix_3d_no_rot, 672#if 0 673 /* Don't use this function for now - it fails when the projection matrix 674 * is premultiplied by a translation (ala Chromium's tilesort SPU). 675 */ 676 invert_matrix_perspective, 677#else 678 invert_matrix_general, 679#endif 680 invert_matrix_3d, /* lazy! */ 681 invert_matrix_2d_no_rot, 682 invert_matrix_3d 683}; 684 685/** 686 * Compute inverse of a transformation matrix. 687 * 688 * \param mat pointer to a GLmatrix structure. The matrix inverse will be 689 * stored in the GLmatrix::inv attribute. 690 * 691 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). 692 * 693 * Calls the matrix inversion function in inv_mat_tab corresponding to the 694 * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag, 695 * and copies the identity matrix into GLmatrix::inv. 696 */ 697static GLboolean matrix_invert( GLmatrix *mat ) 698{ 699 if (inv_mat_tab[mat->type](mat)) { 700 mat->flags &= ~MAT_FLAG_SINGULAR; 701 return GL_TRUE; 702 } else { 703 mat->flags |= MAT_FLAG_SINGULAR; 704 MEMCPY( mat->inv, Identity, sizeof(Identity) ); 705 return GL_FALSE; 706 } 707} 708 709/*@}*/ 710 711 712/**********************************************************************/ 713/** \name Matrix generation */ 714/*@{*/ 715 716/** 717 * Generate a 4x4 transformation matrix from glRotate parameters, and 718 * post-multiply the input matrix by it. 719 * 720 * \author 721 * This function was contributed by Erich Boleyn (erich@uruk.org). 722 * Optimizations contributed by Rudolf Opalla (rudi@khm.de). 723 */ 724void 725_math_matrix_rotate( GLmatrix *mat, 726 GLfloat angle, GLfloat x, GLfloat y, GLfloat z ) 727{ 728 GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c; 729 GLfloat m[16]; 730 GLboolean optimized; 731 732 s = (GLfloat) sin( angle * DEG2RAD ); 733 c = (GLfloat) cos( angle * DEG2RAD ); 734 735 MEMCPY(m, Identity, sizeof(GLfloat)*16); 736 optimized = GL_FALSE; 737 738#define M(row,col) m[col*4+row] 739 740 if (x == 0.0F) { 741 if (y == 0.0F) { 742 if (z != 0.0F) { 743 optimized = GL_TRUE; 744 /* rotate only around z-axis */ 745 M(0,0) = c; 746 M(1,1) = c; 747 if (z < 0.0F) { 748 M(0,1) = s; 749 M(1,0) = -s; 750 } 751 else { 752 M(0,1) = -s; 753 M(1,0) = s; 754 } 755 } 756 } 757 else if (z == 0.0F) { 758 optimized = GL_TRUE; 759 /* rotate only around y-axis */ 760 M(0,0) = c; 761 M(2,2) = c; 762 if (y < 0.0F) { 763 M(0,2) = -s; 764 M(2,0) = s; 765 } 766 else { 767 M(0,2) = s; 768 M(2,0) = -s; 769 } 770 } 771 } 772 else if (y == 0.0F) { 773 if (z == 0.0F) { 774 optimized = GL_TRUE; 775 /* rotate only around x-axis */ 776 M(1,1) = c; 777 M(2,2) = c; 778 if (x < 0.0F) { 779 M(1,2) = s; 780 M(2,1) = -s; 781 } 782 else { 783 M(1,2) = -s; 784 M(2,1) = s; 785 } 786 } 787 } 788 789 if (!optimized) { 790 const GLfloat mag = SQRTF(x * x + y * y + z * z); 791 792 if (mag <= 1.0e-4) { 793 /* no rotation, leave mat as-is */ 794 return; 795 } 796 797 x /= mag; 798 y /= mag; 799 z /= mag; 800 801 802 /* 803 * Arbitrary axis rotation matrix. 804 * 805 * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied 806 * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation 807 * (which is about the X-axis), and the two composite transforms 808 * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary 809 * from the arbitrary axis to the X-axis then back. They are 810 * all elementary rotations. 811 * 812 * Rz' is a rotation about the Z-axis, to bring the axis vector 813 * into the x-z plane. Then Ry' is applied, rotating about the 814 * Y-axis to bring the axis vector parallel with the X-axis. The 815 * rotation about the X-axis is then performed. Ry and Rz are 816 * simply the respective inverse transforms to bring the arbitrary 817 * axis back to it's original orientation. The first transforms 818 * Rz' and Ry' are considered inverses, since the data from the 819 * arbitrary axis gives you info on how to get to it, not how 820 * to get away from it, and an inverse must be applied. 821 * 822 * The basic calculation used is to recognize that the arbitrary 823 * axis vector (x, y, z), since it is of unit length, actually 824 * represents the sines and cosines of the angles to rotate the 825 * X-axis to the same orientation, with theta being the angle about 826 * Z and phi the angle about Y (in the order described above) 827 * as follows: 828 * 829 * cos ( theta ) = x / sqrt ( 1 - z^2 ) 830 * sin ( theta ) = y / sqrt ( 1 - z^2 ) 831 * 832 * cos ( phi ) = sqrt ( 1 - z^2 ) 833 * sin ( phi ) = z 834 * 835 * Note that cos ( phi ) can further be inserted to the above 836 * formulas: 837 * 838 * cos ( theta ) = x / cos ( phi ) 839 * sin ( theta ) = y / sin ( phi ) 840 * 841 * ...etc. Because of those relations and the standard trigonometric 842 * relations, it is pssible to reduce the transforms down to what 843 * is used below. It may be that any primary axis chosen will give the 844 * same results (modulo a sign convention) using thie method. 845 * 846 * Particularly nice is to notice that all divisions that might 847 * have caused trouble when parallel to certain planes or 848 * axis go away with care paid to reducing the expressions. 849 * After checking, it does perform correctly under all cases, since 850 * in all the cases of division where the denominator would have 851 * been zero, the numerator would have been zero as well, giving 852 * the expected result. 853 */ 854 855 xx = x * x; 856 yy = y * y; 857 zz = z * z; 858 xy = x * y; 859 yz = y * z; 860 zx = z * x; 861 xs = x * s; 862 ys = y * s; 863 zs = z * s; 864 one_c = 1.0F - c; 865 866 /* We already hold the identity-matrix so we can skip some statements */ 867 M(0,0) = (one_c * xx) + c; 868 M(0,1) = (one_c * xy) - zs; 869 M(0,2) = (one_c * zx) + ys; 870/* M(0,3) = 0.0F; */ 871 872 M(1,0) = (one_c * xy) + zs; 873 M(1,1) = (one_c * yy) + c; 874 M(1,2) = (one_c * yz) - xs; 875/* M(1,3) = 0.0F; */ 876 877 M(2,0) = (one_c * zx) - ys; 878 M(2,1) = (one_c * yz) + xs; 879 M(2,2) = (one_c * zz) + c; 880/* M(2,3) = 0.0F; */ 881 882/* 883 M(3,0) = 0.0F; 884 M(3,1) = 0.0F; 885 M(3,2) = 0.0F; 886 M(3,3) = 1.0F; 887*/ 888 } 889#undef M 890 891 matrix_multf( mat, m, MAT_FLAG_ROTATION ); 892} 893 894/** 895 * Apply a perspective projection matrix. 896 * 897 * \param mat matrix to apply the projection. 898 * \param left left clipping plane coordinate. 899 * \param right right clipping plane coordinate. 900 * \param bottom bottom clipping plane coordinate. 901 * \param top top clipping plane coordinate. 902 * \param nearval distance to the near clipping plane. 903 * \param farval distance to the far clipping plane. 904 * 905 * Creates the projection matrix and multiplies it with \p mat, marking the 906 * MAT_FLAG_PERSPECTIVE flag. 907 */ 908void 909_math_matrix_frustum( GLmatrix *mat, 910 GLfloat left, GLfloat right, 911 GLfloat bottom, GLfloat top, 912 GLfloat nearval, GLfloat farval ) 913{ 914 GLfloat x, y, a, b, c, d; 915 GLfloat m[16]; 916 917 x = (2.0F*nearval) / (right-left); 918 y = (2.0F*nearval) / (top-bottom); 919 a = (right+left) / (right-left); 920 b = (top+bottom) / (top-bottom); 921 c = -(farval+nearval) / ( farval-nearval); 922 d = -(2.0F*farval*nearval) / (farval-nearval); /* error? */ 923 924#define M(row,col) m[col*4+row] 925 M(0,0) = x; M(0,1) = 0.0F; M(0,2) = a; M(0,3) = 0.0F; 926 M(1,0) = 0.0F; M(1,1) = y; M(1,2) = b; M(1,3) = 0.0F; 927 M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = c; M(2,3) = d; 928 M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = -1.0F; M(3,3) = 0.0F; 929#undef M 930 931 matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE ); 932} 933 934/** 935 * Apply an orthographic projection matrix. 936 * 937 * \param mat matrix to apply the projection. 938 * \param left left clipping plane coordinate. 939 * \param right right clipping plane coordinate. 940 * \param bottom bottom clipping plane coordinate. 941 * \param top top clipping plane coordinate. 942 * \param nearval distance to the near clipping plane. 943 * \param farval distance to the far clipping plane. 944 * 945 * Creates the projection matrix and multiplies it with \p mat, marking the 946 * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags. 947 */ 948void 949_math_matrix_ortho( GLmatrix *mat, 950 GLfloat left, GLfloat right, 951 GLfloat bottom, GLfloat top, 952 GLfloat nearval, GLfloat farval ) 953{ 954 GLfloat x, y, z; 955 GLfloat tx, ty, tz; 956 GLfloat m[16]; 957 958 x = 2.0F / (right-left); 959 y = 2.0F / (top-bottom); 960 z = -2.0F / (farval-nearval); 961 tx = -(right+left) / (right-left); 962 ty = -(top+bottom) / (top-bottom); 963 tz = -(farval+nearval) / (farval-nearval); 964 965#define M(row,col) m[col*4+row] 966 M(0,0) = x; M(0,1) = 0.0F; M(0,2) = 0.0F; M(0,3) = tx; 967 M(1,0) = 0.0F; M(1,1) = y; M(1,2) = 0.0F; M(1,3) = ty; 968 M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = z; M(2,3) = tz; 969 M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = 0.0F; M(3,3) = 1.0F; 970#undef M 971 972 matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION)); 973} 974 975/** 976 * Multiply a matrix with a general scaling matrix. 977 * 978 * \param mat matrix. 979 * \param x x axis scale factor. 980 * \param y y axis scale factor. 981 * \param z z axis scale factor. 982 * 983 * Multiplies in-place the elements of \p mat by the scale factors. Checks if 984 * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE 985 * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and 986 * MAT_DIRTY_INVERSE dirty flags. 987 */ 988void 989_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) 990{ 991 GLfloat *m = mat->m; 992 m[0] *= x; m[4] *= y; m[8] *= z; 993 m[1] *= x; m[5] *= y; m[9] *= z; 994 m[2] *= x; m[6] *= y; m[10] *= z; 995 m[3] *= x; m[7] *= y; m[11] *= z; 996 997 if (fabs(x - y) < 1e-8 && fabs(x - z) < 1e-8) 998 mat->flags |= MAT_FLAG_UNIFORM_SCALE; 999 else 1000 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1001 1002 mat->flags |= (MAT_DIRTY_TYPE | 1003 MAT_DIRTY_INVERSE); 1004} 1005 1006/** 1007 * Multiply a matrix with a translation matrix. 1008 * 1009 * \param mat matrix. 1010 * \param x translation vector x coordinate. 1011 * \param y translation vector y coordinate. 1012 * \param z translation vector z coordinate. 1013 * 1014 * Adds the translation coordinates to the elements of \p mat in-place. Marks 1015 * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE 1016 * dirty flags. 1017 */ 1018void 1019_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z ) 1020{ 1021 GLfloat *m = mat->m; 1022 m[12] = m[0] * x + m[4] * y + m[8] * z + m[12]; 1023 m[13] = m[1] * x + m[5] * y + m[9] * z + m[13]; 1024 m[14] = m[2] * x + m[6] * y + m[10] * z + m[14]; 1025 m[15] = m[3] * x + m[7] * y + m[11] * z + m[15]; 1026 1027 mat->flags |= (MAT_FLAG_TRANSLATION | 1028 MAT_DIRTY_TYPE | 1029 MAT_DIRTY_INVERSE); 1030} 1031 1032/** 1033 * Set a matrix to the identity matrix. 1034 * 1035 * \param mat matrix. 1036 * 1037 * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL. 1038 * Sets the matrix type to identity, and clear the dirty flags. 1039 */ 1040void 1041_math_matrix_set_identity( GLmatrix *mat ) 1042{ 1043 MEMCPY( mat->m, Identity, 16*sizeof(GLfloat) ); 1044 1045 if (mat->inv) 1046 MEMCPY( mat->inv, Identity, 16*sizeof(GLfloat) ); 1047 1048 mat->type = MATRIX_IDENTITY; 1049 mat->flags &= ~(MAT_DIRTY_FLAGS| 1050 MAT_DIRTY_TYPE| 1051 MAT_DIRTY_INVERSE); 1052} 1053 1054/*@}*/ 1055 1056 1057/**********************************************************************/ 1058/** \name Matrix analysis */ 1059/*@{*/ 1060 1061#define ZERO(x) (1<<x) 1062#define ONE(x) (1<<(x+16)) 1063 1064#define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14)) 1065#define MASK_NO_2D_SCALE ( ONE(0) | ONE(5)) 1066 1067#define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\ 1068 ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\ 1069 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1070 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1071 1072#define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \ 1073 ZERO(1) | ZERO(9) | \ 1074 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1075 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1076 1077#define MASK_2D ( ZERO(8) | \ 1078 ZERO(9) | \ 1079 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\ 1080 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1081 1082 1083#define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \ 1084 ZERO(1) | ZERO(9) | \ 1085 ZERO(2) | ZERO(6) | \ 1086 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1087 1088#define MASK_3D ( \ 1089 \ 1090 \ 1091 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) ) 1092 1093 1094#define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\ 1095 ZERO(1) | ZERO(13) |\ 1096 ZERO(2) | ZERO(6) | \ 1097 ZERO(3) | ZERO(7) | ZERO(15) ) 1098 1099#define SQ(x) ((x)*(x)) 1100 1101/** 1102 * Determine type and flags from scratch. 1103 * 1104 * \param mat matrix. 1105 * 1106 * This is expensive enough to only want to do it once. 1107 */ 1108static void analyse_from_scratch( GLmatrix *mat ) 1109{ 1110 const GLfloat *m = mat->m; 1111 GLuint mask = 0; 1112 GLuint i; 1113 1114 for (i = 0 ; i < 16 ; i++) { 1115 if (m[i] == 0.0) mask |= (1<<i); 1116 } 1117 1118 if (m[0] == 1.0F) mask |= (1<<16); 1119 if (m[5] == 1.0F) mask |= (1<<21); 1120 if (m[10] == 1.0F) mask |= (1<<26); 1121 if (m[15] == 1.0F) mask |= (1<<31); 1122 1123 mat->flags &= ~MAT_FLAGS_GEOMETRY; 1124 1125 /* Check for translation - no-one really cares 1126 */ 1127 if ((mask & MASK_NO_TRX) != MASK_NO_TRX) 1128 mat->flags |= MAT_FLAG_TRANSLATION; 1129 1130 /* Do the real work 1131 */ 1132 if (mask == (GLuint) MASK_IDENTITY) { 1133 mat->type = MATRIX_IDENTITY; 1134 } 1135 else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) { 1136 mat->type = MATRIX_2D_NO_ROT; 1137 1138 if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE) 1139 mat->flags = MAT_FLAG_GENERAL_SCALE; 1140 } 1141 else if ((mask & MASK_2D) == (GLuint) MASK_2D) { 1142 GLfloat mm = DOT2(m, m); 1143 GLfloat m4m4 = DOT2(m+4,m+4); 1144 GLfloat mm4 = DOT2(m,m+4); 1145 1146 mat->type = MATRIX_2D; 1147 1148 /* Check for scale */ 1149 if (SQ(mm-1) > SQ(1e-6) || 1150 SQ(m4m4-1) > SQ(1e-6)) 1151 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1152 1153 /* Check for rotation */ 1154 if (SQ(mm4) > SQ(1e-6)) 1155 mat->flags |= MAT_FLAG_GENERAL_3D; 1156 else 1157 mat->flags |= MAT_FLAG_ROTATION; 1158 1159 } 1160 else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) { 1161 mat->type = MATRIX_3D_NO_ROT; 1162 1163 /* Check for scale */ 1164 if (SQ(m[0]-m[5]) < SQ(1e-6) && 1165 SQ(m[0]-m[10]) < SQ(1e-6)) { 1166 if (SQ(m[0]-1.0) > SQ(1e-6)) { 1167 mat->flags |= MAT_FLAG_UNIFORM_SCALE; 1168 } 1169 } 1170 else { 1171 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1172 } 1173 } 1174 else if ((mask & MASK_3D) == (GLuint) MASK_3D) { 1175 GLfloat c1 = DOT3(m,m); 1176 GLfloat c2 = DOT3(m+4,m+4); 1177 GLfloat c3 = DOT3(m+8,m+8); 1178 GLfloat d1 = DOT3(m, m+4); 1179 GLfloat cp[3]; 1180 1181 mat->type = MATRIX_3D; 1182 1183 /* Check for scale */ 1184 if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) { 1185 if (SQ(c1-1.0) > SQ(1e-6)) 1186 mat->flags |= MAT_FLAG_UNIFORM_SCALE; 1187 /* else no scale at all */ 1188 } 1189 else { 1190 mat->flags |= MAT_FLAG_GENERAL_SCALE; 1191 } 1192 1193 /* Check for rotation */ 1194 if (SQ(d1) < SQ(1e-6)) { 1195 CROSS3( cp, m, m+4 ); 1196 SUB_3V( cp, cp, (m+8) ); 1197 if (LEN_SQUARED_3FV(cp) < SQ(1e-6)) 1198 mat->flags |= MAT_FLAG_ROTATION; 1199 else 1200 mat->flags |= MAT_FLAG_GENERAL_3D; 1201 } 1202 else { 1203 mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */ 1204 } 1205 } 1206 else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) { 1207 mat->type = MATRIX_PERSPECTIVE; 1208 mat->flags |= MAT_FLAG_GENERAL; 1209 } 1210 else { 1211 mat->type = MATRIX_GENERAL; 1212 mat->flags |= MAT_FLAG_GENERAL; 1213 } 1214} 1215 1216/** 1217 * Analyze a matrix given that its flags are accurate. 1218 * 1219 * This is the more common operation, hopefully. 1220 */ 1221static void analyse_from_flags( GLmatrix *mat ) 1222{ 1223 const GLfloat *m = mat->m; 1224 1225 if (TEST_MAT_FLAGS(mat, 0)) { 1226 mat->type = MATRIX_IDENTITY; 1227 } 1228 else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION | 1229 MAT_FLAG_UNIFORM_SCALE | 1230 MAT_FLAG_GENERAL_SCALE))) { 1231 if ( m[10]==1.0F && m[14]==0.0F ) { 1232 mat->type = MATRIX_2D_NO_ROT; 1233 } 1234 else { 1235 mat->type = MATRIX_3D_NO_ROT; 1236 } 1237 } 1238 else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) { 1239 if ( m[ 8]==0.0F 1240 && m[ 9]==0.0F 1241 && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) { 1242 mat->type = MATRIX_2D; 1243 } 1244 else { 1245 mat->type = MATRIX_3D; 1246 } 1247 } 1248 else if ( m[4]==0.0F && m[12]==0.0F 1249 && m[1]==0.0F && m[13]==0.0F 1250 && m[2]==0.0F && m[6]==0.0F 1251 && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) { 1252 mat->type = MATRIX_PERSPECTIVE; 1253 } 1254 else { 1255 mat->type = MATRIX_GENERAL; 1256 } 1257} 1258 1259/** 1260 * Analyze and update a matrix. 1261 * 1262 * \param mat matrix. 1263 * 1264 * If the matrix type is dirty then calls either analyse_from_scratch() or 1265 * analyse_from_flags() to determine its type, according to whether the flags 1266 * are dirty or not, respectively. If the matrix has an inverse and it's dirty 1267 * then calls matrix_invert(). Finally clears the dirty flags. 1268 */ 1269void 1270_math_matrix_analyse( GLmatrix *mat ) 1271{ 1272 if (mat->flags & MAT_DIRTY_TYPE) { 1273 if (mat->flags & MAT_DIRTY_FLAGS) 1274 analyse_from_scratch( mat ); 1275 else 1276 analyse_from_flags( mat ); 1277 } 1278 1279 if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) { 1280 matrix_invert( mat ); 1281 } 1282 1283 mat->flags &= ~(MAT_DIRTY_FLAGS| 1284 MAT_DIRTY_TYPE| 1285 MAT_DIRTY_INVERSE); 1286} 1287 1288/*@}*/ 1289 1290 1291/**********************************************************************/ 1292/** \name Matrix setup */ 1293/*@{*/ 1294 1295/** 1296 * Copy a matrix. 1297 * 1298 * \param to destination matrix. 1299 * \param from source matrix. 1300 * 1301 * Copies all fields in GLmatrix, creating an inverse array if necessary. 1302 */ 1303void 1304_math_matrix_copy( GLmatrix *to, const GLmatrix *from ) 1305{ 1306 MEMCPY( to->m, from->m, sizeof(Identity) ); 1307 to->flags = from->flags; 1308 to->type = from->type; 1309 1310 if (to->inv != 0) { 1311 if (from->inv == 0) { 1312 matrix_invert( to ); 1313 } 1314 else { 1315 MEMCPY(to->inv, from->inv, sizeof(GLfloat)*16); 1316 } 1317 } 1318} 1319 1320/** 1321 * Loads a matrix array into GLmatrix. 1322 * 1323 * \param m matrix array. 1324 * \param mat matrix. 1325 * 1326 * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY 1327 * flags. 1328 */ 1329void 1330_math_matrix_loadf( GLmatrix *mat, const GLfloat *m ) 1331{ 1332 MEMCPY( mat->m, m, 16*sizeof(GLfloat) ); 1333 mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY); 1334} 1335 1336/** 1337 * Matrix constructor. 1338 * 1339 * \param m matrix. 1340 * 1341 * Initialize the GLmatrix fields. 1342 */ 1343void 1344_math_matrix_ctr( GLmatrix *m ) 1345{ 1346 m->m = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 ); 1347 if (m->m) 1348 MEMCPY( m->m, Identity, sizeof(Identity) ); 1349 m->inv = NULL; 1350 m->type = MATRIX_IDENTITY; 1351 m->flags = 0; 1352} 1353 1354/** 1355 * Matrix destructor. 1356 * 1357 * \param m matrix. 1358 * 1359 * Frees the data in a GLmatrix. 1360 */ 1361void 1362_math_matrix_dtr( GLmatrix *m ) 1363{ 1364 if (m->m) { 1365 ALIGN_FREE( m->m ); 1366 m->m = NULL; 1367 } 1368 if (m->inv) { 1369 ALIGN_FREE( m->inv ); 1370 m->inv = NULL; 1371 } 1372} 1373 1374/** 1375 * Allocate a matrix inverse. 1376 * 1377 * \param m matrix. 1378 * 1379 * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity. 1380 */ 1381void 1382_math_matrix_alloc_inv( GLmatrix *m ) 1383{ 1384 if (!m->inv) { 1385 m->inv = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 ); 1386 if (m->inv) 1387 MEMCPY( m->inv, Identity, 16 * sizeof(GLfloat) ); 1388 } 1389} 1390 1391/*@}*/ 1392 1393 1394/**********************************************************************/ 1395/** \name Matrix transpose */ 1396/*@{*/ 1397 1398/** 1399 * Transpose a GLfloat matrix. 1400 * 1401 * \param to destination array. 1402 * \param from source array. 1403 */ 1404void 1405_math_transposef( GLfloat to[16], const GLfloat from[16] ) 1406{ 1407 to[0] = from[0]; 1408 to[1] = from[4]; 1409 to[2] = from[8]; 1410 to[3] = from[12]; 1411 to[4] = from[1]; 1412 to[5] = from[5]; 1413 to[6] = from[9]; 1414 to[7] = from[13]; 1415 to[8] = from[2]; 1416 to[9] = from[6]; 1417 to[10] = from[10]; 1418 to[11] = from[14]; 1419 to[12] = from[3]; 1420 to[13] = from[7]; 1421 to[14] = from[11]; 1422 to[15] = from[15]; 1423} 1424 1425/** 1426 * Transpose a GLdouble matrix. 1427 * 1428 * \param to destination array. 1429 * \param from source array. 1430 */ 1431void 1432_math_transposed( GLdouble to[16], const GLdouble from[16] ) 1433{ 1434 to[0] = from[0]; 1435 to[1] = from[4]; 1436 to[2] = from[8]; 1437 to[3] = from[12]; 1438 to[4] = from[1]; 1439 to[5] = from[5]; 1440 to[6] = from[9]; 1441 to[7] = from[13]; 1442 to[8] = from[2]; 1443 to[9] = from[6]; 1444 to[10] = from[10]; 1445 to[11] = from[14]; 1446 to[12] = from[3]; 1447 to[13] = from[7]; 1448 to[14] = from[11]; 1449 to[15] = from[15]; 1450} 1451 1452/** 1453 * Transpose a GLdouble matrix and convert to GLfloat. 1454 * 1455 * \param to destination array. 1456 * \param from source array. 1457 */ 1458void 1459_math_transposefd( GLfloat to[16], const GLdouble from[16] ) 1460{ 1461 to[0] = (GLfloat) from[0]; 1462 to[1] = (GLfloat) from[4]; 1463 to[2] = (GLfloat) from[8]; 1464 to[3] = (GLfloat) from[12]; 1465 to[4] = (GLfloat) from[1]; 1466 to[5] = (GLfloat) from[5]; 1467 to[6] = (GLfloat) from[9]; 1468 to[7] = (GLfloat) from[13]; 1469 to[8] = (GLfloat) from[2]; 1470 to[9] = (GLfloat) from[6]; 1471 to[10] = (GLfloat) from[10]; 1472 to[11] = (GLfloat) from[14]; 1473 to[12] = (GLfloat) from[3]; 1474 to[13] = (GLfloat) from[7]; 1475 to[14] = (GLfloat) from[11]; 1476 to[15] = (GLfloat) from[15]; 1477} 1478 1479/*@}*/ 1480 1481