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