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 #include <GLES2/gl2.h>
37 #include <stdio.h>
38 #include <math.h>
39 #include <assert.h>
40 #include <string.h>
41
42 #include "../src/mesa/main/macros.h"
43
44 #include "m_matrix.h"
45
46 #define _mesa_debug(...)
47 /**
48 * \defgroup MatFlags MAT_FLAG_XXX-flags
49 *
50 * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
51 * It would be nice to make all these flags private to m_matrix.c
52 */
53 /*@{*/
54 #define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag.
55 * (Not actually used - the identity
56 * matrix is identified by the absense
57 * of all other flags.)
58 */
59 #define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */
60 #define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */
61 #define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */
62 #define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */
63 #define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */
64 #define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */
65 #define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */
66 #define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */
67 #define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */
68 #define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */
69 #define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */
70
71 /** angle preserving matrix flags mask */
72 #define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
73 MAT_FLAG_TRANSLATION | \
74 MAT_FLAG_UNIFORM_SCALE)
75
76 /** geometry related matrix flags mask */
77 #define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
78 MAT_FLAG_ROTATION | \
79 MAT_FLAG_TRANSLATION | \
80 MAT_FLAG_UNIFORM_SCALE | \
81 MAT_FLAG_GENERAL_SCALE | \
82 MAT_FLAG_GENERAL_3D | \
83 MAT_FLAG_PERSPECTIVE | \
84 MAT_FLAG_SINGULAR)
85
86 /** length preserving matrix flags mask */
87 #define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
88 MAT_FLAG_TRANSLATION)
89
90
91 /** 3D (non-perspective) matrix flags mask */
92 #define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
93 MAT_FLAG_TRANSLATION | \
94 MAT_FLAG_UNIFORM_SCALE | \
95 MAT_FLAG_GENERAL_SCALE | \
96 MAT_FLAG_GENERAL_3D)
97
98 /** dirty matrix flags mask */
99 #define MAT_DIRTY (MAT_DIRTY_TYPE | \
100 MAT_DIRTY_FLAGS | \
101 MAT_DIRTY_INVERSE)
102
103 /*@}*/
104
105
106 /**
107 * Test geometry related matrix flags.
108 *
109 * \param mat a pointer to a GLmatrix structure.
110 * \param a flags mask.
111 *
112 * \returns non-zero if all geometry related matrix flags are contained within
113 * the mask, or zero otherwise.
114 */
115 #define TEST_MAT_FLAGS(mat, a) \
116 ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
117
118
119
120 /**
121 * Names of the corresponding GLmatrixtype values.
122 */
123 static const char *types[] = {
124 "MATRIX_GENERAL",
125 "MATRIX_IDENTITY",
126 "MATRIX_3D_NO_ROT",
127 "MATRIX_PERSPECTIVE",
128 "MATRIX_2D",
129 "MATRIX_2D_NO_ROT",
130 "MATRIX_3D"
131 };
132
133
134 /**
135 * Identity matrix.
136 */
137 static GLfloat Identity[16] = {
138 1.0, 0.0, 0.0, 0.0,
139 0.0, 1.0, 0.0, 0.0,
140 0.0, 0.0, 1.0, 0.0,
141 0.0, 0.0, 0.0, 1.0
142 };
143
144
145
146 /**********************************************************************/
147 /** \name Matrix multiplication */
148 /*@{*/
149
150 #define A(row,col) a[(col<<2)+row]
151 #define B(row,col) b[(col<<2)+row]
152 #define P(row,col) product[(col<<2)+row]
153
154 /**
155 * Perform a full 4x4 matrix multiplication.
156 *
157 * \param a matrix.
158 * \param b matrix.
159 * \param product will receive the product of \p a and \p b.
160 *
161 * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
162 *
163 * \note KW: 4*16 = 64 multiplications
164 *
165 * \author This \c matmul was contributed by Thomas Malik
166 */
matmul4(GLfloat * product,const GLfloat * a,const GLfloat * b)167 static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b )
168 {
169 assert(product != b);
170 GLint i;
171 for (i = 0; i < 4; i++) {
172 const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3);
173 P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
174 P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
175 P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
176 P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3);
177 }
178 }
179
180 /**
181 * Multiply two matrices known to occupy only the top three rows, such
182 * as typical model matrices, and orthogonal matrices.
183 *
184 * \param a matrix.
185 * \param b matrix.
186 * \param product will receive the product of \p a and \p b.
187 */
matmul34(GLfloat * product,const GLfloat * a,const GLfloat * b)188 static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b )
189 {
190 GLint i;
191 for (i = 0; i < 3; i++) {
192 const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3);
193 P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0);
194 P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1);
195 P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2);
196 P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3;
197 }
198 P(3,0) = 0;
199 P(3,1) = 0;
200 P(3,2) = 0;
201 P(3,3) = 1;
202 }
203
204 #undef A
205 #undef B
206 #undef P
207
208 /**
209 * Multiply a matrix by an array of floats with known properties.
210 *
211 * \param mat pointer to a GLmatrix structure containing the left multiplication
212 * matrix, and that will receive the product result.
213 * \param m right multiplication matrix array.
214 * \param flags flags of the matrix \p m.
215 *
216 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
217 * if both matrices are 3D, or matmul4() otherwise.
218 */
matrix_multf(GLmatrix * mat,const GLfloat * m,GLuint flags)219 static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags )
220 {
221 mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
222
223 if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D))
224 matmul34( mat->m, mat->m, m );
225 else
226 matmul4( mat->m, mat->m, m );
227 }
228
229 /**
230 * Matrix multiplication.
231 *
232 * \param dest destination matrix.
233 * \param a left matrix.
234 * \param b right matrix.
235 *
236 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
237 * if both matrices are 3D, or matmul4() otherwise.
238 */
239 void
_math_matrix_mul_matrix(GLmatrix * dest,const GLmatrix * a,const GLmatrix * b)240 _math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b )
241 {
242 dest->flags = (a->flags |
243 b->flags |
244 MAT_DIRTY_TYPE |
245 MAT_DIRTY_INVERSE);
246
247 if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D))
248 matmul34( dest->m, a->m, b->m );
249 else
250 matmul4( dest->m, a->m, b->m );
251 }
252
253 /**
254 * Matrix multiplication.
255 *
256 * \param dest left and destination matrix.
257 * \param m right matrix array.
258 *
259 * Marks the matrix flags with general flag, and type and inverse dirty flags.
260 * Calls matmul4() for the multiplication.
261 */
262 void
_math_matrix_mul_floats(GLmatrix * dest,const GLfloat * m)263 _math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m )
264 {
265 dest->flags |= (MAT_FLAG_GENERAL |
266 MAT_DIRTY_TYPE |
267 MAT_DIRTY_INVERSE |
268 MAT_DIRTY_FLAGS);
269
270 matmul4( dest->m, dest->m, m );
271 }
272
273 /*@}*/
274
275
276 /**********************************************************************/
277 /** \name Matrix output */
278 /*@{*/
279
280 /**
281 * Print a matrix array.
282 *
283 * \param m matrix array.
284 *
285 * Called by _math_matrix_print() to print a matrix or its inverse.
286 */
print_matrix_floats(const GLfloat m[16])287 static void print_matrix_floats( const GLfloat m[16] )
288 {
289 int i;
290 for (i=0;i<4;i++) {
291 _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
292 }
293 }
294
295 /**
296 * Dumps the contents of a GLmatrix structure.
297 *
298 * \param m pointer to the GLmatrix structure.
299 */
300 void
_math_matrix_print(const GLmatrix * m)301 _math_matrix_print( const GLmatrix *m )
302 {
303 _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
304 print_matrix_floats(m->m);
305 _mesa_debug(NULL, "Inverse: \n");
306 if (m->inv) {
307 GLfloat prod[16];
308 print_matrix_floats(m->inv);
309 matmul4(prod, m->m, m->inv);
310 _mesa_debug(NULL, "Mat * Inverse:\n");
311 print_matrix_floats(prod);
312 }
313 else {
314 _mesa_debug(NULL, " - not available\n");
315 }
316 }
317
318 /*@}*/
319
320
321 /**
322 * References an element of 4x4 matrix.
323 *
324 * \param m matrix array.
325 * \param c column of the desired element.
326 * \param r row of the desired element.
327 *
328 * \return value of the desired element.
329 *
330 * Calculate the linear storage index of the element and references it.
331 */
332 #define MAT(m,r,c) (m)[(c)*4+(r)]
333
334
335 /**********************************************************************/
336 /** \name Matrix inversion */
337 /*@{*/
338
339 /**
340 * Swaps the values of two floating pointer variables.
341 *
342 * Used by invert_matrix_general() to swap the row pointers.
343 */
344 #define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
345
346 /**
347 * Compute inverse of 4x4 transformation matrix.
348 *
349 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
350 * stored in the GLmatrix::inv attribute.
351 *
352 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
353 *
354 * \author
355 * Code contributed by Jacques Leroy jle@star.be
356 *
357 * Calculates the inverse matrix by performing the gaussian matrix reduction
358 * with partial pivoting followed by back/substitution with the loops manually
359 * unrolled.
360 */
invert_matrix_general(GLmatrix * mat)361 static GLboolean invert_matrix_general( GLmatrix *mat )
362 {
363 const GLfloat *m = mat->m;
364 GLfloat *out = mat->inv;
365 GLfloat wtmp[4][8];
366 GLfloat m0, m1, m2, m3, s;
367 GLfloat *r0, *r1, *r2, *r3;
368
369 r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
370
371 r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1),
372 r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3),
373 r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
374
375 r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1),
376 r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3),
377 r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
378
379 r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1),
380 r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3),
381 r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
382
383 r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1),
384 r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3),
385 r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
386
387 /* choose pivot - or die */
388 if (FABSF(r3[0])>FABSF(r2[0])) SWAP_ROWS(r3, r2);
389 if (FABSF(r2[0])>FABSF(r1[0])) SWAP_ROWS(r2, r1);
390 if (FABSF(r1[0])>FABSF(r0[0])) SWAP_ROWS(r1, r0);
391 if (0.0 == r0[0]) return GL_FALSE;
392
393 /* eliminate first variable */
394 m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0];
395 s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
396 s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
397 s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
398 s = r0[4];
399 if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
400 s = r0[5];
401 if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
402 s = r0[6];
403 if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
404 s = r0[7];
405 if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
406
407 /* choose pivot - or die */
408 if (FABSF(r3[1])>FABSF(r2[1])) SWAP_ROWS(r3, r2);
409 if (FABSF(r2[1])>FABSF(r1[1])) SWAP_ROWS(r2, r1);
410 if (0.0 == r1[1]) return GL_FALSE;
411
412 /* eliminate second variable */
413 m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1];
414 r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2];
415 r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3];
416 s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
417 s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
418 s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
419 s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }
420
421 /* choose pivot - or die */
422 if (FABSF(r3[2])>FABSF(r2[2])) SWAP_ROWS(r3, r2);
423 if (0.0 == r2[2]) return GL_FALSE;
424
425 /* eliminate third variable */
426 m3 = r3[2]/r2[2];
427 r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
428 r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6],
429 r3[7] -= m3 * r2[7];
430
431 /* last check */
432 if (0.0 == r3[3]) return GL_FALSE;
433
434 s = 1.0F/r3[3]; /* now back substitute row 3 */
435 r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s;
436
437 m2 = r2[3]; /* now back substitute row 2 */
438 s = 1.0F/r2[2];
439 r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
440 r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
441 m1 = r1[3];
442 r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
443 r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
444 m0 = r0[3];
445 r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
446 r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
447
448 m1 = r1[2]; /* now back substitute row 1 */
449 s = 1.0F/r1[1];
450 r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
451 r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
452 m0 = r0[2];
453 r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
454 r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
455
456 m0 = r0[1]; /* now back substitute row 0 */
457 s = 1.0F/r0[0];
458 r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
459 r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
460
461 MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5],
462 MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7],
463 MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5],
464 MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7],
465 MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5],
466 MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7],
467 MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5],
468 MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7];
469
470 return GL_TRUE;
471 }
472 #undef SWAP_ROWS
473
474 /**
475 * Compute inverse of a general 3d transformation matrix.
476 *
477 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
478 * stored in the GLmatrix::inv attribute.
479 *
480 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
481 *
482 * \author Adapted from graphics gems II.
483 *
484 * Calculates the inverse of the upper left by first calculating its
485 * determinant and multiplying it to the symmetric adjust matrix of each
486 * element. Finally deals with the translation part by transforming the
487 * original translation vector using by the calculated submatrix inverse.
488 */
invert_matrix_3d_general(GLmatrix * mat)489 static GLboolean invert_matrix_3d_general( GLmatrix *mat )
490 {
491 const GLfloat *in = mat->m;
492 GLfloat *out = mat->inv;
493 GLfloat pos, neg, t;
494 GLfloat det;
495
496 /* Calculate the determinant of upper left 3x3 submatrix and
497 * determine if the matrix is singular.
498 */
499 pos = neg = 0.0;
500 t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2);
501 if (t >= 0.0) pos += t; else neg += t;
502
503 t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2);
504 if (t >= 0.0) pos += t; else neg += t;
505
506 t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2);
507 if (t >= 0.0) pos += t; else neg += t;
508
509 t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2);
510 if (t >= 0.0) pos += t; else neg += t;
511
512 t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2);
513 if (t >= 0.0) pos += t; else neg += t;
514
515 t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2);
516 if (t >= 0.0) pos += t; else neg += t;
517
518 det = pos + neg;
519
520 if (det*det < 1e-25)
521 return GL_FALSE;
522
523 det = 1.0F / det;
524 MAT(out,0,0) = ( (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det);
525 MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det);
526 MAT(out,0,2) = ( (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det);
527 MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det);
528 MAT(out,1,1) = ( (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det);
529 MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det);
530 MAT(out,2,0) = ( (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det);
531 MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det);
532 MAT(out,2,2) = ( (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det);
533
534 /* Do the translation part */
535 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
536 MAT(in,1,3) * MAT(out,0,1) +
537 MAT(in,2,3) * MAT(out,0,2) );
538 MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
539 MAT(in,1,3) * MAT(out,1,1) +
540 MAT(in,2,3) * MAT(out,1,2) );
541 MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
542 MAT(in,1,3) * MAT(out,2,1) +
543 MAT(in,2,3) * MAT(out,2,2) );
544
545 return GL_TRUE;
546 }
547
548 /**
549 * Compute inverse of a 3d transformation matrix.
550 *
551 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
552 * stored in the GLmatrix::inv attribute.
553 *
554 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
555 *
556 * If the matrix is not an angle preserving matrix then calls
557 * invert_matrix_3d_general for the actual calculation. Otherwise calculates
558 * the inverse matrix analyzing and inverting each of the scaling, rotation and
559 * translation parts.
560 */
invert_matrix_3d(GLmatrix * mat)561 static GLboolean invert_matrix_3d( GLmatrix *mat )
562 {
563 const GLfloat *in = mat->m;
564 GLfloat *out = mat->inv;
565
566 if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) {
567 return invert_matrix_3d_general( mat );
568 }
569
570 if (mat->flags & MAT_FLAG_UNIFORM_SCALE) {
571 GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) +
572 MAT(in,0,1) * MAT(in,0,1) +
573 MAT(in,0,2) * MAT(in,0,2));
574
575 if (scale == 0.0)
576 return GL_FALSE;
577
578 scale = 1.0F / scale;
579
580 /* Transpose and scale the 3 by 3 upper-left submatrix. */
581 MAT(out,0,0) = scale * MAT(in,0,0);
582 MAT(out,1,0) = scale * MAT(in,0,1);
583 MAT(out,2,0) = scale * MAT(in,0,2);
584 MAT(out,0,1) = scale * MAT(in,1,0);
585 MAT(out,1,1) = scale * MAT(in,1,1);
586 MAT(out,2,1) = scale * MAT(in,1,2);
587 MAT(out,0,2) = scale * MAT(in,2,0);
588 MAT(out,1,2) = scale * MAT(in,2,1);
589 MAT(out,2,2) = scale * MAT(in,2,2);
590 }
591 else if (mat->flags & MAT_FLAG_ROTATION) {
592 /* Transpose the 3 by 3 upper-left submatrix. */
593 MAT(out,0,0) = MAT(in,0,0);
594 MAT(out,1,0) = MAT(in,0,1);
595 MAT(out,2,0) = MAT(in,0,2);
596 MAT(out,0,1) = MAT(in,1,0);
597 MAT(out,1,1) = MAT(in,1,1);
598 MAT(out,2,1) = MAT(in,1,2);
599 MAT(out,0,2) = MAT(in,2,0);
600 MAT(out,1,2) = MAT(in,2,1);
601 MAT(out,2,2) = MAT(in,2,2);
602 }
603 else {
604 /* pure translation */
605 memcpy( out, Identity, sizeof(Identity) );
606 MAT(out,0,3) = - MAT(in,0,3);
607 MAT(out,1,3) = - MAT(in,1,3);
608 MAT(out,2,3) = - MAT(in,2,3);
609 return GL_TRUE;
610 }
611
612 if (mat->flags & MAT_FLAG_TRANSLATION) {
613 /* Do the translation part */
614 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
615 MAT(in,1,3) * MAT(out,0,1) +
616 MAT(in,2,3) * MAT(out,0,2) );
617 MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
618 MAT(in,1,3) * MAT(out,1,1) +
619 MAT(in,2,3) * MAT(out,1,2) );
620 MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
621 MAT(in,1,3) * MAT(out,2,1) +
622 MAT(in,2,3) * MAT(out,2,2) );
623 }
624 else {
625 MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0;
626 }
627
628 return GL_TRUE;
629 }
630
631 /**
632 * Compute inverse of an identity transformation matrix.
633 *
634 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
635 * stored in the GLmatrix::inv attribute.
636 *
637 * \return always GL_TRUE.
638 *
639 * Simply copies Identity into GLmatrix::inv.
640 */
invert_matrix_identity(GLmatrix * mat)641 static GLboolean invert_matrix_identity( GLmatrix *mat )
642 {
643 memcpy( mat->inv, Identity, sizeof(Identity) );
644 return GL_TRUE;
645 }
646
647 /**
648 * Compute inverse of a no-rotation 3d transformation matrix.
649 *
650 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
651 * stored in the GLmatrix::inv attribute.
652 *
653 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
654 *
655 * Calculates the
656 */
invert_matrix_3d_no_rot(GLmatrix * mat)657 static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat )
658 {
659 const GLfloat *in = mat->m;
660 GLfloat *out = mat->inv;
661
662 if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 )
663 return GL_FALSE;
664
665 memcpy( out, Identity, 16 * sizeof(GLfloat) );
666 MAT(out,0,0) = 1.0F / MAT(in,0,0);
667 MAT(out,1,1) = 1.0F / MAT(in,1,1);
668 MAT(out,2,2) = 1.0F / MAT(in,2,2);
669
670 if (mat->flags & MAT_FLAG_TRANSLATION) {
671 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
672 MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
673 MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2));
674 }
675
676 return GL_TRUE;
677 }
678
679 /**
680 * Compute inverse of a no-rotation 2d transformation matrix.
681 *
682 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
683 * stored in the GLmatrix::inv attribute.
684 *
685 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
686 *
687 * Calculates the inverse matrix by applying the inverse scaling and
688 * translation to the identity matrix.
689 */
invert_matrix_2d_no_rot(GLmatrix * mat)690 static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat )
691 {
692 const GLfloat *in = mat->m;
693 GLfloat *out = mat->inv;
694
695 if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0)
696 return GL_FALSE;
697
698 memcpy( out, Identity, 16 * sizeof(GLfloat) );
699 MAT(out,0,0) = 1.0F / MAT(in,0,0);
700 MAT(out,1,1) = 1.0F / MAT(in,1,1);
701
702 if (mat->flags & MAT_FLAG_TRANSLATION) {
703 MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
704 MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
705 }
706
707 return GL_TRUE;
708 }
709
710 #if 0
711 /* broken */
712 static GLboolean invert_matrix_perspective( GLmatrix *mat )
713 {
714 const GLfloat *in = mat->m;
715 GLfloat *out = mat->inv;
716
717 if (MAT(in,2,3) == 0)
718 return GL_FALSE;
719
720 memcpy( out, Identity, 16 * sizeof(GLfloat) );
721
722 MAT(out,0,0) = 1.0F / MAT(in,0,0);
723 MAT(out,1,1) = 1.0F / MAT(in,1,1);
724
725 MAT(out,0,3) = MAT(in,0,2);
726 MAT(out,1,3) = MAT(in,1,2);
727
728 MAT(out,2,2) = 0;
729 MAT(out,2,3) = -1;
730
731 MAT(out,3,2) = 1.0F / MAT(in,2,3);
732 MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2);
733
734 return GL_TRUE;
735 }
736 #endif
737
738 /**
739 * Matrix inversion function pointer type.
740 */
741 typedef GLboolean (*inv_mat_func)( GLmatrix *mat );
742
743 /**
744 * Table of the matrix inversion functions according to the matrix type.
745 */
746 static inv_mat_func inv_mat_tab[7] = {
747 invert_matrix_general,
748 invert_matrix_identity,
749 invert_matrix_3d_no_rot,
750 #if 0
751 /* Don't use this function for now - it fails when the projection matrix
752 * is premultiplied by a translation (ala Chromium's tilesort SPU).
753 */
754 invert_matrix_perspective,
755 #else
756 invert_matrix_general,
757 #endif
758 invert_matrix_3d, /* lazy! */
759 invert_matrix_2d_no_rot,
760 invert_matrix_3d
761 };
762
763 /**
764 * Compute inverse of a transformation matrix.
765 *
766 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
767 * stored in the GLmatrix::inv attribute.
768 *
769 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
770 *
771 * Calls the matrix inversion function in inv_mat_tab corresponding to the
772 * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag,
773 * and copies the identity matrix into GLmatrix::inv.
774 */
matrix_invert(GLmatrix * mat)775 static GLboolean matrix_invert( GLmatrix *mat )
776 {
777 if (inv_mat_tab[mat->type](mat)) {
778 mat->flags &= ~MAT_FLAG_SINGULAR;
779 return GL_TRUE;
780 } else {
781 mat->flags |= MAT_FLAG_SINGULAR;
782 memcpy( mat->inv, Identity, sizeof(Identity) );
783 return GL_FALSE;
784 }
785 }
786
787 /*@}*/
788
789
790 /**********************************************************************/
791 /** \name Matrix generation */
792 /*@{*/
793
794 /**
795 * Generate a 4x4 transformation matrix from glRotate parameters, and
796 * post-multiply the input matrix by it.
797 *
798 * \author
799 * This function was contributed by Erich Boleyn (erich@uruk.org).
800 * Optimizations contributed by Rudolf Opalla (rudi@khm.de).
801 */
802 void
_math_matrix_rotate(GLmatrix * mat,GLfloat angle,GLfloat x,GLfloat y,GLfloat z)803 _math_matrix_rotate( GLmatrix *mat,
804 GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
805 {
806 GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
807 GLfloat m[16];
808 GLboolean optimized;
809
810 s = (GLfloat) sinf( angle * (M_PI / 180.0f) );
811 c = (GLfloat) cosf( angle * (M_PI / 180.0f) );
812
813 memcpy(m, Identity, sizeof(GLfloat)*16);
814 optimized = GL_FALSE;
815
816 #define M(row,col) m[col*4+row]
817
818 if (x == 0.0F) {
819 if (y == 0.0F) {
820 if (z != 0.0F) {
821 optimized = GL_TRUE;
822 /* rotate only around z-axis */
823 M(0,0) = c;
824 M(1,1) = c;
825 if (z < 0.0F) {
826 M(0,1) = s;
827 M(1,0) = -s;
828 }
829 else {
830 M(0,1) = -s;
831 M(1,0) = s;
832 }
833 }
834 }
835 else if (z == 0.0F) {
836 optimized = GL_TRUE;
837 /* rotate only around y-axis */
838 M(0,0) = c;
839 M(2,2) = c;
840 if (y < 0.0F) {
841 M(0,2) = -s;
842 M(2,0) = s;
843 }
844 else {
845 M(0,2) = s;
846 M(2,0) = -s;
847 }
848 }
849 }
850 else if (y == 0.0F) {
851 if (z == 0.0F) {
852 optimized = GL_TRUE;
853 /* rotate only around x-axis */
854 M(1,1) = c;
855 M(2,2) = c;
856 if (x < 0.0F) {
857 M(1,2) = s;
858 M(2,1) = -s;
859 }
860 else {
861 M(1,2) = -s;
862 M(2,1) = s;
863 }
864 }
865 }
866
867 if (!optimized) {
868 const GLfloat mag = SQRTF(x * x + y * y + z * z);
869
870 if (mag <= 1.0e-4) {
871 /* no rotation, leave mat as-is */
872 return;
873 }
874
875 x /= mag;
876 y /= mag;
877 z /= mag;
878
879
880 /*
881 * Arbitrary axis rotation matrix.
882 *
883 * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
884 * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation
885 * (which is about the X-axis), and the two composite transforms
886 * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
887 * from the arbitrary axis to the X-axis then back. They are
888 * all elementary rotations.
889 *
890 * Rz' is a rotation about the Z-axis, to bring the axis vector
891 * into the x-z plane. Then Ry' is applied, rotating about the
892 * Y-axis to bring the axis vector parallel with the X-axis. The
893 * rotation about the X-axis is then performed. Ry and Rz are
894 * simply the respective inverse transforms to bring the arbitrary
895 * axis back to it's original orientation. The first transforms
896 * Rz' and Ry' are considered inverses, since the data from the
897 * arbitrary axis gives you info on how to get to it, not how
898 * to get away from it, and an inverse must be applied.
899 *
900 * The basic calculation used is to recognize that the arbitrary
901 * axis vector (x, y, z), since it is of unit length, actually
902 * represents the sines and cosines of the angles to rotate the
903 * X-axis to the same orientation, with theta being the angle about
904 * Z and phi the angle about Y (in the order described above)
905 * as follows:
906 *
907 * cos ( theta ) = x / sqrt ( 1 - z^2 )
908 * sin ( theta ) = y / sqrt ( 1 - z^2 )
909 *
910 * cos ( phi ) = sqrt ( 1 - z^2 )
911 * sin ( phi ) = z
912 *
913 * Note that cos ( phi ) can further be inserted to the above
914 * formulas:
915 *
916 * cos ( theta ) = x / cos ( phi )
917 * sin ( theta ) = y / sin ( phi )
918 *
919 * ...etc. Because of those relations and the standard trigonometric
920 * relations, it is pssible to reduce the transforms down to what
921 * is used below. It may be that any primary axis chosen will give the
922 * same results (modulo a sign convention) using thie method.
923 *
924 * Particularly nice is to notice that all divisions that might
925 * have caused trouble when parallel to certain planes or
926 * axis go away with care paid to reducing the expressions.
927 * After checking, it does perform correctly under all cases, since
928 * in all the cases of division where the denominator would have
929 * been zero, the numerator would have been zero as well, giving
930 * the expected result.
931 */
932
933 xx = x * x;
934 yy = y * y;
935 zz = z * z;
936 xy = x * y;
937 yz = y * z;
938 zx = z * x;
939 xs = x * s;
940 ys = y * s;
941 zs = z * s;
942 one_c = 1.0F - c;
943
944 /* We already hold the identity-matrix so we can skip some statements */
945 M(0,0) = (one_c * xx) + c;
946 M(0,1) = (one_c * xy) - zs;
947 M(0,2) = (one_c * zx) + ys;
948 /* M(0,3) = 0.0F; */
949
950 M(1,0) = (one_c * xy) + zs;
951 M(1,1) = (one_c * yy) + c;
952 M(1,2) = (one_c * yz) - xs;
953 /* M(1,3) = 0.0F; */
954
955 M(2,0) = (one_c * zx) - ys;
956 M(2,1) = (one_c * yz) + xs;
957 M(2,2) = (one_c * zz) + c;
958 /* M(2,3) = 0.0F; */
959
960 /*
961 M(3,0) = 0.0F;
962 M(3,1) = 0.0F;
963 M(3,2) = 0.0F;
964 M(3,3) = 1.0F;
965 */
966 }
967 #undef M
968
969 matrix_multf( mat, m, MAT_FLAG_ROTATION );
970 }
971
972 /**
973 * Apply a perspective projection matrix.
974 *
975 * \param mat matrix to apply the projection.
976 * \param left left clipping plane coordinate.
977 * \param right right clipping plane coordinate.
978 * \param bottom bottom clipping plane coordinate.
979 * \param top top clipping plane coordinate.
980 * \param nearval distance to the near clipping plane.
981 * \param farval distance to the far clipping plane.
982 *
983 * Creates the projection matrix and multiplies it with \p mat, marking the
984 * MAT_FLAG_PERSPECTIVE flag.
985 */
986 void
_math_matrix_frustum(GLmatrix * mat,GLfloat left,GLfloat right,GLfloat bottom,GLfloat top,GLfloat nearval,GLfloat farval)987 _math_matrix_frustum( GLmatrix *mat,
988 GLfloat left, GLfloat right,
989 GLfloat bottom, GLfloat top,
990 GLfloat nearval, GLfloat farval )
991 {
992 GLfloat x, y, a, b, c, d;
993 GLfloat m[16];
994
995 x = (2.0F*nearval) / (right-left);
996 y = (2.0F*nearval) / (top-bottom);
997 a = (right+left) / (right-left);
998 b = (top+bottom) / (top-bottom);
999 c = -(farval+nearval) / ( farval-nearval);
1000 d = -(2.0F*farval*nearval) / (farval-nearval); /* error? */
1001
1002 if (0)
1003 {
1004 c /= farval; // linearize z in vs by gl_Position.z *= gl_Position.w
1005 d /= farval;
1006 }
1007
1008 #define M(row,col) m[col*4+row]
1009 M(0,0) = x; M(0,1) = 0.0F; M(0,2) = a; M(0,3) = 0.0F;
1010 M(1,0) = 0.0F; M(1,1) = y; M(1,2) = b; M(1,3) = 0.0F;
1011 M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = c; M(2,3) = d;
1012 M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = -1.0F; M(3,3) = 0.0F;
1013 #undef M
1014
1015 matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE );
1016 }
1017
1018 /**
1019 * Apply an orthographic projection matrix.
1020 *
1021 * \param mat matrix to apply the projection.
1022 * \param left left clipping plane coordinate.
1023 * \param right right clipping plane coordinate.
1024 * \param bottom bottom clipping plane coordinate.
1025 * \param top top clipping plane coordinate.
1026 * \param nearval distance to the near clipping plane.
1027 * \param farval distance to the far clipping plane.
1028 *
1029 * Creates the projection matrix and multiplies it with \p mat, marking the
1030 * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
1031 */
1032 void
_math_matrix_ortho(GLmatrix * mat,GLfloat left,GLfloat right,GLfloat bottom,GLfloat top,GLfloat nearval,GLfloat farval)1033 _math_matrix_ortho( GLmatrix *mat,
1034 GLfloat left, GLfloat right,
1035 GLfloat bottom, GLfloat top,
1036 GLfloat nearval, GLfloat farval )
1037 {
1038 GLfloat m[16];
1039
1040 #define M(row,col) m[col*4+row]
1041 M(0,0) = 2.0F / (right-left);
1042 M(0,1) = 0.0F;
1043 M(0,2) = 0.0F;
1044 M(0,3) = -(right+left) / (right-left);
1045
1046 M(1,0) = 0.0F;
1047 M(1,1) = 2.0F / (top-bottom);
1048 M(1,2) = 0.0F;
1049 M(1,3) = -(top+bottom) / (top-bottom);
1050
1051 M(2,0) = 0.0F;
1052 M(2,1) = 0.0F;
1053 M(2,2) = -2.0F / (farval-nearval);
1054 M(2,3) = -(farval+nearval) / (farval-nearval);
1055
1056 M(3,0) = 0.0F;
1057 M(3,1) = 0.0F;
1058 M(3,2) = 0.0F;
1059 M(3,3) = 1.0F;
1060 #undef M
1061
1062 matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION));
1063 }
1064
1065 // multiplies mat by a perspective transform matrix
_math_matrix_perspective(GLmatrix * mat,GLfloat fovy,GLfloat aspect,GLfloat zNear,GLfloat zFar)1066 void _math_matrix_perspective(GLmatrix * mat, GLfloat fovy, GLfloat aspect,
1067 GLfloat zNear, GLfloat zFar)
1068 {
1069 GLfloat xmin, xmax, ymin, ymax;
1070
1071 ymax = zNear * tan(fovy * M_PI / 360.0);
1072 ymin = -ymax;
1073 xmin = ymin * aspect;
1074 xmax = ymax * aspect;
1075
1076 _math_matrix_frustum(mat, xmin, xmax, ymin, ymax, zNear, zFar);
1077 }
1078
1079 // multiplies mat by a look at matrix
_math_matrix_lookat(GLmatrix * mat,GLfloat eyex,GLfloat eyey,GLfloat eyez,GLfloat centerx,GLfloat centery,GLfloat centerz,GLfloat upx,GLfloat upy,GLfloat upz)1080 void _math_matrix_lookat(GLmatrix * mat, GLfloat eyex, GLfloat eyey, GLfloat eyez,
1081 GLfloat centerx, GLfloat centery, GLfloat centerz,
1082 GLfloat upx, GLfloat upy, GLfloat upz)
1083 {
1084 GLfloat m[16];
1085 GLfloat x[3], y[3], z[3];
1086 GLfloat mag;
1087
1088 /* Make rotation matrix */
1089
1090 /* Z vector */
1091 z[0] = eyex - centerx;
1092 z[1] = eyey - centery;
1093 z[2] = eyez - centerz;
1094 mag = sqrt(z[0] * z[0] + z[1] * z[1] + z[2] * z[2]);
1095 if (mag) { /* mpichler, 19950515 */
1096 z[0] /= mag;
1097 z[1] /= mag;
1098 z[2] /= mag;
1099 }
1100
1101 /* Y vector */
1102 y[0] = upx;
1103 y[1] = upy;
1104 y[2] = upz;
1105
1106 /* X vector = Y cross Z */
1107 x[0] = y[1] * z[2] - y[2] * z[1];
1108 x[1] = -y[0] * z[2] + y[2] * z[0];
1109 x[2] = y[0] * z[1] - y[1] * z[0];
1110
1111 /* Recompute Y = Z cross X */
1112 y[0] = z[1] * x[2] - z[2] * x[1];
1113 y[1] = -z[0] * x[2] + z[2] * x[0];
1114 y[2] = z[0] * x[1] - z[1] * x[0];
1115
1116 /* mpichler, 19950515 */
1117 /* cross product gives area of parallelogram, which is < 1.0 for
1118 * non-perpendicular unit-length vectors; so normalize x, y here
1119 */
1120
1121 mag = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
1122 if (mag) {
1123 x[0] /= mag;
1124 x[1] /= mag;
1125 x[2] /= mag;
1126 }
1127
1128 mag = sqrt(y[0] * y[0] + y[1] * y[1] + y[2] * y[2]);
1129 if (mag) {
1130 y[0] /= mag;
1131 y[1] /= mag;
1132 y[2] /= mag;
1133 }
1134
1135 #define M(row,col) m[col*4+row]
1136 M(0, 0) = x[0];
1137 M(0, 1) = x[1];
1138 M(0, 2) = x[2];
1139 M(0, 3) = 0.0;
1140 M(1, 0) = y[0];
1141 M(1, 1) = y[1];
1142 M(1, 2) = y[2];
1143 M(1, 3) = 0.0;
1144 M(2, 0) = z[0];
1145 M(2, 1) = z[1];
1146 M(2, 2) = z[2];
1147 M(2, 3) = 0.0;
1148 M(3, 0) = 0.0;
1149 M(3, 1) = 0.0;
1150 M(3, 2) = 0.0;
1151 M(3, 3) = 1.0;
1152 #undef M
1153
1154 GLfloat translate[16] =
1155 {
1156 1, 0, 0, 0,
1157 0, 1, 0, 0,
1158 0, 0, 1, 0,
1159 -eyex, -eyey, -eyez, 1,
1160 };
1161
1162 _math_matrix_mul_floats(mat, m);
1163
1164 _math_matrix_mul_floats(mat, translate);
1165
1166 /* Translate Eye to Origin */
1167 // glTranslated(-eyex, -eyey, -eyez);
1168
1169 }
1170
1171 /**
1172 * Multiply a matrix with a general scaling matrix.
1173 *
1174 * \param mat matrix.
1175 * \param x x axis scale factor.
1176 * \param y y axis scale factor.
1177 * \param z z axis scale factor.
1178 *
1179 * Multiplies in-place the elements of \p mat by the scale factors. Checks if
1180 * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
1181 * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
1182 * MAT_DIRTY_INVERSE dirty flags.
1183 */
1184 void
_math_matrix_scale(GLmatrix * mat,GLfloat x,GLfloat y,GLfloat z)1185 _math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
1186 {
1187 GLfloat *m = mat->m;
1188 m[0] *= x; m[4] *= y; m[8] *= z;
1189 m[1] *= x; m[5] *= y; m[9] *= z;
1190 m[2] *= x; m[6] *= y; m[10] *= z;
1191 m[3] *= x; m[7] *= y; m[11] *= z;
1192
1193 if (FABSF(x - y) < 1e-8 && FABSF(x - z) < 1e-8)
1194 mat->flags |= MAT_FLAG_UNIFORM_SCALE;
1195 else
1196 mat->flags |= MAT_FLAG_GENERAL_SCALE;
1197
1198 mat->flags |= (MAT_DIRTY_TYPE |
1199 MAT_DIRTY_INVERSE);
1200 }
1201
1202 /**
1203 * Multiply a matrix with a translation matrix.
1204 *
1205 * \param mat matrix.
1206 * \param x translation vector x coordinate.
1207 * \param y translation vector y coordinate.
1208 * \param z translation vector z coordinate.
1209 *
1210 * Adds the translation coordinates to the elements of \p mat in-place. Marks
1211 * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
1212 * dirty flags.
1213 */
1214 void
_math_matrix_translate(GLmatrix * mat,GLfloat x,GLfloat y,GLfloat z)1215 _math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
1216 {
1217 GLfloat *m = mat->m;
1218 m[12] = m[0] * x + m[4] * y + m[8] * z + m[12];
1219 m[13] = m[1] * x + m[5] * y + m[9] * z + m[13];
1220 m[14] = m[2] * x + m[6] * y + m[10] * z + m[14];
1221 m[15] = m[3] * x + m[7] * y + m[11] * z + m[15];
1222
1223 mat->flags |= (MAT_FLAG_TRANSLATION |
1224 MAT_DIRTY_TYPE |
1225 MAT_DIRTY_INVERSE);
1226 }
1227
1228
1229 /**
1230 * Set matrix to do viewport and depthrange mapping.
1231 * Transforms Normalized Device Coords to window/Z values.
1232 */
1233 void
_math_matrix_viewport(GLmatrix * m,GLint x,GLint y,GLint width,GLint height,GLfloat zNear,GLfloat zFar,GLfloat depthMax)1234 _math_matrix_viewport(GLmatrix *m, GLint x, GLint y, GLint width, GLint height,
1235 GLfloat zNear, GLfloat zFar, GLfloat depthMax)
1236 {
1237 m->m[MAT_SX] = (GLfloat) width / 2.0F;
1238 m->m[MAT_TX] = m->m[MAT_SX] + x;
1239 m->m[MAT_SY] = (GLfloat) height / 2.0F;
1240 m->m[MAT_TY] = m->m[MAT_SY] + y;
1241 m->m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0F);
1242 m->m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0F + zNear);
1243 m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION;
1244 m->type = MATRIX_3D_NO_ROT;
1245 }
1246
1247
1248 /**
1249 * Set a matrix to the identity matrix.
1250 *
1251 * \param mat matrix.
1252 *
1253 * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
1254 * Sets the matrix type to identity, and clear the dirty flags.
1255 */
1256 void
_math_matrix_set_identity(GLmatrix * mat)1257 _math_matrix_set_identity( GLmatrix *mat )
1258 {
1259 memcpy( mat->m, Identity, 16*sizeof(GLfloat) );
1260
1261 if (mat->inv)
1262 memcpy( mat->inv, Identity, 16*sizeof(GLfloat) );
1263
1264 mat->type = MATRIX_IDENTITY;
1265 mat->flags &= ~(MAT_DIRTY_FLAGS|
1266 MAT_DIRTY_TYPE|
1267 MAT_DIRTY_INVERSE);
1268 }
1269
1270 /*@}*/
1271
1272
1273 /**********************************************************************/
1274 /** \name Matrix analysis */
1275 /*@{*/
1276
1277 #define ZERO(x) (1<<x)
1278 #define ONE(x) (1<<(x+16))
1279
1280 #define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14))
1281 #define MASK_NO_2D_SCALE ( ONE(0) | ONE(5))
1282
1283 #define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\
1284 ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\
1285 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1286 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1287
1288 #define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \
1289 ZERO(1) | ZERO(9) | \
1290 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1291 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1292
1293 #define MASK_2D ( ZERO(8) | \
1294 ZERO(9) | \
1295 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1296 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1297
1298
1299 #define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \
1300 ZERO(1) | ZERO(9) | \
1301 ZERO(2) | ZERO(6) | \
1302 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1303
1304 #define MASK_3D ( \
1305 \
1306 \
1307 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1308
1309
1310 #define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\
1311 ZERO(1) | ZERO(13) |\
1312 ZERO(2) | ZERO(6) | \
1313 ZERO(3) | ZERO(7) | ZERO(15) )
1314
1315 #define SQ(x) ((x)*(x))
1316
1317 /**
1318 * Determine type and flags from scratch.
1319 *
1320 * \param mat matrix.
1321 *
1322 * This is expensive enough to only want to do it once.
1323 */
analyse_from_scratch(GLmatrix * mat)1324 static void analyse_from_scratch( GLmatrix *mat )
1325 {
1326 const GLfloat *m = mat->m;
1327 GLuint mask = 0;
1328 GLuint i;
1329
1330 for (i = 0 ; i < 16 ; i++) {
1331 if (m[i] == 0.0) mask |= (1<<i);
1332 }
1333
1334 if (m[0] == 1.0F) mask |= (1<<16);
1335 if (m[5] == 1.0F) mask |= (1<<21);
1336 if (m[10] == 1.0F) mask |= (1<<26);
1337 if (m[15] == 1.0F) mask |= (1<<31);
1338
1339 mat->flags &= ~MAT_FLAGS_GEOMETRY;
1340
1341 /* Check for translation - no-one really cares
1342 */
1343 if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
1344 mat->flags |= MAT_FLAG_TRANSLATION;
1345
1346 /* Do the real work
1347 */
1348 if (mask == (GLuint) MASK_IDENTITY) {
1349 mat->type = MATRIX_IDENTITY;
1350 }
1351 else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) {
1352 mat->type = MATRIX_2D_NO_ROT;
1353
1354 if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE)
1355 mat->flags |= MAT_FLAG_GENERAL_SCALE;
1356 }
1357 else if ((mask & MASK_2D) == (GLuint) MASK_2D) {
1358 GLfloat mm = DOT2(m, m);
1359 GLfloat m4m4 = DOT2(m+4,m+4);
1360 GLfloat mm4 = DOT2(m,m+4);
1361
1362 mat->type = MATRIX_2D;
1363
1364 /* Check for scale */
1365 if (SQ(mm-1) > SQ(1e-6) ||
1366 SQ(m4m4-1) > SQ(1e-6))
1367 mat->flags |= MAT_FLAG_GENERAL_SCALE;
1368
1369 /* Check for rotation */
1370 if (SQ(mm4) > SQ(1e-6))
1371 mat->flags |= MAT_FLAG_GENERAL_3D;
1372 else
1373 mat->flags |= MAT_FLAG_ROTATION;
1374
1375 }
1376 else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) {
1377 mat->type = MATRIX_3D_NO_ROT;
1378
1379 /* Check for scale */
1380 if (SQ(m[0]-m[5]) < SQ(1e-6) &&
1381 SQ(m[0]-m[10]) < SQ(1e-6)) {
1382 if (SQ(m[0]-1.0) > SQ(1e-6)) {
1383 mat->flags |= MAT_FLAG_UNIFORM_SCALE;
1384 }
1385 }
1386 else {
1387 mat->flags |= MAT_FLAG_GENERAL_SCALE;
1388 }
1389 }
1390 else if ((mask & MASK_3D) == (GLuint) MASK_3D) {
1391 GLfloat c1 = DOT3(m,m);
1392 GLfloat c2 = DOT3(m+4,m+4);
1393 GLfloat c3 = DOT3(m+8,m+8);
1394 GLfloat d1 = DOT3(m, m+4);
1395 GLfloat cp[3];
1396
1397 mat->type = MATRIX_3D;
1398
1399 /* Check for scale */
1400 if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) {
1401 if (SQ(c1-1.0) > SQ(1e-6))
1402 mat->flags |= MAT_FLAG_UNIFORM_SCALE;
1403 /* else no scale at all */
1404 }
1405 else {
1406 mat->flags |= MAT_FLAG_GENERAL_SCALE;
1407 }
1408
1409 /* Check for rotation */
1410 if (SQ(d1) < SQ(1e-6)) {
1411 CROSS3( cp, m, m+4 );
1412 SUB_3V( cp, cp, (m+8) );
1413 if (LEN_SQUARED_3FV(cp) < SQ(1e-6))
1414 mat->flags |= MAT_FLAG_ROTATION;
1415 else
1416 mat->flags |= MAT_FLAG_GENERAL_3D;
1417 }
1418 else {
1419 mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */
1420 }
1421 }
1422 else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) {
1423 mat->type = MATRIX_PERSPECTIVE;
1424 mat->flags |= MAT_FLAG_GENERAL;
1425 }
1426 else {
1427 mat->type = MATRIX_GENERAL;
1428 mat->flags |= MAT_FLAG_GENERAL;
1429 }
1430 }
1431
1432 /**
1433 * Analyze a matrix given that its flags are accurate.
1434 *
1435 * This is the more common operation, hopefully.
1436 */
analyse_from_flags(GLmatrix * mat)1437 static void analyse_from_flags( GLmatrix *mat )
1438 {
1439 const GLfloat *m = mat->m;
1440
1441 if (TEST_MAT_FLAGS(mat, 0)) {
1442 mat->type = MATRIX_IDENTITY;
1443 }
1444 else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION |
1445 MAT_FLAG_UNIFORM_SCALE |
1446 MAT_FLAG_GENERAL_SCALE))) {
1447 if ( m[10]==1.0F && m[14]==0.0F ) {
1448 mat->type = MATRIX_2D_NO_ROT;
1449 }
1450 else {
1451 mat->type = MATRIX_3D_NO_ROT;
1452 }
1453 }
1454 else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) {
1455 if ( m[ 8]==0.0F
1456 && m[ 9]==0.0F
1457 && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) {
1458 mat->type = MATRIX_2D;
1459 }
1460 else {
1461 mat->type = MATRIX_3D;
1462 }
1463 }
1464 else if ( m[4]==0.0F && m[12]==0.0F
1465 && m[1]==0.0F && m[13]==0.0F
1466 && m[2]==0.0F && m[6]==0.0F
1467 && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) {
1468 mat->type = MATRIX_PERSPECTIVE;
1469 }
1470 else {
1471 mat->type = MATRIX_GENERAL;
1472 }
1473 }
1474
1475 /**
1476 * Analyze and update a matrix.
1477 *
1478 * \param mat matrix.
1479 *
1480 * If the matrix type is dirty then calls either analyse_from_scratch() or
1481 * analyse_from_flags() to determine its type, according to whether the flags
1482 * are dirty or not, respectively. If the matrix has an inverse and it's dirty
1483 * then calls matrix_invert(). Finally clears the dirty flags.
1484 */
1485 void
_math_matrix_analyse(GLmatrix * mat)1486 _math_matrix_analyse( GLmatrix *mat )
1487 {
1488 if (mat->flags & MAT_DIRTY_TYPE) {
1489 if (mat->flags & MAT_DIRTY_FLAGS)
1490 analyse_from_scratch( mat );
1491 else
1492 analyse_from_flags( mat );
1493 }
1494
1495 if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) {
1496 matrix_invert( mat );
1497 mat->flags &= ~MAT_DIRTY_INVERSE;
1498 }
1499
1500 mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE);
1501 }
1502
1503 /*@}*/
1504
1505
1506 /**
1507 * Test if the given matrix preserves vector lengths.
1508 */
1509 GLboolean
_math_matrix_is_length_preserving(const GLmatrix * m)1510 _math_matrix_is_length_preserving( const GLmatrix *m )
1511 {
1512 return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING);
1513 }
1514
1515
1516 /**
1517 * Test if the given matrix does any rotation.
1518 * (or perhaps if the upper-left 3x3 is non-identity)
1519 */
1520 GLboolean
_math_matrix_has_rotation(const GLmatrix * m)1521 _math_matrix_has_rotation( const GLmatrix *m )
1522 {
1523 if (m->flags & (MAT_FLAG_GENERAL |
1524 MAT_FLAG_ROTATION |
1525 MAT_FLAG_GENERAL_3D |
1526 MAT_FLAG_PERSPECTIVE))
1527 return GL_TRUE;
1528 else
1529 return GL_FALSE;
1530 }
1531
1532
1533 GLboolean
_math_matrix_is_general_scale(const GLmatrix * m)1534 _math_matrix_is_general_scale( const GLmatrix *m )
1535 {
1536 return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE;
1537 }
1538
1539
1540 GLboolean
_math_matrix_is_dirty(const GLmatrix * m)1541 _math_matrix_is_dirty( const GLmatrix *m )
1542 {
1543 return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE;
1544 }
1545
1546
1547 /**********************************************************************/
1548 /** \name Matrix setup */
1549 /*@{*/
1550
1551 /**
1552 * Copy a matrix.
1553 *
1554 * \param to destination matrix.
1555 * \param from source matrix.
1556 *
1557 * Copies all fields in GLmatrix, creating an inverse array if necessary.
1558 */
1559 void
_math_matrix_copy(GLmatrix * to,const GLmatrix * from)1560 _math_matrix_copy( GLmatrix *to, const GLmatrix *from )
1561 {
1562 memcpy( to->m, from->m, sizeof(Identity) );
1563 to->flags = from->flags;
1564 to->type = from->type;
1565
1566 if (to->inv != 0) {
1567 if (from->inv == 0) {
1568 matrix_invert( to );
1569 }
1570 else {
1571 memcpy(to->inv, from->inv, sizeof(GLfloat)*16);
1572 }
1573 }
1574 }
1575
1576 /**
1577 * Loads a matrix array into GLmatrix.
1578 *
1579 * \param m matrix array.
1580 * \param mat matrix.
1581 *
1582 * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
1583 * flags.
1584 */
1585 void
_math_matrix_loadf(GLmatrix * mat,const GLfloat * m)1586 _math_matrix_loadf( GLmatrix *mat, const GLfloat *m )
1587 {
1588 memcpy( mat->m, m, 16*sizeof(GLfloat) );
1589 mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);
1590 }
1591
1592 /**
1593 * Matrix constructor.
1594 *
1595 * \param m matrix.
1596 *
1597 * Initialize the GLmatrix fields.
1598 */
1599 void
_math_matrix_ctr(GLmatrix * m)1600 _math_matrix_ctr( GLmatrix *m )
1601 {
1602 //m->m = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 );
1603 if (m->m)
1604 memcpy( m->m, Identity, sizeof(Identity) );
1605 m->inv = NULL;
1606 m->type = MATRIX_IDENTITY;
1607 m->flags = 0;
1608 }
1609
1610 /**
1611 * Matrix destructor.
1612 *
1613 * \param m matrix.
1614 *
1615 * Frees the data in a GLmatrix.
1616 */
1617 void
_math_matrix_dtr(GLmatrix * m)1618 _math_matrix_dtr( GLmatrix *m )
1619 {
1620 if (m->m) {
1621 //ALIGN_FREE( m->m );
1622 //m->m = NULL;
1623 }
1624 if (m->inv) {
1625 free( m->inv );
1626 m->inv = NULL;
1627 }
1628 }
1629
1630 /**
1631 * Allocate a matrix inverse.
1632 *
1633 * \param m matrix.
1634 *
1635 * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity.
1636 */
1637 void
_math_matrix_alloc_inv(GLmatrix * m)1638 _math_matrix_alloc_inv( GLmatrix *m )
1639 {
1640 if (!m->inv) {
1641 m->inv = (GLfloat *) malloc( 16 * sizeof(GLfloat));
1642 if (m->inv)
1643 memcpy( m->inv, Identity, 16 * sizeof(GLfloat) );
1644 }
1645 }
1646
1647 /*@}*/
1648
1649
1650 /**********************************************************************/
1651 /** \name Matrix transpose */
1652 /*@{*/
1653
1654 /**
1655 * Transpose a GLfloat matrix.
1656 *
1657 * \param to destination array.
1658 * \param from source array.
1659 */
1660 void
_math_transposef(GLfloat to[16],const GLfloat from[16])1661 _math_transposef( GLfloat to[16], const GLfloat from[16] )
1662 {
1663 to[0] = from[0];
1664 to[1] = from[4];
1665 to[2] = from[8];
1666 to[3] = from[12];
1667 to[4] = from[1];
1668 to[5] = from[5];
1669 to[6] = from[9];
1670 to[7] = from[13];
1671 to[8] = from[2];
1672 to[9] = from[6];
1673 to[10] = from[10];
1674 to[11] = from[14];
1675 to[12] = from[3];
1676 to[13] = from[7];
1677 to[14] = from[11];
1678 to[15] = from[15];
1679 }
1680
1681
1682 /**
1683 * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This
1684 * function is used for transforming clipping plane equations and spotlight
1685 * directions.
1686 * Mathematically, u = v * m.
1687 * Input: v - input vector
1688 * m - transformation matrix
1689 * Output: u - transformed vector
1690 */
1691 void
_mesa_transform_vector(GLfloat u[4],const GLfloat v[4],const GLfloat m[16])1692 _mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] )
1693 {
1694 const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3];
1695 #define M(row,col) m[row + col*4]
1696 u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0);
1697 u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1);
1698 u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2);
1699 u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3);
1700 #undef M
1701 }
1702