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1 /*
2  * Mesa 3-D graphics library
3  *
4  * Copyright (C) 1999-2005  Brian Paul   All Rights Reserved.
5  *
6  * Permission is hereby granted, free of charge, to any person obtaining a
7  * copy of this software and associated documentation files (the "Software"),
8  * to deal in the Software without restriction, including without limitation
9  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
10  * and/or sell copies of the Software, and to permit persons to whom the
11  * Software is furnished to do so, subject to the following conditions:
12  *
13  * The above copyright notice and this permission notice shall be included
14  * in all copies or substantial portions of the Software.
15  *
16  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
17  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
18  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
19  * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
20  * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
21  * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
22  * 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 <stddef.h>
37 
38 #include "c99_math.h"
39 #include "main/errors.h"
40 #include "main/glheader.h"
41 #include "main/macros.h"
42 #define MATH_ASM_PTR_SIZE sizeof(void *)
43 #include "math/m_vector_asm.h"
44 
45 #include "m_matrix.h"
46 
47 #include "util/u_memory.h"
48 
49 
50 /**
51  * \defgroup MatFlags MAT_FLAG_XXX-flags
52  *
53  * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
54  */
55 /*@{*/
56 #define MAT_FLAG_IDENTITY       0     /**< is an identity matrix flag.
57                                        *   (Not actually used - the identity
58                                        *   matrix is identified by the absence
59                                        *   of all other flags.)
60                                        */
61 #define MAT_FLAG_GENERAL        0x1   /**< is a general matrix flag */
62 #define MAT_FLAG_ROTATION       0x2   /**< is a rotation matrix flag */
63 #define MAT_FLAG_TRANSLATION    0x4   /**< is a translation matrix flag */
64 #define MAT_FLAG_UNIFORM_SCALE  0x8   /**< is an uniform scaling matrix flag */
65 #define MAT_FLAG_GENERAL_SCALE  0x10  /**< is a general scaling matrix flag */
66 #define MAT_FLAG_GENERAL_3D     0x20  /**< general 3D matrix flag */
67 #define MAT_FLAG_PERSPECTIVE    0x40  /**< is a perspective proj matrix flag */
68 #define MAT_FLAG_SINGULAR       0x80  /**< is a singular matrix flag */
69 #define MAT_DIRTY_TYPE          0x100  /**< matrix type is dirty */
70 #define MAT_DIRTY_FLAGS         0x200  /**< matrix flags are dirty */
71 #define MAT_DIRTY_INVERSE       0x400  /**< matrix inverse is dirty */
72 
73 /** angle preserving matrix flags mask */
74 #define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
75 				    MAT_FLAG_TRANSLATION | \
76 				    MAT_FLAG_UNIFORM_SCALE)
77 
78 /** geometry related matrix flags mask */
79 #define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
80 			    MAT_FLAG_ROTATION | \
81 			    MAT_FLAG_TRANSLATION | \
82 			    MAT_FLAG_UNIFORM_SCALE | \
83 			    MAT_FLAG_GENERAL_SCALE | \
84 			    MAT_FLAG_GENERAL_3D | \
85 			    MAT_FLAG_PERSPECTIVE | \
86 	                    MAT_FLAG_SINGULAR)
87 
88 /** length preserving matrix flags mask */
89 #define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
90 				     MAT_FLAG_TRANSLATION)
91 
92 
93 /** 3D (non-perspective) matrix flags mask */
94 #define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
95 		      MAT_FLAG_TRANSLATION | \
96 		      MAT_FLAG_UNIFORM_SCALE | \
97 		      MAT_FLAG_GENERAL_SCALE | \
98 		      MAT_FLAG_GENERAL_3D)
99 
100 /** dirty matrix flags mask */
101 #define MAT_DIRTY          (MAT_DIRTY_TYPE | \
102 			    MAT_DIRTY_FLAGS | \
103 			    MAT_DIRTY_INVERSE)
104 
105 /*@}*/
106 
107 
108 /**
109  * Test geometry related matrix flags.
110  *
111  * \param mat a pointer to a GLmatrix structure.
112  * \param a flags mask.
113  *
114  * \returns non-zero if all geometry related matrix flags are contained within
115  * the mask, or zero otherwise.
116  */
117 #define TEST_MAT_FLAGS(mat, a)  \
118     ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
119 
120 
121 
122 /**
123  * Names of the corresponding GLmatrixtype values.
124  */
125 static const char *types[] = {
126    "MATRIX_GENERAL",
127    "MATRIX_IDENTITY",
128    "MATRIX_3D_NO_ROT",
129    "MATRIX_PERSPECTIVE",
130    "MATRIX_2D",
131    "MATRIX_2D_NO_ROT",
132    "MATRIX_3D"
133 };
134 
135 
136 /**
137  * Identity matrix.
138  */
139 static const GLfloat Identity[16] = {
140    1.0, 0.0, 0.0, 0.0,
141    0.0, 1.0, 0.0, 0.0,
142    0.0, 0.0, 1.0, 0.0,
143    0.0, 0.0, 0.0, 1.0
144 };
145 
146 
147 
148 /**********************************************************************/
149 /** \name Matrix multiplication */
150 /*@{*/
151 
152 #define A(row,col)  a[(col<<2)+row]
153 #define B(row,col)  b[(col<<2)+row]
154 #define P(row,col)  product[(col<<2)+row]
155 
156 /**
157  * Perform a full 4x4 matrix multiplication.
158  *
159  * \param a matrix.
160  * \param b matrix.
161  * \param product will receive the product of \p a and \p b.
162  *
163  * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
164  *
165  * \note KW: 4*16 = 64 multiplications
166  *
167  * \author This \c matmul was contributed by Thomas Malik
168  */
matmul4(GLfloat * product,const GLfloat * a,const GLfloat * b)169 static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b )
170 {
171    GLint i;
172    for (i = 0; i < 4; i++) {
173       const GLfloat ai0=A(i,0),  ai1=A(i,1),  ai2=A(i,2),  ai3=A(i,3);
174       P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
175       P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
176       P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
177       P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3);
178    }
179 }
180 
181 /**
182  * Multiply two matrices known to occupy only the top three rows, such
183  * as typical model matrices, and orthogonal matrices.
184  *
185  * \param a matrix.
186  * \param b matrix.
187  * \param product will receive the product of \p a and \p b.
188  */
matmul34(GLfloat * product,const GLfloat * a,const GLfloat * b)189 static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b )
190 {
191    GLint i;
192    for (i = 0; i < 3; i++) {
193       const GLfloat ai0=A(i,0),  ai1=A(i,1),  ai2=A(i,2),  ai3=A(i,3);
194       P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0);
195       P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1);
196       P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2);
197       P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3;
198    }
199    P(3,0) = 0;
200    P(3,1) = 0;
201    P(3,2) = 0;
202    P(3,3) = 1;
203 }
204 
205 #undef A
206 #undef B
207 #undef P
208 
209 /**
210  * Multiply a matrix by an array of floats with known properties.
211  *
212  * \param mat pointer to a GLmatrix structure containing the left multiplication
213  * matrix, and that will receive the product result.
214  * \param m right multiplication matrix array.
215  * \param flags flags of the matrix \p m.
216  *
217  * Joins both flags and marks the type and inverse as dirty.  Calls matmul34()
218  * if both matrices are 3D, or matmul4() otherwise.
219  */
matrix_multf(GLmatrix * mat,const GLfloat * m,GLuint flags)220 static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags )
221 {
222    mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
223 
224    if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D))
225       matmul34( mat->m, mat->m, m );
226    else
227       matmul4( mat->m, mat->m, m );
228 }
229 
230 /**
231  * Matrix multiplication.
232  *
233  * \param dest destination matrix.
234  * \param a left matrix.
235  * \param b right matrix.
236  *
237  * Joins both flags and marks the type and inverse as dirty.  Calls matmul34()
238  * if both matrices are 3D, or matmul4() otherwise.
239  */
240 void
_math_matrix_mul_matrix(GLmatrix * dest,const GLmatrix * a,const GLmatrix * b)241 _math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b )
242 {
243    dest->flags = (a->flags |
244 		  b->flags |
245 		  MAT_DIRTY_TYPE |
246 		  MAT_DIRTY_INVERSE);
247 
248    if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D))
249       matmul34( dest->m, a->m, b->m );
250    else
251       matmul4( dest->m, a->m, b->m );
252 }
253 
254 /**
255  * Matrix multiplication.
256  *
257  * \param dest left and destination matrix.
258  * \param m right matrix array.
259  *
260  * Marks the matrix flags with general flag, and type and inverse dirty flags.
261  * Calls matmul4() for the multiplication.
262  */
263 void
_math_matrix_mul_floats(GLmatrix * dest,const GLfloat * m)264 _math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m )
265 {
266    dest->flags |= (MAT_FLAG_GENERAL |
267 		   MAT_DIRTY_TYPE |
268 		   MAT_DIRTY_INVERSE |
269                    MAT_DIRTY_FLAGS);
270 
271    matmul4( dest->m, dest->m, m );
272 }
273 
274 /*@}*/
275 
276 
277 /**********************************************************************/
278 /** \name Matrix output */
279 /*@{*/
280 
281 /**
282  * Print a matrix array.
283  *
284  * \param m matrix array.
285  *
286  * Called by _math_matrix_print() to print a matrix or its inverse.
287  */
print_matrix_floats(const GLfloat m[16])288 static void print_matrix_floats( const GLfloat m[16] )
289 {
290    int i;
291    for (i=0;i<4;i++) {
292       _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
293    }
294 }
295 
296 /**
297  * Dumps the contents of a GLmatrix structure.
298  *
299  * \param m pointer to the GLmatrix structure.
300  */
301 void
_math_matrix_print(const GLmatrix * m)302 _math_matrix_print( const GLmatrix *m )
303 {
304    GLfloat prod[16];
305 
306    _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
307    print_matrix_floats(m->m);
308    _mesa_debug(NULL, "Inverse: \n");
309    print_matrix_floats(m->inv);
310    matmul4(prod, m->m, m->inv);
311    _mesa_debug(NULL, "Mat * Inverse:\n");
312    print_matrix_floats(prod);
313 }
314 
315 /*@}*/
316 
317 
318 /**
319  * References an element of 4x4 matrix.
320  *
321  * \param m matrix array.
322  * \param c column of the desired element.
323  * \param r row of the desired element.
324  *
325  * \return value of the desired element.
326  *
327  * Calculate the linear storage index of the element and references it.
328  */
329 #define MAT(m,r,c) (m)[(c)*4+(r)]
330 
331 
332 /**********************************************************************/
333 /** \name Matrix inversion */
334 /*@{*/
335 
336 /**
337  * Swaps the values of two floating point variables.
338  *
339  * Used by invert_matrix_general() to swap the row pointers.
340  */
341 #define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
342 
343 /**
344  * Compute inverse of 4x4 transformation matrix.
345  *
346  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
347  * stored in the GLmatrix::inv attribute.
348  *
349  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
350  *
351  * \author
352  * Code contributed by Jacques Leroy jle@star.be
353  *
354  * Calculates the inverse matrix by performing the gaussian matrix reduction
355  * with partial pivoting followed by back/substitution with the loops manually
356  * unrolled.
357  */
invert_matrix_general(GLmatrix * mat)358 static GLboolean invert_matrix_general( GLmatrix *mat )
359 {
360    const GLfloat *m = mat->m;
361    GLfloat *out = mat->inv;
362    GLfloat wtmp[4][8];
363    GLfloat m0, m1, m2, m3, s;
364    GLfloat *r0, *r1, *r2, *r3;
365 
366    r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
367 
368    r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1),
369    r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3),
370    r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
371 
372    r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1),
373    r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3),
374    r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
375 
376    r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1),
377    r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3),
378    r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
379 
380    r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1),
381    r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3),
382    r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
383 
384    /* choose pivot - or die */
385    if (fabsf(r3[0])>fabsf(r2[0])) SWAP_ROWS(r3, r2);
386    if (fabsf(r2[0])>fabsf(r1[0])) SWAP_ROWS(r2, r1);
387    if (fabsf(r1[0])>fabsf(r0[0])) SWAP_ROWS(r1, r0);
388    if (0.0F == r0[0])  return GL_FALSE;
389 
390    /* eliminate first variable     */
391    m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0];
392    s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
393    s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
394    s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
395    s = r0[4];
396    if (s != 0.0F) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
397    s = r0[5];
398    if (s != 0.0F) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
399    s = r0[6];
400    if (s != 0.0F) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
401    s = r0[7];
402    if (s != 0.0F) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
403 
404    /* choose pivot - or die */
405    if (fabsf(r3[1])>fabsf(r2[1])) SWAP_ROWS(r3, r2);
406    if (fabsf(r2[1])>fabsf(r1[1])) SWAP_ROWS(r2, r1);
407    if (0.0F == r1[1])  return GL_FALSE;
408 
409    /* eliminate second variable */
410    m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1];
411    r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2];
412    r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3];
413    s = r1[4]; if (0.0F != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
414    s = r1[5]; if (0.0F != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
415    s = r1[6]; if (0.0F != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
416    s = r1[7]; if (0.0F != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }
417 
418    /* choose pivot - or die */
419    if (fabsf(r3[2])>fabsf(r2[2])) SWAP_ROWS(r3, r2);
420    if (0.0F == r2[2])  return GL_FALSE;
421 
422    /* eliminate third variable */
423    m3 = r3[2]/r2[2];
424    r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
425    r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6],
426    r3[7] -= m3 * r2[7];
427 
428    /* last check */
429    if (0.0F == r3[3]) return GL_FALSE;
430 
431    s = 1.0F/r3[3];             /* now back substitute row 3 */
432    r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s;
433 
434    m2 = r2[3];                 /* now back substitute row 2 */
435    s  = 1.0F/r2[2];
436    r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
437    r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
438    m1 = r1[3];
439    r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
440    r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
441    m0 = r0[3];
442    r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
443    r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
444 
445    m1 = r1[2];                 /* now back substitute row 1 */
446    s  = 1.0F/r1[1];
447    r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
448    r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
449    m0 = r0[2];
450    r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
451    r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
452 
453    m0 = r0[1];                 /* now back substitute row 0 */
454    s  = 1.0F/r0[0];
455    r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
456    r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
457 
458    MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5],
459    MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7],
460    MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5],
461    MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7],
462    MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5],
463    MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7],
464    MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5],
465    MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7];
466 
467    return GL_TRUE;
468 }
469 #undef SWAP_ROWS
470 
471 /**
472  * Compute inverse of a general 3d transformation matrix.
473  *
474  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
475  * stored in the GLmatrix::inv attribute.
476  *
477  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
478  *
479  * \author Adapted from graphics gems II.
480  *
481  * Calculates the inverse of the upper left by first calculating its
482  * determinant and multiplying it to the symmetric adjust matrix of each
483  * element. Finally deals with the translation part by transforming the
484  * original translation vector using by the calculated submatrix inverse.
485  */
invert_matrix_3d_general(GLmatrix * mat)486 static GLboolean invert_matrix_3d_general( GLmatrix *mat )
487 {
488    const GLfloat *in = mat->m;
489    GLfloat *out = mat->inv;
490    GLfloat pos, neg, t;
491    GLfloat det;
492 
493    /* Calculate the determinant of upper left 3x3 submatrix and
494     * determine if the matrix is singular.
495     */
496    pos = neg = 0.0;
497    t =  MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2);
498    if (t >= 0.0F) pos += t; else neg += t;
499 
500    t =  MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2);
501    if (t >= 0.0F) pos += t; else neg += t;
502 
503    t =  MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2);
504    if (t >= 0.0F) pos += t; else neg += t;
505 
506    t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2);
507    if (t >= 0.0F) pos += t; else neg += t;
508 
509    t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2);
510    if (t >= 0.0F) pos += t; else neg += t;
511 
512    t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2);
513    if (t >= 0.0F) pos += t; else neg += t;
514 
515    det = pos + neg;
516 
517    if (fabsf(det) < 1e-25F)
518       return GL_FALSE;
519 
520    det = 1.0F / det;
521    MAT(out,0,0) = (  (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det);
522    MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det);
523    MAT(out,0,2) = (  (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det);
524    MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det);
525    MAT(out,1,1) = (  (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det);
526    MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det);
527    MAT(out,2,0) = (  (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det);
528    MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det);
529    MAT(out,2,2) = (  (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det);
530 
531    /* Do the translation part */
532    MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
533 		     MAT(in,1,3) * MAT(out,0,1) +
534 		     MAT(in,2,3) * MAT(out,0,2) );
535    MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
536 		     MAT(in,1,3) * MAT(out,1,1) +
537 		     MAT(in,2,3) * MAT(out,1,2) );
538    MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
539 		     MAT(in,1,3) * MAT(out,2,1) +
540 		     MAT(in,2,3) * MAT(out,2,2) );
541 
542    return GL_TRUE;
543 }
544 
545 /**
546  * Compute inverse of a 3d transformation matrix.
547  *
548  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
549  * stored in the GLmatrix::inv attribute.
550  *
551  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
552  *
553  * If the matrix is not an angle preserving matrix then calls
554  * invert_matrix_3d_general for the actual calculation. Otherwise calculates
555  * the inverse matrix analyzing and inverting each of the scaling, rotation and
556  * translation parts.
557  */
invert_matrix_3d(GLmatrix * mat)558 static GLboolean invert_matrix_3d( GLmatrix *mat )
559 {
560    const GLfloat *in = mat->m;
561    GLfloat *out = mat->inv;
562 
563    if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) {
564       return invert_matrix_3d_general( mat );
565    }
566 
567    if (mat->flags & MAT_FLAG_UNIFORM_SCALE) {
568       GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) +
569                        MAT(in,0,1) * MAT(in,0,1) +
570                        MAT(in,0,2) * MAT(in,0,2));
571 
572       if (scale == 0.0F)
573          return GL_FALSE;
574 
575       scale = 1.0F / scale;
576 
577       /* Transpose and scale the 3 by 3 upper-left submatrix. */
578       MAT(out,0,0) = scale * MAT(in,0,0);
579       MAT(out,1,0) = scale * MAT(in,0,1);
580       MAT(out,2,0) = scale * MAT(in,0,2);
581       MAT(out,0,1) = scale * MAT(in,1,0);
582       MAT(out,1,1) = scale * MAT(in,1,1);
583       MAT(out,2,1) = scale * MAT(in,1,2);
584       MAT(out,0,2) = scale * MAT(in,2,0);
585       MAT(out,1,2) = scale * MAT(in,2,1);
586       MAT(out,2,2) = scale * MAT(in,2,2);
587    }
588    else if (mat->flags & MAT_FLAG_ROTATION) {
589       /* Transpose the 3 by 3 upper-left submatrix. */
590       MAT(out,0,0) = MAT(in,0,0);
591       MAT(out,1,0) = MAT(in,0,1);
592       MAT(out,2,0) = MAT(in,0,2);
593       MAT(out,0,1) = MAT(in,1,0);
594       MAT(out,1,1) = MAT(in,1,1);
595       MAT(out,2,1) = MAT(in,1,2);
596       MAT(out,0,2) = MAT(in,2,0);
597       MAT(out,1,2) = MAT(in,2,1);
598       MAT(out,2,2) = MAT(in,2,2);
599    }
600    else {
601       /* pure translation */
602       memcpy( out, Identity, sizeof(Identity) );
603       MAT(out,0,3) = - MAT(in,0,3);
604       MAT(out,1,3) = - MAT(in,1,3);
605       MAT(out,2,3) = - MAT(in,2,3);
606       return GL_TRUE;
607    }
608 
609    if (mat->flags & MAT_FLAG_TRANSLATION) {
610       /* Do the translation part */
611       MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
612 			MAT(in,1,3) * MAT(out,0,1) +
613 			MAT(in,2,3) * MAT(out,0,2) );
614       MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
615 			MAT(in,1,3) * MAT(out,1,1) +
616 			MAT(in,2,3) * MAT(out,1,2) );
617       MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
618 			MAT(in,1,3) * MAT(out,2,1) +
619 			MAT(in,2,3) * MAT(out,2,2) );
620    }
621    else {
622       MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0;
623    }
624 
625    return GL_TRUE;
626 }
627 
628 /**
629  * Compute inverse of an identity transformation matrix.
630  *
631  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
632  * stored in the GLmatrix::inv attribute.
633  *
634  * \return always GL_TRUE.
635  *
636  * Simply copies Identity into GLmatrix::inv.
637  */
invert_matrix_identity(GLmatrix * mat)638 static GLboolean invert_matrix_identity( GLmatrix *mat )
639 {
640    memcpy( mat->inv, Identity, sizeof(Identity) );
641    return GL_TRUE;
642 }
643 
644 /**
645  * Compute inverse of a no-rotation 3d transformation matrix.
646  *
647  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
648  * stored in the GLmatrix::inv attribute.
649  *
650  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
651  *
652  * Calculates the
653  */
invert_matrix_3d_no_rot(GLmatrix * mat)654 static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat )
655 {
656    const GLfloat *in = mat->m;
657    GLfloat *out = mat->inv;
658 
659    if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 )
660       return GL_FALSE;
661 
662    memcpy( out, Identity, sizeof(Identity) );
663    MAT(out,0,0) = 1.0F / MAT(in,0,0);
664    MAT(out,1,1) = 1.0F / MAT(in,1,1);
665    MAT(out,2,2) = 1.0F / MAT(in,2,2);
666 
667    if (mat->flags & MAT_FLAG_TRANSLATION) {
668       MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
669       MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
670       MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2));
671    }
672 
673    return GL_TRUE;
674 }
675 
676 /**
677  * Compute inverse of a no-rotation 2d transformation matrix.
678  *
679  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
680  * stored in the GLmatrix::inv attribute.
681  *
682  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
683  *
684  * Calculates the inverse matrix by applying the inverse scaling and
685  * translation to the identity matrix.
686  */
invert_matrix_2d_no_rot(GLmatrix * mat)687 static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat )
688 {
689    const GLfloat *in = mat->m;
690    GLfloat *out = mat->inv;
691 
692    if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0)
693       return GL_FALSE;
694 
695    memcpy( out, Identity, sizeof(Identity) );
696    MAT(out,0,0) = 1.0F / MAT(in,0,0);
697    MAT(out,1,1) = 1.0F / MAT(in,1,1);
698 
699    if (mat->flags & MAT_FLAG_TRANSLATION) {
700       MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
701       MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
702    }
703 
704    return GL_TRUE;
705 }
706 
707 #if 0
708 /* broken */
709 static GLboolean invert_matrix_perspective( GLmatrix *mat )
710 {
711    const GLfloat *in = mat->m;
712    GLfloat *out = mat->inv;
713 
714    if (MAT(in,2,3) == 0)
715       return GL_FALSE;
716 
717    memcpy( out, Identity, sizeof(Identity) );
718 
719    MAT(out,0,0) = 1.0F / MAT(in,0,0);
720    MAT(out,1,1) = 1.0F / MAT(in,1,1);
721 
722    MAT(out,0,3) = MAT(in,0,2);
723    MAT(out,1,3) = MAT(in,1,2);
724 
725    MAT(out,2,2) = 0;
726    MAT(out,2,3) = -1;
727 
728    MAT(out,3,2) = 1.0F / MAT(in,2,3);
729    MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2);
730 
731    return GL_TRUE;
732 }
733 #endif
734 
735 /**
736  * Matrix inversion function pointer type.
737  */
738 typedef GLboolean (*inv_mat_func)( GLmatrix *mat );
739 
740 /**
741  * Table of the matrix inversion functions according to the matrix type.
742  */
743 static inv_mat_func inv_mat_tab[7] = {
744    invert_matrix_general,
745    invert_matrix_identity,
746    invert_matrix_3d_no_rot,
747 #if 0
748    /* Don't use this function for now - it fails when the projection matrix
749     * is premultiplied by a translation (ala Chromium's tilesort SPU).
750     */
751    invert_matrix_perspective,
752 #else
753    invert_matrix_general,
754 #endif
755    invert_matrix_3d,		/* lazy! */
756    invert_matrix_2d_no_rot,
757    invert_matrix_3d
758 };
759 
760 /**
761  * Compute inverse of a transformation matrix.
762  *
763  * \param mat pointer to a GLmatrix structure. The matrix inverse will be
764  * stored in the GLmatrix::inv attribute.
765  *
766  * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
767  *
768  * Calls the matrix inversion function in inv_mat_tab corresponding to the
769  * given matrix type.  In case of failure, updates the MAT_FLAG_SINGULAR flag,
770  * and copies the identity matrix into GLmatrix::inv.
771  */
matrix_invert(GLmatrix * mat)772 static GLboolean matrix_invert( GLmatrix *mat )
773 {
774    if (inv_mat_tab[mat->type](mat)) {
775       mat->flags &= ~MAT_FLAG_SINGULAR;
776       return GL_TRUE;
777    } else {
778       mat->flags |= MAT_FLAG_SINGULAR;
779       memcpy( mat->inv, Identity, sizeof(Identity) );
780       return GL_FALSE;
781    }
782 }
783 
784 /*@}*/
785 
786 
787 /**********************************************************************/
788 /** \name Matrix generation */
789 /*@{*/
790 
791 /**
792  * Generate a 4x4 transformation matrix from glRotate parameters, and
793  * post-multiply the input matrix by it.
794  *
795  * \author
796  * This function was contributed by Erich Boleyn (erich@uruk.org).
797  * Optimizations contributed by Rudolf Opalla (rudi@khm.de).
798  */
799 void
_math_matrix_rotate(GLmatrix * mat,GLfloat angle,GLfloat x,GLfloat y,GLfloat z)800 _math_matrix_rotate( GLmatrix *mat,
801 		     GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
802 {
803    GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
804    GLfloat m[16];
805    GLboolean optimized;
806 
807    s = sinf( angle * M_PI / 180.0 );
808    c = cosf( angle * M_PI / 180.0 );
809 
810    memcpy(m, Identity, sizeof(Identity));
811    optimized = GL_FALSE;
812 
813 #define M(row,col)  m[col*4+row]
814 
815    if (x == 0.0F) {
816       if (y == 0.0F) {
817          if (z != 0.0F) {
818             optimized = GL_TRUE;
819             /* rotate only around z-axis */
820             M(0,0) = c;
821             M(1,1) = c;
822             if (z < 0.0F) {
823                M(0,1) = s;
824                M(1,0) = -s;
825             }
826             else {
827                M(0,1) = -s;
828                M(1,0) = s;
829             }
830          }
831       }
832       else if (z == 0.0F) {
833          optimized = GL_TRUE;
834          /* rotate only around y-axis */
835          M(0,0) = c;
836          M(2,2) = c;
837          if (y < 0.0F) {
838             M(0,2) = -s;
839             M(2,0) = s;
840          }
841          else {
842             M(0,2) = s;
843             M(2,0) = -s;
844          }
845       }
846    }
847    else if (y == 0.0F) {
848       if (z == 0.0F) {
849          optimized = GL_TRUE;
850          /* rotate only around x-axis */
851          M(1,1) = c;
852          M(2,2) = c;
853          if (x < 0.0F) {
854             M(1,2) = s;
855             M(2,1) = -s;
856          }
857          else {
858             M(1,2) = -s;
859             M(2,1) = s;
860          }
861       }
862    }
863 
864    if (!optimized) {
865       const GLfloat mag = sqrtf(x * x + y * y + z * z);
866 
867       if (mag <= 1.0e-4F) {
868          /* no rotation, leave mat as-is */
869          return;
870       }
871 
872       x /= mag;
873       y /= mag;
874       z /= mag;
875 
876 
877       /*
878        *     Arbitrary axis rotation matrix.
879        *
880        *  This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
881        *  like so:  Rz * Ry * T * Ry' * Rz'.  T is the final rotation
882        *  (which is about the X-axis), and the two composite transforms
883        *  Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
884        *  from the arbitrary axis to the X-axis then back.  They are
885        *  all elementary rotations.
886        *
887        *  Rz' is a rotation about the Z-axis, to bring the axis vector
888        *  into the x-z plane.  Then Ry' is applied, rotating about the
889        *  Y-axis to bring the axis vector parallel with the X-axis.  The
890        *  rotation about the X-axis is then performed.  Ry and Rz are
891        *  simply the respective inverse transforms to bring the arbitrary
892        *  axis back to its original orientation.  The first transforms
893        *  Rz' and Ry' are considered inverses, since the data from the
894        *  arbitrary axis gives you info on how to get to it, not how
895        *  to get away from it, and an inverse must be applied.
896        *
897        *  The basic calculation used is to recognize that the arbitrary
898        *  axis vector (x, y, z), since it is of unit length, actually
899        *  represents the sines and cosines of the angles to rotate the
900        *  X-axis to the same orientation, with theta being the angle about
901        *  Z and phi the angle about Y (in the order described above)
902        *  as follows:
903        *
904        *  cos ( theta ) = x / sqrt ( 1 - z^2 )
905        *  sin ( theta ) = y / sqrt ( 1 - z^2 )
906        *
907        *  cos ( phi ) = sqrt ( 1 - z^2 )
908        *  sin ( phi ) = z
909        *
910        *  Note that cos ( phi ) can further be inserted to the above
911        *  formulas:
912        *
913        *  cos ( theta ) = x / cos ( phi )
914        *  sin ( theta ) = y / sin ( phi )
915        *
916        *  ...etc.  Because of those relations and the standard trigonometric
917        *  relations, it is pssible to reduce the transforms down to what
918        *  is used below.  It may be that any primary axis chosen will give the
919        *  same results (modulo a sign convention) using thie method.
920        *
921        *  Particularly nice is to notice that all divisions that might
922        *  have caused trouble when parallel to certain planes or
923        *  axis go away with care paid to reducing the expressions.
924        *  After checking, it does perform correctly under all cases, since
925        *  in all the cases of division where the denominator would have
926        *  been zero, the numerator would have been zero as well, giving
927        *  the expected result.
928        */
929 
930       xx = x * x;
931       yy = y * y;
932       zz = z * z;
933       xy = x * y;
934       yz = y * z;
935       zx = z * x;
936       xs = x * s;
937       ys = y * s;
938       zs = z * s;
939       one_c = 1.0F - c;
940 
941       /* We already hold the identity-matrix so we can skip some statements */
942       M(0,0) = (one_c * xx) + c;
943       M(0,1) = (one_c * xy) - zs;
944       M(0,2) = (one_c * zx) + ys;
945 /*    M(0,3) = 0.0F; */
946 
947       M(1,0) = (one_c * xy) + zs;
948       M(1,1) = (one_c * yy) + c;
949       M(1,2) = (one_c * yz) - xs;
950 /*    M(1,3) = 0.0F; */
951 
952       M(2,0) = (one_c * zx) - ys;
953       M(2,1) = (one_c * yz) + xs;
954       M(2,2) = (one_c * zz) + c;
955 /*    M(2,3) = 0.0F; */
956 
957 /*
958       M(3,0) = 0.0F;
959       M(3,1) = 0.0F;
960       M(3,2) = 0.0F;
961       M(3,3) = 1.0F;
962 */
963    }
964 #undef M
965 
966    matrix_multf( mat, m, MAT_FLAG_ROTATION );
967 }
968 
969 /**
970  * Apply a perspective projection matrix.
971  *
972  * \param mat matrix to apply the projection.
973  * \param left left clipping plane coordinate.
974  * \param right right clipping plane coordinate.
975  * \param bottom bottom clipping plane coordinate.
976  * \param top top clipping plane coordinate.
977  * \param nearval distance to the near clipping plane.
978  * \param farval distance to the far clipping plane.
979  *
980  * Creates the projection matrix and multiplies it with \p mat, marking the
981  * MAT_FLAG_PERSPECTIVE flag.
982  */
983 void
_math_matrix_frustum(GLmatrix * mat,GLfloat left,GLfloat right,GLfloat bottom,GLfloat top,GLfloat nearval,GLfloat farval)984 _math_matrix_frustum( GLmatrix *mat,
985 		      GLfloat left, GLfloat right,
986 		      GLfloat bottom, GLfloat top,
987 		      GLfloat nearval, GLfloat farval )
988 {
989    GLfloat x, y, a, b, c, d;
990    GLfloat m[16];
991 
992    x = (2.0F*nearval) / (right-left);
993    y = (2.0F*nearval) / (top-bottom);
994    a = (right+left) / (right-left);
995    b = (top+bottom) / (top-bottom);
996    c = -(farval+nearval) / ( farval-nearval);
997    d = -(2.0F*farval*nearval) / (farval-nearval);  /* error? */
998 
999 #define M(row,col)  m[col*4+row]
1000    M(0,0) = x;     M(0,1) = 0.0F;  M(0,2) = a;      M(0,3) = 0.0F;
1001    M(1,0) = 0.0F;  M(1,1) = y;     M(1,2) = b;      M(1,3) = 0.0F;
1002    M(2,0) = 0.0F;  M(2,1) = 0.0F;  M(2,2) = c;      M(2,3) = d;
1003    M(3,0) = 0.0F;  M(3,1) = 0.0F;  M(3,2) = -1.0F;  M(3,3) = 0.0F;
1004 #undef M
1005 
1006    matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE );
1007 }
1008 
1009 /**
1010  * Create an orthographic projection matrix.
1011  *
1012  * \param m float array in which to store the project matrix
1013  * \param left left clipping plane coordinate.
1014  * \param right right clipping plane coordinate.
1015  * \param bottom bottom clipping plane coordinate.
1016  * \param top top clipping plane coordinate.
1017  * \param nearval distance to the near clipping plane.
1018  * \param farval distance to the far clipping plane.
1019  *
1020  * Creates the projection matrix and stored the values in \p m.  As with other
1021  * OpenGL matrices, the data is stored in column-major ordering.
1022  */
1023 void
_math_float_ortho(float * m,float left,float right,float bottom,float top,float nearval,float farval)1024 _math_float_ortho(float *m,
1025                   float left, float right,
1026                   float bottom, float top,
1027                   float nearval, float farval)
1028 {
1029 #define M(row,col)  m[col*4+row]
1030    M(0,0) = 2.0F / (right-left);
1031    M(0,1) = 0.0F;
1032    M(0,2) = 0.0F;
1033    M(0,3) = -(right+left) / (right-left);
1034 
1035    M(1,0) = 0.0F;
1036    M(1,1) = 2.0F / (top-bottom);
1037    M(1,2) = 0.0F;
1038    M(1,3) = -(top+bottom) / (top-bottom);
1039 
1040    M(2,0) = 0.0F;
1041    M(2,1) = 0.0F;
1042    M(2,2) = -2.0F / (farval-nearval);
1043    M(2,3) = -(farval+nearval) / (farval-nearval);
1044 
1045    M(3,0) = 0.0F;
1046    M(3,1) = 0.0F;
1047    M(3,2) = 0.0F;
1048    M(3,3) = 1.0F;
1049 #undef M
1050 }
1051 
1052 /**
1053  * Apply an orthographic projection matrix.
1054  *
1055  * \param mat matrix to apply the projection.
1056  * \param left left clipping plane coordinate.
1057  * \param right right clipping plane coordinate.
1058  * \param bottom bottom clipping plane coordinate.
1059  * \param top top clipping plane coordinate.
1060  * \param nearval distance to the near clipping plane.
1061  * \param farval distance to the far clipping plane.
1062  *
1063  * Creates the projection matrix and multiplies it with \p mat, marking the
1064  * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
1065  */
1066 void
_math_matrix_ortho(GLmatrix * mat,GLfloat left,GLfloat right,GLfloat bottom,GLfloat top,GLfloat nearval,GLfloat farval)1067 _math_matrix_ortho( GLmatrix *mat,
1068 		    GLfloat left, GLfloat right,
1069 		    GLfloat bottom, GLfloat top,
1070 		    GLfloat nearval, GLfloat farval )
1071 {
1072    GLfloat m[16];
1073 
1074    _math_float_ortho(m, left, right, bottom, top, nearval, farval);
1075    matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION));
1076 }
1077 
1078 /**
1079  * Multiply a matrix with a general scaling matrix.
1080  *
1081  * \param mat matrix.
1082  * \param x x axis scale factor.
1083  * \param y y axis scale factor.
1084  * \param z z axis scale factor.
1085  *
1086  * Multiplies in-place the elements of \p mat by the scale factors. Checks if
1087  * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
1088  * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
1089  * MAT_DIRTY_INVERSE dirty flags.
1090  */
1091 void
_math_matrix_scale(GLmatrix * mat,GLfloat x,GLfloat y,GLfloat z)1092 _math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
1093 {
1094    GLfloat *m = mat->m;
1095    m[0] *= x;   m[4] *= y;   m[8]  *= z;
1096    m[1] *= x;   m[5] *= y;   m[9]  *= z;
1097    m[2] *= x;   m[6] *= y;   m[10] *= z;
1098    m[3] *= x;   m[7] *= y;   m[11] *= z;
1099 
1100    if (fabsf(x - y) < 1e-8F && fabsf(x - z) < 1e-8F)
1101       mat->flags |= MAT_FLAG_UNIFORM_SCALE;
1102    else
1103       mat->flags |= MAT_FLAG_GENERAL_SCALE;
1104 
1105    mat->flags |= (MAT_DIRTY_TYPE |
1106 		  MAT_DIRTY_INVERSE);
1107 }
1108 
1109 /**
1110  * Multiply a matrix with a translation matrix.
1111  *
1112  * \param mat matrix.
1113  * \param x translation vector x coordinate.
1114  * \param y translation vector y coordinate.
1115  * \param z translation vector z coordinate.
1116  *
1117  * Adds the translation coordinates to the elements of \p mat in-place.  Marks
1118  * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
1119  * dirty flags.
1120  */
1121 void
_math_matrix_translate(GLmatrix * mat,GLfloat x,GLfloat y,GLfloat z)1122 _math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
1123 {
1124    GLfloat *m = mat->m;
1125    m[12] = m[0] * x + m[4] * y + m[8]  * z + m[12];
1126    m[13] = m[1] * x + m[5] * y + m[9]  * z + m[13];
1127    m[14] = m[2] * x + m[6] * y + m[10] * z + m[14];
1128    m[15] = m[3] * x + m[7] * y + m[11] * z + m[15];
1129 
1130    mat->flags |= (MAT_FLAG_TRANSLATION |
1131 		  MAT_DIRTY_TYPE |
1132 		  MAT_DIRTY_INVERSE);
1133 }
1134 
1135 
1136 /**
1137  * Set matrix to do viewport and depthrange mapping.
1138  * Transforms Normalized Device Coords to window/Z values.
1139  */
1140 void
_math_matrix_viewport(GLmatrix * m,const float scale[3],const float translate[3],double depthMax)1141 _math_matrix_viewport(GLmatrix *m, const float scale[3],
1142                       const float translate[3], double depthMax)
1143 {
1144    m->m[MAT_SX] = scale[0];
1145    m->m[MAT_TX] = translate[0];
1146    m->m[MAT_SY] = scale[1];
1147    m->m[MAT_TY] = translate[1];
1148    m->m[MAT_SZ] = depthMax*scale[2];
1149    m->m[MAT_TZ] = depthMax*translate[2];
1150    m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION;
1151    m->type = MATRIX_3D_NO_ROT;
1152 }
1153 
1154 
1155 /**
1156  * Set a matrix to the identity matrix.
1157  *
1158  * \param mat matrix.
1159  *
1160  * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
1161  * Sets the matrix type to identity, and clear the dirty flags.
1162  */
1163 void
_math_matrix_set_identity(GLmatrix * mat)1164 _math_matrix_set_identity( GLmatrix *mat )
1165 {
1166    STATIC_ASSERT(MATRIX_M == offsetof(GLmatrix, m));
1167    STATIC_ASSERT(MATRIX_INV == offsetof(GLmatrix, inv));
1168 
1169    memcpy( mat->m, Identity, sizeof(Identity) );
1170    memcpy( mat->inv, Identity, sizeof(Identity) );
1171 
1172    mat->type = MATRIX_IDENTITY;
1173    mat->flags &= ~(MAT_DIRTY_FLAGS|
1174 		   MAT_DIRTY_TYPE|
1175 		   MAT_DIRTY_INVERSE);
1176 }
1177 
1178 /*@}*/
1179 
1180 
1181 /**********************************************************************/
1182 /** \name Matrix analysis */
1183 /*@{*/
1184 
1185 #define ZERO(x) (1<<x)
1186 #define ONE(x)  (1<<(x+16))
1187 
1188 #define MASK_NO_TRX      (ZERO(12) | ZERO(13) | ZERO(14))
1189 #define MASK_NO_2D_SCALE ( ONE(0)  | ONE(5))
1190 
1191 #define MASK_IDENTITY    ( ONE(0)  | ZERO(4)  | ZERO(8)  | ZERO(12) |\
1192 			  ZERO(1)  |  ONE(5)  | ZERO(9)  | ZERO(13) |\
1193 			  ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
1194 			  ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )
1195 
1196 #define MASK_2D_NO_ROT   (           ZERO(4)  | ZERO(8)  |           \
1197 			  ZERO(1)  |            ZERO(9)  |           \
1198 			  ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
1199 			  ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )
1200 
1201 #define MASK_2D          (                      ZERO(8)  |           \
1202 			                        ZERO(9)  |           \
1203 			  ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
1204 			  ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )
1205 
1206 
1207 #define MASK_3D_NO_ROT   (           ZERO(4)  | ZERO(8)  |           \
1208 			  ZERO(1)  |            ZERO(9)  |           \
1209 			  ZERO(2)  | ZERO(6)  |                      \
1210 			  ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )
1211 
1212 #define MASK_3D          (                                           \
1213 			                                             \
1214 			                                             \
1215 			  ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )
1216 
1217 
1218 #define MASK_PERSPECTIVE (           ZERO(4)  |            ZERO(12) |\
1219 			  ZERO(1)  |                       ZERO(13) |\
1220 			  ZERO(2)  | ZERO(6)  |                      \
1221 			  ZERO(3)  | ZERO(7)  |            ZERO(15) )
1222 
1223 #define SQ(x) ((x)*(x))
1224 
1225 /**
1226  * Determine type and flags from scratch.
1227  *
1228  * \param mat matrix.
1229  *
1230  * This is expensive enough to only want to do it once.
1231  */
analyse_from_scratch(GLmatrix * mat)1232 static void analyse_from_scratch( GLmatrix *mat )
1233 {
1234    const GLfloat *m = mat->m;
1235    GLuint mask = 0;
1236    GLuint i;
1237 
1238    for (i = 0 ; i < 16 ; i++) {
1239       if (m[i] == 0.0F) mask |= (1<<i);
1240    }
1241 
1242    if (m[0] == 1.0F) mask |= (1<<16);
1243    if (m[5] == 1.0F) mask |= (1<<21);
1244    if (m[10] == 1.0F) mask |= (1<<26);
1245    if (m[15] == 1.0F) mask |= (1<<31);
1246 
1247    mat->flags &= ~MAT_FLAGS_GEOMETRY;
1248 
1249    /* Check for translation - no-one really cares
1250     */
1251    if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
1252       mat->flags |= MAT_FLAG_TRANSLATION;
1253 
1254    /* Do the real work
1255     */
1256    if (mask == (GLuint) MASK_IDENTITY) {
1257       mat->type = MATRIX_IDENTITY;
1258    }
1259    else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) {
1260       mat->type = MATRIX_2D_NO_ROT;
1261 
1262       if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE)
1263 	 mat->flags |= MAT_FLAG_GENERAL_SCALE;
1264    }
1265    else if ((mask & MASK_2D) == (GLuint) MASK_2D) {
1266       GLfloat mm = DOT2(m, m);
1267       GLfloat m4m4 = DOT2(m+4,m+4);
1268       GLfloat mm4 = DOT2(m,m+4);
1269 
1270       mat->type = MATRIX_2D;
1271 
1272       /* Check for scale */
1273       if (SQ(mm-1) > SQ(1e-6F) ||
1274 	  SQ(m4m4-1) > SQ(1e-6F))
1275 	 mat->flags |= MAT_FLAG_GENERAL_SCALE;
1276 
1277       /* Check for rotation */
1278       if (SQ(mm4) > SQ(1e-6F))
1279 	 mat->flags |= MAT_FLAG_GENERAL_3D;
1280       else
1281 	 mat->flags |= MAT_FLAG_ROTATION;
1282 
1283    }
1284    else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) {
1285       mat->type = MATRIX_3D_NO_ROT;
1286 
1287       /* Check for scale */
1288       if (SQ(m[0]-m[5]) < SQ(1e-6F) &&
1289 	  SQ(m[0]-m[10]) < SQ(1e-6F)) {
1290 	 if (SQ(m[0]-1.0F) > SQ(1e-6F)) {
1291 	    mat->flags |= MAT_FLAG_UNIFORM_SCALE;
1292          }
1293       }
1294       else {
1295 	 mat->flags |= MAT_FLAG_GENERAL_SCALE;
1296       }
1297    }
1298    else if ((mask & MASK_3D) == (GLuint) MASK_3D) {
1299       GLfloat c1 = DOT3(m,m);
1300       GLfloat c2 = DOT3(m+4,m+4);
1301       GLfloat c3 = DOT3(m+8,m+8);
1302       GLfloat d1 = DOT3(m, m+4);
1303       GLfloat cp[3];
1304 
1305       mat->type = MATRIX_3D;
1306 
1307       /* Check for scale */
1308       if (SQ(c1-c2) < SQ(1e-6F) && SQ(c1-c3) < SQ(1e-6F)) {
1309 	 if (SQ(c1-1.0F) > SQ(1e-6F))
1310 	    mat->flags |= MAT_FLAG_UNIFORM_SCALE;
1311 	 /* else no scale at all */
1312       }
1313       else {
1314 	 mat->flags |= MAT_FLAG_GENERAL_SCALE;
1315       }
1316 
1317       /* Check for rotation */
1318       if (SQ(d1) < SQ(1e-6F)) {
1319 	 CROSS3( cp, m, m+4 );
1320 	 SUB_3V( cp, cp, (m+8) );
1321 	 if (LEN_SQUARED_3FV(cp) < SQ(1e-6F))
1322 	    mat->flags |= MAT_FLAG_ROTATION;
1323 	 else
1324 	    mat->flags |= MAT_FLAG_GENERAL_3D;
1325       }
1326       else {
1327 	 mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */
1328       }
1329    }
1330    else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) {
1331       mat->type = MATRIX_PERSPECTIVE;
1332       mat->flags |= MAT_FLAG_GENERAL;
1333    }
1334    else {
1335       mat->type = MATRIX_GENERAL;
1336       mat->flags |= MAT_FLAG_GENERAL;
1337    }
1338 }
1339 
1340 /**
1341  * Analyze a matrix given that its flags are accurate.
1342  *
1343  * This is the more common operation, hopefully.
1344  */
analyse_from_flags(GLmatrix * mat)1345 static void analyse_from_flags( GLmatrix *mat )
1346 {
1347    const GLfloat *m = mat->m;
1348 
1349    if (TEST_MAT_FLAGS(mat, 0)) {
1350       mat->type = MATRIX_IDENTITY;
1351    }
1352    else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION |
1353 				 MAT_FLAG_UNIFORM_SCALE |
1354 				 MAT_FLAG_GENERAL_SCALE))) {
1355       if ( m[10]==1.0F && m[14]==0.0F ) {
1356 	 mat->type = MATRIX_2D_NO_ROT;
1357       }
1358       else {
1359 	 mat->type = MATRIX_3D_NO_ROT;
1360       }
1361    }
1362    else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) {
1363       if (                                 m[ 8]==0.0F
1364             &&                             m[ 9]==0.0F
1365             && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) {
1366 	 mat->type = MATRIX_2D;
1367       }
1368       else {
1369 	 mat->type = MATRIX_3D;
1370       }
1371    }
1372    else if (                 m[4]==0.0F                 && m[12]==0.0F
1373             && m[1]==0.0F                               && m[13]==0.0F
1374             && m[2]==0.0F && m[6]==0.0F
1375             && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) {
1376       mat->type = MATRIX_PERSPECTIVE;
1377    }
1378    else {
1379       mat->type = MATRIX_GENERAL;
1380    }
1381 }
1382 
1383 /**
1384  * Analyze and update a matrix.
1385  *
1386  * \param mat matrix.
1387  *
1388  * If the matrix type is dirty then calls either analyse_from_scratch() or
1389  * analyse_from_flags() to determine its type, according to whether the flags
1390  * are dirty or not, respectively. If the matrix has an inverse and it's dirty
1391  * then calls matrix_invert(). Finally clears the dirty flags.
1392  */
1393 void
_math_matrix_analyse(GLmatrix * mat)1394 _math_matrix_analyse( GLmatrix *mat )
1395 {
1396    if (mat->flags & MAT_DIRTY_TYPE) {
1397       if (mat->flags & MAT_DIRTY_FLAGS)
1398 	 analyse_from_scratch( mat );
1399       else
1400 	 analyse_from_flags( mat );
1401    }
1402 
1403    if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) {
1404       matrix_invert( mat );
1405       mat->flags &= ~MAT_DIRTY_INVERSE;
1406    }
1407 
1408    mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE);
1409 }
1410 
1411 /*@}*/
1412 
1413 
1414 /**
1415  * Test if the given matrix preserves vector lengths.
1416  */
1417 GLboolean
_math_matrix_is_length_preserving(const GLmatrix * m)1418 _math_matrix_is_length_preserving( const GLmatrix *m )
1419 {
1420    return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING);
1421 }
1422 
1423 
1424 /**
1425  * Test if the given matrix does any rotation.
1426  * (or perhaps if the upper-left 3x3 is non-identity)
1427  */
1428 GLboolean
_math_matrix_has_rotation(const GLmatrix * m)1429 _math_matrix_has_rotation( const GLmatrix *m )
1430 {
1431    if (m->flags & (MAT_FLAG_GENERAL |
1432                    MAT_FLAG_ROTATION |
1433                    MAT_FLAG_GENERAL_3D |
1434                    MAT_FLAG_PERSPECTIVE))
1435       return GL_TRUE;
1436    else
1437       return GL_FALSE;
1438 }
1439 
1440 
1441 GLboolean
_math_matrix_is_general_scale(const GLmatrix * m)1442 _math_matrix_is_general_scale( const GLmatrix *m )
1443 {
1444    return (m->flags & MAT_FLAG_GENERAL_SCALE) ? GL_TRUE : GL_FALSE;
1445 }
1446 
1447 
1448 GLboolean
_math_matrix_is_dirty(const GLmatrix * m)1449 _math_matrix_is_dirty( const GLmatrix *m )
1450 {
1451    return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE;
1452 }
1453 
1454 
1455 /**********************************************************************/
1456 /** \name Matrix setup */
1457 /*@{*/
1458 
1459 /**
1460  * Copy a matrix.
1461  *
1462  * \param to destination matrix.
1463  * \param from source matrix.
1464  *
1465  * Copies all fields in GLmatrix, creating an inverse array if necessary.
1466  */
1467 void
_math_matrix_copy(GLmatrix * to,const GLmatrix * from)1468 _math_matrix_copy( GLmatrix *to, const GLmatrix *from )
1469 {
1470    memcpy(to->m, from->m, 16 * sizeof(GLfloat));
1471    memcpy(to->inv, from->inv, 16 * sizeof(GLfloat));
1472    to->flags = from->flags;
1473    to->type = from->type;
1474 }
1475 
1476 /**
1477  * Loads a matrix array into GLmatrix.
1478  *
1479  * \param m matrix array.
1480  * \param mat matrix.
1481  *
1482  * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
1483  * flags.
1484  */
1485 void
_math_matrix_loadf(GLmatrix * mat,const GLfloat * m)1486 _math_matrix_loadf( GLmatrix *mat, const GLfloat *m )
1487 {
1488    memcpy( mat->m, m, 16*sizeof(GLfloat) );
1489    mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);
1490 }
1491 
1492 /**
1493  * Matrix constructor.
1494  *
1495  * \param m matrix.
1496  *
1497  * Initialize the GLmatrix fields.
1498  */
1499 void
_math_matrix_ctr(GLmatrix * m)1500 _math_matrix_ctr( GLmatrix *m )
1501 {
1502    m->m = align_malloc( 16 * sizeof(GLfloat), 16 );
1503    if (m->m)
1504       memcpy( m->m, Identity, sizeof(Identity) );
1505    m->inv = align_malloc( 16 * sizeof(GLfloat), 16 );
1506    if (m->inv)
1507       memcpy( m->inv, Identity, sizeof(Identity) );
1508    m->type = MATRIX_IDENTITY;
1509    m->flags = 0;
1510 }
1511 
1512 /**
1513  * Matrix destructor.
1514  *
1515  * \param m matrix.
1516  *
1517  * Frees the data in a GLmatrix.
1518  */
1519 void
_math_matrix_dtr(GLmatrix * m)1520 _math_matrix_dtr( GLmatrix *m )
1521 {
1522    align_free( m->m );
1523    m->m = NULL;
1524 
1525    align_free( m->inv );
1526    m->inv = NULL;
1527 }
1528 
1529 /*@}*/
1530 
1531 
1532 /**********************************************************************/
1533 /** \name Matrix transpose */
1534 /*@{*/
1535 
1536 /**
1537  * Transpose a GLfloat matrix.
1538  *
1539  * \param to destination array.
1540  * \param from source array.
1541  */
1542 void
_math_transposef(GLfloat to[16],const GLfloat from[16])1543 _math_transposef( GLfloat to[16], const GLfloat from[16] )
1544 {
1545    to[0] = from[0];
1546    to[1] = from[4];
1547    to[2] = from[8];
1548    to[3] = from[12];
1549    to[4] = from[1];
1550    to[5] = from[5];
1551    to[6] = from[9];
1552    to[7] = from[13];
1553    to[8] = from[2];
1554    to[9] = from[6];
1555    to[10] = from[10];
1556    to[11] = from[14];
1557    to[12] = from[3];
1558    to[13] = from[7];
1559    to[14] = from[11];
1560    to[15] = from[15];
1561 }
1562 
1563 /**
1564  * Transpose a GLdouble matrix.
1565  *
1566  * \param to destination array.
1567  * \param from source array.
1568  */
1569 void
_math_transposed(GLdouble to[16],const GLdouble from[16])1570 _math_transposed( GLdouble to[16], const GLdouble from[16] )
1571 {
1572    to[0] = from[0];
1573    to[1] = from[4];
1574    to[2] = from[8];
1575    to[3] = from[12];
1576    to[4] = from[1];
1577    to[5] = from[5];
1578    to[6] = from[9];
1579    to[7] = from[13];
1580    to[8] = from[2];
1581    to[9] = from[6];
1582    to[10] = from[10];
1583    to[11] = from[14];
1584    to[12] = from[3];
1585    to[13] = from[7];
1586    to[14] = from[11];
1587    to[15] = from[15];
1588 }
1589 
1590 /**
1591  * Transpose a GLdouble matrix and convert to GLfloat.
1592  *
1593  * \param to destination array.
1594  * \param from source array.
1595  */
1596 void
_math_transposefd(GLfloat to[16],const GLdouble from[16])1597 _math_transposefd( GLfloat to[16], const GLdouble from[16] )
1598 {
1599    to[0] = (GLfloat) from[0];
1600    to[1] = (GLfloat) from[4];
1601    to[2] = (GLfloat) from[8];
1602    to[3] = (GLfloat) from[12];
1603    to[4] = (GLfloat) from[1];
1604    to[5] = (GLfloat) from[5];
1605    to[6] = (GLfloat) from[9];
1606    to[7] = (GLfloat) from[13];
1607    to[8] = (GLfloat) from[2];
1608    to[9] = (GLfloat) from[6];
1609    to[10] = (GLfloat) from[10];
1610    to[11] = (GLfloat) from[14];
1611    to[12] = (GLfloat) from[3];
1612    to[13] = (GLfloat) from[7];
1613    to[14] = (GLfloat) from[11];
1614    to[15] = (GLfloat) from[15];
1615 }
1616 
1617 /*@}*/
1618 
1619 
1620 /**
1621  * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix.  This
1622  * function is used for transforming clipping plane equations and spotlight
1623  * directions.
1624  * Mathematically,  u = v * m.
1625  * Input:  v - input vector
1626  *         m - transformation matrix
1627  * Output:  u - transformed vector
1628  */
1629 void
_mesa_transform_vector(GLfloat u[4],const GLfloat v[4],const GLfloat m[16])1630 _mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] )
1631 {
1632    const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3];
1633 #define M(row,col)  m[row + col*4]
1634    u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0);
1635    u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1);
1636    u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2);
1637    u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3);
1638 #undef M
1639 }
1640