2 * Mesa 3-D graphics library
5 * Copyright (C) 1999-2005 Brian Paul All Rights Reserved.
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:
14 * The above copyright notice and this permission notice shall be included
15 * in all copies or substantial portions of the Software.
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.
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
37 #include "main/glheader.h"
38 #include "main/imports.h"
39 #include "main/macros.h"
45 * \defgroup MatFlags MAT_FLAG_XXX-flags
47 * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
48 * It would be nice to make all these flags private to m_matrix.c
51 #define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag.
52 * (Not actually used - the identity
53 * matrix is identified by the absense
54 * of all other flags.)
56 #define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */
57 #define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */
58 #define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */
59 #define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */
60 #define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */
61 #define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */
62 #define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */
63 #define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */
64 #define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */
65 #define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */
66 #define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */
68 /** angle preserving matrix flags mask */
69 #define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
70 MAT_FLAG_TRANSLATION | \
71 MAT_FLAG_UNIFORM_SCALE)
73 /** geometry related matrix flags mask */
74 #define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
76 MAT_FLAG_TRANSLATION | \
77 MAT_FLAG_UNIFORM_SCALE | \
78 MAT_FLAG_GENERAL_SCALE | \
79 MAT_FLAG_GENERAL_3D | \
80 MAT_FLAG_PERSPECTIVE | \
83 /** length preserving matrix flags mask */
84 #define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
88 /** 3D (non-perspective) matrix flags mask */
89 #define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
90 MAT_FLAG_TRANSLATION | \
91 MAT_FLAG_UNIFORM_SCALE | \
92 MAT_FLAG_GENERAL_SCALE | \
95 /** dirty matrix flags mask */
96 #define MAT_DIRTY (MAT_DIRTY_TYPE | \
104 * Test geometry related matrix flags.
106 * \param mat a pointer to a GLmatrix structure.
107 * \param a flags mask.
109 * \returns non-zero if all geometry related matrix flags are contained within
110 * the mask, or zero otherwise.
112 #define TEST_MAT_FLAGS(mat, a) \
113 ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
118 * Names of the corresponding GLmatrixtype values.
120 static const char *types
[] = {
124 "MATRIX_PERSPECTIVE",
134 static GLfloat Identity
[16] = {
143 /**********************************************************************/
144 /** \name Matrix multiplication */
147 #define A(row,col) a[(col<<2)+row]
148 #define B(row,col) b[(col<<2)+row]
149 #define P(row,col) product[(col<<2)+row]
152 * Perform a full 4x4 matrix multiplication.
156 * \param product will receive the product of \p a and \p b.
158 * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
160 * \note KW: 4*16 = 64 multiplications
162 * \author This \c matmul was contributed by Thomas Malik
164 static void matmul4( GLfloat
*product
, const GLfloat
*a
, const GLfloat
*b
)
167 for (i
= 0; i
< 4; i
++) {
168 const GLfloat ai0
=A(i
,0), ai1
=A(i
,1), ai2
=A(i
,2), ai3
=A(i
,3);
169 P(i
,0) = ai0
* B(0,0) + ai1
* B(1,0) + ai2
* B(2,0) + ai3
* B(3,0);
170 P(i
,1) = ai0
* B(0,1) + ai1
* B(1,1) + ai2
* B(2,1) + ai3
* B(3,1);
171 P(i
,2) = ai0
* B(0,2) + ai1
* B(1,2) + ai2
* B(2,2) + ai3
* B(3,2);
172 P(i
,3) = ai0
* B(0,3) + ai1
* B(1,3) + ai2
* B(2,3) + ai3
* B(3,3);
177 * Multiply two matrices known to occupy only the top three rows, such
178 * as typical model matrices, and orthogonal matrices.
182 * \param product will receive the product of \p a and \p b.
184 static void matmul34( GLfloat
*product
, const GLfloat
*a
, const GLfloat
*b
)
187 for (i
= 0; i
< 3; i
++) {
188 const GLfloat ai0
=A(i
,0), ai1
=A(i
,1), ai2
=A(i
,2), ai3
=A(i
,3);
189 P(i
,0) = ai0
* B(0,0) + ai1
* B(1,0) + ai2
* B(2,0);
190 P(i
,1) = ai0
* B(0,1) + ai1
* B(1,1) + ai2
* B(2,1);
191 P(i
,2) = ai0
* B(0,2) + ai1
* B(1,2) + ai2
* B(2,2);
192 P(i
,3) = ai0
* B(0,3) + ai1
* B(1,3) + ai2
* B(2,3) + ai3
;
205 * Multiply a matrix by an array of floats with known properties.
207 * \param mat pointer to a GLmatrix structure containing the left multiplication
208 * matrix, and that will receive the product result.
209 * \param m right multiplication matrix array.
210 * \param flags flags of the matrix \p m.
212 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
213 * if both matrices are 3D, or matmul4() otherwise.
215 static void matrix_multf( GLmatrix
*mat
, const GLfloat
*m
, GLuint flags
)
217 mat
->flags
|= (flags
| MAT_DIRTY_TYPE
| MAT_DIRTY_INVERSE
);
219 if (TEST_MAT_FLAGS(mat
, MAT_FLAGS_3D
))
220 matmul34( mat
->m
, mat
->m
, m
);
222 matmul4( mat
->m
, mat
->m
, m
);
226 * Matrix multiplication.
228 * \param dest destination matrix.
229 * \param a left matrix.
230 * \param b right matrix.
232 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
233 * if both matrices are 3D, or matmul4() otherwise.
236 _math_matrix_mul_matrix( GLmatrix
*dest
, const GLmatrix
*a
, const GLmatrix
*b
)
238 dest
->flags
= (a
->flags
|
243 if (TEST_MAT_FLAGS(dest
, MAT_FLAGS_3D
))
244 matmul34( dest
->m
, a
->m
, b
->m
);
246 matmul4( dest
->m
, a
->m
, b
->m
);
250 * Matrix multiplication.
252 * \param dest left and destination matrix.
253 * \param m right matrix array.
255 * Marks the matrix flags with general flag, and type and inverse dirty flags.
256 * Calls matmul4() for the multiplication.
259 _math_matrix_mul_floats( GLmatrix
*dest
, const GLfloat
*m
)
261 dest
->flags
|= (MAT_FLAG_GENERAL
|
266 matmul4( dest
->m
, dest
->m
, m
);
272 /**********************************************************************/
273 /** \name Matrix output */
277 * Print a matrix array.
279 * \param m matrix array.
281 * Called by _math_matrix_print() to print a matrix or its inverse.
283 static void print_matrix_floats( const GLfloat m
[16] )
287 _mesa_debug(NULL
,"\t%f %f %f %f\n", m
[i
], m
[4+i
], m
[8+i
], m
[12+i
] );
292 * Dumps the contents of a GLmatrix structure.
294 * \param m pointer to the GLmatrix structure.
297 _math_matrix_print( const GLmatrix
*m
)
299 _mesa_debug(NULL
, "Matrix type: %s, flags: %x\n", types
[m
->type
], m
->flags
);
300 print_matrix_floats(m
->m
);
301 _mesa_debug(NULL
, "Inverse: \n");
304 print_matrix_floats(m
->inv
);
305 matmul4(prod
, m
->m
, m
->inv
);
306 _mesa_debug(NULL
, "Mat * Inverse:\n");
307 print_matrix_floats(prod
);
310 _mesa_debug(NULL
, " - not available\n");
318 * References an element of 4x4 matrix.
320 * \param m matrix array.
321 * \param c column of the desired element.
322 * \param r row of the desired element.
324 * \return value of the desired element.
326 * Calculate the linear storage index of the element and references it.
328 #define MAT(m,r,c) (m)[(c)*4+(r)]
331 /**********************************************************************/
332 /** \name Matrix inversion */
336 * Swaps the values of two floating pointer variables.
338 * Used by invert_matrix_general() to swap the row pointers.
340 #define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
343 * Compute inverse of 4x4 transformation matrix.
345 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
346 * stored in the GLmatrix::inv attribute.
348 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
351 * Code contributed by Jacques Leroy jle@star.be
353 * Calculates the inverse matrix by performing the gaussian matrix reduction
354 * with partial pivoting followed by back/substitution with the loops manually
357 static GLboolean
invert_matrix_general( GLmatrix
*mat
)
359 const GLfloat
*m
= mat
->m
;
360 GLfloat
*out
= mat
->inv
;
362 GLfloat m0
, m1
, m2
, m3
, s
;
363 GLfloat
*r0
, *r1
, *r2
, *r3
;
365 r0
= wtmp
[0], r1
= wtmp
[1], r2
= wtmp
[2], r3
= wtmp
[3];
367 r0
[0] = MAT(m
,0,0), r0
[1] = MAT(m
,0,1),
368 r0
[2] = MAT(m
,0,2), r0
[3] = MAT(m
,0,3),
369 r0
[4] = 1.0, r0
[5] = r0
[6] = r0
[7] = 0.0,
371 r1
[0] = MAT(m
,1,0), r1
[1] = MAT(m
,1,1),
372 r1
[2] = MAT(m
,1,2), r1
[3] = MAT(m
,1,3),
373 r1
[5] = 1.0, r1
[4] = r1
[6] = r1
[7] = 0.0,
375 r2
[0] = MAT(m
,2,0), r2
[1] = MAT(m
,2,1),
376 r2
[2] = MAT(m
,2,2), r2
[3] = MAT(m
,2,3),
377 r2
[6] = 1.0, r2
[4] = r2
[5] = r2
[7] = 0.0,
379 r3
[0] = MAT(m
,3,0), r3
[1] = MAT(m
,3,1),
380 r3
[2] = MAT(m
,3,2), r3
[3] = MAT(m
,3,3),
381 r3
[7] = 1.0, r3
[4] = r3
[5] = r3
[6] = 0.0;
383 /* choose pivot - or die */
384 if (FABSF(r3
[0])>FABSF(r2
[0])) SWAP_ROWS(r3
, r2
);
385 if (FABSF(r2
[0])>FABSF(r1
[0])) SWAP_ROWS(r2
, r1
);
386 if (FABSF(r1
[0])>FABSF(r0
[0])) SWAP_ROWS(r1
, r0
);
387 if (0.0 == r0
[0]) return GL_FALSE
;
389 /* eliminate first variable */
390 m1
= r1
[0]/r0
[0]; m2
= r2
[0]/r0
[0]; m3
= r3
[0]/r0
[0];
391 s
= r0
[1]; r1
[1] -= m1
* s
; r2
[1] -= m2
* s
; r3
[1] -= m3
* s
;
392 s
= r0
[2]; r1
[2] -= m1
* s
; r2
[2] -= m2
* s
; r3
[2] -= m3
* s
;
393 s
= r0
[3]; r1
[3] -= m1
* s
; r2
[3] -= m2
* s
; r3
[3] -= m3
* s
;
395 if (s
!= 0.0) { r1
[4] -= m1
* s
; r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
397 if (s
!= 0.0) { r1
[5] -= m1
* s
; r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
399 if (s
!= 0.0) { r1
[6] -= m1
* s
; r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
401 if (s
!= 0.0) { r1
[7] -= m1
* s
; r2
[7] -= m2
* s
; r3
[7] -= m3
* s
; }
403 /* choose pivot - or die */
404 if (FABSF(r3
[1])>FABSF(r2
[1])) SWAP_ROWS(r3
, r2
);
405 if (FABSF(r2
[1])>FABSF(r1
[1])) SWAP_ROWS(r2
, r1
);
406 if (0.0 == r1
[1]) return GL_FALSE
;
408 /* eliminate second variable */
409 m2
= r2
[1]/r1
[1]; m3
= r3
[1]/r1
[1];
410 r2
[2] -= m2
* r1
[2]; r3
[2] -= m3
* r1
[2];
411 r2
[3] -= m2
* r1
[3]; r3
[3] -= m3
* r1
[3];
412 s
= r1
[4]; if (0.0 != s
) { r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
413 s
= r1
[5]; if (0.0 != s
) { r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
414 s
= r1
[6]; if (0.0 != s
) { r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
415 s
= r1
[7]; if (0.0 != s
) { r2
[7] -= m2
* s
; r3
[7] -= m3
* s
; }
417 /* choose pivot - or die */
418 if (FABSF(r3
[2])>FABSF(r2
[2])) SWAP_ROWS(r3
, r2
);
419 if (0.0 == r2
[2]) return GL_FALSE
;
421 /* eliminate third variable */
423 r3
[3] -= m3
* r2
[3], r3
[4] -= m3
* r2
[4],
424 r3
[5] -= m3
* r2
[5], r3
[6] -= m3
* r2
[6],
428 if (0.0 == r3
[3]) return GL_FALSE
;
430 s
= 1.0F
/r3
[3]; /* now back substitute row 3 */
431 r3
[4] *= s
; r3
[5] *= s
; r3
[6] *= s
; r3
[7] *= s
;
433 m2
= r2
[3]; /* now back substitute row 2 */
435 r2
[4] = s
* (r2
[4] - r3
[4] * m2
), r2
[5] = s
* (r2
[5] - r3
[5] * m2
),
436 r2
[6] = s
* (r2
[6] - r3
[6] * m2
), r2
[7] = s
* (r2
[7] - r3
[7] * m2
);
438 r1
[4] -= r3
[4] * m1
, r1
[5] -= r3
[5] * m1
,
439 r1
[6] -= r3
[6] * m1
, r1
[7] -= r3
[7] * m1
;
441 r0
[4] -= r3
[4] * m0
, r0
[5] -= r3
[5] * m0
,
442 r0
[6] -= r3
[6] * m0
, r0
[7] -= r3
[7] * m0
;
444 m1
= r1
[2]; /* now back substitute row 1 */
446 r1
[4] = s
* (r1
[4] - r2
[4] * m1
), r1
[5] = s
* (r1
[5] - r2
[5] * m1
),
447 r1
[6] = s
* (r1
[6] - r2
[6] * m1
), r1
[7] = s
* (r1
[7] - r2
[7] * m1
);
449 r0
[4] -= r2
[4] * m0
, r0
[5] -= r2
[5] * m0
,
450 r0
[6] -= r2
[6] * m0
, r0
[7] -= r2
[7] * m0
;
452 m0
= r0
[1]; /* now back substitute row 0 */
454 r0
[4] = s
* (r0
[4] - r1
[4] * m0
), r0
[5] = s
* (r0
[5] - r1
[5] * m0
),
455 r0
[6] = s
* (r0
[6] - r1
[6] * m0
), r0
[7] = s
* (r0
[7] - r1
[7] * m0
);
457 MAT(out
,0,0) = r0
[4]; MAT(out
,0,1) = r0
[5],
458 MAT(out
,0,2) = r0
[6]; MAT(out
,0,3) = r0
[7],
459 MAT(out
,1,0) = r1
[4]; MAT(out
,1,1) = r1
[5],
460 MAT(out
,1,2) = r1
[6]; MAT(out
,1,3) = r1
[7],
461 MAT(out
,2,0) = r2
[4]; MAT(out
,2,1) = r2
[5],
462 MAT(out
,2,2) = r2
[6]; MAT(out
,2,3) = r2
[7],
463 MAT(out
,3,0) = r3
[4]; MAT(out
,3,1) = r3
[5],
464 MAT(out
,3,2) = r3
[6]; MAT(out
,3,3) = r3
[7];
471 * Compute inverse of a general 3d transformation matrix.
473 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
474 * stored in the GLmatrix::inv attribute.
476 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
478 * \author Adapted from graphics gems II.
480 * Calculates the inverse of the upper left by first calculating its
481 * determinant and multiplying it to the symmetric adjust matrix of each
482 * element. Finally deals with the translation part by transforming the
483 * original translation vector using by the calculated submatrix inverse.
485 static GLboolean
invert_matrix_3d_general( GLmatrix
*mat
)
487 const GLfloat
*in
= mat
->m
;
488 GLfloat
*out
= mat
->inv
;
492 /* Calculate the determinant of upper left 3x3 submatrix and
493 * determine if the matrix is singular.
496 t
= MAT(in
,0,0) * MAT(in
,1,1) * MAT(in
,2,2);
497 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
499 t
= MAT(in
,1,0) * MAT(in
,2,1) * MAT(in
,0,2);
500 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
502 t
= MAT(in
,2,0) * MAT(in
,0,1) * MAT(in
,1,2);
503 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
505 t
= -MAT(in
,2,0) * MAT(in
,1,1) * MAT(in
,0,2);
506 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
508 t
= -MAT(in
,1,0) * MAT(in
,0,1) * MAT(in
,2,2);
509 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
511 t
= -MAT(in
,0,0) * MAT(in
,2,1) * MAT(in
,1,2);
512 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
520 MAT(out
,0,0) = ( (MAT(in
,1,1)*MAT(in
,2,2) - MAT(in
,2,1)*MAT(in
,1,2) )*det
);
521 MAT(out
,0,1) = (- (MAT(in
,0,1)*MAT(in
,2,2) - MAT(in
,2,1)*MAT(in
,0,2) )*det
);
522 MAT(out
,0,2) = ( (MAT(in
,0,1)*MAT(in
,1,2) - MAT(in
,1,1)*MAT(in
,0,2) )*det
);
523 MAT(out
,1,0) = (- (MAT(in
,1,0)*MAT(in
,2,2) - MAT(in
,2,0)*MAT(in
,1,2) )*det
);
524 MAT(out
,1,1) = ( (MAT(in
,0,0)*MAT(in
,2,2) - MAT(in
,2,0)*MAT(in
,0,2) )*det
);
525 MAT(out
,1,2) = (- (MAT(in
,0,0)*MAT(in
,1,2) - MAT(in
,1,0)*MAT(in
,0,2) )*det
);
526 MAT(out
,2,0) = ( (MAT(in
,1,0)*MAT(in
,2,1) - MAT(in
,2,0)*MAT(in
,1,1) )*det
);
527 MAT(out
,2,1) = (- (MAT(in
,0,0)*MAT(in
,2,1) - MAT(in
,2,0)*MAT(in
,0,1) )*det
);
528 MAT(out
,2,2) = ( (MAT(in
,0,0)*MAT(in
,1,1) - MAT(in
,1,0)*MAT(in
,0,1) )*det
);
530 /* Do the translation part */
531 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0) +
532 MAT(in
,1,3) * MAT(out
,0,1) +
533 MAT(in
,2,3) * MAT(out
,0,2) );
534 MAT(out
,1,3) = - (MAT(in
,0,3) * MAT(out
,1,0) +
535 MAT(in
,1,3) * MAT(out
,1,1) +
536 MAT(in
,2,3) * MAT(out
,1,2) );
537 MAT(out
,2,3) = - (MAT(in
,0,3) * MAT(out
,2,0) +
538 MAT(in
,1,3) * MAT(out
,2,1) +
539 MAT(in
,2,3) * MAT(out
,2,2) );
545 * Compute inverse of a 3d transformation matrix.
547 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
548 * stored in the GLmatrix::inv attribute.
550 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
552 * If the matrix is not an angle preserving matrix then calls
553 * invert_matrix_3d_general for the actual calculation. Otherwise calculates
554 * the inverse matrix analyzing and inverting each of the scaling, rotation and
557 static GLboolean
invert_matrix_3d( GLmatrix
*mat
)
559 const GLfloat
*in
= mat
->m
;
560 GLfloat
*out
= mat
->inv
;
562 if (!TEST_MAT_FLAGS(mat
, MAT_FLAGS_ANGLE_PRESERVING
)) {
563 return invert_matrix_3d_general( mat
);
566 if (mat
->flags
& MAT_FLAG_UNIFORM_SCALE
) {
567 GLfloat scale
= (MAT(in
,0,0) * MAT(in
,0,0) +
568 MAT(in
,0,1) * MAT(in
,0,1) +
569 MAT(in
,0,2) * MAT(in
,0,2));
574 scale
= 1.0F
/ scale
;
576 /* Transpose and scale the 3 by 3 upper-left submatrix. */
577 MAT(out
,0,0) = scale
* MAT(in
,0,0);
578 MAT(out
,1,0) = scale
* MAT(in
,0,1);
579 MAT(out
,2,0) = scale
* MAT(in
,0,2);
580 MAT(out
,0,1) = scale
* MAT(in
,1,0);
581 MAT(out
,1,1) = scale
* MAT(in
,1,1);
582 MAT(out
,2,1) = scale
* MAT(in
,1,2);
583 MAT(out
,0,2) = scale
* MAT(in
,2,0);
584 MAT(out
,1,2) = scale
* MAT(in
,2,1);
585 MAT(out
,2,2) = scale
* MAT(in
,2,2);
587 else if (mat
->flags
& MAT_FLAG_ROTATION
) {
588 /* Transpose the 3 by 3 upper-left submatrix. */
589 MAT(out
,0,0) = MAT(in
,0,0);
590 MAT(out
,1,0) = MAT(in
,0,1);
591 MAT(out
,2,0) = MAT(in
,0,2);
592 MAT(out
,0,1) = MAT(in
,1,0);
593 MAT(out
,1,1) = MAT(in
,1,1);
594 MAT(out
,2,1) = MAT(in
,1,2);
595 MAT(out
,0,2) = MAT(in
,2,0);
596 MAT(out
,1,2) = MAT(in
,2,1);
597 MAT(out
,2,2) = MAT(in
,2,2);
600 /* pure translation */
601 memcpy( out
, Identity
, sizeof(Identity
) );
602 MAT(out
,0,3) = - MAT(in
,0,3);
603 MAT(out
,1,3) = - MAT(in
,1,3);
604 MAT(out
,2,3) = - MAT(in
,2,3);
608 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
609 /* Do the translation part */
610 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0) +
611 MAT(in
,1,3) * MAT(out
,0,1) +
612 MAT(in
,2,3) * MAT(out
,0,2) );
613 MAT(out
,1,3) = - (MAT(in
,0,3) * MAT(out
,1,0) +
614 MAT(in
,1,3) * MAT(out
,1,1) +
615 MAT(in
,2,3) * MAT(out
,1,2) );
616 MAT(out
,2,3) = - (MAT(in
,0,3) * MAT(out
,2,0) +
617 MAT(in
,1,3) * MAT(out
,2,1) +
618 MAT(in
,2,3) * MAT(out
,2,2) );
621 MAT(out
,0,3) = MAT(out
,1,3) = MAT(out
,2,3) = 0.0;
628 * Compute inverse of an identity transformation matrix.
630 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
631 * stored in the GLmatrix::inv attribute.
633 * \return always GL_TRUE.
635 * Simply copies Identity into GLmatrix::inv.
637 static GLboolean
invert_matrix_identity( GLmatrix
*mat
)
639 memcpy( mat
->inv
, Identity
, sizeof(Identity
) );
644 * Compute inverse of a no-rotation 3d transformation matrix.
646 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
647 * stored in the GLmatrix::inv attribute.
649 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
653 static GLboolean
invert_matrix_3d_no_rot( GLmatrix
*mat
)
655 const GLfloat
*in
= mat
->m
;
656 GLfloat
*out
= mat
->inv
;
658 if (MAT(in
,0,0) == 0 || MAT(in
,1,1) == 0 || MAT(in
,2,2) == 0 )
661 memcpy( out
, Identity
, 16 * sizeof(GLfloat
) );
662 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
663 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
664 MAT(out
,2,2) = 1.0F
/ MAT(in
,2,2);
666 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
667 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0));
668 MAT(out
,1,3) = - (MAT(in
,1,3) * MAT(out
,1,1));
669 MAT(out
,2,3) = - (MAT(in
,2,3) * MAT(out
,2,2));
676 * Compute inverse of a no-rotation 2d transformation matrix.
678 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
679 * stored in the GLmatrix::inv attribute.
681 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
683 * Calculates the inverse matrix by applying the inverse scaling and
684 * translation to the identity matrix.
686 static GLboolean
invert_matrix_2d_no_rot( GLmatrix
*mat
)
688 const GLfloat
*in
= mat
->m
;
689 GLfloat
*out
= mat
->inv
;
691 if (MAT(in
,0,0) == 0 || MAT(in
,1,1) == 0)
694 memcpy( out
, Identity
, 16 * sizeof(GLfloat
) );
695 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
696 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
698 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
699 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0));
700 MAT(out
,1,3) = - (MAT(in
,1,3) * MAT(out
,1,1));
708 static GLboolean
invert_matrix_perspective( GLmatrix
*mat
)
710 const GLfloat
*in
= mat
->m
;
711 GLfloat
*out
= mat
->inv
;
713 if (MAT(in
,2,3) == 0)
716 memcpy( out
, Identity
, 16 * sizeof(GLfloat
) );
718 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
719 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
721 MAT(out
,0,3) = MAT(in
,0,2);
722 MAT(out
,1,3) = MAT(in
,1,2);
727 MAT(out
,3,2) = 1.0F
/ MAT(in
,2,3);
728 MAT(out
,3,3) = MAT(in
,2,2) * MAT(out
,3,2);
735 * Matrix inversion function pointer type.
737 typedef GLboolean (*inv_mat_func
)( GLmatrix
*mat
);
740 * Table of the matrix inversion functions according to the matrix type.
742 static inv_mat_func inv_mat_tab
[7] = {
743 invert_matrix_general
,
744 invert_matrix_identity
,
745 invert_matrix_3d_no_rot
,
747 /* Don't use this function for now - it fails when the projection matrix
748 * is premultiplied by a translation (ala Chromium's tilesort SPU).
750 invert_matrix_perspective
,
752 invert_matrix_general
,
754 invert_matrix_3d
, /* lazy! */
755 invert_matrix_2d_no_rot
,
760 * Compute inverse of a transformation matrix.
762 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
763 * stored in the GLmatrix::inv attribute.
765 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
767 * Calls the matrix inversion function in inv_mat_tab corresponding to the
768 * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag,
769 * and copies the identity matrix into GLmatrix::inv.
771 static GLboolean
matrix_invert( GLmatrix
*mat
)
773 if (inv_mat_tab
[mat
->type
](mat
)) {
774 mat
->flags
&= ~MAT_FLAG_SINGULAR
;
777 mat
->flags
|= MAT_FLAG_SINGULAR
;
778 memcpy( mat
->inv
, Identity
, sizeof(Identity
) );
786 /**********************************************************************/
787 /** \name Matrix generation */
791 * Generate a 4x4 transformation matrix from glRotate parameters, and
792 * post-multiply the input matrix by it.
795 * This function was contributed by Erich Boleyn (erich@uruk.org).
796 * Optimizations contributed by Rudolf Opalla (rudi@khm.de).
799 _math_matrix_rotate( GLmatrix
*mat
,
800 GLfloat angle
, GLfloat x
, GLfloat y
, GLfloat z
)
802 GLfloat xx
, yy
, zz
, xy
, yz
, zx
, xs
, ys
, zs
, one_c
, s
, c
;
806 s
= (GLfloat
) sin( angle
* DEG2RAD
);
807 c
= (GLfloat
) cos( angle
* DEG2RAD
);
809 memcpy(m
, Identity
, sizeof(GLfloat
)*16);
810 optimized
= GL_FALSE
;
812 #define M(row,col) m[col*4+row]
818 /* rotate only around z-axis */
831 else if (z
== 0.0F
) {
833 /* rotate only around y-axis */
846 else if (y
== 0.0F
) {
849 /* rotate only around x-axis */
864 const GLfloat mag
= SQRTF(x
* x
+ y
* y
+ z
* z
);
867 /* no rotation, leave mat as-is */
877 * Arbitrary axis rotation matrix.
879 * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
880 * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation
881 * (which is about the X-axis), and the two composite transforms
882 * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
883 * from the arbitrary axis to the X-axis then back. They are
884 * all elementary rotations.
886 * Rz' is a rotation about the Z-axis, to bring the axis vector
887 * into the x-z plane. Then Ry' is applied, rotating about the
888 * Y-axis to bring the axis vector parallel with the X-axis. The
889 * rotation about the X-axis is then performed. Ry and Rz are
890 * simply the respective inverse transforms to bring the arbitrary
891 * axis back to its original orientation. The first transforms
892 * Rz' and Ry' are considered inverses, since the data from the
893 * arbitrary axis gives you info on how to get to it, not how
894 * to get away from it, and an inverse must be applied.
896 * The basic calculation used is to recognize that the arbitrary
897 * axis vector (x, y, z), since it is of unit length, actually
898 * represents the sines and cosines of the angles to rotate the
899 * X-axis to the same orientation, with theta being the angle about
900 * Z and phi the angle about Y (in the order described above)
903 * cos ( theta ) = x / sqrt ( 1 - z^2 )
904 * sin ( theta ) = y / sqrt ( 1 - z^2 )
906 * cos ( phi ) = sqrt ( 1 - z^2 )
909 * Note that cos ( phi ) can further be inserted to the above
912 * cos ( theta ) = x / cos ( phi )
913 * sin ( theta ) = y / sin ( phi )
915 * ...etc. Because of those relations and the standard trigonometric
916 * relations, it is pssible to reduce the transforms down to what
917 * is used below. It may be that any primary axis chosen will give the
918 * same results (modulo a sign convention) using thie method.
920 * Particularly nice is to notice that all divisions that might
921 * have caused trouble when parallel to certain planes or
922 * axis go away with care paid to reducing the expressions.
923 * After checking, it does perform correctly under all cases, since
924 * in all the cases of division where the denominator would have
925 * been zero, the numerator would have been zero as well, giving
926 * the expected result.
940 /* We already hold the identity-matrix so we can skip some statements */
941 M(0,0) = (one_c
* xx
) + c
;
942 M(0,1) = (one_c
* xy
) - zs
;
943 M(0,2) = (one_c
* zx
) + ys
;
946 M(1,0) = (one_c
* xy
) + zs
;
947 M(1,1) = (one_c
* yy
) + c
;
948 M(1,2) = (one_c
* yz
) - xs
;
951 M(2,0) = (one_c
* zx
) - ys
;
952 M(2,1) = (one_c
* yz
) + xs
;
953 M(2,2) = (one_c
* zz
) + c
;
965 matrix_multf( mat
, m
, MAT_FLAG_ROTATION
);
969 * Apply a perspective projection matrix.
971 * \param mat matrix to apply the projection.
972 * \param left left clipping plane coordinate.
973 * \param right right clipping plane coordinate.
974 * \param bottom bottom clipping plane coordinate.
975 * \param top top clipping plane coordinate.
976 * \param nearval distance to the near clipping plane.
977 * \param farval distance to the far clipping plane.
979 * Creates the projection matrix and multiplies it with \p mat, marking the
980 * MAT_FLAG_PERSPECTIVE flag.
983 _math_matrix_frustum( GLmatrix
*mat
,
984 GLfloat left
, GLfloat right
,
985 GLfloat bottom
, GLfloat top
,
986 GLfloat nearval
, GLfloat farval
)
988 GLfloat x
, y
, a
, b
, c
, d
;
991 x
= (2.0F
*nearval
) / (right
-left
);
992 y
= (2.0F
*nearval
) / (top
-bottom
);
993 a
= (right
+left
) / (right
-left
);
994 b
= (top
+bottom
) / (top
-bottom
);
995 c
= -(farval
+nearval
) / ( farval
-nearval
);
996 d
= -(2.0F
*farval
*nearval
) / (farval
-nearval
); /* error? */
998 #define M(row,col) m[col*4+row]
999 M(0,0) = x
; M(0,1) = 0.0F
; M(0,2) = a
; M(0,3) = 0.0F
;
1000 M(1,0) = 0.0F
; M(1,1) = y
; M(1,2) = b
; M(1,3) = 0.0F
;
1001 M(2,0) = 0.0F
; M(2,1) = 0.0F
; M(2,2) = c
; M(2,3) = d
;
1002 M(3,0) = 0.0F
; M(3,1) = 0.0F
; M(3,2) = -1.0F
; M(3,3) = 0.0F
;
1005 matrix_multf( mat
, m
, MAT_FLAG_PERSPECTIVE
);
1009 * Apply an orthographic projection matrix.
1011 * \param mat matrix to apply the projection.
1012 * \param left left clipping plane coordinate.
1013 * \param right right clipping plane coordinate.
1014 * \param bottom bottom clipping plane coordinate.
1015 * \param top top clipping plane coordinate.
1016 * \param nearval distance to the near clipping plane.
1017 * \param farval distance to the far clipping plane.
1019 * Creates the projection matrix and multiplies it with \p mat, marking the
1020 * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
1023 _math_matrix_ortho( GLmatrix
*mat
,
1024 GLfloat left
, GLfloat right
,
1025 GLfloat bottom
, GLfloat top
,
1026 GLfloat nearval
, GLfloat farval
)
1030 #define M(row,col) m[col*4+row]
1031 M(0,0) = 2.0F
/ (right
-left
);
1034 M(0,3) = -(right
+left
) / (right
-left
);
1037 M(1,1) = 2.0F
/ (top
-bottom
);
1039 M(1,3) = -(top
+bottom
) / (top
-bottom
);
1043 M(2,2) = -2.0F
/ (farval
-nearval
);
1044 M(2,3) = -(farval
+nearval
) / (farval
-nearval
);
1052 matrix_multf( mat
, m
, (MAT_FLAG_GENERAL_SCALE
|MAT_FLAG_TRANSLATION
));
1056 * Multiply a matrix with a general scaling matrix.
1058 * \param mat matrix.
1059 * \param x x axis scale factor.
1060 * \param y y axis scale factor.
1061 * \param z z axis scale factor.
1063 * Multiplies in-place the elements of \p mat by the scale factors. Checks if
1064 * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
1065 * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
1066 * MAT_DIRTY_INVERSE dirty flags.
1069 _math_matrix_scale( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
)
1071 GLfloat
*m
= mat
->m
;
1072 m
[0] *= x
; m
[4] *= y
; m
[8] *= z
;
1073 m
[1] *= x
; m
[5] *= y
; m
[9] *= z
;
1074 m
[2] *= x
; m
[6] *= y
; m
[10] *= z
;
1075 m
[3] *= x
; m
[7] *= y
; m
[11] *= z
;
1077 if (FABSF(x
- y
) < 1e-8 && FABSF(x
- z
) < 1e-8)
1078 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1080 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1082 mat
->flags
|= (MAT_DIRTY_TYPE
|
1087 * Multiply a matrix with a translation matrix.
1089 * \param mat matrix.
1090 * \param x translation vector x coordinate.
1091 * \param y translation vector y coordinate.
1092 * \param z translation vector z coordinate.
1094 * Adds the translation coordinates to the elements of \p mat in-place. Marks
1095 * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
1099 _math_matrix_translate( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
)
1101 GLfloat
*m
= mat
->m
;
1102 m
[12] = m
[0] * x
+ m
[4] * y
+ m
[8] * z
+ m
[12];
1103 m
[13] = m
[1] * x
+ m
[5] * y
+ m
[9] * z
+ m
[13];
1104 m
[14] = m
[2] * x
+ m
[6] * y
+ m
[10] * z
+ m
[14];
1105 m
[15] = m
[3] * x
+ m
[7] * y
+ m
[11] * z
+ m
[15];
1107 mat
->flags
|= (MAT_FLAG_TRANSLATION
|
1114 * Set matrix to do viewport and depthrange mapping.
1115 * Transforms Normalized Device Coords to window/Z values.
1118 _math_matrix_viewport(GLmatrix
*m
, GLint x
, GLint y
, GLint width
, GLint height
,
1119 GLfloat zNear
, GLfloat zFar
, GLfloat depthMax
)
1121 m
->m
[MAT_SX
] = (GLfloat
) width
/ 2.0F
;
1122 m
->m
[MAT_TX
] = m
->m
[MAT_SX
] + x
;
1123 m
->m
[MAT_SY
] = (GLfloat
) height
/ 2.0F
;
1124 m
->m
[MAT_TY
] = m
->m
[MAT_SY
] + y
;
1125 m
->m
[MAT_SZ
] = depthMax
* ((zFar
- zNear
) / 2.0F
);
1126 m
->m
[MAT_TZ
] = depthMax
* ((zFar
- zNear
) / 2.0F
+ zNear
);
1127 m
->flags
= MAT_FLAG_GENERAL_SCALE
| MAT_FLAG_TRANSLATION
;
1128 m
->type
= MATRIX_3D_NO_ROT
;
1133 * Set a matrix to the identity matrix.
1135 * \param mat matrix.
1137 * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
1138 * Sets the matrix type to identity, and clear the dirty flags.
1141 _math_matrix_set_identity( GLmatrix
*mat
)
1143 memcpy( mat
->m
, Identity
, 16*sizeof(GLfloat
) );
1146 memcpy( mat
->inv
, Identity
, 16*sizeof(GLfloat
) );
1148 mat
->type
= MATRIX_IDENTITY
;
1149 mat
->flags
&= ~(MAT_DIRTY_FLAGS
|
1157 /**********************************************************************/
1158 /** \name Matrix analysis */
1161 #define ZERO(x) (1<<x)
1162 #define ONE(x) (1<<(x+16))
1164 #define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14))
1165 #define MASK_NO_2D_SCALE ( ONE(0) | ONE(5))
1167 #define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\
1168 ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\
1169 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1170 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1172 #define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \
1173 ZERO(1) | ZERO(9) | \
1174 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1175 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1177 #define MASK_2D ( ZERO(8) | \
1179 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1180 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1183 #define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \
1184 ZERO(1) | ZERO(9) | \
1185 ZERO(2) | ZERO(6) | \
1186 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1191 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1194 #define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\
1195 ZERO(1) | ZERO(13) |\
1196 ZERO(2) | ZERO(6) | \
1197 ZERO(3) | ZERO(7) | ZERO(15) )
1199 #define SQ(x) ((x)*(x))
1202 * Determine type and flags from scratch.
1204 * \param mat matrix.
1206 * This is expensive enough to only want to do it once.
1208 static void analyse_from_scratch( GLmatrix
*mat
)
1210 const GLfloat
*m
= mat
->m
;
1214 for (i
= 0 ; i
< 16 ; i
++) {
1215 if (m
[i
] == 0.0) mask
|= (1<<i
);
1218 if (m
[0] == 1.0F
) mask
|= (1<<16);
1219 if (m
[5] == 1.0F
) mask
|= (1<<21);
1220 if (m
[10] == 1.0F
) mask
|= (1<<26);
1221 if (m
[15] == 1.0F
) mask
|= (1<<31);
1223 mat
->flags
&= ~MAT_FLAGS_GEOMETRY
;
1225 /* Check for translation - no-one really cares
1227 if ((mask
& MASK_NO_TRX
) != MASK_NO_TRX
)
1228 mat
->flags
|= MAT_FLAG_TRANSLATION
;
1232 if (mask
== (GLuint
) MASK_IDENTITY
) {
1233 mat
->type
= MATRIX_IDENTITY
;
1235 else if ((mask
& MASK_2D_NO_ROT
) == (GLuint
) MASK_2D_NO_ROT
) {
1236 mat
->type
= MATRIX_2D_NO_ROT
;
1238 if ((mask
& MASK_NO_2D_SCALE
) != MASK_NO_2D_SCALE
)
1239 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1241 else if ((mask
& MASK_2D
) == (GLuint
) MASK_2D
) {
1242 GLfloat mm
= DOT2(m
, m
);
1243 GLfloat m4m4
= DOT2(m
+4,m
+4);
1244 GLfloat mm4
= DOT2(m
,m
+4);
1246 mat
->type
= MATRIX_2D
;
1248 /* Check for scale */
1249 if (SQ(mm
-1) > SQ(1e-6) ||
1250 SQ(m4m4
-1) > SQ(1e-6))
1251 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1253 /* Check for rotation */
1254 if (SQ(mm4
) > SQ(1e-6))
1255 mat
->flags
|= MAT_FLAG_GENERAL_3D
;
1257 mat
->flags
|= MAT_FLAG_ROTATION
;
1260 else if ((mask
& MASK_3D_NO_ROT
) == (GLuint
) MASK_3D_NO_ROT
) {
1261 mat
->type
= MATRIX_3D_NO_ROT
;
1263 /* Check for scale */
1264 if (SQ(m
[0]-m
[5]) < SQ(1e-6) &&
1265 SQ(m
[0]-m
[10]) < SQ(1e-6)) {
1266 if (SQ(m
[0]-1.0) > SQ(1e-6)) {
1267 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1271 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1274 else if ((mask
& MASK_3D
) == (GLuint
) MASK_3D
) {
1275 GLfloat c1
= DOT3(m
,m
);
1276 GLfloat c2
= DOT3(m
+4,m
+4);
1277 GLfloat c3
= DOT3(m
+8,m
+8);
1278 GLfloat d1
= DOT3(m
, m
+4);
1281 mat
->type
= MATRIX_3D
;
1283 /* Check for scale */
1284 if (SQ(c1
-c2
) < SQ(1e-6) && SQ(c1
-c3
) < SQ(1e-6)) {
1285 if (SQ(c1
-1.0) > SQ(1e-6))
1286 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1287 /* else no scale at all */
1290 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1293 /* Check for rotation */
1294 if (SQ(d1
) < SQ(1e-6)) {
1295 CROSS3( cp
, m
, m
+4 );
1296 SUB_3V( cp
, cp
, (m
+8) );
1297 if (LEN_SQUARED_3FV(cp
) < SQ(1e-6))
1298 mat
->flags
|= MAT_FLAG_ROTATION
;
1300 mat
->flags
|= MAT_FLAG_GENERAL_3D
;
1303 mat
->flags
|= MAT_FLAG_GENERAL_3D
; /* shear, etc */
1306 else if ((mask
& MASK_PERSPECTIVE
) == MASK_PERSPECTIVE
&& m
[11]==-1.0F
) {
1307 mat
->type
= MATRIX_PERSPECTIVE
;
1308 mat
->flags
|= MAT_FLAG_GENERAL
;
1311 mat
->type
= MATRIX_GENERAL
;
1312 mat
->flags
|= MAT_FLAG_GENERAL
;
1317 * Analyze a matrix given that its flags are accurate.
1319 * This is the more common operation, hopefully.
1321 static void analyse_from_flags( GLmatrix
*mat
)
1323 const GLfloat
*m
= mat
->m
;
1325 if (TEST_MAT_FLAGS(mat
, 0)) {
1326 mat
->type
= MATRIX_IDENTITY
;
1328 else if (TEST_MAT_FLAGS(mat
, (MAT_FLAG_TRANSLATION
|
1329 MAT_FLAG_UNIFORM_SCALE
|
1330 MAT_FLAG_GENERAL_SCALE
))) {
1331 if ( m
[10]==1.0F
&& m
[14]==0.0F
) {
1332 mat
->type
= MATRIX_2D_NO_ROT
;
1335 mat
->type
= MATRIX_3D_NO_ROT
;
1338 else if (TEST_MAT_FLAGS(mat
, MAT_FLAGS_3D
)) {
1341 && m
[2]==0.0F
&& m
[6]==0.0F
&& m
[10]==1.0F
&& m
[14]==0.0F
) {
1342 mat
->type
= MATRIX_2D
;
1345 mat
->type
= MATRIX_3D
;
1348 else if ( m
[4]==0.0F
&& m
[12]==0.0F
1349 && m
[1]==0.0F
&& m
[13]==0.0F
1350 && m
[2]==0.0F
&& m
[6]==0.0F
1351 && m
[3]==0.0F
&& m
[7]==0.0F
&& m
[11]==-1.0F
&& m
[15]==0.0F
) {
1352 mat
->type
= MATRIX_PERSPECTIVE
;
1355 mat
->type
= MATRIX_GENERAL
;
1360 * Analyze and update a matrix.
1362 * \param mat matrix.
1364 * If the matrix type is dirty then calls either analyse_from_scratch() or
1365 * analyse_from_flags() to determine its type, according to whether the flags
1366 * are dirty or not, respectively. If the matrix has an inverse and it's dirty
1367 * then calls matrix_invert(). Finally clears the dirty flags.
1370 _math_matrix_analyse( GLmatrix
*mat
)
1372 if (mat
->flags
& MAT_DIRTY_TYPE
) {
1373 if (mat
->flags
& MAT_DIRTY_FLAGS
)
1374 analyse_from_scratch( mat
);
1376 analyse_from_flags( mat
);
1379 if (mat
->inv
&& (mat
->flags
& MAT_DIRTY_INVERSE
)) {
1380 matrix_invert( mat
);
1381 mat
->flags
&= ~MAT_DIRTY_INVERSE
;
1384 mat
->flags
&= ~(MAT_DIRTY_FLAGS
| MAT_DIRTY_TYPE
);
1391 * Test if the given matrix preserves vector lengths.
1394 _math_matrix_is_length_preserving( const GLmatrix
*m
)
1396 return TEST_MAT_FLAGS( m
, MAT_FLAGS_LENGTH_PRESERVING
);
1401 * Test if the given matrix does any rotation.
1402 * (or perhaps if the upper-left 3x3 is non-identity)
1405 _math_matrix_has_rotation( const GLmatrix
*m
)
1407 if (m
->flags
& (MAT_FLAG_GENERAL
|
1409 MAT_FLAG_GENERAL_3D
|
1410 MAT_FLAG_PERSPECTIVE
))
1418 _math_matrix_is_general_scale( const GLmatrix
*m
)
1420 return (m
->flags
& MAT_FLAG_GENERAL_SCALE
) ? GL_TRUE
: GL_FALSE
;
1425 _math_matrix_is_dirty( const GLmatrix
*m
)
1427 return (m
->flags
& MAT_DIRTY
) ? GL_TRUE
: GL_FALSE
;
1431 /**********************************************************************/
1432 /** \name Matrix setup */
1438 * \param to destination matrix.
1439 * \param from source matrix.
1441 * Copies all fields in GLmatrix, creating an inverse array if necessary.
1444 _math_matrix_copy( GLmatrix
*to
, const GLmatrix
*from
)
1446 memcpy( to
->m
, from
->m
, sizeof(Identity
) );
1447 to
->flags
= from
->flags
;
1448 to
->type
= from
->type
;
1451 if (from
->inv
== 0) {
1452 matrix_invert( to
);
1455 memcpy(to
->inv
, from
->inv
, sizeof(GLfloat
)*16);
1461 * Loads a matrix array into GLmatrix.
1463 * \param m matrix array.
1464 * \param mat matrix.
1466 * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
1470 _math_matrix_loadf( GLmatrix
*mat
, const GLfloat
*m
)
1472 memcpy( mat
->m
, m
, 16*sizeof(GLfloat
) );
1473 mat
->flags
= (MAT_FLAG_GENERAL
| MAT_DIRTY
);
1477 * Matrix constructor.
1481 * Initialize the GLmatrix fields.
1484 _math_matrix_ctr( GLmatrix
*m
)
1486 m
->m
= (GLfloat
*) _mesa_align_malloc( 16 * sizeof(GLfloat
), 16 );
1488 memcpy( m
->m
, Identity
, sizeof(Identity
) );
1490 m
->type
= MATRIX_IDENTITY
;
1495 * Matrix destructor.
1499 * Frees the data in a GLmatrix.
1502 _math_matrix_dtr( GLmatrix
*m
)
1505 _mesa_align_free( m
->m
);
1509 _mesa_align_free( m
->inv
);
1515 * Allocate a matrix inverse.
1519 * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity.
1522 _math_matrix_alloc_inv( GLmatrix
*m
)
1525 m
->inv
= (GLfloat
*) _mesa_align_malloc( 16 * sizeof(GLfloat
), 16 );
1527 memcpy( m
->inv
, Identity
, 16 * sizeof(GLfloat
) );
1534 /**********************************************************************/
1535 /** \name Matrix transpose */
1539 * Transpose a GLfloat matrix.
1541 * \param to destination array.
1542 * \param from source array.
1545 _math_transposef( GLfloat to
[16], const GLfloat from
[16] )
1566 * Transpose a GLdouble matrix.
1568 * \param to destination array.
1569 * \param from source array.
1572 _math_transposed( GLdouble to
[16], const GLdouble from
[16] )
1593 * Transpose a GLdouble matrix and convert to GLfloat.
1595 * \param to destination array.
1596 * \param from source array.
1599 _math_transposefd( GLfloat to
[16], const GLdouble from
[16] )
1601 to
[0] = (GLfloat
) from
[0];
1602 to
[1] = (GLfloat
) from
[4];
1603 to
[2] = (GLfloat
) from
[8];
1604 to
[3] = (GLfloat
) from
[12];
1605 to
[4] = (GLfloat
) from
[1];
1606 to
[5] = (GLfloat
) from
[5];
1607 to
[6] = (GLfloat
) from
[9];
1608 to
[7] = (GLfloat
) from
[13];
1609 to
[8] = (GLfloat
) from
[2];
1610 to
[9] = (GLfloat
) from
[6];
1611 to
[10] = (GLfloat
) from
[10];
1612 to
[11] = (GLfloat
) from
[14];
1613 to
[12] = (GLfloat
) from
[3];
1614 to
[13] = (GLfloat
) from
[7];
1615 to
[14] = (GLfloat
) from
[11];
1616 to
[15] = (GLfloat
) from
[15];
1623 * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This
1624 * function is used for transforming clipping plane equations and spotlight
1626 * Mathematically, u = v * m.
1627 * Input: v - input vector
1628 * m - transformation matrix
1629 * Output: u - transformed vector
1632 _mesa_transform_vector( GLfloat u
[4], const GLfloat v
[4], const GLfloat m
[16] )
1634 const GLfloat v0
= v
[0], v1
= v
[1], v2
= v
[2], v3
= v
[3];
1635 #define M(row,col) m[row + col*4]
1636 u
[0] = v0
* M(0,0) + v1
* M(1,0) + v2
* M(2,0) + v3
* M(3,0);
1637 u
[1] = v0
* M(0,1) + v1
* M(1,1) + v2
* M(2,1) + v3
* M(3,1);
1638 u
[2] = v0
* M(0,2) + v1
* M(1,2) + v2
* M(2,2) + v3
* M(3,2);
1639 u
[3] = v0
* M(0,3) + v1
* M(1,3) + v2
* M(2,3) + v3
* M(3,3);