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
39 * \defgroup MatFlags MAT_FLAG_XXX-flags
41 * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
42 * It would be nice to make all these flags private to m_matrix.c
45 #define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag.
46 * (Not actually used - the identity
47 * matrix is identified by the absense
48 * of all other flags.)
50 #define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */
51 #define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */
52 #define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */
53 #define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */
54 #define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */
55 #define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */
56 #define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */
57 #define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */
58 #define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */
59 #define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */
60 #define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */
62 /** angle preserving matrix flags mask */
63 #define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
64 MAT_FLAG_TRANSLATION | \
65 MAT_FLAG_UNIFORM_SCALE)
67 /** geometry related matrix flags mask */
68 #define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
70 MAT_FLAG_TRANSLATION | \
71 MAT_FLAG_UNIFORM_SCALE | \
72 MAT_FLAG_GENERAL_SCALE | \
73 MAT_FLAG_GENERAL_3D | \
74 MAT_FLAG_PERSPECTIVE | \
77 /** length preserving matrix flags mask */
78 #define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
82 /** 3D (non-perspective) matrix flags mask */
83 #define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
84 MAT_FLAG_TRANSLATION | \
85 MAT_FLAG_UNIFORM_SCALE | \
86 MAT_FLAG_GENERAL_SCALE | \
89 /** dirty matrix flags mask */
90 #define MAT_DIRTY (MAT_DIRTY_TYPE | \
98 * Test geometry related matrix flags.
100 * \param mat a pointer to a GLmatrix structure.
101 * \param a flags mask.
103 * \returns non-zero if all geometry related matrix flags are contained within
104 * the mask, or zero otherwise.
106 #define TEST_MAT_FLAGS(mat, a) \
107 ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
112 * Names of the corresponding GLmatrixtype values.
114 static const char *types
[] = {
118 "MATRIX_PERSPECTIVE",
128 static GLfloat Identity
[16] = {
137 /**********************************************************************/
138 /** \name Matrix multiplication */
141 #define A(row,col) a[(col<<2)+row]
142 #define B(row,col) b[(col<<2)+row]
143 #define P(row,col) product[(col<<2)+row]
146 * Perform a full 4x4 matrix multiplication.
150 * \param product will receive the product of \p a and \p b.
152 * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
154 * \note KW: 4*16 = 64 multiplications
156 * \author This \c matmul was contributed by Thomas Malik
158 static void matmul4( GLfloat
*product
, const GLfloat
*a
, const GLfloat
*b
)
161 for (i
= 0; i
< 4; i
++) {
162 const GLfloat ai0
=A(i
,0), ai1
=A(i
,1), ai2
=A(i
,2), ai3
=A(i
,3);
163 P(i
,0) = ai0
* B(0,0) + ai1
* B(1,0) + ai2
* B(2,0) + ai3
* B(3,0);
164 P(i
,1) = ai0
* B(0,1) + ai1
* B(1,1) + ai2
* B(2,1) + ai3
* B(3,1);
165 P(i
,2) = ai0
* B(0,2) + ai1
* B(1,2) + ai2
* B(2,2) + ai3
* B(3,2);
166 P(i
,3) = ai0
* B(0,3) + ai1
* B(1,3) + ai2
* B(2,3) + ai3
* B(3,3);
171 * Multiply two matrices known to occupy only the top three rows, such
172 * as typical model matrices, and orthogonal matrices.
176 * \param product will receive the product of \p a and \p b.
178 static void matmul34( GLfloat
*product
, const GLfloat
*a
, const GLfloat
*b
)
181 for (i
= 0; i
< 3; i
++) {
182 const GLfloat ai0
=A(i
,0), ai1
=A(i
,1), ai2
=A(i
,2), ai3
=A(i
,3);
183 P(i
,0) = ai0
* B(0,0) + ai1
* B(1,0) + ai2
* B(2,0);
184 P(i
,1) = ai0
* B(0,1) + ai1
* B(1,1) + ai2
* B(2,1);
185 P(i
,2) = ai0
* B(0,2) + ai1
* B(1,2) + ai2
* B(2,2);
186 P(i
,3) = ai0
* B(0,3) + ai1
* B(1,3) + ai2
* B(2,3) + ai3
;
199 * Multiply a matrix by an array of floats with known properties.
201 * \param mat pointer to a GLmatrix structure containing the left multiplication
202 * matrix, and that will receive the product result.
203 * \param m right multiplication matrix array.
204 * \param flags flags of the matrix \p m.
206 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
207 * if both matrices are 3D, or matmul4() otherwise.
209 static void matrix_multf( GLmatrix
*mat
, const GLfloat
*m
, GLuint flags
)
211 mat
->flags
|= (flags
| MAT_DIRTY_TYPE
| MAT_DIRTY_INVERSE
);
213 if (TEST_MAT_FLAGS(mat
, MAT_FLAGS_3D
))
214 matmul34( mat
->m
, mat
->m
, m
);
216 matmul4( mat
->m
, mat
->m
, m
);
220 * Matrix multiplication.
222 * \param dest destination matrix.
223 * \param a left matrix.
224 * \param b right matrix.
226 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
227 * if both matrices are 3D, or matmul4() otherwise.
230 _math_matrix_mul_matrix( GLmatrix
*dest
, const GLmatrix
*a
, const GLmatrix
*b
)
232 dest
->flags
= (a
->flags
|
237 if (TEST_MAT_FLAGS(dest
, MAT_FLAGS_3D
))
238 matmul34( dest
->m
, a
->m
, b
->m
);
240 matmul4( dest
->m
, a
->m
, b
->m
);
244 * Matrix multiplication.
246 * \param dest left and destination matrix.
247 * \param m right matrix array.
249 * Marks the matrix flags with general flag, and type and inverse dirty flags.
250 * Calls matmul4() for the multiplication.
253 _math_matrix_mul_floats( GLmatrix
*dest
, const GLfloat
*m
)
255 dest
->flags
|= (MAT_FLAG_GENERAL
|
260 matmul4( dest
->m
, dest
->m
, m
);
266 /**********************************************************************/
267 /** \name Matrix output */
271 * Print a matrix array.
273 * \param m matrix array.
275 * Called by _math_matrix_print() to print a matrix or its inverse.
277 static void print_matrix_floats( const GLfloat m
[16] )
281 _mesa_debug(NULL
,"\t%f %f %f %f\n", m
[i
], m
[4+i
], m
[8+i
], m
[12+i
] );
286 * Dumps the contents of a GLmatrix structure.
288 * \param m pointer to the GLmatrix structure.
291 _math_matrix_print( const GLmatrix
*m
)
293 _mesa_debug(NULL
, "Matrix type: %s, flags: %x\n", types
[m
->type
], m
->flags
);
294 print_matrix_floats(m
->m
);
295 _mesa_debug(NULL
, "Inverse: \n");
298 print_matrix_floats(m
->inv
);
299 matmul4(prod
, m
->m
, m
->inv
);
300 _mesa_debug(NULL
, "Mat * Inverse:\n");
301 print_matrix_floats(prod
);
304 _mesa_debug(NULL
, " - not available\n");
312 * References an element of 4x4 matrix.
314 * \param m matrix array.
315 * \param c column of the desired element.
316 * \param r row of the desired element.
318 * \return value of the desired element.
320 * Calculate the linear storage index of the element and references it.
322 #define MAT(m,r,c) (m)[(c)*4+(r)]
325 /**********************************************************************/
326 /** \name Matrix inversion */
330 * Swaps the values of two floating pointer variables.
332 * Used by invert_matrix_general() to swap the row pointers.
334 #define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
337 * Compute inverse of 4x4 transformation matrix.
339 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
340 * stored in the GLmatrix::inv attribute.
342 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
345 * Code contributed by Jacques Leroy jle@star.be
347 * Calculates the inverse matrix by performing the gaussian matrix reduction
348 * with partial pivoting followed by back/substitution with the loops manually
351 static GLboolean
invert_matrix_general( GLmatrix
*mat
)
353 const GLfloat
*m
= mat
->m
;
354 GLfloat
*out
= mat
->inv
;
356 GLfloat m0
, m1
, m2
, m3
, s
;
357 GLfloat
*r0
, *r1
, *r2
, *r3
;
359 r0
= wtmp
[0], r1
= wtmp
[1], r2
= wtmp
[2], r3
= wtmp
[3];
361 r0
[0] = MAT(m
,0,0), r0
[1] = MAT(m
,0,1),
362 r0
[2] = MAT(m
,0,2), r0
[3] = MAT(m
,0,3),
363 r0
[4] = 1.0, r0
[5] = r0
[6] = r0
[7] = 0.0,
365 r1
[0] = MAT(m
,1,0), r1
[1] = MAT(m
,1,1),
366 r1
[2] = MAT(m
,1,2), r1
[3] = MAT(m
,1,3),
367 r1
[5] = 1.0, r1
[4] = r1
[6] = r1
[7] = 0.0,
369 r2
[0] = MAT(m
,2,0), r2
[1] = MAT(m
,2,1),
370 r2
[2] = MAT(m
,2,2), r2
[3] = MAT(m
,2,3),
371 r2
[6] = 1.0, r2
[4] = r2
[5] = r2
[7] = 0.0,
373 r3
[0] = MAT(m
,3,0), r3
[1] = MAT(m
,3,1),
374 r3
[2] = MAT(m
,3,2), r3
[3] = MAT(m
,3,3),
375 r3
[7] = 1.0, r3
[4] = r3
[5] = r3
[6] = 0.0;
377 /* choose pivot - or die */
378 if (FABSF(r3
[0])>FABSF(r2
[0])) SWAP_ROWS(r3
, r2
);
379 if (FABSF(r2
[0])>FABSF(r1
[0])) SWAP_ROWS(r2
, r1
);
380 if (FABSF(r1
[0])>FABSF(r0
[0])) SWAP_ROWS(r1
, r0
);
381 if (0.0 == r0
[0]) return GL_FALSE
;
383 /* eliminate first variable */
384 m1
= r1
[0]/r0
[0]; m2
= r2
[0]/r0
[0]; m3
= r3
[0]/r0
[0];
385 s
= r0
[1]; r1
[1] -= m1
* s
; r2
[1] -= m2
* s
; r3
[1] -= m3
* s
;
386 s
= r0
[2]; r1
[2] -= m1
* s
; r2
[2] -= m2
* s
; r3
[2] -= m3
* s
;
387 s
= r0
[3]; r1
[3] -= m1
* s
; r2
[3] -= m2
* s
; r3
[3] -= m3
* s
;
389 if (s
!= 0.0) { r1
[4] -= m1
* s
; r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
391 if (s
!= 0.0) { r1
[5] -= m1
* s
; r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
393 if (s
!= 0.0) { r1
[6] -= m1
* s
; r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
395 if (s
!= 0.0) { r1
[7] -= m1
* s
; r2
[7] -= m2
* s
; r3
[7] -= m3
* s
; }
397 /* choose pivot - or die */
398 if (FABSF(r3
[1])>FABSF(r2
[1])) SWAP_ROWS(r3
, r2
);
399 if (FABSF(r2
[1])>FABSF(r1
[1])) SWAP_ROWS(r2
, r1
);
400 if (0.0 == r1
[1]) return GL_FALSE
;
402 /* eliminate second variable */
403 m2
= r2
[1]/r1
[1]; m3
= r3
[1]/r1
[1];
404 r2
[2] -= m2
* r1
[2]; r3
[2] -= m3
* r1
[2];
405 r2
[3] -= m2
* r1
[3]; r3
[3] -= m3
* r1
[3];
406 s
= r1
[4]; if (0.0 != s
) { r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
407 s
= r1
[5]; if (0.0 != s
) { r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
408 s
= r1
[6]; if (0.0 != s
) { r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
409 s
= r1
[7]; if (0.0 != s
) { r2
[7] -= m2
* s
; r3
[7] -= m3
* s
; }
411 /* choose pivot - or die */
412 if (FABSF(r3
[2])>FABSF(r2
[2])) SWAP_ROWS(r3
, r2
);
413 if (0.0 == r2
[2]) return GL_FALSE
;
415 /* eliminate third variable */
417 r3
[3] -= m3
* r2
[3], r3
[4] -= m3
* r2
[4],
418 r3
[5] -= m3
* r2
[5], r3
[6] -= m3
* r2
[6],
422 if (0.0 == r3
[3]) return GL_FALSE
;
424 s
= 1.0F
/r3
[3]; /* now back substitute row 3 */
425 r3
[4] *= s
; r3
[5] *= s
; r3
[6] *= s
; r3
[7] *= s
;
427 m2
= r2
[3]; /* now back substitute row 2 */
429 r2
[4] = s
* (r2
[4] - r3
[4] * m2
), r2
[5] = s
* (r2
[5] - r3
[5] * m2
),
430 r2
[6] = s
* (r2
[6] - r3
[6] * m2
), r2
[7] = s
* (r2
[7] - r3
[7] * m2
);
432 r1
[4] -= r3
[4] * m1
, r1
[5] -= r3
[5] * m1
,
433 r1
[6] -= r3
[6] * m1
, r1
[7] -= r3
[7] * m1
;
435 r0
[4] -= r3
[4] * m0
, r0
[5] -= r3
[5] * m0
,
436 r0
[6] -= r3
[6] * m0
, r0
[7] -= r3
[7] * m0
;
438 m1
= r1
[2]; /* now back substitute row 1 */
440 r1
[4] = s
* (r1
[4] - r2
[4] * m1
), r1
[5] = s
* (r1
[5] - r2
[5] * m1
),
441 r1
[6] = s
* (r1
[6] - r2
[6] * m1
), r1
[7] = s
* (r1
[7] - r2
[7] * m1
);
443 r0
[4] -= r2
[4] * m0
, r0
[5] -= r2
[5] * m0
,
444 r0
[6] -= r2
[6] * m0
, r0
[7] -= r2
[7] * m0
;
446 m0
= r0
[1]; /* now back substitute row 0 */
448 r0
[4] = s
* (r0
[4] - r1
[4] * m0
), r0
[5] = s
* (r0
[5] - r1
[5] * m0
),
449 r0
[6] = s
* (r0
[6] - r1
[6] * m0
), r0
[7] = s
* (r0
[7] - r1
[7] * m0
);
451 MAT(out
,0,0) = r0
[4]; MAT(out
,0,1) = r0
[5],
452 MAT(out
,0,2) = r0
[6]; MAT(out
,0,3) = r0
[7],
453 MAT(out
,1,0) = r1
[4]; MAT(out
,1,1) = r1
[5],
454 MAT(out
,1,2) = r1
[6]; MAT(out
,1,3) = r1
[7],
455 MAT(out
,2,0) = r2
[4]; MAT(out
,2,1) = r2
[5],
456 MAT(out
,2,2) = r2
[6]; MAT(out
,2,3) = r2
[7],
457 MAT(out
,3,0) = r3
[4]; MAT(out
,3,1) = r3
[5],
458 MAT(out
,3,2) = r3
[6]; MAT(out
,3,3) = r3
[7];
465 * Compute inverse of a general 3d transformation matrix.
467 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
468 * stored in the GLmatrix::inv attribute.
470 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
472 * \author Adapted from graphics gems II.
474 * Calculates the inverse of the upper left by first calculating its
475 * determinant and multiplying it to the symmetric adjust matrix of each
476 * element. Finally deals with the translation part by transforming the
477 * original translation vector using by the calculated submatrix inverse.
479 static GLboolean
invert_matrix_3d_general( GLmatrix
*mat
)
481 const GLfloat
*in
= mat
->m
;
482 GLfloat
*out
= mat
->inv
;
486 /* Calculate the determinant of upper left 3x3 submatrix and
487 * determine if the matrix is singular.
490 t
= MAT(in
,0,0) * MAT(in
,1,1) * MAT(in
,2,2);
491 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
493 t
= MAT(in
,1,0) * MAT(in
,2,1) * MAT(in
,0,2);
494 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
496 t
= MAT(in
,2,0) * MAT(in
,0,1) * MAT(in
,1,2);
497 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
499 t
= -MAT(in
,2,0) * MAT(in
,1,1) * MAT(in
,0,2);
500 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
502 t
= -MAT(in
,1,0) * MAT(in
,0,1) * MAT(in
,2,2);
503 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
505 t
= -MAT(in
,0,0) * MAT(in
,2,1) * MAT(in
,1,2);
506 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
514 MAT(out
,0,0) = ( (MAT(in
,1,1)*MAT(in
,2,2) - MAT(in
,2,1)*MAT(in
,1,2) )*det
);
515 MAT(out
,0,1) = (- (MAT(in
,0,1)*MAT(in
,2,2) - MAT(in
,2,1)*MAT(in
,0,2) )*det
);
516 MAT(out
,0,2) = ( (MAT(in
,0,1)*MAT(in
,1,2) - MAT(in
,1,1)*MAT(in
,0,2) )*det
);
517 MAT(out
,1,0) = (- (MAT(in
,1,0)*MAT(in
,2,2) - MAT(in
,2,0)*MAT(in
,1,2) )*det
);
518 MAT(out
,1,1) = ( (MAT(in
,0,0)*MAT(in
,2,2) - MAT(in
,2,0)*MAT(in
,0,2) )*det
);
519 MAT(out
,1,2) = (- (MAT(in
,0,0)*MAT(in
,1,2) - MAT(in
,1,0)*MAT(in
,0,2) )*det
);
520 MAT(out
,2,0) = ( (MAT(in
,1,0)*MAT(in
,2,1) - MAT(in
,2,0)*MAT(in
,1,1) )*det
);
521 MAT(out
,2,1) = (- (MAT(in
,0,0)*MAT(in
,2,1) - MAT(in
,2,0)*MAT(in
,0,1) )*det
);
522 MAT(out
,2,2) = ( (MAT(in
,0,0)*MAT(in
,1,1) - MAT(in
,1,0)*MAT(in
,0,1) )*det
);
524 /* Do the translation part */
525 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0) +
526 MAT(in
,1,3) * MAT(out
,0,1) +
527 MAT(in
,2,3) * MAT(out
,0,2) );
528 MAT(out
,1,3) = - (MAT(in
,0,3) * MAT(out
,1,0) +
529 MAT(in
,1,3) * MAT(out
,1,1) +
530 MAT(in
,2,3) * MAT(out
,1,2) );
531 MAT(out
,2,3) = - (MAT(in
,0,3) * MAT(out
,2,0) +
532 MAT(in
,1,3) * MAT(out
,2,1) +
533 MAT(in
,2,3) * MAT(out
,2,2) );
539 * Compute inverse of a 3d transformation matrix.
541 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
542 * stored in the GLmatrix::inv attribute.
544 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
546 * If the matrix is not an angle preserving matrix then calls
547 * invert_matrix_3d_general for the actual calculation. Otherwise calculates
548 * the inverse matrix analyzing and inverting each of the scaling, rotation and
551 static GLboolean
invert_matrix_3d( GLmatrix
*mat
)
553 const GLfloat
*in
= mat
->m
;
554 GLfloat
*out
= mat
->inv
;
556 if (!TEST_MAT_FLAGS(mat
, MAT_FLAGS_ANGLE_PRESERVING
)) {
557 return invert_matrix_3d_general( mat
);
560 if (mat
->flags
& MAT_FLAG_UNIFORM_SCALE
) {
561 GLfloat scale
= (MAT(in
,0,0) * MAT(in
,0,0) +
562 MAT(in
,0,1) * MAT(in
,0,1) +
563 MAT(in
,0,2) * MAT(in
,0,2));
568 scale
= 1.0F
/ scale
;
570 /* Transpose and scale the 3 by 3 upper-left submatrix. */
571 MAT(out
,0,0) = scale
* MAT(in
,0,0);
572 MAT(out
,1,0) = scale
* MAT(in
,0,1);
573 MAT(out
,2,0) = scale
* MAT(in
,0,2);
574 MAT(out
,0,1) = scale
* MAT(in
,1,0);
575 MAT(out
,1,1) = scale
* MAT(in
,1,1);
576 MAT(out
,2,1) = scale
* MAT(in
,1,2);
577 MAT(out
,0,2) = scale
* MAT(in
,2,0);
578 MAT(out
,1,2) = scale
* MAT(in
,2,1);
579 MAT(out
,2,2) = scale
* MAT(in
,2,2);
581 else if (mat
->flags
& MAT_FLAG_ROTATION
) {
582 /* Transpose the 3 by 3 upper-left submatrix. */
583 MAT(out
,0,0) = MAT(in
,0,0);
584 MAT(out
,1,0) = MAT(in
,0,1);
585 MAT(out
,2,0) = MAT(in
,0,2);
586 MAT(out
,0,1) = MAT(in
,1,0);
587 MAT(out
,1,1) = MAT(in
,1,1);
588 MAT(out
,2,1) = MAT(in
,1,2);
589 MAT(out
,0,2) = MAT(in
,2,0);
590 MAT(out
,1,2) = MAT(in
,2,1);
591 MAT(out
,2,2) = MAT(in
,2,2);
594 /* pure translation */
595 memcpy( out
, Identity
, sizeof(Identity
) );
596 MAT(out
,0,3) = - MAT(in
,0,3);
597 MAT(out
,1,3) = - MAT(in
,1,3);
598 MAT(out
,2,3) = - MAT(in
,2,3);
602 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
603 /* Do the translation part */
604 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0) +
605 MAT(in
,1,3) * MAT(out
,0,1) +
606 MAT(in
,2,3) * MAT(out
,0,2) );
607 MAT(out
,1,3) = - (MAT(in
,0,3) * MAT(out
,1,0) +
608 MAT(in
,1,3) * MAT(out
,1,1) +
609 MAT(in
,2,3) * MAT(out
,1,2) );
610 MAT(out
,2,3) = - (MAT(in
,0,3) * MAT(out
,2,0) +
611 MAT(in
,1,3) * MAT(out
,2,1) +
612 MAT(in
,2,3) * MAT(out
,2,2) );
615 MAT(out
,0,3) = MAT(out
,1,3) = MAT(out
,2,3) = 0.0;
622 * Compute inverse of an identity transformation matrix.
624 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
625 * stored in the GLmatrix::inv attribute.
627 * \return always GL_TRUE.
629 * Simply copies Identity into GLmatrix::inv.
631 static GLboolean
invert_matrix_identity( GLmatrix
*mat
)
633 memcpy( mat
->inv
, Identity
, sizeof(Identity
) );
638 * Compute inverse of a no-rotation 3d transformation matrix.
640 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
641 * stored in the GLmatrix::inv attribute.
643 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
647 static GLboolean
invert_matrix_3d_no_rot( GLmatrix
*mat
)
649 const GLfloat
*in
= mat
->m
;
650 GLfloat
*out
= mat
->inv
;
652 if (MAT(in
,0,0) == 0 || MAT(in
,1,1) == 0 || MAT(in
,2,2) == 0 )
655 memcpy( out
, Identity
, 16 * sizeof(GLfloat
) );
656 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
657 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
658 MAT(out
,2,2) = 1.0F
/ MAT(in
,2,2);
660 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
661 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0));
662 MAT(out
,1,3) = - (MAT(in
,1,3) * MAT(out
,1,1));
663 MAT(out
,2,3) = - (MAT(in
,2,3) * MAT(out
,2,2));
670 * Compute inverse of a no-rotation 2d transformation matrix.
672 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
673 * stored in the GLmatrix::inv attribute.
675 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
677 * Calculates the inverse matrix by applying the inverse scaling and
678 * translation to the identity matrix.
680 static GLboolean
invert_matrix_2d_no_rot( GLmatrix
*mat
)
682 const GLfloat
*in
= mat
->m
;
683 GLfloat
*out
= mat
->inv
;
685 if (MAT(in
,0,0) == 0 || MAT(in
,1,1) == 0)
688 memcpy( out
, Identity
, 16 * sizeof(GLfloat
) );
689 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
690 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
692 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
693 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0));
694 MAT(out
,1,3) = - (MAT(in
,1,3) * MAT(out
,1,1));
702 static GLboolean
invert_matrix_perspective( GLmatrix
*mat
)
704 const GLfloat
*in
= mat
->m
;
705 GLfloat
*out
= mat
->inv
;
707 if (MAT(in
,2,3) == 0)
710 memcpy( out
, Identity
, 16 * sizeof(GLfloat
) );
712 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
713 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
715 MAT(out
,0,3) = MAT(in
,0,2);
716 MAT(out
,1,3) = MAT(in
,1,2);
721 MAT(out
,3,2) = 1.0F
/ MAT(in
,2,3);
722 MAT(out
,3,3) = MAT(in
,2,2) * MAT(out
,3,2);
729 * Matrix inversion function pointer type.
731 typedef GLboolean (*inv_mat_func
)( GLmatrix
*mat
);
734 * Table of the matrix inversion functions according to the matrix type.
736 static inv_mat_func inv_mat_tab
[7] = {
737 invert_matrix_general
,
738 invert_matrix_identity
,
739 invert_matrix_3d_no_rot
,
741 /* Don't use this function for now - it fails when the projection matrix
742 * is premultiplied by a translation (ala Chromium's tilesort SPU).
744 invert_matrix_perspective
,
746 invert_matrix_general
,
748 invert_matrix_3d
, /* lazy! */
749 invert_matrix_2d_no_rot
,
754 * Compute inverse of a transformation matrix.
756 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
757 * stored in the GLmatrix::inv attribute.
759 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
761 * Calls the matrix inversion function in inv_mat_tab corresponding to the
762 * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag,
763 * and copies the identity matrix into GLmatrix::inv.
765 static GLboolean
matrix_invert( GLmatrix
*mat
)
767 if (inv_mat_tab
[mat
->type
](mat
)) {
768 mat
->flags
&= ~MAT_FLAG_SINGULAR
;
771 mat
->flags
|= MAT_FLAG_SINGULAR
;
772 memcpy( mat
->inv
, Identity
, sizeof(Identity
) );
780 /**********************************************************************/
781 /** \name Matrix generation */
785 * Generate a 4x4 transformation matrix from glRotate parameters, and
786 * post-multiply the input matrix by it.
789 * This function was contributed by Erich Boleyn (erich@uruk.org).
790 * Optimizations contributed by Rudolf Opalla (rudi@khm.de).
793 _math_matrix_rotate( GLmatrix
*mat
,
794 GLfloat angle
, GLfloat x
, GLfloat y
, GLfloat z
)
796 GLfloat xx
, yy
, zz
, xy
, yz
, zx
, xs
, ys
, zs
, one_c
, s
, c
;
800 s
= (GLfloat
) sin( angle
* DEG2RAD
);
801 c
= (GLfloat
) cos( angle
* DEG2RAD
);
803 memcpy(m
, Identity
, sizeof(GLfloat
)*16);
804 optimized
= GL_FALSE
;
806 #define M(row,col) m[col*4+row]
812 /* rotate only around z-axis */
825 else if (z
== 0.0F
) {
827 /* rotate only around y-axis */
840 else if (y
== 0.0F
) {
843 /* rotate only around x-axis */
858 const GLfloat mag
= SQRTF(x
* x
+ y
* y
+ z
* z
);
861 /* no rotation, leave mat as-is */
871 * Arbitrary axis rotation matrix.
873 * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
874 * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation
875 * (which is about the X-axis), and the two composite transforms
876 * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
877 * from the arbitrary axis to the X-axis then back. They are
878 * all elementary rotations.
880 * Rz' is a rotation about the Z-axis, to bring the axis vector
881 * into the x-z plane. Then Ry' is applied, rotating about the
882 * Y-axis to bring the axis vector parallel with the X-axis. The
883 * rotation about the X-axis is then performed. Ry and Rz are
884 * simply the respective inverse transforms to bring the arbitrary
885 * axis back to its original orientation. The first transforms
886 * Rz' and Ry' are considered inverses, since the data from the
887 * arbitrary axis gives you info on how to get to it, not how
888 * to get away from it, and an inverse must be applied.
890 * The basic calculation used is to recognize that the arbitrary
891 * axis vector (x, y, z), since it is of unit length, actually
892 * represents the sines and cosines of the angles to rotate the
893 * X-axis to the same orientation, with theta being the angle about
894 * Z and phi the angle about Y (in the order described above)
897 * cos ( theta ) = x / sqrt ( 1 - z^2 )
898 * sin ( theta ) = y / sqrt ( 1 - z^2 )
900 * cos ( phi ) = sqrt ( 1 - z^2 )
903 * Note that cos ( phi ) can further be inserted to the above
906 * cos ( theta ) = x / cos ( phi )
907 * sin ( theta ) = y / sin ( phi )
909 * ...etc. Because of those relations and the standard trigonometric
910 * relations, it is pssible to reduce the transforms down to what
911 * is used below. It may be that any primary axis chosen will give the
912 * same results (modulo a sign convention) using thie method.
914 * Particularly nice is to notice that all divisions that might
915 * have caused trouble when parallel to certain planes or
916 * axis go away with care paid to reducing the expressions.
917 * After checking, it does perform correctly under all cases, since
918 * in all the cases of division where the denominator would have
919 * been zero, the numerator would have been zero as well, giving
920 * the expected result.
934 /* We already hold the identity-matrix so we can skip some statements */
935 M(0,0) = (one_c
* xx
) + c
;
936 M(0,1) = (one_c
* xy
) - zs
;
937 M(0,2) = (one_c
* zx
) + ys
;
940 M(1,0) = (one_c
* xy
) + zs
;
941 M(1,1) = (one_c
* yy
) + c
;
942 M(1,2) = (one_c
* yz
) - xs
;
945 M(2,0) = (one_c
* zx
) - ys
;
946 M(2,1) = (one_c
* yz
) + xs
;
947 M(2,2) = (one_c
* zz
) + c
;
959 matrix_multf( mat
, m
, MAT_FLAG_ROTATION
);
963 * Apply a perspective projection matrix.
965 * \param mat matrix to apply the projection.
966 * \param left left clipping plane coordinate.
967 * \param right right clipping plane coordinate.
968 * \param bottom bottom clipping plane coordinate.
969 * \param top top clipping plane coordinate.
970 * \param nearval distance to the near clipping plane.
971 * \param farval distance to the far clipping plane.
973 * Creates the projection matrix and multiplies it with \p mat, marking the
974 * MAT_FLAG_PERSPECTIVE flag.
977 _math_matrix_frustum( GLmatrix
*mat
,
978 GLfloat left
, GLfloat right
,
979 GLfloat bottom
, GLfloat top
,
980 GLfloat nearval
, GLfloat farval
)
982 GLfloat x
, y
, a
, b
, c
, d
;
985 x
= (2.0F
*nearval
) / (right
-left
);
986 y
= (2.0F
*nearval
) / (top
-bottom
);
987 a
= (right
+left
) / (right
-left
);
988 b
= (top
+bottom
) / (top
-bottom
);
989 c
= -(farval
+nearval
) / ( farval
-nearval
);
990 d
= -(2.0F
*farval
*nearval
) / (farval
-nearval
); /* error? */
992 #define M(row,col) m[col*4+row]
993 M(0,0) = x
; M(0,1) = 0.0F
; M(0,2) = a
; M(0,3) = 0.0F
;
994 M(1,0) = 0.0F
; M(1,1) = y
; M(1,2) = b
; M(1,3) = 0.0F
;
995 M(2,0) = 0.0F
; M(2,1) = 0.0F
; M(2,2) = c
; M(2,3) = d
;
996 M(3,0) = 0.0F
; M(3,1) = 0.0F
; M(3,2) = -1.0F
; M(3,3) = 0.0F
;
999 matrix_multf( mat
, m
, MAT_FLAG_PERSPECTIVE
);
1003 * Apply an orthographic projection matrix.
1005 * \param mat matrix to apply the projection.
1006 * \param left left clipping plane coordinate.
1007 * \param right right clipping plane coordinate.
1008 * \param bottom bottom clipping plane coordinate.
1009 * \param top top clipping plane coordinate.
1010 * \param nearval distance to the near clipping plane.
1011 * \param farval distance to the far clipping plane.
1013 * Creates the projection matrix and multiplies it with \p mat, marking the
1014 * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
1017 _math_matrix_ortho( GLmatrix
*mat
,
1018 GLfloat left
, GLfloat right
,
1019 GLfloat bottom
, GLfloat top
,
1020 GLfloat nearval
, GLfloat farval
)
1024 #define M(row,col) m[col*4+row]
1025 M(0,0) = 2.0F
/ (right
-left
);
1028 M(0,3) = -(right
+left
) / (right
-left
);
1031 M(1,1) = 2.0F
/ (top
-bottom
);
1033 M(1,3) = -(top
+bottom
) / (top
-bottom
);
1037 M(2,2) = -2.0F
/ (farval
-nearval
);
1038 M(2,3) = -(farval
+nearval
) / (farval
-nearval
);
1046 matrix_multf( mat
, m
, (MAT_FLAG_GENERAL_SCALE
|MAT_FLAG_TRANSLATION
));
1050 * Multiply a matrix with a general scaling matrix.
1052 * \param mat matrix.
1053 * \param x x axis scale factor.
1054 * \param y y axis scale factor.
1055 * \param z z axis scale factor.
1057 * Multiplies in-place the elements of \p mat by the scale factors. Checks if
1058 * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
1059 * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
1060 * MAT_DIRTY_INVERSE dirty flags.
1063 _math_matrix_scale( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
)
1065 GLfloat
*m
= mat
->m
;
1066 m
[0] *= x
; m
[4] *= y
; m
[8] *= z
;
1067 m
[1] *= x
; m
[5] *= y
; m
[9] *= z
;
1068 m
[2] *= x
; m
[6] *= y
; m
[10] *= z
;
1069 m
[3] *= x
; m
[7] *= y
; m
[11] *= z
;
1071 if (FABSF(x
- y
) < 1e-8 && FABSF(x
- z
) < 1e-8)
1072 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1074 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1076 mat
->flags
|= (MAT_DIRTY_TYPE
|
1081 * Multiply a matrix with a translation matrix.
1083 * \param mat matrix.
1084 * \param x translation vector x coordinate.
1085 * \param y translation vector y coordinate.
1086 * \param z translation vector z coordinate.
1088 * Adds the translation coordinates to the elements of \p mat in-place. Marks
1089 * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
1093 _math_matrix_translate( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
)
1095 GLfloat
*m
= mat
->m
;
1096 m
[12] = m
[0] * x
+ m
[4] * y
+ m
[8] * z
+ m
[12];
1097 m
[13] = m
[1] * x
+ m
[5] * y
+ m
[9] * z
+ m
[13];
1098 m
[14] = m
[2] * x
+ m
[6] * y
+ m
[10] * z
+ m
[14];
1099 m
[15] = m
[3] * x
+ m
[7] * y
+ m
[11] * z
+ m
[15];
1101 mat
->flags
|= (MAT_FLAG_TRANSLATION
|
1108 * Set matrix to do viewport and depthrange mapping.
1109 * Transforms Normalized Device Coords to window/Z values.
1112 _math_matrix_viewport(GLmatrix
*m
, GLint x
, GLint y
, GLint width
, GLint height
,
1113 GLfloat zNear
, GLfloat zFar
, GLfloat depthMax
)
1115 m
->m
[MAT_SX
] = (GLfloat
) width
/ 2.0F
;
1116 m
->m
[MAT_TX
] = m
->m
[MAT_SX
] + x
;
1117 m
->m
[MAT_SY
] = (GLfloat
) height
/ 2.0F
;
1118 m
->m
[MAT_TY
] = m
->m
[MAT_SY
] + y
;
1119 m
->m
[MAT_SZ
] = depthMax
* ((zFar
- zNear
) / 2.0F
);
1120 m
->m
[MAT_TZ
] = depthMax
* ((zFar
- zNear
) / 2.0F
+ zNear
);
1121 m
->flags
= MAT_FLAG_GENERAL_SCALE
| MAT_FLAG_TRANSLATION
;
1122 m
->type
= MATRIX_3D_NO_ROT
;
1127 * Set a matrix to the identity matrix.
1129 * \param mat matrix.
1131 * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
1132 * Sets the matrix type to identity, and clear the dirty flags.
1135 _math_matrix_set_identity( GLmatrix
*mat
)
1137 memcpy( mat
->m
, Identity
, 16*sizeof(GLfloat
) );
1140 memcpy( mat
->inv
, Identity
, 16*sizeof(GLfloat
) );
1142 mat
->type
= MATRIX_IDENTITY
;
1143 mat
->flags
&= ~(MAT_DIRTY_FLAGS
|
1151 /**********************************************************************/
1152 /** \name Matrix analysis */
1155 #define ZERO(x) (1<<x)
1156 #define ONE(x) (1<<(x+16))
1158 #define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14))
1159 #define MASK_NO_2D_SCALE ( ONE(0) | ONE(5))
1161 #define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\
1162 ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\
1163 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1164 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1166 #define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \
1167 ZERO(1) | ZERO(9) | \
1168 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1169 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1171 #define MASK_2D ( ZERO(8) | \
1173 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1174 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1177 #define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \
1178 ZERO(1) | ZERO(9) | \
1179 ZERO(2) | ZERO(6) | \
1180 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1185 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1188 #define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\
1189 ZERO(1) | ZERO(13) |\
1190 ZERO(2) | ZERO(6) | \
1191 ZERO(3) | ZERO(7) | ZERO(15) )
1193 #define SQ(x) ((x)*(x))
1196 * Determine type and flags from scratch.
1198 * \param mat matrix.
1200 * This is expensive enough to only want to do it once.
1202 static void analyse_from_scratch( GLmatrix
*mat
)
1204 const GLfloat
*m
= mat
->m
;
1208 for (i
= 0 ; i
< 16 ; i
++) {
1209 if (m
[i
] == 0.0) mask
|= (1<<i
);
1212 if (m
[0] == 1.0F
) mask
|= (1<<16);
1213 if (m
[5] == 1.0F
) mask
|= (1<<21);
1214 if (m
[10] == 1.0F
) mask
|= (1<<26);
1215 if (m
[15] == 1.0F
) mask
|= (1<<31);
1217 mat
->flags
&= ~MAT_FLAGS_GEOMETRY
;
1219 /* Check for translation - no-one really cares
1221 if ((mask
& MASK_NO_TRX
) != MASK_NO_TRX
)
1222 mat
->flags
|= MAT_FLAG_TRANSLATION
;
1226 if (mask
== (GLuint
) MASK_IDENTITY
) {
1227 mat
->type
= MATRIX_IDENTITY
;
1229 else if ((mask
& MASK_2D_NO_ROT
) == (GLuint
) MASK_2D_NO_ROT
) {
1230 mat
->type
= MATRIX_2D_NO_ROT
;
1232 if ((mask
& MASK_NO_2D_SCALE
) != MASK_NO_2D_SCALE
)
1233 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1235 else if ((mask
& MASK_2D
) == (GLuint
) MASK_2D
) {
1236 GLfloat mm
= DOT2(m
, m
);
1237 GLfloat m4m4
= DOT2(m
+4,m
+4);
1238 GLfloat mm4
= DOT2(m
,m
+4);
1240 mat
->type
= MATRIX_2D
;
1242 /* Check for scale */
1243 if (SQ(mm
-1) > SQ(1e-6) ||
1244 SQ(m4m4
-1) > SQ(1e-6))
1245 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1247 /* Check for rotation */
1248 if (SQ(mm4
) > SQ(1e-6))
1249 mat
->flags
|= MAT_FLAG_GENERAL_3D
;
1251 mat
->flags
|= MAT_FLAG_ROTATION
;
1254 else if ((mask
& MASK_3D_NO_ROT
) == (GLuint
) MASK_3D_NO_ROT
) {
1255 mat
->type
= MATRIX_3D_NO_ROT
;
1257 /* Check for scale */
1258 if (SQ(m
[0]-m
[5]) < SQ(1e-6) &&
1259 SQ(m
[0]-m
[10]) < SQ(1e-6)) {
1260 if (SQ(m
[0]-1.0) > SQ(1e-6)) {
1261 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1265 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1268 else if ((mask
& MASK_3D
) == (GLuint
) MASK_3D
) {
1269 GLfloat c1
= DOT3(m
,m
);
1270 GLfloat c2
= DOT3(m
+4,m
+4);
1271 GLfloat c3
= DOT3(m
+8,m
+8);
1272 GLfloat d1
= DOT3(m
, m
+4);
1275 mat
->type
= MATRIX_3D
;
1277 /* Check for scale */
1278 if (SQ(c1
-c2
) < SQ(1e-6) && SQ(c1
-c3
) < SQ(1e-6)) {
1279 if (SQ(c1
-1.0) > SQ(1e-6))
1280 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1281 /* else no scale at all */
1284 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1287 /* Check for rotation */
1288 if (SQ(d1
) < SQ(1e-6)) {
1289 CROSS3( cp
, m
, m
+4 );
1290 SUB_3V( cp
, cp
, (m
+8) );
1291 if (LEN_SQUARED_3FV(cp
) < SQ(1e-6))
1292 mat
->flags
|= MAT_FLAG_ROTATION
;
1294 mat
->flags
|= MAT_FLAG_GENERAL_3D
;
1297 mat
->flags
|= MAT_FLAG_GENERAL_3D
; /* shear, etc */
1300 else if ((mask
& MASK_PERSPECTIVE
) == MASK_PERSPECTIVE
&& m
[11]==-1.0F
) {
1301 mat
->type
= MATRIX_PERSPECTIVE
;
1302 mat
->flags
|= MAT_FLAG_GENERAL
;
1305 mat
->type
= MATRIX_GENERAL
;
1306 mat
->flags
|= MAT_FLAG_GENERAL
;
1311 * Analyze a matrix given that its flags are accurate.
1313 * This is the more common operation, hopefully.
1315 static void analyse_from_flags( GLmatrix
*mat
)
1317 const GLfloat
*m
= mat
->m
;
1319 if (TEST_MAT_FLAGS(mat
, 0)) {
1320 mat
->type
= MATRIX_IDENTITY
;
1322 else if (TEST_MAT_FLAGS(mat
, (MAT_FLAG_TRANSLATION
|
1323 MAT_FLAG_UNIFORM_SCALE
|
1324 MAT_FLAG_GENERAL_SCALE
))) {
1325 if ( m
[10]==1.0F
&& m
[14]==0.0F
) {
1326 mat
->type
= MATRIX_2D_NO_ROT
;
1329 mat
->type
= MATRIX_3D_NO_ROT
;
1332 else if (TEST_MAT_FLAGS(mat
, MAT_FLAGS_3D
)) {
1335 && m
[2]==0.0F
&& m
[6]==0.0F
&& m
[10]==1.0F
&& m
[14]==0.0F
) {
1336 mat
->type
= MATRIX_2D
;
1339 mat
->type
= MATRIX_3D
;
1342 else if ( m
[4]==0.0F
&& m
[12]==0.0F
1343 && m
[1]==0.0F
&& m
[13]==0.0F
1344 && m
[2]==0.0F
&& m
[6]==0.0F
1345 && m
[3]==0.0F
&& m
[7]==0.0F
&& m
[11]==-1.0F
&& m
[15]==0.0F
) {
1346 mat
->type
= MATRIX_PERSPECTIVE
;
1349 mat
->type
= MATRIX_GENERAL
;
1354 * Analyze and update a matrix.
1356 * \param mat matrix.
1358 * If the matrix type is dirty then calls either analyse_from_scratch() or
1359 * analyse_from_flags() to determine its type, according to whether the flags
1360 * are dirty or not, respectively. If the matrix has an inverse and it's dirty
1361 * then calls matrix_invert(). Finally clears the dirty flags.
1364 _math_matrix_analyse( GLmatrix
*mat
)
1366 if (mat
->flags
& MAT_DIRTY_TYPE
) {
1367 if (mat
->flags
& MAT_DIRTY_FLAGS
)
1368 analyse_from_scratch( mat
);
1370 analyse_from_flags( mat
);
1373 if (mat
->inv
&& (mat
->flags
& MAT_DIRTY_INVERSE
)) {
1374 matrix_invert( mat
);
1375 mat
->flags
&= ~MAT_DIRTY_INVERSE
;
1378 mat
->flags
&= ~(MAT_DIRTY_FLAGS
| MAT_DIRTY_TYPE
);
1385 * Test if the given matrix preserves vector lengths.
1388 _math_matrix_is_length_preserving( const GLmatrix
*m
)
1390 return TEST_MAT_FLAGS( m
, MAT_FLAGS_LENGTH_PRESERVING
);
1395 * Test if the given matrix does any rotation.
1396 * (or perhaps if the upper-left 3x3 is non-identity)
1399 _math_matrix_has_rotation( const GLmatrix
*m
)
1401 if (m
->flags
& (MAT_FLAG_GENERAL
|
1403 MAT_FLAG_GENERAL_3D
|
1404 MAT_FLAG_PERSPECTIVE
))
1412 _math_matrix_is_general_scale( const GLmatrix
*m
)
1414 return (m
->flags
& MAT_FLAG_GENERAL_SCALE
) ? GL_TRUE
: GL_FALSE
;
1419 _math_matrix_is_dirty( const GLmatrix
*m
)
1421 return (m
->flags
& MAT_DIRTY
) ? GL_TRUE
: GL_FALSE
;
1425 /**********************************************************************/
1426 /** \name Matrix setup */
1432 * \param to destination matrix.
1433 * \param from source matrix.
1435 * Copies all fields in GLmatrix, creating an inverse array if necessary.
1438 _math_matrix_copy( GLmatrix
*to
, const GLmatrix
*from
)
1440 memcpy( to
->m
, from
->m
, sizeof(Identity
) );
1441 to
->flags
= from
->flags
;
1442 to
->type
= from
->type
;
1445 if (from
->inv
== 0) {
1446 matrix_invert( to
);
1449 memcpy(to
->inv
, from
->inv
, sizeof(GLfloat
)*16);
1455 * Loads a matrix array into GLmatrix.
1457 * \param m matrix array.
1458 * \param mat matrix.
1460 * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
1464 _math_matrix_loadf( GLmatrix
*mat
, const GLfloat
*m
)
1466 memcpy( mat
->m
, m
, 16*sizeof(GLfloat
) );
1467 mat
->flags
= (MAT_FLAG_GENERAL
| MAT_DIRTY
);
1471 * Matrix constructor.
1475 * Initialize the GLmatrix fields.
1478 _math_matrix_ctr( GLmatrix
*m
)
1480 m
->m
= (GLfloat
*) _mesa_align_malloc( 16 * sizeof(GLfloat
), 16 );
1482 memcpy( m
->m
, Identity
, sizeof(Identity
) );
1484 m
->type
= MATRIX_IDENTITY
;
1489 * Matrix destructor.
1493 * Frees the data in a GLmatrix.
1496 _math_matrix_dtr( GLmatrix
*m
)
1499 _mesa_align_free( m
->m
);
1503 _mesa_align_free( m
->inv
);
1509 * Allocate a matrix inverse.
1513 * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity.
1516 _math_matrix_alloc_inv( GLmatrix
*m
)
1519 m
->inv
= (GLfloat
*) _mesa_align_malloc( 16 * sizeof(GLfloat
), 16 );
1521 memcpy( m
->inv
, Identity
, 16 * sizeof(GLfloat
) );
1528 /**********************************************************************/
1529 /** \name Matrix transpose */
1533 * Transpose a GLfloat matrix.
1535 * \param to destination array.
1536 * \param from source array.
1539 _math_transposef( GLfloat to
[16], const GLfloat from
[16] )
1560 * Transpose a GLdouble matrix.
1562 * \param to destination array.
1563 * \param from source array.
1566 _math_transposed( GLdouble to
[16], const GLdouble from
[16] )
1587 * Transpose a GLdouble matrix and convert to GLfloat.
1589 * \param to destination array.
1590 * \param from source array.
1593 _math_transposefd( GLfloat to
[16], const GLdouble from
[16] )
1595 to
[0] = (GLfloat
) from
[0];
1596 to
[1] = (GLfloat
) from
[4];
1597 to
[2] = (GLfloat
) from
[8];
1598 to
[3] = (GLfloat
) from
[12];
1599 to
[4] = (GLfloat
) from
[1];
1600 to
[5] = (GLfloat
) from
[5];
1601 to
[6] = (GLfloat
) from
[9];
1602 to
[7] = (GLfloat
) from
[13];
1603 to
[8] = (GLfloat
) from
[2];
1604 to
[9] = (GLfloat
) from
[6];
1605 to
[10] = (GLfloat
) from
[10];
1606 to
[11] = (GLfloat
) from
[14];
1607 to
[12] = (GLfloat
) from
[3];
1608 to
[13] = (GLfloat
) from
[7];
1609 to
[14] = (GLfloat
) from
[11];
1610 to
[15] = (GLfloat
) from
[15];
1617 * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This
1618 * function is used for transforming clipping plane equations and spotlight
1620 * Mathematically, u = v * m.
1621 * Input: v - input vector
1622 * m - transformation matrix
1623 * Output: u - transformed vector
1626 _mesa_transform_vector( GLfloat u
[4], const GLfloat v
[4], const GLfloat m
[16] )
1628 const GLfloat v0
= v
[0], v1
= v
[1], v2
= v
[2], v3
= v
[3];
1629 #define M(row,col) m[row + col*4]
1630 u
[0] = v0
* M(0,0) + v1
* M(1,0) + v2
* M(2,0) + v3
* M(3,0);
1631 u
[1] = v0
* M(0,1) + v1
* M(1,1) + v2
* M(2,1) + v3
* M(3,1);
1632 u
[2] = v0
* M(0,2) + v1
* M(1,2) + v2
* M(2,2) + v3
* M(3,2);
1633 u
[3] = v0
* M(0,3) + v1
* M(1,3) + v2
* M(2,3) + v3
* M(3,3);