2 * Mesa 3-D graphics library
4 * Copyright (C) 1999-2005 Brian Paul All Rights Reserved.
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:
13 * The above copyright notice and this permission notice shall be included
14 * in all copies or substantial portions of the Software.
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.
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 #include "main/errors.h"
40 #include "main/glheader.h"
41 #include "main/imports.h"
42 #include "main/macros.h"
43 #define MATH_ASM_PTR_SIZE sizeof(void *)
44 #include "math/m_vector_asm.h"
50 * \defgroup MatFlags MAT_FLAG_XXX-flags
52 * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
55 #define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag.
56 * (Not actually used - the identity
57 * matrix is identified by the absence
58 * of all other flags.)
60 #define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */
61 #define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */
62 #define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */
63 #define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */
64 #define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */
65 #define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */
66 #define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */
67 #define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */
68 #define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */
69 #define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */
70 #define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */
72 /** angle preserving matrix flags mask */
73 #define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
74 MAT_FLAG_TRANSLATION | \
75 MAT_FLAG_UNIFORM_SCALE)
77 /** geometry related matrix flags mask */
78 #define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
80 MAT_FLAG_TRANSLATION | \
81 MAT_FLAG_UNIFORM_SCALE | \
82 MAT_FLAG_GENERAL_SCALE | \
83 MAT_FLAG_GENERAL_3D | \
84 MAT_FLAG_PERSPECTIVE | \
87 /** length preserving matrix flags mask */
88 #define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
92 /** 3D (non-perspective) matrix flags mask */
93 #define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
94 MAT_FLAG_TRANSLATION | \
95 MAT_FLAG_UNIFORM_SCALE | \
96 MAT_FLAG_GENERAL_SCALE | \
99 /** dirty matrix flags mask */
100 #define MAT_DIRTY (MAT_DIRTY_TYPE | \
108 * Test geometry related matrix flags.
110 * \param mat a pointer to a GLmatrix structure.
111 * \param a flags mask.
113 * \returns non-zero if all geometry related matrix flags are contained within
114 * the mask, or zero otherwise.
116 #define TEST_MAT_FLAGS(mat, a) \
117 ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
122 * Names of the corresponding GLmatrixtype values.
124 static const char *types
[] = {
128 "MATRIX_PERSPECTIVE",
138 static const GLfloat Identity
[16] = {
147 /**********************************************************************/
148 /** \name Matrix multiplication */
151 #define A(row,col) a[(col<<2)+row]
152 #define B(row,col) b[(col<<2)+row]
153 #define P(row,col) product[(col<<2)+row]
156 * Perform a full 4x4 matrix multiplication.
160 * \param product will receive the product of \p a and \p b.
162 * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
164 * \note KW: 4*16 = 64 multiplications
166 * \author This \c matmul was contributed by Thomas Malik
168 static void matmul4( GLfloat
*product
, const GLfloat
*a
, const GLfloat
*b
)
171 for (i
= 0; i
< 4; i
++) {
172 const GLfloat ai0
=A(i
,0), ai1
=A(i
,1), ai2
=A(i
,2), ai3
=A(i
,3);
173 P(i
,0) = ai0
* B(0,0) + ai1
* B(1,0) + ai2
* B(2,0) + ai3
* B(3,0);
174 P(i
,1) = ai0
* B(0,1) + ai1
* B(1,1) + ai2
* B(2,1) + ai3
* B(3,1);
175 P(i
,2) = ai0
* B(0,2) + ai1
* B(1,2) + ai2
* B(2,2) + ai3
* B(3,2);
176 P(i
,3) = ai0
* B(0,3) + ai1
* B(1,3) + ai2
* B(2,3) + ai3
* B(3,3);
181 * Multiply two matrices known to occupy only the top three rows, such
182 * as typical model matrices, and orthogonal matrices.
186 * \param product will receive the product of \p a and \p b.
188 static void matmul34( GLfloat
*product
, const GLfloat
*a
, const GLfloat
*b
)
191 for (i
= 0; i
< 3; i
++) {
192 const GLfloat ai0
=A(i
,0), ai1
=A(i
,1), ai2
=A(i
,2), ai3
=A(i
,3);
193 P(i
,0) = ai0
* B(0,0) + ai1
* B(1,0) + ai2
* B(2,0);
194 P(i
,1) = ai0
* B(0,1) + ai1
* B(1,1) + ai2
* B(2,1);
195 P(i
,2) = ai0
* B(0,2) + ai1
* B(1,2) + ai2
* B(2,2);
196 P(i
,3) = ai0
* B(0,3) + ai1
* B(1,3) + ai2
* B(2,3) + ai3
;
209 * Multiply a matrix by an array of floats with known properties.
211 * \param mat pointer to a GLmatrix structure containing the left multiplication
212 * matrix, and that will receive the product result.
213 * \param m right multiplication matrix array.
214 * \param flags flags of the matrix \p m.
216 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
217 * if both matrices are 3D, or matmul4() otherwise.
219 static void matrix_multf( GLmatrix
*mat
, const GLfloat
*m
, GLuint flags
)
221 mat
->flags
|= (flags
| MAT_DIRTY_TYPE
| MAT_DIRTY_INVERSE
);
223 if (TEST_MAT_FLAGS(mat
, MAT_FLAGS_3D
))
224 matmul34( mat
->m
, mat
->m
, m
);
226 matmul4( mat
->m
, mat
->m
, m
);
230 * Matrix multiplication.
232 * \param dest destination matrix.
233 * \param a left matrix.
234 * \param b right matrix.
236 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
237 * if both matrices are 3D, or matmul4() otherwise.
240 _math_matrix_mul_matrix( GLmatrix
*dest
, const GLmatrix
*a
, const GLmatrix
*b
)
242 dest
->flags
= (a
->flags
|
247 if (TEST_MAT_FLAGS(dest
, MAT_FLAGS_3D
))
248 matmul34( dest
->m
, a
->m
, b
->m
);
250 matmul4( dest
->m
, a
->m
, b
->m
);
254 * Matrix multiplication.
256 * \param dest left and destination matrix.
257 * \param m right matrix array.
259 * Marks the matrix flags with general flag, and type and inverse dirty flags.
260 * Calls matmul4() for the multiplication.
263 _math_matrix_mul_floats( GLmatrix
*dest
, const GLfloat
*m
)
265 dest
->flags
|= (MAT_FLAG_GENERAL
|
270 matmul4( dest
->m
, dest
->m
, m
);
276 /**********************************************************************/
277 /** \name Matrix output */
281 * Print a matrix array.
283 * \param m matrix array.
285 * Called by _math_matrix_print() to print a matrix or its inverse.
287 static void print_matrix_floats( const GLfloat m
[16] )
291 _mesa_debug(NULL
,"\t%f %f %f %f\n", m
[i
], m
[4+i
], m
[8+i
], m
[12+i
] );
296 * Dumps the contents of a GLmatrix structure.
298 * \param m pointer to the GLmatrix structure.
301 _math_matrix_print( const GLmatrix
*m
)
305 _mesa_debug(NULL
, "Matrix type: %s, flags: %x\n", types
[m
->type
], m
->flags
);
306 print_matrix_floats(m
->m
);
307 _mesa_debug(NULL
, "Inverse: \n");
308 print_matrix_floats(m
->inv
);
309 matmul4(prod
, m
->m
, m
->inv
);
310 _mesa_debug(NULL
, "Mat * Inverse:\n");
311 print_matrix_floats(prod
);
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 point 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 (0.0F
== 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
!= 0.0F
) { r1
[4] -= m1
* s
; r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
397 if (s
!= 0.0F
) { r1
[5] -= m1
* s
; r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
399 if (s
!= 0.0F
) { r1
[6] -= m1
* s
; r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
401 if (s
!= 0.0F
) { 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 (0.0F
== 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 (0.0F
!= s
) { r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
413 s
= r1
[5]; if (0.0F
!= s
) { r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
414 s
= r1
[6]; if (0.0F
!= s
) { r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
415 s
= r1
[7]; if (0.0F
!= 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 (0.0F
== 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 (0.0F
== 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
>= 0.0F
) pos
+= t
; else neg
+= t
;
499 t
= MAT(in
,1,0) * MAT(in
,2,1) * MAT(in
,0,2);
500 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
502 t
= MAT(in
,2,0) * MAT(in
,0,1) * MAT(in
,1,2);
503 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
505 t
= -MAT(in
,2,0) * MAT(in
,1,1) * MAT(in
,0,2);
506 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
508 t
= -MAT(in
,1,0) * MAT(in
,0,1) * MAT(in
,2,2);
509 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
511 t
= -MAT(in
,0,0) * MAT(in
,2,1) * MAT(in
,1,2);
512 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
516 if (fabsf(det
) < 1e-25F
)
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
, sizeof(Identity
) );
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
, sizeof(Identity
) );
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
, sizeof(Identity
) );
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
= sinf( angle
* M_PI
/ 180.0 );
807 c
= cosf( angle
* M_PI
/ 180.0 );
809 memcpy(m
, Identity
, sizeof(Identity
));
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
);
866 if (mag
<= 1.0e-4F
) {
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-8F
&& fabsf(x
- z
) < 1e-8F
)
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
, const float scale
[3],
1119 const float translate
[3], double depthMax
)
1121 m
->m
[MAT_SX
] = scale
[0];
1122 m
->m
[MAT_TX
] = translate
[0];
1123 m
->m
[MAT_SY
] = scale
[1];
1124 m
->m
[MAT_TY
] = translate
[1];
1125 m
->m
[MAT_SZ
] = depthMax
*scale
[2];
1126 m
->m
[MAT_TZ
] = depthMax
*translate
[2];
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 STATIC_ASSERT(MATRIX_M
== offsetof(GLmatrix
, m
));
1144 STATIC_ASSERT(MATRIX_INV
== offsetof(GLmatrix
, inv
));
1146 memcpy( mat
->m
, Identity
, sizeof(Identity
) );
1147 memcpy( mat
->inv
, Identity
, sizeof(Identity
) );
1149 mat
->type
= MATRIX_IDENTITY
;
1150 mat
->flags
&= ~(MAT_DIRTY_FLAGS
|
1158 /**********************************************************************/
1159 /** \name Matrix analysis */
1162 #define ZERO(x) (1<<x)
1163 #define ONE(x) (1<<(x+16))
1165 #define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14))
1166 #define MASK_NO_2D_SCALE ( ONE(0) | ONE(5))
1168 #define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\
1169 ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\
1170 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1171 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1173 #define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \
1174 ZERO(1) | ZERO(9) | \
1175 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1176 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1178 #define MASK_2D ( ZERO(8) | \
1180 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1181 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1184 #define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \
1185 ZERO(1) | ZERO(9) | \
1186 ZERO(2) | ZERO(6) | \
1187 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1192 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1195 #define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\
1196 ZERO(1) | ZERO(13) |\
1197 ZERO(2) | ZERO(6) | \
1198 ZERO(3) | ZERO(7) | ZERO(15) )
1200 #define SQ(x) ((x)*(x))
1203 * Determine type and flags from scratch.
1205 * \param mat matrix.
1207 * This is expensive enough to only want to do it once.
1209 static void analyse_from_scratch( GLmatrix
*mat
)
1211 const GLfloat
*m
= mat
->m
;
1215 for (i
= 0 ; i
< 16 ; i
++) {
1216 if (m
[i
] == 0.0F
) mask
|= (1<<i
);
1219 if (m
[0] == 1.0F
) mask
|= (1<<16);
1220 if (m
[5] == 1.0F
) mask
|= (1<<21);
1221 if (m
[10] == 1.0F
) mask
|= (1<<26);
1222 if (m
[15] == 1.0F
) mask
|= (1<<31);
1224 mat
->flags
&= ~MAT_FLAGS_GEOMETRY
;
1226 /* Check for translation - no-one really cares
1228 if ((mask
& MASK_NO_TRX
) != MASK_NO_TRX
)
1229 mat
->flags
|= MAT_FLAG_TRANSLATION
;
1233 if (mask
== (GLuint
) MASK_IDENTITY
) {
1234 mat
->type
= MATRIX_IDENTITY
;
1236 else if ((mask
& MASK_2D_NO_ROT
) == (GLuint
) MASK_2D_NO_ROT
) {
1237 mat
->type
= MATRIX_2D_NO_ROT
;
1239 if ((mask
& MASK_NO_2D_SCALE
) != MASK_NO_2D_SCALE
)
1240 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1242 else if ((mask
& MASK_2D
) == (GLuint
) MASK_2D
) {
1243 GLfloat mm
= DOT2(m
, m
);
1244 GLfloat m4m4
= DOT2(m
+4,m
+4);
1245 GLfloat mm4
= DOT2(m
,m
+4);
1247 mat
->type
= MATRIX_2D
;
1249 /* Check for scale */
1250 if (SQ(mm
-1) > SQ(1e-6F
) ||
1251 SQ(m4m4
-1) > SQ(1e-6F
))
1252 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1254 /* Check for rotation */
1255 if (SQ(mm4
) > SQ(1e-6F
))
1256 mat
->flags
|= MAT_FLAG_GENERAL_3D
;
1258 mat
->flags
|= MAT_FLAG_ROTATION
;
1261 else if ((mask
& MASK_3D_NO_ROT
) == (GLuint
) MASK_3D_NO_ROT
) {
1262 mat
->type
= MATRIX_3D_NO_ROT
;
1264 /* Check for scale */
1265 if (SQ(m
[0]-m
[5]) < SQ(1e-6F
) &&
1266 SQ(m
[0]-m
[10]) < SQ(1e-6F
)) {
1267 if (SQ(m
[0]-1.0F
) > SQ(1e-6F
)) {
1268 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1272 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1275 else if ((mask
& MASK_3D
) == (GLuint
) MASK_3D
) {
1276 GLfloat c1
= DOT3(m
,m
);
1277 GLfloat c2
= DOT3(m
+4,m
+4);
1278 GLfloat c3
= DOT3(m
+8,m
+8);
1279 GLfloat d1
= DOT3(m
, m
+4);
1282 mat
->type
= MATRIX_3D
;
1284 /* Check for scale */
1285 if (SQ(c1
-c2
) < SQ(1e-6F
) && SQ(c1
-c3
) < SQ(1e-6F
)) {
1286 if (SQ(c1
-1.0F
) > SQ(1e-6F
))
1287 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1288 /* else no scale at all */
1291 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1294 /* Check for rotation */
1295 if (SQ(d1
) < SQ(1e-6F
)) {
1296 CROSS3( cp
, m
, m
+4 );
1297 SUB_3V( cp
, cp
, (m
+8) );
1298 if (LEN_SQUARED_3FV(cp
) < SQ(1e-6F
))
1299 mat
->flags
|= MAT_FLAG_ROTATION
;
1301 mat
->flags
|= MAT_FLAG_GENERAL_3D
;
1304 mat
->flags
|= MAT_FLAG_GENERAL_3D
; /* shear, etc */
1307 else if ((mask
& MASK_PERSPECTIVE
) == MASK_PERSPECTIVE
&& m
[11]==-1.0F
) {
1308 mat
->type
= MATRIX_PERSPECTIVE
;
1309 mat
->flags
|= MAT_FLAG_GENERAL
;
1312 mat
->type
= MATRIX_GENERAL
;
1313 mat
->flags
|= MAT_FLAG_GENERAL
;
1318 * Analyze a matrix given that its flags are accurate.
1320 * This is the more common operation, hopefully.
1322 static void analyse_from_flags( GLmatrix
*mat
)
1324 const GLfloat
*m
= mat
->m
;
1326 if (TEST_MAT_FLAGS(mat
, 0)) {
1327 mat
->type
= MATRIX_IDENTITY
;
1329 else if (TEST_MAT_FLAGS(mat
, (MAT_FLAG_TRANSLATION
|
1330 MAT_FLAG_UNIFORM_SCALE
|
1331 MAT_FLAG_GENERAL_SCALE
))) {
1332 if ( m
[10]==1.0F
&& m
[14]==0.0F
) {
1333 mat
->type
= MATRIX_2D_NO_ROT
;
1336 mat
->type
= MATRIX_3D_NO_ROT
;
1339 else if (TEST_MAT_FLAGS(mat
, MAT_FLAGS_3D
)) {
1342 && m
[2]==0.0F
&& m
[6]==0.0F
&& m
[10]==1.0F
&& m
[14]==0.0F
) {
1343 mat
->type
= MATRIX_2D
;
1346 mat
->type
= MATRIX_3D
;
1349 else if ( m
[4]==0.0F
&& m
[12]==0.0F
1350 && m
[1]==0.0F
&& m
[13]==0.0F
1351 && m
[2]==0.0F
&& m
[6]==0.0F
1352 && m
[3]==0.0F
&& m
[7]==0.0F
&& m
[11]==-1.0F
&& m
[15]==0.0F
) {
1353 mat
->type
= MATRIX_PERSPECTIVE
;
1356 mat
->type
= MATRIX_GENERAL
;
1361 * Analyze and update a matrix.
1363 * \param mat matrix.
1365 * If the matrix type is dirty then calls either analyse_from_scratch() or
1366 * analyse_from_flags() to determine its type, according to whether the flags
1367 * are dirty or not, respectively. If the matrix has an inverse and it's dirty
1368 * then calls matrix_invert(). Finally clears the dirty flags.
1371 _math_matrix_analyse( GLmatrix
*mat
)
1373 if (mat
->flags
& MAT_DIRTY_TYPE
) {
1374 if (mat
->flags
& MAT_DIRTY_FLAGS
)
1375 analyse_from_scratch( mat
);
1377 analyse_from_flags( mat
);
1380 if (mat
->inv
&& (mat
->flags
& MAT_DIRTY_INVERSE
)) {
1381 matrix_invert( mat
);
1382 mat
->flags
&= ~MAT_DIRTY_INVERSE
;
1385 mat
->flags
&= ~(MAT_DIRTY_FLAGS
| MAT_DIRTY_TYPE
);
1392 * Test if the given matrix preserves vector lengths.
1395 _math_matrix_is_length_preserving( const GLmatrix
*m
)
1397 return TEST_MAT_FLAGS( m
, MAT_FLAGS_LENGTH_PRESERVING
);
1402 * Test if the given matrix does any rotation.
1403 * (or perhaps if the upper-left 3x3 is non-identity)
1406 _math_matrix_has_rotation( const GLmatrix
*m
)
1408 if (m
->flags
& (MAT_FLAG_GENERAL
|
1410 MAT_FLAG_GENERAL_3D
|
1411 MAT_FLAG_PERSPECTIVE
))
1419 _math_matrix_is_general_scale( const GLmatrix
*m
)
1421 return (m
->flags
& MAT_FLAG_GENERAL_SCALE
) ? GL_TRUE
: GL_FALSE
;
1426 _math_matrix_is_dirty( const GLmatrix
*m
)
1428 return (m
->flags
& MAT_DIRTY
) ? GL_TRUE
: GL_FALSE
;
1432 /**********************************************************************/
1433 /** \name Matrix setup */
1439 * \param to destination matrix.
1440 * \param from source matrix.
1442 * Copies all fields in GLmatrix, creating an inverse array if necessary.
1445 _math_matrix_copy( GLmatrix
*to
, const GLmatrix
*from
)
1447 memcpy(to
->m
, from
->m
, 16 * sizeof(GLfloat
));
1448 memcpy(to
->inv
, from
->inv
, 16 * sizeof(GLfloat
));
1449 to
->flags
= from
->flags
;
1450 to
->type
= from
->type
;
1454 * Loads a matrix array into GLmatrix.
1456 * \param m matrix array.
1457 * \param mat matrix.
1459 * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
1463 _math_matrix_loadf( GLmatrix
*mat
, const GLfloat
*m
)
1465 memcpy( mat
->m
, m
, 16*sizeof(GLfloat
) );
1466 mat
->flags
= (MAT_FLAG_GENERAL
| MAT_DIRTY
);
1470 * Matrix constructor.
1474 * Initialize the GLmatrix fields.
1477 _math_matrix_ctr( GLmatrix
*m
)
1479 m
->m
= _mesa_align_malloc( 16 * sizeof(GLfloat
), 16 );
1481 memcpy( m
->m
, Identity
, sizeof(Identity
) );
1482 m
->inv
= _mesa_align_malloc( 16 * sizeof(GLfloat
), 16 );
1484 memcpy( m
->inv
, Identity
, sizeof(Identity
) );
1485 m
->type
= MATRIX_IDENTITY
;
1490 * Matrix destructor.
1494 * Frees the data in a GLmatrix.
1497 _math_matrix_dtr( GLmatrix
*m
)
1499 _mesa_align_free( m
->m
);
1502 _mesa_align_free( m
->inv
);
1509 /**********************************************************************/
1510 /** \name Matrix transpose */
1514 * Transpose a GLfloat matrix.
1516 * \param to destination array.
1517 * \param from source array.
1520 _math_transposef( GLfloat to
[16], const GLfloat from
[16] )
1541 * Transpose a GLdouble matrix.
1543 * \param to destination array.
1544 * \param from source array.
1547 _math_transposed( GLdouble to
[16], const GLdouble from
[16] )
1568 * Transpose a GLdouble matrix and convert to GLfloat.
1570 * \param to destination array.
1571 * \param from source array.
1574 _math_transposefd( GLfloat to
[16], const GLdouble from
[16] )
1576 to
[0] = (GLfloat
) from
[0];
1577 to
[1] = (GLfloat
) from
[4];
1578 to
[2] = (GLfloat
) from
[8];
1579 to
[3] = (GLfloat
) from
[12];
1580 to
[4] = (GLfloat
) from
[1];
1581 to
[5] = (GLfloat
) from
[5];
1582 to
[6] = (GLfloat
) from
[9];
1583 to
[7] = (GLfloat
) from
[13];
1584 to
[8] = (GLfloat
) from
[2];
1585 to
[9] = (GLfloat
) from
[6];
1586 to
[10] = (GLfloat
) from
[10];
1587 to
[11] = (GLfloat
) from
[14];
1588 to
[12] = (GLfloat
) from
[3];
1589 to
[13] = (GLfloat
) from
[7];
1590 to
[14] = (GLfloat
) from
[11];
1591 to
[15] = (GLfloat
) from
[15];
1598 * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This
1599 * function is used for transforming clipping plane equations and spotlight
1601 * Mathematically, u = v * m.
1602 * Input: v - input vector
1603 * m - transformation matrix
1604 * Output: u - transformed vector
1607 _mesa_transform_vector( GLfloat u
[4], const GLfloat v
[4], const GLfloat m
[16] )
1609 const GLfloat v0
= v
[0], v1
= v
[1], v2
= v
[2], v3
= v
[3];
1610 #define M(row,col) m[row + col*4]
1611 u
[0] = v0
* M(0,0) + v1
* M(1,0) + v2
* M(2,0) + v3
* M(3,0);
1612 u
[1] = v0
* M(0,1) + v1
* M(1,1) + v2
* M(2,1) + v3
* M(3,1);
1613 u
[2] = v0
* M(0,2) + v1
* M(1,2) + v2
* M(2,2) + v3
* M(3,2);
1614 u
[3] = v0
* M(0,3) + v1
* M(1,3) + v2
* M(2,3) + v3
* M(3,3);