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
38 #include "main/errors.h"
39 #include "main/glheader.h"
40 #include "main/imports.h"
41 #include "main/macros.h"
47 * \defgroup MatFlags MAT_FLAG_XXX-flags
49 * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
52 #define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag.
53 * (Not actually used - the identity
54 * matrix is identified by the absence
55 * of all other flags.)
57 #define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */
58 #define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */
59 #define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */
60 #define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */
61 #define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */
62 #define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */
63 #define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */
64 #define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */
65 #define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */
66 #define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */
67 #define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */
69 /** angle preserving matrix flags mask */
70 #define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
71 MAT_FLAG_TRANSLATION | \
72 MAT_FLAG_UNIFORM_SCALE)
74 /** geometry related matrix flags mask */
75 #define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
77 MAT_FLAG_TRANSLATION | \
78 MAT_FLAG_UNIFORM_SCALE | \
79 MAT_FLAG_GENERAL_SCALE | \
80 MAT_FLAG_GENERAL_3D | \
81 MAT_FLAG_PERSPECTIVE | \
84 /** length preserving matrix flags mask */
85 #define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
89 /** 3D (non-perspective) matrix flags mask */
90 #define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
91 MAT_FLAG_TRANSLATION | \
92 MAT_FLAG_UNIFORM_SCALE | \
93 MAT_FLAG_GENERAL_SCALE | \
96 /** dirty matrix flags mask */
97 #define MAT_DIRTY (MAT_DIRTY_TYPE | \
105 * Test geometry related matrix flags.
107 * \param mat a pointer to a GLmatrix structure.
108 * \param a flags mask.
110 * \returns non-zero if all geometry related matrix flags are contained within
111 * the mask, or zero otherwise.
113 #define TEST_MAT_FLAGS(mat, a) \
114 ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
119 * Names of the corresponding GLmatrixtype values.
121 static const char *types
[] = {
125 "MATRIX_PERSPECTIVE",
135 static const GLfloat Identity
[16] = {
144 /**********************************************************************/
145 /** \name Matrix multiplication */
148 #define A(row,col) a[(col<<2)+row]
149 #define B(row,col) b[(col<<2)+row]
150 #define P(row,col) product[(col<<2)+row]
153 * Perform a full 4x4 matrix multiplication.
157 * \param product will receive the product of \p a and \p b.
159 * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
161 * \note KW: 4*16 = 64 multiplications
163 * \author This \c matmul was contributed by Thomas Malik
165 static void matmul4( GLfloat
*product
, const GLfloat
*a
, const GLfloat
*b
)
168 for (i
= 0; i
< 4; i
++) {
169 const GLfloat ai0
=A(i
,0), ai1
=A(i
,1), ai2
=A(i
,2), ai3
=A(i
,3);
170 P(i
,0) = ai0
* B(0,0) + ai1
* B(1,0) + ai2
* B(2,0) + ai3
* B(3,0);
171 P(i
,1) = ai0
* B(0,1) + ai1
* B(1,1) + ai2
* B(2,1) + ai3
* B(3,1);
172 P(i
,2) = ai0
* B(0,2) + ai1
* B(1,2) + ai2
* B(2,2) + ai3
* B(3,2);
173 P(i
,3) = ai0
* B(0,3) + ai1
* B(1,3) + ai2
* B(2,3) + ai3
* B(3,3);
178 * Multiply two matrices known to occupy only the top three rows, such
179 * as typical model matrices, and orthogonal matrices.
183 * \param product will receive the product of \p a and \p b.
185 static void matmul34( GLfloat
*product
, const GLfloat
*a
, const GLfloat
*b
)
188 for (i
= 0; i
< 3; i
++) {
189 const GLfloat ai0
=A(i
,0), ai1
=A(i
,1), ai2
=A(i
,2), ai3
=A(i
,3);
190 P(i
,0) = ai0
* B(0,0) + ai1
* B(1,0) + ai2
* B(2,0);
191 P(i
,1) = ai0
* B(0,1) + ai1
* B(1,1) + ai2
* B(2,1);
192 P(i
,2) = ai0
* B(0,2) + ai1
* B(1,2) + ai2
* B(2,2);
193 P(i
,3) = ai0
* B(0,3) + ai1
* B(1,3) + ai2
* B(2,3) + ai3
;
206 * Multiply a matrix by an array of floats with known properties.
208 * \param mat pointer to a GLmatrix structure containing the left multiplication
209 * matrix, and that will receive the product result.
210 * \param m right multiplication matrix array.
211 * \param flags flags of the matrix \p m.
213 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
214 * if both matrices are 3D, or matmul4() otherwise.
216 static void matrix_multf( GLmatrix
*mat
, const GLfloat
*m
, GLuint flags
)
218 mat
->flags
|= (flags
| MAT_DIRTY_TYPE
| MAT_DIRTY_INVERSE
);
220 if (TEST_MAT_FLAGS(mat
, MAT_FLAGS_3D
))
221 matmul34( mat
->m
, mat
->m
, m
);
223 matmul4( mat
->m
, mat
->m
, m
);
227 * Matrix multiplication.
229 * \param dest destination matrix.
230 * \param a left matrix.
231 * \param b right matrix.
233 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
234 * if both matrices are 3D, or matmul4() otherwise.
237 _math_matrix_mul_matrix( GLmatrix
*dest
, const GLmatrix
*a
, const GLmatrix
*b
)
239 dest
->flags
= (a
->flags
|
244 if (TEST_MAT_FLAGS(dest
, MAT_FLAGS_3D
))
245 matmul34( dest
->m
, a
->m
, b
->m
);
247 matmul4( dest
->m
, a
->m
, b
->m
);
251 * Matrix multiplication.
253 * \param dest left and destination matrix.
254 * \param m right matrix array.
256 * Marks the matrix flags with general flag, and type and inverse dirty flags.
257 * Calls matmul4() for the multiplication.
260 _math_matrix_mul_floats( GLmatrix
*dest
, const GLfloat
*m
)
262 dest
->flags
|= (MAT_FLAG_GENERAL
|
267 matmul4( dest
->m
, dest
->m
, m
);
273 /**********************************************************************/
274 /** \name Matrix output */
278 * Print a matrix array.
280 * \param m matrix array.
282 * Called by _math_matrix_print() to print a matrix or its inverse.
284 static void print_matrix_floats( const GLfloat m
[16] )
288 _mesa_debug(NULL
,"\t%f %f %f %f\n", m
[i
], m
[4+i
], m
[8+i
], m
[12+i
] );
293 * Dumps the contents of a GLmatrix structure.
295 * \param m pointer to the GLmatrix structure.
298 _math_matrix_print( const GLmatrix
*m
)
302 _mesa_debug(NULL
, "Matrix type: %s, flags: %x\n", types
[m
->type
], m
->flags
);
303 print_matrix_floats(m
->m
);
304 _mesa_debug(NULL
, "Inverse: \n");
305 print_matrix_floats(m
->inv
);
306 matmul4(prod
, m
->m
, m
->inv
);
307 _mesa_debug(NULL
, "Mat * Inverse:\n");
308 print_matrix_floats(prod
);
315 * References an element of 4x4 matrix.
317 * \param m matrix array.
318 * \param c column of the desired element.
319 * \param r row of the desired element.
321 * \return value of the desired element.
323 * Calculate the linear storage index of the element and references it.
325 #define MAT(m,r,c) (m)[(c)*4+(r)]
328 /**********************************************************************/
329 /** \name Matrix inversion */
333 * Swaps the values of two floating point variables.
335 * Used by invert_matrix_general() to swap the row pointers.
337 #define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
340 * Compute inverse of 4x4 transformation matrix.
342 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
343 * stored in the GLmatrix::inv attribute.
345 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
348 * Code contributed by Jacques Leroy jle@star.be
350 * Calculates the inverse matrix by performing the gaussian matrix reduction
351 * with partial pivoting followed by back/substitution with the loops manually
354 static GLboolean
invert_matrix_general( GLmatrix
*mat
)
356 const GLfloat
*m
= mat
->m
;
357 GLfloat
*out
= mat
->inv
;
359 GLfloat m0
, m1
, m2
, m3
, s
;
360 GLfloat
*r0
, *r1
, *r2
, *r3
;
362 r0
= wtmp
[0], r1
= wtmp
[1], r2
= wtmp
[2], r3
= wtmp
[3];
364 r0
[0] = MAT(m
,0,0), r0
[1] = MAT(m
,0,1),
365 r0
[2] = MAT(m
,0,2), r0
[3] = MAT(m
,0,3),
366 r0
[4] = 1.0, r0
[5] = r0
[6] = r0
[7] = 0.0,
368 r1
[0] = MAT(m
,1,0), r1
[1] = MAT(m
,1,1),
369 r1
[2] = MAT(m
,1,2), r1
[3] = MAT(m
,1,3),
370 r1
[5] = 1.0, r1
[4] = r1
[6] = r1
[7] = 0.0,
372 r2
[0] = MAT(m
,2,0), r2
[1] = MAT(m
,2,1),
373 r2
[2] = MAT(m
,2,2), r2
[3] = MAT(m
,2,3),
374 r2
[6] = 1.0, r2
[4] = r2
[5] = r2
[7] = 0.0,
376 r3
[0] = MAT(m
,3,0), r3
[1] = MAT(m
,3,1),
377 r3
[2] = MAT(m
,3,2), r3
[3] = MAT(m
,3,3),
378 r3
[7] = 1.0, r3
[4] = r3
[5] = r3
[6] = 0.0;
380 /* choose pivot - or die */
381 if (fabsf(r3
[0])>fabsf(r2
[0])) SWAP_ROWS(r3
, r2
);
382 if (fabsf(r2
[0])>fabsf(r1
[0])) SWAP_ROWS(r2
, r1
);
383 if (fabsf(r1
[0])>fabsf(r0
[0])) SWAP_ROWS(r1
, r0
);
384 if (0.0F
== r0
[0]) return GL_FALSE
;
386 /* eliminate first variable */
387 m1
= r1
[0]/r0
[0]; m2
= r2
[0]/r0
[0]; m3
= r3
[0]/r0
[0];
388 s
= r0
[1]; r1
[1] -= m1
* s
; r2
[1] -= m2
* s
; r3
[1] -= m3
* s
;
389 s
= r0
[2]; r1
[2] -= m1
* s
; r2
[2] -= m2
* s
; r3
[2] -= m3
* s
;
390 s
= r0
[3]; r1
[3] -= m1
* s
; r2
[3] -= m2
* s
; r3
[3] -= m3
* s
;
392 if (s
!= 0.0F
) { r1
[4] -= m1
* s
; r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
394 if (s
!= 0.0F
) { r1
[5] -= m1
* s
; r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
396 if (s
!= 0.0F
) { r1
[6] -= m1
* s
; r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
398 if (s
!= 0.0F
) { r1
[7] -= m1
* s
; r2
[7] -= m2
* s
; r3
[7] -= m3
* s
; }
400 /* choose pivot - or die */
401 if (fabsf(r3
[1])>fabsf(r2
[1])) SWAP_ROWS(r3
, r2
);
402 if (fabsf(r2
[1])>fabsf(r1
[1])) SWAP_ROWS(r2
, r1
);
403 if (0.0F
== r1
[1]) return GL_FALSE
;
405 /* eliminate second variable */
406 m2
= r2
[1]/r1
[1]; m3
= r3
[1]/r1
[1];
407 r2
[2] -= m2
* r1
[2]; r3
[2] -= m3
* r1
[2];
408 r2
[3] -= m2
* r1
[3]; r3
[3] -= m3
* r1
[3];
409 s
= r1
[4]; if (0.0F
!= s
) { r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
410 s
= r1
[5]; if (0.0F
!= s
) { r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
411 s
= r1
[6]; if (0.0F
!= s
) { r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
412 s
= r1
[7]; if (0.0F
!= s
) { r2
[7] -= m2
* s
; r3
[7] -= m3
* s
; }
414 /* choose pivot - or die */
415 if (fabsf(r3
[2])>fabsf(r2
[2])) SWAP_ROWS(r3
, r2
);
416 if (0.0F
== r2
[2]) return GL_FALSE
;
418 /* eliminate third variable */
420 r3
[3] -= m3
* r2
[3], r3
[4] -= m3
* r2
[4],
421 r3
[5] -= m3
* r2
[5], r3
[6] -= m3
* r2
[6],
425 if (0.0F
== r3
[3]) return GL_FALSE
;
427 s
= 1.0F
/r3
[3]; /* now back substitute row 3 */
428 r3
[4] *= s
; r3
[5] *= s
; r3
[6] *= s
; r3
[7] *= s
;
430 m2
= r2
[3]; /* now back substitute row 2 */
432 r2
[4] = s
* (r2
[4] - r3
[4] * m2
), r2
[5] = s
* (r2
[5] - r3
[5] * m2
),
433 r2
[6] = s
* (r2
[6] - r3
[6] * m2
), r2
[7] = s
* (r2
[7] - r3
[7] * m2
);
435 r1
[4] -= r3
[4] * m1
, r1
[5] -= r3
[5] * m1
,
436 r1
[6] -= r3
[6] * m1
, r1
[7] -= r3
[7] * m1
;
438 r0
[4] -= r3
[4] * m0
, r0
[5] -= r3
[5] * m0
,
439 r0
[6] -= r3
[6] * m0
, r0
[7] -= r3
[7] * m0
;
441 m1
= r1
[2]; /* now back substitute row 1 */
443 r1
[4] = s
* (r1
[4] - r2
[4] * m1
), r1
[5] = s
* (r1
[5] - r2
[5] * m1
),
444 r1
[6] = s
* (r1
[6] - r2
[6] * m1
), r1
[7] = s
* (r1
[7] - r2
[7] * m1
);
446 r0
[4] -= r2
[4] * m0
, r0
[5] -= r2
[5] * m0
,
447 r0
[6] -= r2
[6] * m0
, r0
[7] -= r2
[7] * m0
;
449 m0
= r0
[1]; /* now back substitute row 0 */
451 r0
[4] = s
* (r0
[4] - r1
[4] * m0
), r0
[5] = s
* (r0
[5] - r1
[5] * m0
),
452 r0
[6] = s
* (r0
[6] - r1
[6] * m0
), r0
[7] = s
* (r0
[7] - r1
[7] * m0
);
454 MAT(out
,0,0) = r0
[4]; MAT(out
,0,1) = r0
[5],
455 MAT(out
,0,2) = r0
[6]; MAT(out
,0,3) = r0
[7],
456 MAT(out
,1,0) = r1
[4]; MAT(out
,1,1) = r1
[5],
457 MAT(out
,1,2) = r1
[6]; MAT(out
,1,3) = r1
[7],
458 MAT(out
,2,0) = r2
[4]; MAT(out
,2,1) = r2
[5],
459 MAT(out
,2,2) = r2
[6]; MAT(out
,2,3) = r2
[7],
460 MAT(out
,3,0) = r3
[4]; MAT(out
,3,1) = r3
[5],
461 MAT(out
,3,2) = r3
[6]; MAT(out
,3,3) = r3
[7];
468 * Compute inverse of a general 3d transformation matrix.
470 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
471 * stored in the GLmatrix::inv attribute.
473 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
475 * \author Adapted from graphics gems II.
477 * Calculates the inverse of the upper left by first calculating its
478 * determinant and multiplying it to the symmetric adjust matrix of each
479 * element. Finally deals with the translation part by transforming the
480 * original translation vector using by the calculated submatrix inverse.
482 static GLboolean
invert_matrix_3d_general( GLmatrix
*mat
)
484 const GLfloat
*in
= mat
->m
;
485 GLfloat
*out
= mat
->inv
;
489 /* Calculate the determinant of upper left 3x3 submatrix and
490 * determine if the matrix is singular.
493 t
= MAT(in
,0,0) * MAT(in
,1,1) * MAT(in
,2,2);
494 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
496 t
= MAT(in
,1,0) * MAT(in
,2,1) * MAT(in
,0,2);
497 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
499 t
= MAT(in
,2,0) * MAT(in
,0,1) * MAT(in
,1,2);
500 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
502 t
= -MAT(in
,2,0) * MAT(in
,1,1) * MAT(in
,0,2);
503 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
505 t
= -MAT(in
,1,0) * MAT(in
,0,1) * MAT(in
,2,2);
506 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
508 t
= -MAT(in
,0,0) * MAT(in
,2,1) * MAT(in
,1,2);
509 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
513 if (fabsf(det
) < 1e-25F
)
517 MAT(out
,0,0) = ( (MAT(in
,1,1)*MAT(in
,2,2) - MAT(in
,2,1)*MAT(in
,1,2) )*det
);
518 MAT(out
,0,1) = (- (MAT(in
,0,1)*MAT(in
,2,2) - MAT(in
,2,1)*MAT(in
,0,2) )*det
);
519 MAT(out
,0,2) = ( (MAT(in
,0,1)*MAT(in
,1,2) - MAT(in
,1,1)*MAT(in
,0,2) )*det
);
520 MAT(out
,1,0) = (- (MAT(in
,1,0)*MAT(in
,2,2) - MAT(in
,2,0)*MAT(in
,1,2) )*det
);
521 MAT(out
,1,1) = ( (MAT(in
,0,0)*MAT(in
,2,2) - MAT(in
,2,0)*MAT(in
,0,2) )*det
);
522 MAT(out
,1,2) = (- (MAT(in
,0,0)*MAT(in
,1,2) - MAT(in
,1,0)*MAT(in
,0,2) )*det
);
523 MAT(out
,2,0) = ( (MAT(in
,1,0)*MAT(in
,2,1) - MAT(in
,2,0)*MAT(in
,1,1) )*det
);
524 MAT(out
,2,1) = (- (MAT(in
,0,0)*MAT(in
,2,1) - MAT(in
,2,0)*MAT(in
,0,1) )*det
);
525 MAT(out
,2,2) = ( (MAT(in
,0,0)*MAT(in
,1,1) - MAT(in
,1,0)*MAT(in
,0,1) )*det
);
527 /* Do the translation part */
528 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0) +
529 MAT(in
,1,3) * MAT(out
,0,1) +
530 MAT(in
,2,3) * MAT(out
,0,2) );
531 MAT(out
,1,3) = - (MAT(in
,0,3) * MAT(out
,1,0) +
532 MAT(in
,1,3) * MAT(out
,1,1) +
533 MAT(in
,2,3) * MAT(out
,1,2) );
534 MAT(out
,2,3) = - (MAT(in
,0,3) * MAT(out
,2,0) +
535 MAT(in
,1,3) * MAT(out
,2,1) +
536 MAT(in
,2,3) * MAT(out
,2,2) );
542 * Compute inverse of a 3d transformation matrix.
544 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
545 * stored in the GLmatrix::inv attribute.
547 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
549 * If the matrix is not an angle preserving matrix then calls
550 * invert_matrix_3d_general for the actual calculation. Otherwise calculates
551 * the inverse matrix analyzing and inverting each of the scaling, rotation and
554 static GLboolean
invert_matrix_3d( GLmatrix
*mat
)
556 const GLfloat
*in
= mat
->m
;
557 GLfloat
*out
= mat
->inv
;
559 if (!TEST_MAT_FLAGS(mat
, MAT_FLAGS_ANGLE_PRESERVING
)) {
560 return invert_matrix_3d_general( mat
);
563 if (mat
->flags
& MAT_FLAG_UNIFORM_SCALE
) {
564 GLfloat scale
= (MAT(in
,0,0) * MAT(in
,0,0) +
565 MAT(in
,0,1) * MAT(in
,0,1) +
566 MAT(in
,0,2) * MAT(in
,0,2));
571 scale
= 1.0F
/ scale
;
573 /* Transpose and scale the 3 by 3 upper-left submatrix. */
574 MAT(out
,0,0) = scale
* MAT(in
,0,0);
575 MAT(out
,1,0) = scale
* MAT(in
,0,1);
576 MAT(out
,2,0) = scale
* MAT(in
,0,2);
577 MAT(out
,0,1) = scale
* MAT(in
,1,0);
578 MAT(out
,1,1) = scale
* MAT(in
,1,1);
579 MAT(out
,2,1) = scale
* MAT(in
,1,2);
580 MAT(out
,0,2) = scale
* MAT(in
,2,0);
581 MAT(out
,1,2) = scale
* MAT(in
,2,1);
582 MAT(out
,2,2) = scale
* MAT(in
,2,2);
584 else if (mat
->flags
& MAT_FLAG_ROTATION
) {
585 /* Transpose the 3 by 3 upper-left submatrix. */
586 MAT(out
,0,0) = MAT(in
,0,0);
587 MAT(out
,1,0) = MAT(in
,0,1);
588 MAT(out
,2,0) = MAT(in
,0,2);
589 MAT(out
,0,1) = MAT(in
,1,0);
590 MAT(out
,1,1) = MAT(in
,1,1);
591 MAT(out
,2,1) = MAT(in
,1,2);
592 MAT(out
,0,2) = MAT(in
,2,0);
593 MAT(out
,1,2) = MAT(in
,2,1);
594 MAT(out
,2,2) = MAT(in
,2,2);
597 /* pure translation */
598 memcpy( out
, Identity
, sizeof(Identity
) );
599 MAT(out
,0,3) = - MAT(in
,0,3);
600 MAT(out
,1,3) = - MAT(in
,1,3);
601 MAT(out
,2,3) = - MAT(in
,2,3);
605 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
606 /* Do the translation part */
607 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0) +
608 MAT(in
,1,3) * MAT(out
,0,1) +
609 MAT(in
,2,3) * MAT(out
,0,2) );
610 MAT(out
,1,3) = - (MAT(in
,0,3) * MAT(out
,1,0) +
611 MAT(in
,1,3) * MAT(out
,1,1) +
612 MAT(in
,2,3) * MAT(out
,1,2) );
613 MAT(out
,2,3) = - (MAT(in
,0,3) * MAT(out
,2,0) +
614 MAT(in
,1,3) * MAT(out
,2,1) +
615 MAT(in
,2,3) * MAT(out
,2,2) );
618 MAT(out
,0,3) = MAT(out
,1,3) = MAT(out
,2,3) = 0.0;
625 * Compute inverse of an identity transformation matrix.
627 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
628 * stored in the GLmatrix::inv attribute.
630 * \return always GL_TRUE.
632 * Simply copies Identity into GLmatrix::inv.
634 static GLboolean
invert_matrix_identity( GLmatrix
*mat
)
636 memcpy( mat
->inv
, Identity
, sizeof(Identity
) );
641 * Compute inverse of a no-rotation 3d transformation matrix.
643 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
644 * stored in the GLmatrix::inv attribute.
646 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
650 static GLboolean
invert_matrix_3d_no_rot( GLmatrix
*mat
)
652 const GLfloat
*in
= mat
->m
;
653 GLfloat
*out
= mat
->inv
;
655 if (MAT(in
,0,0) == 0 || MAT(in
,1,1) == 0 || MAT(in
,2,2) == 0 )
658 memcpy( out
, Identity
, sizeof(Identity
) );
659 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
660 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
661 MAT(out
,2,2) = 1.0F
/ MAT(in
,2,2);
663 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
664 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0));
665 MAT(out
,1,3) = - (MAT(in
,1,3) * MAT(out
,1,1));
666 MAT(out
,2,3) = - (MAT(in
,2,3) * MAT(out
,2,2));
673 * Compute inverse of a no-rotation 2d transformation matrix.
675 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
676 * stored in the GLmatrix::inv attribute.
678 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
680 * Calculates the inverse matrix by applying the inverse scaling and
681 * translation to the identity matrix.
683 static GLboolean
invert_matrix_2d_no_rot( GLmatrix
*mat
)
685 const GLfloat
*in
= mat
->m
;
686 GLfloat
*out
= mat
->inv
;
688 if (MAT(in
,0,0) == 0 || MAT(in
,1,1) == 0)
691 memcpy( out
, Identity
, sizeof(Identity
) );
692 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
693 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
695 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
696 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0));
697 MAT(out
,1,3) = - (MAT(in
,1,3) * MAT(out
,1,1));
705 static GLboolean
invert_matrix_perspective( GLmatrix
*mat
)
707 const GLfloat
*in
= mat
->m
;
708 GLfloat
*out
= mat
->inv
;
710 if (MAT(in
,2,3) == 0)
713 memcpy( out
, Identity
, sizeof(Identity
) );
715 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
716 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
718 MAT(out
,0,3) = MAT(in
,0,2);
719 MAT(out
,1,3) = MAT(in
,1,2);
724 MAT(out
,3,2) = 1.0F
/ MAT(in
,2,3);
725 MAT(out
,3,3) = MAT(in
,2,2) * MAT(out
,3,2);
732 * Matrix inversion function pointer type.
734 typedef GLboolean (*inv_mat_func
)( GLmatrix
*mat
);
737 * Table of the matrix inversion functions according to the matrix type.
739 static inv_mat_func inv_mat_tab
[7] = {
740 invert_matrix_general
,
741 invert_matrix_identity
,
742 invert_matrix_3d_no_rot
,
744 /* Don't use this function for now - it fails when the projection matrix
745 * is premultiplied by a translation (ala Chromium's tilesort SPU).
747 invert_matrix_perspective
,
749 invert_matrix_general
,
751 invert_matrix_3d
, /* lazy! */
752 invert_matrix_2d_no_rot
,
757 * Compute inverse of a transformation matrix.
759 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
760 * stored in the GLmatrix::inv attribute.
762 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
764 * Calls the matrix inversion function in inv_mat_tab corresponding to the
765 * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag,
766 * and copies the identity matrix into GLmatrix::inv.
768 static GLboolean
matrix_invert( GLmatrix
*mat
)
770 if (inv_mat_tab
[mat
->type
](mat
)) {
771 mat
->flags
&= ~MAT_FLAG_SINGULAR
;
774 mat
->flags
|= MAT_FLAG_SINGULAR
;
775 memcpy( mat
->inv
, Identity
, sizeof(Identity
) );
783 /**********************************************************************/
784 /** \name Matrix generation */
788 * Generate a 4x4 transformation matrix from glRotate parameters, and
789 * post-multiply the input matrix by it.
792 * This function was contributed by Erich Boleyn (erich@uruk.org).
793 * Optimizations contributed by Rudolf Opalla (rudi@khm.de).
796 _math_matrix_rotate( GLmatrix
*mat
,
797 GLfloat angle
, GLfloat x
, GLfloat y
, GLfloat z
)
799 GLfloat xx
, yy
, zz
, xy
, yz
, zx
, xs
, ys
, zs
, one_c
, s
, c
;
803 s
= sinf( angle
* M_PI
/ 180.0 );
804 c
= cosf( angle
* M_PI
/ 180.0 );
806 memcpy(m
, Identity
, sizeof(Identity
));
807 optimized
= GL_FALSE
;
809 #define M(row,col) m[col*4+row]
815 /* rotate only around z-axis */
828 else if (z
== 0.0F
) {
830 /* rotate only around y-axis */
843 else if (y
== 0.0F
) {
846 /* rotate only around x-axis */
861 const GLfloat mag
= sqrtf(x
* x
+ y
* y
+ z
* z
);
863 if (mag
<= 1.0e-4F
) {
864 /* no rotation, leave mat as-is */
874 * Arbitrary axis rotation matrix.
876 * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
877 * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation
878 * (which is about the X-axis), and the two composite transforms
879 * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
880 * from the arbitrary axis to the X-axis then back. They are
881 * all elementary rotations.
883 * Rz' is a rotation about the Z-axis, to bring the axis vector
884 * into the x-z plane. Then Ry' is applied, rotating about the
885 * Y-axis to bring the axis vector parallel with the X-axis. The
886 * rotation about the X-axis is then performed. Ry and Rz are
887 * simply the respective inverse transforms to bring the arbitrary
888 * axis back to its original orientation. The first transforms
889 * Rz' and Ry' are considered inverses, since the data from the
890 * arbitrary axis gives you info on how to get to it, not how
891 * to get away from it, and an inverse must be applied.
893 * The basic calculation used is to recognize that the arbitrary
894 * axis vector (x, y, z), since it is of unit length, actually
895 * represents the sines and cosines of the angles to rotate the
896 * X-axis to the same orientation, with theta being the angle about
897 * Z and phi the angle about Y (in the order described above)
900 * cos ( theta ) = x / sqrt ( 1 - z^2 )
901 * sin ( theta ) = y / sqrt ( 1 - z^2 )
903 * cos ( phi ) = sqrt ( 1 - z^2 )
906 * Note that cos ( phi ) can further be inserted to the above
909 * cos ( theta ) = x / cos ( phi )
910 * sin ( theta ) = y / sin ( phi )
912 * ...etc. Because of those relations and the standard trigonometric
913 * relations, it is pssible to reduce the transforms down to what
914 * is used below. It may be that any primary axis chosen will give the
915 * same results (modulo a sign convention) using thie method.
917 * Particularly nice is to notice that all divisions that might
918 * have caused trouble when parallel to certain planes or
919 * axis go away with care paid to reducing the expressions.
920 * After checking, it does perform correctly under all cases, since
921 * in all the cases of division where the denominator would have
922 * been zero, the numerator would have been zero as well, giving
923 * the expected result.
937 /* We already hold the identity-matrix so we can skip some statements */
938 M(0,0) = (one_c
* xx
) + c
;
939 M(0,1) = (one_c
* xy
) - zs
;
940 M(0,2) = (one_c
* zx
) + ys
;
943 M(1,0) = (one_c
* xy
) + zs
;
944 M(1,1) = (one_c
* yy
) + c
;
945 M(1,2) = (one_c
* yz
) - xs
;
948 M(2,0) = (one_c
* zx
) - ys
;
949 M(2,1) = (one_c
* yz
) + xs
;
950 M(2,2) = (one_c
* zz
) + c
;
962 matrix_multf( mat
, m
, MAT_FLAG_ROTATION
);
966 * Apply a perspective projection matrix.
968 * \param mat matrix to apply the projection.
969 * \param left left clipping plane coordinate.
970 * \param right right clipping plane coordinate.
971 * \param bottom bottom clipping plane coordinate.
972 * \param top top clipping plane coordinate.
973 * \param nearval distance to the near clipping plane.
974 * \param farval distance to the far clipping plane.
976 * Creates the projection matrix and multiplies it with \p mat, marking the
977 * MAT_FLAG_PERSPECTIVE flag.
980 _math_matrix_frustum( GLmatrix
*mat
,
981 GLfloat left
, GLfloat right
,
982 GLfloat bottom
, GLfloat top
,
983 GLfloat nearval
, GLfloat farval
)
985 GLfloat x
, y
, a
, b
, c
, d
;
988 x
= (2.0F
*nearval
) / (right
-left
);
989 y
= (2.0F
*nearval
) / (top
-bottom
);
990 a
= (right
+left
) / (right
-left
);
991 b
= (top
+bottom
) / (top
-bottom
);
992 c
= -(farval
+nearval
) / ( farval
-nearval
);
993 d
= -(2.0F
*farval
*nearval
) / (farval
-nearval
); /* error? */
995 #define M(row,col) m[col*4+row]
996 M(0,0) = x
; M(0,1) = 0.0F
; M(0,2) = a
; M(0,3) = 0.0F
;
997 M(1,0) = 0.0F
; M(1,1) = y
; M(1,2) = b
; M(1,3) = 0.0F
;
998 M(2,0) = 0.0F
; M(2,1) = 0.0F
; M(2,2) = c
; M(2,3) = d
;
999 M(3,0) = 0.0F
; M(3,1) = 0.0F
; M(3,2) = -1.0F
; M(3,3) = 0.0F
;
1002 matrix_multf( mat
, m
, MAT_FLAG_PERSPECTIVE
);
1006 * Apply an orthographic projection matrix.
1008 * \param mat matrix to apply the projection.
1009 * \param left left clipping plane coordinate.
1010 * \param right right clipping plane coordinate.
1011 * \param bottom bottom clipping plane coordinate.
1012 * \param top top clipping plane coordinate.
1013 * \param nearval distance to the near clipping plane.
1014 * \param farval distance to the far clipping plane.
1016 * Creates the projection matrix and multiplies it with \p mat, marking the
1017 * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
1020 _math_matrix_ortho( GLmatrix
*mat
,
1021 GLfloat left
, GLfloat right
,
1022 GLfloat bottom
, GLfloat top
,
1023 GLfloat nearval
, GLfloat farval
)
1027 #define M(row,col) m[col*4+row]
1028 M(0,0) = 2.0F
/ (right
-left
);
1031 M(0,3) = -(right
+left
) / (right
-left
);
1034 M(1,1) = 2.0F
/ (top
-bottom
);
1036 M(1,3) = -(top
+bottom
) / (top
-bottom
);
1040 M(2,2) = -2.0F
/ (farval
-nearval
);
1041 M(2,3) = -(farval
+nearval
) / (farval
-nearval
);
1049 matrix_multf( mat
, m
, (MAT_FLAG_GENERAL_SCALE
|MAT_FLAG_TRANSLATION
));
1053 * Multiply a matrix with a general scaling matrix.
1055 * \param mat matrix.
1056 * \param x x axis scale factor.
1057 * \param y y axis scale factor.
1058 * \param z z axis scale factor.
1060 * Multiplies in-place the elements of \p mat by the scale factors. Checks if
1061 * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
1062 * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
1063 * MAT_DIRTY_INVERSE dirty flags.
1066 _math_matrix_scale( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
)
1068 GLfloat
*m
= mat
->m
;
1069 m
[0] *= x
; m
[4] *= y
; m
[8] *= z
;
1070 m
[1] *= x
; m
[5] *= y
; m
[9] *= z
;
1071 m
[2] *= x
; m
[6] *= y
; m
[10] *= z
;
1072 m
[3] *= x
; m
[7] *= y
; m
[11] *= z
;
1074 if (fabsf(x
- y
) < 1e-8F
&& fabsf(x
- z
) < 1e-8F
)
1075 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1077 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1079 mat
->flags
|= (MAT_DIRTY_TYPE
|
1084 * Multiply a matrix with a translation matrix.
1086 * \param mat matrix.
1087 * \param x translation vector x coordinate.
1088 * \param y translation vector y coordinate.
1089 * \param z translation vector z coordinate.
1091 * Adds the translation coordinates to the elements of \p mat in-place. Marks
1092 * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
1096 _math_matrix_translate( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
)
1098 GLfloat
*m
= mat
->m
;
1099 m
[12] = m
[0] * x
+ m
[4] * y
+ m
[8] * z
+ m
[12];
1100 m
[13] = m
[1] * x
+ m
[5] * y
+ m
[9] * z
+ m
[13];
1101 m
[14] = m
[2] * x
+ m
[6] * y
+ m
[10] * z
+ m
[14];
1102 m
[15] = m
[3] * x
+ m
[7] * y
+ m
[11] * z
+ m
[15];
1104 mat
->flags
|= (MAT_FLAG_TRANSLATION
|
1111 * Set matrix to do viewport and depthrange mapping.
1112 * Transforms Normalized Device Coords to window/Z values.
1115 _math_matrix_viewport(GLmatrix
*m
, const float scale
[3],
1116 const float translate
[3], double depthMax
)
1118 m
->m
[MAT_SX
] = scale
[0];
1119 m
->m
[MAT_TX
] = translate
[0];
1120 m
->m
[MAT_SY
] = scale
[1];
1121 m
->m
[MAT_TY
] = translate
[1];
1122 m
->m
[MAT_SZ
] = depthMax
*scale
[2];
1123 m
->m
[MAT_TZ
] = depthMax
*translate
[2];
1124 m
->flags
= MAT_FLAG_GENERAL_SCALE
| MAT_FLAG_TRANSLATION
;
1125 m
->type
= MATRIX_3D_NO_ROT
;
1130 * Set a matrix to the identity matrix.
1132 * \param mat matrix.
1134 * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
1135 * Sets the matrix type to identity, and clear the dirty flags.
1138 _math_matrix_set_identity( GLmatrix
*mat
)
1140 memcpy( mat
->m
, Identity
, sizeof(Identity
) );
1141 memcpy( mat
->inv
, Identity
, sizeof(Identity
) );
1143 mat
->type
= MATRIX_IDENTITY
;
1144 mat
->flags
&= ~(MAT_DIRTY_FLAGS
|
1152 /**********************************************************************/
1153 /** \name Matrix analysis */
1156 #define ZERO(x) (1<<x)
1157 #define ONE(x) (1<<(x+16))
1159 #define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14))
1160 #define MASK_NO_2D_SCALE ( ONE(0) | ONE(5))
1162 #define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\
1163 ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\
1164 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1165 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1167 #define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \
1168 ZERO(1) | ZERO(9) | \
1169 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1170 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1172 #define MASK_2D ( ZERO(8) | \
1174 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1175 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1178 #define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \
1179 ZERO(1) | ZERO(9) | \
1180 ZERO(2) | ZERO(6) | \
1181 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1186 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1189 #define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\
1190 ZERO(1) | ZERO(13) |\
1191 ZERO(2) | ZERO(6) | \
1192 ZERO(3) | ZERO(7) | ZERO(15) )
1194 #define SQ(x) ((x)*(x))
1197 * Determine type and flags from scratch.
1199 * \param mat matrix.
1201 * This is expensive enough to only want to do it once.
1203 static void analyse_from_scratch( GLmatrix
*mat
)
1205 const GLfloat
*m
= mat
->m
;
1209 for (i
= 0 ; i
< 16 ; i
++) {
1210 if (m
[i
] == 0.0F
) mask
|= (1<<i
);
1213 if (m
[0] == 1.0F
) mask
|= (1<<16);
1214 if (m
[5] == 1.0F
) mask
|= (1<<21);
1215 if (m
[10] == 1.0F
) mask
|= (1<<26);
1216 if (m
[15] == 1.0F
) mask
|= (1<<31);
1218 mat
->flags
&= ~MAT_FLAGS_GEOMETRY
;
1220 /* Check for translation - no-one really cares
1222 if ((mask
& MASK_NO_TRX
) != MASK_NO_TRX
)
1223 mat
->flags
|= MAT_FLAG_TRANSLATION
;
1227 if (mask
== (GLuint
) MASK_IDENTITY
) {
1228 mat
->type
= MATRIX_IDENTITY
;
1230 else if ((mask
& MASK_2D_NO_ROT
) == (GLuint
) MASK_2D_NO_ROT
) {
1231 mat
->type
= MATRIX_2D_NO_ROT
;
1233 if ((mask
& MASK_NO_2D_SCALE
) != MASK_NO_2D_SCALE
)
1234 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1236 else if ((mask
& MASK_2D
) == (GLuint
) MASK_2D
) {
1237 GLfloat mm
= DOT2(m
, m
);
1238 GLfloat m4m4
= DOT2(m
+4,m
+4);
1239 GLfloat mm4
= DOT2(m
,m
+4);
1241 mat
->type
= MATRIX_2D
;
1243 /* Check for scale */
1244 if (SQ(mm
-1) > SQ(1e-6F
) ||
1245 SQ(m4m4
-1) > SQ(1e-6F
))
1246 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1248 /* Check for rotation */
1249 if (SQ(mm4
) > SQ(1e-6F
))
1250 mat
->flags
|= MAT_FLAG_GENERAL_3D
;
1252 mat
->flags
|= MAT_FLAG_ROTATION
;
1255 else if ((mask
& MASK_3D_NO_ROT
) == (GLuint
) MASK_3D_NO_ROT
) {
1256 mat
->type
= MATRIX_3D_NO_ROT
;
1258 /* Check for scale */
1259 if (SQ(m
[0]-m
[5]) < SQ(1e-6F
) &&
1260 SQ(m
[0]-m
[10]) < SQ(1e-6F
)) {
1261 if (SQ(m
[0]-1.0F
) > SQ(1e-6F
)) {
1262 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1266 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1269 else if ((mask
& MASK_3D
) == (GLuint
) MASK_3D
) {
1270 GLfloat c1
= DOT3(m
,m
);
1271 GLfloat c2
= DOT3(m
+4,m
+4);
1272 GLfloat c3
= DOT3(m
+8,m
+8);
1273 GLfloat d1
= DOT3(m
, m
+4);
1276 mat
->type
= MATRIX_3D
;
1278 /* Check for scale */
1279 if (SQ(c1
-c2
) < SQ(1e-6F
) && SQ(c1
-c3
) < SQ(1e-6F
)) {
1280 if (SQ(c1
-1.0F
) > SQ(1e-6F
))
1281 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1282 /* else no scale at all */
1285 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1288 /* Check for rotation */
1289 if (SQ(d1
) < SQ(1e-6F
)) {
1290 CROSS3( cp
, m
, m
+4 );
1291 SUB_3V( cp
, cp
, (m
+8) );
1292 if (LEN_SQUARED_3FV(cp
) < SQ(1e-6F
))
1293 mat
->flags
|= MAT_FLAG_ROTATION
;
1295 mat
->flags
|= MAT_FLAG_GENERAL_3D
;
1298 mat
->flags
|= MAT_FLAG_GENERAL_3D
; /* shear, etc */
1301 else if ((mask
& MASK_PERSPECTIVE
) == MASK_PERSPECTIVE
&& m
[11]==-1.0F
) {
1302 mat
->type
= MATRIX_PERSPECTIVE
;
1303 mat
->flags
|= MAT_FLAG_GENERAL
;
1306 mat
->type
= MATRIX_GENERAL
;
1307 mat
->flags
|= MAT_FLAG_GENERAL
;
1312 * Analyze a matrix given that its flags are accurate.
1314 * This is the more common operation, hopefully.
1316 static void analyse_from_flags( GLmatrix
*mat
)
1318 const GLfloat
*m
= mat
->m
;
1320 if (TEST_MAT_FLAGS(mat
, 0)) {
1321 mat
->type
= MATRIX_IDENTITY
;
1323 else if (TEST_MAT_FLAGS(mat
, (MAT_FLAG_TRANSLATION
|
1324 MAT_FLAG_UNIFORM_SCALE
|
1325 MAT_FLAG_GENERAL_SCALE
))) {
1326 if ( m
[10]==1.0F
&& m
[14]==0.0F
) {
1327 mat
->type
= MATRIX_2D_NO_ROT
;
1330 mat
->type
= MATRIX_3D_NO_ROT
;
1333 else if (TEST_MAT_FLAGS(mat
, MAT_FLAGS_3D
)) {
1336 && m
[2]==0.0F
&& m
[6]==0.0F
&& m
[10]==1.0F
&& m
[14]==0.0F
) {
1337 mat
->type
= MATRIX_2D
;
1340 mat
->type
= MATRIX_3D
;
1343 else if ( m
[4]==0.0F
&& m
[12]==0.0F
1344 && m
[1]==0.0F
&& m
[13]==0.0F
1345 && m
[2]==0.0F
&& m
[6]==0.0F
1346 && m
[3]==0.0F
&& m
[7]==0.0F
&& m
[11]==-1.0F
&& m
[15]==0.0F
) {
1347 mat
->type
= MATRIX_PERSPECTIVE
;
1350 mat
->type
= MATRIX_GENERAL
;
1355 * Analyze and update a matrix.
1357 * \param mat matrix.
1359 * If the matrix type is dirty then calls either analyse_from_scratch() or
1360 * analyse_from_flags() to determine its type, according to whether the flags
1361 * are dirty or not, respectively. If the matrix has an inverse and it's dirty
1362 * then calls matrix_invert(). Finally clears the dirty flags.
1365 _math_matrix_analyse( GLmatrix
*mat
)
1367 if (mat
->flags
& MAT_DIRTY_TYPE
) {
1368 if (mat
->flags
& MAT_DIRTY_FLAGS
)
1369 analyse_from_scratch( mat
);
1371 analyse_from_flags( mat
);
1374 if (mat
->inv
&& (mat
->flags
& MAT_DIRTY_INVERSE
)) {
1375 matrix_invert( mat
);
1376 mat
->flags
&= ~MAT_DIRTY_INVERSE
;
1379 mat
->flags
&= ~(MAT_DIRTY_FLAGS
| MAT_DIRTY_TYPE
);
1386 * Test if the given matrix preserves vector lengths.
1389 _math_matrix_is_length_preserving( const GLmatrix
*m
)
1391 return TEST_MAT_FLAGS( m
, MAT_FLAGS_LENGTH_PRESERVING
);
1396 * Test if the given matrix does any rotation.
1397 * (or perhaps if the upper-left 3x3 is non-identity)
1400 _math_matrix_has_rotation( const GLmatrix
*m
)
1402 if (m
->flags
& (MAT_FLAG_GENERAL
|
1404 MAT_FLAG_GENERAL_3D
|
1405 MAT_FLAG_PERSPECTIVE
))
1413 _math_matrix_is_general_scale( const GLmatrix
*m
)
1415 return (m
->flags
& MAT_FLAG_GENERAL_SCALE
) ? GL_TRUE
: GL_FALSE
;
1420 _math_matrix_is_dirty( const GLmatrix
*m
)
1422 return (m
->flags
& MAT_DIRTY
) ? GL_TRUE
: GL_FALSE
;
1426 /**********************************************************************/
1427 /** \name Matrix setup */
1433 * \param to destination matrix.
1434 * \param from source matrix.
1436 * Copies all fields in GLmatrix, creating an inverse array if necessary.
1439 _math_matrix_copy( GLmatrix
*to
, const GLmatrix
*from
)
1441 memcpy(to
->m
, from
->m
, 16 * sizeof(GLfloat
));
1442 memcpy(to
->inv
, from
->inv
, 16 * sizeof(GLfloat
));
1443 to
->flags
= from
->flags
;
1444 to
->type
= from
->type
;
1448 * Loads a matrix array into GLmatrix.
1450 * \param m matrix array.
1451 * \param mat matrix.
1453 * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
1457 _math_matrix_loadf( GLmatrix
*mat
, const GLfloat
*m
)
1459 memcpy( mat
->m
, m
, 16*sizeof(GLfloat
) );
1460 mat
->flags
= (MAT_FLAG_GENERAL
| MAT_DIRTY
);
1464 * Matrix constructor.
1468 * Initialize the GLmatrix fields.
1471 _math_matrix_ctr( GLmatrix
*m
)
1473 m
->m
= _mesa_align_malloc( 16 * sizeof(GLfloat
), 16 );
1475 memcpy( m
->m
, Identity
, sizeof(Identity
) );
1476 m
->inv
= _mesa_align_malloc( 16 * sizeof(GLfloat
), 16 );
1478 memcpy( m
->inv
, Identity
, sizeof(Identity
) );
1479 m
->type
= MATRIX_IDENTITY
;
1484 * Matrix destructor.
1488 * Frees the data in a GLmatrix.
1491 _math_matrix_dtr( GLmatrix
*m
)
1493 _mesa_align_free( m
->m
);
1496 _mesa_align_free( m
->inv
);
1503 /**********************************************************************/
1504 /** \name Matrix transpose */
1508 * Transpose a GLfloat matrix.
1510 * \param to destination array.
1511 * \param from source array.
1514 _math_transposef( GLfloat to
[16], const GLfloat from
[16] )
1535 * Transpose a GLdouble matrix.
1537 * \param to destination array.
1538 * \param from source array.
1541 _math_transposed( GLdouble to
[16], const GLdouble from
[16] )
1562 * Transpose a GLdouble matrix and convert to GLfloat.
1564 * \param to destination array.
1565 * \param from source array.
1568 _math_transposefd( GLfloat to
[16], const GLdouble from
[16] )
1570 to
[0] = (GLfloat
) from
[0];
1571 to
[1] = (GLfloat
) from
[4];
1572 to
[2] = (GLfloat
) from
[8];
1573 to
[3] = (GLfloat
) from
[12];
1574 to
[4] = (GLfloat
) from
[1];
1575 to
[5] = (GLfloat
) from
[5];
1576 to
[6] = (GLfloat
) from
[9];
1577 to
[7] = (GLfloat
) from
[13];
1578 to
[8] = (GLfloat
) from
[2];
1579 to
[9] = (GLfloat
) from
[6];
1580 to
[10] = (GLfloat
) from
[10];
1581 to
[11] = (GLfloat
) from
[14];
1582 to
[12] = (GLfloat
) from
[3];
1583 to
[13] = (GLfloat
) from
[7];
1584 to
[14] = (GLfloat
) from
[11];
1585 to
[15] = (GLfloat
) from
[15];
1592 * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This
1593 * function is used for transforming clipping plane equations and spotlight
1595 * Mathematically, u = v * m.
1596 * Input: v - input vector
1597 * m - transformation matrix
1598 * Output: u - transformed vector
1601 _mesa_transform_vector( GLfloat u
[4], const GLfloat v
[4], const GLfloat m
[16] )
1603 const GLfloat v0
= v
[0], v1
= v
[1], v2
= v
[2], v3
= v
[3];
1604 #define M(row,col) m[row + col*4]
1605 u
[0] = v0
* M(0,0) + v1
* M(1,0) + v2
* M(2,0) + v3
* M(3,0);
1606 u
[1] = v0
* M(0,1) + v1
* M(1,1) + v2
* M(2,1) + v3
* M(3,1);
1607 u
[2] = v0
* M(0,2) + v1
* M(1,2) + v2
* M(2,2) + v3
* M(3,2);
1608 u
[3] = v0
* M(0,3) + v1
* M(1,3) + v2
* M(2,3) + v3
* M(3,3);