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/macros.h"
42 #define MATH_ASM_PTR_SIZE sizeof(void *)
43 #include "math/m_vector_asm.h"
47 #include "util/u_memory.h"
51 * \defgroup MatFlags MAT_FLAG_XXX-flags
53 * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
56 #define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag.
57 * (Not actually used - the identity
58 * matrix is identified by the absence
59 * of all other flags.)
61 #define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */
62 #define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */
63 #define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */
64 #define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */
65 #define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */
66 #define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */
67 #define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */
68 #define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */
69 #define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */
70 #define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */
71 #define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */
73 /** angle preserving matrix flags mask */
74 #define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
75 MAT_FLAG_TRANSLATION | \
76 MAT_FLAG_UNIFORM_SCALE)
78 /** geometry related matrix flags mask */
79 #define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
81 MAT_FLAG_TRANSLATION | \
82 MAT_FLAG_UNIFORM_SCALE | \
83 MAT_FLAG_GENERAL_SCALE | \
84 MAT_FLAG_GENERAL_3D | \
85 MAT_FLAG_PERSPECTIVE | \
88 /** length preserving matrix flags mask */
89 #define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
93 /** 3D (non-perspective) matrix flags mask */
94 #define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
95 MAT_FLAG_TRANSLATION | \
96 MAT_FLAG_UNIFORM_SCALE | \
97 MAT_FLAG_GENERAL_SCALE | \
100 /** dirty matrix flags mask */
101 #define MAT_DIRTY (MAT_DIRTY_TYPE | \
109 * Test geometry related matrix flags.
111 * \param mat a pointer to a GLmatrix structure.
112 * \param a flags mask.
114 * \returns non-zero if all geometry related matrix flags are contained within
115 * the mask, or zero otherwise.
117 #define TEST_MAT_FLAGS(mat, a) \
118 ((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
123 * Names of the corresponding GLmatrixtype values.
125 static const char *types
[] = {
129 "MATRIX_PERSPECTIVE",
139 static const GLfloat Identity
[16] = {
148 /**********************************************************************/
149 /** \name Matrix multiplication */
152 #define A(row,col) a[(col<<2)+row]
153 #define B(row,col) b[(col<<2)+row]
154 #define P(row,col) product[(col<<2)+row]
157 * Perform a full 4x4 matrix multiplication.
161 * \param product will receive the product of \p a and \p b.
163 * \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
165 * \note KW: 4*16 = 64 multiplications
167 * \author This \c matmul was contributed by Thomas Malik
169 static void matmul4( GLfloat
*product
, const GLfloat
*a
, const GLfloat
*b
)
172 for (i
= 0; i
< 4; i
++) {
173 const GLfloat ai0
=A(i
,0), ai1
=A(i
,1), ai2
=A(i
,2), ai3
=A(i
,3);
174 P(i
,0) = ai0
* B(0,0) + ai1
* B(1,0) + ai2
* B(2,0) + ai3
* B(3,0);
175 P(i
,1) = ai0
* B(0,1) + ai1
* B(1,1) + ai2
* B(2,1) + ai3
* B(3,1);
176 P(i
,2) = ai0
* B(0,2) + ai1
* B(1,2) + ai2
* B(2,2) + ai3
* B(3,2);
177 P(i
,3) = ai0
* B(0,3) + ai1
* B(1,3) + ai2
* B(2,3) + ai3
* B(3,3);
182 * Multiply two matrices known to occupy only the top three rows, such
183 * as typical model matrices, and orthogonal matrices.
187 * \param product will receive the product of \p a and \p b.
189 static void matmul34( GLfloat
*product
, const GLfloat
*a
, const GLfloat
*b
)
192 for (i
= 0; i
< 3; i
++) {
193 const GLfloat ai0
=A(i
,0), ai1
=A(i
,1), ai2
=A(i
,2), ai3
=A(i
,3);
194 P(i
,0) = ai0
* B(0,0) + ai1
* B(1,0) + ai2
* B(2,0);
195 P(i
,1) = ai0
* B(0,1) + ai1
* B(1,1) + ai2
* B(2,1);
196 P(i
,2) = ai0
* B(0,2) + ai1
* B(1,2) + ai2
* B(2,2);
197 P(i
,3) = ai0
* B(0,3) + ai1
* B(1,3) + ai2
* B(2,3) + ai3
;
210 * Multiply a matrix by an array of floats with known properties.
212 * \param mat pointer to a GLmatrix structure containing the left multiplication
213 * matrix, and that will receive the product result.
214 * \param m right multiplication matrix array.
215 * \param flags flags of the matrix \p m.
217 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
218 * if both matrices are 3D, or matmul4() otherwise.
220 static void matrix_multf( GLmatrix
*mat
, const GLfloat
*m
, GLuint flags
)
222 mat
->flags
|= (flags
| MAT_DIRTY_TYPE
| MAT_DIRTY_INVERSE
);
224 if (TEST_MAT_FLAGS(mat
, MAT_FLAGS_3D
))
225 matmul34( mat
->m
, mat
->m
, m
);
227 matmul4( mat
->m
, mat
->m
, m
);
231 * Matrix multiplication.
233 * \param dest destination matrix.
234 * \param a left matrix.
235 * \param b right matrix.
237 * Joins both flags and marks the type and inverse as dirty. Calls matmul34()
238 * if both matrices are 3D, or matmul4() otherwise.
241 _math_matrix_mul_matrix( GLmatrix
*dest
, const GLmatrix
*a
, const GLmatrix
*b
)
243 dest
->flags
= (a
->flags
|
248 if (TEST_MAT_FLAGS(dest
, MAT_FLAGS_3D
))
249 matmul34( dest
->m
, a
->m
, b
->m
);
251 matmul4( dest
->m
, a
->m
, b
->m
);
255 * Matrix multiplication.
257 * \param dest left and destination matrix.
258 * \param m right matrix array.
260 * Marks the matrix flags with general flag, and type and inverse dirty flags.
261 * Calls matmul4() for the multiplication.
264 _math_matrix_mul_floats( GLmatrix
*dest
, const GLfloat
*m
)
266 dest
->flags
|= (MAT_FLAG_GENERAL
|
271 matmul4( dest
->m
, dest
->m
, m
);
277 /**********************************************************************/
278 /** \name Matrix output */
282 * Print a matrix array.
284 * \param m matrix array.
286 * Called by _math_matrix_print() to print a matrix or its inverse.
288 static void print_matrix_floats( const GLfloat m
[16] )
292 _mesa_debug(NULL
,"\t%f %f %f %f\n", m
[i
], m
[4+i
], m
[8+i
], m
[12+i
] );
297 * Dumps the contents of a GLmatrix structure.
299 * \param m pointer to the GLmatrix structure.
302 _math_matrix_print( const GLmatrix
*m
)
306 _mesa_debug(NULL
, "Matrix type: %s, flags: %x\n", types
[m
->type
], m
->flags
);
307 print_matrix_floats(m
->m
);
308 _mesa_debug(NULL
, "Inverse: \n");
309 print_matrix_floats(m
->inv
);
310 matmul4(prod
, m
->m
, m
->inv
);
311 _mesa_debug(NULL
, "Mat * Inverse:\n");
312 print_matrix_floats(prod
);
319 * References an element of 4x4 matrix.
321 * \param m matrix array.
322 * \param c column of the desired element.
323 * \param r row of the desired element.
325 * \return value of the desired element.
327 * Calculate the linear storage index of the element and references it.
329 #define MAT(m,r,c) (m)[(c)*4+(r)]
332 /**********************************************************************/
333 /** \name Matrix inversion */
337 * Swaps the values of two floating point variables.
339 * Used by invert_matrix_general() to swap the row pointers.
341 #define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
344 * Compute inverse of 4x4 transformation matrix.
346 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
347 * stored in the GLmatrix::inv attribute.
349 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
352 * Code contributed by Jacques Leroy jle@star.be
354 * Calculates the inverse matrix by performing the gaussian matrix reduction
355 * with partial pivoting followed by back/substitution with the loops manually
358 static GLboolean
invert_matrix_general( GLmatrix
*mat
)
360 const GLfloat
*m
= mat
->m
;
361 GLfloat
*out
= mat
->inv
;
363 GLfloat m0
, m1
, m2
, m3
, s
;
364 GLfloat
*r0
, *r1
, *r2
, *r3
;
366 r0
= wtmp
[0], r1
= wtmp
[1], r2
= wtmp
[2], r3
= wtmp
[3];
368 r0
[0] = MAT(m
,0,0), r0
[1] = MAT(m
,0,1),
369 r0
[2] = MAT(m
,0,2), r0
[3] = MAT(m
,0,3),
370 r0
[4] = 1.0, r0
[5] = r0
[6] = r0
[7] = 0.0,
372 r1
[0] = MAT(m
,1,0), r1
[1] = MAT(m
,1,1),
373 r1
[2] = MAT(m
,1,2), r1
[3] = MAT(m
,1,3),
374 r1
[5] = 1.0, r1
[4] = r1
[6] = r1
[7] = 0.0,
376 r2
[0] = MAT(m
,2,0), r2
[1] = MAT(m
,2,1),
377 r2
[2] = MAT(m
,2,2), r2
[3] = MAT(m
,2,3),
378 r2
[6] = 1.0, r2
[4] = r2
[5] = r2
[7] = 0.0,
380 r3
[0] = MAT(m
,3,0), r3
[1] = MAT(m
,3,1),
381 r3
[2] = MAT(m
,3,2), r3
[3] = MAT(m
,3,3),
382 r3
[7] = 1.0, r3
[4] = r3
[5] = r3
[6] = 0.0;
384 /* choose pivot - or die */
385 if (fabsf(r3
[0])>fabsf(r2
[0])) SWAP_ROWS(r3
, r2
);
386 if (fabsf(r2
[0])>fabsf(r1
[0])) SWAP_ROWS(r2
, r1
);
387 if (fabsf(r1
[0])>fabsf(r0
[0])) SWAP_ROWS(r1
, r0
);
388 if (0.0F
== r0
[0]) return GL_FALSE
;
390 /* eliminate first variable */
391 m1
= r1
[0]/r0
[0]; m2
= r2
[0]/r0
[0]; m3
= r3
[0]/r0
[0];
392 s
= r0
[1]; r1
[1] -= m1
* s
; r2
[1] -= m2
* s
; r3
[1] -= m3
* s
;
393 s
= r0
[2]; r1
[2] -= m1
* s
; r2
[2] -= m2
* s
; r3
[2] -= m3
* s
;
394 s
= r0
[3]; r1
[3] -= m1
* s
; r2
[3] -= m2
* s
; r3
[3] -= m3
* s
;
396 if (s
!= 0.0F
) { r1
[4] -= m1
* s
; r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
398 if (s
!= 0.0F
) { r1
[5] -= m1
* s
; r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
400 if (s
!= 0.0F
) { r1
[6] -= m1
* s
; r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
402 if (s
!= 0.0F
) { r1
[7] -= m1
* s
; r2
[7] -= m2
* s
; r3
[7] -= m3
* s
; }
404 /* choose pivot - or die */
405 if (fabsf(r3
[1])>fabsf(r2
[1])) SWAP_ROWS(r3
, r2
);
406 if (fabsf(r2
[1])>fabsf(r1
[1])) SWAP_ROWS(r2
, r1
);
407 if (0.0F
== r1
[1]) return GL_FALSE
;
409 /* eliminate second variable */
410 m2
= r2
[1]/r1
[1]; m3
= r3
[1]/r1
[1];
411 r2
[2] -= m2
* r1
[2]; r3
[2] -= m3
* r1
[2];
412 r2
[3] -= m2
* r1
[3]; r3
[3] -= m3
* r1
[3];
413 s
= r1
[4]; if (0.0F
!= s
) { r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
414 s
= r1
[5]; if (0.0F
!= s
) { r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
415 s
= r1
[6]; if (0.0F
!= s
) { r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
416 s
= r1
[7]; if (0.0F
!= s
) { r2
[7] -= m2
* s
; r3
[7] -= m3
* s
; }
418 /* choose pivot - or die */
419 if (fabsf(r3
[2])>fabsf(r2
[2])) SWAP_ROWS(r3
, r2
);
420 if (0.0F
== r2
[2]) return GL_FALSE
;
422 /* eliminate third variable */
424 r3
[3] -= m3
* r2
[3], r3
[4] -= m3
* r2
[4],
425 r3
[5] -= m3
* r2
[5], r3
[6] -= m3
* r2
[6],
429 if (0.0F
== r3
[3]) return GL_FALSE
;
431 s
= 1.0F
/r3
[3]; /* now back substitute row 3 */
432 r3
[4] *= s
; r3
[5] *= s
; r3
[6] *= s
; r3
[7] *= s
;
434 m2
= r2
[3]; /* now back substitute row 2 */
436 r2
[4] = s
* (r2
[4] - r3
[4] * m2
), r2
[5] = s
* (r2
[5] - r3
[5] * m2
),
437 r2
[6] = s
* (r2
[6] - r3
[6] * m2
), r2
[7] = s
* (r2
[7] - r3
[7] * m2
);
439 r1
[4] -= r3
[4] * m1
, r1
[5] -= r3
[5] * m1
,
440 r1
[6] -= r3
[6] * m1
, r1
[7] -= r3
[7] * m1
;
442 r0
[4] -= r3
[4] * m0
, r0
[5] -= r3
[5] * m0
,
443 r0
[6] -= r3
[6] * m0
, r0
[7] -= r3
[7] * m0
;
445 m1
= r1
[2]; /* now back substitute row 1 */
447 r1
[4] = s
* (r1
[4] - r2
[4] * m1
), r1
[5] = s
* (r1
[5] - r2
[5] * m1
),
448 r1
[6] = s
* (r1
[6] - r2
[6] * m1
), r1
[7] = s
* (r1
[7] - r2
[7] * m1
);
450 r0
[4] -= r2
[4] * m0
, r0
[5] -= r2
[5] * m0
,
451 r0
[6] -= r2
[6] * m0
, r0
[7] -= r2
[7] * m0
;
453 m0
= r0
[1]; /* now back substitute row 0 */
455 r0
[4] = s
* (r0
[4] - r1
[4] * m0
), r0
[5] = s
* (r0
[5] - r1
[5] * m0
),
456 r0
[6] = s
* (r0
[6] - r1
[6] * m0
), r0
[7] = s
* (r0
[7] - r1
[7] * m0
);
458 MAT(out
,0,0) = r0
[4]; MAT(out
,0,1) = r0
[5],
459 MAT(out
,0,2) = r0
[6]; MAT(out
,0,3) = r0
[7],
460 MAT(out
,1,0) = r1
[4]; MAT(out
,1,1) = r1
[5],
461 MAT(out
,1,2) = r1
[6]; MAT(out
,1,3) = r1
[7],
462 MAT(out
,2,0) = r2
[4]; MAT(out
,2,1) = r2
[5],
463 MAT(out
,2,2) = r2
[6]; MAT(out
,2,3) = r2
[7],
464 MAT(out
,3,0) = r3
[4]; MAT(out
,3,1) = r3
[5],
465 MAT(out
,3,2) = r3
[6]; MAT(out
,3,3) = r3
[7];
472 * Compute inverse of a general 3d transformation matrix.
474 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
475 * stored in the GLmatrix::inv attribute.
477 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
479 * \author Adapted from graphics gems II.
481 * Calculates the inverse of the upper left by first calculating its
482 * determinant and multiplying it to the symmetric adjust matrix of each
483 * element. Finally deals with the translation part by transforming the
484 * original translation vector using by the calculated submatrix inverse.
486 static GLboolean
invert_matrix_3d_general( GLmatrix
*mat
)
488 const GLfloat
*in
= mat
->m
;
489 GLfloat
*out
= mat
->inv
;
493 /* Calculate the determinant of upper left 3x3 submatrix and
494 * determine if the matrix is singular.
497 t
= MAT(in
,0,0) * MAT(in
,1,1) * MAT(in
,2,2);
498 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
500 t
= MAT(in
,1,0) * MAT(in
,2,1) * MAT(in
,0,2);
501 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
503 t
= MAT(in
,2,0) * MAT(in
,0,1) * MAT(in
,1,2);
504 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
506 t
= -MAT(in
,2,0) * MAT(in
,1,1) * MAT(in
,0,2);
507 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
509 t
= -MAT(in
,1,0) * MAT(in
,0,1) * MAT(in
,2,2);
510 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
512 t
= -MAT(in
,0,0) * MAT(in
,2,1) * MAT(in
,1,2);
513 if (t
>= 0.0F
) pos
+= t
; else neg
+= t
;
517 if (fabsf(det
) < 1e-25F
)
521 MAT(out
,0,0) = ( (MAT(in
,1,1)*MAT(in
,2,2) - MAT(in
,2,1)*MAT(in
,1,2) )*det
);
522 MAT(out
,0,1) = (- (MAT(in
,0,1)*MAT(in
,2,2) - MAT(in
,2,1)*MAT(in
,0,2) )*det
);
523 MAT(out
,0,2) = ( (MAT(in
,0,1)*MAT(in
,1,2) - MAT(in
,1,1)*MAT(in
,0,2) )*det
);
524 MAT(out
,1,0) = (- (MAT(in
,1,0)*MAT(in
,2,2) - MAT(in
,2,0)*MAT(in
,1,2) )*det
);
525 MAT(out
,1,1) = ( (MAT(in
,0,0)*MAT(in
,2,2) - MAT(in
,2,0)*MAT(in
,0,2) )*det
);
526 MAT(out
,1,2) = (- (MAT(in
,0,0)*MAT(in
,1,2) - MAT(in
,1,0)*MAT(in
,0,2) )*det
);
527 MAT(out
,2,0) = ( (MAT(in
,1,0)*MAT(in
,2,1) - MAT(in
,2,0)*MAT(in
,1,1) )*det
);
528 MAT(out
,2,1) = (- (MAT(in
,0,0)*MAT(in
,2,1) - MAT(in
,2,0)*MAT(in
,0,1) )*det
);
529 MAT(out
,2,2) = ( (MAT(in
,0,0)*MAT(in
,1,1) - MAT(in
,1,0)*MAT(in
,0,1) )*det
);
531 /* Do the translation part */
532 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0) +
533 MAT(in
,1,3) * MAT(out
,0,1) +
534 MAT(in
,2,3) * MAT(out
,0,2) );
535 MAT(out
,1,3) = - (MAT(in
,0,3) * MAT(out
,1,0) +
536 MAT(in
,1,3) * MAT(out
,1,1) +
537 MAT(in
,2,3) * MAT(out
,1,2) );
538 MAT(out
,2,3) = - (MAT(in
,0,3) * MAT(out
,2,0) +
539 MAT(in
,1,3) * MAT(out
,2,1) +
540 MAT(in
,2,3) * MAT(out
,2,2) );
546 * Compute inverse of a 3d transformation matrix.
548 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
549 * stored in the GLmatrix::inv attribute.
551 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
553 * If the matrix is not an angle preserving matrix then calls
554 * invert_matrix_3d_general for the actual calculation. Otherwise calculates
555 * the inverse matrix analyzing and inverting each of the scaling, rotation and
558 static GLboolean
invert_matrix_3d( GLmatrix
*mat
)
560 const GLfloat
*in
= mat
->m
;
561 GLfloat
*out
= mat
->inv
;
563 if (!TEST_MAT_FLAGS(mat
, MAT_FLAGS_ANGLE_PRESERVING
)) {
564 return invert_matrix_3d_general( mat
);
567 if (mat
->flags
& MAT_FLAG_UNIFORM_SCALE
) {
568 GLfloat scale
= (MAT(in
,0,0) * MAT(in
,0,0) +
569 MAT(in
,0,1) * MAT(in
,0,1) +
570 MAT(in
,0,2) * MAT(in
,0,2));
575 scale
= 1.0F
/ scale
;
577 /* Transpose and scale the 3 by 3 upper-left submatrix. */
578 MAT(out
,0,0) = scale
* MAT(in
,0,0);
579 MAT(out
,1,0) = scale
* MAT(in
,0,1);
580 MAT(out
,2,0) = scale
* MAT(in
,0,2);
581 MAT(out
,0,1) = scale
* MAT(in
,1,0);
582 MAT(out
,1,1) = scale
* MAT(in
,1,1);
583 MAT(out
,2,1) = scale
* MAT(in
,1,2);
584 MAT(out
,0,2) = scale
* MAT(in
,2,0);
585 MAT(out
,1,2) = scale
* MAT(in
,2,1);
586 MAT(out
,2,2) = scale
* MAT(in
,2,2);
588 else if (mat
->flags
& MAT_FLAG_ROTATION
) {
589 /* Transpose the 3 by 3 upper-left submatrix. */
590 MAT(out
,0,0) = MAT(in
,0,0);
591 MAT(out
,1,0) = MAT(in
,0,1);
592 MAT(out
,2,0) = MAT(in
,0,2);
593 MAT(out
,0,1) = MAT(in
,1,0);
594 MAT(out
,1,1) = MAT(in
,1,1);
595 MAT(out
,2,1) = MAT(in
,1,2);
596 MAT(out
,0,2) = MAT(in
,2,0);
597 MAT(out
,1,2) = MAT(in
,2,1);
598 MAT(out
,2,2) = MAT(in
,2,2);
601 /* pure translation */
602 memcpy( out
, Identity
, sizeof(Identity
) );
603 MAT(out
,0,3) = - MAT(in
,0,3);
604 MAT(out
,1,3) = - MAT(in
,1,3);
605 MAT(out
,2,3) = - MAT(in
,2,3);
609 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
610 /* Do the translation part */
611 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0) +
612 MAT(in
,1,3) * MAT(out
,0,1) +
613 MAT(in
,2,3) * MAT(out
,0,2) );
614 MAT(out
,1,3) = - (MAT(in
,0,3) * MAT(out
,1,0) +
615 MAT(in
,1,3) * MAT(out
,1,1) +
616 MAT(in
,2,3) * MAT(out
,1,2) );
617 MAT(out
,2,3) = - (MAT(in
,0,3) * MAT(out
,2,0) +
618 MAT(in
,1,3) * MAT(out
,2,1) +
619 MAT(in
,2,3) * MAT(out
,2,2) );
622 MAT(out
,0,3) = MAT(out
,1,3) = MAT(out
,2,3) = 0.0;
629 * Compute inverse of an identity transformation matrix.
631 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
632 * stored in the GLmatrix::inv attribute.
634 * \return always GL_TRUE.
636 * Simply copies Identity into GLmatrix::inv.
638 static GLboolean
invert_matrix_identity( GLmatrix
*mat
)
640 memcpy( mat
->inv
, Identity
, sizeof(Identity
) );
645 * Compute inverse of a no-rotation 3d transformation matrix.
647 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
648 * stored in the GLmatrix::inv attribute.
650 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
654 static GLboolean
invert_matrix_3d_no_rot( GLmatrix
*mat
)
656 const GLfloat
*in
= mat
->m
;
657 GLfloat
*out
= mat
->inv
;
659 if (MAT(in
,0,0) == 0 || MAT(in
,1,1) == 0 || MAT(in
,2,2) == 0 )
662 memcpy( out
, Identity
, sizeof(Identity
) );
663 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
664 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
665 MAT(out
,2,2) = 1.0F
/ MAT(in
,2,2);
667 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
668 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0));
669 MAT(out
,1,3) = - (MAT(in
,1,3) * MAT(out
,1,1));
670 MAT(out
,2,3) = - (MAT(in
,2,3) * MAT(out
,2,2));
677 * Compute inverse of a no-rotation 2d transformation matrix.
679 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
680 * stored in the GLmatrix::inv attribute.
682 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
684 * Calculates the inverse matrix by applying the inverse scaling and
685 * translation to the identity matrix.
687 static GLboolean
invert_matrix_2d_no_rot( GLmatrix
*mat
)
689 const GLfloat
*in
= mat
->m
;
690 GLfloat
*out
= mat
->inv
;
692 if (MAT(in
,0,0) == 0 || MAT(in
,1,1) == 0)
695 memcpy( out
, Identity
, sizeof(Identity
) );
696 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
697 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
699 if (mat
->flags
& MAT_FLAG_TRANSLATION
) {
700 MAT(out
,0,3) = - (MAT(in
,0,3) * MAT(out
,0,0));
701 MAT(out
,1,3) = - (MAT(in
,1,3) * MAT(out
,1,1));
709 static GLboolean
invert_matrix_perspective( GLmatrix
*mat
)
711 const GLfloat
*in
= mat
->m
;
712 GLfloat
*out
= mat
->inv
;
714 if (MAT(in
,2,3) == 0)
717 memcpy( out
, Identity
, sizeof(Identity
) );
719 MAT(out
,0,0) = 1.0F
/ MAT(in
,0,0);
720 MAT(out
,1,1) = 1.0F
/ MAT(in
,1,1);
722 MAT(out
,0,3) = MAT(in
,0,2);
723 MAT(out
,1,3) = MAT(in
,1,2);
728 MAT(out
,3,2) = 1.0F
/ MAT(in
,2,3);
729 MAT(out
,3,3) = MAT(in
,2,2) * MAT(out
,3,2);
736 * Matrix inversion function pointer type.
738 typedef GLboolean (*inv_mat_func
)( GLmatrix
*mat
);
741 * Table of the matrix inversion functions according to the matrix type.
743 static inv_mat_func inv_mat_tab
[7] = {
744 invert_matrix_general
,
745 invert_matrix_identity
,
746 invert_matrix_3d_no_rot
,
748 /* Don't use this function for now - it fails when the projection matrix
749 * is premultiplied by a translation (ala Chromium's tilesort SPU).
751 invert_matrix_perspective
,
753 invert_matrix_general
,
755 invert_matrix_3d
, /* lazy! */
756 invert_matrix_2d_no_rot
,
761 * Compute inverse of a transformation matrix.
763 * \param mat pointer to a GLmatrix structure. The matrix inverse will be
764 * stored in the GLmatrix::inv attribute.
766 * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
768 * Calls the matrix inversion function in inv_mat_tab corresponding to the
769 * given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag,
770 * and copies the identity matrix into GLmatrix::inv.
772 static GLboolean
matrix_invert( GLmatrix
*mat
)
774 if (inv_mat_tab
[mat
->type
](mat
)) {
775 mat
->flags
&= ~MAT_FLAG_SINGULAR
;
778 mat
->flags
|= MAT_FLAG_SINGULAR
;
779 memcpy( mat
->inv
, Identity
, sizeof(Identity
) );
787 /**********************************************************************/
788 /** \name Matrix generation */
792 * Generate a 4x4 transformation matrix from glRotate parameters, and
793 * post-multiply the input matrix by it.
796 * This function was contributed by Erich Boleyn (erich@uruk.org).
797 * Optimizations contributed by Rudolf Opalla (rudi@khm.de).
800 _math_matrix_rotate( GLmatrix
*mat
,
801 GLfloat angle
, GLfloat x
, GLfloat y
, GLfloat z
)
803 GLfloat xx
, yy
, zz
, xy
, yz
, zx
, xs
, ys
, zs
, one_c
, s
, c
;
807 s
= sinf( angle
* M_PI
/ 180.0 );
808 c
= cosf( angle
* M_PI
/ 180.0 );
810 memcpy(m
, Identity
, sizeof(Identity
));
811 optimized
= GL_FALSE
;
813 #define M(row,col) m[col*4+row]
819 /* rotate only around z-axis */
832 else if (z
== 0.0F
) {
834 /* rotate only around y-axis */
847 else if (y
== 0.0F
) {
850 /* rotate only around x-axis */
865 const GLfloat mag
= sqrtf(x
* x
+ y
* y
+ z
* z
);
867 if (mag
<= 1.0e-4F
) {
868 /* no rotation, leave mat as-is */
878 * Arbitrary axis rotation matrix.
880 * This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
881 * like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation
882 * (which is about the X-axis), and the two composite transforms
883 * Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
884 * from the arbitrary axis to the X-axis then back. They are
885 * all elementary rotations.
887 * Rz' is a rotation about the Z-axis, to bring the axis vector
888 * into the x-z plane. Then Ry' is applied, rotating about the
889 * Y-axis to bring the axis vector parallel with the X-axis. The
890 * rotation about the X-axis is then performed. Ry and Rz are
891 * simply the respective inverse transforms to bring the arbitrary
892 * axis back to its original orientation. The first transforms
893 * Rz' and Ry' are considered inverses, since the data from the
894 * arbitrary axis gives you info on how to get to it, not how
895 * to get away from it, and an inverse must be applied.
897 * The basic calculation used is to recognize that the arbitrary
898 * axis vector (x, y, z), since it is of unit length, actually
899 * represents the sines and cosines of the angles to rotate the
900 * X-axis to the same orientation, with theta being the angle about
901 * Z and phi the angle about Y (in the order described above)
904 * cos ( theta ) = x / sqrt ( 1 - z^2 )
905 * sin ( theta ) = y / sqrt ( 1 - z^2 )
907 * cos ( phi ) = sqrt ( 1 - z^2 )
910 * Note that cos ( phi ) can further be inserted to the above
913 * cos ( theta ) = x / cos ( phi )
914 * sin ( theta ) = y / sin ( phi )
916 * ...etc. Because of those relations and the standard trigonometric
917 * relations, it is pssible to reduce the transforms down to what
918 * is used below. It may be that any primary axis chosen will give the
919 * same results (modulo a sign convention) using thie method.
921 * Particularly nice is to notice that all divisions that might
922 * have caused trouble when parallel to certain planes or
923 * axis go away with care paid to reducing the expressions.
924 * After checking, it does perform correctly under all cases, since
925 * in all the cases of division where the denominator would have
926 * been zero, the numerator would have been zero as well, giving
927 * the expected result.
941 /* We already hold the identity-matrix so we can skip some statements */
942 M(0,0) = (one_c
* xx
) + c
;
943 M(0,1) = (one_c
* xy
) - zs
;
944 M(0,2) = (one_c
* zx
) + ys
;
947 M(1,0) = (one_c
* xy
) + zs
;
948 M(1,1) = (one_c
* yy
) + c
;
949 M(1,2) = (one_c
* yz
) - xs
;
952 M(2,0) = (one_c
* zx
) - ys
;
953 M(2,1) = (one_c
* yz
) + xs
;
954 M(2,2) = (one_c
* zz
) + c
;
966 matrix_multf( mat
, m
, MAT_FLAG_ROTATION
);
970 * Apply a perspective projection matrix.
972 * \param mat matrix to apply the projection.
973 * \param left left clipping plane coordinate.
974 * \param right right clipping plane coordinate.
975 * \param bottom bottom clipping plane coordinate.
976 * \param top top clipping plane coordinate.
977 * \param nearval distance to the near clipping plane.
978 * \param farval distance to the far clipping plane.
980 * Creates the projection matrix and multiplies it with \p mat, marking the
981 * MAT_FLAG_PERSPECTIVE flag.
984 _math_matrix_frustum( GLmatrix
*mat
,
985 GLfloat left
, GLfloat right
,
986 GLfloat bottom
, GLfloat top
,
987 GLfloat nearval
, GLfloat farval
)
989 GLfloat x
, y
, a
, b
, c
, d
;
992 x
= (2.0F
*nearval
) / (right
-left
);
993 y
= (2.0F
*nearval
) / (top
-bottom
);
994 a
= (right
+left
) / (right
-left
);
995 b
= (top
+bottom
) / (top
-bottom
);
996 c
= -(farval
+nearval
) / ( farval
-nearval
);
997 d
= -(2.0F
*farval
*nearval
) / (farval
-nearval
); /* error? */
999 #define M(row,col) m[col*4+row]
1000 M(0,0) = x
; M(0,1) = 0.0F
; M(0,2) = a
; M(0,3) = 0.0F
;
1001 M(1,0) = 0.0F
; M(1,1) = y
; M(1,2) = b
; M(1,3) = 0.0F
;
1002 M(2,0) = 0.0F
; M(2,1) = 0.0F
; M(2,2) = c
; M(2,3) = d
;
1003 M(3,0) = 0.0F
; M(3,1) = 0.0F
; M(3,2) = -1.0F
; M(3,3) = 0.0F
;
1006 matrix_multf( mat
, m
, MAT_FLAG_PERSPECTIVE
);
1010 * Create an orthographic projection matrix.
1012 * \param m float array in which to store the project matrix
1013 * \param left left clipping plane coordinate.
1014 * \param right right clipping plane coordinate.
1015 * \param bottom bottom clipping plane coordinate.
1016 * \param top top clipping plane coordinate.
1017 * \param nearval distance to the near clipping plane.
1018 * \param farval distance to the far clipping plane.
1020 * Creates the projection matrix and stored the values in \p m. As with other
1021 * OpenGL matrices, the data is stored in column-major ordering.
1024 _math_float_ortho(float *m
,
1025 float left
, float right
,
1026 float bottom
, float top
,
1027 float nearval
, float farval
)
1029 #define M(row,col) m[col*4+row]
1030 M(0,0) = 2.0F
/ (right
-left
);
1033 M(0,3) = -(right
+left
) / (right
-left
);
1036 M(1,1) = 2.0F
/ (top
-bottom
);
1038 M(1,3) = -(top
+bottom
) / (top
-bottom
);
1042 M(2,2) = -2.0F
/ (farval
-nearval
);
1043 M(2,3) = -(farval
+nearval
) / (farval
-nearval
);
1053 * Apply an orthographic projection matrix.
1055 * \param mat matrix to apply the projection.
1056 * \param left left clipping plane coordinate.
1057 * \param right right clipping plane coordinate.
1058 * \param bottom bottom clipping plane coordinate.
1059 * \param top top clipping plane coordinate.
1060 * \param nearval distance to the near clipping plane.
1061 * \param farval distance to the far clipping plane.
1063 * Creates the projection matrix and multiplies it with \p mat, marking the
1064 * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
1067 _math_matrix_ortho( GLmatrix
*mat
,
1068 GLfloat left
, GLfloat right
,
1069 GLfloat bottom
, GLfloat top
,
1070 GLfloat nearval
, GLfloat farval
)
1074 _math_float_ortho(m
, left
, right
, bottom
, top
, nearval
, farval
);
1075 matrix_multf( mat
, m
, (MAT_FLAG_GENERAL_SCALE
|MAT_FLAG_TRANSLATION
));
1079 * Multiply a matrix with a general scaling matrix.
1081 * \param mat matrix.
1082 * \param x x axis scale factor.
1083 * \param y y axis scale factor.
1084 * \param z z axis scale factor.
1086 * Multiplies in-place the elements of \p mat by the scale factors. Checks if
1087 * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
1088 * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
1089 * MAT_DIRTY_INVERSE dirty flags.
1092 _math_matrix_scale( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
)
1094 GLfloat
*m
= mat
->m
;
1095 m
[0] *= x
; m
[4] *= y
; m
[8] *= z
;
1096 m
[1] *= x
; m
[5] *= y
; m
[9] *= z
;
1097 m
[2] *= x
; m
[6] *= y
; m
[10] *= z
;
1098 m
[3] *= x
; m
[7] *= y
; m
[11] *= z
;
1100 if (fabsf(x
- y
) < 1e-8F
&& fabsf(x
- z
) < 1e-8F
)
1101 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1103 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1105 mat
->flags
|= (MAT_DIRTY_TYPE
|
1110 * Multiply a matrix with a translation matrix.
1112 * \param mat matrix.
1113 * \param x translation vector x coordinate.
1114 * \param y translation vector y coordinate.
1115 * \param z translation vector z coordinate.
1117 * Adds the translation coordinates to the elements of \p mat in-place. Marks
1118 * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
1122 _math_matrix_translate( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
)
1124 GLfloat
*m
= mat
->m
;
1125 m
[12] = m
[0] * x
+ m
[4] * y
+ m
[8] * z
+ m
[12];
1126 m
[13] = m
[1] * x
+ m
[5] * y
+ m
[9] * z
+ m
[13];
1127 m
[14] = m
[2] * x
+ m
[6] * y
+ m
[10] * z
+ m
[14];
1128 m
[15] = m
[3] * x
+ m
[7] * y
+ m
[11] * z
+ m
[15];
1130 mat
->flags
|= (MAT_FLAG_TRANSLATION
|
1137 * Set matrix to do viewport and depthrange mapping.
1138 * Transforms Normalized Device Coords to window/Z values.
1141 _math_matrix_viewport(GLmatrix
*m
, const float scale
[3],
1142 const float translate
[3], double depthMax
)
1144 m
->m
[MAT_SX
] = scale
[0];
1145 m
->m
[MAT_TX
] = translate
[0];
1146 m
->m
[MAT_SY
] = scale
[1];
1147 m
->m
[MAT_TY
] = translate
[1];
1148 m
->m
[MAT_SZ
] = depthMax
*scale
[2];
1149 m
->m
[MAT_TZ
] = depthMax
*translate
[2];
1150 m
->flags
= MAT_FLAG_GENERAL_SCALE
| MAT_FLAG_TRANSLATION
;
1151 m
->type
= MATRIX_3D_NO_ROT
;
1156 * Set a matrix to the identity matrix.
1158 * \param mat matrix.
1160 * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
1161 * Sets the matrix type to identity, and clear the dirty flags.
1164 _math_matrix_set_identity( GLmatrix
*mat
)
1166 STATIC_ASSERT(MATRIX_M
== offsetof(GLmatrix
, m
));
1167 STATIC_ASSERT(MATRIX_INV
== offsetof(GLmatrix
, inv
));
1169 memcpy( mat
->m
, Identity
, sizeof(Identity
) );
1170 memcpy( mat
->inv
, Identity
, sizeof(Identity
) );
1172 mat
->type
= MATRIX_IDENTITY
;
1173 mat
->flags
&= ~(MAT_DIRTY_FLAGS
|
1181 /**********************************************************************/
1182 /** \name Matrix analysis */
1185 #define ZERO(x) (1<<x)
1186 #define ONE(x) (1<<(x+16))
1188 #define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14))
1189 #define MASK_NO_2D_SCALE ( ONE(0) | ONE(5))
1191 #define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\
1192 ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\
1193 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1194 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1196 #define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \
1197 ZERO(1) | ZERO(9) | \
1198 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1199 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1201 #define MASK_2D ( ZERO(8) | \
1203 ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
1204 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1207 #define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \
1208 ZERO(1) | ZERO(9) | \
1209 ZERO(2) | ZERO(6) | \
1210 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1215 ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
1218 #define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\
1219 ZERO(1) | ZERO(13) |\
1220 ZERO(2) | ZERO(6) | \
1221 ZERO(3) | ZERO(7) | ZERO(15) )
1223 #define SQ(x) ((x)*(x))
1226 * Determine type and flags from scratch.
1228 * \param mat matrix.
1230 * This is expensive enough to only want to do it once.
1232 static void analyse_from_scratch( GLmatrix
*mat
)
1234 const GLfloat
*m
= mat
->m
;
1238 for (i
= 0 ; i
< 16 ; i
++) {
1239 if (m
[i
] == 0.0F
) mask
|= (1<<i
);
1242 if (m
[0] == 1.0F
) mask
|= (1<<16);
1243 if (m
[5] == 1.0F
) mask
|= (1<<21);
1244 if (m
[10] == 1.0F
) mask
|= (1<<26);
1245 if (m
[15] == 1.0F
) mask
|= (1<<31);
1247 mat
->flags
&= ~MAT_FLAGS_GEOMETRY
;
1249 /* Check for translation - no-one really cares
1251 if ((mask
& MASK_NO_TRX
) != MASK_NO_TRX
)
1252 mat
->flags
|= MAT_FLAG_TRANSLATION
;
1256 if (mask
== (GLuint
) MASK_IDENTITY
) {
1257 mat
->type
= MATRIX_IDENTITY
;
1259 else if ((mask
& MASK_2D_NO_ROT
) == (GLuint
) MASK_2D_NO_ROT
) {
1260 mat
->type
= MATRIX_2D_NO_ROT
;
1262 if ((mask
& MASK_NO_2D_SCALE
) != MASK_NO_2D_SCALE
)
1263 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1265 else if ((mask
& MASK_2D
) == (GLuint
) MASK_2D
) {
1266 GLfloat mm
= DOT2(m
, m
);
1267 GLfloat m4m4
= DOT2(m
+4,m
+4);
1268 GLfloat mm4
= DOT2(m
,m
+4);
1270 mat
->type
= MATRIX_2D
;
1272 /* Check for scale */
1273 if (SQ(mm
-1) > SQ(1e-6F
) ||
1274 SQ(m4m4
-1) > SQ(1e-6F
))
1275 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1277 /* Check for rotation */
1278 if (SQ(mm4
) > SQ(1e-6F
))
1279 mat
->flags
|= MAT_FLAG_GENERAL_3D
;
1281 mat
->flags
|= MAT_FLAG_ROTATION
;
1284 else if ((mask
& MASK_3D_NO_ROT
) == (GLuint
) MASK_3D_NO_ROT
) {
1285 mat
->type
= MATRIX_3D_NO_ROT
;
1287 /* Check for scale */
1288 if (SQ(m
[0]-m
[5]) < SQ(1e-6F
) &&
1289 SQ(m
[0]-m
[10]) < SQ(1e-6F
)) {
1290 if (SQ(m
[0]-1.0F
) > SQ(1e-6F
)) {
1291 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1295 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1298 else if ((mask
& MASK_3D
) == (GLuint
) MASK_3D
) {
1299 GLfloat c1
= DOT3(m
,m
);
1300 GLfloat c2
= DOT3(m
+4,m
+4);
1301 GLfloat c3
= DOT3(m
+8,m
+8);
1302 GLfloat d1
= DOT3(m
, m
+4);
1305 mat
->type
= MATRIX_3D
;
1307 /* Check for scale */
1308 if (SQ(c1
-c2
) < SQ(1e-6F
) && SQ(c1
-c3
) < SQ(1e-6F
)) {
1309 if (SQ(c1
-1.0F
) > SQ(1e-6F
))
1310 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1311 /* else no scale at all */
1314 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1317 /* Check for rotation */
1318 if (SQ(d1
) < SQ(1e-6F
)) {
1319 CROSS3( cp
, m
, m
+4 );
1320 SUB_3V( cp
, cp
, (m
+8) );
1321 if (LEN_SQUARED_3FV(cp
) < SQ(1e-6F
))
1322 mat
->flags
|= MAT_FLAG_ROTATION
;
1324 mat
->flags
|= MAT_FLAG_GENERAL_3D
;
1327 mat
->flags
|= MAT_FLAG_GENERAL_3D
; /* shear, etc */
1330 else if ((mask
& MASK_PERSPECTIVE
) == MASK_PERSPECTIVE
&& m
[11]==-1.0F
) {
1331 mat
->type
= MATRIX_PERSPECTIVE
;
1332 mat
->flags
|= MAT_FLAG_GENERAL
;
1335 mat
->type
= MATRIX_GENERAL
;
1336 mat
->flags
|= MAT_FLAG_GENERAL
;
1341 * Analyze a matrix given that its flags are accurate.
1343 * This is the more common operation, hopefully.
1345 static void analyse_from_flags( GLmatrix
*mat
)
1347 const GLfloat
*m
= mat
->m
;
1349 if (TEST_MAT_FLAGS(mat
, 0)) {
1350 mat
->type
= MATRIX_IDENTITY
;
1352 else if (TEST_MAT_FLAGS(mat
, (MAT_FLAG_TRANSLATION
|
1353 MAT_FLAG_UNIFORM_SCALE
|
1354 MAT_FLAG_GENERAL_SCALE
))) {
1355 if ( m
[10]==1.0F
&& m
[14]==0.0F
) {
1356 mat
->type
= MATRIX_2D_NO_ROT
;
1359 mat
->type
= MATRIX_3D_NO_ROT
;
1362 else if (TEST_MAT_FLAGS(mat
, MAT_FLAGS_3D
)) {
1365 && m
[2]==0.0F
&& m
[6]==0.0F
&& m
[10]==1.0F
&& m
[14]==0.0F
) {
1366 mat
->type
= MATRIX_2D
;
1369 mat
->type
= MATRIX_3D
;
1372 else if ( m
[4]==0.0F
&& m
[12]==0.0F
1373 && m
[1]==0.0F
&& m
[13]==0.0F
1374 && m
[2]==0.0F
&& m
[6]==0.0F
1375 && m
[3]==0.0F
&& m
[7]==0.0F
&& m
[11]==-1.0F
&& m
[15]==0.0F
) {
1376 mat
->type
= MATRIX_PERSPECTIVE
;
1379 mat
->type
= MATRIX_GENERAL
;
1384 * Analyze and update a matrix.
1386 * \param mat matrix.
1388 * If the matrix type is dirty then calls either analyse_from_scratch() or
1389 * analyse_from_flags() to determine its type, according to whether the flags
1390 * are dirty or not, respectively. If the matrix has an inverse and it's dirty
1391 * then calls matrix_invert(). Finally clears the dirty flags.
1394 _math_matrix_analyse( GLmatrix
*mat
)
1396 if (mat
->flags
& MAT_DIRTY_TYPE
) {
1397 if (mat
->flags
& MAT_DIRTY_FLAGS
)
1398 analyse_from_scratch( mat
);
1400 analyse_from_flags( mat
);
1403 if (mat
->inv
&& (mat
->flags
& MAT_DIRTY_INVERSE
)) {
1404 matrix_invert( mat
);
1405 mat
->flags
&= ~MAT_DIRTY_INVERSE
;
1408 mat
->flags
&= ~(MAT_DIRTY_FLAGS
| MAT_DIRTY_TYPE
);
1415 * Test if the given matrix preserves vector lengths.
1418 _math_matrix_is_length_preserving( const GLmatrix
*m
)
1420 return TEST_MAT_FLAGS( m
, MAT_FLAGS_LENGTH_PRESERVING
);
1425 * Test if the given matrix does any rotation.
1426 * (or perhaps if the upper-left 3x3 is non-identity)
1429 _math_matrix_has_rotation( const GLmatrix
*m
)
1431 if (m
->flags
& (MAT_FLAG_GENERAL
|
1433 MAT_FLAG_GENERAL_3D
|
1434 MAT_FLAG_PERSPECTIVE
))
1442 _math_matrix_is_general_scale( const GLmatrix
*m
)
1444 return (m
->flags
& MAT_FLAG_GENERAL_SCALE
) ? GL_TRUE
: GL_FALSE
;
1449 _math_matrix_is_dirty( const GLmatrix
*m
)
1451 return (m
->flags
& MAT_DIRTY
) ? GL_TRUE
: GL_FALSE
;
1455 /**********************************************************************/
1456 /** \name Matrix setup */
1462 * \param to destination matrix.
1463 * \param from source matrix.
1465 * Copies all fields in GLmatrix, creating an inverse array if necessary.
1468 _math_matrix_copy( GLmatrix
*to
, const GLmatrix
*from
)
1470 memcpy(to
->m
, from
->m
, 16 * sizeof(GLfloat
));
1471 memcpy(to
->inv
, from
->inv
, 16 * sizeof(GLfloat
));
1472 to
->flags
= from
->flags
;
1473 to
->type
= from
->type
;
1477 * Loads a matrix array into GLmatrix.
1479 * \param m matrix array.
1480 * \param mat matrix.
1482 * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
1486 _math_matrix_loadf( GLmatrix
*mat
, const GLfloat
*m
)
1488 memcpy( mat
->m
, m
, 16*sizeof(GLfloat
) );
1489 mat
->flags
= (MAT_FLAG_GENERAL
| MAT_DIRTY
);
1493 * Matrix constructor.
1497 * Initialize the GLmatrix fields.
1500 _math_matrix_ctr( GLmatrix
*m
)
1502 m
->m
= align_malloc( 16 * sizeof(GLfloat
), 16 );
1504 memcpy( m
->m
, Identity
, sizeof(Identity
) );
1505 m
->inv
= align_malloc( 16 * sizeof(GLfloat
), 16 );
1507 memcpy( m
->inv
, Identity
, sizeof(Identity
) );
1508 m
->type
= MATRIX_IDENTITY
;
1513 * Matrix destructor.
1517 * Frees the data in a GLmatrix.
1520 _math_matrix_dtr( GLmatrix
*m
)
1525 align_free( m
->inv
);
1532 /**********************************************************************/
1533 /** \name Matrix transpose */
1537 * Transpose a GLfloat matrix.
1539 * \param to destination array.
1540 * \param from source array.
1543 _math_transposef( GLfloat to
[16], const GLfloat from
[16] )
1564 * Transpose a GLdouble matrix.
1566 * \param to destination array.
1567 * \param from source array.
1570 _math_transposed( GLdouble to
[16], const GLdouble from
[16] )
1591 * Transpose a GLdouble matrix and convert to GLfloat.
1593 * \param to destination array.
1594 * \param from source array.
1597 _math_transposefd( GLfloat to
[16], const GLdouble from
[16] )
1599 to
[0] = (GLfloat
) from
[0];
1600 to
[1] = (GLfloat
) from
[4];
1601 to
[2] = (GLfloat
) from
[8];
1602 to
[3] = (GLfloat
) from
[12];
1603 to
[4] = (GLfloat
) from
[1];
1604 to
[5] = (GLfloat
) from
[5];
1605 to
[6] = (GLfloat
) from
[9];
1606 to
[7] = (GLfloat
) from
[13];
1607 to
[8] = (GLfloat
) from
[2];
1608 to
[9] = (GLfloat
) from
[6];
1609 to
[10] = (GLfloat
) from
[10];
1610 to
[11] = (GLfloat
) from
[14];
1611 to
[12] = (GLfloat
) from
[3];
1612 to
[13] = (GLfloat
) from
[7];
1613 to
[14] = (GLfloat
) from
[11];
1614 to
[15] = (GLfloat
) from
[15];
1621 * Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This
1622 * function is used for transforming clipping plane equations and spotlight
1624 * Mathematically, u = v * m.
1625 * Input: v - input vector
1626 * m - transformation matrix
1627 * Output: u - transformed vector
1630 _mesa_transform_vector( GLfloat u
[4], const GLfloat v
[4], const GLfloat m
[16] )
1632 const GLfloat v0
= v
[0], v1
= v
[1], v2
= v
[2], v3
= v
[3];
1633 #define M(row,col) m[row + col*4]
1634 u
[0] = v0
* M(0,0) + v1
* M(1,0) + v2
* M(2,0) + v3
* M(3,0);
1635 u
[1] = v0
* M(0,1) + v1
* M(1,1) + v2
* M(2,1) + v3
* M(3,1);
1636 u
[2] = v0
* M(0,2) + v1
* M(1,2) + v2
* M(2,2) + v3
* M(3,2);
1637 u
[3] = v0
* M(0,3) + v1
* M(1,3) + v2
* M(2,3) + v3
* M(3,3);