2 * Mesa 3-D graphics library
5 * Copyright (C) 1999-2005 Brian Paul All Rights Reserved.
7 * Permission is hereby granted, free of charge, to any person obtaining a
8 * copy of this software and associated documentation files (the "Software"),
9 * to deal in the Software without restriction, including without limitation
10 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
11 * and/or sell copies of the Software, and to permit persons to whom the
12 * Software is furnished to do so, subject to the following conditions:
14 * The above copyright notice and this permission notice shall be included
15 * in all copies or substantial portions of the Software.
17 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
18 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
19 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
20 * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
21 * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
22 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
31 * -# 4x4 transformation matrices are stored in memory in column major order.
32 * -# Points/vertices are to be thought of as column vectors.
33 * -# Transformation of a point p by a matrix M is: p' = M * p
46 * \defgroup MatFlags MAT_FLAG_XXX-flags
48 * Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
49 * It would be nice to make all these flags private to m_matrix.c
52 #define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag.
53 * (Not actually used - the identity
54 * matrix is identified by the absense
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 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
)
300 _mesa_debug(NULL
, "Matrix type: %s, flags: %x\n", types
[m
->type
], m
->flags
);
301 print_matrix_floats(m
->m
);
302 _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
);
311 _mesa_debug(NULL
, " - not available\n");
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 pointer 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 (0.0 == 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
!= 0.0) { r1
[4] -= m1
* s
; r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
398 if (s
!= 0.0) { r1
[5] -= m1
* s
; r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
400 if (s
!= 0.0) { r1
[6] -= m1
* s
; r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
402 if (s
!= 0.0) { 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 (0.0 == 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 (0.0 != s
) { r2
[4] -= m2
* s
; r3
[4] -= m3
* s
; }
414 s
= r1
[5]; if (0.0 != s
) { r2
[5] -= m2
* s
; r3
[5] -= m3
* s
; }
415 s
= r1
[6]; if (0.0 != s
) { r2
[6] -= m2
* s
; r3
[6] -= m3
* s
; }
416 s
= r1
[7]; if (0.0 != 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 (0.0 == 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 (0.0 == 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
>= 0.0) pos
+= t
; else neg
+= t
;
500 t
= MAT(in
,1,0) * MAT(in
,2,1) * MAT(in
,0,2);
501 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
503 t
= MAT(in
,2,0) * MAT(in
,0,1) * MAT(in
,1,2);
504 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
506 t
= -MAT(in
,2,0) * MAT(in
,1,1) * MAT(in
,0,2);
507 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
509 t
= -MAT(in
,1,0) * MAT(in
,0,1) * MAT(in
,2,2);
510 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
512 t
= -MAT(in
,0,0) * MAT(in
,2,1) * MAT(in
,1,2);
513 if (t
>= 0.0) pos
+= t
; else neg
+= t
;
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
, 16 * sizeof(GLfloat
) );
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
, 16 * sizeof(GLfloat
) );
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
, 16 * sizeof(GLfloat
) );
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
= (GLfloat
) _mesa_sin( angle
* DEG2RAD
);
808 c
= (GLfloat
) _mesa_cos( angle
* DEG2RAD
);
810 MEMCPY(m
, Identity
, sizeof(GLfloat
)*16);
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
);
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 it's 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 * Apply an orthographic projection matrix.
1012 * \param mat matrix to apply the projection.
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 multiplies it with \p mat, marking the
1021 * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
1024 _math_matrix_ortho( GLmatrix
*mat
,
1025 GLfloat left
, GLfloat right
,
1026 GLfloat bottom
, GLfloat top
,
1027 GLfloat nearval
, GLfloat farval
)
1031 #define M(row,col) m[col*4+row]
1032 M(0,0) = 2.0F
/ (right
-left
);
1035 M(0,3) = -(right
+left
) / (right
-left
);
1038 M(1,1) = 2.0F
/ (top
-bottom
);
1040 M(1,3) = -(top
+bottom
) / (top
-bottom
);
1044 M(2,2) = -2.0F
/ (farval
-nearval
);
1045 M(2,3) = -(farval
+nearval
) / (farval
-nearval
);
1053 matrix_multf( mat
, m
, (MAT_FLAG_GENERAL_SCALE
|MAT_FLAG_TRANSLATION
));
1057 * Multiply a matrix with a general scaling matrix.
1059 * \param mat matrix.
1060 * \param x x axis scale factor.
1061 * \param y y axis scale factor.
1062 * \param z z axis scale factor.
1064 * Multiplies in-place the elements of \p mat by the scale factors. Checks if
1065 * the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
1066 * flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
1067 * MAT_DIRTY_INVERSE dirty flags.
1070 _math_matrix_scale( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
)
1072 GLfloat
*m
= mat
->m
;
1073 m
[0] *= x
; m
[4] *= y
; m
[8] *= z
;
1074 m
[1] *= x
; m
[5] *= y
; m
[9] *= z
;
1075 m
[2] *= x
; m
[6] *= y
; m
[10] *= z
;
1076 m
[3] *= x
; m
[7] *= y
; m
[11] *= z
;
1078 if (FABSF(x
- y
) < 1e-8 && FABSF(x
- z
) < 1e-8)
1079 mat
->flags
|= MAT_FLAG_UNIFORM_SCALE
;
1081 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1083 mat
->flags
|= (MAT_DIRTY_TYPE
|
1088 * Multiply a matrix with a translation matrix.
1090 * \param mat matrix.
1091 * \param x translation vector x coordinate.
1092 * \param y translation vector y coordinate.
1093 * \param z translation vector z coordinate.
1095 * Adds the translation coordinates to the elements of \p mat in-place. Marks
1096 * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
1100 _math_matrix_translate( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
)
1102 GLfloat
*m
= mat
->m
;
1103 m
[12] = m
[0] * x
+ m
[4] * y
+ m
[8] * z
+ m
[12];
1104 m
[13] = m
[1] * x
+ m
[5] * y
+ m
[9] * z
+ m
[13];
1105 m
[14] = m
[2] * x
+ m
[6] * y
+ m
[10] * z
+ m
[14];
1106 m
[15] = m
[3] * x
+ m
[7] * y
+ m
[11] * z
+ m
[15];
1108 mat
->flags
|= (MAT_FLAG_TRANSLATION
|
1115 * Set matrix to do viewport and depthrange mapping.
1116 * Transforms Normalized Device Coords to window/Z values.
1119 _math_matrix_viewport(GLmatrix
*m
, GLint x
, GLint y
, GLint width
, GLint height
,
1120 GLfloat zNear
, GLfloat zFar
, GLfloat depthMax
)
1122 m
->m
[MAT_SX
] = (GLfloat
) width
/ 2.0F
;
1123 m
->m
[MAT_TX
] = m
->m
[MAT_SX
] + x
;
1124 m
->m
[MAT_SY
] = (GLfloat
) height
/ 2.0F
;
1125 m
->m
[MAT_TY
] = m
->m
[MAT_SY
] + y
;
1126 m
->m
[MAT_SZ
] = depthMax
* ((zFar
- zNear
) / 2.0F
);
1127 m
->m
[MAT_TZ
] = depthMax
* ((zFar
- zNear
) / 2.0F
+ zNear
);
1128 m
->flags
= MAT_FLAG_GENERAL_SCALE
| MAT_FLAG_TRANSLATION
;
1129 m
->type
= MATRIX_3D_NO_ROT
;
1134 * Set a matrix to the identity matrix.
1136 * \param mat matrix.
1138 * Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
1139 * Sets the matrix type to identity, and clear the dirty flags.
1142 _math_matrix_set_identity( GLmatrix
*mat
)
1144 MEMCPY( mat
->m
, Identity
, 16*sizeof(GLfloat
) );
1147 MEMCPY( mat
->inv
, Identity
, 16*sizeof(GLfloat
) );
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
] == 0.0) 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-6) ||
1251 SQ(m4m4
-1) > SQ(1e-6))
1252 mat
->flags
|= MAT_FLAG_GENERAL_SCALE
;
1254 /* Check for rotation */
1255 if (SQ(mm4
) > SQ(1e-6))
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-6) &&
1266 SQ(m
[0]-m
[10]) < SQ(1e-6)) {
1267 if (SQ(m
[0]-1.0) > SQ(1e-6)) {
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-6) && SQ(c1
-c3
) < SQ(1e-6)) {
1286 if (SQ(c1
-1.0) > SQ(1e-6))
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-6)) {
1296 CROSS3( cp
, m
, m
+4 );
1297 SUB_3V( cp
, cp
, (m
+8) );
1298 if (LEN_SQUARED_3FV(cp
) < SQ(1e-6))
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
);
1384 mat
->flags
&= ~(MAT_DIRTY_FLAGS
|
1393 * Test if the given matrix preserves vector lengths.
1396 _math_matrix_is_length_preserving( const GLmatrix
*m
)
1398 return TEST_MAT_FLAGS( m
, MAT_FLAGS_LENGTH_PRESERVING
);
1403 * Test if the given matrix does any rotation.
1404 * (or perhaps if the upper-left 3x3 is non-identity)
1407 _math_matrix_has_rotation( const GLmatrix
*m
)
1409 if (m
->flags
& (MAT_FLAG_GENERAL
|
1411 MAT_FLAG_GENERAL_3D
|
1412 MAT_FLAG_PERSPECTIVE
))
1420 _math_matrix_is_general_scale( const GLmatrix
*m
)
1422 return (m
->flags
& MAT_FLAG_GENERAL_SCALE
) ? GL_TRUE
: GL_FALSE
;
1427 _math_matrix_is_dirty( const GLmatrix
*m
)
1429 return (m
->flags
& MAT_DIRTY
) ? GL_TRUE
: GL_FALSE
;
1433 /**********************************************************************/
1434 /** \name Matrix setup */
1440 * \param to destination matrix.
1441 * \param from source matrix.
1443 * Copies all fields in GLmatrix, creating an inverse array if necessary.
1446 _math_matrix_copy( GLmatrix
*to
, const GLmatrix
*from
)
1448 MEMCPY( to
->m
, from
->m
, sizeof(Identity
) );
1449 to
->flags
= from
->flags
;
1450 to
->type
= from
->type
;
1453 if (from
->inv
== 0) {
1454 matrix_invert( to
);
1457 MEMCPY(to
->inv
, from
->inv
, sizeof(GLfloat
)*16);
1463 * Loads a matrix array into GLmatrix.
1465 * \param m matrix array.
1466 * \param mat matrix.
1468 * Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
1472 _math_matrix_loadf( GLmatrix
*mat
, const GLfloat
*m
)
1474 MEMCPY( mat
->m
, m
, 16*sizeof(GLfloat
) );
1475 mat
->flags
= (MAT_FLAG_GENERAL
| MAT_DIRTY
);
1479 * Matrix constructor.
1483 * Initialize the GLmatrix fields.
1486 _math_matrix_ctr( GLmatrix
*m
)
1488 m
->m
= (GLfloat
*) ALIGN_MALLOC( 16 * sizeof(GLfloat
), 16 );
1490 MEMCPY( m
->m
, Identity
, sizeof(Identity
) );
1492 m
->type
= MATRIX_IDENTITY
;
1497 * Matrix destructor.
1501 * Frees the data in a GLmatrix.
1504 _math_matrix_dtr( GLmatrix
*m
)
1511 ALIGN_FREE( m
->inv
);
1517 * Allocate a matrix inverse.
1521 * Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity.
1524 _math_matrix_alloc_inv( GLmatrix
*m
)
1527 m
->inv
= (GLfloat
*) ALIGN_MALLOC( 16 * sizeof(GLfloat
), 16 );
1529 MEMCPY( m
->inv
, Identity
, 16 * sizeof(GLfloat
) );
1536 /**********************************************************************/
1537 /** \name Matrix transpose */
1541 * Transpose a GLfloat matrix.
1543 * \param to destination array.
1544 * \param from source array.
1547 _math_transposef( GLfloat to
[16], const GLfloat from
[16] )
1568 * Transpose a GLdouble matrix.
1570 * \param to destination array.
1571 * \param from source array.
1574 _math_transposed( GLdouble to
[16], const GLdouble from
[16] )
1595 * Transpose a GLdouble matrix and convert to GLfloat.
1597 * \param to destination array.
1598 * \param from source array.
1601 _math_transposefd( GLfloat to
[16], const GLdouble from
[16] )
1603 to
[0] = (GLfloat
) from
[0];
1604 to
[1] = (GLfloat
) from
[4];
1605 to
[2] = (GLfloat
) from
[8];
1606 to
[3] = (GLfloat
) from
[12];
1607 to
[4] = (GLfloat
) from
[1];
1608 to
[5] = (GLfloat
) from
[5];
1609 to
[6] = (GLfloat
) from
[9];
1610 to
[7] = (GLfloat
) from
[13];
1611 to
[8] = (GLfloat
) from
[2];
1612 to
[9] = (GLfloat
) from
[6];
1613 to
[10] = (GLfloat
) from
[10];
1614 to
[11] = (GLfloat
) from
[14];
1615 to
[12] = (GLfloat
) from
[3];
1616 to
[13] = (GLfloat
) from
[7];
1617 to
[14] = (GLfloat
) from
[11];
1618 to
[15] = (GLfloat
) from
[15];