3 * Mesa 3-D graphics library
5 * Copyright (C) 1995-2000 Brian Paul
7 * This library is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU Library General Public
9 * License as published by the Free Software Foundation; either
10 * version 2 of the License, or (at your option) any later version.
12 * This library is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 * Library General Public License for more details.
17 * You should have received a copy of the GNU Library General Public
18 * License along with this library; if not, write to the Free
19 * Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
34 * This code was contributed by Marc Buffat (buffat@mecaflu.ec-lyon.fr).
40 /* implementation de gluProject et gluUnproject */
41 /* M. Buffat 17/2/95 */
46 * Transform a point (column vector) by a 4x4 matrix. I.e. out = m * in
47 * Input: m - the 4x4 matrix
49 * Output: out - the resulting 4x1 vector.
52 transform_point(GLdouble out
[4], const GLdouble m
[16], const GLdouble in
[4])
54 #define M(row,col) m[col*4+row]
56 M(0, 0) * in
[0] + M(0, 1) * in
[1] + M(0, 2) * in
[2] + M(0, 3) * in
[3];
58 M(1, 0) * in
[0] + M(1, 1) * in
[1] + M(1, 2) * in
[2] + M(1, 3) * in
[3];
60 M(2, 0) * in
[0] + M(2, 1) * in
[1] + M(2, 2) * in
[2] + M(2, 3) * in
[3];
62 M(3, 0) * in
[0] + M(3, 1) * in
[1] + M(3, 2) * in
[2] + M(3, 3) * in
[3];
70 * Perform a 4x4 matrix multiplication (product = a x b).
71 * Input: a, b - matrices to multiply
72 * Output: product - product of a and b
75 matmul(GLdouble
* product
, const GLdouble
* a
, const GLdouble
* b
)
77 /* This matmul was contributed by Thomas Malik */
81 #define A(row,col) a[(col<<2)+row]
82 #define B(row,col) b[(col<<2)+row]
83 #define T(row,col) temp[(col<<2)+row]
86 for (i
= 0; i
< 4; i
++) {
88 A(i
, 0) * B(0, 0) + A(i
, 1) * B(1, 0) + A(i
, 2) * B(2, 0) + A(i
,
92 A(i
, 0) * B(0, 1) + A(i
, 1) * B(1, 1) + A(i
, 2) * B(2, 1) + A(i
,
96 A(i
, 0) * B(0, 2) + A(i
, 1) * B(1, 2) + A(i
, 2) * B(2, 2) + A(i
,
100 A(i
, 0) * B(0, 3) + A(i
, 1) * B(1, 3) + A(i
, 2) * B(2, 3) + A(i
,
108 MEMCPY(product
, temp
, 16 * sizeof(GLdouble
));
114 * Compute inverse of 4x4 transformation matrix.
115 * Code contributed by Jacques Leroy jle@star.be
116 * Return GL_TRUE for success, GL_FALSE for failure (singular matrix)
119 invert_matrix(const GLdouble
* m
, GLdouble
* out
)
121 /* NB. OpenGL Matrices are COLUMN major. */
122 #define SWAP_ROWS(a, b) { GLdouble *_tmp = a; (a)=(b); (b)=_tmp; }
123 #define MAT(m,r,c) (m)[(c)*4+(r)]
126 GLdouble m0
, m1
, m2
, m3
, s
;
127 GLdouble
*r0
, *r1
, *r2
, *r3
;
129 r0
= wtmp
[0], r1
= wtmp
[1], r2
= wtmp
[2], r3
= wtmp
[3];
131 r0
[0] = MAT(m
, 0, 0), r0
[1] = MAT(m
, 0, 1),
132 r0
[2] = MAT(m
, 0, 2), r0
[3] = MAT(m
, 0, 3),
133 r0
[4] = 1.0, r0
[5] = r0
[6] = r0
[7] = 0.0,
134 r1
[0] = MAT(m
, 1, 0), r1
[1] = MAT(m
, 1, 1),
135 r1
[2] = MAT(m
, 1, 2), r1
[3] = MAT(m
, 1, 3),
136 r1
[5] = 1.0, r1
[4] = r1
[6] = r1
[7] = 0.0,
137 r2
[0] = MAT(m
, 2, 0), r2
[1] = MAT(m
, 2, 1),
138 r2
[2] = MAT(m
, 2, 2), r2
[3] = MAT(m
, 2, 3),
139 r2
[6] = 1.0, r2
[4] = r2
[5] = r2
[7] = 0.0,
140 r3
[0] = MAT(m
, 3, 0), r3
[1] = MAT(m
, 3, 1),
141 r3
[2] = MAT(m
, 3, 2), r3
[3] = MAT(m
, 3, 3),
142 r3
[7] = 1.0, r3
[4] = r3
[5] = r3
[6] = 0.0;
144 /* choose pivot - or die */
145 if (fabs(r3
[0]) > fabs(r2
[0]))
147 if (fabs(r2
[0]) > fabs(r1
[0]))
149 if (fabs(r1
[0]) > fabs(r0
[0]))
154 /* eliminate first variable */
195 /* choose pivot - or die */
196 if (fabs(r3
[1]) > fabs(r2
[1]))
198 if (fabs(r2
[1]) > fabs(r1
[1]))
203 /* eliminate second variable */
231 /* choose pivot - or die */
232 if (fabs(r3
[2]) > fabs(r2
[2]))
237 /* eliminate third variable */
239 r3
[3] -= m3
* r2
[3], r3
[4] -= m3
* r2
[4],
240 r3
[5] -= m3
* r2
[5], r3
[6] -= m3
* r2
[6], r3
[7] -= m3
* r2
[7];
246 s
= 1.0 / r3
[3]; /* now back substitute row 3 */
252 m2
= r2
[3]; /* now back substitute row 2 */
254 r2
[4] = s
* (r2
[4] - r3
[4] * m2
), r2
[5] = s
* (r2
[5] - r3
[5] * m2
),
255 r2
[6] = s
* (r2
[6] - r3
[6] * m2
), r2
[7] = s
* (r2
[7] - r3
[7] * m2
);
257 r1
[4] -= r3
[4] * m1
, r1
[5] -= r3
[5] * m1
,
258 r1
[6] -= r3
[6] * m1
, r1
[7] -= r3
[7] * m1
;
260 r0
[4] -= r3
[4] * m0
, r0
[5] -= r3
[5] * m0
,
261 r0
[6] -= r3
[6] * m0
, r0
[7] -= r3
[7] * m0
;
263 m1
= r1
[2]; /* now back substitute row 1 */
265 r1
[4] = s
* (r1
[4] - r2
[4] * m1
), r1
[5] = s
* (r1
[5] - r2
[5] * m1
),
266 r1
[6] = s
* (r1
[6] - r2
[6] * m1
), r1
[7] = s
* (r1
[7] - r2
[7] * m1
);
268 r0
[4] -= r2
[4] * m0
, r0
[5] -= r2
[5] * m0
,
269 r0
[6] -= r2
[6] * m0
, r0
[7] -= r2
[7] * m0
;
271 m0
= r0
[1]; /* now back substitute row 0 */
273 r0
[4] = s
* (r0
[4] - r1
[4] * m0
), r0
[5] = s
* (r0
[5] - r1
[5] * m0
),
274 r0
[6] = s
* (r0
[6] - r1
[6] * m0
), r0
[7] = s
* (r0
[7] - r1
[7] * m0
);
276 MAT(out
, 0, 0) = r0
[4];
277 MAT(out
, 0, 1) = r0
[5], MAT(out
, 0, 2) = r0
[6];
278 MAT(out
, 0, 3) = r0
[7], MAT(out
, 1, 0) = r1
[4];
279 MAT(out
, 1, 1) = r1
[5], MAT(out
, 1, 2) = r1
[6];
280 MAT(out
, 1, 3) = r1
[7], MAT(out
, 2, 0) = r2
[4];
281 MAT(out
, 2, 1) = r2
[5], MAT(out
, 2, 2) = r2
[6];
282 MAT(out
, 2, 3) = r2
[7], MAT(out
, 3, 0) = r3
[4];
283 MAT(out
, 3, 1) = r3
[5], MAT(out
, 3, 2) = r3
[6];
284 MAT(out
, 3, 3) = r3
[7];
294 /* projection du point (objx,objy,obz) sur l'ecran (winx,winy,winz) */
296 gluProject(GLdouble objx
, GLdouble objy
, GLdouble objz
,
297 const GLdouble model
[16], const GLdouble proj
[16],
298 const GLint viewport
[4],
299 GLdouble
* winx
, GLdouble
* winy
, GLdouble
* winz
)
301 /* matrice de transformation */
302 GLdouble in
[4], out
[4];
304 /* initilise la matrice et le vecteur a transformer */
309 transform_point(out
, model
, in
);
310 transform_point(in
, proj
, out
);
312 /* d'ou le resultat normalise entre -1 et 1 */
320 /* en coordonnees ecran */
321 *winx
= viewport
[0] + (1 + in
[0]) * viewport
[2] / 2;
322 *winy
= viewport
[1] + (1 + in
[1]) * viewport
[3] / 2;
323 /* entre 0 et 1 suivant z */
324 *winz
= (1 + in
[2]) / 2;
330 /* transformation du point ecran (winx,winy,winz) en point objet */
332 gluUnProject(GLdouble winx
, GLdouble winy
, GLdouble winz
,
333 const GLdouble model
[16], const GLdouble proj
[16],
334 const GLint viewport
[4],
335 GLdouble
* objx
, GLdouble
* objy
, GLdouble
* objz
)
337 /* matrice de transformation */
338 GLdouble m
[16], A
[16];
339 GLdouble in
[4], out
[4];
341 /* transformation coordonnees normalisees entre -1 et 1 */
342 in
[0] = (winx
- viewport
[0]) * 2 / viewport
[2] - 1.0;
343 in
[1] = (winy
- viewport
[1]) * 2 / viewport
[3] - 1.0;
344 in
[2] = 2 * winz
- 1.0;
347 /* calcul transformation inverse */
348 matmul(A
, proj
, model
);
349 if (!invert_matrix(A
, m
))
352 /* d'ou les coordonnees objets */
353 transform_point(out
, m
, in
);
356 *objx
= out
[0] / out
[3];
357 *objy
= out
[1] / out
[3];
358 *objz
= out
[2] / out
[3];
365 * This is like gluUnProject but also takes near and far DepthRange values.
367 #ifdef GLU_VERSION_1_3
369 gluUnProject4(GLdouble winx
, GLdouble winy
, GLdouble winz
, GLdouble clipw
,
370 const GLdouble modelMatrix
[16],
371 const GLdouble projMatrix
[16],
372 const GLint viewport
[4],
373 GLclampd nearZ
, GLclampd farZ
,
374 GLdouble
* objx
, GLdouble
* objy
, GLdouble
* objz
,
377 /* matrice de transformation */
378 GLdouble m
[16], A
[16];
379 GLdouble in
[4], out
[4];
380 GLdouble z
= nearZ
+ winz
* (farZ
- nearZ
);
382 /* transformation coordonnees normalisees entre -1 et 1 */
383 in
[0] = (winx
- viewport
[0]) * 2 / viewport
[2] - 1.0;
384 in
[1] = (winy
- viewport
[1]) * 2 / viewport
[3] - 1.0;
385 in
[2] = 2.0 * z
- 1.0;
388 /* calcul transformation inverse */
389 matmul(A
, projMatrix
, modelMatrix
);
390 if (!invert_matrix(A
, m
))
393 /* d'ou les coordonnees objets */
394 transform_point(out
, m
, in
);
397 *objx
= out
[0] / out
[3];
398 *objy
= out
[1] / out
[3];
399 *objz
= out
[2] / out
[3];