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];