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/* $Id: project.c,v 1.2 2003-08-22 20:11:43 brianp Exp $ */
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* Mesa 3-D graphics library
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* Copyright (C) 1995-2000 Brian Paul
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Library General Public
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* License as published by the Free Software Foundation; either
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* version 2 of the License, or (at your option) any later version.
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Library General Public License for more details.
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* You should have received a copy of the GNU Library General Public
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* License along with this library; if not, write to the Free
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* Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
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* This code was contributed by Marc Buffat (buffat@mecaflu.ec-lyon.fr).
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/* implementation de gluProject et gluUnproject */
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/* M. Buffat 17/2/95 */
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* Transform a point (column vector) by a 4x4 matrix. I.e. out = m * in
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* Input: m - the 4x4 matrix
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* Output: out - the resulting 4x1 vector.
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transform_point(GLdouble out[4], const GLdouble m[16], const GLdouble in[4])
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#define M(row,col) m[col*4+row]
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M(0, 0) * in[0] + M(0, 1) * in[1] + M(0, 2) * in[2] + M(0, 3) * in[3];
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M(1, 0) * in[0] + M(1, 1) * in[1] + M(1, 2) * in[2] + M(1, 3) * in[3];
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M(2, 0) * in[0] + M(2, 1) * in[1] + M(2, 2) * in[2] + M(2, 3) * in[3];
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M(3, 0) * in[0] + M(3, 1) * in[1] + M(3, 2) * in[2] + M(3, 3) * in[3];
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* Perform a 4x4 matrix multiplication (product = a x b).
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* Input: a, b - matrices to multiply
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* Output: product - product of a and b
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matmul(GLdouble * product, const GLdouble * a, const GLdouble * b)
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/* This matmul was contributed by Thomas Malik */
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#define A(row,col) a[(col<<2)+row]
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#define B(row,col) b[(col<<2)+row]
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#define T(row,col) temp[(col<<2)+row]
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for (i = 0; i < 4; i++) {
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A(i, 0) * B(0, 0) + A(i, 1) * B(1, 0) + A(i, 2) * B(2, 0) + A(i,
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A(i, 0) * B(0, 1) + A(i, 1) * B(1, 1) + A(i, 2) * B(2, 1) + A(i,
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A(i, 0) * B(0, 2) + A(i, 1) * B(1, 2) + A(i, 2) * B(2, 2) + A(i,
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A(i, 0) * B(0, 3) + A(i, 1) * B(1, 3) + A(i, 2) * B(2, 3) + A(i,
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MEMCPY(product, temp, 16 * sizeof(GLdouble));
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* Compute inverse of 4x4 transformation matrix.
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* Code contributed by Jacques Leroy jle@star.be
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* Return GL_TRUE for success, GL_FALSE for failure (singular matrix)
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invert_matrix(const GLdouble * m, GLdouble * out)
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/* NB. OpenGL Matrices are COLUMN major. */
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#define SWAP_ROWS(a, b) { GLdouble *_tmp = a; (a)=(b); (b)=_tmp; }
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#define MAT(m,r,c) (m)[(c)*4+(r)]
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GLdouble m0, m1, m2, m3, s;
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GLdouble *r0, *r1, *r2, *r3;
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r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
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r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1),
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r0[2] = MAT(m, 0, 2), r0[3] = MAT(m, 0, 3),
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r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
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r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1),
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r1[2] = MAT(m, 1, 2), r1[3] = MAT(m, 1, 3),
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r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
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r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1),
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r2[2] = MAT(m, 2, 2), r2[3] = MAT(m, 2, 3),
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r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
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r3[0] = MAT(m, 3, 0), r3[1] = MAT(m, 3, 1),
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r3[2] = MAT(m, 3, 2), r3[3] = MAT(m, 3, 3),
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r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
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/* choose pivot - or die */
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if (fabs(r3[0]) > fabs(r2[0]))
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if (fabs(r2[0]) > fabs(r1[0]))
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if (fabs(r1[0]) > fabs(r0[0]))
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/* eliminate first variable */
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/* choose pivot - or die */
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if (fabs(r3[1]) > fabs(r2[1]))
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if (fabs(r2[1]) > fabs(r1[1]))
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/* eliminate second variable */
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/* choose pivot - or die */
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if (fabs(r3[2]) > fabs(r2[2]))
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/* eliminate third variable */
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r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
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r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7];
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s = 1.0 / r3[3]; /* now back substitute row 3 */
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m2 = r2[3]; /* now back substitute row 2 */
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r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
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r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
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r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
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r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
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r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
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r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
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m1 = r1[2]; /* now back substitute row 1 */
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r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
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r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
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r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
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r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
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m0 = r0[1]; /* now back substitute row 0 */
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r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
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r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
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MAT(out, 0, 0) = r0[4];
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MAT(out, 0, 1) = r0[5], MAT(out, 0, 2) = r0[6];
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MAT(out, 0, 3) = r0[7], MAT(out, 1, 0) = r1[4];
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MAT(out, 1, 1) = r1[5], MAT(out, 1, 2) = r1[6];
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MAT(out, 1, 3) = r1[7], MAT(out, 2, 0) = r2[4];
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MAT(out, 2, 1) = r2[5], MAT(out, 2, 2) = r2[6];
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MAT(out, 2, 3) = r2[7], MAT(out, 3, 0) = r3[4];
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MAT(out, 3, 1) = r3[5], MAT(out, 3, 2) = r3[6];
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MAT(out, 3, 3) = r3[7];
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/* projection du point (objx,objy,obz) sur l'ecran (winx,winy,winz) */
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gluProject(GLdouble objx, GLdouble objy, GLdouble objz,
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const GLdouble model[16], const GLdouble proj[16],
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const GLint viewport[4],
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GLdouble * winx, GLdouble * winy, GLdouble * winz)
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/* matrice de transformation */
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GLdouble in[4], out[4];
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/* initilise la matrice et le vecteur a transformer */
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transform_point(out, model, in);
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transform_point(in, proj, out);
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/* d'ou le resultat normalise entre -1 et 1 */
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/* en coordonnees ecran */
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*winx = viewport[0] + (1 + in[0]) * viewport[2] / 2;
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*winy = viewport[1] + (1 + in[1]) * viewport[3] / 2;
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/* entre 0 et 1 suivant z */
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*winz = (1 + in[2]) / 2;
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/* transformation du point ecran (winx,winy,winz) en point objet */
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gluUnProject(GLdouble winx, GLdouble winy, GLdouble winz,
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const GLdouble model[16], const GLdouble proj[16],
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const GLint viewport[4],
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GLdouble * objx, GLdouble * objy, GLdouble * objz)
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/* matrice de transformation */
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GLdouble m[16], A[16];
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GLdouble in[4], out[4];
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/* transformation coordonnees normalisees entre -1 et 1 */
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in[0] = (winx - viewport[0]) * 2 / viewport[2] - 1.0;
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in[1] = (winy - viewport[1]) * 2 / viewport[3] - 1.0;
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in[2] = 2 * winz - 1.0;
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/* calcul transformation inverse */
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matmul(A, proj, model);
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/* d'ou les coordonnees objets */
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transform_point(out, m, in);
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*objx = out[0] / out[3];
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*objy = out[1] / out[3];
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*objz = out[2] / out[3];
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* This is like gluUnProject but also takes near and far DepthRange values.
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#ifdef GLU_VERSION_1_3
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gluUnProject4(GLdouble winx, GLdouble winy, GLdouble winz, GLdouble clipw,
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const GLdouble modelMatrix[16],
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const GLdouble projMatrix[16],
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const GLint viewport[4],
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GLclampd nearZ, GLclampd farZ,
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GLdouble * objx, GLdouble * objy, GLdouble * objz,
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/* matrice de transformation */
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GLdouble m[16], A[16];
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GLdouble in[4], out[4];
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GLdouble z = nearZ + winz * (farZ - nearZ);
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/* transformation coordonnees normalisees entre -1 et 1 */
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in[0] = (winx - viewport[0]) * 2 / viewport[2] - 1.0;
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in[1] = (winy - viewport[1]) * 2 / viewport[3] - 1.0;
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in[2] = 2.0 * z - 1.0;
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/* calcul transformation inverse */
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matmul(A, projMatrix, modelMatrix);
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/* d'ou les coordonnees objets */
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transform_point(out, m, in);
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*objx = out[0] / out[3];
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*objy = out[1] / out[3];
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*objz = out[2] / out[3];