src/glu/mini/project.c - third_party/mesa - Git at Google

 /* $Id: project.c,v 1.2 2003-08-22 20:11:43 brianp Exp $ */

 /*
  * Mesa 3-D graphics library
  * Version:  3.3
  * Copyright (C) 1995-2000  Brian Paul
  *
  * This library is free software; you can redistribute it and/or
  * modify it under the terms of the GNU Library General Public
  * License as published by the Free Software Foundation; either
  * version 2 of the License, or (at your option) any later version.
  *
  * This library is distributed in the hope that it will be useful,
  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  * Library General Public License for more details.
  *
  * You should have received a copy of the GNU Library General Public
  * License along with this library; if not, write to the Free
  * Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
  */


 #ifdef PC_HEADER
 #include "all.h"
 #else
 #include <stdio.h>
 #include <string.h>
 #include <math.h>
 #include "gluP.h"
 #endif


 /*
  * This code was contributed by Marc Buffat (buffat@mecaflu.ec-lyon.fr).
  * Thanks Marc!!!
  */


 /* implementation de gluProject et gluUnproject */
 /* M. Buffat 17/2/95 */


 /*
  * Transform a point (column vector) by a 4x4 matrix.  I.e.  out = m * in
  * Input:  m - the 4x4 matrix
  *         in - the 4x1 vector
  * Output:  out - the resulting 4x1 vector.
  */
 static void
 transform_point(GLdouble out[4], const GLdouble m[16], const GLdouble in[4])
 {
 #define M(row,col)  m[col*4+row]
    out[0] =
       M(0, 0) * in[0] + M(0, 1) * in[1] + M(0, 2) * in[2] + M(0, 3) * in[3];
    out[1] =
       M(1, 0) * in[0] + M(1, 1) * in[1] + M(1, 2) * in[2] + M(1, 3) * in[3];
    out[2] =
       M(2, 0) * in[0] + M(2, 1) * in[1] + M(2, 2) * in[2] + M(2, 3) * in[3];
    out[3] =
       M(3, 0) * in[0] + M(3, 1) * in[1] + M(3, 2) * in[2] + M(3, 3) * in[3];
 #undef M
 }


 /*
  * Perform a 4x4 matrix multiplication  (product = a x b).
  * Input:  a, b - matrices to multiply
  * Output:  product - product of a and b
  */
 static void
 matmul(GLdouble * product, const GLdouble * a, const GLdouble * b)
 {
    /* This matmul was contributed by Thomas Malik */
    GLdouble temp[16];
    GLint i;

 #define A(row,col)  a[(col<<2)+row]
 #define B(row,col)  b[(col<<2)+row]
 #define T(row,col)  temp[(col<<2)+row]

    /* i-te Zeile */
    for (i = 0; i < 4; i++) {
       T(i, 0) =
 	 A(i, 0) * B(0, 0) + A(i, 1) * B(1, 0) + A(i, 2) * B(2, 0) + A(i,
 								       3) *
 	 B(3, 0);
       T(i, 1) =
 	 A(i, 0) * B(0, 1) + A(i, 1) * B(1, 1) + A(i, 2) * B(2, 1) + A(i,
 								       3) *
 	 B(3, 1);
       T(i, 2) =
 	 A(i, 0) * B(0, 2) + A(i, 1) * B(1, 2) + A(i, 2) * B(2, 2) + A(i,
 								       3) *
 	 B(3, 2);
       T(i, 3) =
 	 A(i, 0) * B(0, 3) + A(i, 1) * B(1, 3) + A(i, 2) * B(2, 3) + A(i,
 								       3) *
 	 B(3, 3);
    }

 #undef A
 #undef B
 #undef T
    MEMCPY(product, temp, 16 * sizeof(GLdouble));
 }


 /*
  * Compute inverse of 4x4 transformation matrix.
  * Code contributed by Jacques Leroy jle@star.be
  * Return GL_TRUE for success, GL_FALSE for failure (singular matrix)
  */
 static GLboolean
 invert_matrix(const GLdouble * m, GLdouble * out)
 {
 /* NB. OpenGL Matrices are COLUMN major. */
 #define SWAP_ROWS(a, b) { GLdouble *_tmp = a; (a)=(b); (b)=_tmp; }
 #define MAT(m,r,c) (m)[(c)*4+(r)]

    GLdouble wtmp[4][8];
    GLdouble m0, m1, m2, m3, s;
    GLdouble *r0, *r1, *r2, *r3;

    r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];

    r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1),
       r0[2] = MAT(m, 0, 2), r0[3] = MAT(m, 0, 3),
       r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
       r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1),
       r1[2] = MAT(m, 1, 2), r1[3] = MAT(m, 1, 3),
       r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
       r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1),
       r2[2] = MAT(m, 2, 2), r2[3] = MAT(m, 2, 3),
       r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
       r3[0] = MAT(m, 3, 0), r3[1] = MAT(m, 3, 1),
       r3[2] = MAT(m, 3, 2), r3[3] = MAT(m, 3, 3),
       r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;

    /* choose pivot - or die */
    if (fabs(r3[0]) > fabs(r2[0]))
       SWAP_ROWS(r3, r2);
    if (fabs(r2[0]) > fabs(r1[0]))
       SWAP_ROWS(r2, r1);
    if (fabs(r1[0]) > fabs(r0[0]))
       SWAP_ROWS(r1, r0);
    if (0.0 == r0[0])
       return GL_FALSE;

    /* eliminate first variable     */
    m1 = r1[0] / r0[0];
    m2 = r2[0] / r0[0];
    m3 = r3[0] / r0[0];
    s = r0[1];
    r1[1] -= m1 * s;
    r2[1] -= m2 * s;
    r3[1] -= m3 * s;
    s = r0[2];
    r1[2] -= m1 * s;
    r2[2] -= m2 * s;
    r3[2] -= m3 * s;
    s = r0[3];
    r1[3] -= m1 * s;
    r2[3] -= m2 * s;
    r3[3] -= m3 * s;
    s = r0[4];
    if (s != 0.0) {
       r1[4] -= m1 * s;
       r2[4] -= m2 * s;
       r3[4] -= m3 * s;
    }
    s = r0[5];
    if (s != 0.0) {
       r1[5] -= m1 * s;
       r2[5] -= m2 * s;
       r3[5] -= m3 * s;
    }
    s = r0[6];
    if (s != 0.0) {
       r1[6] -= m1 * s;
       r2[6] -= m2 * s;
       r3[6] -= m3 * s;
    }
    s = r0[7];
    if (s != 0.0) {
       r1[7] -= m1 * s;
       r2[7] -= m2 * s;
       r3[7] -= m3 * s;
    }

    /* choose pivot - or die */
    if (fabs(r3[1]) > fabs(r2[1]))
       SWAP_ROWS(r3, r2);
    if (fabs(r2[1]) > fabs(r1[1]))
       SWAP_ROWS(r2, r1);
    if (0.0 == r1[1])
       return GL_FALSE;

    /* eliminate second variable */
    m2 = r2[1] / r1[1];
    m3 = r3[1] / r1[1];
    r2[2] -= m2 * r1[2];
    r3[2] -= m3 * r1[2];
    r2[3] -= m2 * r1[3];
    r3[3] -= m3 * r1[3];
    s = r1[4];
    if (0.0 != s) {
       r2[4] -= m2 * s;
       r3[4] -= m3 * s;
    }
    s = r1[5];
    if (0.0 != s) {
       r2[5] -= m2 * s;
       r3[5] -= m3 * s;
    }
    s = r1[6];
    if (0.0 != s) {
       r2[6] -= m2 * s;
       r3[6] -= m3 * s;
    }
    s = r1[7];
    if (0.0 != s) {
       r2[7] -= m2 * s;
       r3[7] -= m3 * s;
    }

    /* choose pivot - or die */
    if (fabs(r3[2]) > fabs(r2[2]))
       SWAP_ROWS(r3, r2);
    if (0.0 == r2[2])
       return GL_FALSE;

    /* eliminate third variable */
    m3 = r3[2] / r2[2];
    r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
       r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7];

    /* last check */
    if (0.0 == r3[3])
       return GL_FALSE;

    s = 1.0 / r3[3];		/* now back substitute row 3 */
    r3[4] *= s;
    r3[5] *= s;
    r3[6] *= s;
    r3[7] *= s;

    m2 = r2[3];			/* now back substitute row 2 */
    s = 1.0 / r2[2];
    r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
       r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
    m1 = r1[3];
    r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
       r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
    m0 = r0[3];
    r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
       r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;

    m1 = r1[2];			/* now back substitute row 1 */
    s = 1.0 / r1[1];
    r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
       r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
    m0 = r0[2];
    r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
       r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;

    m0 = r0[1];			/* now back substitute row 0 */
    s = 1.0 / r0[0];
    r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
       r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);

    MAT(out, 0, 0) = r0[4];
    MAT(out, 0, 1) = r0[5], MAT(out, 0, 2) = r0[6];
    MAT(out, 0, 3) = r0[7], MAT(out, 1, 0) = r1[4];
    MAT(out, 1, 1) = r1[5], MAT(out, 1, 2) = r1[6];
    MAT(out, 1, 3) = r1[7], MAT(out, 2, 0) = r2[4];
    MAT(out, 2, 1) = r2[5], MAT(out, 2, 2) = r2[6];
    MAT(out, 2, 3) = r2[7], MAT(out, 3, 0) = r3[4];
    MAT(out, 3, 1) = r3[5], MAT(out, 3, 2) = r3[6];
    MAT(out, 3, 3) = r3[7];

    return GL_TRUE;

 #undef MAT
 #undef SWAP_ROWS
 }


 /* projection du point (objx,objy,obz) sur l'ecran (winx,winy,winz) */
 GLint GLAPIENTRY
 gluProject(GLdouble objx, GLdouble objy, GLdouble objz,
 	   const GLdouble model[16], const GLdouble proj[16],
 	   const GLint viewport[4],
 	   GLdouble * winx, GLdouble * winy, GLdouble * winz)
 {
    /* matrice de transformation */
    GLdouble in[4], out[4];

    /* initilise la matrice et le vecteur a transformer */
    in[0] = objx;
    in[1] = objy;
    in[2] = objz;
    in[3] = 1.0;
    transform_point(out, model, in);
    transform_point(in, proj, out);

    /* d'ou le resultat normalise entre -1 et 1 */
    if (in[3] == 0.0)
       return GL_FALSE;

    in[0] /= in[3];
    in[1] /= in[3];
    in[2] /= in[3];

    /* en coordonnees ecran */
    *winx = viewport[0] + (1 + in[0]) * viewport[2] / 2;
    *winy = viewport[1] + (1 + in[1]) * viewport[3] / 2;
    /* entre 0 et 1 suivant z */
    *winz = (1 + in[2]) / 2;
    return GL_TRUE;
 }


 /* transformation du point ecran (winx,winy,winz) en point objet */
 GLint GLAPIENTRY
 gluUnProject(GLdouble winx, GLdouble winy, GLdouble winz,
 	     const GLdouble model[16], const GLdouble proj[16],
 	     const GLint viewport[4],
 	     GLdouble * objx, GLdouble * objy, GLdouble * objz)
 {
    /* matrice de transformation */
    GLdouble m[16], A[16];
    GLdouble in[4], out[4];

    /* transformation coordonnees normalisees entre -1 et 1 */
    in[0] = (winx - viewport[0]) * 2 / viewport[2] - 1.0;
    in[1] = (winy - viewport[1]) * 2 / viewport[3] - 1.0;
    in[2] = 2 * winz - 1.0;
    in[3] = 1.0;

    /* calcul transformation inverse */
    matmul(A, proj, model);
    invert_matrix(A, m);

    /* d'ou les coordonnees objets */
    transform_point(out, m, in);
    if (out[3] == 0.0)
       return GL_FALSE;
    *objx = out[0] / out[3];
    *objy = out[1] / out[3];
    *objz = out[2] / out[3];
    return GL_TRUE;
 }


 /*
  * New in GLU 1.3
  * This is like gluUnProject but also takes near and far DepthRange values.
  */
 #ifdef GLU_VERSION_1_3
 GLint GLAPIENTRY
 gluUnProject4(GLdouble winx, GLdouble winy, GLdouble winz, GLdouble clipw,
 	      const GLdouble modelMatrix[16],
 	      const GLdouble projMatrix[16],
 	      const GLint viewport[4],
 	      GLclampd nearZ, GLclampd farZ,
 	      GLdouble * objx, GLdouble * objy, GLdouble * objz,
 	      GLdouble * objw)
 {
    /* matrice de transformation */
    GLdouble m[16], A[16];
    GLdouble in[4], out[4];
    GLdouble z = nearZ + winz * (farZ - nearZ);

    /* transformation coordonnees normalisees entre -1 et 1 */
    in[0] = (winx - viewport[0]) * 2 / viewport[2] - 1.0;
    in[1] = (winy - viewport[1]) * 2 / viewport[3] - 1.0;
    in[2] = 2.0 * z - 1.0;
    in[3] = clipw;

    /* calcul transformation inverse */
    matmul(A, projMatrix, modelMatrix);
    invert_matrix(A, m);

    /* d'ou les coordonnees objets */
    transform_point(out, m, in);
    if (out[3] == 0.0)
       return GL_FALSE;
    *objx = out[0] / out[3];
    *objy = out[1] / out[3];
    *objz = out[2] / out[3];
    *objw = out[3];
    return GL_TRUE;
 }
 #endif
	/* $Id: project.c,v 1.2 2003-08-22 20:11:43 brianp Exp $ */

	/*
	* Mesa 3-D graphics library
	* Version: 3.3
	* Copyright (C) 1995-2000 Brian Paul
	*
	* This library is free software; you can redistribute it and/or
	* modify it under the terms of the GNU Library General Public
	* License as published by the Free Software Foundation; either
	* version 2 of the License, or (at your option) any later version.
	*
	* This library is distributed in the hope that it will be useful,
	* but WITHOUT ANY WARRANTY; without even the implied warranty of
	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
	* Library General Public License for more details.
	*
	* You should have received a copy of the GNU Library General Public
	* License along with this library; if not, write to the Free
	* Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
	*/


	#ifdef PC_HEADER
	#include "all.h"
	#else
	#include <stdio.h>
	#include <string.h>
	#include <math.h>
	#include "gluP.h"
	#endif


	/*
	* This code was contributed by Marc Buffat (buffat@mecaflu.ec-lyon.fr).
	* Thanks Marc!!!
	*/



	/* implementation de gluProject et gluUnproject */
	/* M. Buffat 17/2/95 */



	/*
	* Transform a point (column vector) by a 4x4 matrix. I.e. out = m * in
	* Input: m - the 4x4 matrix
	* in - the 4x1 vector
	* Output: out - the resulting 4x1 vector.
	*/
	static void
	transform_point(GLdouble out[4], const GLdouble m[16], const GLdouble in[4])
	{
	#define M(row,col) m[col*4+row]
	out[0] =
	M(0, 0) * in[0] + M(0, 1) * in[1] + M(0, 2) * in[2] + M(0, 3) * in[3];
	out[1] =
	M(1, 0) * in[0] + M(1, 1) * in[1] + M(1, 2) * in[2] + M(1, 3) * in[3];
	out[2] =
	M(2, 0) * in[0] + M(2, 1) * in[1] + M(2, 2) * in[2] + M(2, 3) * in[3];
	out[3] =
	M(3, 0) * in[0] + M(3, 1) * in[1] + M(3, 2) * in[2] + M(3, 3) * in[3];
	#undef M
	}




	/*
	* Perform a 4x4 matrix multiplication (product = a x b).
	* Input: a, b - matrices to multiply
	* Output: product - product of a and b
	*/
	static void
	matmul(GLdouble * product, const GLdouble * a, const GLdouble * b)
	{
	/* This matmul was contributed by Thomas Malik */
	GLdouble temp[16];
	GLint i;

	#define A(row,col) a[(col<<2)+row]
	#define B(row,col) b[(col<<2)+row]
	#define T(row,col) temp[(col<<2)+row]

	/* i-te Zeile */
	for (i = 0; i < 4; i++) {
	T(i, 0) =
	A(i, 0) * B(0, 0) + A(i, 1) * B(1, 0) + A(i, 2) * B(2, 0) + A(i,
	3) *
	B(3, 0);
	T(i, 1) =
	A(i, 0) * B(0, 1) + A(i, 1) * B(1, 1) + A(i, 2) * B(2, 1) + A(i,
	3) *
	B(3, 1);
	T(i, 2) =
	A(i, 0) * B(0, 2) + A(i, 1) * B(1, 2) + A(i, 2) * B(2, 2) + A(i,
	3) *
	B(3, 2);
	T(i, 3) =
	A(i, 0) * B(0, 3) + A(i, 1) * B(1, 3) + A(i, 2) * B(2, 3) + A(i,
	3) *
	B(3, 3);
	}

	#undef A
	#undef B
	#undef T
	MEMCPY(product, temp, 16 * sizeof(GLdouble));
	}



	/*
	* Compute inverse of 4x4 transformation matrix.
	* Code contributed by Jacques Leroy jle@star.be
	* Return GL_TRUE for success, GL_FALSE for failure (singular matrix)
	*/
	static GLboolean
	invert_matrix(const GLdouble * m, GLdouble * out)
	{
	/* NB. OpenGL Matrices are COLUMN major. */
	#define SWAP_ROWS(a, b) { GLdouble *_tmp = a; (a)=(b); (b)=_tmp; }
	#define MAT(m,r,c) (m)[(c)*4+(r)]

	GLdouble wtmp[4][8];
	GLdouble m0, m1, m2, m3, s;
	GLdouble r0, r1, r2, r3;

	r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];

	r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1),
	r0[2] = MAT(m, 0, 2), r0[3] = MAT(m, 0, 3),
	r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
	r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1),
	r1[2] = MAT(m, 1, 2), r1[3] = MAT(m, 1, 3),
	r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
	r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1),
	r2[2] = MAT(m, 2, 2), r2[3] = MAT(m, 2, 3),
	r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
	r3[0] = MAT(m, 3, 0), r3[1] = MAT(m, 3, 1),
	r3[2] = MAT(m, 3, 2), r3[3] = MAT(m, 3, 3),
	r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;

	/* choose pivot - or die */
	if (fabs(r3[0]) > fabs(r2[0]))
	SWAP_ROWS(r3, r2);
	if (fabs(r2[0]) > fabs(r1[0]))
	SWAP_ROWS(r2, r1);
	if (fabs(r1[0]) > fabs(r0[0]))
	SWAP_ROWS(r1, r0);
	if (0.0 == r0[0])
	return GL_FALSE;

	/* eliminate first variable */
	m1 = r1[0] / r0[0];
	m2 = r2[0] / r0[0];
	m3 = r3[0] / r0[0];
	s = r0[1];
	r1[1] -= m1 * s;
	r2[1] -= m2 * s;
	r3[1] -= m3 * s;
	s = r0[2];
	r1[2] -= m1 * s;
	r2[2] -= m2 * s;
	r3[2] -= m3 * s;
	s = r0[3];
	r1[3] -= m1 * s;
	r2[3] -= m2 * s;
	r3[3] -= m3 * s;
	s = r0[4];
	if (s != 0.0) {
	r1[4] -= m1 * s;
	r2[4] -= m2 * s;
	r3[4] -= m3 * s;
	}
	s = r0[5];
	if (s != 0.0) {
	r1[5] -= m1 * s;
	r2[5] -= m2 * s;
	r3[5] -= m3 * s;
	}
	s = r0[6];
	if (s != 0.0) {
	r1[6] -= m1 * s;
	r2[6] -= m2 * s;
	r3[6] -= m3 * s;
	}
	s = r0[7];
	if (s != 0.0) {
	r1[7] -= m1 * s;
	r2[7] -= m2 * s;
	r3[7] -= m3 * s;
	}

	/* choose pivot - or die */
	if (fabs(r3[1]) > fabs(r2[1]))
	SWAP_ROWS(r3, r2);
	if (fabs(r2[1]) > fabs(r1[1]))
	SWAP_ROWS(r2, r1);
	if (0.0 == r1[1])
	return GL_FALSE;

	/* eliminate second variable */
	m2 = r2[1] / r1[1];
	m3 = r3[1] / r1[1];
	r2[2] -= m2 * r1[2];
	r3[2] -= m3 * r1[2];
	r2[3] -= m2 * r1[3];
	r3[3] -= m3 * r1[3];
	s = r1[4];
	if (0.0 != s) {
	r2[4] -= m2 * s;
	r3[4] -= m3 * s;
	}
	s = r1[5];
	if (0.0 != s) {
	r2[5] -= m2 * s;
	r3[5] -= m3 * s;
	}
	s = r1[6];
	if (0.0 != s) {
	r2[6] -= m2 * s;
	r3[6] -= m3 * s;
	}
	s = r1[7];
	if (0.0 != s) {
	r2[7] -= m2 * s;
	r3[7] -= m3 * s;
	}

	/* choose pivot - or die */
	if (fabs(r3[2]) > fabs(r2[2]))
	SWAP_ROWS(r3, r2);
	if (0.0 == r2[2])
	return GL_FALSE;

	/* eliminate third variable */
	m3 = r3[2] / r2[2];
	r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
	r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7];

	/* last check */
	if (0.0 == r3[3])
	return GL_FALSE;

	s = 1.0 / r3[3]; /* now back substitute row 3 */
	r3[4] *= s;
	r3[5] *= s;
	r3[6] *= s;
	r3[7] *= s;

	m2 = r2[3]; /* now back substitute row 2 */
	s = 1.0 / r2[2];
	r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
	r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
	m1 = r1[3];
	r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
	r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
	m0 = r0[3];
	r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
	r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;

	m1 = r1[2]; /* now back substitute row 1 */
	s = 1.0 / r1[1];
	r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
	r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
	m0 = r0[2];
	r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
	r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;

	m0 = r0[1]; /* now back substitute row 0 */
	s = 1.0 / r0[0];
	r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
	r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);

	MAT(out, 0, 0) = r0[4];
	MAT(out, 0, 1) = r0[5], MAT(out, 0, 2) = r0[6];
	MAT(out, 0, 3) = r0[7], MAT(out, 1, 0) = r1[4];
	MAT(out, 1, 1) = r1[5], MAT(out, 1, 2) = r1[6];
	MAT(out, 1, 3) = r1[7], MAT(out, 2, 0) = r2[4];
	MAT(out, 2, 1) = r2[5], MAT(out, 2, 2) = r2[6];
	MAT(out, 2, 3) = r2[7], MAT(out, 3, 0) = r3[4];
	MAT(out, 3, 1) = r3[5], MAT(out, 3, 2) = r3[6];
	MAT(out, 3, 3) = r3[7];

	return GL_TRUE;

	#undef MAT
	#undef SWAP_ROWS
	}



	/* projection du point (objx,objy,obz) sur l'ecran (winx,winy,winz) */
	GLint GLAPIENTRY
	gluProject(GLdouble objx, GLdouble objy, GLdouble objz,
	const GLdouble model[16], const GLdouble proj[16],
	const GLint viewport[4],
	GLdouble * winx, GLdouble * winy, GLdouble * winz)
	{
	/* matrice de transformation */
	GLdouble in[4], out[4];

	/* initilise la matrice et le vecteur a transformer */
	in[0] = objx;
	in[1] = objy;
	in[2] = objz;
	in[3] = 1.0;
	transform_point(out, model, in);
	transform_point(in, proj, out);

	/* d'ou le resultat normalise entre -1 et 1 */
	if (in[3] == 0.0)
	return GL_FALSE;

	in[0] /= in[3];
	in[1] /= in[3];
	in[2] /= in[3];

	/* en coordonnees ecran */
	winx = viewport[0] + (1 + in[0]) viewport[2] / 2;
	winy = viewport[1] + (1 + in[1]) viewport[3] / 2;
	/* entre 0 et 1 suivant z */
	*winz = (1 + in[2]) / 2;
	return GL_TRUE;
	}



	/* transformation du point ecran (winx,winy,winz) en point objet */
	GLint GLAPIENTRY
	gluUnProject(GLdouble winx, GLdouble winy, GLdouble winz,
	const GLdouble model[16], const GLdouble proj[16],
	const GLint viewport[4],
	GLdouble * objx, GLdouble * objy, GLdouble * objz)
	{
	/* matrice de transformation */
	GLdouble m[16], A[16];
	GLdouble in[4], out[4];

	/* transformation coordonnees normalisees entre -1 et 1 */
	in[0] = (winx - viewport[0]) * 2 / viewport[2] - 1.0;
	in[1] = (winy - viewport[1]) * 2 / viewport[3] - 1.0;
	in[2] = 2 * winz - 1.0;
	in[3] = 1.0;

	/* calcul transformation inverse */
	matmul(A, proj, model);
	invert_matrix(A, m);

	/* d'ou les coordonnees objets */
	transform_point(out, m, in);
	if (out[3] == 0.0)
	return GL_FALSE;
	*objx = out[0] / out[3];
	*objy = out[1] / out[3];
	*objz = out[2] / out[3];
	return GL_TRUE;
	}


	/*
	* New in GLU 1.3
	* This is like gluUnProject but also takes near and far DepthRange values.
	*/
	#ifdef GLU_VERSION_1_3
	GLint GLAPIENTRY
	gluUnProject4(GLdouble winx, GLdouble winy, GLdouble winz, GLdouble clipw,
	const GLdouble modelMatrix[16],
	const GLdouble projMatrix[16],
	const GLint viewport[4],
	GLclampd nearZ, GLclampd farZ,
	GLdouble * objx, GLdouble * objy, GLdouble * objz,
	GLdouble * objw)
	{
	/* matrice de transformation */
	GLdouble m[16], A[16];
	GLdouble in[4], out[4];
	GLdouble z = nearZ + winz * (farZ - nearZ);

	/* transformation coordonnees normalisees entre -1 et 1 */
	in[0] = (winx - viewport[0]) * 2 / viewport[2] - 1.0;
	in[1] = (winy - viewport[1]) * 2 / viewport[3] - 1.0;
	in[2] = 2.0 * z - 1.0;
	in[3] = clipw;

	/* calcul transformation inverse */
	matmul(A, projMatrix, modelMatrix);
	invert_matrix(A, m);

	/* d'ou les coordonnees objets */
	transform_point(out, m, in);
	if (out[3] == 0.0)
	return GL_FALSE;
	*objx = out[0] / out[3];
	*objy = out[1] / out[3];
	*objz = out[2] / out[3];
	*objw = out[3];
	return GL_TRUE;
	}
	#endif