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/* $Id: project.c,v 1.4 1997/05/28 02:29:38 brianp Exp $ */
/*
* Mesa 3-D graphics library
* Version: 2.3
* Copyright (C) 1995-1997 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.
*/
/*
* $Log: project.c,v $
* Revision 1.4 1997/05/28 02:29:38 brianp
* added support for precompiled headers (PCH), inserted APIENTRY keyword
*
* Revision 1.3 1997/04/11 23:22:42 brianp
* added divide by zero checks to gluProject() and gluUnproject()
*
* Revision 1.2 1997/01/29 19:05:29 brianp
* faster invert_matrix() function from Stephane Rehel
*
* Revision 1.1 1996/09/27 01:19:39 brianp
* Initial revision
*
*/
#ifdef PCH
#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) );
}
static GLdouble Identity[16] = {
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0
};
/*
* Compute the inverse of a 4x4 matrix. Contributed by scotter@lafn.org
*/
static void invert_matrix_general( const GLdouble *m, GLdouble *out )
{
/* NB. OpenGL Matrices are COLUMN major. */
#define MAT(m,r,c) (m)[(c)*4+(r)]
/* Here's some shorthand converting standard (row,column) to index. */
#define m11 MAT(m,0,0)
#define m12 MAT(m,0,1)
#define m13 MAT(m,0,2)
#define m14 MAT(m,0,3)
#define m21 MAT(m,1,0)
#define m22 MAT(m,1,1)
#define m23 MAT(m,1,2)
#define m24 MAT(m,1,3)
#define m31 MAT(m,2,0)
#define m32 MAT(m,2,1)
#define m33 MAT(m,2,2)
#define m34 MAT(m,2,3)
#define m41 MAT(m,3,0)
#define m42 MAT(m,3,1)
#define m43 MAT(m,3,2)
#define m44 MAT(m,3,3)
GLdouble det;
GLdouble d12, d13, d23, d24, d34, d41;
GLdouble tmp[16]; /* Allow out == in. */
/* Inverse = adjoint / det. (See linear algebra texts.)*/
/* pre-compute 2x2 dets for last two rows when computing */
/* cofactors of first two rows. */
d12 = (m31*m42-m41*m32);
d13 = (m31*m43-m41*m33);
d23 = (m32*m43-m42*m33);
d24 = (m32*m44-m42*m34);
d34 = (m33*m44-m43*m34);
d41 = (m34*m41-m44*m31);
tmp[0] = (m22 * d34 - m23 * d24 + m24 * d23);
tmp[1] = -(m21 * d34 + m23 * d41 + m24 * d13);
tmp[2] = (m21 * d24 + m22 * d41 + m24 * d12);
tmp[3] = -(m21 * d23 - m22 * d13 + m23 * d12);
/* Compute determinant as early as possible using these cofactors. */
det = m11 * tmp[0] + m12 * tmp[1] + m13 * tmp[2] + m14 * tmp[3];
/* Run singularity test. */
if (det == 0.0) {
/* printf("invert_matrix: Warning: Singular matrix.\n"); */
MEMCPY( out, Identity, 16*sizeof(GLdouble) );
}
else {
GLdouble invDet = 1.0 / det;
/* Compute rest of inverse. */
tmp[0] *= invDet;
tmp[1] *= invDet;
tmp[2] *= invDet;
tmp[3] *= invDet;
tmp[4] = -(m12 * d34 - m13 * d24 + m14 * d23) * invDet;
tmp[5] = (m11 * d34 + m13 * d41 + m14 * d13) * invDet;
tmp[6] = -(m11 * d24 + m12 * d41 + m14 * d12) * invDet;
tmp[7] = (m11 * d23 - m12 * d13 + m13 * d12) * invDet;
/* Pre-compute 2x2 dets for first two rows when computing */
/* cofactors of last two rows. */
d12 = m11*m22-m21*m12;
d13 = m11*m23-m21*m13;
d23 = m12*m23-m22*m13;
d24 = m12*m24-m22*m14;
d34 = m13*m24-m23*m14;
d41 = m14*m21-m24*m11;
tmp[8] = (m42 * d34 - m43 * d24 + m44 * d23) * invDet;
tmp[9] = -(m41 * d34 + m43 * d41 + m44 * d13) * invDet;
tmp[10] = (m41 * d24 + m42 * d41 + m44 * d12) * invDet;
tmp[11] = -(m41 * d23 - m42 * d13 + m43 * d12) * invDet;
tmp[12] = -(m32 * d34 - m33 * d24 + m34 * d23) * invDet;
tmp[13] = (m31 * d34 + m33 * d41 + m34 * d13) * invDet;
tmp[14] = -(m31 * d24 + m32 * d41 + m34 * d12) * invDet;
tmp[15] = (m31 * d23 - m32 * d13 + m33 * d12) * invDet;
MEMCPY(out, tmp, 16*sizeof(GLdouble));
}
#undef m11
#undef m12
#undef m13
#undef m14
#undef m21
#undef m22
#undef m23
#undef m24
#undef m31
#undef m32
#undef m33
#undef m34
#undef m41
#undef m42
#undef m43
#undef m44
#undef MAT
}
/*
* Invert matrix m. This algorithm contributed by Stephane Rehel
* <rehel@worldnet.fr>
*/
static void invert_matrix( const GLdouble *m, GLdouble *out )
{
/* NB. OpenGL Matrices are COLUMN major. */
#define MAT(m,r,c) (m)[(c)*4+(r)]
/* Here's some shorthand converting standard (row,column) to index. */
#define m11 MAT(m,0,0)
#define m12 MAT(m,0,1)
#define m13 MAT(m,0,2)
#define m14 MAT(m,0,3)
#define m21 MAT(m,1,0)
#define m22 MAT(m,1,1)
#define m23 MAT(m,1,2)
#define m24 MAT(m,1,3)
#define m31 MAT(m,2,0)
#define m32 MAT(m,2,1)
#define m33 MAT(m,2,2)
#define m34 MAT(m,2,3)
#define m41 MAT(m,3,0)
#define m42 MAT(m,3,1)
#define m43 MAT(m,3,2)
#define m44 MAT(m,3,3)
register GLdouble det;
GLdouble tmp[16]; /* Allow out == in. */
if( m41 != 0. || m42 != 0. || m43 != 0. || m44 != 1. ) {
invert_matrix_general(m, out);
return;
}
/* Inverse = adjoint / det. (See linear algebra texts.)*/
tmp[0]= m22 * m33 - m23 * m32;
tmp[1]= m23 * m31 - m21 * m33;
tmp[2]= m21 * m32 - m22 * m31;
/* Compute determinant as early as possible using these cofactors. */
det= m11 * tmp[0] + m12 * tmp[1] + m13 * tmp[2];
/* Run singularity test. */
if (det == 0.0) {
/* printf("invert_matrix: Warning: Singular matrix.\n"); */
MEMCPY( out, Identity, 16*sizeof(GLdouble) );
}
else {
GLdouble d12, d13, d23, d24, d34, d41;
register GLdouble im11, im12, im13, im14;
det= 1. / det;
/* Compute rest of inverse. */
tmp[0] *= det;
tmp[1] *= det;
tmp[2] *= det;
tmp[3] = 0.;
im11= m11 * det;
im12= m12 * det;
im13= m13 * det;
im14= m14 * det;
tmp[4] = im13 * m32 - im12 * m33;
tmp[5] = im11 * m33 - im13 * m31;
tmp[6] = im12 * m31 - im11 * m32;
tmp[7] = 0.;
/* Pre-compute 2x2 dets for first two rows when computing */
/* cofactors of last two rows. */
d12 = im11*m22 - m21*im12;
d13 = im11*m23 - m21*im13;
d23 = im12*m23 - m22*im13;
d24 = im12*m24 - m22*im14;
d34 = im13*m24 - m23*im14;
d41 = im14*m21 - m24*im11;
tmp[8] = d23;
tmp[9] = -d13;
tmp[10] = d12;
tmp[11] = 0.;
tmp[12] = -(m32 * d34 - m33 * d24 + m34 * d23);
tmp[13] = (m31 * d34 + m33 * d41 + m34 * d13);
tmp[14] = -(m31 * d24 + m32 * d41 + m34 * d12);
tmp[15] = 1.;
MEMCPY(out, tmp, 16*sizeof(GLdouble));
}
#undef m11
#undef m12
#undef m13
#undef m14
#undef m21
#undef m22
#undef m23
#undef m24
#undef m31
#undef m32
#undef m33
#undef m34
#undef m41
#undef m42
#undef m43
#undef m44
#undef MAT
}
/* projection du point (objx,objy,obz) sur l'ecran (winx,winy,winz) */
GLint APIENTRY 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 APIENTRY 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;
}
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.