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/*
* The 3D Studio File Format Library
* Copyright (C) 1996-2001 by J.E. Hoffmann <je-h@gmx.net>
* All rights reserved.
*
* This program is free software; you can redistribute it and/or modify it
* under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or (at
* your option) any later version.
*
* This program 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 Lesser General Public
* License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*
* $Id: matrix.c,v 1.10 2004/11/16 07:41:44 efalk Exp $
*/
#define LIB3DS_EXPORT
#include <lib3ds/matrix.h>
#include <lib3ds/quat.h>
#include <lib3ds/vector.h>
#include <string.h>
#include <math.h>
/*!
* \defgroup matrix Matrix Mathematics
*
* \author J.E. Hoffmann <je-h@gmx.net>
*/
/*!
* \typedef Lib3dsMatrix
* \ingroup matrix
*/
/*!
* Clear a matrix to all zeros.
*
* \param m Matrix to be cleared.
*
* \ingroup matrix
*/
void
lib3ds_matrix_zero(Lib3dsMatrix m)
{
int i,j;
for (i=0; i<4; i++) {
for (j=0; j<4; j++) m[i][j]=0.0f;
}
}
/*!
* Set a matrix to identity.
*
* \param m Matrix to be set.
*
* \ingroup matrix
*/
void
lib3ds_matrix_identity(Lib3dsMatrix m)
{
int i,j;
for (i=0; i<4; i++) {
for (j=0; j<4; j++) m[i][j]=0.0;
}
for (i=0; i<4; i++) m[i][i]=1.0;
}
/*!
* Copy a matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_copy(Lib3dsMatrix dest, Lib3dsMatrix src)
{
memcpy(dest, src, sizeof(Lib3dsMatrix));
}
/*!
* Negate a matrix -- all elements negated.
*
* \ingroup matrix
*/
void
lib3ds_matrix_neg(Lib3dsMatrix m)
{
int i,j;
for (j=0; j<4; j++) {
for (i=0; i<4; i++) {
m[j][i]=-m[j][i];
}
}
}
/*!
* Set all matrix elements to their absolute value.
*
* \ingroup matrix
*/
void
lib3ds_matrix_abs(Lib3dsMatrix m)
{
int i,j;
for (j=0; j<4; j++) {
for (i=0; i<4; i++) {
m[j][i]=(Lib3dsFloat)fabs(m[j][i]);
}
}
}
/*!
* Transpose a matrix in place.
*
* \ingroup matrix
*/
void
lib3ds_matrix_transpose(Lib3dsMatrix m)
{
int i,j;
Lib3dsFloat swp;
for (j=0; j<4; j++) {
for (i=j+1; i<4; i++) {
swp=m[j][i];
m[j][i]=m[i][j];
m[i][j]=swp;
}
}
}
/*!
* Add two matrices.
*
* \ingroup matrix
*/
void
lib3ds_matrix_add(Lib3dsMatrix m, Lib3dsMatrix a, Lib3dsMatrix b)
{
int i,j;
for (j=0; j<4; j++) {
for (i=0; i<4; i++) {
m[j][i]=a[j][i]+b[j][i];
}
}
}
/*!
* Subtract two matrices.
*
* \param m Result.
* \param a Addend.
* \param b Minuend.
*
* \ingroup matrix
*/
void
lib3ds_matrix_sub(Lib3dsMatrix m, Lib3dsMatrix a, Lib3dsMatrix b)
{
int i,j;
for (j=0; j<4; j++) {
for (i=0; i<4; i++) {
m[j][i]=a[j][i]-b[j][i];
}
}
}
/*!
* Multiply two matrices.
*
* \param m Result.
* \param a Left matrix.
* \param b Right matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_mul(Lib3dsMatrix m, Lib3dsMatrix a, Lib3dsMatrix b)
{
int i,j,k;
Lib3dsFloat ab;
for (j=0; j<4; j++) {
for (i=0; i<4; i++) {
ab=0.0f;
for (k=0; k<4; k++) ab+=a[k][i]*b[j][k];
m[j][i]=ab;
}
}
}
/*!
* Multiply a matrix by a scalar.
*
* \param m Matrix to be set.
* \param k Scalar.
*
* \ingroup matrix
*/
void
lib3ds_matrix_scalar(Lib3dsMatrix m, Lib3dsFloat k)
{
int i,j;
for (j=0; j<4; j++) {
for (i=0; i<4; i++) {
m[j][i]*=k;
}
}
}
static Lib3dsFloat
det2x2(
Lib3dsFloat a, Lib3dsFloat b,
Lib3dsFloat c, Lib3dsFloat d)
{
return((a)*(d)-(b)*(c));
}
static Lib3dsFloat
det3x3(
Lib3dsFloat a1, Lib3dsFloat a2, Lib3dsFloat a3,
Lib3dsFloat b1, Lib3dsFloat b2, Lib3dsFloat b3,
Lib3dsFloat c1, Lib3dsFloat c2, Lib3dsFloat c3)
{
return(
a1*det2x2(b2,b3,c2,c3)-
b1*det2x2(a2,a3,c2,c3)+
c1*det2x2(a2,a3,b2,b3)
);
}
/*!
* Find determinant of a matrix.
*
* \ingroup matrix
*/
Lib3dsFloat
lib3ds_matrix_det(Lib3dsMatrix m)
{
Lib3dsFloat a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4,d1,d2,d3,d4;
a1 = m[0][0];
b1 = m[1][0];
c1 = m[2][0];
d1 = m[3][0];
a2 = m[0][1];
b2 = m[1][1];
c2 = m[2][1];
d2 = m[3][1];
a3 = m[0][2];
b3 = m[1][2];
c3 = m[2][2];
d3 = m[3][2];
a4 = m[0][3];
b4 = m[1][3];
c4 = m[2][3];
d4 = m[3][3];
return(
a1 * det3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4)-
b1 * det3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4)+
c1 * det3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4)-
d1 * det3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4)
);
}
/*!
* Find the adjoint of a matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_adjoint(Lib3dsMatrix m)
{
Lib3dsFloat a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4,d1,d2,d3,d4;
a1 = m[0][0];
b1 = m[1][0];
c1 = m[2][0];
d1 = m[3][0];
a2 = m[0][1];
b2 = m[1][1];
c2 = m[2][1];
d2 = m[3][1];
a3 = m[0][2];
b3 = m[1][2];
c3 = m[2][2];
d3 = m[3][2];
a4 = m[0][3];
b4 = m[1][3];
c4 = m[2][3];
d4 = m[3][3];
m[0][0]= det3x3 (b2, b3, b4, c2, c3, c4, d2, d3, d4);
m[0][1]= -det3x3 (a2, a3, a4, c2, c3, c4, d2, d3, d4);
m[0][2]= det3x3 (a2, a3, a4, b2, b3, b4, d2, d3, d4);
m[0][3]= -det3x3 (a2, a3, a4, b2, b3, b4, c2, c3, c4);
m[1][0]= -det3x3 (b1, b3, b4, c1, c3, c4, d1, d3, d4);
m[1][1]= det3x3 (a1, a3, a4, c1, c3, c4, d1, d3, d4);
m[1][2]= -det3x3 (a1, a3, a4, b1, b3, b4, d1, d3, d4);
m[1][3]= det3x3 (a1, a3, a4, b1, b3, b4, c1, c3, c4);
m[2][0]= det3x3 (b1, b2, b4, c1, c2, c4, d1, d2, d4);
m[2][1]= -det3x3 (a1, a2, a4, c1, c2, c4, d1, d2, d4);
m[2][2]= det3x3 (a1, a2, a4, b1, b2, b4, d1, d2, d4);
m[2][3]= -det3x3 (a1, a2, a4, b1, b2, b4, c1, c2, c4);
m[3][0]= -det3x3 (b1, b2, b3, c1, c2, c3, d1, d2, d3);
m[3][1]= det3x3 (a1, a2, a3, c1, c2, c3, d1, d2, d3);
m[3][2]= -det3x3 (a1, a2, a3, b1, b2, b3, d1, d2, d3);
m[3][3]= det3x3 (a1, a2, a3, b1, b2, b3, c1, c2, c3);
}
/*!
* Invert a matrix in place.
*
* \param m Matrix to invert.
*
* \return LIB3DS_TRUE on success, LIB3DS_FALSE on failure.
* \ingroup matrix
*
* GGemsII, K.Wu, Fast Matrix Inversion
*/
Lib3dsBool
lib3ds_matrix_inv(Lib3dsMatrix m)
{
int i,j,k;
int pvt_i[4], pvt_j[4]; /* Locations of pivot elements */
Lib3dsFloat pvt_val; /* Value of current pivot element */
Lib3dsFloat hold; /* Temporary storage */
Lib3dsFloat determinat;
determinat = 1.0f;
for (k=0; k<4; k++) {
/* Locate k'th pivot element */
pvt_val=m[k][k]; /* Initialize for search */
pvt_i[k]=k;
pvt_j[k]=k;
for (i=k; i<4; i++) {
for (j=k; j<4; j++) {
if (fabs(m[i][j]) > fabs(pvt_val)) {
pvt_i[k]=i;
pvt_j[k]=j;
pvt_val=m[i][j];
}
}
}
/* Product of pivots, gives determinant when finished */
determinat*=pvt_val;
if (fabs(determinat)<LIB3DS_EPSILON) {
return(LIB3DS_FALSE); /* Matrix is singular (zero determinant) */
}
/* "Interchange" rows (with sign change stuff) */
i=pvt_i[k];
if (i!=k) { /* If rows are different */
for (j=0; j<4; j++) {
hold=-m[k][j];
m[k][j]=m[i][j];
m[i][j]=hold;
}
}
/* "Interchange" columns */
j=pvt_j[k];
if (j!=k) { /* If columns are different */
for (i=0; i<4; i++) {
hold=-m[i][k];
m[i][k]=m[i][j];
m[i][j]=hold;
}
}
/* Divide column by minus pivot value */
for (i=0; i<4; i++) {
if (i!=k) m[i][k]/=( -pvt_val) ;
}
/* Reduce the matrix */
for (i=0; i<4; i++) {
hold = m[i][k];
for (j=0; j<4; j++) {
if (i!=k && j!=k) m[i][j]+=hold*m[k][j];
}
}
/* Divide row by pivot */
for (j=0; j<4; j++) {
if (j!=k) m[k][j]/=pvt_val;
}
/* Replace pivot by reciprocal (at last we can touch it). */
m[k][k] = 1.0f/pvt_val;
}
/* That was most of the work, one final pass of row/column interchange */
/* to finish */
for (k=4-2; k>=0; k--) { /* Don't need to work with 1 by 1 corner*/
i=pvt_j[k]; /* Rows to swap correspond to pivot COLUMN */
if (i!=k) { /* If rows are different */
for(j=0; j<4; j++) {
hold = m[k][j];
m[k][j]=-m[i][j];
m[i][j]=hold;
}
}
j=pvt_i[k]; /* Columns to swap correspond to pivot ROW */
if (j!=k) /* If columns are different */
for (i=0; i<4; i++) {
hold=m[i][k];
m[i][k]=-m[i][j];
m[i][j]=hold;
}
}
return(LIB3DS_TRUE);
}
/*!
* Apply a translation to a matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_translate_xyz(Lib3dsMatrix m, Lib3dsFloat x, Lib3dsFloat y, Lib3dsFloat z)
{
int i;
for (i=0; i<3; i++) {
m[3][i]+= m[0][i]*x + m[1][i]*y + m[2][i]*z;
}
}
/*!
* Apply a translation to a matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_translate(Lib3dsMatrix m, Lib3dsVector t)
{
int i;
for (i=0; i<3; i++) {
m[3][i]+= m[0][i]*t[0] + m[1][i]*t[1] + m[2][i]*t[2];
}
}
/*!
* Apply scale factors to a matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_scale_xyz(Lib3dsMatrix m, Lib3dsFloat x, Lib3dsFloat y, Lib3dsFloat z)
{
int i;
for (i=0; i<4; i++) {
m[0][i]*=x;
m[1][i]*=y;
m[2][i]*=z;
}
}
/*!
* Apply scale factors to a matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_scale(Lib3dsMatrix m, Lib3dsVector s)
{
int i;
for (i=0; i<4; i++) {
m[0][i]*=s[0];
m[1][i]*=s[1];
m[2][i]*=s[2];
}
}
/*!
* Apply a rotation about the x axis to a matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_rotate_x(Lib3dsMatrix m, Lib3dsFloat phi)
{
Lib3dsFloat SinPhi,CosPhi;
Lib3dsFloat a1[4],a2[4];
SinPhi=(Lib3dsFloat)sin(phi);
CosPhi=(Lib3dsFloat)cos(phi);
memcpy(a1,m[1],4*sizeof(Lib3dsFloat));
memcpy(a2,m[2],4*sizeof(Lib3dsFloat));
m[1][0]=CosPhi*a1[0]+SinPhi*a2[0];
m[1][1]=CosPhi*a1[1]+SinPhi*a2[1];
m[1][2]=CosPhi*a1[2]+SinPhi*a2[2];
m[1][3]=CosPhi*a1[3]+SinPhi*a2[3];
m[2][0]=-SinPhi*a1[0]+CosPhi*a2[0];
m[2][1]=-SinPhi*a1[1]+CosPhi*a2[1];
m[2][2]=-SinPhi*a1[2]+CosPhi*a2[2];
m[2][3]=-SinPhi*a1[3]+CosPhi*a2[3];
}
/*!
* Apply a rotation about the y axis to a matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_rotate_y(Lib3dsMatrix m, Lib3dsFloat phi)
{
Lib3dsFloat SinPhi,CosPhi;
Lib3dsFloat a0[4],a2[4];
SinPhi=(Lib3dsFloat)sin(phi);
CosPhi=(Lib3dsFloat)cos(phi);
memcpy(a0,m[0],4*sizeof(Lib3dsFloat));
memcpy(a2,m[2],4*sizeof(Lib3dsFloat));
m[0][0]=CosPhi*a0[0]-SinPhi*a2[0];
m[0][1]=CosPhi*a0[1]-SinPhi*a2[1];
m[0][2]=CosPhi*a0[2]-SinPhi*a2[2];
m[0][3]=CosPhi*a0[3]-SinPhi*a2[3];
m[2][0]=SinPhi*a0[0]+CosPhi*a2[0];
m[2][1]=SinPhi*a0[1]+CosPhi*a2[1];
m[2][2]=SinPhi*a0[2]+CosPhi*a2[2];
m[2][3]=SinPhi*a0[3]+CosPhi*a2[3];
}
/*!
* Apply a rotation about the z axis to a matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_rotate_z(Lib3dsMatrix m, Lib3dsFloat phi)
{
Lib3dsFloat SinPhi,CosPhi;
Lib3dsFloat a0[4],a1[4];
SinPhi=(Lib3dsFloat)sin(phi);
CosPhi=(Lib3dsFloat)cos(phi);
memcpy(a0,m[0],4*sizeof(Lib3dsFloat));
memcpy(a1,m[1],4*sizeof(Lib3dsFloat));
m[0][0]=CosPhi*a0[0]+SinPhi*a1[0];
m[0][1]=CosPhi*a0[1]+SinPhi*a1[1];
m[0][2]=CosPhi*a0[2]+SinPhi*a1[2];
m[0][3]=CosPhi*a0[3]+SinPhi*a1[3];
m[1][0]=-SinPhi*a0[0]+CosPhi*a1[0];
m[1][1]=-SinPhi*a0[1]+CosPhi*a1[1];
m[1][2]=-SinPhi*a0[2]+CosPhi*a1[2];
m[1][3]=-SinPhi*a0[3]+CosPhi*a1[3];
}
/*!
* Apply a rotation about an arbitrary axis to a matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_rotate(Lib3dsMatrix m, Lib3dsQuat q)
{
Lib3dsFloat s,xs,ys,zs,wx,wy,wz,xx,xy,xz,yy,yz,zz,l;
Lib3dsMatrix a,b;
lib3ds_matrix_copy(a, m);
l=q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3];
if (fabs(l)<LIB3DS_EPSILON) {
s=1.0f;
}
else {
s=2.0f/l;
}
xs = q[0] * s; ys = q[1] * s; zs = q[2] * s;
wx = q[3] * xs; wy = q[3] * ys; wz = q[3] * zs;
xx = q[0] * xs; xy = q[0] * ys; xz = q[0] * zs;
yy = q[1] * ys; yz = q[1] * zs; zz = q[2] * zs;
b[0][0]=1.0f - (yy +zz);
b[1][0]=xy - wz;
b[2][0]=xz + wy;
b[0][1]=xy + wz;
b[1][1]=1.0f - (xx +zz);
b[2][1]=yz - wx;
b[0][2]=xz - wy;
b[1][2]=yz + wx;
b[2][2]=1.0f - (xx + yy);
b[3][0]=b[3][1]=b[3][2]=b[0][3]=b[1][3]=b[2][3]=0.0f;
b[3][3]=1.0f;
lib3ds_matrix_mul(m,a,b);
}
/*!
* Apply a rotation about an arbitrary axis to a matrix.
*
* \ingroup matrix
*/
void
lib3ds_matrix_rotate_axis(Lib3dsMatrix m, Lib3dsVector axis, Lib3dsFloat angle)
{
Lib3dsQuat q;
lib3ds_quat_axis_angle(q,axis,angle);
lib3ds_matrix_rotate(m,q);
}
/*!
* Compute a camera matrix based on position, target and roll.
*
* Generates a translate/rotate matrix that maps world coordinates
* to camera coordinates. Resulting matrix does not include perspective
* transform.
*
* \param matrix Destination matrix.
* \param pos Camera position
* \param tgt Camera target
* \param roll Roll angle
*
* \ingroup matrix
*/
void
lib3ds_matrix_camera(Lib3dsMatrix matrix, Lib3dsVector pos,
Lib3dsVector tgt, Lib3dsFloat roll)
{
Lib3dsMatrix M,R;
Lib3dsVector x, y, z;
lib3ds_vector_sub(y, tgt, pos);
lib3ds_vector_normalize(y);
if (y[0] != 0. || y[1] != 0) {
z[0] = 0;
z[1] = 0;
z[2] = 1.0;
}
else { /* Special case: looking straight up or down z axis */
z[0] = -1.0;
z[1] = 0;
z[2] = 0;
}
lib3ds_vector_cross(x, y, z);
lib3ds_vector_cross(z, x, y);
lib3ds_vector_normalize(x);
lib3ds_vector_normalize(z);
lib3ds_matrix_identity(M);
M[0][0] = x[0];
M[1][0] = x[1];
M[2][0] = x[2];
M[0][1] = y[0];
M[1][1] = y[1];
M[2][1] = y[2];
M[0][2] = z[0];
M[1][2] = z[1];
M[2][2] = z[2];
lib3ds_matrix_identity(R);
lib3ds_matrix_rotate_y(R, roll);
lib3ds_matrix_mul(matrix, R,M);
lib3ds_matrix_translate_xyz(matrix, -pos[0],-pos[1],-pos[2]);
}
/*!
* \ingroup matrix
*/
void
lib3ds_matrix_dump(Lib3dsMatrix matrix)
{
int i,j;
for (i=0; i<4; ++i) {
for (j=0; j<4; ++j) {
printf("%f ", matrix[j][i]);
}
printf("\n");
}
}
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