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/*
Matrix Inversion
by Richard Carling
from "Graphics Gems", Academic Press, 1990
*/
#define SMALL_NUMBER 1.e-8
/*
* inverse( original_matrix, inverse_matrix )
*
* calculate the inverse of a 4x4 matrix
*
* -1
* A = ___1__ adjoint A
* det A
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
typedef float Matrix4[4][4];
static void adjoint(Matrix4 in, Matrix4 out);
static float det4x4(Matrix4 m);
static float det3x3(float a1, float a2, float a3,
float b1, float b2, float b3,
float c1, float c2, float c3 );
static float det2x2( float a, float b, float c, float d);
void mat4Inverse( Matrix4 dst, Matrix4 src )
{
int i, j;
float det;
/* calculate the adjoint matrix */
adjoint( src, dst );
/* calculate the 4x4 determinent
* if the determinent is zero,
* then the inverse matrix is not unique.
*/
det = det4x4( src );
if ( fabs( det ) < SMALL_NUMBER) {
printf("Non-singular matrix, no inverse!\n");
exit(12);
}
/* scale the adjoint matrix to get the inverse */
for (i=0; i<4; i++)
for(j=0; j<4; j++)
dst[i][j] = dst[i][j] / det;
}
/*
* adjoint( original_matrix, inverse_matrix )
*
* calculate the adjoint of a 4x4 matrix
*
* Let a denote the minor determinant of matrix A obtained by
* ij
*
* deleting the ith row and jth column from A.
*
* i+j
* Let b = (-1) a
* ij ji
*
* The matrix B = (b ) is the adjoint of A
* ij
*/
static void adjoint( Matrix4 in, Matrix4 out )
{
float a1, a2, a3, a4, b1, b2, b3, b4;
float c1, c2, c3, c4, d1, d2, d3, d4;
/* assign to individual variable names to aid */
/* selecting correct values */
a1 = in[0][0]; b1 = in[0][1];
c1 = in[0][2]; d1 = in[0][3];
a2 = in[1][0]; b2 = in[1][1];
c2 = in[1][2]; d2 = in[1][3];
a3 = in[2][0]; b3 = in[2][1];
c3 = in[2][2]; d3 = in[2][3];
a4 = in[3][0]; b4 = in[3][1];
c4 = in[3][2]; d4 = in[3][3];
/* row column labeling reversed since we transpose rows & columns */
out[0][0] = det3x3( b2, b3, b4, c2, c3, c4, d2, d3, d4);
out[1][0] = - det3x3( a2, a3, a4, c2, c3, c4, d2, d3, d4);
out[2][0] = det3x3( a2, a3, a4, b2, b3, b4, d2, d3, d4);
out[3][0] = - det3x3( a2, a3, a4, b2, b3, b4, c2, c3, c4);
out[0][1] = - det3x3( b1, b3, b4, c1, c3, c4, d1, d3, d4);
out[1][1] = det3x3( a1, a3, a4, c1, c3, c4, d1, d3, d4);
out[2][1] = - det3x3( a1, a3, a4, b1, b3, b4, d1, d3, d4);
out[3][1] = det3x3( a1, a3, a4, b1, b3, b4, c1, c3, c4);
out[0][2] = det3x3( b1, b2, b4, c1, c2, c4, d1, d2, d4);
out[1][2] = - det3x3( a1, a2, a4, c1, c2, c4, d1, d2, d4);
out[2][2] = det3x3( a1, a2, a4, b1, b2, b4, d1, d2, d4);
out[3][2] = - det3x3( a1, a2, a4, b1, b2, b4, c1, c2, c4);
out[0][3] = - det3x3( b1, b2, b3, c1, c2, c3, d1, d2, d3);
out[1][3] = det3x3( a1, a2, a3, c1, c2, c3, d1, d2, d3);
out[2][3] = - det3x3( a1, a2, a3, b1, b2, b3, d1, d2, d3);
out[3][3] = det3x3( a1, a2, a3, b1, b2, b3, c1, c2, c3);
}
/*
* float = det4x4( matrix )
*
* calculate the determinent of a 4x4 matrix.
*/
static float det4x4( Matrix4 m )
{
float ans;
float a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4, d1, d2, d3, d4;
/* assign to individual variable names to aid selecting */
/* correct elements */
a1 = m[0][0]; b1 = m[0][1];
c1 = m[0][2]; d1 = m[0][3];
a2 = m[1][0]; b2 = m[1][1];
c2 = m[1][2]; d2 = m[1][3];
a3 = m[2][0]; b3 = m[2][1];
c3 = m[2][2]; d3 = m[2][3];
a4 = m[3][0]; b4 = m[3][1];
c4 = m[3][2]; d4 = m[3][3];
ans = 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);
return ans;
}
/*
* float = det3x3( a1, a2, a3, b1, b2, b3, c1, c2, c3 )
*
* calculate the determinent of a 3x3 matrix
* in the form
*
* | a1, b1, c1 |
* | a2, b2, c2 |
* | a3, b3, c3 |
*/
static float det3x3( float a1, float a2, float a3,
float b1, float b2, float b3,
float c1, float c2, float c3 )
{
float ans;
ans = a1 * det2x2( b2, b3, c2, c3 )
- b1 * det2x2( a2, a3, c2, c3 )
+ c1 * det2x2( a2, a3, b2, b3 );
return ans;
}
/*
* float = det2x2( float a, float b, float c, float d )
*
* calculate the determinent of a 2x2 matrix.
*/
static float det2x2( float a, float b, float c, float d)
{
float ans;
ans = a * d - b * c;
return ans;
}
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