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/************************************************************************
4x4 Matrix class
$Id: mat4.cxx 427 2004-09-27 04:45:31Z garland $
************************************************************************/
#include <gfx/gfx.h>
#include <gfx/mat4.h>
namespace gfx
{
Mat4 Mat4::I()
{
return Mat4(Vec4(1,0,0,0),Vec4(0,1,0,0),Vec4(0,0,1,0),Vec4(0,0,0,1));
}
Mat4 translation_matrix(const Vec3& d)
{
return Mat4(Vec4(1, 0, 0, d[0]),
Vec4(0, 1, 0, d[1]),
Vec4(0, 0, 1, d[2]),
Vec4(0, 0, 0, 1));
}
Mat4 scaling_matrix(const Vec3& s)
{
return Mat4(Vec4(s[0], 0, 0, 0),
Vec4(0, s[1], 0, 0),
Vec4(0, 0, s[2], 0),
Vec4(0, 0, 0, 1));
}
Mat4 rotation_matrix_rad(double theta, const Vec3& axis)
{
double c=cos(theta), s=sin(theta),
xx=axis[0]*axis[0], yy=axis[1]*axis[1], zz=axis[2]*axis[2],
xy=axis[0]*axis[1], yz=axis[1]*axis[2], xz=axis[0]*axis[2];
double xs=axis[0]*s, ys=axis[1]*s, zs=axis[2]*s;
Mat4 M;
M(0,0)=xx*(1-c)+c; M(0,1)=xy*(1-c)-zs; M(0,2)=xz*(1-c)+ys; M(0,3) = 0;
M(1,0)=xy*(1-c)+zs; M(1,1)=yy*(1-c)+c; M(1,2)=yz*(1-c)-xs; M(1,3)=0;
M(2,0)=xz*(1-c)-ys; M(2,1)=yz*(1-c)+xs; M(2,2)=zz*(1-c)+c; M(2,3)=0;
M(3,0)=0; M(3,1)=0; M(3,2)=0; M(3,3)=1;
return M;
}
Mat4 perspective_matrix(double fovy, double aspect, double zmin, double zmax)
{
double A, B;
Mat4 M;
if( zmax==0.0 )
{
A = B = 1.0;
}
else
{
A = (zmax+zmin)/(zmin-zmax);
B = (2*zmax*zmin)/(zmin-zmax);
}
double f = 1.0/tan(fovy*M_PI/180.0/2.0);
M(0,0) = f/aspect;
M(1,1) = f;
M(2,2) = A;
M(2,3) = B;
M(3,2) = -1;
M(3,3) = 0;
return M;
}
Mat4 lookat_matrix(const Vec3& from, const Vec3& at, const Vec3& v_up)
{
Vec3 up = v_up; unitize(up);
Vec3 f = at - from; unitize(f);
Vec3 s=f^up;
Vec3 u=s^f;
// NOTE: These steps are left out of the GL man page!!
unitize(s);
unitize(u);
Mat4 M(Vec4(s, 0), Vec4(u, 0), Vec4(-f, 0), Vec4(0, 0, 0, 1));
return M * translation_matrix(-from);
}
Mat4 viewport_matrix(double w, double h)
{
return scaling_matrix(Vec3(w/2.0, -h/2.0, 1)) *
translation_matrix(Vec3(1, -1, 0));
}
Mat4 operator*(const Mat4& n, const Mat4& m)
{
Mat4 A;
int i,j;
for(i=0;i<4;i++)
for(j=0;j<4;j++)
A(i,j) = n[i]*m.col(j);
return A;
}
Mat4 adjoint(const Mat4& m)
{
Mat4 A;
A[0] = cross( m[1], m[2], m[3]);
A[1] = cross(-m[0], m[2], m[3]);
A[2] = cross( m[0], m[1], m[3]);
A[3] = cross(-m[0], m[1], m[2]);
return A;
}
double invert_cramer(Mat4& inv, const Mat4& m)
{
Mat4 A = adjoint(m);
double d = A[0] * m[0];
if( d==0.0 )
return 0.0;
inv = transpose(A) / d;
return d;
}
// Matrix inversion code for 4x4 matrices using Gaussian elimination
// with partial pivoting. This is a specialized version of a
// procedure originally due to Paul Heckbert <[email protected]>.
//
// Returns determinant of A, and B=inverse(A)
// If matrix A is singular, returns 0 and leaves trash in B.
//
#define SWAP(a, b, t) {t = a; a = b; b = t;}
double invert(Mat4& B, const Mat4& m)
{
Mat4 A = m;
int i, j, k;
double max, t, det, pivot;
/*---------- forward elimination ----------*/
for (i=0; i<4; i++) /* put identity matrix in B */
for (j=0; j<4; j++)
B(i, j) = (double)(i==j);
det = 1.0;
for (i=0; i<4; i++) { /* eliminate in column i, below diag */
max = -1.;
for (k=i; k<4; k++) /* find pivot for column i */
if (fabs(A(k, i)) > max) {
max = fabs(A(k, i));
j = k;
}
if (max<=0.) return 0.; /* if no nonzero pivot, PUNT */
if (j!=i) { /* swap rows i and j */
for (k=i; k<4; k++)
SWAP(A(i, k), A(j, k), t);
for (k=0; k<4; k++)
SWAP(B(i, k), B(j, k), t);
det = -det;
}
pivot = A(i, i);
det *= pivot;
for (k=i+1; k<4; k++) /* only do elems to right of pivot */
A(i, k) /= pivot;
for (k=0; k<4; k++)
B(i, k) /= pivot;
/* we know that A(i, i) will be set to 1, so don't bother to do it */
for (j=i+1; j<4; j++) { /* eliminate in rows below i */
t = A(j, i); /* we're gonna zero this guy */
for (k=i+1; k<4; k++) /* subtract scaled row i from row j */
A(j, k) -= A(i, k)*t; /* (ignore k<=i, we know they're 0) */
for (k=0; k<4; k++)
B(j, k) -= B(i, k)*t;
}
}
/*---------- backward elimination ----------*/
for (i=4-1; i>0; i--) { /* eliminate in column i, above diag */
for (j=0; j<i; j++) { /* eliminate in rows above i */
t = A(j, i); /* we're gonna zero this guy */
for (k=0; k<4; k++) /* subtract scaled row i from row j */
B(j, k) -= B(i, k)*t;
}
}
return det;
}
} // namespace gfx
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