void RayCaster::Compute(const Matrix<3,4>& camera, const Vec4& plane) {
Mat4 M;
M.slice<0, 0, 3, 4> () = camera;
M.slice<3, 0, 1, 4> () = plane.as_row();
svd.compute(M);
double du = 1. / (camera[2] * atretina(svd.backsub(makeVector(1,0,1,0))));
double dv = 1. / (camera[2] * atretina(svd.backsub(makeVector(0,1,1,0))));
double dw = 1. / (camera[2] * atretina(svd.backsub(makeVector(0,0,1,0))));
depth_eqn = makeVector(du-dw, dv-dw, dw);
}
// Intersect a ray from pixel
Vec4 IntersectRay(const Vec3& pixel, const Matrix<3, 4>& camera, const Vec4& plane) {
// Solve for x:
// x*w = 0 { w is the plane normal }
// C*x = y { C is the camera matrix, y is its image position }
//
// x is the solution to Mx=b with:
//
// M = [ C11 C12 C13 C14 ]
// [ C21 C22 C23 C24 ]
// [ C31 C32 C33 C34 ]
// [ w1 w2 w3 w4 ]
//
// b = [ y1 y2 y3 0 ]
Mat4 M;
M.slice<0, 0, 3, 4> () = camera;
M.slice<3, 0, 1, 4> () = plane.as_row();
Vec4 b = Zeros;
b.slice<0, 3> () = pixel;
return SVD<4>(M).backsub(b);
}
