// world-to-camera matrix
AffineTransform3d Camera::getMatrix() {
AffineTransform3d orient;
// prinicpal axes of camera.
// a matrix with these as its columns would make a cam coord in put it in
// world coords. we want the opposite.
Vec3d z = -direction.unit();
Vec3d x = ( up ^ z ).unit();
Vec3d y = ( z ^ x ).unit();
std::copy(x.begin(), x.end(), orient.mat.row(0));
std::copy(y.begin(), y.end(), orient.mat.row(1));
std::copy(z.begin(), z.end(), orient.mat.row(2));
transpose(&orient.inv, orient.mat);
return orient * translation(-position);
}
