I dont understand why M^{-1} can be interpreted as transforming the ray direction to be orthogonal to the plane. It doesn't make sense to me, that if initially the ray is parallel to the plane, then after the transformation it will be orthogonal to that plane.
Gundam
@OillyNoodle I think it do not change the direction of the ray. It just can be regarded as an extra axis, say t. So any feasible solution is just a point in cordinate uvt, just like the a xyz Cartesian coordinate system we use in 3D space.
jasonx
If the ray were initially parallel to the plane then no linear transformation could make it intersect the plane. However we assume there is a intersection point and the ray is not parallel to the plane, so we can apply a linear transformation to transform the ray to be orthogonal to the uv plane.
I dont understand why M^{-1} can be interpreted as transforming the ray direction to be orthogonal to the plane. It doesn't make sense to me, that if initially the ray is parallel to the plane, then after the transformation it will be orthogonal to that plane.
@OillyNoodle I think it do not change the direction of the ray. It just can be regarded as an extra axis, say t. So any feasible solution is just a point in cordinate uvt, just like the a xyz Cartesian coordinate system we use in 3D space.
If the ray were initially parallel to the plane then no linear transformation could make it intersect the plane. However we assume there is a intersection point and the ray is not parallel to the plane, so we can apply a linear transformation to transform the ray to be orthogonal to the uv plane.