I can define a plane in 3D space using three 3D points (
p2) that all lie in the plane and that form a non-degenerate triangle. Calculating the normal of the plane is as simple as calculating the cross product of any two non-parallel 3D vectors that lie in the plane, for instance
(p1 - p0) and
(p2 - p0). So far, so good.
But what if I use homogeneous coordinates for my points? How do I find the normal of the plane then? Of course, if all points have
w != 0, I could simply normalize them (divide by
w) and treat them as regular 3D points. But what if one or more points have
w == 0?
The way I see it, there are three possible answers to this question:
- You do it the same way. If so, please explain how to calculate the cross product of two 3D vectors defined using homogeneous coordinates.
- You do it some other way. If so, please explain how.
- You can't, your question makes no sense and you are clearly confused. If so, please explain why.