Lets say I have two orthogonal planes defined by three 3D points each. The normals of the two planes should be orthogonal of course. These normals could be computed by taking the difference of two different pair points and then taking the cross product of the two resulted difference vectors. My problem is that I can't get my head about these difference vectors because they are aren't unique i.e. I can get the same difference vector with different points coordinates. That means if the two sets of points in the two orthogonal planes were carefully chosen we can end up with the same normal vector (may be a different magnitude) which breaks down the condition of orthogonality.
My original problem assumes the following:
- Points on the same plane have the same z value.
- Within a certain vicinity, the neighbouring points are on the same plane.
So I originally only have one 3D point, I try based on my assumptions to create two virtual 3D points by moving about my original point, in x and y direction while having z fixed. I know I'm missing something basic here but I can't figure it out due to my limited math skills. Any help would be appreciated.