Given a point on a plane A, I want to be able to map to a corresponding point on plane B. I have a set of N corresponding pairs of reference points between the two planes, however, the overall mapping is not a simple affine transform (no homographies for me).Things I have tried:For a given point, find the three closest reference points in planeA, compute barrycentric coordinates of that triangle, and then applythat transform to the corresponding reference points in plane B. Howit failed: sometimes the three closest points were nearly collinear,so errors were huge. Also, there was no consistency in the mappingwhen crossing borders. It was very jittery.Compute all possible triangles given the N reference points (N^3).    Order them by size. For the given point, find the smallest triangle    that it's in. This fixes the linearly of the points problem, but was    still extremely jittery and slow.Start with a triangulated plane A. Iterate through the reference    points, adding each one to the reference plane. Every time you add a    point it exists in at least one triangle. Break that triangle into    three triangles using the new reference point as a vertex. You end    up with plane A triangulated so you can map from plane A to plane B    with ease. Issues: You can prove that every triangle will have a    point that is on the edge of the planes. This results in huge errors    if your reference points are far from the edge of the planes.I feel like this should be a fairly standard problem. Are there standard algorithms/libraries for this?
Map points from one plane into another
graph algorithms