I have two set of M 2D points (A, B) that are scaled to <0,1> intervals in both dimensions. How can I create a mapping function, that will map the set A to the set B if I select manually few points from both sets that should be mapped to each other? I have something like this:
I select N points from both sets
A1 - B1 A2 - B2 . . . . An - Bn
From them, how to create a mapping function that can be used to map remaining points (and also maps A1 - An to B1 - Bn).
An+1 - Bn+1 . . . . Am - Bm
I have tried to use RBF interpolation. However, this solution is not working correctly and if selected points are close to each other (their mutual distances are short), RBF fails. I have tried various basis functions as well, some work better (cubic, multiquadric), some not at all (TPS, Gauss), but overall, it is still useless.