I am not sure I understand what Thin-Plate-Splines are.
I thought it was the name of a regularization technique for b-splines surface fitting (i.e. approximation smoothing, not exact interpolation). But reading papers, I understand they are a new type of splines (i.e. not b-splines), built out of the linear combination of RBF (Radial Basis Functions) - and the addition of a plane, to offset things.
I am a bit lost. Can anyone shed some light on this?