Currently I am investigating interpolation of 3D data with radial basis functions (RBF) and I am wondering that there are quite a few families of such (see table1 here).
However, I cannot find any discussion for engineers about the intuitive choice of them. The are basically these aspects which differ across the RBF families:
truncated power function with polynomials slide 21
oscillatory RBF slide 36
Euclid's hat functions slide 44
Buhmanns RBF slide 49 Looks pretty much like a polynomial RBF from Wendland to me :(
So why do we need so many of them? In my work I have to choose one of them, but I cannot justify the choice. :( So if someone asks me for that, I just tell that "I had a good dice"...