RadialBasisFunction

• Note, that the distance function in the code is expected to return the square of the distance. Therefore, the automatic radial basis function is defined as

• r02=Median[Flatten[Table[Drop[distmat[[i]], {i}], {i, Length[pts]}]]]; radbasfunc=((Sqrt[#+r02/4])&);

• where r02 represents the median of the squared distances between the control points.

• Other possible radial basis functions could be:

• Inverse multiquadric , coded as

• RadialBasisFunction→((1/Sqrt[#+r0^2])&)

• Thin plate spline , coded as

• RadialBasisFunction→(If[#=0,0.,#*(Log[#]/2-Log[r0])]&)

• Gaussian , coded as

• RadialBasisFunction→((Exp[-#/(2r0^2)])&)

• For all these choices, you have to specify r0 outside the Interpolation routine. This could be done by

In[11]:=