RadialBasisFunction is an option to Interpolation when Method → "RBF" is specified. The value Automatic is default. Automatic means "multiquadric" function with r0 as half the median value of all the off-diagonal distances between the control points.
  • 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
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