greenRBF

% Green's RBF, as defined in :
 David T. Sandwell, Biharmonic spline interpolation of GEOS-3 and SEASAT altimeter data, Geophysical Research Letters, 2, 139-142, 1987.
 
 Note: this is the same RBF used for interpolation in griddata, when the
   'v4' method is specified. Using this RBF and no trend
   ('PolynomialDegree' = -1) will reproduce the same result as griddata
   function.

0001 function fx = greenRBF(r)
0002 %% Green's RBF, as defined in :
0003 % David T. Sandwell, Biharmonic spline interpolation of GEOS-3 and SEASAT altimeter data, Geophysical Research Letters, 2, 139-142, 1987.
0004 %
0005 % Note: this is the same RBF used for interpolation in griddata, when the
0006 %   'v4' method is specified. Using this RBF and no trend
0007 %   ('PolynomialDegree' = -1) will reproduce the same result as griddata
0008 %   function.
0009 
0010 fx = (r.^2) .* (log(r)-1);
0011 fx(r==0) = 0; % Fix singularity of Green's function at 0
0012 
0013 end
0014