This repository is a translation of the biharmonic spline interpolation code of matlab. Also has a rough translation of the mergesimpts (Merge Similar Points) built-in matlab function. mergesimpts was reverse-engineered so I wouldn't know if it is an exact match.
GDATAV4 MATLAB 4 GRIDDATA interpolation
Reference: David T. Sandwell, Biharmonic spline interpolation of GEOS-3 and SEASAT altimeter data, Geophysical Research Letters, 2, 139-142 1987. Describes interpolation using value or gradient of value in any dimension.