Interpolation: Splines

The thin-plate spline method fits a spline function to the observations. The fitted function agrees with the observation values at the observation points. The coefficients of the functional fit can be stored for later use. For n observation points, this requires the solution of n simulatneous equations and the inversion of an nxn matrix. As a result, a spline fit is limited to a reasonable number of points. In Spherekit, if more than 500 points are entered, the domain is broken up into overlapping regions, and a surface fit is performed on each region. Points lying in more than one region are assigned a value that is a weighted average of the multiple estimates.

The thin plate spline function can be any of the following forms:

f(d)= d2log d
f(d)= d2log d2
f(d)= d2(log d - 1)

where d is the spherical distance.


References

Franke (1982), Harder and Desmarias (1972), and Sandwell (1987).