MOVING LEAST-SQUARES INTERPOLATION WITH THIN-PLATE SPLINES AND RADIAL BASIS FUNCTIONS

Moving least-squares methods for interpolation or approximation of scattered data are well known, and can suffer from defects, such as flat spots in the Shepard method, and edge effects inherited from a polynomial basis in the higher degree cases. We investigate methods based on thin-plate splines and on other radial basis functions. It turns out that a small support of the weight function leads to a small support for the "spline basis" and associated efficiency in the evaluation of the approximant. The edge effects seem minimal and good interpolants of scattered data can be obtained.