ALGORITHMS FOR CARDINAL INTERPOLATION USING BOX SPLINES AND RADIAL BASIS FUNCTIONS

We describe an algorithm for (bivariate) cardinal interpolation which can be applied to translates of "basis functions" which include box splines or radial basis functions. The algorithm is based on a representation of the Fourier transform of the fundamental interpolant, hence Fast Fourier Transform methods are available. In numerical tests the 4-directional box spline (transformed to the characteristical submodule of Z2), the thin plate spline, and the multiquadric case give comparably equal and good results.