Curve and surface interpolation using rational radial basis functions

Abstract

This paper addresses the problem of reconstructing two-dimensional curves and three-dimensional surfaces from scattered, sparse measurements. We extend the rational Gaussian (RaG) functions introduced by Goshtasby (1993) to general rational radial basis functions and develop a method to compute the smoothness parameters for the shape model by considering the adjacency relation of the control points. Experimental results demonstrate substantial improvements over the original RaG-based method when the input data is sparse and the distribution of the control points is highly nonuniform