A Critical Comparison of Some Methods for Interpolation of Scattered Data

Abstract

This report is concerned with methods for solving the scattered data interpolation problem: Given points x (subscript k), y (subscript k), f (subscript) k, k =1, ..., N, construct a smooth function, F (x,y), so that Fxk, ryk = fk, k -1, ...,N. A comparison of 29 methods for solution of this problem has been made. Each of the methods is discussed and the results of extensive testing for their properties and appropriate values of their parameters is given. Both local and global methods are considered. Comparisons of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation are made. A large number (over 200) of pages of perspective plots of surfaces are given. Suggestions for improvement of some methods are made, and methods which have poor approximation properties are identified.