This paper presents a method of constructing a smooth function of
two or more variables that interpolates data values at arbitrarily
distributed points. Shepard’s method for fitting a surface to data
values at scattered points in the plane has the advantages of a
small storage requirement and an easy generalization to more than
two independent variables, but suffers from low accuracy and a high
computational cost relative to some alteative methods.
Localizations of this method have reasonably low computational
costs, but remain relatively inaccurate. We describe a modified
Shepard’s method that, without sacrificing the advantages, has
accuracy comparable to other local methods. Computational
efficiency is also improved by using a cell method for
nearest-neighbor searching. Test results for two and three
independent variables are presented.