Shepard’s method of “metric interpolation” to bivariate and multivariate interpolation

Abstract

Shepard developed a scheme for interpolation to arbitrarily spaced discrete bivariate data. This scheme provides an explicit global representation for an interpolant which satisfies a maximum principle and which reproduces constant functions. The interpolation method is basically an inverse distance formula which is generalized to any Euclidean metric. These techniques extend to include interpolation to partial derivative data at the interpolation points.