A method of bivariate interpolation and smooth surface fitting based on local procedures

Abstract

A method is designed for interpolating values given at points of a rectangular grid in a plane by a smooth bivariate function z = z ( x, y ). The interpolating function is a bicubic polynomial in each cell of the rectangular grid. Emphasis is on avoiding excessive undulation between given grid points. The proposed method is an extension of the method of univariate interpolation developed earlier by the author and is likewise based on local procedures.