Scattered data interpolation on the 2-dimensional surface through Shepard-like technique

Abstract

In the current paper, the problem of interpolation of scattered data on two-dimensional surfaces is considered by proposing an extension to the Shepard method and its modified version to surfaces. Each proposed operator is a linear combination of basis functions whose coefficients are the values of the function or its Taylor of first-order expansions at the interpolation points using both functional and derivative data. Numerical tests are given to show the interpolation performance, where several numerical results show a good approximation accuracy of the proposed operator.