Interpolation by Bivariate Quadratic Polynomials and Applications to the Scattered Data Interpolation Problem

As specified by Little [7], the triangular Shepard method can be generalized to higher dimensions and to set of more than three points. In line with this idea, the hexagonal Shepard method has been recently introduced by combining six-points basis functions with quadratic Lagrange polynomials interpolating on these points and the error of approximation has been carried out by adapting, to the case of six points, the technique developed in [4]. As for the triangular Shepard method, the use of appropriate set of six-points is crucial both for the accuracy and the computational cost of the hexagonal Shepard method. In this paper we discuss about some algorithm to find useful six-tuple of points in a fast manner without the use of any triangulation of the nodes.