Lagrange interpolation of functions by quadratic polynomials on nodes which are vertices of a triangulation has been recently studied and local six-tuples of vertices which assure the uniqueness and the optimal-order of the interpolation polynomial are known. Following Little’s idea and theoretical results on the approximation order and accuracy of the triangular Shepard method, we introduce an hexagonal Shepard operator with quadratic precision and cubic approximation order for scattered data approximation without least square fit.

This presentation is part of Minisymposium “MS2 - Interpolation and Approximation Methods in Imaging (4 parts)”
organized by: Alessandra De Rossi (University of Torino) , Costanza Conti (University of Firenze) , Francesco Dell'Accio (University of Calabria) .

Authors:

Filomena Di Tommaso (University of Calabria)

Francesco Dell'Accio (University of Calabria)

Keywords:

approximation, computer graphics, image reconstruction, interpolation