Title: Smooth natural neighbour interpolants over the whole domain

Authors: Hisamoto Hiyoshi, Kokichi Sugihara

Addresses: Department of Computer Science, Faculty of Engineering, Gunma University, Kiryu, Japan. ' Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan

Abstract: The natural neighbour interpolation is a potential interpolation method for multidimensional data. However, only globally C1 interpolants have been known so far. In this paper we propose a globally C2 interpolant, and write it in an explicit form. When the data are supplied to the interpolant from a third-degree polynomial, the interpolant can reproduce that polynomial exactly. The idea used to derive the interpolant is applicable to obtain a globally Cq interpolant for an arbitrary non-negative integer q. Hence, this paper gets rid of the continuity limitation of the natural neighbour interpolation, and thus leads it to a new research stage.

Keywords: finite element method; FEM; meshless method; natural element method; natural neighbour interpolation; Voronoi diagram.

DOI: 10.1504/IJCSE.2007.014460

International Journal of Computational Science and Engineering, 2007 Vol.3 No.1, pp.3 - 13

Published online: 09 Jul 2007 *

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