Smooth natural neighbour interpolants over the whole domain. (10th July 2007)

• Record Type: Journal Article
• Authors: Hiyoshi, Hisamoto; Sugihara, Kokichi
• Is Part Of: International journal of computational science and engineering. Volume 3:Number 1(2007)
• Page Start: 3
• Page End: 13
• Publication Date: 2007-07-10
• Subjects: finite element method -- FEM -- meshless method -- natural element method -- natural neighbour interpolation -- Voronoi diagram; Computer science -- Mathematics -- Periodicals; Computer simulation -- Mathematical aspects -- Periodicals; Computational intelligence -- Periodicals; 004.015105
• Languages: English
• ISSNs: 1742-7185

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.