Smooth natural neighbour interpolants over the whole domain
by Hisamoto Hiyoshi, Kokichi Sugihara
International Journal of Computational Science and Engineering (IJCSE), Vol. 3, No. 1, 2007

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 C^q 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.

Online publication date: Mon, 09-Jul-2007

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