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.
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