Improving the Global Continuity of Voronoi - Based Interpolation

An interpolation method based on Voronoi diagrams, called a natural neighbor interpolation, is a potential interpolation method for multivariate data. However, only globally C interpolants have been known so far. In this paper, we propose a globally C interpolant, and write it in an explicit form. When data are supplied from a third-degree polynomial, the proposed interpolant can reproduce it exactly. In addition, by extending the underlying idea, for an arbitrary non-negative integer k, we can obtain a globally C interpolant as well. Thus this paper gets rid of a limitation on the continuity of natural neighbor interpolation, and leads it to a new research stage.