An Efficient Natural Neighbour Interpolation Algorithm for Geoscientific Modelling

Abstract

Although the properties of natural neighbour interpolation and its usefulness with scattered and irregularly spaced data are well-known, its implementation is still a problem in practice, especially in three and higher dimensions. We present in this paper an algorithm to implement the method in two and three dimensions, but it can be generalized to higher dimensions. Our algorithm, which uses the concept of flipping in a triangulation, has the same time com- plexity as the insertion of a single point in a Voronoi diagram or a Delaunay triangulation.