Spatial Statistics Based on Voronoi Polygons

Most early programs (and far too many recent ones) have taken a purely metric approach to the interpolation (or contouring) problem for arbitrarily distributed data points. They collected all data points within a given distance from the estimation point, or the nearest six, or other variants intended to select both a "reasonable" number of data points, and also to select a "surrounding" set. Most of these approaches could be shown to be inadequate by the judicious selection of awkwardly distributed data sets. A subsequent approach involved the triangulation of the data set, followed by a local polynomial (or linear) patch within each triangle. Two problems arose with this: firstly many triangulations of a given data set were possible, and the same set could not be guaranteed if the data were re-entered in a different order; and secondly local patches, which were defined to merge with adjacent triangles with a given level of continuity (usually slope) were therefor discontinuous at higher levels (usually curvature) and this was very visible in the resulting map.