Natural neighbor interpolation
Natural neighbor interpolation is a method of spatial interpolation, developed by Robin Sibson. The method is based on Voronoi tessellation of a discrete set of spatial points. This has advantages over simpler methods of interpolation, such as nearest-neighbor interpolation, in that it provides a smoother approximation to the underlying "true" function.
The basic equation is:
where is the estimate at, are the weights and are the known data at. The weights,, are calculated by finding how much of each of the surrounding areas is "stolen" when inserting into the tessellation.
;Sibson weights
where is the volume of the new cell centered in, and is the volume of the intersection between the new cell centered in and the old cell centered in.
;Laplace weights
where is the measure of the interface between the cells linked to and in the Voronoi diagram and, the distance between and.
