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 in 2D is:

where G ( x , y ) is the estimate at ( x , y ) , w i are the weights and f ( x i , y i ) are the known data at ( x i , y i ) . The weights, w i , are calculated by finding how much of each of the surrounding areas is "stolen" when inserting ( x , y ) into the tessellation.