# Natural neighbor

Natural neighbor interpolation. The colored circles. which represent the interpolating weights, wi, are generated using the ratio of the shaded area to that of the cell area of the surrounding points. The shaded area is due to the insertion of the point to be interpolated into the Voronoi tessellation

Natural neighbor interpolation is a method of spatial interpolation, developed by Robin Sibson.[1] 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 more smooth approximation to the underlying "true" function.

The basic equation in 2D is:

$G(x,y)=\sum^n_{i=1}{w_if(x_i,y_i)}$

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.