# Natural neighbor

Natural neighbor interpolation. The area of the green circles are the interpolating weights, wi. The purple-shaded region is the new Voronoi cell, after inserting the point to be interpolated (black dot). The weights represent the intersection areas of the purple-cell with each of the 7 surrounding cells.

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 smoother 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.