# Natural neighbor interpolation

(Redirected from 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 seven 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:

${\displaystyle G(x,y)=\sum _{i=1}^{n}{w_{i}f(x_{i},y_{i})}}$

where ${\displaystyle G(x,y)}$ is the estimate at ${\displaystyle (x,y)}$, ${\displaystyle w_{i}}$ are the weights and ${\displaystyle f(x_{i},y_{i})}$ are the known data at ${\displaystyle (x_{i},y_{i})}$. The weights, ${\displaystyle w_{i}}$, are calculated by finding how much of each of the surrounding areas is "stolen" when inserting ${\displaystyle (x,y)}$ into the tessellation.