Natural neighbour 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 ${\displaystyle G(x,y)}$ 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.

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