# Natural neighbor interpolation

**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:

where is the estimate at , are the weights and are the known data at . The weights, , are calculated by finding how much of each of the surrounding areas is "stolen" when inserting into the tessellation.

## See also

## References

- ↑ Sibson, R. (1981). "A brief description of natural neighbor interpolation (Chapter 2)". In V. Barnett.
*Interpreting Multivariate Data*. Chichester: John Wiley. pp. 21–36.

## External links

- Natural Neighbor Interpolation
- Implementation notes for natural neighbor, and comparison to other interpolation methods
- Interactive Voronoi diagram and natural neighbor interpolation visualization

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