Natural neighbor 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 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.
- Sibson weights
where A(x) is the volume of the new cell centered in x, and A(xi) is the volume of the intersection between the new cell centered in x and the old cell centered in xi.
- Sibson, R. (1981). "A brief description of natural neighbor interpolation (Chapter 2)". In V. Barnett (ed.). Interpreting Multivariate Data. Chichester: John Wiley. pp. 21–36.
- N.H. Christ; R. Friedberg, R.; T.D. Lee (1982). "Weights of links and plaquettes in a random lattice". Nuclear Physics B. 210 (3): 337–346.
- V.V. Belikov; V.D. Ivanov; V.K. Kontorovich; S.A. Korytnik; A.Y. Semenov (1997). "The non-Sibsonian interpolation: A new method of interpolation of the values of a function on an arbitrary set of points". Computational mathematics and mathematical physics. 37 (1): 9–15.
- Natural Neighbor Interpolation
- Implementation notes for natural neighbor, and comparison to other interpolation methods
- Interactive Voronoi diagram and natural neighbor interpolation visualization
- Fast, discrete natural neighbor interpolation in 3D on the CPU