Natural neighbor interpolation

Natural neighbor interpolation. The area of the green circles are the interpolating weights, w_i. 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:

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

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.

See also

• Inverse distance weighting
• Multivariate interpolation

References

1. 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