Natural neighbor

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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 7 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^n_{i=1}{w_if(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.

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References[edit]

  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. 

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