Natural neighbor

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, in that it provides a more smooth 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 natural neighbour method proposes a measure for the computation of the weights, and the selection of the interpolating neighbors

The natural neighbor method utilizes the change to the Voronoi tessellation to compute weights. The weights, w_i, are by utilization of the area "stolen" from the surrounding points when inserting a new point into the tessellation. Each weight may be computed by dividing the section of the new tessellated region that lies within the tessellated region of each original neighboring tessellated polygon.

See also

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