Natural neighbor

Natural neighbor
Natural neighbor interpolation. The colored circles. which represent the interpolating weights, wi, are generated using the ratio of the shaded area to that of the cell area of the surrounding points. The shaded area is due to the insertion of the point to be interpolated into the Voronoi tessellation

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), wi are the weights and f(xi,yi) are the known data at (xi,yi). 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, wi, 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

Stub icon This applied mathematics-related article is a stub. You can help Wikipedia by expanding it.