Natural neighbor interpolation

From Wikipedia, the free encyclopedia
  (Redirected from Natural neighbor)
Jump to navigation Jump to search
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 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:

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.

See also[edit]

References[edit]

  1. ^ Sibson, R. (1981). "A brief description of natural neighbor interpolation (Chapter 2)". In V. Barnett. Interpolating Multivariate Data. Chichester: John Wiley. pp. 21–36. 

External links[edit]