Natural-neighbor interpolation

Natural-neighbor interpolation or Sibson 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.

, are calculated by finding how much of each of the surrounding areas is "stolen" when inserting

where A(x) is the volume of the new cell centered in x, and A(xi) is the volume of the intersection between the new cell centered in x and the old cell centered in xi.

There are several useful properties of natural neighbor interpolation:[4] Natural neighbor interpolation has also been implemented in a discrete form, which has been demonstrated to be computationally more efficient in at least some circumstances.

[5] A form of discrete natural neighbor interpolation has also been developed that gives a measure of interpolation uncertainty.

This applied mathematics–related article is a stub.

Natural neighbor interpolation with Sibson weights. 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 with Laplace weights. The interface l(x i ) between the cells linked to x and x i is in blue, while the distance d(x i ) between x and x i is in red.