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[[image:Natural-neighbors-coefficients-example.png|300px|thumb|right|Natural neighbor interpolation. The colored circles. which represent the interpolating weights, w<sub>i</sub>, 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]].<ref>{{cite book |last=Sibson |first=R. |editor=V. Barnett |title=Interpreting Multivariate Data |year=1981 |publisher=John Wiley |location=Chichester |pages=21–36 |chapter=A brief description of natural neighbor interpolation (Chapter 2) }}</ref> The method is based on [[Voronoi diagram|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 more smooth approximation to the underlying "true" function. | |||
The basic equation in 2D is: | |||
:<math>G(x,y)=\sum^n_{i=1}{w_if(x_i,y_i)}</math> | |||
where <math>G(x,y)</math> is the estimate at <math>(x,y)</math>, <math>w_i</math> are the weights and <math>f(x_i,y_i)</math> are the known data at <math>(x_i, y_i)</math>. The weights, <math>w_i</math>, are calculated by finding how much of each of the surrounding areas is "stolen" when inserting <math>(x,y)</math> into the tessellation. | |||
==See also== | |||
* [[Inverse distance weighting]] | |||
* [[Multivariate interpolation]] | |||
==References== | |||
{{reflist}} | |||
==External links== | |||
* [http://dilbert.engr.ucdavis.edu/~suku/nem/nem_intro/node3.html Natural Neighbor Interpolation] | |||
* [http://www.ems-i.com/gmshelp/Interpolation/Interpolation_Schemes/Natural_Neighbor_Interpolation.htm Introduction to natural neighbors] | |||
* [http://interpolate3d.googlecode.com/files/Report.pdf Implementation notes for natural neighbor, and comparison to other interpolation methods] | |||
* [http://alexbeutel.com/webgl/voronoi.html Interactive Voronoi diagram and natural neighbor interpolation visualization] | |||
[[Category:Multivariate interpolation]] | |||
{{Mathapplied-stub}} | |||
Revision as of 23:05, 21 January 2014
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 more smooth 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
References
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External links
- Natural Neighbor Interpolation
- Introduction to natural neighbors
- Implementation notes for natural neighbor, and comparison to other interpolation methods
- Interactive Voronoi diagram and natural neighbor interpolation visualization
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