Natural neighbor
Encyclopedia
Natural neighbor interpolation is a method of spatial interpolation, developed by Robin Sibson
. 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:
where
is the estimate at 
, 
are the weights and 
are the known data at 
. 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,
, 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.
Robin Sibson
Robin Sibson is a British mathematician and educator.He has been a fellow of King's College, Cambridge, professor of statistics at the University of Bath and then vice-chancellor of the University of Kent...
. The method is based on Voronoi tessellation
Voronoi diagram
In mathematics, a Voronoi diagram is a special kind of decomposition of a given space, e.g., a metric space, determined by distances to a specified family of objects in the space...
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:
where
is the estimate at , are the weights and are the known data at . The natural neighbour method proposes a measure for the computation of the weights, and the selection of the interpolating neighborsThe natural neighbor method utilizes the change to the Voronoi tessellation to compute weights. The weights,
, 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
- Inverse distance weightingInverse distance weightingInverse distance weighting is a method for multivariate interpolation, a process of assigning values to unknown points by using values from usually scattered set of known points...
- Nearest neighbor interpolationNearest neighbor interpolationNearest-neighbor interpolation is a simple method of multivariate interpolation in one or more dimensions....
- Multivariate interpolationMultivariate interpolationIn numerical analysis, multivariate interpolation or spatial interpolation is interpolation on functions of more than one variable.The function to be interpolated is known at given points and the interpolation problem consist of yielding values at arbitrary points .-Regular grid:For function...