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Discrete Sibson Interpolation
March/April 2006 (vol. 12 no. 2)
pp. 243-253

Abstract—Natural-neighbor interpolation methods, such as Sibson's method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibson's method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibson's interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d{\hbox{-}}\rm dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and 3D interpolation (3D) with computation times of a few seconds.

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Index Terms:
Scattered data interpolation, natural-neighbor interpolation, graphics hardware.
Sung W. Park, Lars Linsen, Oliver Kreylos, John D. Owens, Bernd Hamann, "Discrete Sibson Interpolation," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 2, pp. 243-253, March-April 2006, doi:10.1109/TVCG.2006.27
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