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Issue No. 02 - March/April (2006 vol. 12)
ISSN: 1077-2626
pp: 243-253
<p><b>Abstract</b>—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 <tmath>d{\hbox{-}}\rm dimensional</tmath> 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.</p>
Scattered data interpolation, natural-neighbor interpolation, graphics hardware.

O. Kreylos, J. D. Owens, B. Hamann, L. Linsen and S. W. Park, "Discrete Sibson Interpolation," in IEEE Transactions on Visualization & Computer Graphics, vol. 12, no. , pp. 243-253, 2006.
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