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IEEE Trans Vis Comput Graph. 2006 Mar-Apr;12(2):243-53.

Discrete Sibson interpolation.

Author information

1
Institute for Data Analysis and Visualization, Department of Computer Science, University of California, Davis 95616, USA. sunpark@ucdavis.edu

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-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.

PMID:
16509383
DOI:
10.1109/TVCG.2006.27
[Indexed for MEDLINE]
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