Year: 2006
Type: article
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.
DOI: 10.1109/tvcg.2006.27
Authors: S.W. Park, L. Linsen, O. Kreylos, J.D. Owens, B. Hamann
Institutions: University of California, Davis, Universität Greifswald
Language: English
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: INFORMATICS OF HUMAN AND Monkey Brain Atlases, Career: A Proposal Regarding the Unification of Data Reduction and Multiresolution Methods for Use in Scientific Visualization and the Education in Scientific Visualization, G311307661, Multiresolution- and Topology-Based Visualization of Large Scientific Data Sets in Parallel and Distributed Computing Environments
OpenAlex ID: W2147762997