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

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.

Authors+Show Affiliations

Institute for Data Analysis and Visualization, Department of Computer Science, University of California, Davis 95616, USA. sunpark@ucdavis.eduNo affiliation info availableNo affiliation info availableNo affiliation info availableNo affiliation info available

Pub Type(s)

Evaluation Study
Journal Article
Research Support, N.I.H., Extramural
Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.

Language

eng

PubMed ID

16509383

Citation

Park, Sung W., et al. "Discrete Sibson Interpolation." IEEE Transactions On Visualization and Computer Graphics, vol. 12, no. 2, 2006, pp. 243-53.
Park SW, Linsen L, Kreylos O, et al. Discrete Sibson interpolation. IEEE Trans Vis Comput Graph. 2006;12(2):243-53.
Park, S. W., Linsen, L., Kreylos, O., Owens, J. D., & Hamann, B. (2006). Discrete Sibson interpolation. IEEE Transactions On Visualization and Computer Graphics, 12(2), 243-53.
Park SW, et al. Discrete Sibson Interpolation. IEEE Trans Vis Comput Graph. 2006 Mar-Apr;12(2):243-53. PubMed PMID: 16509383.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Discrete Sibson interpolation. AU - Park,Sung W, AU - Linsen,Lars, AU - Kreylos,Oliver, AU - Owens,John D, AU - Hamann,Bernd, PY - 2006/3/3/pubmed PY - 2006/3/30/medline PY - 2006/3/3/entrez SP - 243 EP - 53 JF - IEEE transactions on visualization and computer graphics JO - IEEE Trans Vis Comput Graph VL - 12 IS - 2 N2 - 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. SN - 1077-2626 UR - https://www.unboundmedicine.com/medline/citation/16509383/Discrete_Sibson_interpolation_ DB - PRIME DP - Unbound Medicine ER -