Discrete Sibson interpolation
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-dimens...
| Veröffentlicht in: | IEEE transactions on visualization and computer graphics. - 1996. - 12(2006), 2 vom: 06. März, Seite 243-53 |
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| 1. Verfasser: | |
| Weitere Verfasser: | , , , |
| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2006
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on visualization and computer graphics |
| Schlagworte: | 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. |
| Zusammenfassung: | 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 |
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| Beschreibung: | Date Completed 29.03.2006 Date Revised 10.12.2019 published: Print Citation Status MEDLINE |
| ISSN: | 1941-0506 |