Discrete Sibson interpolation
| Autor: | Bernd Hamann, Sung W. Park, Oliver Kreylos, John D. Owens, Lars Linsen |
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| Rok vydání: | 2006 |
| Předmět: |
graphics hardware
Theoretical computer science Computer science Graphics hardware Information Storage and Retrieval Rendering (computer graphics) Regular grid User-Computer Interface Imaging Three-Dimensional Engineering scattered-data interpolation graphics hardware volume visualization Nearest-neighbor interpolation Image Interpretation Computer-Assisted Computer Graphics ComputingMethodologies_COMPUTERGRAPHICS scattered data interpolation Trilinear interpolation Numerical Analysis Computer-Assisted Signal Processing Computer-Assisted Image Enhancement Computational geometry Computer Graphics and Computer-Aided Design Data point Natural neighbor interpolation Signal Processing Computer Vision and Pattern Recognition Voronoi diagram natural-neighbor interpolation Algorithm Algorithms Software Interpolation |
| Zdroj: | Park, Sung; Linsen, Lars; Kreylos, Oliver; Owens, John D.; & Hamann, Bernd. (2006). Discrete Sibson Interpolation. IEEE Transactions on Visualization and Computer Graphics, 12. doi: 10.1109/TVCG.2006.27. UC Davis: Institute for Data Analysis and Visualization. Retrieved from: http://www.escholarship.org/uc/item/27v9h554 Park, Sung W; Linsen, Lars; Kreylos, Oliver; Owens, John D; & Hamann, Bernd Hamann. (2006). Discrete Sibson interpolation. IEEE Transactions on Visualization and Computer Graphics, 12(2), 243-253. UC Davis: Retrieved from: http://www.escholarship.org/uc/item/88c9892g |
| ISSN: | 1077-2626 |
| DOI: | 10.1109/tvcg.2006.27 |
| Popis: | 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 three-dimensional interpolation(3D) with computation times of a few seconds. |
| Databáze: | OpenAIRE |
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