Rhein, Markus ; Kalbe, Thomas (2009)
Quasi-interpolation by Quadratic C1-Splines on Truncated Octahedral Partitions.
In: Computer Aided Geometric Design, 26 (8)
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
We describe an approximating scheme for the smooth reconstruction of discrete data on volumetric grids. A local quasi-interpolation method for quadratic C1-splines on uniform tetrahedral partitions is used to achieve a globally smooth function. The Bernstein-Bézier coefficients of the piecewise polynomials are thereby directly determined by appropriate combinations of the data values. We explicitly give a construction scheme for a family of quasi-interpolation operators and prove that the splines and their derivatives can provide an approximation order two for smooth functions. The optimal approximation of the derivatives and the simple averaging rules for the coefficients recommend this method for high quality visualization of volume data. Numerical tests confirm the approximation properties and show the efficient computation of the splines.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2009 |
| Autor(en): | Rhein, Markus ; Kalbe, Thomas |
| Art des Eintrags: | Bibliographie |
| Titel: | Quasi-interpolation by Quadratic C1-Splines on Truncated Octahedral Partitions |
| Sprache: | Englisch |
| Publikationsjahr: | 2009 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Computer Aided Geometric Design |
| Jahrgang/Volume einer Zeitschrift: | 26 |
| (Heft-)Nummer: | 8 |
| Kurzbeschreibung (Abstract): | We describe an approximating scheme for the smooth reconstruction of discrete data on volumetric grids. A local quasi-interpolation method for quadratic C1-splines on uniform tetrahedral partitions is used to achieve a globally smooth function. The Bernstein-Bézier coefficients of the piecewise polynomials are thereby directly determined by appropriate combinations of the data values. We explicitly give a construction scheme for a family of quasi-interpolation operators and prove that the splines and their derivatives can provide an approximation order two for smooth functions. The optimal approximation of the derivatives and the simple averaging rules for the coefficients recommend this method for high quality visualization of volume data. Numerical tests confirm the approximation properties and show the efficient computation of the splines. |
| Freie Schlagworte: | Visualization, Trivariate splines, Volume data, Approximation |
| Fachbereich(e)/-gebiet(e): | 20 Fachbereich Informatik 20 Fachbereich Informatik > Graphisch-Interaktive Systeme |
| Hinterlegungsdatum: | 12 Nov 2018 11:16 |
| Letzte Änderung: | 12 Nov 2018 11:16 |
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