Variational trivariate fitting using Worsey-Piper macro elements on tetrahedral partitions (Q554548)
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scientific article; zbMATH DE number 5936076
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Variational trivariate fitting using Worsey-Piper macro elements on tetrahedral partitions |
scientific article; zbMATH DE number 5936076 |
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Variational trivariate fitting using Worsey-Piper macro elements on tetrahedral partitions (English)
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4 August 2011
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The authors present a method to construct a trivariate \(C^1\) quadratic spline that approximates a set of Lagrangian data scattered over a subset of \(\mathbb R^3\) in an \(L_2\) sense, and that simultaneously minimizes an energy functional. The method is based on the approach of \textit{A. J. Worsey} and \textit{B. Piper} [Comput. Aided Geom. Des. 5, No.~3, 177--186 (1988; Zbl 0654.65008)] for decomposing the basic domain that contains all data points into a number of tetrahedra and on solving the corresponding local problems on these tetrahedra. The convergence properties of this approach are investigated and some examples are provided.
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minimal energy
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Worsey-Piper split
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variational spline
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approximation
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smoothing
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fitting
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numerical examples
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Lagrangian data scattered
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convergence
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