Triangular \(C^m\) interpolation by rational functions (Q2724925)
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scientific article; zbMATH DE number 1618429
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Triangular \(C^m\) interpolation by rational functions |
scientific article; zbMATH DE number 1618429 |
Statements
4 March 2002
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triangular rational
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interpolant
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\(C^m\)-interpolation
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triangulation
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piecewise rational interpolant
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error estimate
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interpolation over triangle
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Triangular \(C^m\) interpolation by rational functions (English)
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Interpolation over triangles is an essential problem in computer aided geometric design. Using Bernstein-Bézier technique, the authors construct piecewise rational local \(C^m\)-interpolants of given \(C^m\)-data \((m=1, 2,\dots)\) on a triangulation \(T\). Local interpolant means that the interpolant restricted on any triangle of \(T\) depends only on the data defined on that triangle. For \(m=1\) and \(m=2\), the constructions are similar to that of \textit{G. Herron} [SIAM J. Numer. Anal. 22, 811-819 (1985; Zbl 0593.65008)] and of \textit{X. Liu} and \textit{Y. Zhu} [Comput. Aided Geom. Des. 12, No. 4, 329-348 (1995; Zbl 0875.68841)]. The interpolation error is estimated. Some numerical examples are given.
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