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  Quasi-Interpolation by Quadratic Piecewise Polynomials in Three Variables

Nürnberger, G., Rössl, C., Zeilfelder, F., & Seidel, H.-P. (2005). Quasi-Interpolation by Quadratic Piecewise Polynomials in Three Variables. Computer Aided Geometric Design, 22, 221-249.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2778-6 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2779-4
Genre: Journal Article

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 Creators:
Nürnberger, Günther, Author
Rössl, Christian1, Author           
Zeilfelder, Frank1, Author           
Seidel, Hans-Peter1, Author           
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

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 Abstract: A quasi-interpolation method for quadratic piecewise polynomials in three variables is described which can be used for the efficient reconstruction and visualization of gridded volume data. We analyze the smoothness properties of the trivariate splines. We prove that the splines yield nearly optimal approximation order while simultaneously its piecewise derivatives provide optimal approximation of the derivatives of smooth functions. The constants of the corresponding error bounds are given explicitly. Numerical tests confirm the results and the efficiency of the method.

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Language(s): eng - English
 Dates: 2005-05-012005
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: eDoc: 278995
Other: Local-ID: C125675300671F7B-817E7400112458E6C1256F1D002EAAC1-nrsz:qiqpp:2004
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Title: Computer Aided Geometric Design
Source Genre: Journal
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Pages: - Volume / Issue: 22 Sequence Number: - Start / End Page: 221 - 249 Identifier: -