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Journal Article

Quasi-Interpolation by Quadratic Piecewise Polynomials in Three Variables

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Rössl,  Christian
Computer Graphics, MPI for Informatics, Max Planck Society;

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Zeilfelder,  Frank
Computer Graphics, MPI for Informatics, Max Planck Society;

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Seidel,  Hans-Peter       
Computer Graphics, MPI for Informatics, Max Planck Society;

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Citation

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.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-2778-6
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.