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The dimension of $C^1$ splines of arbitrary degree on a tetrahedral partition

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Hangelbroek,  Thomas
Computer Graphics, MPI for Informatics, Max Planck Society;

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

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MPI-I-2003-4-005.pdf
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Citation

Hangelbroek, T., Nürnberger, G., Rössl, C., Seidel, H.-P., & Zeilfelder, F.(2003). The dimension of $C^1$ splines of arbitrary degree on a tetrahedral partition (MPI-I-2003-4-005). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-6887-A
Abstract
We consider the linear space of piecewise polynomials in three variables which are globally smooth, i.e., trivariate $C^1$ splines. The splines are defined on a uniform tetrahedral partition $\Delta$, which is a natural generalization of the four-directional mesh. By using Bernstein-B{\´e}zier techniques, we establish formulae for the dimension of the $C^1$ splines of arbitrary degree.