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MPI-I-2003-4-005

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

Hangelbroek, Thomas and Nürnberger, Günther and Roessl, Christian and Seidel, Hans-Peter Seidel and Zeilfelder, Frank

MPI-I-2003-4-005. April 2003, 39 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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.

Acknowledgement:
References to related material:

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Hide details for BibTeXBibTeX
@TECHREPORT{HangelbroekNürnbergerRoesslSeidelZeilfelder2003,
  AUTHOR = {Hangelbroek, Thomas and N{\"u}rnberger, G{\"u}nther and Roessl, Christian and Seidel, Hans-Peter Seidel and Zeilfelder, Frank},
  TITLE = {The dimension of $C^1$ splines of arbitrary degree on a tetrahedral partition},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2003-4-005},
  MONTH = {April},
  YEAR = {2003},
  ISSN = {0946-011X},
}