MPI-INF/SWS Research Reports 1991-2021
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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
April 2003, 39 pages.
.Status: available - back from printing
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.
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URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2003-4-005
BibTeX@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},
}