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Proceedings Article, Paper
@InProceedings
Beitrag in Tagungsband, Workshop

Author, Editor
Author(s):
Berberich, Eric
Kerber, Michael
dblp
dblp
Editor(s):
Petitjean, Sylvaindblp
Not MPII Editor(s):
Petitjean, Sylvain
BibTeX cite key*:
bk-aosogo-08
Title, Booktitle
Title*:
Arrangements on Surfaces of Genus One: Tori and Dupin Cyclides
bk-arrangements-eurocg08.pdf (543.69 KB)
Booktitle*:
24th European Workshop on Computational Geometry - Collection of Abstracts
Event, URLs
Conference URL::
http://eurocg08.loria.fr/
Downloading URL:
Event Address*:
Nancy, France
Language:
English
Event Date*
(no longer used):
Organization:
Event Start Date:
18 March 2008
Event End Date:
20 March 2008
Publisher
Name*:

This proceedings has no publisher!
URL:
Address*:
No publisher
Type:
Vol, No, Year, pp.
Series:
Volume:
Number:
Month:
March
Pages:
209-212
Year*:
2008
VG Wort Pages:
4
ISBN/ISSN:
2-905267-57-7
Sequence Number:
DOI:
Note, Abstract, ©
Note:
An extended version of this article has appeared under the name
"Exact Arrangements on Tori and Dupin Cyclides" in the Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling, pp 59-66
(LaTeX) Abstract:
An algorithm is presented to compute the exact arrangement induced by
arbitrary algebraic surfaces on a parametrized ring Dupin cyclide,
including the special case of the torus.
The intersection of an algebraic surface of degree $n$ with a reference
cyclide is represented as a real algebraic curve of bi-degree $(2n,2n)$
in the cyclide's two-dimensional parameter space.
We use Eigenwillig and Kerber~\cite{ek-exact} to compute a planar arrangement
of such curves
and extend their approach to obtain more asymptotic information about curves
approaching the boundary of the cyclide's parameter space.
With that, we can base our implementation on a general software
framework by Berberich~et.~al.~\cite{bfhmw-samtdaosafs-07} to construct
the arrangement on the cyclide. Our contribution provides the demanded
techniques to model the special topology of the reference surface of genus one.
Our experiments show no combinatorial overhead of the framework,
i.e., the overall performance is strongly coupled to the efficiency of the
implementation for arrangements of algebraic plane curves.
Download
Access Level:
Public

Correlation
MPG Unit:
Max-Planck-Institut für Informatik
MPG Subunit:
Algorithms and Complexity Group
Audience:
experts only
Appearance:
MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort



BibTeX Entry:

@INPROCEEDINGS{bk-aosogo-08,
AUTHOR = {Berberich, Eric and Kerber, Michael},
EDITOR = {Petitjean, Sylvain},
TITLE = {Arrangements on Surfaces of Genus One: Tori and Dupin Cyclides},
BOOKTITLE = {24th European Workshop on Computational Geometry - Collection of Abstracts},
YEAR = {2008},
PAGES = {209--212},
ADDRESS = {Nancy, France},
MONTH = {March},
ISBN = {2-905267-57-7},
NOTE = {An extended version of this article has appeared under the name
"Exact Arrangements on Tori and Dupin Cyclides" in the Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling, pp 59-66},
}


Entry last modified by Michael Kerber, 03/03/2009
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Editor(s)
Michael Kerber
Created
06/26/2008 04:03:35 PM
Revision
0.



Editor
Michael Kerber



Edit Date
06/26/2008 04:03:36 PM




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