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Proceedings Article, Paper
@InProceedings
Beitrag in Tagungsband, Workshop

Author, Editor
Author(s):
Berberich, Eric
Kerber, Michael
dblp
dblp
Editor(s):
Haines, Eric
McGuire, Morgan
dblp
dblp
Not MPII Editor(s):
Haines, Eric
McGuire, Morgan
BibTeX cite key*:
bk-eatdc-08
Title, Booktitle
Title*:
Exact Arrangements on Tori and Dupin Cyclides
bk_eaotadc_auth_prep.pdf (551.33 KB)
Booktitle*:
Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling
Event, URLs
Conference URL::
http://www.cs.sunysb.edu/spm08/
Downloading URL:
Event Address*:
Stony Brook, USA
Language:
English
Event Date*
(no longer used):
Organization:
Association for Computing Machinery (ACM)
Event Start Date:
2 June 2008
Event End Date:
4 June 2008
Publisher
Name*:
ACM
URL:
Address*:
New York, USA
Type:
Vol, No, Year, pp.
Series:
Volume:
Number:
Month:
June
Pages:
59-66
Year*:
2008
VG Wort Pages:
10
ISBN/ISSN:
978-1-60558-106-4
Sequence Number:
DOI:
10.1145/1364901.1364912
Note, Abstract, ©
(LaTeX) Abstract:
An algorithm and implementation is presented to compute the exact arrangement
induced by arbitrary algebraic surfaces on a parametrized ring Dupin cyclide.
The family of Dupin cyclides contains as a special case 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 two-dimensional parameter space of the cyclide.
We use Eigenwillig and Kerber:
``Exact and Efficient 2D-Arrangements of Arbitrary Algebraic Curves'',
SODA~2008, 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 the general software framework
by Berberich~et.~al.: ``Sweeping and Maintaining Two-Dimensional
Arrangements on Surfaces: A First Step'', ESA~2007.
Our contribution provides the demanded techniques to model the special
geometry of surfaces intersecting a cyclide
and the special topology of the reference surface of genus one.
The contained implementation is complete and does not assume generic position.
Our experiments show that the combinatorial overhead of the framework
does not harm the efficiency of the method. Our experiments show that the
overall performance is strongly coupled to the efficiency of the
implementation for arrangements of algebraic plane curves.
Keywords:
Dupin ring cyclide, torus, arrangements, surfaces, generic programming, CGAL, exact geometric computation, robustness
Copyright Message:
Copyright ACM, 2008
This is the authors' version of the work.
It is posted here by permission of ACM for your personal use.
Not for redistribution. The definitive version was published in the
Proceedings of the ACM Solid and Physical Modelling Symposium (SPM 2008), http://doi.acm.org/10.1145/1364901.1364912
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-eatdc-08,
AUTHOR = {Berberich, Eric and Kerber, Michael},
EDITOR = {Haines, Eric and McGuire, Morgan},
TITLE = {Exact Arrangements on Tori and Dupin Cyclides},
BOOKTITLE = {Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling},
PUBLISHER = {ACM},
YEAR = {2008},
ORGANIZATION = {Association for Computing Machinery (ACM)},
PAGES = {59--66},
ADDRESS = {Stony Brook, USA},
MONTH = {June},
ISBN = {978-1-60558-106-4},
DOI = {10.1145/1364901.1364912},
}


Entry last modified by Michael Kerber, 03/03/2009
Hide details for Edit History (please click the blue arrow to see the details)Edit History (please click the blue arrow to see the details)

Editor(s)
Eric Berberich
Created
06/24/2008 06:23:00 PM
Revisions
3.
2.
1.
0.
Editor(s)
Michael Kerber
Eric Berberich
Eric Berberich
Eric Berberich
Edit Dates
06/26/2008 03:19:25 PM
06/24/2008 06:35:56 PM
06/24/2008 06:23:56 PM
06/24/2008 06:23:00 PM


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