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Author, Editor

Author(s):

Berberich, Eric
Kerber, Michael

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dblp



Editor(s):

Haines, Eric
McGuire, Morgan

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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

URL of the conference:

http://www.cs.sunysb.edu/spm08/

URL for downloading the paper:


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
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Editor(s)
Eric Berberich
Created
06/24/2008 06:23:00 PM
Revisions
3.
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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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