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Proceedings Article, Paper
@InProceedings
Beitrag in Tagungsband, Workshop

Author, Editor
Author(s):
Berberich, Eric
Kerber, Michael
Sagraloff, Michael		dblp
dblp
dblp
Editor(s):
Petitjean, Sylvaindblp
Not MPII Editor(s):
Petitjean, Sylvain
BibTeX cite key*:
bks-gaoasbopa-08
Title, Booktitle
Title*:
Geometric Analysis of Algebraic Surfaces Based on Planar Arrangements
bks-exact-eurocg08.pdf (193.49 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:
29-32
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 Geometric-Topological Analysis of Algebraic Surfaces" in the Proceedings of the 24th ACM Symposium on Computational Geometry, 2008, pp 164-173
(LaTeX) Abstract:
We present a method to compute the exact topology of a real algebraic surface
$S$, implicitly given by a polynomial $f \in \mathbb{Q}[x,y,z]$ of arbitrary
degree $N$.
Additionally, our analysis provides geometric information as it
supports the computation of arbitrary precise samples of $S$
including critical points.
We use a projection approach,
similar to Collins' cylindrical algebraic decomposition (cad).
In comparison we reduce the number of output cells to $O(N^5)$ by constructing
a special planar arrangement instead of a full cad in the projection plane.
Furthermore, our approach applies numerical and combinatorial methods to
minimize costly symbolic computations. The algorithm handles all sorts of
degeneracies without transforming the surface into a generic position.
We provide a complete \Cpp-implementation of the algorithm that shows
good performance for many well-known examples from algebraic geometry.
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{bks-gaoasbopa-08,
AUTHOR = {Berberich, Eric and Kerber, Michael and Sagraloff, Michael},
 EDITOR = {Petitjean, Sylvain},
 TITLE = {Geometric Analysis of Algebraic Surfaces Based on Planar Arrangements},
 BOOKTITLE = {24th European Workshop on Computational Geometry - Collection of Abstracts},
 YEAR = {2008},
 PAGES = {29--32},
 ADDRESS = {Nancy, France},
 MONTH = {March},
 ISBN = {2-905267-57-7},
 NOTE = {An extended version of this article has appeared under the name
"Exact Geometric-Topological Analysis of Algebraic Surfaces" in the Proceedings of the 24th ACM Symposium on Computational Geometry, 2008, pp 164-173},
}

Entry last modified by Michael Kerber, 03/03/2009
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Editor(s)
Michael Kerber		Created
06/26/2008 15:55:56
Revision
0.



Editor
Michael Kerber



Edit Date
06/26/2008 03:55:56 PM



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