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 Author, Editor
 Author(s): Berberich, Eric Kerber, Michael Sagraloff, Michael dblp dblp dblp
 Editor(s): Petitjean, Sylvain dblp 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
 URL of the conference: http://eurocg08.loria.fr/ URL for downloading the paper: 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: 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},
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},
}