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Author, Editor

Author(s):

Berberich, Eric
Kerber, Michael
Sagraloff, Michael

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Editor(s):

Petitjean, Sylvain

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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, 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 03:55:56 PM
Revision
0.



Editor
Michael Kerber



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



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