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Proceedings Article, Paper
@InProceedings
Beitrag in Tagungsband, Workshop

Author, Editor
Author(s):
Berberich, Eric
Caroli, Manuel
Wolpert, Nicola
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Not MPG Author(s):
Wolpert, Nicola
Editor(s):
BibTeX cite key*:
BCW-ECARC2007
Title, Booktitle
Title*:
Exact Computation of Arrangements of Rotated Conics
main.pdf (166.67 KB)
Booktitle*:
Proceedings of 23rd European Workshop on Computational Geometry
Event, URLs
Conference URL::
http://ewcg07.tugraz.at/
Downloading URL:
Event Address*:
Graz, Austria
Language:
English
Event Date*
(no longer used):
Organization:
Event Start Date:
19 March 2007
Event End Date:
21 March 2007
Publisher
Name*:
Technische Universitaet Graz
URL:
http://www.ub.tugraz.at/Verlag
Address*:
Graz, Austria
Type:
Vol, No, Year, pp.
Series:
Volume:
Number:
Month:
March
Pages:
231-234
Year*:
2007
VG Wort Pages:
4
ISBN/ISSN:
978-3-902465-62-7
Sequence Number:
DOI:
Note, Abstract, ©
(LaTeX) Abstract:
Transformations of geometric objects, like translation and rotation,
are fundamental operations in CAD-systems. Rotations trigger
the need to deal with trigonometric functions, which is hard to
achieve when aiming for exact and robust implementation.

We show how we efficiently compute the planar arrangement
of conics rotated by angles that can be constructed
with straightedge and compass. Well-known examples are multiples of
$45{^{\circ}}$, $30{^{\circ}}$, and $15{^{\circ}}$.
The main problem one has to solve is root-isolation of univariate
polynomials $p(x)\in \mathbb{Q}(\sqrt{c_1})\ldots(\sqrt{c_d})[x]$, for which
we use a modified version of the Descartes method.
For $d=1$,
%In the case $p(x)\in \mathbb{Q}(\sqrt{c})[x]$
we additionally present a new method that isolates the real roots
of $p$ by using root isolation for polynomials $q(x)\in\mathbb{Q}[x]$ only.
We show results of our benchmark experiences comparing both
methods.
Keywords:
Conics, Transformation, Rotation, Arrangements
Download
Access Level:
Public

Correlation
MPG Unit:
Max-Planck-Institut für Informatik
MPG Subunit:
Algorithms and Complexity Group
External Affiliations:
Hochschule für Technik Stuttgart
Research Context:
Computational Geometry
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{BCW-ECARC2007,
AUTHOR = {Berberich, Eric and Caroli, Manuel and Wolpert, Nicola},
TITLE = {Exact Computation of Arrangements of Rotated Conics},
BOOKTITLE = {Proceedings of 23rd European Workshop on Computational Geometry},
PUBLISHER = {Technische Universitaet Graz},
YEAR = {2007},
PAGES = {231--234},
ADDRESS = {Graz, Austria},
MONTH = {March},
ISBN = {978-3-902465-62-7},
}


Entry last modified by Eric Berberich, 02/28/2008
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Editor(s)
Eric Berberich
Created
03/06/2007 11:21:24 AM
Revisions
4.
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Editor(s)
Eric Berberich
Eric Berberich
Eric Berberich
Eric Berberich
Eric Berberich
Edit Dates
04/07/2007 02:04:25 PM
04/07/2007 02:03:57 PM
04/07/2007 02:01:15 PM
03/06/2007 11:23:20 AM
03/06/2007 11:21:24 AM


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