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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

URL of the conference:

http://ewcg07.tugraz.at/

URL for downloading the paper:


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



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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
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Editor(s)
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Eric Berberich
Eric Berberich
Eric Berberich
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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
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