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Author, Editor(s)

Author(s):

Berberich, Eric
Sagraloff, Michael

dblp
dblp



BibTeX cite key*:

bs-agffgtaas-cagd-09

Title

Title*:

A Generic and Flexible Framework for the Geometrical and Topological Analysis of (Algebraic) Surfaces

Journal

Journal Title*:

Computer Aided Geometric Design (CAGD)

Journal's URL:

http://www.elsevier.com/locate/cagd

Download URL
for the article:

http://dx.doi.org/10.1016/j.cagd.2009.03.006

Language:

English

Publisher

Publisher's
Name:

Elsevier

Publisher's URL:


Publisher's
Address:

Amsterdam, The Netherlands

ISSN:

0167-8396

Vol, No, pp, Date

Volume*:

26

Number:

6

Publishing Date:

August 2009

Pages*:

627-647

Number of
VG Pages:

20

Page Start:

627

Page End:

647

Sequence Number:


DOI:

10.1016/j.cagd.2009.03.006

Note, Abstract, ©

Note:


(LaTeX) Abstract:

We present a generic framework on a set of surfaces S in R^3 that provides their geometric and topological analysis in order to support various algorithms and applications in computational geometry. Our implementation follows the generic programming paradigm, that is, to support a certain family of surfaces, we require a small set of types and some basic operations on them, all collected in a model of the newly presented SurfaceTraits_3 concept. The framework obtains geometric and topological information on a non-empty set of surfaces in two steps. First, important 0- and 1-dimensional features are projected onto the xy-plane, obtaining an arrangement A"S with certain properties. Second, for each of its components, a sample point is lifted back to R^3 while detecting intersections with the given surfaces. For the projection we rely on Cgal's Arrangement_2 package as basic tool. Anyhow, the complexity of the output is high, and thus, we particularly regard the framework as key ingredient for querying information on and constructing geometric objects from a small set of surfaces. Examples are meshing of single surfaces, the computation of space-curves defined by two surfaces, to compute lower envelopes of surfaces, or as a basic step to compute an efficient representation of a three-dimensional arrangement. We show that the well-known family of (semi-)algebraic surfaces fulfills the framework's requirements. As robust implementations on these surfaces are lacking these days, we consider the framework to be an important step to fill this gap. In particular, we instantiate the framework by a fully-fledged model for special algebraic surfaces, namely quadrics. This instantiation already supports main tasks demanded from rotational robot motion planning, for example, as expected to compute a Piano Mover's instance.

URL for the Abstract:


Categories,
Keywords:

algebraic surface, cylindrical algebraic decomposition, exact geometric computation, generic programming, topology computation

HyperLinks / References / URLs:


Copyright Message:


Personal Comments:


Download
Access Level:

Public

Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Algorithms and Complexity Group

Audience:

popular

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BibTeX Entry:

@ARTICLE{bs-agffgtaas-cagd-09,
AUTHOR = {Berberich, Eric and Sagraloff, Michael},
TITLE = {A Generic and Flexible Framework for the Geometrical and Topological Analysis of (Algebraic) Surfaces},
JOURNAL = {Computer Aided Geometric Design (CAGD)},
PUBLISHER = {Elsevier},
YEAR = {2009},
NUMBER = {6},
VOLUME = {26},
PAGES = {627--647},
ADDRESS = {Amsterdam, The Netherlands},
MONTH = {August},
ISBN = {0167-8396},
DOI = {10.1016/j.cagd.2009.03.006},
}


Entry last modified by Michael Sagraloff, 01/20/2011
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Editor(s)
[Library]
Created
01/20/2010 12:30:41 PM
Revisions
8.
7.
6.
5.
4.
Editor(s)
Michael Sagraloff
Anja Becker
Eric Berberich
Eric Berberich
Eric Berberich
Edit Dates
20.01.2011 10:02:21
01.03.2010 13:40:53
01/20/2010 12:36:33 PM
01/20/2010 12:33:53 PM
01/20/2010 12:33:06 PM
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