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Author, Editor(s)

Author(s):

Schömer, Elmar
Wolpert, Nicola

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Not MPG Author(s):

Schömer, Elmar

BibTeX cite key*:

sw-eeaccaq-05

Title

Title*:

An Exact and Efficient Approach for Computing a Cell in an Arrangement of Quadrics

Journal

Journal Title*:

Computational Geometry

Journal's URL:


Download URL
for the article:

http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6TYS-4H6XKWX-1-1&_cdi=5626&_user=43521&_orig=search&_coverDate=01%2F31%2F2006&_sk=999669998&view=c&wchp=dGLzVlz-zSkzS&md5=796eb62b3d59d3af6748c974e0cea964&ie=/sdarticle.pdf

Language:

English

Publisher

Publisher's
Name:


Publisher's URL:


Publisher's
Address:


ISSN:


Vol, No, pp, Date

Volume*:

33

Number:

1-2

Publishing Date:

2006

Pages*:

65 - 97

Number of
VG Pages:


Page Start:


Page End:


Sequence Number:


DOI:


Note, Abstract, ©

Note:


(LaTeX) Abstract:

We present an approach for the exact and efficient computation of a cell in an arrangement of quadric surfaces. All calculations are based on exact rational algebraic methods and provide the correct mathematical results in all, even degenerate, cases. By projection, the spatial problem is reduced to the one of computing planar arrangements of algebraic curves. We succeed in locating all event points in these arrangements, including tangential intersections and singular points. By introducing an additional curve, which we call the Jacobi curve, we are able to find non-singular tangential intersections. We show that the coordinates of the singular points in our special projected planar arrangements are roots of quadratic polynomials. The coefficients of these polynomials are usually rational and contain at most a single square root. A prototypical implementation indicates that our approach leads to good performance in practice.

URL for the Abstract:

http://portal.acm.org/citation.cfm?id=1125450&dl=acm&coll=&CFID=15151515&CFTOKEN=6184618
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TYS-4H6XKWX-1&_user=43521&_coverDate=01%2F31%2F2006&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000004638&_version=1&_urlVersion=0&_userid=43521&md5=ab050fce578c50706ddeded5a5a4cceb

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Keywords:


HyperLinks / References / URLs:


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Personal Comments:


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Access Level:

Public

Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Algorithms and Complexity Group

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BibTeX Entry:

@ARTICLE{sw-eeaccaq-05,
AUTHOR = {Sch{\"o}mer, Elmar and Wolpert, Nicola},
TITLE = {An Exact and Efficient Approach for Computing a Cell in an Arrangement of Quadrics},
JOURNAL = {Computational Geometry},
YEAR = {2006},
NUMBER = {1-2},
VOLUME = {33},
PAGES = {65 -- 97},
}


Entry last modified by Christine Kiesel, 02/07/2007
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Editor(s)
Nicola Wolpert
Created
01/17/2005 03:05:17 PM
Revisions
3.
2.
1.
0.
Editor(s)
Christine Kiesel
Christine Kiesel
Christine Kiesel
Nicola Wolpert
Edit Dates
07.02.2007 18:10:27
13.06.2006 11:08:16
13.06.2006 11:07:53
01/17/2005 03:05:17 PM
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