MPI-INF D1 Publications: Journal Article: An Exact and Efficient Approach for Computing a Cell in an Arrangement of Quadrics

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Author(s):

Schömer, Elmar
Wolpert, Nicola

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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

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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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Download Access Level:	Public

Correlation

MPG Unit:	Max-Planck-Institut für Informatik

MPG Subunit:	Algorithms and Complexity Group
Appearance:	MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort

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

Edit History (please click the blue arrow to see the details)

	Editor(s) Nicola Wolpert	Created 01/17/2005 15:05:17
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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