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Author, Editor

Author(s):

Geismann, Nicola
Hemmer, Michael
Schömer, Elmar

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Editor(s):





BibTeX cite key*:

ghs-qsi-01

Title, Booktitle

Title*:

Computing a 3-dimensional Cell in an Arrangement of Quadrics: Exactly and Actually!

Booktitle*:

Proceedings of the 17th Annual Symposium on Computational Geometry (SCG-01)

Event, URLs

URL of the conference:

http://www.cs.tufts.edu/EECS/scg01

URL for downloading the paper:


Event Address*:

Boston, Massachusetts

Language:

English

Event Date*
(no longer used):

June, 3-5

Organization:

ACM SIGACT and SIGGRAPH

Event Start Date:

23 September 2019

Event End Date:

23 September 2019

Publisher

Name*:

ACM

URL:


Address*:

New York

Type:


Vol, No, Year, pp.

Series:


Volume:


Number:


Month:


Pages:

264-273

Year*:

2001

VG Wort Pages:


ISBN/ISSN:


Sequence Number:


DOI:




Note, Abstract, ©


(LaTeX) Abstract:

We present two approaches to the problem of calculating a cell in a
3-dimensional arrangement of quadrics. The first approach solves the
problem using rational arithmetic. It works with reductions to
planar arrangements of algebraic curves. Degenerate
situations such as tangential intersections and self-intersections of
curves are intrinsic to the planar arrangements we obtain.
The coordinates of the intersection points are given by
the roots of univariate polynomials.
We succeed in locating all intersection points either by extended
local box hit counting arguments or by globally characterizing
them with simple square root expressions.
The latter is realized by a clever factorization of the univariate
polynomials. Only the combination of these two results
facilitates a practical and implementable algorithm.

The second approach operates directly in 3-space by applying
classical solid modeling techniques. Whereas the first
approach guarantees a correct solution in every case the second one
may fail in some degenerate situations. But with the
help of verified floating point arithmetic it can detect these
critical cases and is faster if the quadrics are in general
position.



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Access Level:


Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Algorithms and Complexity Group

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{ghs-qsi-01,
AUTHOR = {Geismann, Nicola and Hemmer, Michael and Sch{\"o}mer, Elmar},
TITLE = {Computing a 3-dimensional Cell in an Arrangement of Quadrics: Exactly and Actually!},
BOOKTITLE = {Proceedings of the 17th Annual Symposium on Computational Geometry (SCG-01)},
PUBLISHER = {ACM},
YEAR = {2001},
ORGANIZATION = {ACM SIGACT and SIGGRAPH},
PAGES = {264--273},
ADDRESS = {Boston, Massachusetts},
}


Entry last modified by Uwe Brahm, 03/02/2010
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Editor(s)
Elmar Schoemer
Created
03/13/2002 02:36:40 PM
Revisions
3.
2.
1.
0.
Editor(s)
Uwe Brahm
Elmar Schoemer
Elmar Schoemer
Elmar Schoemer
Edit Dates
04/29/2002 02:49:59 PM
13/03/2002 15:02:30
13/03/2002 14:43:08
13/03/2002 14:36:41