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  An Exact, Complete and Efficient Implementation for Computing Planar Maps of Quadric Intersection Curves

Berberich, E., Hemmer, M., Kettner, L., Schömer, E., & Wolpert, N. (2005). An Exact, Complete and Efficient Implementation for Computing Planar Maps of Quadric Intersection Curves. In 21st Annual Symposium on Computational Geometry (SCG'05) (pp. 99-106). New York, USA: ACM.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-25AE-D Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-25AF-B
Genre: Conference Paper

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 Creators:
Berberich, Eric1, Author           
Hemmer, Michael1, Author           
Kettner, Lutz1, Author           
Schömer, Elmar1, Author           
Wolpert, Nicola1, Author           
Mitchell, Joe, Editor
Rote, Günter, Editor
Kettner, Lutz1, Editor           
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: We present the first exact, complete and efficient implementation that computes for a given set $P=\{p_1,\dots,p_n\}$ of quadric surfaces the planar map induced by all intersection curves $p_1\cap p_i$, $2\leq i\leq n$, running on the surface of $p_1$. The vertices in this graph are the singular and $x$-extreme points of the curves as well as all intersection points of pairs of curves. Two vertices are connected by an edge if the underlying points are connected by a branch of one of the curves. Our work is based on and extends ideas developed in~[20] and~[9]. Our implementation is {\em complete} in the sense that it can handle all kind of inputs including all degenerate ones where intersection curves have singularities or pairs of curves intersect with high multiplicity. It is {\em exact} in that it always computes the mathematical correct result. It is {\em efficient} measured in running times.

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Language(s): eng - English
 Dates: 2006-05-112005
 Publication Status: Issued
 Pages: -
 Publishing info: New York, USA : ACM
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 279188
Other: Local-ID: C1256428004B93B8-F477E647B2943C59C12570B30054504C-bhksw-eceicpmqic-05
 Degree: -

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Title: Untitled Event
Place of Event: Pisa, Italy
Start-/End Date: 2005-06-06

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Title: 21st Annual Symposium on Computational Geometry (SCG'05)
Source Genre: Proceedings
 Creator(s):
Affiliations:
Publ. Info: New York, USA : ACM
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 99 - 106 Identifier: ISBN: 1-58113-991-8