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  Exact, Efficient and Complete Arrangement Computation for Cubic Curves

Eigenwillig, A., Kettner, L., Schömer, E., & Wolpert, N. (2006). Exact, Efficient and Complete Arrangement Computation for Cubic Curves. Computational Geometry, 35, 36-73.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-22C2-8 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-22C3-6
Genre: Journal Article

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EKSW-Cubics-CGTA-authprep.pdf (Any fulltext), 494KB
 
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Copyright © 2005 Elsevier B.V. All rights reserved. This article has been published in Computational Geometry 35(1-2), August 2006, Pages 36-73.
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 Creators:
Eigenwillig, Arno1, Author           
Kettner, Lutz1, Author           
Schömer, Elmar1, Author           
Wolpert, Nicola1, Author           
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: The Bentley-Ottmann sweep-line method can compute the arrangement of planar curves, provided a number of geometric primitives operating on the curves are available. We discuss the reduction of the primitives to the analysis of curves and curve pairs, and describe efficient realizations of these analyses for planar algebraic curves of degree three or less. We obtain a \emph{complete}, \emph{exact}, and \emph{efficient\/} algorithm for computing arrangements of cubic curves. Special cases of cubic curves are conics as well as implicitized cubic splines and B\'ezier curves. The algorithm is \emph{complete\/} in that it handles all possible degeneracies such as tangential intersections and singularities. It is \emph{exact\/} in that it provides the mathematically correct result. It is \emph{efficient\/} in that it can handle hundreds of curves with a quarter million of segments in the final arrangement. The algorithm has been implemented in C\texttt{++} as an \textsc{Exacus} library called \textsc{CubiX}.

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Language(s): eng - English
 Dates: 2007-02-102006
 Publication Status: Issued
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: eDoc: 314461
Other: Local-ID: C1256428004B93B8-9FBA65AC1148D2AEC1257176004AA8EE-eksw-eecaccc-06
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Title: Computational Geometry
Source Genre: Journal
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Pages: - Volume / Issue: 35 Sequence Number: - Start / End Page: 36 - 73 Identifier: ISSN: 0925-7721