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  Complete, Exact and Efficient Computations with Cubic Curves

Eigenwillig, A., Kettner, L., Schömer, E., & Wolpert, N. (2004). Complete, Exact and Efficient Computations with Cubic Curves. In Proceedings of the Twentieth Annual Symposium on Computational Geometry: (SCG'04) (pp. 409-418). New York, USA: ACM.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2A58-9 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2A59-7
Genre: Conference Paper

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 Creators:
Eigenwillig, Arno1, Author           
Kettner, Lutz1, Author           
Schömer, Elmar1, Author           
Wolpert, Nicola1, Author           
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: The Bentley-Ottmann sweep-line method can be used to compute the arrangement of planar curves provided a number of geometric primitives operating on the curves are available. We discuss the mathematics of the primitives for planar algebraic curves of degree three or less and derive efficient realizations. As a result, we obtain a complete, exact, and efficient algorithm for computing arrangements of cubic curves. Conics and cubic splines are special cases of cubic curves. The algorithm is complete in that it handles all possible degeneracies including singularities. It is exact in that it provides the mathematically correct result. It is efficient in that it can handle hundreds of curves with a quarter million of segments in the final arrangement.

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Language(s): eng - English
 Dates: 2005-06-062004
 Publication Status: Issued
 Pages: -
 Publishing info: New York, USA : ACM
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 232006
Other: Local-ID: C1256428004B93B8-CD6033B3A701DCD5C1256F87003EB777-Eigenwillig2004a
 Degree: -

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Title: Untitled Event
Place of Event: Brooklyn, New York, USA
Start-/End Date: 2004-06-09

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Title: Proceedings of the Twentieth Annual Symposium on Computational Geometry : (SCG'04)
Source Genre: Proceedings
 Creator(s):
Affiliations:
Publ. Info: New York, USA : ACM
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 409 - 418 Identifier: -