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On The Topology of Planar Algebraic Curves

Jinsan Cheng 1 Sylvain Lazard 1 Luis Peñaranda 1 Marc Pouget 1 Fabrice Rouillier 2, 3 Elias P. Tsigaridas 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 SALSA - Solvers for Algebraic Systems and Applications
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
3 LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We introduce a method to compute the topology of planar algebraic curves. The curve may not be in generic position and may have vertical asymptotes. The algebraic tools are rational univariate representation for zero-dimensional ideals and multiplicities in these ideals. Experiments show the efficiency of our algorithm.
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Conference papers
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https://hal.inria.fr/inria-00329754
Contributor : Marc Pouget <>
Submitted on : Monday, October 13, 2008 - 1:41:56 PM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM
Long-term archiving on: : Tuesday, October 9, 2012 - 12:02:08 PM

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  • HAL Id : inria-00329754, version 1

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Jinsan Cheng, Sylvain Lazard, Luis Peñaranda, Marc Pouget, Fabrice Rouillier, et al.. On The Topology of Planar Algebraic Curves. 24th European Workshop on Computational Geometry - EuroCG 2008, Mar 2008, Nancy, France. pp.213--216. ⟨inria-00329754⟩

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