On The Topology of Planar Algebraic Curves

Jinsan Cheng (1) , Sylvain Lazard (1) , Luis Mariano Peñaranda (1) , Marc Pouget (1) , Fabrice Rouillier (2) , Elias P. P. Tsigaridas (1)

1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
2 SALSA - Solvers for Algebraic Systems and Applications

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.

Domaines: Géométrie algorithmique [cs.CG]

Jinsan Cheng, Sylvain Lazard, Luis Mariano 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⟩