Numerical Algorithm for the Topology of Singular Plane Curves

George Krait 1 Sylvain Lazard 1 Guillaume Moroz 1 Marc Pouget 1
1 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : We are interested in computing the topology of plane singular curves. For this, the singular points must be isolated. Numerical methods for isolating singular points are efficient but not certified in general. We are interested in developing certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. In this setting, we show that the singularities can be encoded by a regular square system whose isolation can be certified by numerical methods. This type of curves appears naturally in robotics applications and scientific visualization.
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George Krait, Sylvain Lazard, Guillaume Moroz, Marc Pouget. Numerical Algorithm for the Topology of Singular Plane Curves. EuroCG'19 - 35th European Workshop on Computational Geometry, Mar 2019, Utrecht, Netherlands. ⟨hal-02294028⟩

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