Isolating the singularities of the plane projection of a generic space curve

George Krait (1) , Sylvain Lazard (1) , Guillaume Moroz (1) , Marc Pouget (1)

1 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm

Isolating the singularities of a plane curve is the first step towards computing its topology. For this, numerical methods 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. This type of curves appears naturally in robotics applications and scientific visualization. In this setting, we show that the singularities can be encoded by a regular square system whose solutions can be isolated with certified numerical methods. Our analysis is conditioned by assumptions that we prove to be generic using transversality theory, we also provide a semi-algorithm to check their validity.

Mots clés: Transversality; Generic Singularities; Certified Numerical Algorithms; Interval Analysis; Singular Curve Topology

Domaines: Calcul formel [cs.SC]; Géométrie algorithmique [cs.CG]

George Krait, Sylvain Lazard, Guillaume Moroz, Marc Pouget. Isolating the singularities of the plane projection of a generic space curve. 2020. ⟨hal-02612412⟩