George Krait (Gamble) will defend his thesis, entitled : Isolating the Singularities of the Plane Projection of Generic Space Curves and Applications in Robotics, on Tuesday, Mai 4th 2021 at 9:30 am.
Abstract
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. Finally, we present experiments in visualization and robotics, some of which are not reachable by other methods, and discuss the efficiency of our method.
Keywords: Transversality, Generic Singularities, Certified Numerical Algorithms, Interval Arithmetic, Singular Curve Topology
Composition of the jury
Reviewers: Nicolas Delanoue (Université d’Angers, ISTIA)
Sonia Pérez-Díaz (University of Alcala)
Examiners: Pierrick Gaudry (CNRS, Loria)
Sylvain Lazard -directeur- (INRIA Nancy Grand Est, Loria)
Guillaume Moroz -co-directeur- (INRIA Nancy Grand Est, Loria)
Erika Ottaviano (University of Cassino and Southern Lazio)
Guest: Marc Pouget (INRIA Nancy Grand Est, Loria)
The event will take place on Teams.
