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Habilitation à diriger des recherches

Contributions au calcul géométrique effectif avec des objets courbes de faible degré

Sylvain Petitjean 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The physical world in which we live is essentially geometric. Geometric computing is a central building block in many fields, such as computer-aided design, computer graphics, robotics, computer vision and many others. For over three decades, computational geometry has been dedicated to supplying a solid foundation for the study of geometric algorithms which are relevant to all these applications. It has historically and traditionally focussed on the treatment of linear objects. For many applications, it is necessary to manipulate more general objects such as complex curves and surfaces. There are numerous issues involved in extending the repertoire of computational geometry to curved objects, namely: a complete rework of even its most basic data structures and algorithms; the massive intrusion of algebraic issues; the explosion of the number of degenerate cases...

This habilitation thesis contributes to the unfolding of an effective geometric computing dedicated to low-degree curved objects. It summarizes my main contributions on the subject over recent years. Let us mention in particular: an exact, optimal and efficient algorithm for computing a parameterization of the intersection of two quadrics with integer coefficients; the characterization of the relative position of two projective conics with low-degree geometric predicates, uncovered using algebraic invariant theory; the characterization of the degeneracies in the problem of real common tangents to four spheres; the convexity of the cone of directions of lines piercing three disjoint balls, and the important consequences of this result in geometric transversal theory. The manuscript concludes with an overview of many research directions to extend the results obtained thus far.
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Habilitation à diriger des recherches
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Contributor : Sylvain Petitjean <>
Submitted on : Wednesday, November 14, 2007 - 2:27:27 PM
Last modification on : Monday, September 23, 2019 - 5:12:21 PM
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  • HAL Id : tel-00187348, version 1



Sylvain Petitjean. Contributions au calcul géométrique effectif avec des objets courbes de faible degré. Génie logiciel [cs.SE]. Institut National Polytechnique de Lorraine - INPL, 2007. ⟨tel-00187348⟩



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