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De la géométrie algorithmique au calcul géométrique

Sylvain Pion 1
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this thesis, we define efficient and generic methods in order to solve
the robustness problems that arise in the field of computational geometry,
and we concentrate especially on the exact evaluation of the geometric
We investigated methods based on modular arithmetic, which led us to
develop simple and efficient algorithms to reconstruct the sign in this
number representation.
We also developed new kinds of arithmetic filters,
which allow to speed up the exact computation of predicates, working
around the cost of traditionnal solutions based on generic
multiprecision computations.
Our methods are based on the use of interval arithmetic,
which allows an efficient and simple use, combined to an automatic
generation tool of the predicates code.
These solutions are now available in the CGAL library of geometric
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Contributor : Sylvain Pion <>
Submitted on : Thursday, December 22, 2005 - 4:41:38 PM
Last modification on : Saturday, March 13, 2021 - 3:32:26 AM
Long-term archiving on: : Saturday, April 3, 2010 - 7:49:16 PM


  • HAL Id : tel-00011258, version 1



Sylvain Pion. De la géométrie algorithmique au calcul géométrique. Modélisation et simulation. Université Nice Sophia Antipolis, 1999. Français. ⟨tel-00011258⟩



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