RAIRO - Theoretical Informatics and Applications

Research Article

Formally certified floating-point filters for homogeneous geometric predicates

Guillaume Melquionda1 and Sylvain Piona2

a1 Laboratoire de l'informatique du parallélisme, UMR 5668 CNRS, ENS Lyon, INRIA, UCBL, 46 allée d'Italie, 69364 Lyon Cedex 07, France; Guillaume.Melquiond@ens-lyon.fr

a2 INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis, France; Sylvain.Pion@sophia.inria.fr

Abstract

Floating-point arithmetic provides a fast but inexact way of computing geometric predicates. In order for these predicates to be exact, it is important to rule out all the numerical situations where floating-point computations could lead to wrong results. Taking into account all the potential problems is a tedious work to do by hand. We study in this paper a floating-point implementation of a filter for the orientation-2 predicate, and how a formal and partially automatized verification of this algorithm avoided many pitfalls. The presented method is not limited to this particular predicate, it can easily be used to produce correct semi-static floating-point filters for other geometric predicates.

(Online publication April 24 2007)

Key Words:

  • Geometric predicates;
  • semi-static filters;
  • formal proofs;
  • floating-point

Mathematics Subject Classification:

  • 65D18;
  • 65G50;
  • 68Q60
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