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Formally certified floating-point filters for homogeneous geometric predicates

Published online by Cambridge University Press:  24 April 2007

Guillaume Melquiond  and
Sylvain Pion
Guillaume Melquiond
Affiliation:
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
Sylvain Pion
Affiliation:
INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis, France; Sylvain.Pion@sophia.inria.fr
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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.

Keywords

Geometric predicatessemi-static filtersformal proofsfloating-point
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 41 , Issue 1: Real Numbers , January 2007 , pp. 57 - 69
Copyright
© EDP Sciences, 2007

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