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Melquiond, Guillaume; Pion, Sylvain
Formally certified floating-point filters for homogeneous geometric predicates. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, 41 no. 1 (2007), p. 57-69
Texte intégral djvu | pdf | Analyses MR 2330043 | Zbl 1133.65010
Class. Math.: 65D18, 65G50, 68Q60
Mots clés: geometric predicates, semi-static filters, formal proofs, floating-point

URL stable: http://www.numdam.org/item?id=ITA_2007__41_1_57_0

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Résumé

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.

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