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.
@article{ITA_2007__41_1_57_0,
author = {Melquiond, Guillaume and Pion, Sylvain},
title = {Formally certified floating-point filters for homogeneous geometric predicates},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {41},
year = {2007},
pages = {57-69},
doi = {10.1051/ita:2007005},
mrnumber = {2330043},
zbl = {1133.65010},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2007__41_1_57_0}
}
Melquiond, Guillaume; Pion, Sylvain. Formally certified floating-point filters for homogeneous geometric predicates. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) pp. 57-69. doi : 10.1051/ita:2007005. http://gdmltest.u-ga.fr/item/ITA_2007__41_1_57_0/
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