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Interval Arithmetic Yields Efficient Dynamic Filters for Computational Geometry

Abstract : We discuss interval techniques for speeding up the exact evaluation of geometric predicates and describe an efficient implementation of interval arithmetic that is strongly influenced by the rounding modes of the widely used IEEE 754 standard. Using this approach we engineer an efficient floating point filter for the computation of the sign of a determinant that works for arbitrary dimensions. Furthermore we show how to use our interval techniques for exact linear optimization problems of low dimension as they arise in geometric computing. We validate our approach experimentally, comparing it with other static, dynamic and semi-static filters.
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https://hal.inria.fr/inria-00344516
Contributor : Sylvain Pion <>
Submitted on : Friday, December 5, 2008 - 2:53:16 AM
Last modification on : Thursday, September 20, 2018 - 7:54:02 AM
Long-term archiving on: : Monday, June 7, 2010 - 11:47:11 PM

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  • HAL Id : inria-00344516, version 1

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Hervé Brönnimann, Christoph Burnikel, Sylvain Pion. Interval Arithmetic Yields Efficient Dynamic Filters for Computational Geometry. 14th Annual ACM Symposium on Computational Geometry (SCG), Jun 1998, Minneapolis, United States. pp.165-174. ⟨inria-00344516⟩

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