(Enter summary)
Abstract: This article first recalls with some examples the damages that numerical inaccuracy of floating
point arithmetic can cause during geometric computations, in methods from Computational Geometry,
Computer Graphics or CADCAM. Then it surveys the various approaches proposed to overcome
inaccuracy difficulties. It seems that the only way to achieve robustness for existing methods from
Computational Geometry is exact computation, it is the "Exact Computation Paradigm" of C.K.
Yap and T. Dub'e.... (Update)
Context of citations to this paper: More .... se[35] 100000004091847875962975319375216640.000000 se[36] 1000000040918478759629753193752166400.000000 se[37] =10000000567641112624826207124609564672.000000 se[38] 100000006944061726476491472742798852096.000000 se[39] Inf #include stdio.h ... Cited by: More
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BibTeX entry: (Update)
D. Michelucci. The robustness issue. Found at http://www.emse.fr/micheluc/english/michelucci.html. http://citeseer.nj.nec.com/361993.html More @misc{ michelucci-robustness,
author = "D. Michelucci",
title = "The robustness issue",
text = "D. Michelucci. The robustness issue. Found at http://www.emse.fr/micheluc/english/michelucci.html.",
url = "citeseer.nj.nec.com/361993.html" }
Citations (may not include all citations):
232
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- Snyder - 1992
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- Fortune, Van Wyk - 1993
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- Dub'e, Yap - 1995
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Introduction to Computer Graphics (context) - Foley, van Dam et al. - 1994
38
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IEEE Foundations of Computer Science (context) - Clarkson, effective - 1992
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The design of linetool a geometric editor (context) - Ericson, Yap - 1988
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Universit'e Paris VII (context) - M'enissier-Morain, PhD - 1994
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Handling algebraic numbers in computer algebra (context) - Duval - 1989
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