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Issue No. 09 - September (1997 vol. 46)
ISSN: 0018-9340
pp: 961-975
ABSTRACT
<p><b>Abstract</b>—Finite-precision leads to many problems in geometric methods from CAD or Computational Geometry. Until now, using exact rational arithmetic was a simple, yet much too slow, solution to be of any practical use in real-scale applications. A recent optimization—the lazy rational arithmetic [<ref rid="bibt09615" type="bib">5</ref>]—seems promising: It defers exact computations until they become either unnecessary (in most cases) or unavoidable; in such a context, only indispensable computations are performed exactly, that is, those without which any given decision cannot be reached safely using only floating-point arithmetic. This paper takes stock of the lazy arithmetic paradigm: principles, functionalities and limits, speed, possible variants and extensions, difficulties, problems solved or left unresolved.</p>
INDEX TERMS
Computational geometry, hash coding, interval arithmetic, robustness, exact rational arithmetic, lazy arithmetic, inconsistencies.
CITATION

D. Michelucci and J. Moreau, "Lazy Arithmetic," in IEEE Transactions on Computers, vol. 46, no. , pp. 961-975, 1997.
doi:10.1109/12.620478
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