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Issue No.09 - September (1997 vol.46)
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
Dominique Michelucci, Jean-Michel Moreau, "Lazy Arithmetic", IEEE Transactions on Computers, vol.46, no. 9, pp. 961-975, September 1997, doi:10.1109/12.620478
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