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Epsilon geometry: building robust algorithms from imprecise computations
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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驴the lazy rational arithmetic [5]驴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.