Abstract :
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-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
Keywords :
computational geometry; digital arithmetic; computational geometry; exact rational arithmetic; geometric methods; hash coding; inconsistencies; interval arithmetic; lazy arithmetic; lazy rational arithmetic; robustness; Application software; Calculus; Character generation; Computational geometry; Cryptography; Digital arithmetic; Floating-point arithmetic; Robustness; Signal design; Solid modeling;
