Proceedings of the twenty-seventh annual symposium on Computational geometry
Computational Geometry: Theory and Applications
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For the first time it is shown how to reduce the cost of performing specific geometric constructions by using rounded arithmetic instead of exact arithmetic. By exploiting a property of floating-point arithmetic called monotonicity, a technique called double-precision geometry can replace exact arithmetic with rounded arithmetic in any efficient algorithm for computing the set of intersections of a set of lines or line segments. The technique reduces the complexity of any such line or segment arrangement algorithm by a constant factor. In addition, double-precision geometry reduces by a factor of N the complexity of rendering segment arrangements on a 2/sup N/*2/sup N/ integer grid such that output segments have grid points as endpoints.