Double precision geometry: a general technique for calculating line and segment intersections using rounded arithmetic

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 arit...

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Bibliographic Details
Published in30th Annual Symposium on Foundations of Computer Science pp. 500 - 505
Main Author Milenkovic, V.
Format Conference Proceeding
LanguageEnglish
Published IEEE Comput. Soc. Press 1989
Subjects
Computational geometry
Computers
Costs
Equations
Failure analysis
Floating-point arithmetic
Hardware
Numerical analysis
Robustness
Standards development
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Summary: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.< >
ISBN:9780818619823
0818619821
DOI:10.1109/SFCS.1989.63525