Further Results on Arithmetic Filters for Geometric Predicates

Details Further Results on Arithmetic Filters for Geometric Predicates Further Results on Arithmetic Filters for Geometric Predicates

1999-07-19

arxiv.org/abs/cs/9907028v1

Comput. Geom. Theory Appl. 1999 13:141-148

Computer Science

Computational Geometry

7 pages 2 figures presented at the 15th European Workshop Comput. Geom., 113--116, 1999 improve previous results (in other pap

Scientific paper

An efficient technique to solve precision problems consists in using exact computations. For geometric predicates, using systematically expensive exact computations can be avoided by the use of filters. The predicate is first evaluated using rounding computations, and an error estimation gives a certificate of the validity of the result. In this note, we studies the statistical efficiency of filters for cosphericity predicate with an assumption of regular distribution of the points. We prove that the expected value of the polynomial corresponding to the in sphere test is greater than epsilon with probability O(epsilon log 1/epsilon) improving the results of a previous paper by the same authors.

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