Further results on arithmetic filters for geometric predicates

An efficient technique to solve precision problems consists in using exact computations. For geometric predicates, using systematically expensive exac t computations can be avoided by the use of filters. The predicate is first evaluated using rounding computations, and an error estimation gives a cer tificate of the validity of the result. In this note, we study the statisti cal efficiency of filters far cosphericity predicate with an assumption of regular distribution of the points. We prove that the expected value of the polynomial corresponding to the insphere test is greater than epsilon with probability O(epsilon log 1/epsilon) improving the results of a previous p aper. (C) 1999 Elsevier Science B.V. All rights reserved.