Effects of a modular filter on geometric applications

Abstract

We report on the effects of a filter based on modular arithmetic that has been introduced recently into the EXACUS library. Our experiments with planar arrangements for curves up to degree four show that the exact construction and comparison of real algebraic numbers are some of the most time consuming operations when solving intersection problems for curved objects. In our experiments the modular filter accelerated the computation for arrangements of cubic curves by a factor of about 6.