Computing Exact Geometric Predicates Using Modular Arithmetic with Single Precision

Abstract: We propose an e cient method that determines the sign of a multivariate polynomial expression with integer coe cients. This is a central operation on which the robustness of many geometric algorithms depends. The method relies on modular computations, for which comparisons are usually thought to require multiprecision. Our novel technique of recursive relaxation of the moduli enables us to carry out sign determination and comparisons by using only oating point computations in single precision. The method is highly parallelizable and is the fastest of all known multiprecision methods from a complexity point of view. We show how to compute a few geometric predicates that reduce to matrix determinants. We discuss implementation e ciency, which can be enhanced by good arithmetic lters. We substantiate these claims by experimental results and comparisons to other existing approaches. This method can be used to generate robust and e cient implementations of geometric algorithms, in...

• Type: Conference
• Year: 1997
• Where: COMPGEOM
• Authors: Hervé Brönnimann, Ioannis Z. Emiris, Victor Y. Pan, Sylvain Pion
• Keywords: COMPGEOM 1997, Discrete Geometry, Geometric Algorithms, Integer Coe Cients, Multivariate Polynomial Expression