Classroom examples of robustness problems in geometric computations

Lutz Kettner, Kurt Mehlhorn, Sylvain Pion, Stefan Schirra, Chee Yap

Research output: Contribution to journalArticle

Abstract

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating-point arithmetic for the assumed real arithmetic may cause implementations to fail. Although this is well known, there are no concrete examples with a comprehensive documentation of what can go wrong and why. In this paper, we provide a case study of what can go wrong and why. For our study, we have chosen two simple algorithms which are often taught, an algorithm for computing convex hulls in the plane and an algorithm for computing Delaunay triangulations in space. We give examples that make the algorithms fail in many different ways. We also show how to construct such examples systematically and discuss the geometry of the floating-point implementation of the orientation predicate. We hope that our work will be useful for teaching computational geometry.

Original languageEnglish (US)
Pages (from-to)61-78
Number of pages18
JournalComputational Geometry: Theory and Applications
Volume40
Issue number1
DOIs
StatePublished - May 1 2008

    Fingerprint

Keywords

  • Floating-point geometry
  • Implementation
  • Numerical robustness problems

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this