Skip to Main content Skip to Navigation
Journal articles

Classroom examples of robustness problems in geometric computations

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.
Complete list of metadatas

Cited literature [27 references]  Display  Hide  Download

https://hal.inria.fr/inria-00344310
Contributor : Sylvain Pion <>
Submitted on : Monday, December 15, 2008 - 10:08:10 PM
Last modification on : Wednesday, August 14, 2019 - 10:46:03 AM
Document(s) archivé(s) le : Monday, June 7, 2010 - 11:44:22 PM

File

RevisedClassroomExamples.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Lutz Kettner, Kurt Mehlhorn, Sylvain Pion, Stefan Schirra, Chee Yap. Classroom examples of robustness problems in geometric computations. Computational Geometry, Elsevier, 2008, 40 (1), pp.61-78. ⟨10.1016/j.comgeo.2007.06.003⟩. ⟨inria-00344310⟩

Share

Metrics

Record views

1003

Files downloads

953