# 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 language English (US) 61-78 18 Computational Geometry: Theory and Applications 40 1 https://doi.org/10.1016/j.comgeo.2007.06.003 Published - May 2008

### Fingerprint

Robustness
Computational geometry
Computational Geometry
Digital arithmetic
Floating-point Arithmetic
Delaunay triangulation
Computing
Floating point
Triangulation
Convex Hull
Predicate
Teaching
Geometry
Model

### Keywords

• Floating-point geometry
• Implementation
• Numerical robustness problems

### ASJC Scopus subject areas

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

### Cite this

Classroom examples of robustness problems in geometric computations. / Kettner, Lutz; Mehlhorn, Kurt; Pion, Sylvain; Schirra, Stefan; Yap, Chee.

In: Computational Geometry: Theory and Applications, Vol. 40, No. 1, 05.2008, p. 61-78.

Research output: Contribution to journalArticle

Kettner, Lutz ; Mehlhorn, Kurt ; Pion, Sylvain ; Schirra, Stefan ; Yap, Chee. / Classroom examples of robustness problems in geometric computations. In: Computational Geometry: Theory and Applications. 2008 ; Vol. 40, No. 1. pp. 61-78.
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