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Conference Paper

Classroom Examples of Robustness Problems in Geometric Computations

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44766

Kettner,  Lutz
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45191

Pion,  Sylvain
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45391

Schirra,  Stefan
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45771

Yap,  Chee
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons43989

Albers,  Susanne
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Kettner, L., Mehlhorn, K., Pion, S., Schirra, S., & Yap, C. (2004). Classroom Examples of Robustness Problems in Geometric Computations. In Algorithms – ESA 2004: 12th Annual European Symposium (pp. 702-713). Berlin, Germany: Springer.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-2A4C-5
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 is no comprehensive documentation of what can go wrong and why. In this extended abstract, we study a simple incremental algorithm for planar convex hulls and give examples which make the algorithm fail in all possible ways. We also show how to construct failure-examples semi-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. The full paper is available at~\url{www.mpi-sb.mpg.de/~mehlhorn/ftp/ClassRoomExamples.ps}. It contains further examples, more theory, and color pictures. We strongly recommend to read the full paper instead of this extended abstract.