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 failureexamples 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 www.mpi-sb.mpg.de/~mehlhorn/ftp/ ClassRooinExamples.ps. It contains further examples, more theory, and color pictures. We strongly recommend to read the full paper instead of this extended abstract.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 702-713 |
| Number of pages | 12 |
| Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Volume | 3221 |
| State | Published - 2004 |
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ASJC Scopus subject areas
- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science
Cite this
Classroom examples of robustness problems in geometric computations. / Kettner, Lutz; Mehlhorn, Kurt; Pion, Sylvain; Schirra, Stefan; Yap, Chee.
In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 3221, 2004, p. 702-713.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Classroom examples of robustness problems in geometric computations
AU - Kettner, Lutz
AU - Mehlhorn, Kurt
AU - Pion, Sylvain
AU - Schirra, Stefan
AU - Yap, Chee
PY - 2004
Y1 - 2004
N2 - 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 failureexamples 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 www.mpi-sb.mpg.de/~mehlhorn/ftp/ ClassRooinExamples.ps. It contains further examples, more theory, and color pictures. We strongly recommend to read the full paper instead of this extended abstract.
AB - 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 failureexamples 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 www.mpi-sb.mpg.de/~mehlhorn/ftp/ ClassRooinExamples.ps. It contains further examples, more theory, and color pictures. We strongly recommend to read the full paper instead of this extended abstract.
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UR - http://www.scopus.com/inward/citedby.url?scp=35048841152&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:35048841152
VL - 3221
SP - 702
EP - 713
JO - Lecture Notes in Computer Science
JF - Lecture Notes in Computer Science
SN - 0302-9743
ER -