Abstract
Algorithms in computational geometry are designed under the assumption of exact real arithmetic. Indiscriminately replacing exact real arithmetic by hardware floating-point arithmetic almost inevitably leads to robustness problems. Kettner et al. provide examples where rounding errors let such straightforward implementations of incremental convex hull computation crash, loop forever, or silently compute garbage. We complement their work by providing problematic examples for another planar convex hull algorithm.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
de Berg, M., Cheong, O., van Krefeld, M., Overmars, M.: Computational Geometry: Algorithms and Applications, 3rd revised edn. Springer, Heidelberg (2008)
ANSI, IEEE Standard 754–1985 : IEEE Standard for Binary Floating-Point Arithmetic (1985). Reprinted in SIGPLAN Notices 22(2), 9–25 (1987)
Kettner, L., Mehlhorn, K., Pion, S., Schirra, S., Yap, C.K.: Classroom examples of robustness problems in geometric computation. Comput. Geom. Theor. Appl. 40(1), 61–78 (2008)
Mehlhorn, K., Näher, S.: LEDA: A Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)
Mörig, M.: Companion Pages to Another Classroom Example of Robustness Problems in Planar Convex Hull Computation. http://wwwisg.cs.uni-magdeburg.de/ag/ClassroomExample/
Preparata, F.P., Shamos, M.I.: Computational Geometry: An Introduction, 1st edn. Springer, Heidelberg (1985)
Schirra, S.: Robustness and precision issues in geometric computation. In: Sack, J.R., Urrutia, J. (eds.) Handbook of Computational Geometry, chap. 14, pp. 597–632. Elsevier, Amsterdam, January 2000
Shewchuk, J.R.: Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete Comput. Geom. 18(3), 305–363 (1997)
Yap, C.K.: Robust geometric computation. In: Handbook of Discrete and Computational Geometry, chap. 41, pp. 927–952, 2nd edn. CRC (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Mörig, M. (2016). Another Classroom Example of Robustness Problems in Planar Convex Hull Computation. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_38
Download citation
DOI: https://doi.org/10.1007/978-3-319-32859-1_38
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-32858-4
Online ISBN: 978-3-319-32859-1
eBook Packages: Computer ScienceComputer Science (R0)