Abstract
This note is meant as a sequel to Steven Fortune's note on ‘Robustness issues in geometric algorithms’ [For96] in these proceedings. We revisit some of the issues raised by him, such as the consistency between the combinatorial and numerical data in geometric algorithms, and then we elaborate on a number of additional topics, including issues in proving correct geometric algorithms meant to be executed with imprecise primitives, and in the rounding of geometric structures so that all their features are exactly representable.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. The MIT Press, Cambridge, Mass., 1990.
S. Fortune and V. Milenkovic. Numerical stability of algorithms for line arrangements. In Proc. 7th Annu. ACM Sympos. Comput. Geom., pages 334–341, 1991.
S. Fortune. Computational geometry. In R. Martin, editor, Directions in Computational Geometry. Information Geometers, 1993. To appear.
S. Fortune. Numerical stability of algorithms for 2-d Delaunay triangulations. Internat. J. Comput. Geom. Appl., 5(1):193–213, 1995.
S. Fortune. Robustness issues in geometric algorithms. In Proc. 1996 Workshop on Applied Computational Geometry, page in these proceedings, 1996.
S. Fortune and C. J. Van Wyk. Efficient exact arithmetic for computational geometry. In Proc. 9th Annu. ACM Sympos. Comput. Geom., pages 163–172, 1993.
Leonidas Guibas and David Marimont. Rounding arrangements dynamically. In Proc. 11th Annu. ACM Sympos. Comput. Geom., pages 190–199, 1995.
L. J. Guibas, D. Salesin, and J. Stolfi. Epsilon geometry: building robust algorithms from imprecise computations. In Proc. 5th Annu. ACM Sympos. Comput. Geom., pages 208–217, 1989.
L. Guibas, D. Salesin, and J. Stolfi. Constructing strongly convex approximate hulls with inaccurate primitives. In Proc. 1st Annu. SIGAL Internat. Sympos. Algorithms, volume 450 of Lecture Notes in Computer Science, pages 261–270. Springer-Verlag, 1990.
D. H. Greene and F. F. Yao. Finite-resolution computational geometry. In Proc. 27th Annu. IEEE Sympos. Found. Comput. Sci., pages 143–152, 1986.
V. J. Milenkovic. Verifiable implementations of geometric algorithms using finite precision arithmetic. Artif. Intell, 37:377–401, 1988.
V. Milenkovic. Rounding face lattices in d dimensions. In Proc. 2nd Canad. Conf. Comput. Geom., pages 40–45, 1990.
N.E. Mnev. The universality thorems on the classification problem of configuration varieties and convex polytope varieties. In O.Y. Viro, editor, Topology and Geometry — Rohlin Seminar, pages 527–544. Springer Verlag, 1989.
D. Pedoe. Geometry, a comprehensive course. Dover Publications, New York, 1970.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Guibas, L.J. (1996). Implementing geometric algorithms robustly. In: Lin, M.C., Manocha, D. (eds) Applied Computational Geometry Towards Geometric Engineering. WACG 1996. Lecture Notes in Computer Science, vol 1148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014477
Download citation
DOI: https://doi.org/10.1007/BFb0014477
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61785-3
Online ISBN: 978-3-540-70680-9
eBook Packages: Springer Book Archive