Robustness issues in geometric algorithms

  • Steven Fortune
Invited Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1148)


Voronoi Diagram Computational Geometry Perturbation Function Geometric Algorithm Predicate Expression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Burnikel, K. Mehlhorn, S. Schirra, How to compute the Voronoi diagram of line segments: theoretical and experimental results. Proc. 2nd Eur. Symp. Alg. (ESA 94), 1994.Google Scholar
  2. 2.
    C. Burnikel, K. Mehlhorn, S. Schirra, On degeneracy in geometric computations, Proc. Fifth Annual Symp. Discrete Algorithms pp. 16–23, 1994.Google Scholar
  3. 3.
    K. L. Clarkson, Safe and effective determinant evaluation, 33th Symp. on Found. Comp. Sci. 387–395, 1992.Google Scholar
  4. 4.
    H. Edelsbrunner, E. Mücke. Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graphics 9(1):66–104, 1990.CrossRefGoogle Scholar
  5. 5.
    S. Fang, B. Bruderlin, X. Zhu, Robustness in solid modelling — a tolerance based, intuitionistic approach, Computer Aided Design, 25:9, 1993.CrossRefGoogle Scholar
  6. 6.
    S. Fortune, Progress in computational geometry, in Directions in Geometric Computing, Ch. 3, pp. 81–128, R. Martin, ed. Information Geometers Ltd, 1993.Google Scholar
  7. 7.
    S. Fortune, C. Van Wyk, Static analysis yields efficient exact integer arithmetic for computational geometry, to appear, Transactions on Graphics. See also Efficient exact arithmetic for computational geometry, Proc. Ninth Ann. Symp. Comp. Geom, pp. 163–172, 1993.Google Scholar
  8. 8.
    S. Fortune, Numerical stability of algorithms for 2d Delaunay triangulations, International Journal of Computational Geometry and Applications, 5(1,2), 193–213, 1995.CrossRefGoogle Scholar
  9. 9.
    S. Fortune, Polyhedral modelling with exact arithmetic, Proc. Third Symp. Solid Modeling and Applications, pp. 225–234, 1995.Google Scholar
  10. 10.
    L. Guibas, D. Marimont, Rounding arrangements dynamically, Proc. Eleventh Ann. Symp. Comp. Geom, pp. 190–199.Google Scholar
  11. 11.
    C. Hoffmann, The problems of accuracy and robustness in geometric computation. Computer 22:31–42 (1989).CrossRefGoogle Scholar
  12. 12.
    D.J. Jackson, Boundary representation modelling with local tolerances, Proc. Third Symp. on Solid Modeling and Applications, pp. 247–254 (1995).Google Scholar
  13. 13.
    P. Jaillon, Proposition d'une arithmétique rationnelle paresseuse et d'un outil d'aide à la saisie d'objets en synthèse d'images, Thèse, Ecole Nationale Superieure des Mines de Saint-Etienne, 1993.Google Scholar
  14. 14.
    S. Näher, The LEDA user manual, Version 3.1, January 16, 1995. LEDA is available by anonymous FTP from in directory /pub/LEDA.Google Scholar
  15. 15.
    Victor Milenkovic, Verifiable implementations of geometric algorithms using finite precision arithmetic. Artificial Intelligence, 37:377–401, 1988.CrossRefGoogle Scholar
  16. 16.
    A. Rege, J. Canny, Fast point location for two-and three-dimesional real algebraic geometry, to appear, 1995.Google Scholar
  17. 17.
    J. R. Shewchuk, Robust adaptive floating-point geometric predicates, Proc. 12th Ann. Symp. Comp. Geom, pp. 141–150.Google Scholar
  18. 18.
    K. Sugihara, M. Iri, Construction of the Voronoi diagram for one million generators in single precision arithmetic, First Can. Conf. Comp. Geom., 1989.Google Scholar
  19. 19.
    C. Yap, T. Dubé, The exact computation paradigm, 452-492, Computing in Euclidean geometry, D.Z. Du, F. Hwang, eds, World Scientific, 1995, second edition.Google Scholar
  20. 20.
    J. Yu, Exact arithmetic solid modeling, Ph.D. Thesis, Purdue University, 1992, available as CSD-TR-92-037.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Steven Fortune
    • 1
  1. 1.AT&T Bell LaboratoriesMurray Hill

Personalised recommendations