Skip to main content
SpringerLink
Log in

An Easy to Use Implementation of Linear Perturbations within Cupgal

  • Conference paper
  • First Online:
Algorithm Engineering (WAE 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1668))

Included in the following conference series:

Abstract

Most geometric algorithms are formulated under the non-degeneracy assumption which usually does not hold in practice. When implementing such an algorithm, a treatment of degenerate cases is necessary to prevent incorrect outputs or crashes. One way to overcome this nontrivial task is to use perturbations. In this paper we describe a generic implementation of efficient random linear perturbations within Cupgal and discuss the practicality of using it examining the convex hull problem, line segment intersection and Delaunay triangulation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Alliez, O. Devillers, and J. Snoeyink. Removing degeneracies by perturbing the problem or perturbing the world. In Proc. 10th Canadian Conference on Computational Geometry (CCCG98), 1998.

    Google Scholar 

  2. N. Amenta, M. Bern, and D. Eppstein. The crust and the β-skeleton: Combinatorial curve reconstruction. Graphical Models and Image Processing, pages 125–135, 1998.

    Google Scholar 

  3. U. Bartuschka, M. Seel, and M. Ziegelmann. Sweep segments easily-a perturbed approach. Manuscript.

    Google Scholar 

  4. C. Burnikel, R. Fleischer, K. Mehlhorn, and S. Schirra. Efficient exact geometric computation made easy. In Proc. 15th ACM Symposium on Computational Geometry (SCG99), 1999. to appear.

    Google Scholar 

  5. C. Burnikel, K. Mehlhorn, and S. Schirra. On degeneracy in geometric computations. In Proc. 5th Annual ACM-SIAM Symp. on Discrete Algorithms, pages 16–23, 1994.

    Google Scholar 

  6. J. Canny and I. Emiris. A general approach to removing degeneracies. SIAM J. Comput., 24:650–664, 1995.

    Article  MathSciNet  Google Scholar 

  7. J. Canny, I. Emiris, and R. Seidel. Efficient perturbations for handling geometric degeneracies. Algorithmica, 19(1-2):219–242, 1997.

    Article  MathSciNet  Google Scholar 

  8. J. Comes. Implementierung von Perturbationen für geometrische Algorithmen. Master’s thesis, Universität des Saarlandes, FB 14 Informatik, 1998. (german).

    Google Scholar 

  9. J. Comes and M. Ziegelmann. An easy to use implementation of linear perturbations within CGAL. Technical report, Max-Planck-Institut für Informatik, Saarbrücken, 1999. to appear.

    Google Scholar 

  10. H. Edelsbrunner and E. Mücke. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graphics, 9(1):67–104, 1990.

    Article  Google Scholar 

  11. A. Fabri, G.-J. Giezeman, L. Kettner, S. Schirra, and S. Schönherr. On the design of CGAL, the computational geometry algorithms library. Technical Report MPII-98-1-007, Max-Planck-Institut für Informatik, Saarbrücken, 1998.

    Google Scholar 

  12. K. Mehlhorn and S. Näher. The implementation of geometric algorithms. In 13th World Computer Congress IFIP94, volume 1, pages 223–231, 1994.

    Google Scholar 

  13. K. Mehlhorn and S. Näher. The LEDA platform for combinatorial and geometric computing. Cambridge University Press, 1999. in press.

    Google Scholar 

  14. D. Michelucci. An ∈-arithmetic for removing degeneracies. In Proc. 12th IEEE Symposium on Computer Arithmetic, pages 230–237, 1995.

    Google Scholar 

  15. E. Mücke. SoS-A first implementation. Master’s thesis, Department of Computer Science Univ. of Illinois at Urbana-Champaign, Urbana III, 1988.

    Google Scholar 

  16. S. Schirra. Parameterized implementations of classical planar convex hull algorithms and extreme point computations. Technical Report MPI-I-98-1-003, Max-Planck-Institut für Informatik, Saarbrücken, 1998.

    Google Scholar 

  17. S. Schirra. A case study on the cost of geometric computing. In Proc. Workshop on Algorithm Engineering and Experimentation (ALENEX99), 1999.

    Google Scholar 

  18. P. Schorn. Limits of the perturbation approach in geometric computing. The Computer Journal, 37(1):35–42, 1994.

    Article  Google Scholar 

  19. R. Seidel. The nature and meaning of perturbations in geometric computing. Discrete and Computational Geometry, 19(1):1–19, 1998.

    Article  MathSciNet  Google Scholar 

  20. C.-K. Yap. A geometric consistency theorem for a symbolic perturbation scheme. J. Comput. Syst. Sci., 40:2–18, 1990.

    Article  MathSciNet  Google Scholar 

  21. C.-K. Yap. Symbolic treatment of geometric degeneracies. Journal of Symbolic Computation, 10:349–370, 1990.

    Article  MathSciNet  Google Scholar 

  22. M. Yvinec, 1999. Personal communication.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universität des Saarlandes, FB 14 Informatik, Im Stadtwald, 66123, Saarbrücken, Germany

    Jochen Comes

  2. Max-Planck-Institut für Informatik, Im Stadtwald, 66123, Saarbrücken, Germany

    Mark Ziegelmann

Authors
  1. Jochen Comes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mark Ziegelmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Duke University, Box 90129, Durham, NC, 27708-0129, USA

    Jeffrey S. Vitter

  2. Department of Computer Science, University of London, King’s College, Strand, London, WC2R 2LS, UK

    Christos D. Zaroliagis

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Comes, J., Ziegelmann, M. (1999). An Easy to Use Implementation of Linear Perturbations within Cupgal . In: Vitter, J.S., Zaroliagis, C.D. (eds) Algorithm Engineering. WAE 1999. Lecture Notes in Computer Science, vol 1668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48318-7_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-48318-7_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66427-7

  • Online ISBN: 978-3-540-48318-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation