Skip to main content
SpringerLink
Log in

A divide-and-conquer algorithm for computing 4-dimensional convex hulls

  • Conference paper
  • First Online:
Book cover Computational Geometry and its Applications (CG 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 333))

Included in the following conference series:

Abstract

This paper contains a description an algorithm for computing four dimensional convex hulls of point sets using the divide-and-conquer paradigm. The algorithm features minimal asymptotic time and memory complexity with respect to the size of its input point set. It is based upon a fully-dual four-dimensional boundary representation (BREP) data structure called Hexblock, also developed by the author, which was inspired by Guibas' and Stolfi's quadedge data structure.

The algorithm was developed in order to quickly compute three-dimensional Delaunay triangulations of large numbers of points. It has been implemented. Also implemented for comparison purposes was a more conventional algorithm for computing such triangulations due to Sever. Preliminary tests suggest that the implementations in fact perform commensurate with theoretical expectations.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. R. Chand and S. S. Kapur. An algorithm for convex polytopes. Jounal of the ACM, 17:78–86, 1970.

    Google Scholar 

  2. D. P. Dobkin and M. J. Laszlo. Primitives for the manipulation of three-dimensional subdivisions. In ACM Siggraph Symposium on Computational Geometry, pages 86–99, Waterloo, Ontario, June 1987.

    Google Scholar 

  3. P. Dornier and S. Paschedag. The animation of simulation results in three dimensions. July 1988. ETH Abt. IIIB Semesterarbeit.

    Google Scholar 

  4. H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, Heidelberg, 1987.

    Google Scholar 

  5. R. L. Graham. An efficient algorithm for determining the convex hull of a finite planar set. Information Processing Letters, 1:132–133, 1972.

    Article  Google Scholar 

  6. L. J. Guibas and J. Stolfi. Primitives for manipulation of general subdivisions and the computation of voronoi diagrams. ACM Transactions on Graphics, 4(2):74–123, 1985.

    Google Scholar 

  7. M. J. Laszlo. A Data Structure for Manipulating Three-Dimensional Subdivisions. Technical Report CS-TR-125-87, Princeton University ComputerScience Department, 1987. thesis.

    Google Scholar 

  8. F. P. Preparata and M. I. Shamos. Computational Geometry: an Introduction. Springer-Verlag, New York, 1985.

    Google Scholar 

  9. R. Seidel. Output-size Sensitive Algorithms for Constructional Problems in Computational Geometry. PhD thesis, Cornell University, Ithaca, New York, January 1987.

    Google Scholar 

  10. M. Sever. Delaunay partitioning in three dimensions and semiconductor models. COMPEL, 5(2):75–93, 1986.

    Google Scholar 

  11. G. Swart. Finding the convex hull facet by facet. Journal of Algorithms, 6:17–48, 1985.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Integrated Systems Laboratory, Federal Institute of Technology at Zürich, Switzerland

    C. E. Buckley

Authors
  1. C. E. Buckley
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hartmut Noltemeier

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Buckley, C.E. (1988). A divide-and-conquer algorithm for computing 4-dimensional convex hulls. In: Noltemeier, H. (eds) Computational Geometry and its Applications. CG 1988. Lecture Notes in Computer Science, vol 333. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50335-8_29

Download citation

  • DOI: https://doi.org/10.1007/3-540-50335-8_29

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50335-4

  • Online ISBN: 978-3-540-45975-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation