Advertisement

Convex Hulls in a 3-Dimensional Space

  • Vladimir Kovalevsky
  • Henrik Schulz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)

Abstract

This paper describes a new algorithm of computing the convex hull of a 3-dimensional object. The convex hull generated by this algorithm is an abstract polyhedron being described by a new data structure, the cell list, suggested by one of the authors. The correctness of the algorithm is proved and experimental results are presented.

Keywords

Convex Hull Convex Combination Convex Polyhedron Convex Object Marching Cube 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Ber00]
    de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry – Algorithms and Applications. Springer, Heidelberg (2000)zbMATHGoogle Scholar
  2. [Cla92]
    Clarkson, K.L., Mehlhorn, K., Seidel, R.: Four results on randomized incremental constructions. In: Comp. Geom.: Theory and Applications, pp. 185–221 (1993); Preliminary version in Proc. Symp. Theor. Aspects of Comp. Sci. (1992)Google Scholar
  3. [Kle01]
    Klette, R., Sun, H.J.: A Global Surface Area Estimation Algorithm for Digital Regular Solids. University of Auckland, CITR-TR-69 (2001)Google Scholar
  4. [Kov89]
    Kovalevsky, V.A.: Finite Topology as Applied to Image Analysis. Computer Vision, Graphics and Image Processing 45(2), 141–161 (1989)CrossRefGoogle Scholar
  5. [Kov93]
    Kovalevsky, V.A.: Digital Geometry based on the Topology of Abstract Cell Complexes. In: Proceedings of the Third International Colloquium Discrete Geometry for Computer Imagery, pp. 259–284. University of Strasbourg (1993)Google Scholar
  6. [Kov01]
    Kovalevsky, V.A.: Algorithms and Data Structures for Computer Topology. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 37–58. Springer, Heidelberg (2002)Google Scholar
  7. [Kov02]
    Kovalevsky, V.A.: Multidimensional Cell Lists for Investigating 3-Manifolds. Discrete Applied Mathematics 125(1), 25–43 (2002)CrossRefMathSciNetGoogle Scholar
  8. [Lor87]
    Lorensen, W.E., Cline, H.E.: Marching Cubes: A High-Resolution 3D Surface Construction Algorithm. Computer Graphics 21(4), 163–169 (1987)CrossRefGoogle Scholar
  9. [Pre85]
    Preparata, F.P., Shamos, M.I.: Computational Geometry – An Introduction. Springer, Heidelberg (1985)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vladimir Kovalevsky
    • 1
  • Henrik Schulz
    • 2
  1. 1. BerlinGermany
  2. 2.Dresden University of TechnologyDresdenGermany

Personalised recommendations