Multi-scale Discrete Surfaces

  • Jasmine Burguet
  • Rémy Malgouyres
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)


In this article, we first propose a method to discretize a surface represented by a polyhedron. Then, we define a data structure used to work on such a discrete surface and that allows us to consider multi-scale discrete surfaces. Then, we explain how to perform easily and quickly boolean set operations on this data structure. Finally, we expose a method to reconstruct the whole surface and we display some results obtained from the boolean set operations.


discretization multi-scale discrete surface boolean set operations 


  1. 1.
    J. BURGUET, R. MALGOUYRES, Strong Thinning and Polyhedric Approximation of a Discrete Surface, Proceedings of DGCI’2000, Uppsala, Sweden, Lecture Notes in Computer Science, vol 1953, Springer, pp222–234, 2000.Google Scholar
  2. 2.
    R.A. FINKEL, J.L. BENTLEY, Quad trees: A data structure for retrieval on composite keys, Acta Informatica, Vol. 4, pp. 1–9, 1974.zbMATHCrossRefGoogle Scholar
  3. 3.
    J.D. FOLEY, A. VAN DAM, S.K. FEINER, J.F. HUGHES, Computer Graphics: introduction and practice (second edition in C), Addison-Wesley.Google Scholar
  4. 4.
    R.A. GOLDSTEIN, R. NAGEL, 3-D Visual Simulation, Simulation, 16(1), pp. 25–31, 1971.CrossRefGoogle Scholar
  5. 5.
    T. HENDERSON, C. HANSEN, CAD-Based Computer Vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(10), pp. 1181–1193, 1989.Google Scholar
  6. 6.
    G.T. HERMAN, Discrete Multidimensional Jordan Surfaces, CVGIP: Graphical Models and Image Processing, 55(5), pp. 507–515, 1992.CrossRefMathSciNetGoogle Scholar
  7. 7.
    G.T. HERMAN, Boundaries in Digital Spaces: Basic Theory, in L.N. KANAL and A. ROSENFELD Ed., Topological Algorithms for Digital Image Processing, Vol. 19 of Machine Intelligence an Pattern Recognition, pp. 233–262, 1996.Google Scholar
  8. 8.
    G.T. HERMAN, Finitary 1-Simply Connected Digital Spaces, GMIP, 1(60), 1998.Google Scholar
  9. 9.
    A. KLINGER, C.R. DYER, Experiments on picture representation using regular decomposition, Computer Graphics and Image Processing, Vol. 5, pp. 68–105, 1976.CrossRefGoogle Scholar
  10. 10.
    A. RAPPOPORT, S. SPITZ, Interactive Boolean Operations for Conceptual Design of 3-D Solids SIGGRAPH 97 Conference Proceedings, Annual Conference Series, pp. 269–278, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jasmine Burguet
    • 1
  • Rémy Malgouyres
    • 1
  1. 1.IUT Département InformatiqueLLAIC1AUBIERE CEDEX

Personalised recommendations