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Combinatorial Properties of Subdivision Meshes

  • Ioannis Ivrissimtzis
  • Hans-Peter Seidel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2768)

Abstract

In this paper we study subdivision from a graph-theoretic point of view. In particular, we study the chromatic numbers of subdivision meshes, that is the number of distinct colors we need for a vertex, face or edge coloring of a subdivision mesh. We show that, unlike the size, the chromatic numbers of subdivision meshes are not larger than the corresponding chromatic numbers of the initial mesh and sometimes are even smaller.

Keywords

Chromatic Number Triangular Mesh Subdivision Scheme Combinatorial Property Initial Mesh 
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.

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References

  1. 1.
    Ivrissimtzis, I., Dodgson, N., Sabin, M.: A generative classification of mesh refinement rules with lattice transformations. Research Report UCAM-CL-TR-542, Cambridge University, Cambridge, UK (2002) Google Scholar
  2. 2.
    Doo, D., Sabin, M.: Behaviour of recursive division surfaces near extraordinary points. Computer-Aided Design 10 (1978) 356–360 Google Scholar
  3. 3.
    Loop, C.T.: Smooth subdivision surfaces based on triangles (1987) Google Scholar
  4. 4.
    Kobbelt, L.: sqrt(3) subdivision. In: Siggraph 00, Conference Proceedings. (2000) 103–112 Google Scholar
  5. 5.
    Catmull, E., Clark, J.: Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Design 10 (1978) 350–355 Google Scholar
  6. 6.
    Jensen, T.R., Toft, B.: Graph coloring problems. New York, NY: John Wiley & Sons. (1995) Google Scholar
  7. 7.
    Tutte, W.: A census of planar triangulations. Can. J. Math. 14 (1962) 21–38 Google Scholar
  8. 8.
    Ivrissimtzis, I., Seidel, H.P.: Polyhedra operators for mesh refinement. In: Proceedings of Geometric Modeling and Processing 2002, Wako, Saitama, Japan, IEEE (2002) 132–137 Google Scholar
  9. 9.
    Grannell, M., Griggs, T., Sirn, J.: Face 2-colourable triangular embeddings of complete graphs. J. Comb. Theory, Ser. B 74 (1998) 8–19Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ioannis Ivrissimtzis
    • 1
  • Hans-Peter Seidel
    • 1
  1. 1.Max-Planck Institute für InformatikSaarbrückenGermany

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