Compact Combinatorial Maps in 3D

  • Xin Feng
  • Yuanzhen Wang
  • Yanlin Weng
  • Yiying Tong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7633)

Abstract

We propose a compact data structure for volumetric meshes of arbitrary topology and bounded valence, which offers cell-face, face-edge, and edge-vertex incidence queries in constant time. Our structure is simple to implement, easy to use, and allows for arbitrary, user-defined volume cells, while remaining very efficient in memory usage compared to previous work.

Keywords

3D mesh data structure Combinatorial maps Cell complex 

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References

  1. 1.
    Alumbaugh, T.J., Jiao, X.: Compact Array-Based Mesh Data Structures. In: Hanks, B.W. (ed.) Engineering, IMR 2005, pp. 485–503. Springer, Heidelberg (2005)Google Scholar
  2. 2.
    Sieger, D., Botsch, M.: Design, Implementation, and Evaluation of the Surface Mesh Data Structure. In: Quadros, W.R. (ed.) Proceedings of the 20th International Meshing Roundtable, vol. 90, pp. 533–550. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Serna, S.P., Stork, A., Fellner, D.W.: Considerations toward a Dynamic Mesh Data Structure. In: SIGRAD Conference, pp. 83–90 (2011)Google Scholar
  4. 4.
    Tautges, T.J., Blacker, T., Mitchell, S.A.: The Whisker Weaving Algorithm: a Connectivity-Based Method for Constructing All-Hexahedral Finite Element Meshes. Int. J. for Numer. Methods in Eng. 39(19), 3327–3349 (1996)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Murdoch, P.: The spatial twist continuum: A connectivity based method for representing all-hexahedral finite element meshes. Finite Elements in Analysis and Design 28(2), 137–149 (1997)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Guibas, L., Stolfi, J.: Primitives for the manipulation of general subdivisions and the computation of voronoi. ACM Trans. Graph. 4(2), 74–123 (1985)MATHCrossRefGoogle Scholar
  7. 7.
    Brisson, E.: Representing geometric structures in d dimensions: topology and order. In: Proceedings of the Fifth Annual Symposium on Computational Geometry, SCG 1989, vol. 9, pp. 218–227. ACM Press (1989)Google Scholar
  8. 8.
    Edmonds, J.R.: A combinatorial representation for polyhedral surfaces. Notices Amer. Math. Soc. 7, 646 (1960)Google Scholar
  9. 9.
    Beall, M.W., Shephard, M.S.: A general topology-based mesh data structure. Int. J. for Numer. Methods in Eng. 40(9), 1573–1596 (1997)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Lienhardt, P.: Topological models for boundary representation: a comparison with n-dimensional generalized maps. Computer-Aided Design 23(1), 59–82 (1991)MATHCrossRefGoogle Scholar
  11. 11.
    Prat, S., Gioia, P., Bertrand, Y.: Connectivity compression in an arbitrary dimension. The Visual Computer 21(8-10), 876–885 (2005)CrossRefGoogle Scholar
  12. 12.
    Blandford, D.K., Blelloch, G.E., Cardoze, D.E., Kadow, C.: Compact Representations of Simplicial Meshes in Two and Three Dimensions. International Journal of Computational Geometry and Applications 15(1), 3–24 (2005)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Celes, W., Paulino, G.H., Espinha, R.: A compact adjacency-based topological data structure for finite element mesh representation. International Journal for Numerical Methods in Engineering 64(11), 1529–1556 (2005)MATHCrossRefGoogle Scholar
  14. 14.
    Damiand, G.: Combinatorial maps. In: CGAL User and Reference Manual, 4.0 edn., CGAL Editorial Board (2012)Google Scholar
  15. 15.
    OVM: OpenVolumeMesh - A Generic and Versatile Index-Based Data Structure for Polytopal Meshes (2012), http://www.openvolumemesh.org/
  16. 16.
    Botsch, M., Steinberg, S., Bischoff, S., Kobbelt, L.: OpenMesh - a generic and efficient polygon mesh data structure. Structure (2002)Google Scholar
  17. 17.
    Kirk, B.S., Peterson, J.W., Stogner, R.H., Carey, G.F.: libmesh: a c++ library for parallel adaptive mesh refinement/coarsening simulations. Eng. with Comput. 22(3), 237–254 (2006)CrossRefGoogle Scholar
  18. 18.
    CGoGN: Combinatorial and Geometric modeling with Generic N-dimensional Maps (2012), http://cgogn.u-strasbg.fr/Wiki/index.php/CGoGN
  19. 19.
    Dobkin, D.P., Laszlo, M.J.: Primitives for the manipulation of three-dimensional subdivisions. In: Proceedings of the third annual Symposium on Computational Geometry, SCG 1987, pp. 86–99. ACM, New York (1987)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xin Feng
    • 1
  • Yuanzhen Wang
    • 1
  • Yanlin Weng
    • 2
  • Yiying Tong
    • 1
  1. 1.Michigan State UniversityUSA
  2. 2.Zhejiang UniversityChina

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