An Algorithm for Decomposing Multi-dimensional Non-manifold Objects into Nearly Manifold Components

  • M. Mostefa Mesmoudi
  • Leila De Floriani
  • Franco Morando
  • Enrico Puppo
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


In this paper we address the problem of building valid representations for non-manifold d-dimensional objects. To this aim, we have developed a combinatorial approach based on decomposing a non-manifold d-dimensional object into an assembly of more regular components, that we call initial quasi-manifolds. We present a decomposition algorithm, whose complexity is slightly super-linear in the total number of simplexes. Our approach provides a rigorous basis for designing efficient dimension-independent data structures for describing non-manifold objects.


Simplicial Complex Hasse Diagram External Vertex Standard Decomposition Abstract Simplicial Complex 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    De Floriani, L., Morando, F., Puppo, E.: A Representation for Abstract Simplicial Complexes: An Analysis and a Comparison. In: Proc. 11th Int. Conf. on Discrete Geometry for Computer Imagery (2003).Google Scholar
  2. 2.
    De Floriani, L., Magillo, P., Morando, F., Puppo, E.: Non-manifold Multi-Tessellation: from meshes to iconic representation of 3D objects. In: Proceed. of 4th Intern. Workshop on Visual Form (IWVF4), C. Arcelli, L.P. Cordella, and G. Sannitidi Baja, editors, LNCS 2059 page 654, Berlin (2001), Springer-Verlag.Google Scholar
  3. 3.
    De Floriani, L., Mesmoudi, M.M., Morando, F., Puppo, E.: Decomposing Nonmanifold Objects in arbitrary Dimensions. Graphical Models, 65, 2–22 (2003)CrossRefGoogle Scholar
  4. 4.
    De Floriani, L., Magillo, P., Puppo, P., Sobrero, D.: A multi-resolution topological representation for non-manifold meshes, Computer-Aided Design, 36(2):141–159.Google Scholar
  5. 5.
    Desaulnier, H., Stewart, N.: An extension of manifold boundary representation to r-sets. ACM Trans. on Graphics, 11(1), 40–60, (1992)CrossRefGoogle Scholar
  6. 6.
    Elter, H., Lienhardt, P.: Different combinatorial models based on the map concept for the representation of sunsets of cellular complexes. In: Proc. IFIP TC 5/WG 5.10 Working Conference on Geometric Modeling in Computer Graphics, 193–212 (1993)Google Scholar
  7. 7.
    Falcidieno, B., Ratto, O.: Two-manifold cell-decomposition of r-sets. In: A. Kilgour and L. Kjelldahl, Eds., Proceedings EUROGRAPHICS '92, 11, 391–404, September (1992)Google Scholar
  8. 8.
    Gueziec, A., Bossen, F., Lazarus, F., Horn, W.: Converting sets of polygons to manifold surfaces by cutting and stitching In: Conference abstracts and applications: SIGGRAPH '98, July 14–21, (1998)Google Scholar
  9. 9.
    Gursoz, E. L., Choi, Y., Prinz, F. B.: Vertex-based representation of non-manifold boundaries, In: M. J. Wozny, J. U. Turner, and K. Preiss, Eds., Geometric Modeling for Product Engineering, North Holland, 107–130, (1990)Google Scholar
  10. 10.
    Hudson, J.F.P,: Piecewise Linear Topology. W.A. Benjamin, Inc., New York (1969)Google Scholar
  11. 11.
    Lee S.H., Lee K., Partial Entity structure: a fast and compact non-manifold boundary representation based on partial topological entities, in Proceedings of the Sixth ACM Symposium on Solid Modeling and Applications, Ann Arbor, Michigan, 2001, pp.159–170Google Scholar
  12. 12.
    Lienhardt, P.: N-dimensional generalized combinatorial maps and cellular quasi-manifolds. Int. Journal of Comp. Geom. and Appl., 4(3), 275–324, (1994)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Melhorn, K.: Data Structures and Algorithms. Springer Publishing Company (1984)Google Scholar
  14. 14.
    Morando, F.: Decomposition and Modeling in the Non-Manifold domain, PhD Thesis, Department of Computer and Information Science, University of Genova, Genova (Italy), February 2003Google Scholar
  15. 15.
    Nabutovsky, A.: Geometry of the space of triangulations of a compact manifold. Comm. Math. Phys., 181, 303–330 (1996)zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Paoluzzi, A., Bernardini, F., Cattani, C., Ferrucci, V.: Dimension-independent modeling with simplicial complexes, ACM Transactions on Graphics, 12(1), 56–102, (1993)CrossRefGoogle Scholar
  17. 17.
    Rossignac, J., Cardoze, D.: Matchmaker: Manifold BReps for non-manifold rsets. In: Willem F. Bronsvoort and David C. Anderson, editors, Proceedings of the Fifth ACM Symposium on Solid Modeling and Applications, 31–41, ACM, June (1999)Google Scholar
  18. 18.
    Rossignac, J.R., O'Connor, M.A.: SGC: A dimension-independent model for point sets with internal structures and incomplete boundaries. In: J.U. Turner, M. J. Wozny and K. Preiss, Eds., Geometric Modeling for Product Engineering, North-Holland, 145–180 (1990)Google Scholar
  19. 19.
    Weiler, K.: The Radial Edge structure: A topological representation for non-manifold geometric boundary modeling. In: M.J. Wozny, H.W. McLauglin, J.L. Encarna\({\tilde c}\)ao (eds), Geometric Modeling for CAD Applications, North-Holland, 1988, 3–36.Google Scholar
  20. 20.
    Weiler, K.: Topological Structures for Geometric Modeling. PhD Thesis, Troy, NY, August (1986)Google Scholar
  21. 21.
    Yamaguchi, Y., Kimura, F.: Non-manifold topology based on coupling entities. IEEE Computer Graphics and Applications, 15(1):42–50, (1995)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • M. Mostefa Mesmoudi
    • 1
  • Leila De Floriani
    • 1
  • Franco Morando
    • 1
  • Enrico Puppo
    • 1
  1. 1.Department of Computer Science (DISI)University of GenovaItaly

Personalised recommendations