Summary
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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).
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.
De Floriani, L., Mesmoudi, M.M., Morando, F., Puppo, E.: Decomposing Nonmanifold Objects in arbitrary Dimensions. Graphical Models, 65, 2–22 (2003)
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.
Desaulnier, H., Stewart, N.: An extension of manifold boundary representation to r-sets. ACM Trans. on Graphics, 11(1), 40–60, (1992)
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)
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)
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)
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)
Hudson, J.F.P,: Piecewise Linear Topology. W.A. Benjamin, Inc., New York (1969)
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.159–170
Lienhardt, P.: N-dimensional generalized combinatorial maps and cellular quasi-manifolds. Int. Journal of Comp. Geom. and Appl., 4(3), 275–324, (1994)
Melhorn, K.: Data Structures and Algorithms. Springer Publishing Company (1984)
Morando, F.: Decomposition and Modeling in the Non-Manifold domain, PhD Thesis, Department of Computer and Information Science, University of Genova, Genova (Italy), February 2003
Nabutovsky, A.: Geometry of the space of triangulations of a compact manifold. Comm. Math. Phys., 181, 303–330 (1996)
Paoluzzi, A., Bernardini, F., Cattani, C., Ferrucci, V.: Dimension-independent modeling with simplicial complexes, ACM Transactions on Graphics, 12(1), 56–102, (1993)
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)
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)
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.
Weiler, K.: Topological Structures for Geometric Modeling. PhD Thesis, Troy, NY, August (1986)
Yamaguchi, Y., Kimura, F.: Non-manifold topology based on coupling entities. IEEE Computer Graphics and Applications, 15(1):42–50, (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mesmoudi, M.M., De Floriani, L., Morando, F., Puppo, E. (2005). An Algorithm for Decomposing Multi-dimensional Non-manifold Objects into Nearly Manifold Components. In: Dodgson, N.A., Floater, M.S., Sabin, M.A. (eds) Advances in Multiresolution for Geometric Modelling. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26808-1_4
Download citation
DOI: https://doi.org/10.1007/3-540-26808-1_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21462-5
Online ISBN: 978-3-540-26808-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)