A Compact Representation for Topological Decompositions of Non-manifold Shapes

David Canino, Leila De Floriani

2013

Abstract

Simplicial complexes are extensively used for discretizing digital shapes in several applications. A structural description of a non-manifold shape can be obtained by decomposing the input shape into a collection of meaningful components with a simpler topology. Here, we consider a unique decomposition of a non-manifold shape into nearly manifold parts, known as the \emph{Manifold-Connected decomposition}, that we extend in arbitrary dimension. We present the \emph{Compact MC-Graph}, an efficient and graph-based representation for this decomposition, which can be combined with any topological data structure for encoding the underlying components. We present the main properties of this representation as well as algorithms for its generation. We also show that this representation may be more compact than many topological data structures, which do not explicitly describe the non-manifold structure of a shape.

References

  1. Attene, M., Giorgi, D., Ferri, M., and Falcidieno, B. (2009). On Converting Sets of Tetrahedra to Combinatorial and PL Manifolds. Comp.-Aid. Des., 26(8):850-864.
  2. Boltcheva, D., Canino, D., Merino Aceituno, S., Léon, J.- C., De Floriani, L., and Hétroy, F. (2011). An Iterative Algorithm for Homology Computation on Simplicial Shapes. Comp.-Aid. Des., 43(11):1457-1467.
  3. Canino, D. (2012). Tools for Modeling and Analysis of Nonmanifold Shapes. PhD thesis, Department of Computer Science, University of Genova, Genova, Italy.
  4. Canino, D. and De Floriani, L. (2011). A Decompositionbased Approach to Modeling and Understanding Arbitrary Shapes. In Proc. of the EG Italy, pages 53-60.
  5. Canino, D. and De Floriani, L. (2012). The Mangrove Topological Data Structure (Mangrove TDS) Library. http://mangrovetds.sourceforge.net.
  6. Canino, D., De Floriani, L., and Weiss, K. (2011). IA : an Adjacency-based Representation for Non-Manifold Simplicial Shapes in Arbitrary Dimensions. Comp. & Graph., 35(3):747-753.
  7. De Floriani, L. and Hui, A. (2005). Data Structures for Simplicial Complexes: an Analysis and a Comparison. In Proc. of the Symp. on Geom. Proc., pages 119-128.
  8. De Floriani, L., Hui, A., Panozzo, D., and Canino, D. (2010). A Dimension-independent Data Structure for Simplicial Complexes. In Proc. of the 19th Int. Mes. Round., pages 403-420.
  9. De Floriani, L., Mesmoudi, M. M., Morando, F., and Puppo, E. (2003). Decomposing Non-manifold Objects in Arbitrary Dimension. Graph. Mod., 65(1/3):2-22.
  10. Desaulniers, H. and Stewart, N. (1992). An Extension of Manifold Boundary Representations to the r-sets. ACM Trans. on Graph., 11(1):40-60.
  11. Edelsbrunner, H. (1987). Algorithms in Combinatorial Geometry. Springer.
  12. Falcidieno, B. and Ratto, O. (1992). Two-manifold Cell-decomposition of r-sets. Comp. Graph. For., 11(3):391- 404.
  13. Gromov, M. (1987). Hyperbolic Groups. Springer.
  14. Gueziec, A., Taubin, G., Lazarus, F., and Horn, W. (1998). Converting Sets of Polygons to Manifold Surfaces by Cutting and Stitching. In Proc. of the IEEE Conf. on Vis., pages 383-390.
  15. Gurung, T., Laney, D., Lindstrom, P., and Rossignac, J. (2011a). SQuad: a Compact Representation for Triangle Meshes. Comp. Graph. For., 30(2):355-364.
  16. Gurung, T., Luffel, M., Lindstrom, P., and Rossignac, J. (2011b). LR: Compact Connectivity Representation for Triangle Meshes. ACM Trans. on Graph., 30(4).
  17. Gurung, T. and Rossignac, J. (2009). SOT: Compact Representation for Tetrahedral Meshes. In Proc. of the ACM Conf. on Sol. and Phys. Mod., pages 79-88.
  18. Hui, A. and De Floriani, L. (2007). A Two-level Topological Decomposition for Non-Manifold Simplicial Shapes. In Proc. of the ACM Conf. on Sol. and Phys. Mod., pages 355-360.
  19. Hui, A. and De Floriani, L. (2009). The Non-Manifold Meshes Repository. http://indy.disi.unige.it/nmcollection.
  20. Hui, A., Vaczlavik, L., and De Floriani, L. (2006). A Decomposition-based Representation for 3D Simplicial Complexes. In Proc. of the Symp. on Geom. Proc., pages 101-110.
  21. Nabutovsky, A. (1996). Geometry of the Space of Triangulations of a Compact Manifold. Comm. in Math. Phys., 181:303-330.
  22. Paoluzzi, A., Bernardini, F., Cattani, C., and Ferrucci, V. (1993). Dimension-Independent Modeling with Simplicial Complexes. ACM Trans. on Graph., 12(1):56- 102.
  23. Pesco, S., Tavares, G., and Lopes, H. (2004). A Stratification Approach for Modeling Two-dimensional Cell Complexes. Comp. & Graph., 28:235-247.
  24. Popovic, J. and Hoppe, H. (1997). Progressive Simplicial Complexes. In Proc. of the ACM SIGGRAPH, pages 217-224.
  25. Rossignac, J. and Cardoze, D. (1999). Matchmaker: manifold BReps for Non-manifold R-sets. In Proc. of the ACM Symp. on Sol. Mod. and Appl., pages 31-41. ACM Press.
  26. Rossignac, J. and O'Connor, M. (1989). A Dimensionindependent Model for Point-sets with Internal Structures and Incomplete Boundaries. In Geom. Mod. for Prod. Eng., pages 145-180. North-Holland.
  27. Samet, H. (2006). Foundations of Multidimensional and Metric Data Structures. Morgan Kaufmann.
  28. Shamir, A. (2008). A Survey on Mesh Segmentation Techniques. Comp. Graph. For., 27(6):1539-1556.
  29. Thakur, A., Banerjee, A. G., and Gupta, S. K. (2009). A Survey of CAD Models Simplification Techniques for Physics-based Simulation Applications. Comp.-Aid. Des., 41(2):65-80.
Download


Paper Citation


in Harvard Style

Canino D. and De Floriani L. (2013). A Compact Representation for Topological Decompositions of Non-manifold Shapes . In Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013) ISBN 978-989-8565-46-4, pages 100-107. DOI: 10.5220/0004294501000107


in Bibtex Style

@conference{grapp13,
author={David Canino and Leila De Floriani},
title={A Compact Representation for Topological Decompositions of Non-manifold Shapes},
booktitle={Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013)},
year={2013},
pages={100-107},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004294501000107},
isbn={978-989-8565-46-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013)
TI - A Compact Representation for Topological Decompositions of Non-manifold Shapes
SN - 978-989-8565-46-4
AU - Canino D.
AU - De Floriani L.
PY - 2013
SP - 100
EP - 107
DO - 10.5220/0004294501000107