Advertisement

Parallel Homology Computation of Meshes

  • Guillaume DamiandEmail author
  • Rocio Gonzalez-Diaz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9667)

Abstract

In this paper, we propose a method to compute, in parallel, the homology groups of closed meshes (i.e., orientable 2D manifolds without boundary) represented by combinatorial maps. Our experiments illustrate the interest of our approach which is really fast on big meshes and which obtains good speed-up when increasing the number of threads.

Keywords

Homology groups computation 2D combinatorial maps Parallel algorithm 

Notes

Acknowledgments

This research was partially supported by Spanish project MTM2015-67072-P and by the French National Agency (ANR), project SoLStiCe ANR-13-BS02-0002-01. We also thank the anonymous reviewers for their valuable comments.

References

  1. 1.
  2. 2.
    Damiand, G.: Combinatorial maps. In: CGAL User and Reference Manual. 3.9th edn (2011). http://www.cgal.org/Pkg/CombinatorialMaps
  3. 3.
    Damiand, G.: Linear cell complex. In: CGAL User and Reference Manual. 4.0edn (2012). http://www.cgal.org/Pkg/LinearCellComplex
  4. 4.
    Damiand, G., Gonzalez-Diaz, R., Peltier, S.: Removal operations in nD generalized maps for efficient homology computation. In: Ferri, M., Frosini, P., Landi, C., Cerri, A., Di Fabio, B. (eds.) CTIC 2012. LNCS, vol. 7309, pp. 20–29. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  5. 5.
    Damiand, G., Gonzalez-Diaz, R., Peltier, S.: Removal and contraction operations in nD generalized maps for efficient homology computation. CoRR, abs/1403.3683 (2014)Google Scholar
  6. 6.
    Damiand, G., Lienhardt, P.: Combinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing. A K Peters/CRC Press, Boca Raton (2014)CrossRefzbMATHGoogle Scholar
  7. 7.
    Damiand, G., Peltier, S., Fuchs, L.: Computing homology for surfaces with generalized maps: application to 3D images. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Remagnino, P., Nefian, A., Meenakshisundaram, G., Pascucci, V., Zara, J., Molineros, J., Theisel, H., Malzbender, T. (eds.) ISVC 2006. LNCS, vol. 4292, pp. 235–244. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Kaczyński, T., Mrozek, M., Ślusarek, M.: Homology computation by reduction of chain complexes. Comput. Math. Appl. 35(4), 59–70 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Lienhardt, P.: N-Dimensional generalized combinatorial maps and cellular quasi-manifolds. Int. J. Comput. Geom. Appl. 4(3), 275–324 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Mäntylä, M.: An Introduction to Solid Modeling. Computer Science Press, College Park (1988)Google Scholar
  11. 11.
    Murty, N.A., Natarajan, V., Vadhiyar, S.: Efficient homology computations on multicore and manycore systems. In: 2013 20th International Conference on High Performance Computing (HiPC), pp. 333–342, December 2013Google Scholar
  12. 12.
    Weiler, K.: Edge-based data structures for solid modeling in curved-surface environments. Comput. Graph. Appl. 5(1), 21–40 (1985)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Univ Lyon, CNRS, LIRIS, UMR5205LyonFrance
  2. 2.Dpto. de Matemática Aplicada IUniversidad de SevillaSevillaSpain

Personalised recommendations