Advertisement

Interactive Curvature Tensor Visualization on Digital Surfaces

  • Hélène Perrier
  • Jérémy Levallois
  • David CoeurjollyEmail author
  • Jean-Philippe Farrugia
  • Jean-Claude Iehl
  • Jacques-Olivier Lachaud
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9647)

Abstract

Interactive visualization is a very convenient tool to explore complex scientific data or to try different parameter settings for a given processing algorithm. In this article, we present a tool to efficiently analyze the curvature tensor on the boundary of potentially large and dynamic digital objects (mean and Gaussian curvatures, principal curvatures, principal directions and normal vector field). More precisely, we combine a fully parallel pipeline on GPU to extract an adaptive triangulated isosurface of the digital object, with a curvature tensor estimation at each surface point based on integral invariants. Integral invariants being parametrized by a given ball radius, our proposal allows to explore interactively different radii and thus select the appropriate scale at which the computation is performed and visualized.

Keywords

Isosurface visualization Digital geometry Curvature estimation GPU 

References

  1. 1.
    Coeurjolly, D., Lachaud, J.-O., Levallois, J.: Integral based curvature estimators in digital geometry. In: Gonzalez-Diaz, R., Jimenez, M.-J., Medrano, B. (eds.) DGCI 2013. LNCS, vol. 7749, pp. 215–227. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. 2.
    Coeurjolly, D., Lachaud, J.O., Levallois, J.: Multigrid convergent principal curvature estimators in digital geometry. Comput. Vis. Image Underst. 129, 27–41 (2014)CrossRefzbMATHGoogle Scholar
  3. 3.
    Dupuy, J., Iehl, J.C., Poulin, P.: GPU Pro 5, chap. Quadtrees on the GPU. A K Peters/CRC Press. http://liris.cnrs.fr/publis/?id=6299
  4. 4.
    Gargantini, I.: An effective way to represent quadtrees. Commun. ACM 25(12), 905–910 (1982)CrossRefzbMATHGoogle Scholar
  5. 5.
    Lachaud, J.O., Coeurjolly, D., Levallois, J.: Robust and convergent curvature and normal estimators with digital integral invariants. In: Modern Approaches to Discrete Curvature. Lecture Notes in Mathematics. Springer International Publishing (2016, forthcoming)Google Scholar
  6. 6.
    Lengyel, E.S., Owens, J.D.: Voxel-based terrain for real-time virtual simulations. University of California at Davis (2010)Google Scholar
  7. 7.
    Levallois, J., Coeurjolly, D., Lachaud, J.-O.: Parameter-free and multigrid convergent digital curvature estimators. In: Barcucci, E., Frosini, A., Rinaldi, S. (eds.) DGCI 2014. LNCS, vol. 8668, pp. 162–175. Springer, Heidelberg (2014)Google Scholar
  8. 8.
    Levallois, J., Coeurjolly, D., Lachaud, J.O.: Scale-space feature extraction on digital surfaces. Comput. Graph. 51, 177–189 (2015)CrossRefGoogle Scholar
  9. 9.
    Lewiner, T., Mello, V., Peixoto, A., Pesco, S., Lopes, H.: Fast generation of pointerless octree duals. Comput. Graph. Forum 29(5), 1661–1669 (2010). http://dx.doi.org/10.1111/j.1467-8659.2010.01775.x CrossRefGoogle Scholar
  10. 10.
    Lobello, R.U., Dupont, F., Denis, F.: Out-of-core adaptive iso-surface extraction from binary volume data. Graph. Models 76(6), 593–608 (2014). http://dx.doi.org/10.1016/j.gmod.2014.06.001 CrossRefGoogle Scholar
  11. 11.
    Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3d surface construction algorithm. ACM Comput. Graph. 21(4), 163–169 (1987)CrossRefGoogle Scholar
  12. 12.
    Pottmann, H., Wallner, J., Huang, Q., Yang, Y.: Integral invariants for robust geometry processing. Comput. Aided Geom. Des. 26(1), 37–60 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Pottmann, H., Wallner, J., Yang, Y., Lai, Y., Hu, S.: Principal curvatures from the integral invariant viewpoint. Comput. Aided Geom. Des. 24(8–9), 428–442 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Schaefer, S., Warren, J.: Dual marching cubes: primal contouring of dual grids. In: Proceedings of 12th Pacific Conference on Computer Graphics and Applications, pPG 2004, pp. 70–76. IEEE (2004)Google Scholar
  15. 15.
    Shu, R., Zhou, C., Kankanhalli, M.S.: Adaptive marching cubes. Visual Comput. 11(4), 202–217 (1995)CrossRefGoogle Scholar
  16. 16.
    Tatarchuk, N., Shopf, J., DeCoro, C.: Real-time isosurface extraction using the GPU programmable geometry pipeline. In: ACM SIGGRApPH 2007 Courses, pp. 122–137. ACM (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Hélène Perrier
    • 1
  • Jérémy Levallois
    • 1
    • 2
  • David Coeurjolly
    • 1
    Email author
  • Jean-Philippe Farrugia
    • 1
  • Jean-Claude Iehl
    • 1
  • Jacques-Olivier Lachaud
    • 2
  1. 1.Université de Lyon, CNRS LIRIS, UMR5205LyonFrance
  2. 2.Université de Savoie Mont Blanc, CNRS LAMA, UMR5127ChambéryFrance

Personalised recommendations