The Visual Computer

, Volume 29, Issue 6–8, pp 739–749 | Cite as

Efficient collision detection for composite finite element simulation of cuts in deformable bodies

  • Jun WuEmail author
  • Christian Dick
  • Rüdiger Westermann
Original Article


Composite finite elements (CFEs) based on a hexahedral discretization of the simulation domain have recently shown their effectiveness in physically based simulation of deformable bodies with changing topology. In this paper we present an efficient collision detection method for CFE simulation of cuts. Our method exploits the specific characteristics of CFEs, i.e., the fact that the number of simulation degrees of freedom is significantly reduced. We show that this feature not only leads to a faster deformation simulation, but also enables a faster collision detection. To address the non-conforming properties of geometric composition and hexahedral discretization, we propose a topology-aware interpolation approach for the computation of penetration depth. We show that this approach leads to accurate collision detection on complex boundaries. Our results demonstrate that by using our method cutting on high-resolution deformable bodies including collision detection and response can be performed at interactive rates.


Cutting Deformable bodies Collision detection Composite finite elements 



The first author, Jun Wu, is supported by the Erasmus Mundus TANDEM, an European Commission funded program.

Supplementary material

(AVI 18.8 MB)


  1. 1.
    Hackbusch, W., Sauter, S.: Composite finite elements for the approximation of pdes on domains with complicated micro-structures. Numer. Math. 75, 447–472 (1997) MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Nesme, M., Kry, P.G., Jeřábková, L., Faure, F.: Preserving topology and elasticity for embedded deformable models. ACM Trans. Graph. 28, 52:1–52:9 (2009) CrossRefGoogle Scholar
  3. 3.
    Dick, C., Georgii, J., Westermann, R.: A hexahedral multigrid approach for simulating cuts in deformable objects. IEEE Trans. Vis. Comput. Graph. 17(11), 1663–1675 (2011) CrossRefGoogle Scholar
  4. 4.
    Jeřábková, L., Bousquet, G., Barbier, S., Faure, F., Allard, J.: Volumetric modeling and interactive cutting of deformable bodies. Prog. Biophys. Mol. Biol. 103(2–3), 217–224 (2010) CrossRefGoogle Scholar
  5. 5.
    Wu, J., Dick, C., Westermann, R.: Interactive high-resolution boundary surfaces for deformable bodies with changing topology. In: Workshop on Virtual Reality Interaction and Physical Simulation (VRIPHYS), pp. 29–38 (2011) Google Scholar
  6. 6.
    Sauter, S., Warnke, R.: Composite finite elements for elliptic boundary value problems with discontinuous coefficients. Computing 77(1), 29–55 (2006) MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Preusser, T., Rumpf, M., Schwen, L.O.: Finite element simulation of bone microstructures. In: Proceedings of the 14th Workshop on the Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields, pp. 52–66 (2007). University of Ulm, July 2007 Google Scholar
  8. 8.
    Liehr, F., Preusser, T., Rumpf, M., Sauter, S., Schwen, L.O.: Composite finite elements for 3d image based computing. Comput. Vis. Sci. 12(4), 171–188 (2009) MathSciNetCrossRefGoogle Scholar
  9. 9.
    Seiler, M., Steinemann, D., Spillmann, J., Harders, M.: Robust interactive cutting based on an adaptive octree simulation mesh. Vis. Comput. 27(6), 519–529 (2011) CrossRefGoogle Scholar
  10. 10.
    Pietroni, N., Ganovelli, F., Cignoni, P., Scopigno, R.: Splitting cubes: a fast and robust technique for virtual cutting. Vis. Comput. 25(3), 227–239 (2009) CrossRefGoogle Scholar
  11. 11.
    Ju, T., Losasso, F., Schaefer, S., Warren, J.: Dual contouring of hermite data. ACM Trans. Graph. 21, 339–346 (2002) CrossRefGoogle Scholar
  12. 12.
    Teschner, M., Kimmerle, S., Heidelberger, B., Zachmann, G., Raghupathi, L., Fuhrmann, A., Cani, M.-P., Faure, F., Magnenat-Thalmann, N., Straßer, W., Volino, P.: Collision detection for deformable objects. Comput. Graph. Forum 24(1), 61–81 (2005) CrossRefGoogle Scholar
  13. 13.
    Teschner, M., Heidelberger, B., Müller, M., Pomerantes, D., Gross, M.H.: Optimized spatial hashing for collision detection of deformable objects. In: The Vision, Modeling, and Visualization Conference, pp. 47–54 (2003) Google Scholar
  14. 14.
    Hoff, K.E. III, Zaferakis, A., Lin, M., Manocha, D.: Fast and simple 2d geometric proximity queries using graphics hardware. In: I3D ’01: Symposium on Interactive 3D Graphics, pp. 145–148. ACM, New York (2001) Google Scholar
  15. 15.
    Heidelberger, B., Teschner, M., Gross, M.: Detection of collisions and self-collisions using image-space techniques. J. WSCG 12(3), 145–152 (2004) Google Scholar
  16. 16.
    Faure, F., Barbier, S., Allard, J., Falipou, F.: Image-based collision detection and response between arbitrary volume objects. In: SCA ’08: Symposium on Computer Animation, pp. 155–162. Eurographics, Zurich (2008) Google Scholar
  17. 17.
    Otaduy, M., Chassot, O., Steinemann, D., Gross, M.: Balanced hierarchies for collision detection between fracturing objects. In: VR ’07: IEEE Virtual Reality Conference, pp. 83–90 (March 2007) CrossRefGoogle Scholar
  18. 18.
    Heo, J.-P., Seong, J.-K., Kim, D., Otaduy, M.A., Hong, J.-M., Tang, M., Yoon, S.-E.: Fastcd: fracturing-aware stable collision detection. In: SCA ’10: Symposium on Computer Animation, pp. 149–158 (2010) Google Scholar
  19. 19.
    Glondu, L., Schvartzman, S., Marchal, M., Dumont, G., Otaduy, M.: Efficient collision detection for brittle fracture. In: SCA ’12: Symposium on Computer Animation, pp. 285–294 (2012) Google Scholar
  20. 20.
    James, D., Pai, D.: Bd-tree: output-sensitive collision detection for reduced deformable models. ACM Trans. Graph. 23, 393–398 (2004) CrossRefGoogle Scholar
  21. 21.
    Schvartzman, S.C., Gascón, J., Otaduy, M.A.: Bounded normal trees for reduced deformations of triangulated surfaces. In: SCA ’09: Symposium on Computer Animation, pp. 75–82 (2009) Google Scholar
  22. 22.
    Barbič, J., James, D.: Subspace self-collision culling. ACM Trans. Graph. 29(4), 81 (2010) Google Scholar
  23. 23.
    Hirota, G., Fisher, S., State, A., Lee, C., Fuchs, H.: An implicit finite element method for elastic solids in contact. In: Proc. the Computer Animation, pp. 136–254 (2001) Google Scholar
  24. 24.
    Fisher, S., Lin, M.C.: Deformed distance fields for simulation of non-penetrating flexible bodies. In: Eurographic Workshop on Computer Animation and Simulation, pp. 99–111 (2001) Google Scholar
  25. 25.
    McAdams, A., Zhu, Y., Selle, A., Empey, M., Tamstorf, R., Teran, J., Sifakis, E.: Efficient elasticity for character skinning with contact and collisions. ACM Trans. Graph. 30, 37:1–37:12 (2011) CrossRefGoogle Scholar
  26. 26.
    Todd, D.: b4wind user’s guide—trilinear interpolation. [Online; accessed, 30 July 2012]
  27. 27.
    Jones, M., Baerentzen, J., Sramek, M.: 3d distance fields: a survey of techniques and applications. IEEE Trans. Vis. Comput. Graph. 12, 581–599 (2006) CrossRefGoogle Scholar
  28. 28.
    Cuisenaire, O.: Region growing Euclidean distance transforms. In: The 9th International Conference on Image Analysis and Processing, pp. 263–270 (1997) CrossRefGoogle Scholar
  29. 29.
    Satherley, R., Jones, M.: Hybrid distance field computation. In: Proc. Volume Graphics, pp. 195–209 (2001) Google Scholar
  30. 30.
    Larsen, E., Gottschalk, S., Lin, M.C., Manocha, D.: Fast proximity queries with swept sphere volumes. Technical report TR99-018, Department of Computer Science, University of North Carolina, 1999 Google Scholar
  31. 31.
    Wu, J., Wang, D., Wang, C., Zhang, Y.: Toward stable and realistic haptic interaction for tooth preparation simulation. J. Comput. Inf. Sci. Eng. 10(2), 021007 (2010) CrossRefGoogle Scholar
  32. 32.
    Barbič, J., James, D.L.: Six-dof haptic rendering of contact between geometrically complex reduced deformable models. IEEE Trans. Haptics 1, 39–52 (2008) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Technische Universität MünchenMunichGermany

Personalised recommendations