Advertisement

The Visual Computer

, Volume 34, Issue 6–8, pp 937–947 | Cite as

Deformation simulation based on model reduction with rigidity-guided sampling

  • Shuo-Ting Chien
  • Chen-Hui HuEmail author
  • Cheng-Yang Huang
  • Yu-Ting Tsai
  • Wen-Chieh Lin
Original Article
  • 152 Downloads

Abstract

The deformation results of previous model reduction methods with external forces applied show noticeable differences from full-scale finite element method (FEM) simulation. We found that data-driven approaches, specifically proper orthogonal decomposition, can be a solution to this nonlinear deformation simulation problem in the subspace. Nevertheless, off-line FEM simulation with an infinite number of possible input forces at different locations makes it infeasible if no prior information is given. We propose rigidity-guided sampling to efficiently select the points of application of forces (force sample points) to construct more effective and compact subspace bases, thereby improving the simulation accuracy of reduced deformable models with applied external forces and still retaining fast run-time performance. The key idea of our approach is that distinct deformations of an object at different force sample points can be estimated prior to FEM simulation. By selecting the force sample points with distinct deformations, the computational cost of off-line FEM simulation can be reduced significantly. Our run-time deformation results are much closer to the full-scale FEM simulation with external forces applied, compared to the results of using only the modal derivative bases while the speedup over full-scale simulation is still substantial.

Keywords

Deformation Model reduction Rigidity fields Finite element method Harmonic fields 

Notes

Acknowledgements

We thank Prof. Jernej Barbič for providing help about Vega FEM [6] in the early stage of this study. We also thank Yan-Ting Liu for making the accompanying video. This work was supported in part by the Ministry of Science and Technology of Taiwan under Grant Nos. 104-2628-E-009-001-MY3 and 105-2221-E-009-095-MY3.

Funding This study was funded in part by the Ministry of Science and Technology of Taiwan under Grant Nos. 104-2628-E-009-001-MY3 and 105-2221-E-009-095-MY3.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

Supplementary material 1 (mp4 39808 KB)

371_2018_1533_MOESM2_ESM.pdf (1.9 mb)
Supplementary material 2 (pdf 1931 KB)

References

  1. 1.
    An, S., Kim, T., James, D.: Optimizing cubature for efficient integration of subspace deformations. ACM Trans. Graph. 27(5), 165:1–165:10 (2008)CrossRefGoogle Scholar
  2. 2.
    Au, O.K.C., Fu, H., Tai, C.L., Cohen-Or, D.: Handle-aware isolines for scalable shape editing. In: ACM SIGGRAPH (2007)Google Scholar
  3. 3.
    Barbič, J., Zhao, Y.: Real-time large-deformation substructuring. In: ACM SIGGRAPH (2011)Google Scholar
  4. 4.
    Barbič, J., James, D.: Real-time subspace integration for St. Venant-Kirchhoff deformable models. In: ACM SIGGRAPH, pp. 982–990 (2005)Google Scholar
  5. 5.
    Bickel, B., Bächer, M., Otaduy, M.A., Matusik, W., Pfister, H., Gross, M.: Capture and modeling of non-linear heterogeneous soft tissue. In: ACM SIGGRAPH, pp. 89:1–89:9 (2009)Google Scholar
  6. 6.
    Barbič, J.: Computer graphics research code. http://www.jernejbarbic.com/code (2009). Accessed 02 Feb 2018
  7. 7.
    Carlberg, K., Farhat, C.: A compact proper orthogonal decomposition basis for optimization-oriented reduced-order models. In: 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (2008)Google Scholar
  8. 8.
    Chatterjee, A.: An introduction to the proper orthogonal decomposition. Curr. Sci. 78(7), 808–817 (2000)Google Scholar
  9. 9.
    Dinh, Q., Marechal, Y.: Toward real-time finite-element simulation on GPU. IEEE Trans. Magn. 52(3), 1–4 (2016)CrossRefGoogle Scholar
  10. 10.
    Farhat, C., Chapman, T., Avery, P.: Structure-preserving, stability, and accuracy properties of the energy-conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models. Int. J. Numer. Methods Eng. 102(5), 1077–1110 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Idelsohn, S.R., Cardona, A.: A reduction method for nonlinear structural dynamic analysis. Comput. Methods Appl. Mech. Eng. 49(3), 253–279 (1985)CrossRefzbMATHGoogle Scholar
  12. 12.
    James, D., Pai, D.: DyRT: dynamic response textures for real time deformation simulation with graphics hardware. ACM Trans. Graph. 21(3), 582–585 (2002)CrossRefGoogle Scholar
  13. 13.
    James, D., Pai, D.: Multiresolution green’s function methods for interactive simulation of large-scale elastostatic objects. ACM Trans. Graph. 22(1), 47–82 (2003)CrossRefGoogle Scholar
  14. 14.
    Kerschen, G., Golinval, J.C., Vakakis, A.F., Bergman, L.A.: The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview. Nonlinear Dyn. 41(1), 147–169 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Koyama, Y., Takayama, K., Umetani, N., Igarashi, T.: Real-time example-based elastic deformation. In: Symposium on Computer Animation, pp. 19–24 (2012)Google Scholar
  16. 16.
    Krysl, P., Lall, S., Marsden, J.E.: Dimensional model reduction in non-linear finite element dynamics of solids and structures. Int. J. Numer. Methods Eng. 51(4), 479–504 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Martin, S., Thomaszewski, B., Grinspun, E., Gross, M.: Example-based elastic materials. In: ACM SIGGRAPH, pp. 72:1–72:8 (2011)Google Scholar
  18. 18.
    Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Hege, H.C., Polthier, K. (eds.) Visualization and Mathematics III, pp. 35–57. Springer, Berlin (2003)Google Scholar
  19. 19.
    Müller, M., Gross, M.: Interactive virtual materials. Proc. Graph. Interface 2004, 239–246 (2004)Google Scholar
  20. 20.
    Müller, M., Keiser, R., Nealen, A., Pauly, M., Gross, M., Alexa, M.: Point based animation of elastic, plastic and melting objects. In: Symposium on Computer Animation, pp. 141–151 (2004)Google Scholar
  21. 21.
    Murtagh, F.: A survey of recent advances in hierarchical clustering algorithms. Comput. J. 26(4), 354–359 (1983)CrossRefzbMATHGoogle Scholar
  22. 22.
    Nealen, A., Mller, M., Keiser, R., Boxerman, E., Carlson, M.: Physically based deformable models in computer graphics. Comput. Graph. Forum 25(4), 809–836 (2006)CrossRefGoogle Scholar
  23. 23.
    Pentland, A., Williams, J.: Good vibrations: modal dynamics for graphics and animation. In: ACM SIGGRAPH, pp. 215–222 (1989)Google Scholar
  24. 24.
    Schilders, W.H., van der Vorst, H.A., Rommes, J.: Model Order Reduction: Theory, Research Aspects and Applications, vol. 13. Springer, Berlin (2008)CrossRefzbMATHGoogle Scholar
  25. 25.
    Shabana, A.A.: Theory of Vibration Volume II: Discrete and Continuous Systems. Springer, New York (1991)zbMATHGoogle Scholar
  26. 26.
    Sifakis, E., Barbic, J.: FEM simulation of 3D deformable solids: a practitioner’s guide to theory, discretization and model reduction. In: ACM SIGGRAPH 2012 Courses, pp. 20:1–20:50 (2012)Google Scholar
  27. 27.
    Sin, F.S., Schroeder, D., Barbič, J.: Vega: non-linear FEM deformable object simulator. Comput. Graph. Forum 32(1), 36–48 (2013)CrossRefGoogle Scholar
  28. 28.
    Sorkine, O., Cohen-Or, D., Lipman, Y., Alexa, M., Rössl, C., Seidel, H.P.: Laplacian surface editing. In: Symposium on Geometry Processing, pp. 175–184 (2004)Google Scholar
  29. 29.
    Von-Tycowicz, C., Schulz, C., Seidel, H.P., Hildebrandt, K.: Real-time nonlinear shape interpolation. ACM Trans. Graph. 34(3), 34:1–34:10 (2015)CrossRefzbMATHGoogle Scholar
  30. 30.
    Yu, D., Kanai, T.: Data-driven subspace enrichment for elastic deformations with collisions. Vis. Comput. 33(6–8), 779–788 (2017)CrossRefGoogle Scholar
  31. 31.
    Zayer, R., Rössl, C., Karni, Z., Seidel, H.P.: Harmonic guidance for surface deformation. Comput. Graph. Forum 24(3), 601–609 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer Science, College of Computer ScienceNational Chiao Tung UniversityHsinchuTaiwan
  2. 2.Department of Computer Science and EngineeringYuan Ze UniversityTaoyuanTaiwan

Personalised recommendations