Verlet with Collisions for Mass Spring Model Simulations

Maciej Kot, Hiroshi Nagahashi


In this paper we study the problem of the interaction of soft bodies modeled with mass spring models (MSM) and static elements of the environment. We show that in such setup it is possible to couple standard time evolution of MSMs with collision responses in a way, that does not require complex processing for multi collision situations while successfully preventing object inter-penetration. Moreover we show how to achieve similar energy dissipation for models with different resolutions when the friction is present.


  1. Atencio, Y. P., Esperanca, C., Cavalcanti, P. R., and Oliveira, A. (2005). A collision detection and response scheme for simplified physically based animation. In XVIII Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI'05), pages 291-298.
  2. Bridson, R., Fedkiw, R., and Anderson, J. (2002). Robust treatment of collisions, contact and friction for cloth animation. ACM Trans. Graph., 21(3):594-603.
  3. Cotin, S., Delingette, H., and Ayache, N. (1998). Efficient Linear Elastic Models of Soft Tissues for Real-time Surgery Simulation. Technical Report RR-3510, INRIA.
  4. Duriez, C., Member, S., Dubois, F., Kheddar, A., and Andriot, C. (2006). Realistic haptic rendering of interacting deformable objects in virtual environments. IEEE Transactions on Visualization and Computer Graphics, 12:36-47.
  5. Faure, F. and Wien, T. U. (1998). Interactive solid animation using linearized displacement constraints. In 9 th Eurographics Workshop on Computer Animation and Simulation. e.
  6. Fisher, S. and Lin, M. C. (2001). Deformed distance fields for simulation of non-penetrating flexible bodies. In Proceedings of the Eurographic workshop on Computer animation and simulation, pages 99-111, New York, NY, USA. Springer-Verlag New York, Inc.
  7. Frenkel, D. (2002). Understanding Molecular Simulation - From Algorithms to Applications. Academic Press.
  8. Hasegawa, S. and Sato, M. (2004). Real-time rigid body simulation for haptic interactions based on contact volume of polygonal objects. Comput. Graph. Forum, 23(3):529-538.
  9. Heidelberger, B., Teschner, M., Keiser, R., Müller, M., and Gross, M. (2004). Consistent penetration depth estimation for deformable collision response. In In Proceedings of Vision, Modeling, Visualization VMV'04, pages 339-346.
  10. James, D. L. and Pai, D. K. (2002). Real time simulation of multizone elastokinematic models. In In Proceedings of the IEEE International Conference on Robotics and Automation, pages 927-932.
  11. Kot, M. and Nagahashi, H. (2014). Collision response in mass spring model simulations. Technical report of IEICE. Multimedia and virtual environment, 113(470):287-290.
  12. Kot, M., Nagahashi, H., and Szymczak, P. (2015). Elastic moduli of simple mass spring models. The Visual Computer, 31(10):1339-1350.
  13. Ladd, A. J. C. (2010). Numerical methods for molecular and continuum dynamics. 3rd Warsaw School of Statistical Physics, B. Cichocki, M. Napiorkowski, J. Piasecki, eds., Warsaw Univesity Press, Warsaw.
  14. Ladd, A. J. C. and Kinney, J. H. (1997). Elastic constants of cellular structures. Physica A: Statistical and Theoretical Physics, 240(1-2):349-360.
  15. Levine, J. A., Bargteil, A. W., Corsi, C., Tessendorf, J., and Geist, R. (2014). A peridynamic perspective on spring-mass fracture. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation.
  16. Liu, T., Bargteil, A. W., O'Brien, J. F., and Kavan, L. (2013). Fast simulation of mass-spring systems. ACM Transactions on Graphics, 32(6):209:1-7. Proceedings of ACM SIGGRAPH Asia 2013, Hong Kong.
  17. Michels, D. L., Sobottka, G. A., and Weber, A. G. (2014). Exponential integrators for stiff elastodynamic problems. ACM Trans. Graph., 33(1):7:1-7:20.
  18. Müller, M., Heidelberger, B., Teschner, M., and Gross, M. (2005). Meshless deformations based on shape matching. ACM Trans. Graph., 24:471-478.
  19. Nealen, A., Müller, M., Keiser, R., Boxerman, E., Carlson, M., and Ageia, N. (2006). Physically based deformable models in computer graphics. Comput. Graph. Forum, 25(4):809-836.
  20. Ostoja-Starzewski, M. (2002). Lattice models in micromechanics. Applied Mechanics Reviews, 55(1):35-60.
  21. Pabst, S., Thomaszewski, B., and Strasser, W. (2009). Anisotropic friction for deformable surfaces and solids. In Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA 7809, pages 149-154, New York, NY, USA. ACM.
  22. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2007). Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press, New York, NY, USA, 3 edition.
  23. Sin, F., Schroeder, D., and Barbic, J. (2013). Vega: Nonlinear fem deformable object simulator. Comput. Graph. Forum, 32(1):36-48.
  24. Steinhauser, M. O. (2008). Computational Multiscale Modeling of Fluids and solids. Springer-Verlag Berlin Heidelberg.
  25. Tuckerman, M., Berne, B. J., and Martyna, G. J. (1992). Reversible multiple time scale molecular dynamics. The Journal of Chemical Physics, 97(3):1990-2001.

Paper Citation

in Harvard Style

Kot M. and Nagahashi H. (2017). Verlet with Collisions for Mass Spring Model Simulations . In Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2017) ISBN 978-989-758-224-0, pages 314-320. DOI: 10.5220/0006269303140320

in Bibtex Style

author={Maciej Kot and Hiroshi Nagahashi},
title={Verlet with Collisions for Mass Spring Model Simulations},
booktitle={Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2017)},

in EndNote Style

JO - Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2017)
TI - Verlet with Collisions for Mass Spring Model Simulations
SN - 978-989-758-224-0
AU - Kot M.
AU - Nagahashi H.
PY - 2017
SP - 314
EP - 320
DO - 10.5220/0006269303140320