“Super-helices for predicting the dynamics of natural hair” by Bertails, Audoly, Cani, Querleux, Leroy, et al. …

  • ©Florence Bertails-Descoubes, Basile Audoly, Marie-Paule Cani, Bernard Querleux, Frédéric Leroy, and Jean-Luc Lévêque




    Super-helices for predicting the dynamics of natural hair



    Simulating human hair is recognized as one of the most difficult tasks in computer animation. In this paper, we show that the Kirchhoff equations for dynamic, inextensible elastic rods can be used for accurately predicting hair motion. These equations fully account for the nonlinear behavior of hair strands with respect to bending and twisting. We introduce a novel deformable model for solving them: each strand is represented by a Super-Helix, i.e., a piecewise helical rod which is animated using the principles of Lagrangian mechanics. This results in a realistic and stable simulation, allowing large time steps. Our second contribution is an in-depth validation of the Super-Helix model, carried out through a series of experiments based on the comparison of real and simulated hair motions. We show that our model efficiently handles a wide range of hair types with a high level of realism.


    1. Anjyo, K., Usami, Y., and Kurihara, T. 1992. A simple method for extracting the natural beauty of hair. 111–120.Google Scholar
    2. Audoly, B., and Pomeau, Y. 2006. Elasticity and Geometry: from hair curls to the nonlinear response of shells. Oxford University Press, Oxford, UK. To appear.Google Scholar
    3. Bando, Y., Chen, B.-Y., and Nishita, T. 2003. Animating hair with loosely connected particles. Computer Graphics Forum (Eurographics’03) 22, 3, 411–418.Google Scholar
    4. Baraff, D., and Witkin, A. 1992. Dynamic simulation of non-penetrating flexible bodies. ACM Computer Graphics (SIGGRAPH’92) 26, 2, 303–308. Google ScholarDigital Library
    5. Bertails, F., Kim, T.-Y., Cani, M.-P., and Neumann, U. 2003. Adaptive wisp tree – a multiresolution control structure for simulating dynamic clustering in hair motion. In ACM SIGGRAPH Symposium on Computer Animation, 207–213. Google ScholarDigital Library
    6. Bertails, F., Ménier, C., and Cani, M.-P. 2005. A practical self-shadowing algorithm for interactive hair animation. In Proc. Graphics Interface, 71–78. Google ScholarDigital Library
    7. Bertails, F., Audoly, B., Querleux, B., Leroy, F., Lévêque, J.-L., and Cani, M.-P. 2005. Predicting natural hair shapes by solving the statics of flexible rods. In Eurographics ’05 (short papers).Google Scholar
    8. Chang, J., Jin, J., and Yu, Y. 2002. A practical model for hair mutual interactions. In ACM SIGGRAPH Symposium on Computer Animation, 73–80. Google ScholarDigital Library
    9. Choe, B., Choi, M., and Ko, H.-S. 2005. Simulating complex hair with robust collision handling. In ACM SIGGRAPH Symposium on Computer Animation, 153–160. Google ScholarDigital Library
    10. Daldegan, A., Thalmann, N. M., Kurihara, T., and Thalmann, D. 1993. An integrated system for modeling, animating and rendering hair. Computer Graphics Forum 12, 3, 211–221.Google ScholarCross Ref
    11. Hadap, S., and Magnenat-Thalmann, N. 2001. Modeling dynamic hair as a continuum. Computer Graphics Forum (Eurographics’01) 20, 3, 329–338.Google Scholar
    12. Hou, T., Klapper, I., and Si, H. 1998. Removing the stiffness of curvature in computing 3-d filaments. J. Comput. Phys. 143, 628–664. Google ScholarDigital Library
    13. Koh, C., and Huang, Z. 2001. A simple physics model to animate human hair modeled in 2D strips in real time. In EG CAS ’01, 127–138. Google ScholarDigital Library
    14. Lee, D.-W., and Ko, H.-S. 2001. Natural hairstyle modeling and animation. Graphical Models 63, 2 (March), 67–85. Google ScholarDigital Library
    15. Lindelof, B., Forslind, B., Hedblad, M., and Kaveus, U. 1988. Human hair form morphology revealed by light and scanning electron microscopy and computer aided three-dimensional reconstruction. Arch. Dermatol. 124, 9, 1359–1363.Google ScholarCross Ref
    16. Marschner, S., Jensen, H., Cammarano, M., Worley, S., and Hanrahan, P. 2003. Light scattering from human hair fibers. ACM Transactions on Graphics (SIGGRAPH’03) 22, 3 (July), 281–290. Google ScholarDigital Library
    17. Nocent, O., and Remion, Y. 2001. Continuous deformation energy for dynamic material splines subject to finite displacements. In EG CAS’01, 87–97. Google ScholarDigital Library
    18. Pai, D. 2002. Strands: Interactive simulation of thin solids using cosserat models. Computer Graphics Forum (Eurographics’02) 21, 3, 347–352.Google Scholar
    19. Plante, E., Cani, M.-P., and Poulin, P. 2001. A layered wisp model for simulating interactions inside long hair. In EG CAS ’01, Springer, Computer Science, 139–148. Google ScholarDigital Library
    20. Qin, H., and Terzopoulos, D. 1996. D-nurbs: A physics-based framework for geometric design. IEEE Trans. on Visualization and Computer Graphics 2, 1, 85–96. Google ScholarDigital Library
    21. Raghupathi, L., Cantin, V., Faure, F., and Cani, M.-P. 2003. Real-time simulation of self-collisions for virtual intestinal surgery. In International Symposium on Surgery Simulation and Soft Tissue Modeling, Springer-Verlag, no. 2673 in Lecture Notes in Computer Science, 15–26. Google ScholarDigital Library
    22. Redon, S., Galoppo, N., and Lin, M. 2005. Adaptive dynamics of articulated bodies. ACM Transactions on Graphics (SIGGRAPH’05) 24, 3, 936–945. Google ScholarDigital Library
    23. Robbins, C. 2002. Chemical and Physical Behavior of Human Hair. 4th ed. Springer.Google Scholar
    24. Rosenblum, R., Carlson, W., and Tripp, E. 1991. Simulating the structure and dynamics of human hair: Modeling, rendering, and animation. The Journal of Visualization and Computer Animation 2, 4, 141–148.Google ScholarCross Ref
    25. Ward, K., and Lin, M. C. 2003. Adaptive grouping and subdivision for simulating hair dynamics. In Proceedings of Pacific Graphics’03, 234–243. Google ScholarDigital Library
    26. Witkin, A., and Welch, W. 1990. Fast animation and control of non-rigid structures. ACM Computer Graphics (SIGGRAPH’90) 24, 4, 243–252. Google ScholarDigital Library
    27. Wolfram, S. 1999. The Mathematica book (4th edition). Cambridge University Press, New York, NY, USA. Google ScholarDigital Library

ACM Digital Library Publication:

Overview Page: