“TRACKS: toward directable thin shells” by Bergou, Mathur, Wardetzky and Grinspun

  • ©Miklós Bergou, Saurabh Mathur, Max Wardetzky, and Eitan Grinspun




    TRACKS: toward directable thin shells



    We combine the often opposing forces of artistic freedom and mathematical determinism to enrich a given animation or simulation of a surface with physically based detail. We present a process called tracking, which takes as input a rough animation or simulation and enhances it with physically simulated detail. Building on the foundation of constrained Lagrangian mechanics, we propose weak-form constraints for tracking the input motion. This method allows the artist to choose where to add details such as characteristic wrinkles and folds of various thin shell materials and dynamical effects of physical forces. We demonstrate multiple applications ranging from enhancing an artist’s animated character to guiding a simulated inanimate object.


    1. Angelidis, A., Neyret, F., Singh, K., and Nowrouzezahrai, D. 2006. A controllable, fast and stable basis for vortex based smoke simulation. In SCA ’06, 25–32. Google ScholarDigital Library
    2. Autodesk. Autodesk Maya Unlimited 8.0.Google Scholar
    3. Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. In Proc. of SIGGRAPH ’98, 43–54. Google ScholarDigital Library
    4. Boxerman, E., and Ascher, U. 2004. Decomposing cloth. In SCA ’04, 153–161. Google ScholarDigital Library
    5. Bridson, R., Fedkiw, R. P., and Anderson, J. 2002. Robust treatment of collisions, contact, and friction for cloth animation. ACM TOG 21, 3 (July), 594–603. Google ScholarDigital Library
    6. Bridson, R., Marino, S., and Fedkiw, R. 2003. Simulation of clothing with folds and wrinkles. In SCA ’03, 28–36. Google ScholarDigital Library
    7. Capell, S., Green, S., Curless, B., Duchamp, T., and Popović, Z. 2002. Interactive skeleton-driven dynamic deformations. ACM TOG 21, 3 (July), 586–593. Google ScholarDigital Library
    8. Capell, S., Burkhart, M., Curless, B., Duchamp, T., and Popović, Z. 2005. Physically based rigging for deformable characters. In SCA ’05, 301–310. Google ScholarDigital Library
    9. Cohen-Steiner, D., Alliez, P., and Desbrun, M. 2004. Variational shape approximation. ACM TOG 23, 3 (Aug.), 905–914. Google ScholarDigital Library
    10. Cohen, M. F. 1992. Interactive spacetime control for animation. In Proc. of SIGGRAPH ’92, 293–302. Google ScholarDigital Library
    11. Cordier, F., and Magnenat-Thalmann, N. 2005. A data-driven approach for real-time clothes simulation. CGF 24, 2 (jun), 173–183.Google Scholar
    12. Cutler, L. D., Gershbein, R., Wang, X. C., Curtis, C., Maigret, E., Prasso, L., and Farson, P. 2005. An art-directed wrinkle system for CG character clothing. In SCA ’05, 117–126. Google ScholarDigital Library
    13. Fattal, R., and Lischinski, D. 2004. Target-driven smoke animation. ACM TOG 23, 3 (Aug.), 441–448. Google ScholarDigital Library
    14. Galoppo, N., Otaduy, M. A., Mecklenburg, P., Gross, M., and Lin, M. C. 2006. Fast simulation of deformable models in contact using dynamic deformation textures. In SCA ’06, 73–82. Google ScholarDigital Library
    15. Gingold, Y., Secord, A., Han, J., Grinspun, E., and Zorin, D. 2004. Simulating fracture and tearing of thin shells. Tech. rep., NYU.Google Scholar
    16. Gleicher, M., Shin, H. J., Kovar, L., and Jepsen, A. 2003. Snap-together motion: assembling run-time animations. In 2003 ACM Symposium on Interactive 3D Graphics, 181–188. Google ScholarDigital Library
    17. Grinspun, E., Krysl, P., and Schröder, P. 2002. CHARMS: a simple framework for adaptive simulation. ACM TOG 21, 3 (July), 281–290. Google ScholarDigital Library
    18. Grinspun, E., Hirani, A. N., Desbrun, M., and Schröder, P. 2003. Discrete shells. In SCA ’03, 62–67. Google ScholarDigital Library
    19. Grinspun, E., Ed. 2006. Discrete differential geometry: an applied introduction. Course Notes. ACM SIGGRAPH ’06.Google ScholarDigital Library
    20. Hadap, S., Bangarter, E., Volino, P., and Magnenat-Thalmann, N. 1999. Animating wrinkles on clothes. In IEEE Viz. ’99, 175–182. Google ScholarDigital Library
    21. Hairer, E., Lubich, C., and Wanner, G. 2006. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. Springer Series in Computational Mathematics. Springer.Google Scholar
    22. Hauth, M., Etzmuss, O., and Strasser, W. 2003. Analysis of numerical methods for the simulation of deformable models. The Visual Computer 19, 7–8, 581–600.Google ScholarDigital Library
    23. Irving, G., Teran, J., and Fedkiw, R. 2004. Invertible finite elements for robust simulation of large deformation. In SCA ’04, 131–140. Google ScholarDigital Library
    24. Kircher, S., and Garland, M. 2006. Editing arbitrarily deforming surface animations. ACM TOG 25, 3 (jul), 1098–1107. Google ScholarDigital Library
    25. Kondo, R., Kanai, T., and Anjyo, K. 2005. Directable animation of elastic objects. In SCA ’05, 127–134. Google ScholarDigital Library
    26. Lanczos, C. 1986. The Variational Principles of Mechanics, fourth ed. Dover.Google Scholar
    27. Loviscach, J. 2006. Wrinkling coarse meshes on the GPU. CGF 25, 3 (Sept.), 467–476.Google Scholar
    28. Ma, L., Hu, J., and Baciu, G. 2006. Generating seams and wrinkles for virtual clothing. In ACM VRCIA ’06, 205–211. Google ScholarDigital Library
    29. Malvern, L. E. 1969. Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
    30. Marsden, J. E., And Ratiu, T. 1994. Introduction to Mechanics and Symmetry, second ed., vol. 17 of Texts in Applied Mathematics. Springer-Verlag.Google Scholar
    31. McNamara, A., Treuille, A., Popović, Z., and Stam, J. 2004. Fluid control using the adjoint method. ACM TOG 23, 3 (Aug.), 449–456. Google ScholarDigital Library
    32. Ng, H. N., and Grimsdale, R. L. 1996. Computer graphics techniques for modeling cloth. IEEE CG&A 16, 5 (Sept.), 28–41. Google ScholarDigital Library
    33. O’Brien, J. F., Bargteil, A. W., and Hodgins, J. K. 2002. Graphical modeling and animation of ductile fracture. ACM TOG 21, 3 (July), 291–294. Google ScholarDigital Library
    34. Park, S. I., and Hodgins, J. K. 2006. Capturing and animating skin deformation in human motion. ACM TOG 25, 3 (July), 881–889. Google ScholarDigital Library
    35. Platt, J. C., and Barr, A. H. 1988. Constraint methods for flexible models. In Proc. of SIGGRAPH ’88, 279–288. Google ScholarDigital Library
    36. Popović, J., Seitz, S., Erdmann, M., Popović, Z., and Witkin, A. 2000. Interactive manipulation of rigid body simulations. In Proc. of SIGGRAPH ’00, 209–218. Google ScholarDigital Library
    37. Popović, J., Seitz, S. M., and Erdmann, M. 2003. Motion sketching for control of rigid-body simulations. ACM TOG 22, 4 (Oct.), 1034–1054. Google ScholarDigital Library
    38. Rasmussen, N., Enright, D., Nguyen, D., Marino, S., Sumner, N., Geiger, W., Hoon, S., and Fedkiw, R. 2004. Directable photorealistic liquids. In SCA ’04, 193–202. Google ScholarDigital Library
    39. Schenk, O., and Gärtner, K. 2006. On fast factorization pivoting methods for symmetric indefinite systems. Elec. Trans. Numer. Anal., 158–179.Google Scholar
    40. Shi, L., and Yu, Y. 2005. Controllable smoke animation with guiding objects. ACM TOG 24, 1 (Jan.), 140–164. Google ScholarDigital Library
    41. Sifakis, E., Neverov, I., and Fedkiw, R. 2005. Automatic determination of facial muscle activations from sparse motion capture marker data. ACM TOG 24, 3 (Aug.), 417–425. Google ScholarDigital Library
    42. Singh, K., and Kokkevis, E. 2000. Skinning characters using surface oriented free-form deformations. In GI ’00, 35–42.Google Scholar
    43. Smith, J., Witkin, A., and Baraff, D. 2001. Fast and controllable simulation of the shattering of brittle objects. CGF 20, 2, 81–91.Google ScholarCross Ref
    44. Strang, G., and Fix, G. 1973. An Analysis of the Finite Element Method. Wellesley-Cambridge Press.Google Scholar
    45. Sumner, R. W., and Popović, J. 2004. Deformation transfer for triangle meshes. ACM TOG 23, 3 (Aug.), 399–405. Google ScholarDigital Library
    46. Terzopoulos, D., and Fleischer, K. 1988. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. In Proc. of SIGGRAPH ’88, 269–278. Google ScholarDigital Library
    47. Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically deformable models. In Proc. of SIGGRAPH ’87, 205–214. Google ScholarDigital Library
    48. Thomas, F., and Johnston, O. 1981. The Illusion of Life: Disney Animation. Hyperion Books, New York.Google Scholar
    49. Thomaszewski, B., and Wacker, M. 2006. Bending Models for Thin Flexible Objects. In WSCG Short Comm.Google Scholar
    50. Thürey, N., Keiser, R., Pauly, M., and Rüde, U. 2006. Detail-preserving fluid control. In SCA ’06, 7–15. Google ScholarDigital Library
    51. Treuille, A., McNamara, A., Popović, Z., and Stam, J. 2003. Keyframe control of smoke simulations. ACM TOG 22, 3 (July), 716–723. Google ScholarDigital Library
    52. Wicke, M., Steinemann, D., and Gross, M. 2005. Efficient animation of point-sampled thin shells. CGF 24, 3 (Sept.), 667–676.Google Scholar
    53. Witkin, A., and Baraff, D., Eds. 2001. Physically Based Modeling: Principles and Practice. Course Notes. ACM SIGGRAPH ’01.Google Scholar
    54. Witkin, A., and Kass, M. 1988. Spacetime constraints. In Proc. of SIGGRAPH ’88, 159–168. Google ScholarDigital Library
    55. Witkin, A., and Welch, W. 1990. Fast animation and control of nonrigid structures. In Proc. of SIGGRAPH ’90, 243–252. Google ScholarDigital Library
    56. Wojtan, C., Mucha, P. J., and Turk, G. 2006. Keyframe control of complex particle systems using the adjoint method. In SCA ’06, 15–24. Google ScholarDigital Library
    57. Zienkiewicz, O. C., and Taylor, R. L. 2000. The finite element method, fifth ed., vol. 1 and 2. Butterworth-Heinemann.Google Scholar
    58. Zordan, V. B., and Hodgins, J. K. 2002. Motion capture-driven simulations that hit and react. In SCA ’02, 89–96. Google ScholarDigital Library
    59. Zorin, D., and Schröder, P., Eds. 1998. Subdivision for Modeling and Animation. Course Notes. ACM SIGGRAPH ’98.Google Scholar

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