“Simulating knitted cloth at the yarn level” by Kaldor, James and Marschner

  • ©Jonathan M. Kaldor, Doug L. James, and Steve Marschner




    Simulating knitted cloth at the yarn level



    Knitted fabric is widely used in clothing because of its unique and stretchy behavior, which is fundamentally different from the behavior of woven cloth. The properties of knits come from the nonlinear, three-dimensional kinematics of long, inter-looping yarns, and despite significant advances in cloth animation we still do not know how to simulate knitted fabric faithfully. Existing cloth simulators mainly adopt elastic-sheet mechanical models inspired by woven materials, focusing less on the model itself than on important simulation challenges such as efficiency, stability, and robustness. We define a new computational model for knits in terms of the motion of yarns, rather than the motion of a sheet. Each yarn is modeled as an inextensible, yet otherwise flexible, B-spline tube. To simulate complex knitted garments, we propose an implicit-explicit integrator, with yarn inextensibility constraints imposed using efficient projections. Friction among yarns is approximated using rigid-body velocity filters, and key yarn-yarn interactions are mediated by stiff penalty forces. Our results show that this simple model predicts the key mechanical properties of different knits, as demonstrated by qualitative comparisons to observed deformations of actual samples in the laboratory, and that the simulator can scale up to substantial animations with complex dynamic motion.


    1. Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. In Proc. SIGGRAPH ’98, ACM Press / ACM SIGGRAPH, 43–54. Google ScholarDigital Library
    2. Baraff, D., Witkin, A., and Kass, M. 2003. Untangling cloth. ACM Trans. Graph. 22, 3, 862–870. Google ScholarDigital Library
    3. Bertails, F., Audoly, B., Cani, M.-P., Querleux, B., Leroy, F., and Lévêque, J.-L. 2006. Super-helices for predicting the dynamics of natural hair. ACM Trans. Graph. 25, 3 (August), 1180–1187. Google ScholarDigital Library
    4. Bhat, K., Twigg, C., Hodgins, J., Khosla, P., Popovic, Z., and Seitz, S. 2003. Estimating cloth simulation parameters from video. In Proc. SCA ’03, Eurographics Association, 37–51. Google ScholarDigital Library
    5. Breen, D., House, D., and Wozn, M. 1994. A particle-based model for simulating the draping behavior of woven cloth. Textile Research Journal 64, 11 (November), 663–685.Google ScholarCross Ref
    6. Bridson, R., Fedkiw, R., and John Anderson. 2002. Robust treatment of collisions, contact and friction for cloth animation. In Proc. SIGGRAPH ’02, ACM Press / ACM SIGGRAPH, 594–603. Google ScholarDigital Library
    7. Bridson, R., Marino, S., and Fedkiw, R. 2003. Simulation of clothing with folds and wrinkles. In Proc. SCA ’03, Eurographics Association, vol. 32, 28–36. Google ScholarDigital Library
    8. Chen, Y., Lin, S., Zhong, H., Xu, Y.-Q., Guo, B., and Shum, H.-Y. 2003. Realistic rendering and animation of knitwear. IEEE Transactions on Visualizations and Computer Graphics 9, 43–55. Google ScholarDigital Library
    9. Choi, K., and Ko, H. 2002. Stable but responsive cloth. In Proc. SIGGRAPH ’02, ACM Press / ACM SIGGRAPH, 604–611. Google ScholarDigital Library
    10. Choi, K., and Lo, T. 2003. An energy model of plain knitted fabric. Textile Research Journal 73, 739–748.Google ScholarCross Ref
    11. Choi, K., and Tandon, S. 2006. An energy model of yarn bending. Journal of the Textile Institute 97, 49–56.Google ScholarCross Ref
    12. Chu, L. 2005. A Framework for Extracting Cloth Descriptors from the Underlying yarn Structure. PhD thesis, University of California, Berkeley.Google Scholar
    13. Demiroz, A., and Dias, T. 2000. A study of the graphical representation of plain-knitted structures part I: Stitch model for the graphical representation of plain-knitted structures. Journal of the Textile Institute 91, 463–480.Google ScholarCross Ref
    14. Eberhardt, B., Weber, A., and Strasser, W. 1996. A fast, flexible, particle-system model for cloth draping. IEEE Computer Graphics and Applications 16, 5, 52–59. Google ScholarDigital Library
    15. Eberhardt, B., Meissner, M., and Strasser, W. 2000. Knit fabrics. In Cloth Modeling and Animation, D. House and D. Breen, Eds. A K Peters, ch. 5, 123–144. Google ScholarDigital Library
    16. Göktepe, O., and Harlock, S. C. 2002. Three-dimensional computer modeling of warp knitted structures. Textile Research Journal 72, 266–272.Google ScholarCross Ref
    17. Goldenthal, R., Harmon, D., Fattal, R., Bercovier, M., and Grinspun, E. 2007. Efficient simulation of inextensible cloth. In Proc. SIGGRAPH ’07, vol. 26. Google ScholarDigital Library
    18. Goldstein, H., Poole, C., and John Safko. 2002. Classical Mechanics, 3rd ed. Addison Wesley.Google Scholar
    19. Grinspun, E., Hirani, A., Desbrun, M., and Schröder, P. 2003. Discrete shells. In Proc. SCA ’03, Eurographics Association, 62–67. Google ScholarDigital Library
    20. Jiang, Y., and Chen, X. 2005. Geometric and algebraic algorithms for modelling yarn in woven fabrics. Journal of the Textile Institute 96, 237–245.Google ScholarCross Ref
    21. Jojic, N., and Huang, T. 1997. Estimating cloth draping parameters from range data. In Proc. Intl Workshop on Synthetic-Natural Hybrid Coding and Three Dimensional Imaging, 73–76.Google Scholar
    22. Kaldor, J., James, D., and Marschner, S., 2008. Simulating cloth at the yarn level. Accepted to SIGGRAPH 2008 Computer Animation Festival, August. Google ScholarDigital Library
    23. Kawabata, S., Niwa, M., and Kawai, H. 1973. The finite deformation theory of plain-weave fabrics part I: The biaxialdeformation theory. Journal of the Textile Institute 64, 21–46.Google ScholarCross Ref
    24. King, M., Jearanaisilawong, P., and Scorate, S. 2005. A continuum constitutive model for the mechanical behavior of woven fabrics. International Journal of Solids and Structures 42, 3867–3896.Google ScholarCross Ref
    25. Müller, M., Heidelberger, B., Hennix, M., and Ratcliff, J. 2006. Position based dynamics. In Proc. Virtual Reality Interactions and Physical Simulations (VRIPhys), Eurographics, 71–80.Google Scholar
    26. Nadler, B., Papadopoulos, P., and Steigmann, D. J. 2006. Multiscale constitutive modeling and numerical simulation of fabric material. International Journal of Solids and Structures 43, 206–221.Google ScholarCross Ref
    27. Nocent, O., Nourrit, J.-M., and Remion, Y. 2001. Towards mechanical level of detail for knitwear simulation. In WSCG 2001 Conference Proceedings, V. Skala, Ed.Google Scholar
    28. Pai, D. 2002. STRANDS: Interactive simulation of thin solids using Cosserat models. In Proc. Eurographics, vol. 21, 347–352.Google ScholarCross Ref
    29. Park, J.-W., and Oh, A.-G. 2003. Bending mechanics of ply yarns. Textile Research Journal 73, 473–479.Google ScholarCross Ref
    30. Park, J.-W., and Oh, A.-G. 2006. Bending rigidity of yarns. Textile Research Journal 76, 478–485.Google ScholarCross Ref
    31. Peirce, F. 1937. The geometry of cloth structure. Journal of the Textile Institute 28, T45–T97.Google ScholarCross Ref
    32. Provot, X. 1995. Deformation constraints in a mass-spring model to describe rigid cloth behavior. In Proc. Graphics Interface ’95, Canadian Human-Computer Communications Society, W. A. Davis and P. Prusinkiewicz, Eds., 147–154.Google Scholar
    33. Rémion, Y., Nourrit, J.-M., and Gillard, D. 1999. Dynamic animation of spline like objects. In Proc. WSCG’99, V. Skala, Ed.Google Scholar
    34. Rivers, A. R., and James, D. L. 2007. FastLSM: Fast lattice shape matching for robust real-time deformation. ACM Trans. Graph. 26, 3, 82. Google ScholarDigital Library
    35. Spillmann, J., and Teschner, M. 2008. An adaptive contact model for the robust simulation of knots. In Proc. Eurographics 2008, vol. 27, 497–506.Google Scholar
    36. Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically deformable models. Computer Graphics 21, 205–214. Google ScholarDigital Library
    37. Theetten, A., Grisoni, L., Duriez, C., and Merlhiot, X. 2007. Quasi-dynamic splines. In Proc. ACM Symposium on Solid and Physical Modeling ’07. Google ScholarDigital Library
    38. Volino, P., and Thalmann, N. M. 2000. Implementing fast cloth simulation with collision response. In Proc. Computer Graphics International, 257–266. Google ScholarDigital Library
    39. Warren, W. 1990. The elastic properties of woven polymeric fabric. Polymer Engineering and Science 30, 1309–1313.Google ScholarCross Ref
    40. Zeng, X., Tan, V. B. C., and Shin, V. P. W. 2006. Modelling inter-yarn friction in woven fabric armor. International Journal for Numerical Methods in Engineering 66, 1309–1330.Google ScholarCross Ref

ACM Digital Library Publication: