Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-24T17:53:18.340Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

Published online by Cambridge University Press:  03 June 2015

Yan Li ,
I-Liang Chern ,
Joung-Dong Kim  and
Xiaolin Li
Yan Li*
Affiliation:
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA
I-Liang Chern*
Affiliation:
Department of Applied Mathematics, Center of Mathematical Modeling and Scientific Computing, National Chiao Tung University, Hsin Chu, 300, Taiwan Department of Mathematics, National Taiwan University, Taipei, 106, Taiwan National Center for Theoretical Sciences, Taipei Office, Taipei, 106, Taiwan
Joung-Dong Kim*
Affiliation:
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA
Xiaolin Li*
Affiliation:
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Get access

Abstract

We use front tracking data structures and functions to model the dynamic evolution of fabric surface. We represent the fabric surface by a triangulated mesh with preset equilibrium side length. The stretching and wrinkling of the surface are modeled by the mass-spring system. The external driving force is added to the fabric motion through the “Impulse method” which computes the velocity of the point mass by superposition of momentum. The mass-spring system is a nonlinear ODE system. Added by the numerical and computational analysis, we show that the spring system has an upper bound of the eigen frequency. We analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the eigen-frequency This upper bound plays an important role in determining the numerical stability and accuracy of the ODE system. Based on this analysis, we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion. We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.

Keywords

74B2065D1765Z05Front trackingspring modeleigen frequency
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 5 , November 2013 , pp. 1228 - 1251
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Fedkiw, R.Selle, A., Lentine, M.A mass spring model for hair simulation. ACM Transactions on Graphics (Proceedings of the ACM SIGGRAPH’08 conference), 27, 2008.Google Scholar
[2]Aono, M., Breen, D., and Wozny, M.Fitting a woven cloth model to a curved surface: mapping algorithms. Computer-Aided Design, 26(4):278–292, April 1994.CrossRefGoogle Scholar
[3]Aono, M., Denti, P., Breen, D., and Wozny, M.Fitting a woven cloth model to a curved surface: dart insertion. IEEE Computer Graphics and Applications, 16(5):60–70, September 1996.Google Scholar
[4]Ascher, U. and Boxerman, E.On the modified conjugate gradient method in cloth simulation. The Visual Computer, 19(7-8):523–531, December 2003.Google Scholar
[5]Baraff, D. and Witkin, A.Large steps in cloth simulation. In Proceedings of ACM SIGGRAPH 98, pages 43–54. ACM Press, 1998.Google Scholar
[6]Bargmann, R.Real time cloth simulation. Master’s thesis, Ecoly Polytechnique Fédérale de Lausanne (EPFL) / Eidgenössische Technische Hoschschule Zörich (ETHZ), Lausanne / Zurich, Switzerland, 2003.Google Scholar
[7]Bez, H., Bricis, A., and Ascough, J.A collision detection method with applications in CAD systems for the apparel industry. Computer-Aided Design, 28(1):27–32, 1996.Google Scholar
[8]Bo, W., Liu, X., Glimm, J., and Li, X.Primary breakup of a high speed liquid jet. ASME Journal of Fluids Engineering, submitted, 2010.Google Scholar
[8][9]Breen, D.A particle-based model for simulating the draping behavior of woven cloth. PhD thesis, Rensselaer Polytechnic Institute, 1993.Google Scholar
[10]Breen, D., House, D., and Wozny, M.Predicting the drape of woven cloth using interacting particles. In Proceedings of ACM SIGGRAPH 94, pages 365–372. ACM Press, 1994.Google Scholar
[11]Bridson, R., Marino, S., and Fedkiw, R.Simulation of clothing with folds and wrinkles. In Proceedingsof ACM SIGGRAPH/Eurographics Symposiumon Computer Animation (SCA 2003), pages 28–36. ACM Press, 2003.Google Scholar
[12]Bridson, Robert, Fedkiw, Ronald, and Anderson, John. Robust treatment of collisions, contact and friction for cloth animation. ACM Transactions on Graphics, 21:594–603, 2002.Google Scholar
[13]Butcher, J. C.The numerical analysis of ordinary differential equations : Runge-Kutta and general linear methods. 1987.Google Scholar
[14]Carignan, M., Yang, Y., Magnenat-Thalmann, N., and Thalmann, D.Dressing animated synthetic actors with complex deformable clothes. In Computer Graphics (Proceedings of ACM SIGGRAPH 92), pages 99–104. ACM Press, 1992.Google Scholar
[15]Choi, K.-J. and Ko, H.-S.Stable but responsive cloth. ACM Transactions on Graphics, 21:604–611, 2002.Google Scholar
[16]Du, Jian, Fix, Brian, Glimm, James, Jia, Xicheng, Li, Xiaolin, Li, Yunhua, and Wu, Lingling. A simple package for front tracking. J. Comput. Phys., 213:613–628, 2006.Google Scholar
[17]Eberhardt, B., Meißner, M., and Straßer, W.Knit fabrics. In House, D. and Breen, D., editors, Cloth Modeling and Animation, pages 123–144. Peters, A.K., 2000.Google Scholar
[18]Eberhardt, B., Weber, A., and Straßer, W.A fast, flexible, particle-system model for cloth draping. IEEE Computer Graphics and Applications, 16(5):52–59, September 1996.Google Scholar
[19]George, E., Glimm, J., Li, X. L., Li, Y. H., and Liu, X. F.The influence of scale-breaking phenomena on turbulent mixing rates. Phys. Rev. E, 73:016304, 2006.Google Scholar
[20]Barr, A. H.Platt, J. C.Constraints methods for flexible models. In SIGGRAPH ‘88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques, pages 279–288, 1988.Google Scholar
[21]Kim, J.-D., Li, Y., and Li, X.-L.Simulation of parachute FSI using the front tracking method. Journal of Fluids and Structures, 37:101–119, 2013.Google Scholar
[22]Provot, X.Deformation constraints in a mass-spring model to describe rigid cloth behavior. In Proceedings of Graphics Interface (GI 1995), pages 147–154. Canadian Computer-Human Communications Society, 1995.Google Scholar
[23]Samulyak, R., Lu, T., Parks, P., Glimm, J., and Li, X.Simulation of pellet ablation for tokamak fuelling with itaps front tracking. Journal of Physics: Conf. Series, 125:012081, 2008.Google Scholar
[24]Terzopoulos, D. and Fleischer, K.Deformable models. The Visual Computer, 4(6):306–331, December 1988.Google Scholar
[25]Terzopoulos, D. and Fleischer, K.Modeling inelastic deformation: viscoelasticity, plasticity, fracture. In Computer Graphics (Proceedings of ACM SIGGRAPH 88), pages 269–278. ACM Press, July 1988.Google Scholar
[26]Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K.Elastically deformable models. In Computer Graphics (Proceedings of ACM SIGGRAPH 87), pages 205–214. ACM Press, July 1987.Google Scholar
[27]Terzopoulos, D. and Waters, K.Analysis and synthesis of facial image sequences using physical and anatomical models. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 15:569–579, 1993.Google Scholar
[28]Volino, P., Courchesne, M., and Magnenat-Thalmann, N.Versatile and efficient techniques for simulating cloth and other deformable objects. In Proceedings of ACM SIGGRAPH 95, pages 137–144. ACM Press, 1995.Google Scholar