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Analysis of numerical methods for the simulation of deformable models

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Abstract

Simulating deformable objects based on physical laws has become the most popular technique for modeling textiles, skin, or volumetric soft objects like human tissue. The physical model leads to an ordinary differential equation. Recently, several approaches to fast algorithms have been proposed.

In this work, more profound numerical background about numerical stiffness is provided. Stiff equations impose stability restrictions on a numerical integrator. Some one-step and multistep methods with adequate stability properties are presented. For an efficient implementation, the inexact Newton method is discussed. Applications to 2D and 3D elasticity problems show that the discussed methods are faster and give higher-quality solutions than the commonly used linearized Euler method.

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References

  1. Atanackovic TM, Guran A (2000) Theory of elasticity for scientists and engineers. Birkhäuser, Boston

  2. Baraff D, Witkin A (1998) Large steps in cloth simulation. In: Cohen M (ed) Proceedings of SIGGRAPH ’98, Orlando, FL, July 1998, pp 43–54. ACM SIGGRAPH, Addison-Wesley, Reading, MA

  3. Bathe KL (1982) Finite element methods. Prentice-Hall, Englewood Cliffs, NJ

  4. Breen DE, House DH, Wozny MJ (1994) Predicting the drape of woven cloth using interacting particles. In: Glassner A (ed) Proceedings of SIGGRAPH ’94, Orlando, FL, July 1994, pp 365–372. ACM SIGGRAPH, ACM Press, New York

  5. Debunne G, Desbrun M, Barr A, Cani M-P (1999) Interactive multiresolution animation of deformable models. In: Magnenat-Thalmann N, Thalmann D (eds) Proceedings of Computer Animation and Simulation ’99, Milan, September 1999, pp 133–144. Springer, Berlin Heidelberg New York

  6. Debunne G, Desbrun M, Cani M-P, Barr AH (2001) Dynamic real-time deformations using space and time adaptive sampling. In: Proceedings of SIGGRAPH ’01, Computer Graphics, Los Angeles, August 2001, pp 31–36

  7. Desbrun M, Schröder P, Barr A (1999) Interactive animation of structured deformable objects. In: Proceedings of Graphics Interface 99, Kingston, ON, Canada, June 1999, pp 1–8

  8. Eberhardt B, Weber A, Strasser W (1996) A fast, flexible, particle-system model for cloth draping. IEEE Comput Graph Appl 16(5):52–60

    Article  Google Scholar 

  9. Eberhardt B, Etzmuss O, Hauth M (2000) Implicit-explicit schemes for fast animation with particle systems. In: Proceedings of the Eurographics computer animation and simulation workshop, Interlaken, Switzerland, August 2000, pp 137–151

  10. Etzmuss O, Gross J, Strasser W (2001) Deriving a particle system from continuum mechanics. Trans Vis Comput Graph (in press)

  11. Freund RW, Hochbruck M (1994) On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling. Numer Linear Algebra Appl 1(4):403–420

    Article  MathSciNet  Google Scholar 

  12. Hairer E, Wanner G (1996) Solving ordinary differential equations II, 2nd edn. Springer, Berlin Heidelberg New York, Berlin

  13. Hairer E, Wanner G (1999) Stiff differential equations solved by Radau methods. J Comput Appl Math 111(1–2):93–111

  14. Hauth M, Etzmuss O (2001) A high performance solver for the animation of deformable objects using advanced numerical methods. In: Proceedings of Eurographics, Manchester, UK, September 2001, pp 137–151

  15. House DH, Breen DE (eds) (2000) Cloth modeling and animation. AK Peters, Natick, MA

  16. James DL, Pai DK (1999) ArtDefo – accurate real time deformable objects. In: Proceedings of SIGGRAPH ’99, Computer Graphics, Los Angeles, August 1999, pp 65–72. ACM SIGGRAPH, ACM Press, New York

  17. Kang Y-M, Choi J-H, Cho H-G, Lee D-H, Park C-J. Real-time animation technique for flexible and thin objects. In: Proceedings of WSCG 2000, Pilsen, Czech Republic, February 2000, pp 322–329

  18. Lin M, Gottschalk S (1998) Collision detection between geometric models: a survey. In: Proceedings of the IMA conference on mathematics of surfaces, Winchester, UK, September 1998, pp 37–56

  19. Mezger J, Kimmerle S, Etzmuss O (2002) Improved collision detection and response techniques for cloth animation. Technical Report WSI-2002-5, Universität Tübingen, Tübingen, Germany

  20. O’Brien JF, Hodgins JK (1999) Graphical modeling and animation of brittle. In: Proceedings of SIGGRAPH ’99, Computer Graphics, Los Angeles, August 1999, pp 137–146. Addison Wesley Longman, Reading, MA

  21. Picinbono G, Delingette H, Ayache N (2001) Non-linear anisotropic elasticity for real-time surgery simulation. In: Proceedings of the IEEE International Conference Robotics and Automation 2001, Seoul, South Korea, May 2001

  22. Platt JC, Barr AH (1988) Constraint methods for flexible models. In: Dill J (ed) Proceedings of SIGGRAPH ’88, Atlanta, Georgia, August 1988, pp 279–288. ACM SIGGRAPH, Addison-Wesley, Reading, MA

  23. Press WH, Teukolski SA, Vetterling WT, Flannery BP (1988) Numerical recipes in C: the art of scientific computing, 1st edn. Cambridge University Press, Cambridge, UK

    MathSciNet  Google Scholar 

  24. Provot X (1995) Deformation constraints in a mass-spring model to describe rigid cloth behavior. In: Davis WA, Prusinkiewicz P (eds) Proceedings of Graphics Interface ’95, Quebec, May 1995, pp 147–154

  25. Rheinboldt WC (1998) Methods for solving systems of nonlinear equations. In: CBMS-NSF regional conference series in applied mathematics, vol 70, 2nd edn. SIAM

  26. Saad Y (1996) Iterative methods for sparse linear systems. PWS, Boston

  27. Terzopoulos D, Fleischer K (1988) Deformable models. Vis Comput 4:306–331

    Article  Google Scholar 

  28. Volino P, Magnenat-Thalmann N (1994) Efficient self-collision detection on smoothly discretized surface animations using geometrical shape regularity. In: Computer Graphics Forum (Eurographics’94 Conference Issue) 13(3):155–166

  29. Volino P, Magnenat-Thalmann N (2000a) Accurate collision response on polygonal meshes. In: Proceedings of the Computer Animation Conference, Philadelphia, May 2000, pp 154—163. IEEE Press New York

  30. Volino P, Magnenat-Thalmann N (2000b) Implementing fast cloth simulation with collision response. In: Proceedings of Computer Graphics International (CGI’00), Geneva, Switzerland, June 2000, pp 257–268. IEEE Press, New York

  31. Volino P, Magnenat-Thalmann N (2001) Comparing efficiency of integration methods for cloth animation. In: Proceedings of Computer Graphics International (CGI’01), Hong Kong, July 2001, pp 265–274. IEEE Press, New York

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Authors and Affiliations

  1. WSI/GRIS, Universität Tübingen, Germany

    Michael Hauth, Olaf Etzmuss & Wolfgang Strasser

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  1. Michael Hauth
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  2. Olaf Etzmuss
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  3. Wolfgang Strasser
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Correspondence to Michael Hauth.

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Hauth, M., Etzmuss, O. & Strasser, W. Analysis of numerical methods for the simulation of deformable models. Vis Comput 19, 581–600 (2003). https://doi.org/10.1007/s00371-003-0206-2

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