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Deriving a Particle System from Continuum Mechanics for the Animation of Deformable Objects
October-December 2003 (vol. 9 no. 4)
pp. 538-550

Abstract—Mass-spring and particle systems have been widely employed in computer graphics to model deformable objects because they allow fast numerical solutions. In this work, we establish a link between these discrete models and classical mathematical elasticity. It turns out that discrete systems can be derived from a continuum model by a finite difference formulation and approximate classical continuum models unless the deformations are large. In this work, we present the derivation of a particle system from a continuum model, compare it to the models of classical elasticity theory, and assess its accuracy. In this way, we gain insight into the way discrete systems work and we are able to specify the correct scaling when the discretization is changed. Physical material parameters that describe materials in continuum mechanics are also used in the derived particle system.

[1] D. Baraff and A. Witkin, "Large Steps in Cloth Simulation," Proc. Siggraph 98, Annual Conference Series, ACM, New York, July 1998, pp. 43-54.
[2] K.L. Bathe, Finite Element Methods. Prentice Hall, 1982.
[3] D. Bielser, V.A. Maiwald, and M.H. Gross, Interactive Cuts through 3-Dimensional Soft Tissue Computer Graphics Forum, vol. 18, no. 3, pp. 31-38, Sept. 1999.
[4] D.E. Breen,D.H. House,, and M. J. Wozny,“Predicting the drape of woven cloth using interacting particles,” Computer Graphics (SIGGRAPH’94 Proc.), A. Glassner, ed., vol. 28, pp. 365-372, July 1994.
[5] S. Cotin, H. Delingette, and N. Ayache, Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation IEEE Trans. Visualization and Computer Graphics, vol. 5, no. 1, pp. 62-73, 1999.
[6] S.M. Day, Efficient Simulation of Constant Q Using Coarse-Grained Memory Variables Bulletin Seismic Soc. Am., vol. 88, no. 4, pp. 1051-1062, 1998.
[7] G. Debunne, M. Desbrun, M.-P. Cani, and A.H. Barr, Dynamic Real-Time Deformations Using Space and Time Adaptive Sampling Computer Graphics (SIGGRAPH '01 Proc.), 2001.
[8] H. Delingette, S. Cotin, and N. Ayache, A Hybrid Elastic Model Allowing Real-Time Cutting, Deformations and Force-Feedback for Surgery Training and Simulation Proc. Computer Animation Conf., 2000.
[9] M.P. DoCarmo, Differential Geometry of Curves and Surfaces. Englewood Cliffs, N.J.: Prentice Hall, 1976.
[10] B. Eberhardt, O. Etzmuß, and M. Hauth, Implicit-Explicit Schemes for Fast Animation with Particle Systems Proc. Eurographics Workshop Computer Animation and Simulation (EGCAS-00), 2000.
[11] B. Eberhardt, A. Weber, and W. Straßer, A Fast, Flexible, Particle-System Model for Cloth Draping IEEE Computer Graphics and Applications, vol. 16, no. 5, pp. 52-60, Sept. 1996.
[12] J.W. Eischen and R. Bigliani, Continuum versus Particle Representation Cloth Modeling and Animation, D.H. House and D.E. Breen, eds., chapter 4, pp. 79-122, 2000.
[13] J.W. Eischen, S. Deng, and T.G. Clapp, Finite-Element Modeling and Control of Flexible Fabric Parts IEEE Computer Graphics and Applications, vol. 16, no. 5, pp. 71-80, 1996.
[14] J. Groß, O. Etzmuß, M. Hauth, and G. Bueß, Modelling Viscoelasticity in Soft Tissues Proc. Int'l Workshop Deformable Modeling and Soft Tissue Simulation, 2001.
[15] M. Hauth and O. Etzmuß, A High Performance Solver for the Animation of Deformable Objects Using Advanced Numerical Methods Proc. Eurographics, 2001.
[16] Cloth Modeling and Animation, D.H. House and D.E. Breen, ed. AK Peters, 2000.
[17] E.S.K.I. Kay, Applying Finite Element Analysis to the Memory Variable Formulation of Wave Propagation in Anelastic Media Geophysics, vol. 64, no. 1, 1999,
[18] M. Kass, An Introduction to Physically Based Modeling, Chapter: Introduction to Continuum Dynamics for Computer Graphics Siggraph '95 Course Notes, 1995.
[19] S. Kawabata, The Standardization and Analysis of Hand Evaluation. Osaka: The Textile Machinery Soc. of Japan, 1980.
[20] E. Klingbeil, Tensorrechnung für Ingenieure. BI Wissenschaftsverlag, 1989.
[21] U. Kühnapfel, H.K. Cakmak, and H. Maass, Endoscopic Surgery Training Using Virtual Reality and Deformable Tissue Simulation Computers&Graphics, vol. 24, 2000.
[22] J.F. O'Brien and J.K. Hodgins, "Graphical Modeling and Animation of Brittle Fracture," Proc. Siggraph 99, ACM, New York, Aug. 1999, pp. 137-146.
[23] X. Provot, Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior Proc. Graphics Interface '95, pp. 147-154, 1995.
[24] W. Reeves, "Particle Systems—A Technique for Modeling a Class of Fuzzy Objects," Computer Graphics, vol. 17, no. 3, July 1983, pp. 359-376.
[25] H. Stephani and G. Kluge, Theoretische Mechanik. Spektrum Akademischer Verlag, 1995.
[26] D. Terzopoulos and K. Fleischer, Deformable Models The Visual Computer, vol. 4, pp. 306-331, 1988.
[27] A. Van Gelder, Approximate Simulation of Elastic Membranes by Triangle Meshes J. Graphics Tools, vol. 3, pp. 21-42, 1998.
[28] P. Volino and N. Magnenat-Thalmann, Developing Simulation Techniques for an Interactive Clothing System Proc. Int'l Conf. Virtual Systems and Multimedia '97, pp. 109-118, 1997.

Index Terms:
Deformable objects, simulation, animation, cloth modeling, particle systems, continuum mechanics, finite differences.
Olaf Etzmuss, Joachim Gross, Wolfgang Strasser, "Deriving a Particle System from Continuum Mechanics for the Animation of Deformable Objects," IEEE Transactions on Visualization and Computer Graphics, vol. 9, no. 4, pp. 538-550, Oct.-Dec. 2003, doi:10.1109/TVCG.2003.1260747
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