| | This Article | |
| |
| |
| | Share | |
| |
| |
| | Bibliographic References | |
| |
| |
| | Add to: | |
| |
 Digg
 Furl
 Spurl
 Blink
 Simpy
 Google
 Del.icio.us
 Y!MyWeb
| |
| | Search | |
| |
| |
| | |
Modal Warping: Real-Time Simulation of Large Rotational Deformation and Manipulation
January/February 2005 (vol. 11 no. 1)
pp. 91-101
This paper proposes a real-time simulation technique for large deformations. Green's nonlinear strain tensor accurately models large deformations; however, time stepping of the resulting nonlinear system can be computationally expensive. Modal analysis based on a linear strain tensor has been shown to be suitable for real-time simulation, but is accurate only for moderately small deformations. In the present work, we identify the rotational component of an infinitesimal deformation and extend traditional linear modal analysis to track that component. We then develop a procedure to integrate the small rotations occurring at the nodal points. An interesting feature of our formulation is that it can implement both position and orientation constraints in a straightforward manner. These constraints can be used to interactively manipulate the shape of a deformable solid by dragging/twisting a set of nodes. Experiments show that the proposed technique runs in real-time, even for a complex model, and that it can simulate large bending and/or twisting deformations with acceptable realism.
[1] 91 T. Belytschko, W. Kam, and B. Moran, Nonlinear Finite Elements for Continua and Structures. New York: John Wiley & Sons, 2003.[2] S. Capell, S. Green, B. Curless, T. Duchamp, and Z. Popovic, “Interactive Skeleton-Driven Dynamic Deformations,” ACM Trans. Graphics (Proc. ACM SIGGRAPH 2002), vol. 21, no. 3, pp. 586-593, 2002.[3] G. Debunne, M. Desbrun, M.-P. Cani, and A.H. Barr, “Dynamic Real-Time Deformations Using Space and Time Adaptive Sampling,” Computer Graphics (Proc. ACM SIGGRAPH 2001), vol. 35, pp. 31-36, 2001.[4] O. Etzmuss, M. Keckeisen, and W. Strasser, “A Fast Finite Element Solution for Cloth Modeling,” Proc. Pacific Graphics 2003, pp. 244-251, 2003.[5] C.A. Felippa, “A Systematic Approach to the Element-Independent Corotational Dynamics of Finite Elements,” Technical Report CU-CAS-00-03, Center for Aerospace Structures, Colorado, 2000.[6] S. Gibson and B. Mirtich, “A Survey of Deformable Modeling In Computer Graphics,” Technical Report TR-97-19, Mitsubishi Electric Research Lab., Cambridge, Mass., 1997.[7] E. Grinspun, P. Krysl, and P. Schröder, “CHARMS: A Simple Framework for Adaptive Simulation,” ACM Trans. Graphics (Proc. ACM SIGGRAPH 2002), vol. 21, no. 3, pp. 281-290, 2002.[8] K.K. Hauser, C. Shen, and J.F. O'Brien, “Interactive Deformation Using Modal Analysis with Constraints,” Proc. Graphics Interface 2003, pp. 247-255, 2003.[9] D.L. James and K. Fatahalian, “Precomputing Interactive Dynamic Deformable Scenes,” ACM Trans. Graphics (Proc. ACM SIGGRAPH 2003), vol. 22, no. 3, pp. 879-887, 2003.[10] D.L. James and D.K. Pai, “DyRT: Dynamic Response Textures for Real Time Deformation Simulation with Graphics Hardware,” ACM Trans. Graphics (Proc. ACM SIGGRAPH 2002), vol. 21, no. 3, pp. 582-585, 2002.[11] D.L. James and D.K. Pai, “BD-Tree: Output-Sensitive Collision Detection for Reduced Deformable Models,” ACM Trans. Graphics (Proc. ACM SIGGRAPH 2004), vol. 23, no. 3, pp. 393-398, 2004.[12] P.G. Kry, D.L. James, and D.K. Pai, “Eigenskin: Real Time Large Deformation Character Skinning in Hardware,” Proc. ACM SIGGRAPH Symp. Computer Animation 2002, pp. 153-159, 2002.[13] R.B. Lehoucq, D.C. Sorensen, and C. Yang, ARPACK Users' Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM, 1998.[14] M. Müller, J. Dorsey, L. McMillan, R. Jagnow, and B. Cutler, “Stable Real-Time Deformations,” Proc. ACM SIGGRAPH Symp. Computer Animation 2002, pp. 49-54, 2002.[15] M. Müller and M. Gross, “Interactive Virtual Materials,” Proc. Graphics Interface 2004, pp. 239-246, 2004.[16] Y. Nakamura and H. Hanafusa, “Inverse Kinematics Solutions with Singularity Robustness for Robot Manipulator Control,” J. Dynamic Systems, Measurement, and Control, vol. 108, pp. 163-171, 1986.[17] J.F. O'Brien and J.K. Hodgins, “Graphical Modeling and Animation of Brittle Fracture,” Computer Graphics (Proc. ACM SIGGRAPH '99), vol. 33, no. 4, pp. 137-146, 1999.[18] J.F. O'Brien, C. Shen, and C.M. Gatchalian, “Synthesizing Sounds from Rigid-Body Simulations,” Proc. ACM SIGGRAPH Symp. Computer Animation, pp. 175-182, 2002.[19] A. Pentland and J. Williams, “Good Vibrations: Model Dynamics for Graphics and Animation,” Computer Graphics (Proc. ACM SIGGRAPH '89), vol. 23, no. 3, pp. 207-214, 1989.[20] A.A. Shabana, Theory of Vibration, Volume II: Discrete and Continuous Systems. New York: Springer-Verlag, 1990.[21] A.A. Shabana, Dynamics of Multibody Systems. Cambridge Univ. Press, 1998.[22] J. Stam, “Stochastic Dynamics: Simulating the Effects of Turbulence on Flexible Structures,” Computer Graphics Forum (Proc. EUROGRAPHICS '97), vol. 16, no. 3, pp. 159-164, 1997.[23] D. Terzopoulos and K. Fleischer, “Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture,” Computer Graphics (Proc. ACM SIGGRAPH '88), vol. 22, no. 4, pp. 269-278, 1988.[24] D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically Deformable Models,” Computer Graphics (Proc. ACM SIGGRAPH '87), vol. 21, no. 4, pp. 205-214, 1987.[25] D. Terzopoulos and A. Witkin, “Physically Based Models with Rigid and Deformable Components,” IEEE Computer Graphics and Applications, vol. 8, no. 6, pp. 41-51, 1988.[26] O.C. Zienkiewicz, The Finite Element Method. Maidenhead, Berkshire, England: McGraw-Hill Book Company (UK) Limited, 1977.
Index Terms:
Physically-based modeling, physically-based animation, deformation, modal analysis.
Citation:
Min Gyu Choi, Hyeong-Seok Ko, "Modal Warping: Real-Time Simulation of Large Rotational Deformation and Manipulation," IEEE Transactions on Visualization and Computer Graphics, vol. 11, no. 1, pp. 91-101, Jan./Feb. 2005, doi:10.1109/TVCG.2005.13
