The Community for Technology Leaders
RSS Icon
Issue No.06 - June (2011 vol.17)
pp: 822-835
Nan Zhang , University of Minnesota at Twin Cities, Minneapolis
Huamin Qu , Hong Kong University of Science and Technology, Hong Kong
Robert Sweet , University of Minnesota at Twin Cities, Minneapolis
We propose a new computation model for simulating elastic thin shells at interactive rates. Existing graphical simulation methods are mostly based on dihedral angle energy functions, which need to compute the first order and second order partial derivatives with respect to current vertex positions as bending forces and stiffness matrices. The symbolic derivatives are complicated in nonisometric element deformations. To simplify computing the derivatives, instead of directly constructing the dihedral angle energy, we use the orientation change energy of mesh edges. A continuum-mechanics-based orientation-preserving rod element model is developed to provide the bending forces. The advantage of our method is simple bending force and stiffness matrix computation, since in the rod model, we apply a novel incremental construction of the deformation gradient tensor to linearize both tensile and orientation deformations. Consequently, our model is efficient, easy to implement, and supports both quadrilateral and triangle meshes. It also treats shells and plates uniformly.
Physically based modeling, rod element, bending energy, thin-shell simulation, orientation preserving.
Nan Zhang, Huamin Qu, Robert Sweet, "Orientation-Preserving Rod Elements for Real-Time Thin-Shell Simulation", IEEE Transactions on Visualization & Computer Graphics, vol.17, no. 6, pp. 822-835, June 2011, doi:10.1109/TVCG.2010.92
[1] D. Baraff and A. Witkin, "Large Steps in Cloth Simulation," Proc. ACM SIGGRAPH, pp. 43-54, July 1998.
[2] M. Bergou, M. Wardetzky, S. Robinson, B. Audoly, and E. Grinspun, "Discrete Elastic Rods," Proc. ACM SIGGRAPH, 2008.
[3] F. Bertails, B. Audoly, M.-P. Cani, B. Querleux, F. Leroy, and J.-L. Lévêque, "Super-Helices for Predicting the Dynamics of Natural Hair," Proc. ACM SIGGRAPH, Aug. 2006.
[4] J. Bonet and R.D. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge Univ. Press, 1997.
[5] R. Bridson, R. Fedkiw, and J. Anderson, "Robust Treatment of Collisions, Contact and Friction for Cloth Animation," Proc. ACM SIGGRAPH, pp. 594-603, Aug. 2002.
[6] R. Bridson, S. Marino, and R. Fedkiw, "Simulation of Clothing with Folds and Wrinkles," Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 28-36, Aug. 2003.
[7] G. Celniker and D. Gossard, "Deformable Curve and Surface Finite-Elements for Free-Form Shape Design," Proc. ACM SIGGRAPH, pp. 257-266, Aug. 1991.
[8] K.J. Choi and H.S. Ko, "Stable But Responsive Cloth," Proc. ACM SIGGRAPH, pp. 604-611, 2002.
[9] M.G. Choi, S.Y. Woo, and H. Ko, "Real-Time Simulation of Thin Shell," Computer Graphics Forum, vol. 26, no. 3, pp. 349-354, 2007.
[10] S. Cotin, C. Duriez, J. Lenoir, P. Neumann, and S. Dawson, "New Approaches to Catheter Navigation for Interventional Radiology Simulation," Proc. Int'l Conf. Medical Image Computing and Computer-Assisted Intervention (MICCAI), pp. 534-542, 2005.
[11] A. Garg, E. Grinspun, M. Wardetzky, and D. Zorin, "Cubic Shells," Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 91-98, 2007.
[12] M. Grégoire and E. Schömer, "Interactive Simulation of One-Dimensional Flexible Parts," Computer-Aided Design, vol. 39, no. 8, pp. 694-707, 2007.
[13] E. Grinspun, A.N. Hirani, M. Desbrun, and P. Schröder, "Discrete Shells," Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 62-67, 2003.
[14] X. Guo, X. Li, Y. Bao, X. Gu, and H. Qin, "Meshless Thin-Shell Simulation Based on Global Conformal Parameterization," IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 3, pp. 375-385, May 2006.
[15] M. Hauth and W. Strasser, "Corotational Simulation of Deformable Solids," Proc. Int'l Conf. in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG), pp. 137-145, 2004.
[16] P. Kaufmann, S. Martin, M. Botsch, E. Grinspun, and M. Gross, "Enrichment Textures for Detailed Cutting of Shells," Proc. ACM SIGGRAPH, 2009.
[17] M. Müller, B. Heidelberger, M. Hennix, and J. Ratcliff, "Position Based Dynamics," Proc. Workshop Virtual Reality Interactions and Physical Simulations (VRIPhys), pp. 71-80, 2006.
[18] M. Müller, J. Dorsey, L. McMillan, R. Jagnow, and B. Cutler, "Stable Real-Time Deformations," Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 49-54, Aug. 2002.
[19] O. Nocent and Y. Rémion, "Continuous Deformation Energy for Dynamic Material Splines Subject to Finite Displacements," Proc. Eurographic Workshop Computer Animation and Simulation, pp. 88-97, 2001.
[20] J.F. O'Brien, A.W. Bargteil, and J.K. Hodgins, "Graphical Modeling and Animation of Ductile Fracture," Proc. ACM SIGGRAPH, pp. 291-294, Aug. 2002.
[21] J.F. O'Brien and J.K. Hodgins, "Graphical Modeling and Animation of Brittle Fracture," Proc. ACM SIGGRAPH, pp. 287-296, Aug. 1999.
[22] D.K. Pai, "Strands: Interactive Simulation of Thin Solids Using Cosserat Models," Computer Graphics Forum, vol. 21, no. 3, pp. 347-352, 2002.
[23] X. Provot, "Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior," Proc. Graphics Interface, pp. 147-154, 1995.
[24] H. Qin and D. Terzopoulos, "D-NURBS: A Physics-Based Framework for Geometric Design," IEEE Trans. Visualization and Computer Graphics, vol. 2, no. 1, pp. 85-96, Mar. 1996.
[25] A. Selle, M. Lentine, and R. Fedkiw, "A Mass Spring Model for Hair Simulation," Proc. ACM SIGGRAPH, Aug. 2008.
[26] J. Spillmann and M. Teschner, "Cosserat Nets," to be published in IEEE Trans. Visualization and Computer Graphics, 2009.
[27] D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, "Elastically Deformable Models," Proc. ACM SIGGRAPH, pp. 205-214, 1987.
[28] 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, Nov. 1988.
[29] A. Theetten, L. Grisoni, C. Duriez, and X. Merlhiot, "Quasi-Dynamic splines," Proc. ACM Symp. Solid and Physical Modeling (SPM), 2007.
[30] B. Thomaszewski, M. Wacker, and W. Straßer, "A Consistent Bending Model for Cloth Simulation with Corotational Subdivision Finite Elements," Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, Aug. 2006.
[31] H. Wakamatsu, "Static Modeling of Linear Object Deformation Based on Differential Geometry," Int'l J. Robotics Research, vol. 23, no. 3, pp. 293-311, 2004.
[32] M. Wardetzky, M. Bergou, D. Harmon, D. Zorin, and E. Grinspun, "Discrete Quadratic Curvature Energies," Computer Aided Geometric Design, vol. 24, nos. 8/9, pp. 499-518, Nov. 2007.
[33] M. Wicke, D. Steinemann, and M. Gross, "Efficient Animation of Point-Sampled Thin Shells," Proc. Ann. Conf. European Assoc. for Computer Graphics (EUROGRAPHICS), pp. 667-676, 2005.
[34] X. Zhou, D. Sha, and K.K. Tamma, "On the New Concept and Foundations of an Arbitrary Reference Configuration (ARC) Theory and Formulation for Computational Finite Deformation Applications—Part I: Elasticity," Int'l J. for Computational Methods in Eng. Science and Mechanics, vol. 7, pp. 331-351, 2006.
[35] O.C. Zienkiewicz, The Finite Element Method, fourth ed., vols. 1/2. McGraw-Hill, 1994.
19 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool