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Issue No.02 - March/April (2009 vol.15)
pp: 325-338
Jonas Spillmann , Albert-Ludwigs-University of Freiburg, Freiburg im Breisgau
Cosserat nets are networks of elastic rods that are linked by elastic joints. They allow to represent a large variety of objects such as elastic rings, coarse nets, or truss structures. In this paper, we propose a novel approach to model and dynamically simulate such Cosserat nets. We first derive the static equilibrium of the elastic rod model that supports both bending and twisting deformation modes. We further propose a dynamic model that allows for the efficient simulation of elastic rods. We then focus on the simulation of the Cosserat nets by extending the elastic rod deformation model to branched and looped topologies. To round out the discussion, we evaluate our deformation model. By comparing our deformation model to a reference model, we illustrate both the physical plausibility and the conceptual advantages of the proposed approach.
Jonas Spillmann, "Cosserat Nets", IEEE Transactions on Visualization & Computer Graphics, vol.15, no. 2, pp. 325-338, March/April 2009, doi:10.1109/TVCG.2008.102
[1] J. Brown, J.-C. Latombe, and K. Montgomery, “Real-Time Knot Tying Simulation,” The Visual Computer, vol. 20, nos. 2/3, pp.165-179, 2004.
[2] D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically Deformable Models,” ACM Trans. Graphics (Proc. ACM SIGGRAPH '87), vol. 21, no. 4, pp. 205-214, 1987.
[3] J. Lenoir, P. Meseure, L. Grisoni, and C. Chaillou, “Surgical Thread Simulation,” Modelling and Simulation for Computer-Aided Medicine and Surgery, pp. 102-107, 2002.
[4] R.S. Manning and J.H. Maddocks, “A Continuum Rod Model of Sequence-Dependent DNA Structure,” J. Chemical Physics, vol. 105, pp. 5626-5646, 1996.
[5] D.Q. Cao, D. Liu, and C.H.-T. Wang, “Three Dimensional Nonlinear Dynamics of Slender Structures: Cosserat Rod ElementApproach,” Int'l J. Solids and Structures, vol. 43, nos. 3/4, pp. 760-783, 2006.
[6] D. Pai, “Strands: Interactive Simulation of Thin Solids Using Cosserat Models,” Computer Graphics Forum (Eurographics '02), vol. 21, no. 3, pp. 347-352, 2002.
[7] J. Spillmann and M. Teschner, “CORDE: Cosserat Rod Elements for the Dynamic Simulation of One-Dimensional Elastic Objects,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation (SCA '07), pp. 63-72, 2007.
[8] A. Theetten, L. Grisoni, C. Andriot, and B. Barsky, “Geometrically Exact Dynamic Splines,” technical report, INRIA, 2007.
[9] S. Kehrbaum, “Hamiltonian Formulations of the Equilibrium Conditions Governing Elastic Rods: Qualitative Analysis and Effective Properties,” PhD dissertation, Univ. of Maryland, 1997.
[10] D.J. Dichmann, “Hamiltonian Dynamics of a Spatial Elastica and the Stability of Solitary Waves,” PhD dissertation, Univ. of Maryland, 1994.
[11] S.S. Antman, Nonlinear Problems of Elasticity. Springer Verlag, 1995.
[12] J.T. Chang, J. Jin, and Y. Yu, “A Practical Model for Hair Mutual Interactions,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation (SCA '02), pp. 73-80, 2002.
[13] F. Wang, E. Burdet, A. Dhanik, T. Poston, and C. Teo, “Dynamic Thread for Real-Time Knot-Tying,” Proc. First Joint Eurohaptics Conf. and Symp. Haptic Interfaces for Virtual Environment and Teleoperator Systems (World Haptics '05), pp. 507-508, 2005.
[14] B. Choe, M.G. Choi, and H.-S. Ko, “Simulating Complex Hair with Robust Collision Handling,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation (SCA '05), pp. 153-160, 2005.
[15] M. Servin and C. Lacoursière, “Rigid Body Cable for Virtual Environments,” IEEE Trans. Visualization and Computer Graphics, vol. 14, no. 4, pp. 783-796, July/Aug. 2008.
[16] S. Hadap, “Oriented Strands: Dynamics of Stiff Multi-Body System,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation (SCA '06), pp. 91-100, 2006.
[17] B. Kubiak, N. Pietroni, F. Ganovelli, and M. Fratarcangeli, “A Robust Method for Real-Time Thread Simulation,” Proc. ACM Symp. Virtual Reality Software and Technology (VRST '07), pp. 85-88, 2007.
[18] M. Müller, B. Heidelberger, M. Hennix, and J. Ratcliff, “Position Based Dynamics,” J. Visual Comm. and Image Representation, vol. 18, no. 2, pp. 109-118, 2007.
[19] A. Selle, M.G. Lentine, and R. Fedkiw, “A Mass Spring Model for Hair Simulation,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), 2008.
[20] 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.
[21] Y. Remion, J.-M. Nourrit, and D. Gillard, “A Dynamic Animation Engine for Generic Spline Objects,” J. Visualization and Computer Animation, vol. 11, no. 1, pp. 17-26, 2000.
[22] J. Phillips, A. Ladd, and L.E. Kavraki, “Simulated Knot Tying,” Proc. IEEE Int'l Conf. Robotics and Automation (ICRA '02), pp.841-846, 2002.
[23] J. Kaldor, D.L. James, and S. Marschner, “Simulating Knitted Cloth at the Yarn Level,” Proc. ACM SIGGRAPH, 2008.
[24] F. Bertails, B. Audoly, M.-P. Cani, B. Querleux, F. Leroy, and J.-L. Lévêque, “Super-Helices for Predicting the Dynamics of NaturalHair,” ACM Trans. Graphics, Proc. ACM SIGGRAPH '06, pp. 1180-1187, 2006.
[25] H. Wakamatsu and S. Hirai, “Static Modeling of Linear Object Deformation Based on Differential Geometry,” Int'l J. Robotic Research, vol. 23, no. 3, pp. 293-311, 2004.
[26] A. Theetten, L. Grisoni, C. Duriez, and X. Merlhiot, “Quasi-Dynamic Splines,” Proc. ACM Symp. Solid and Physical Modeling (SPM '07), pp. 409-414, 2007.
[27] M. Bergou, M. Wardetzky, S. Robinson, B. Audoly, and E. Grinspun, “Discrete Elastic Rods,” ACM Trans. Graphics, Proc. ACM SIGGRAPH, 2008,
[28] M. Grégoire and E. Schömer, “Interactive Simulation of One-Dimensional Flexible Parts,” Proc. ACM Symp. Solid and Physical Modeling (SPM '06), pp. 95-103, 2006.
[29] A. Loock and E. Schömer, “A Virtual Environment for Interactive Assembly Simulation: From Rigid Bodies to Deformable Cables,” Proc. Fifth World Multiconference on Systemics, Cybernetics and Informatics (SCI '01), vol. 3, pp. 325-332, 2001.
[30] F. Boyer and D. Primault, “Finite Element of Slender Beams in Finite Transformations: A Geometrically Exact Approach,” Int'l J.Numerical Methods in Eng., vol 59, no. 5, pp. 669-702, 2004.
[31] J. Spillmann and M. Teschner, “An Adaptive Contact Model for the Robust Simulation of Knots,” Computer Graphics Forum, vol. 27, no. 2, pp. 497-506, 2008.
[32] A.L. Schwab and J.P. Meijaard, “How to Draw Euler Angles and Utilize Euler Parameters,” Proc. ASME Int'l Design Eng. Technical Conf. and Computers and Information in Eng. Conf. (IDETC/CIE), 2006.
[33] D. Baraff and A. Witkin, “Large Steps in Cloth Simulation,” Proc. ACM SIGGRAPH '98, pp. 43-54, 1998.
[34] B. Nadler and M.B. Rubin, “Post-Buckling Behavior of Nonlinear Elastic Beams and Three-Dimensional Frames Using the Theory of a Cosserat Point,” Math. and Mechanics of Solids, vol. 9, no. 4, pp. 369-398, 2004.
[35] M. Rubin, Cosserat Theories: Shells, Rods and Points. Kluwer Academic, 2000.
[36] R. Weinstein, J. Teran, and R. Fedkiw, “Dynamic Simulation of Articulated Rigid Bodies with Contact and Collision,” IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 3, pp. 365-374, May/June 2006.
[37] J. Stam, “Stochastic Dynamics: Simulating the Effects of Turbulence on Flexible Structures,” Computer Graphics Forum, vol. 16, no. 4, pp. 159-164, 1997.
[38] J. Stuelpnagel, “On the Parameterization of the Three-Dimensional Rotation Group,” SIAM, vol 6, no. 4, pp. 422-430, 1964.
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