Maxime Tournier
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We present a unification of the two main approaches to simulate deformable solids, namely elasticity and constraints. Elasticity accurately handles soft to moderately stiff objects, but becomes numerically hard as stiffness increases. Constraints efficiently handle high stiffness, but when integrated in time they can suffer from instabilities in the nullspace directions, generating spurious transverse vibrations when pulling hard on thin inextensible objects or articulated rigid bodies. We show that geometric stiffness, the tensor encoding the change of force directions (as opposed to intensities) in response to a change of positions, is the missing piece between the two approaches. This previously neglected stiffness term is easy to implement and dramatically improves the stability of inextensible objects and articulated chains, without adding artificial bending forces. This allows time step increases up to several orders of magnitude using standard linear solvers.
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- Anitescu, M., and Hart, G. D. 2004. A fixed-point iteration approach for multibody dynamics with contact and small friction. Mathematical Programming 101.Google Scholar
- Ascher, U. M., H. Chin, L. R. Petzold, and Reich, S. 1995. Stabilization of Constrained Mechanical Systems with DAEs and Invariant Manifold. Journal of Mechanics of Structures and Machines 23.Google ScholarCross Ref
- Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. In Proc. 25th annual conference on Computer graphics and interactive techniques (ACM SIGGRAPH). Google ScholarDigital Library
- Baraff, D. 1996. Linear-time Dynamics Using Lagrange Multipliers. In Proc. 23th annual conference on Computer graphics and interactive techniques (ACM SIGGRAPH). Google ScholarDigital Library
- Barzel, R., and Barr, A. H. 1988. A Modeling System Based On Dynamic Constraints. In Computer Graphics (Proc. SIGGRAPH). Google ScholarDigital Library
- Bender, J., Müller, M., Otaduy, M. A., and Teschner, M. 2013. Position-based Methods for the Simulation of Solid Objects in Computer Graphics. In Computer Graphics Forum (Eurographics State of the Art Report).Google Scholar
- Bertails, F., Audoly, B., Cani, M.-P., Querleux, B., Leroy, F., and Lévêque, J.-L. 2006. Super-helices for Predicting the Dynamics of Natural Hair. In ACM Transactions on Graphics (Proc. SIGGRAPH). Google ScholarDigital Library
- Bouaziz, S., Martin, S., Liu, T., Kavan, L., and Pauly, M. 2014. Projective Dynamics: Fusing Constraint Projections for Fast Simulation. ACM Transactions on Graphics (Proc. SIGGRAPH). Google ScholarDigital Library
- Cline, M. B., and Pai, D. K. 2003. Post-stabilization for rigid body simulation with contact and constraints. In International Conference on Robotics and Automation.Google Scholar
- Cook, R. D. 1995. Finite Element Modeling for Stress Analysis. JohnWiley & Sons, Inc. Google ScholarDigital Library
- Duriez, C., Dubois, F., Kheddar, A., and Andriot, C. 2008. Realistic Haptic Rendering of Interacting Deformable Objects in Virtual Environments. CoRR.Google Scholar
- Erleben, K. 2013. Numerical Methods for Linear Complementarity Problems in Physics-based Animation. In ACM SIGGRAPH Courses. Google ScholarDigital Library
- Faure, F., Duriez, C., Delingette, H., Allard, J., Gilles, B., Marchesseau, S., Talbot, H., Courtecuisse, H., Bousquet, G., Peterlik, I., and Cotin, S. 2012. SOFA: A Multi-Model Framework for Interactive Physical Simulation. In Soft Tissue Biomechanical Modeling for Computer Assisted Surgery. Springer. http://www.sofa-framework.org.Google Scholar
- Featherstone, R. 1987. Robot Dynamics Algorithm. Kluwer Academic Publishers, Norwell, MA, USA. Google ScholarDigital Library
- García-Fernández, I., Pla-Castells, M., and Martínez-Durá, R. J. 2008. Elevation Cable Modeling for Interactive Simulation of Cranes. In Proc. ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Google ScholarDigital Library
- Gascuel, J.-d., and Gascuel, M.-P. 1994. Displacement constraints for interactive modeling and animation of articulated structures. Visual Computer 10, 4.Google ScholarCross Ref
- Goldenthal, R., Harmon, D., Fattal, R., Bercovier, M., and Grinspun, E. 2007. Efficient Simulation of Inextensible Cloth. ACM Transactions on Graphics (Proc. SIGGRAPH). Google ScholarDigital Library
- Irving, G., Teran, J., and Fedkiw, R. 2004. Invertible finite elements for robust simulation of large deformation. In Proc. ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Google ScholarDigital Library
- Kaufman, D. M., Sueda, S., James, D. L., and Pai, D. K. 2008. Staggered Projections for Frictional Contact in Multibody Systems. ACM Transactions on Graphics (Proc. SIGGRAPH Asia). Google ScholarDigital Library
- Kaufman, D. M., Tamstorf, R., Smith, B., Aubry, J.- M., and Grinspun, E. 2014. Adaptive Nonlinearity for Collisions in Complex Rod Assemblies. ACM Transaction on Graphics (Proc. SIGGRAPH). Google ScholarDigital Library
- Lacoursière, C. 2007. Ghosts and machines: regularized variational methods for interactive simulations of multibodies with dry frictional contacts. PhD thesis, Umeå University.Google Scholar
- Macklin, M., Müller, M., Chentanez, N., and Kim, T.- Y. 2014. Unified Particle Physics for Real-Time Applications. ACM Transactions on Graphics (Proc. SIGGRAPH). Google ScholarDigital Library
- Mirtich, B. 1996. Impulse-based Dynamic Simulation of Rigid Body Systems. PhD thesis, University of California. Google ScholarDigital Library
- Müller, M., Heidelberger, B., Hennix, M., and Ratcliff, J. 2006. Position Based Dynamics. Proc. VRIPhys.Google Scholar
- Narain, R., Samii, A., and O'Brien, J. F. 2012. Adaptive Anisotropic Remeshing for Cloth Simulation. ACM Transactions on Graphics (Proc. SIGGRAPH Asia). Google ScholarDigital Library
- Nealen, A., Müller, M., Keiser, R., Boxerman, E., and Carlson, M. 2006. Physically Based Deformable Models in Computer Graphics. Computer Graphics Forum (Eurographics State of the Art Report).Google Scholar
- Nocedal, J., and Wright, S. J. 2006. Numerical Optimization (2nd ed.). Springer-Verlag.Google Scholar
- Otaduy, M. A., Tamstorf, R., Steinemann, D., and Gross, M. 2009. Implicit Contact Handling for Deformable Objects. Computer Graphics Forum (Proc. of Eurographics).Google Scholar
- Papadopoulo, T., and Lourakis, M. I. A. 2000. Estimating the jacobian of the singular value decomposition: Theory and applications. In Proc. European Conference on Computer Vision. Google ScholarDigital Library
- Provot, X. 1995. Deformation constraints in a mass-spring model to describe rigid cloth behavior. In Proc. Graphics Interface.Google Scholar
- Servin, M., and Lacoursière, C. 2008. Rigid Body Cable for Virtual Environments. IEEE Transactions on Visualization and Computer Graphics 14. Google ScholarDigital Library
- Servin, M., Lacoursière, C., and Melin, N. 2006. Interactive simulation of elastic deformable materials. In Proc. SIGRAD.Google Scholar
- Servin, M., Lacoursière, C., Nordfelth, F., and Bodin, K. 2011. Hybrid, Multiresolution Wires with Massless Frictional Contacts. IEEE Trans. on Visualization and Computer Graphics 17. Google ScholarDigital Library
- Sifakis, E., Shinar, T., Irving, G., and Fedkiw, R. 2007. Hybrid Simulation of Deformable Solids. In Proc. ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Google ScholarDigital Library
- Sueda, S., Jones, G. L., Levin, D. I. W., and Pai, D. K. 2011. Large-scale Dynamic Simulation of Highly Constrained Strands. In ACM Transactions on Graphics (Proc. SIGGRAPH). Google ScholarDigital Library
- Teran, J., Sifakis, E., Irving, G., and Fedkiw, R. 2005. Robust quasistatic finite elements and flesh simulation. In Proc. ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Google ScholarDigital Library
- Thomaszewski, B., Pabst, S., and Strasser, W. 2009. Continuum-based Strain Limiting. Computer Graphics Forum (Proc. Eurographics).Google Scholar
- Tomcin, R., Sibbing, D., and Kobbelt, L. 2014. Efficient enforcement of hard articulation constraints in the presence of closed loops and contacts. Computer Graphics Forum (Proc. Eurographics). Google ScholarDigital Library
- Wang, H., O'brien, J. F., and Ramamoorthi, R. 2010. Multi-Resolution Isotropic Strain Limiting. ACM Transactions on Graphics (Proc. SIGGRAPH Asia). Google ScholarDigital Library
- Weinstein, R., Teran, J., and Fedkiw, R. 2006. Dynamic simulation of articulated rigid bodies with contact and collision. IEEE Transactions on Visualization and Computer Graphics. Google ScholarDigital Library
- Witkin, A. 1997. Physically Based Modeling: Principles and Practice -- Constrained Dynamics. Computer Graphics.Google Scholar
- Zheng, C., and James, D. L. 2011. Toward High-Quality Modal Contact Sound. ACM Transactions on Graphics (Proc. SIGGRAPH). Google ScholarDigital Library
- Zienkiewicz, O. C., and Taylor, R. L. 2000. The Finite Element Method: Solid Mechanics, 5 ed., vol. 2. Butterworth-Heinemann.Google Scholar
Index Terms
- Stable constrained dynamics
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