research-article

Stable constrained dynamics

Authors:

Maxime Tournier,

Matthieu Nesme,

Benjamin Gilles,

François FaureAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 34, Issue 4

Article No.: 132, Pages 1 - 10

https://doi.org/10.1145/2766969

Published: 27 July 2015 Publication History

Abstract

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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References

[1]

Anitescu, M., and Hart, G. D. 2004. A fixed-point iteration approach for multibody dynamics with contact and small friction. Mathematical Programming 101.

[2]

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.

[3]

Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. In Proc. 25th annual conference on Computer graphics and interactive techniques (ACM SIGGRAPH).

Digital Library

[4]

Baraff, D. 1996. Linear-time Dynamics Using Lagrange Multipliers. In Proc. 23th annual conference on Computer graphics and interactive techniques (ACM SIGGRAPH).

Digital Library

[5]

Barzel, R., and Barr, A. H. 1988. A Modeling System Based On Dynamic Constraints. In Computer Graphics (Proc. SIGGRAPH).

Digital Library

[6]

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).

[7]

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).

Digital Library

[8]

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).

Digital Library

[9]

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.

[10]

Cook, R. D. 1995. Finite Element Modeling for Stress Analysis. JohnWiley & Sons, Inc.

Digital Library

[11]

Duriez, C., Dubois, F., Kheddar, A., and Andriot, C. 2008. Realistic Haptic Rendering of Interacting Deformable Objects in Virtual Environments. CoRR.

[12]

Erleben, K. 2013. Numerical Methods for Linear Complementarity Problems in Physics-based Animation. In ACM SIGGRAPH Courses.

Digital Library

[13]

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.

[14]

Featherstone, R. 1987. Robot Dynamics Algorithm. Kluwer Academic Publishers, Norwell, MA, USA.

Digital Library

[15]

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.

Digital Library

[16]

Gascuel, J.-d., and Gascuel, M.-P. 1994. Displacement constraints for interactive modeling and animation of articulated structures. Visual Computer 10, 4.

[17]

Goldenthal, R., Harmon, D., Fattal, R., Bercovier, M., and Grinspun, E. 2007. Efficient Simulation of Inextensible Cloth. ACM Transactions on Graphics (Proc. SIGGRAPH).

Digital Library

[18]

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.

Digital Library

[19]

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).

Digital Library

[20]

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).

Digital Library

[21]

Lacoursière, C. 2007. Ghosts and machines: regularized variational methods for interactive simulations of multibodies with dry frictional contacts. PhD thesis, Umeå University.

[22]

Macklin, M., Müller, M., Chentanez, N., and Kim, T.- Y. 2014. Unified Particle Physics for Real-Time Applications. ACM Transactions on Graphics (Proc. SIGGRAPH).

Digital Library

[23]

Mirtich, B. 1996. Impulse-based Dynamic Simulation of Rigid Body Systems. PhD thesis, University of California.

Digital Library

[24]

Müller, M., Heidelberger, B., Hennix, M., and Ratcliff, J. 2006. Position Based Dynamics. Proc. VRIPhys.

[25]

Narain, R., Samii, A., and O'Brien, J. F. 2012. Adaptive Anisotropic Remeshing for Cloth Simulation. ACM Transactions on Graphics (Proc. SIGGRAPH Asia).

Digital Library

[26]

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).

[27]

Nocedal, J., and Wright, S. J. 2006. Numerical Optimization (2nd ed.). Springer-Verlag.

[28]

Otaduy, M. A., Tamstorf, R., Steinemann, D., and Gross, M. 2009. Implicit Contact Handling for Deformable Objects. Computer Graphics Forum (Proc. of Eurographics).

[29]

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.

Digital Library

[30]

Provot, X. 1995. Deformation constraints in a mass-spring model to describe rigid cloth behavior. In Proc. Graphics Interface.

[31]

Servin, M., and Lacoursière, C. 2008. Rigid Body Cable for Virtual Environments. IEEE Transactions on Visualization and Computer Graphics 14.

Digital Library

[32]

Servin, M., Lacoursière, C., and Melin, N. 2006. Interactive simulation of elastic deformable materials. In Proc. SIGRAD.

[33]

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.

Digital Library

[34]

Sifakis, E., Shinar, T., Irving, G., and Fedkiw, R. 2007. Hybrid Simulation of Deformable Solids. In Proc. ACM SIGGRAPH/Eurographics Symposium on Computer Animation.

Digital Library

[35]

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).

Digital Library

[36]

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.

Digital Library

[37]

Thomaszewski, B., Pabst, S., and Strasser, W. 2009. Continuum-based Strain Limiting. Computer Graphics Forum (Proc. Eurographics).

[38]

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).

Digital Library

[39]

Wang, H., O'brien, J. F., and Ramamoorthi, R. 2010. Multi-Resolution Isotropic Strain Limiting. ACM Transactions on Graphics (Proc. SIGGRAPH Asia).

Digital Library

[40]

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.

Digital Library

[41]

Witkin, A. 1997. Physically Based Modeling: Principles and Practice -- Constrained Dynamics. Computer Graphics.

[42]

Zheng, C., and James, D. L. 2011. Toward High-Quality Modal Contact Sound. ACM Transactions on Graphics (Proc. SIGGRAPH).

Digital Library

[43]

Zienkiewicz, O. C., and Taylor, R. L. 2000. The Finite Element Method: Solid Mechanics, 5 ed., vol. 2. Butterworth-Heinemann.

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Chen YHan YChen JZhang ZMcadams ATeran J(2024)Position-Based Nonlinear Gauss-Seidel for Quasistatic HyperelasticityACM Transactions on Graphics10.1145/365815443:4(1-15)Online publication date: 19-Jul-2024
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Index Terms

Stable constrained dynamics
1. Computing methodologies
  1. Computer graphics
    1. Animation
      1. Physical simulation
    2. Shape modeling
2. Mathematics of computing
  1. Continuous mathematics
    1. Topology
      1. Geometric topology

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 34, Issue 4

August 2015

1307 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2809654

Issue’s Table of Contents

Copyright © 2015 ACM.

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Publication History

Published: 27 July 2015

Published in TOG Volume 34, Issue 4

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Ruan LWang BLiu TChen B(2024)MiNNIE: a Mixed Multigrid Method for Real-time Simulation of Nonlinear Near-Incompressible ElasticsACM Transactions on Graphics10.1145/368775843:6(1-15)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687758
Giles CAndrews S(2024)Adaptive Sub-stepping for Constrained Rigid Body SimulationsProceedings of the 17th ACM SIGGRAPH Conference on Motion, Interaction, and Games10.1145/3677388.3696331(1-6)Online publication date: 21-Nov-2024
https://dl.acm.org/doi/10.1145/3677388.3696331
Chen YHan YChen JZhang ZMcadams ATeran J(2024)Position-Based Nonlinear Gauss-Seidel for Quasistatic HyperelasticityACM Transactions on Graphics10.1145/365815443:4(1-15)Online publication date: 19-Jul-2024
https://doi.org/10.1145/3658154
Zhao Z(2024)A Physics-Embedded Deep Learning Framework for Cloth Simulation2024 Asian Conference on Communication and Networks (ASIANComNet)10.1109/ASIANComNet63184.2024.10811024(1-7)Online publication date: 24-Oct-2024
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