Article

Real-Time subspace integration for St. Venant-Kirchhoff deformable models

Authors:

Jernej Barbič,

Doug L. JamesAuthors Info & Claims

SIGGRAPH '05: ACM SIGGRAPH 2005 Papers

Pages 982 - 990

https://doi.org/10.1145/1186822.1073300

Published: 01 July 2005 Publication History

Abstract

In this paper, we present an approach for fast subspace integration of reduced-coordinate nonlinear deformable models that is suitable for interactive applications in computer graphics and haptics. Our approach exploits dimensional model reduction to build reduced-coordinate deformable models for objects with complex geometry. We exploit the fact that model reduction on large deformation models with linear materials (as commonly used in graphics) result in internal force models that are simply cubic polynomials in reduced coordinates. Coefficients of these polynomials can be precomputed, for efficient runtime evaluation. This allows simulation of nonlinear dynamics using fast implicit Newmark subspace integrators, with subspace integration costs independent of geometric complexity. We present two useful approaches for generating low-dimensional subspace bases: modal derivatives and an interactive sketching technique. Mass-scaled principal component analysis (mass-PCA) is suggested for dimensionality reduction. Finally, several examples are given from computer animation to illustrate high performance, including force-feedback haptic rendering of a complicated object undergoing large deformations.

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References

[1]

Almroth. B. O., Stern, P., and Brogan. F. A. 1978. Automatic Choice of Global Shape Functions in Structural Analysis. AIAA Journal 16, 5, 525--528.

[2]

Baraff, D., and Witkin, A. 1992. Dynamic Simulation of Non-penetrating Flexible Bodies. Computer Graphics (Proc. of ACM SIGGRAPH 92) 26(2), 303--308.

Digital Library

[3]

Baraff, D., and Witkin, A. 1998. Large Steps in Cloth Simulation. In Proc. of ACM SIGGRAPH 98, 43--54.

Digital Library

[4]

Basdogan, C. 2001. Real-time Simulation of Dynamically Deformable Finite Element Models Using Modal Analysis and Spectral Lanczos Decomposition Methods. In Medicine Meets Virtual Reality (MMVR'2001), 46--52.

[5]

Belytschko, T. 2001. Nonlinear Finite Elements for Continua and Structures. Wiley.

[6]

Bonet, J., and Wood. R. D. 1997. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press.

[7]

Bridson. R., Fedkiw, R. P. and Anderson, J. 2002. Robust Treatment of Collisions. Contact, and Friction for Cloth Animation. ACM Trans. on Graphics 21, 3, 594--603.

Digital Library

[8]

Bro-Nielsen, M., and Cotin, S. 1996. Real-time Volumetric Deformable Models for Surgery Simulation using Finite Elements and Condensation. Comp. Graphics Forum 15, 3, 57--66.

[9]

Capell, S., Green. S., Curless. B., Duchamp, T., and Popović, Z. 2002. A Multiresolution Framework for Dynamic Deformations. In Proc. of the Symp. on Comp. Animation 2002, 41--48.

Digital Library

[10]

Capell, S., Green, S., Curless, B., Duchamp, T., and Popović, Z. 2002. Interactive Skeleton-Driven Dynamic Deformations. ACM Trans. on Graphics 21, 3 (July), 586--593.

Digital Library

[11]

Choi, M. G., and Ko. H.-S. 2005. Modal Warping: Real-Time Simulation of Large Rotational Deformation and Manipulation. In IEEE Trans. on Vis. and Comp. Graphics, vol. 11, 91--101.

Digital Library

[12]

Cotin, S., Delingette, H., and Ayache, N. 1999. Realtime Elastic Deformations of Soft Tissues for Surgery Simulation. IEEE Trans. on Vis. and Comp. Graphics 5, 1, 62--73.

Digital Library

[13]

Debunne, G., Desbrun, M., Cani, M.-P., and Barr, A. H. 2001. Dynamic Real-Time Deformations Using Space & Time Adaptive Sampling. In Proc. of ACM SIGGRAPH 2001, 31--36.

Digital Library

[14]

Faloutsos, P., Van De Panne, M., and Terzopoulos, D. 1997. Dynamic Free-Form Deformations for Animation Synthesis. IEEE Trans. on Vis. and Comp. Graphics 3, 3, 201--214.

Digital Library

[15]

Fung, Y. 1977. A First Course in Continuum Mechanics. Prentice-Hall, Englewood Cliffs, NJ.

[16]

Grinspun, E., Krysl, P., and Schröder, P. 2002. CHARMS: A Simple Frame-work for Adaptive Simulation. ACM Trans. on Graphics 21, 3 (July), 281--290.

Digital Library

[17]

Hauser, K. K., Shen, C., and O'Brien, J. F. 2003. Interactive Deformation Using Modal Analysis with Constraints. In Proc. of Graphics Interface.

[18]

Holzapfel, G. A. 2000. Nonlinear Solid Mechanics. Wiley.

[19]

Idelsohn, S. R., and Cardona. A. 1985. A Load-dependent Basis for Reduced Nonlinear Structural Dynamics. Computers and Structures 20, 1--3, 203--210.

[20]

Idelsohn, S. R., and Cardona, A. 1985. A Reduction Method for Nonlinear Structural Dynamic Analysis. Computer Methods in Applied Mechanics and Engineering 49, 253--279.

[21]

Irving, G., Teran, J., and Fedkiw, R. 2004. Invertible Finite Elements for Robust Simulation of Large Deformation. In Proc. of the Symp. on Comp. Animation 2004, 131--140.

Digital Library

[22]

James, D., and Fatahalian. K. 2003. Precomputing Interactive Dynamic Deformable Scenes. In Proc. of ACM SIGGRAPH 2003, ACM, 879--887.

Digital Library

[23]

James, D. L., and Pai, D. K. 1999. Artdefo: Accurate Real Time Deformable Objects. In Proc. of ACM SIGGRAPH 99, vol. 33, 65--72.

Digital Library

[24]

James, D. L., and Pai. D. K. 2002. DyRT: Dynamic Response Textures for Real Time Deformation Simulation with Graphics Hardware. In Proc. of ACM SIGGRAPH 2002.

Digital Library

[25]

James, D. L., and Pai. D. K. 2004. BD-Tree: Output-Sensitive Collision Detection for Reduced Deformable Models. ACM Trans. on Graphics 23, 3 (Aug.), 393--398.

Digital Library

[26]

James, D. L., Barbič, J., and Twigg, C. D. 2004. Squashing Cubes: Automating Deformable Model Construction for Graphics. In Proc. of ACM SIGGRAPH Sketches and Applications.

Digital Library

[27]

Krysl, P., Lall, S., and Marsden, J. E. 2001. Dimensional model reduction in non-linear finite element dynamics of solids and structures. Int. J. for Numerical Methods in Engineering 51, 479--504.

[28]

Lumley, J. L. 1967. The structure of inhomogeneous turbulence. In Atmospheric turbulence and wave propagation, 166--178.

[29]

Metaxas, D., and Terzopoulos, D. 1992. Dynamic Deformation of Solid Primitives with Constraints. Computer Graphics (Proc. of ACM SIGGRAPH 92) 26(2), 309--312.

Digital Library

[30]

Müller, M., and Gross. M. 2004. Interactive Virtual Materials. In Proc. of Graphics Interface 2004, 239--246.

Digital Library

[31]

Müller, M., Dorsey. J., McMillian, L., Jagnow, R., and Cutler, B. 2002. Stable Real-Time Deformations. In Proc. of the Symp. on Comp. Animation 2002, 49--54.

Digital Library

[32]

Müller, M., Teschner, M., and Gross, M. 2004. Physically-Based Simulation of Objects Represented by Surface Meshes. In Proc. of Comp. Graphics Int. (CGI), 26--33.

Digital Library

[33]

Nickell, R. E. 1976. Nonlinear Dynamics by Mode Superposition. Computer Methods in Applied Mechanics and Engineering 7, 107--129.

[34]

O'BRIEN, J., AND HODGINS. J. 1999. Graphical Modeling and Animation of Brittle Fracture. In Proc. of ACM SIGGRAPH 99, 111--120.

Digital Library

[35]

Pai, D. 2002. Strands: Interactive simulation of thin solids using Cosserat models. Computer Graphics Forum 21, 3, 347--352.

[36]

Pentland, A., and Williams, J. July 1989. Good vibrations: Modal dynamics for graphics and animation. Computer Graphics (Proc. of ACM SIGGRAPH 89) 23, 3, 215--222.

Digital Library

[37]

Picinbono, G., Delingette, H., and Ayache, N. 2001. Non-linear and anisotropic elastic soft tissue models for medical simulation. In IEEE Int. Conf. on Robotics and Automation 2001.

[38]

Shabana, A. A. 1990. Theory of Vibration, Volume II: Discrete and Continuous Systems. Springer--Verlag, New York, NY.

[39]

Shinya, M., and Fournier, A. 1992. Stochastic motion - Motion under the influence of wind. Comp. Graphics Forum, 119--128.

[40]

Stam, J. 1997. Stochastic Dynamics: Simulating the Effects of Turbulence on Flexible Structures. Comp. Graphics Forum 16(3).

[41]

Terzopoulos, D., and Witkin, A. 1988. Physically Based Models with Rigid and Deformable Components. IEEE Comp. Graphics & Applications 8, 6, 41--51.

Digital Library

[42]

Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically Deformable Models. Computer Graphics (Proc. of ACM SIGGRAPH 87) 21(4), 205--214.

Digital Library

[43]

Wriggers, P. 2002. Computational Contact Mechanics. John Wiley & Sons, Ltd.

[44]

Zhuang, Y., and Canny, J. 2000. Haptic Interaction with Global Deformations. In Proc. of the IEEE Int. Conf. on Robotics and Automation.

Cited By

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https://dl.acm.org/doi/10.1145/3490168
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Index Terms

Real-Time subspace integration for St. Venant-Kirchhoff deformable models
1. Computing methodologies
  1. Computer graphics
    1. Animation
      1. Physical simulation
    2. Shape modeling
  2. Modeling and simulation
    1. Simulation types and techniques
      1. Simulation by animation
2. Mathematics of computing
  1. Continuous mathematics
    1. Topology
      1. Geometric topology

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cover image ACM Conferences

SIGGRAPH '05: ACM SIGGRAPH 2005 Papers

July 2005

826 pages

ISBN:9781450378253

DOI:10.1145/1186822

Editor:
Markus Gross
Eidgenössische Technische Hochschule Zürich

Copyright © 2005 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 July 2005

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SIGGRAPH '05 Paper Acceptance Rate 98 of 461 submissions, 21%;

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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Cited By

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https://doi.org/10.3934/jcd.2021021
Du TWu KMa PWah SSpielberg ARus DMatusik W(2021)DiffPD: Differentiable Projective DynamicsACM Transactions on Graphics10.1145/349016841:2(1-21)Online publication date: 29-Nov-2021
https://dl.acm.org/doi/10.1145/3490168
Cui QLanglois TSen PKim T(2021)Spiral-spectral fluid simulationACM Transactions on Graphics10.1145/3478513.348053640:6(1-16)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480536
Wang BMatcuk GBarbič J(2021)Modeling of Personalized Anatomy Using Plastic StrainsACM Transactions on Graphics10.1145/344370340:2(1-21)Online publication date: 21-Jun-2021
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Zhao JZhu FXu LTang YLi S(2021)A homogenization method for nonlinear inhomogeneous elastic materialsVirtual Reality & Intelligent Hardware10.1016/j.vrih.2021.01.0023:2(156-170)Online publication date: Apr-2021
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Angles BRebain DMacklin MWyvill BBarthe LLewis JVon Der Pahlen JIzadi SValentin JBouaziz STagliasacchi A(2019)VIPERProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/33402602:2(1-26)Online publication date: 26-Jul-2019
https://dl.acm.org/doi/10.1145/3340260
Holden DDuong BDatta SNowrouzezahrai DLee SSchroeder CBatty CHuang J(2019)Subspace neural physicsProceedings of the 18th annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation10.1145/3309486.3340245(1-12)Online publication date: 26-Jul-2019
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Pan ZManocha D(2018)Active Animations of Reduced Deformable Models with Environment InteractionsACM Transactions on Graphics10.1145/319756537:3(1-17)Online publication date: 7-Aug-2018
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Luo RXu WWang HZhou KYang Y(2018)Physics-Based Quadratic Deformation Using Elastic WeightingIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2017.278333524:12(3188-3199)Online publication date: 1-Dec-2018
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Chien SHu CHuang CTsai YLin W(2018)Deformation simulation based on model reduction with rigidity-guided samplingThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-018-1533-734:6-8(937-947)Online publication date: 1-Jun-2018
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