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Cited by 1,110Computer Graphics and Visualization Techniques3D Shape Modeling and AnalysisAdvanced Numerical Analysis Techniques

The DOI matches its Crossref record.

Elastically deformable models

Open access
Terzopoulos, Demetri, Platt, John, Barr, Alan, Fleischer, Kurt·1987·ACM SIGGRAPH Computer Graphics
DOI 10.1145/37402.37427
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Abstract

The theory of elasticity describes deformable materials such as rubber, cloth, paper, and flexible metals. We employ elasticity theory to construct differential equations that model the behavior of non-rigid curves, surfaces, and solids as a function of time. Elastically deformable models are active: they respond in a natural way to applied forces, constraints, ambient media, and impenetrable obstacles. The models are fundamentally dynamic and realistic animation is created by numerically solving their underlying differential equations. Thus, the description of shape and the description of motion are unified.

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Crossref · 10.1145/37402.37427

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  • Video is the projection of physical processes evolving in time, not merely a sequence of correlated frames.

    “However, video is not merely a sequence of correlated frames; it is the projection of physical processes evolving in time.”

    From PhyStruct-Video: Structured Physics State Spaces for Physically Consistent Video Generation (2025) · cites this paper as [24]

    Section 1.1 contrasts physically based models with prescribed motion, and Section 2 says such models can help reconstruct non-rigid objects from images. The paper does not make the broader claim that video is a projection of physical processes rather than merely correlated frames. Page numbers are unavailable in our copy. (LLM, conf=0.78)

    Experimental — accuracy not yet measured

  • Liquids obey incompressibility and momentum conservation, rigid bodies preserve distances and undergo collisions, and deformable objects follow elastic energy principles.

    “Liquids obey incompressibility and momentum conservation [21,22], rigid bodies preserve distances and undergo collisions [37,21], and deformable objects follow elastic energy principles [24].”

    From PhyStruct-Video: Structured Physics State Spaces for Physically Consistent Video Generation (2025) · cites this paper as [24]

  • PhyStruct-Video's modeling focuses on incompressible fluids, rigid bodies, and simple elastic materials; more complex regimes such as fully turbulent flows, granular materials, plasticity, or electromagnetism are not explicitly handled.

    “Our modeling focuses on incompressible fluids, rigid bodies, and simple elastic materials [21,22,36,24,37].More complex regimes-e.g., fully turbulent flows, granular materials, plasticity, or electromagnetism-are not explicitly handled.”

    From PhyStruct-Video: Structured Physics State Spaces for Physically Consistent Video Generation (2025) · cites this paper as [24]

  • Generated sequences from existing methods often exhibit artifacts such as volume-changing incompressible fluids, interpenetrating rigid bodies, and non-monotonic mechanical energy in closed systems.

    “As a result, generated sequences often exhibit artifacts such as volume-changing “incompressible” fluids, interpenetrating rigid bodies, and non-monotonic mechanical energy in closed systems [21,22,23,24].”

    From PhyStruct-Video: Structured Physics State Spaces for Physically Consistent Video Generation (2025) · cites this paper as [24]

    Section 1.1 says traditional kinematic models do not interact with other objects or forces, and Section 5 describes collision forces used to prevent penetration by elastic models. Neither passage reports that generated sequences often exhibit the claimed artifacts. Searches for volume-changing incompressible fluids, interpenetrating rigid bodies, and non-monotonic mechanical energy in closed systems found no passage addressing those claims. (LLM, conf=0.72)

    Experimental — accuracy not yet measured

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Citations

Cites

No references could be resolved yet.

Research works printed but not linked: 26

  1. Armstrong , W.W. , and Green , M ., " The dynamics of articulated rigid bodies for purposes of animation," Proc . Graphics Interface '85 , Montreal, Canada , 1985 , 407 - 415 . Armstrong, W.W., and Green, M., "The dynamics of articulated rigid bodies for purposes of animation," Proc. Graphics Interface '85, Montreal, Canada, 1985, 407-415.
  2. 10.1145/800031.808573 · DOI
  3. Courant , R. , and Hilbert , D. , Methods of Mathematical Physics , Vol. I , Interscienee , London , 1953 . Courant, R., and Hilbert, D., Methods of Mathematical Physics, Vol. I, Interscienee, London, 1953.
  4. Dahlquist , G. , and Bjorek , A. , Numerical Methods , Prentice-HM1 , Englewood Cliffs , N J , 1974 . Dahlquist, G., and Bjorek, A., Numerical Methods, Prentice-HM1, Englewood Cliffs, N J, 1974.
  5. 10.1007/978-1-4612-6333-3 · DOI
  6. do Carmo , M.P. , Differential Geometry of Curves and Surfaces , Prentice-Hall , Englewood Cliffs , N J, 1974 . do Carmo, M.P., Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, N J, 1974.
  7. Faux , ,I.D., and Pratt~ M.J. , Computational Geometry for Design and Manufacture , Halstead Press , Horwood, NY , 1981 . Faux, ,I.D., and Pratt~ M.J., Computational Geometry for Design and Manufacture, Halstead Press, Horwood, NY, 1981.
  8. 10.1145/15886.15894 · DOI
  9. Fung , Y.C. , Foundations of Solid Mechanics , Prentice- Hall, Englewood Cliffs , N J , 1965 . Fung, Y.C., Foundations of Solid Mechanics, Prentice- Hall, Englewood Cliffs, N J, 1965.
  10. Gelfand~ I.M. ~ and Fomin , S.V. , Calculus of Variations , Prentice-Hall , Englewood Cliffs , N J, 1963 . Gelfand~ I.M.~ and Fomin, S.V., Calculus of Variations, Prentice-Hall, Englewood Cliffs, N J, 1963.
  11. Goldsteln~ H. ClassicalMechanics Addison-Wesley Reading MA 1950. Goldsteln~ H. ClassicalMechanics Addison-Wesley Reading MA 1950.
  12. 10.1145/15886.15901 · DOI
  13. 10.1145/15886.15902 · DOI
  14. 10.1145/800031.808594 · DOI
  15. Landau , L.D. , and Lifshitz , E.M. , Theory of Elasticity , Pergamon Press , London, UK , 1959 . Landau, L.D., and Lifshitz, E.M., Theory of Elasticity, Pergamon Press, London, UK, 1959.
  16. Lapidus , L. , and Pinder , G.F. , Numerical Solution of Partial Differential Equations in Science and Engineering , Wiley , New York, NY , 1982 . Lapidus, L., and Pinder, G.F., Numerical Solution of Partial Differential Equations in Science and Engineering, Wiley, New York, NY, 1982.
  17. 10.1145/15886.15893 · DOI
  18. 10.1145/15886.15903 · DOI
  19. Stoker , J . J . , Nonlinear Elasticity , New York, NY , 1968 . Stoker, J .J ., Nonlinear Elasticity, New York, NY, 1968.
  20. 10.1016/0734-189X(83)90020-8 · DOI
  21. 10.1109/TPAMI.1986.4767807 · DOI
  22. Terzopoulos , D. ~ " On matching deformable models to images: Direct and iterative solutions," Topical Meeting on Machine Vision , Technical Digest Series , Vol. 1~., Optical Society of America, Washington, DC, 1987 , 160 - 167 . Terzopoulos, D.~ "On matching deformable models to images: Direct and iterative solutions," Topical Meeting on Machine Vision, Technical Digest Series, Vol. 1~., Optical Society of America, Washington, DC, 1987, 160-167.
  23. 10.1145/15886.15891 · DOI
  24. 10.5555/20313.20331 · DOI
  25. 10.1145/15886.15895 · DOI
  26. Zienkiewicz , O.C. , The Finite Element Method ; Third edition, McGraw-Hill , London , 1977 . Zienkiewicz, O.C., The Finite Element Method; Third edition, McGraw-Hill, London, 1977.

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Metadata

Authors
Terzopoulos, D., Platt, J., Barr, A., & Fleischer, K.
Affiliations
  • Schlumberger (United States) (US)
  • California Institute of Technology (US)
ORCID
Venue
ACM SIGGRAPH Computer Graphics
Publisher
Association for Computing Machinery (ACM)
Published
1987-08
Volume
21
Issue
4
Pages
205-214
ISSN
0097-8930 (ISSN-L)
DOI
10.1145/37402.37427
OpenAlex
W3006964082
Cited by
1,110
References
0
Citations by year
2026: 6 · 2025: 7 · 2024: 19 · 2023: 22 · 2022: 26 · 2021: 26 · 2020: 23 · 2019: 27 · 2018: 35 · 2017: 33 · 2016: 34 · 2015: 31 · 2014: 37 · 2013: 34 · 2012: 43
FWCI
19.90
Type
journal article
Language
en
Open access
Licence
www.acm.org/publications/policies/copyright_policy#Background (vor)
Locations
  • ACM SIGGRAPH Computer Graphics (publishedVersion)
  • CaltechAUTHORS (California Institute of Technology) (submittedVersion)
Topics
  • Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computer Graphics and Visualization Techniques
  • Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › 3D Shape Modeling and Analysis
  • Physical Sciences › Engineering › Computational Mechanics › Advanced Numerical Analysis Techniques
Keywords
elasticity theory, solid deformation, physics-based animation, differential equations, cloth simulation, obstacle avoidance

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