skip to main content
10.1145/1198555.1198663acmconferencesArticle/Chapter ViewAbstractPublication PagessiggraphConference Proceedingsconference-collections
Article

A discrete model of thin shells

Published: 31 July 2005 Publication History

Abstract

We present a discrete model for the behavior of thin flexible structures, such as hats, leaves, and aluminum cans, which are characterized by a curved undeformed configuration. Previously such models required complex continuum mechanics formulations and correspondingly complex algorithms. We show that a simple shell model can be derived geometrically for triangle meshes and implemented quickly by modifying a standard cloth simulator. Our technique convincingly simulates a variety of curved objects with materials ranging from paper to metal, as we demonstrate with several examples including a comparison of a real and simulated falling hat.This chapter is based on the paper by Grinspun, Hirani, Desbrun, and Schröder which appeared in the Proceedings of the Symposium for Computer Animation 2003 [Grinspun et al. 2003].

References

[1]
ADIFOR, 2002. Argonne National Laboratory / Rice University. http://www-unix.mcs.anl.gov/autodiff/ADIFOR/.
[2]
Arnold, D., 2000. Questions on Shell Theory. Workshop on Elastic Shells: Modeling, Analysis, and Computation. Mathematical Sciences Research Institute, Bekeley.
[3]
Autodiff.org, 2002. http://www.autodiff.org.
[4]
Baraff, D., and Witkin, A. 1998. Large Steps in Cloth Simulation. In Proceedings of SIGGRAPH, 43--54.
[5]
Bobenko, A. I. 2004. A Conformal Energy for Simplicial Surfaces. Published online at http://arxiv.org/abs/math.DG/0406128, August.
[6]
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 (July), 594--603.
[7]
Bridson, R., Marino, S., and Fedkiw, R. 2003. Simulation of Clothing with Folds and Wrinkles. In Proceedings of ACM SIGGRAPH / Eurographics Symposium on Computer Animation, D. Breen and M. Lin, Eds.
[8]
Carignan, M., Yang, Y., Thalmann, N. M., and Thalmann, D. 1992. Dressing Animated Synthetic Actors with Complex Deformable Clothes. In Proceedings of SIGGRAPH, 99--104.
[9]
Celniker, G., and Gossard, D. 1991. Deformable Curve and Surface Finite Elements for Free-Form Shape Design. Computer Graphics (Proceedings of SIGGRAPH 91) 25, 4, 257--266.
[10]
Ciarlet, P. 2000. Mathematical Elasticity. Vol. III, vol. 29 of Studies in Mathematics and its Applications. Amsterdam. Theory of shells.
[11]
Cirak, F., Ortiz, M., and Schröder, P. 2000. Subdivision Surfaces: A New Paradigm for Thin-Shell Finite-Element Analysis. Internat. J. Numer. Methods Engrg. 47, 12, 2039--2072.
[12]
Cirak, F., Scott, M., Antonsson, E., Ortiz, M., and Schröder, P. 2002. Integrated Modeling, Finite-Element Analysis, and Engineering Design for Thin-Shell Structures Using Subdivision. CAD 34, 2, 137--148.
[13]
Cohen-Steiner, D., and Morvan, J.-M. 2003. Restricted Delaunay Triangulations and Normal Cycle. In Proc. 19th Annu. ACM Sympos. Comput. Geom., 237--246.
[14]
Corliss, G., Faure, C., Griewank, A., Hascoët, L., and Naumann, U., Eds. 2001. Automatic Differentiation of Algorithms: From Simulation to Optimization. Springer.
[15]
Desbrun, M., Meyer, M., and Alliez, P. 2002. Intrinsic Parameterizations of Surface Meshes. In Proceedings of Eurographics, 209--218.
[16]
Feynman, C. 1986. Modeling the Appearance of Cloth. MSc thesis, MIT.
[17]
Ge, Z., Kruse, H. P., and Marsden, J. E. 1996. The Limits of Hamiltonian Structures in Three-Dimensional Elasticity, Shells, and Rods. Journal of Nonlinear Science 6, 19--57.
[18]
Gingold, Y., Secord, A., Han, J. Y., Grinspun, E., and Zorin, D. 2004. Poster: A Discrete Model for In-elastic Deformation of Thin Shells. In ACM/Eurographics Symposium on Computer Animation '04.
[19]
Gleicher, M. 1994. A Differential Approach to Graphical Manipulation (Chapter 5). PhD thesis.
[20]
Gray, A. 1998. Modern Differential Geometry of Curves and Surfaces. Second edition. CRC Press.
[21]
Green, S., Turkiyyah, G., and Storti, D. 2002. Subdivision-Based Multilevel Methods for Large Scale Engineering Simulation of Thin Shells. In Proceedings of ACM Solid Modeling, 265--272.
[22]
Greiner, G. 1994. Variational Design and Fairing of Spline Surfaces. Computer Graphics Forum 13, 3, 143--154.
[23]
Grinspun, E., Krysl, P., and Schröder, P. 2002. CHARMS: A Simple Framework for Adaptive Simulation. ACM Transactions on Graphics 21, 3 (July), 281--290.
[24]
Grinspun, E., Hirani, A., Desbrun, M., and Schröder, P. 2003. Discrete Shells. In ACM SIGGRAPH Symposium on Computer Animation. to appear.
[25]
Haumann, R. 1987. Modeling the Physical Behavior of Flexible Objects. In Topics in Physically-based Modeling, Eds. Barr, Barrel, Haumann, Kass, Platt, Terzopoulos, and Witkin, SIGGRAPH Course Notes.
[26]
House, D. H., and Breen, D. E., Eds. 2000. Coth Modeling and Animation. A.K. Peters.
[27]
Kass, M. 1992. CONDOR: Constraint-based Dataflow. In Proceedings of SIGGRAPH, 321--330.
[28]
Kergosien, Y. L., Gotoda, H., and Kunii, T. L. 1994. Bending and Creasing Virtual Paper. IEEE Computer Graphics and Applications, 40--48.
[29]
Meyer, M., Desbrun, M., Schröder, P., and Barr, A. H. 2003. Discrete Differential-Geometry Operators for Triangulated 2-Manifolds. In Visualization and Mathematics III, H.-C. Hege and K. Polthier, Eds. Springer-Verlag, Heidelberg, 35--57.
[30]
Newmark, N. M. 1959. A Method of Computation for Structural Dynamics. ASCE J. of the Engineering Mechanics Division 85, EM 3, 67--94.
[31]
Qin, H., and Terzopoulos, D. 1996. D-NURBS: A Physics-Based Framework for Geometric Design. IEEE Transactions on Visualization and Computer Graphics 2, 1, 85--96.
[32]
Qin, H., and Terzopoulos, D. 1997. Triangular NURBS and their dynamic generalizations. Computer Aided Geometric Design 14, 4, 325--347.
[33]
Terzopoulos, D., and Qin, H. 1994. Dynamic NURBS with Geometric Constraints for Interactive Sculpting. ACM Transactions on Graphics 13, 2, 103--136.
[34]
Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically Deformable Models. In Proceedings of SIGGRAPH, 205--214.
[35]
Welch, W., and Witkin, A. 1992. Variational Surface Modeling. Computer Graphics (Proceedings of SIGGRAPH 92) 26, 2, 157--166.
[36]
West, M., Kane, C., Marsden, J. E., and Ortiz, M. 2000. Variational Integrators, the Newmark Scheme, and Dissipative Systems. In International Conference on Differential Equations 1999, World Scientific, Berlin, 1009--1011.

Cited By

View all
  • (2023)Stable Discrete Bending by Analytic Eigensystem and Adaptive Orthotropic Geometric StiffnessACM Transactions on Graphics10.1145/361837242:6(1-16)Online publication date: 5-Dec-2023
  • (2022)Modeling Tunable Fracture in Hydrogel Shell Structures for Biomedical ApplicationsGels10.3390/gels80805158:8(515)Online publication date: 18-Aug-2022
  • (2022)Stability of a Flexible Asteroid Lander with Landing ControlAerospace10.3390/aerospace91107199:11(719)Online publication date: 16-Nov-2022
  • Show More Cited By
  1. A discrete model of thin shells

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Conferences
    SIGGRAPH '05: ACM SIGGRAPH 2005 Courses
    July 2005
    7157 pages
    ISBN:9781450378338
    DOI:10.1145/1198555
    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]

    Sponsors

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 31 July 2005

    Permissions

    Request permissions for this article.

    Check for updates

    Qualifiers

    • Article

    Acceptance Rates

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

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)27
    • Downloads (Last 6 weeks)3
    Reflects downloads up to 03 Mar 2025

    Other Metrics

    Citations

    Cited By

    View all
    • (2023)Stable Discrete Bending by Analytic Eigensystem and Adaptive Orthotropic Geometric StiffnessACM Transactions on Graphics10.1145/361837242:6(1-16)Online publication date: 5-Dec-2023
    • (2022)Modeling Tunable Fracture in Hydrogel Shell Structures for Biomedical ApplicationsGels10.3390/gels80805158:8(515)Online publication date: 18-Aug-2022
    • (2022)Stability of a Flexible Asteroid Lander with Landing ControlAerospace10.3390/aerospace91107199:11(719)Online publication date: 16-Nov-2022
    • (2011)Bi-manual robotic paper manipulation based on real-time marker tracking and physical modelling2011 IEEE/RSJ International Conference on Intelligent Robots and Systems10.1109/IROS.2011.6094742(1427-1432)Online publication date: Sep-2011

    View Options

    Login options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Figures

    Tables

    Media

    Share

    Share

    Share this Publication link

    Share on social media