Elastic Deformations Using Finite Element Methods in Computer Graphic Applications

  • M. Mascaró
  • A. Mir
  • F. Perales
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1899)


Deformation tools constitute an important topic in computer animation. This paper shows how we can give an exact value to the basic parameters in a dynamical elastic deformation system based on finite elements for 2D objects. We look for an optimal value for the time step ( Δt ) in the dynamical system, and an optimal area for the basic square finite element of the object. Fine time step adjustment is important to reduce the computational cost of the system, and guarantee the realistic look of the result (final deformation of the object). Then several results from different physical conditions are compared, in order to find a good system of measuring the difference between them. Finally, using this measurement parameter we can relate the size of the finite elements with the error between several deformations of the same object. The deformations are rendered using the Open Inventor application (VRML).


elasticity render VRML Open Inventor elastic deformation finite element mesh generator 


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  1. 1.
    Mascaró, M., Mir, A., Perales, F.: Modelado y animación de objetos deformables basado en la teoría de la elasticidad. CEIG 1997, 95–110 (1997)Google Scholar
  2. 2.
    Mascaró, M., Mir, A., Perales, F.: Visualización de deformaciones dinámicas mediante elementos finitos triangulares y cuadrangulares. CEIG 1999, 47–61 (1999)Google Scholar
  3. 3.
    Terzopoulos, D., et al.: Elastically Deformable Models. In: Computer Graphics (Proc. Siggraph), vol. 21(4), pp. 205–214 (1987)Google Scholar
  4. 4.
    Terzopoulos, D., Fleischer, K.: Deformable Models. Visual Computer 21(4), 306–331 (1988)CrossRefGoogle Scholar
  5. 5.
    Terzopoulos, D., Witkin, A., Kass, M.: Dynamic 3D models with local and global deformations: Deformable superquadratics. IEEE Transactions on PAMI 13(7), 703–714 (1991)Google Scholar
  6. 6.
    Palmer, P., Mir, A., González, M.: Simulació Dinàmica i Deformacions. Memoria de investigación. Universidad de las Islas Baleares. Junio (1998)Google Scholar
  7. 7.
    Aono, M.: A Wrinkle Propagation Model for Cloth. In: Proc. CG. Int’l, pp. 95–115. Springer, Heidelberg (1990)Google Scholar
  8. 8.
    Thalmann, N.M., Yang, Y.: Techniques for Cloth Animation. In: M-Thalmann, N., Thalmann, D. (eds.) New Trends in Animation and Visualization, pp. 243–256. John Wiley & Sons, Chichester (1991)Google Scholar
  9. 9.
    Serón, F.J., Badal, J., Sabadell, F.J.: A numerical laboratory for simulation and visualization of seismic wavefields. Geophysical Prospecting 44, 603–642 (1996)CrossRefGoogle Scholar
  10. 10.
    Provot, X.: Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior. INRIA (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • M. Mascaró
    • 1
  • A. Mir
    • 1
  • F. Perales
    • 1
  1. 1.Dep. Matemàtiques i Informàtica. (U. Gráfics i Visió)Universitat de les Illes Balears (UIB)

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