“Energy constraints on parameterized models” by Witkin, Fleischer and Barr

  • ©Andrew P. Witkin, Kurt Fleischer, and Alan H. Barr




    Energy constraints on parameterized models



    A simple but general approach to imposing and solving geometric constraints on parameterized models is introduced, applicable to animation as well as model construction. Constraints are expressed as energy functions, and the energy gradient followed through the model’s parameter space. Intuitively, energy constraints behave like forces that pull and parametrically deform the parts of the model into place. A wide variety of geometric constraints are amenable to this formulation, and may be used to influence arbitrary model parameters. A catalogue of basic constraints is presented, and results are shown.


    1. William W. Armstrong and Mark W. Green, The dynamics of articulated rigid bodies .for purposes of animation, in Visual Computer, Springer-Verlag, 1985, pp. 231-240.]]
    2. Alan H. Barr, Global and Local Deformations of Solid Primitives, Proe. SIGGRAPH, 1984, pp. 21-29,]]
    3. Ronen Barzel and Alan It. Barr, Dynamic Constraints, to appear.]]
    4. Kurt Fleischer and Andrew Witkin, The SPAR modeling testbed, to appear.]]
    5. William C. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-ttall, Englewood Cliffs, N J, 1971]]
    6. Michael Girard and Anthony a Maciejewski, Cornputataional Modeling for the Computer Animation of Legged Figures, Proc. SIGGRAPH, 1985, pp. 263 270]]
    7. Michael Kass, Andrew Witkin, and Demetri Terzopoulos, Snakes: Active Contour Models, Proc. International Conference on Computer Vision, 1987.]]
    8. V. C. Lin, D. C. Gossard, and R. A. Light, Variational Geometry in Computer-Aided Design, Proc. S{GGRAPH, 1981, pp. 171-178]]
    9. Greg Nelson, Juno, a constrait~t-based graphics ~y~tent Computer Graplffcs, Vol. 19 No. 3, July 1985, pp. 235- 243.]]
    10. Thomas W. Sederberg and Scott R. Parry, Free-Form Deformation of Solid Geometric Models, Proc. SIG- GRAPH, 1986, pp. 151-160.]]
    11. Scott N. Steketee and Norman I. Badler, Parametric Keyfvame Interpolation Incorporating Kinetic Adjustment and Phrasing Control, Proc. SIGGRAPII, 1985, pp. 255-262.]]
    12. Demetri Terzopoulos, John P l a t t , Alan Barr, and Kurt Fleischer, Elastically Deformable Models, Proc. SICGRAPH, 1987.]]
    13. Jane Wilhehns and Brian Barsky, Using Dynamic Analysis To Animate Articulated Bodies Such As Humans and Robots, Graphics Interface, 1985.]]

ACM Digital Library Publication: