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Energy constraints on parameterized models

Witkin, Andrew and Fleischer, Kurt and Barr, Alan (1987) Energy constraints on parameterized models. ACM SIGGRAPH Computer Graphics, 21 (4). pp. 225-232. ISSN 0097-8930. doi:10.1145/37402.37429.

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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.

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Additional Information:© 1987 ACM. All images were rendered by Kurt Fleischer using his modeling testbed system (M-BLORB) on a Symbolics LISP Machine. Michael Kass helped design some of the constraints, and provided helpful comments on early ver[s]ions of this paper. We thank Demetri Terzopoulos, John Platt, and Michael Kass for valuable discussions and goop.
Subject Keywords:Constraints, Modeling, Animation
Issue or Number:4
Record Number:CaltechAUTHORS:20170109-144419851
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Official Citation:Andrew Witkin, Kurt Fleischer, and Alan Barr. 1987. Energy constraints on parameterized models. SIGGRAPH Comput. Graph. 21, 4 (August 1987), 225-232. DOI=
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73345
Deposited On:10 Jan 2017 05:14
Last Modified:11 Nov 2021 05:15

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