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 models 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. Keywords --- Constraints, Modeling, Animation 1 Introduction A widely-used approach to modeling is to combine geometric primitives---such as cylinders, blocks, and bicubic patches---with a variety of operators---such as translations, rotations, booleans, and deformations--- to form a model hierarchy. The task of constructing a model within this framework has two parts: building the hie...