Rigid and Deformable Components

In prior work we proposed a class of physically-based models suitable for animating /lezible objects in simulated physical environments {ll. Our original formulation works well in practice for models whose shapes are moderately to highly deformable, but it tends to become numerically ill-conditioned as we increase the rigidity of the models. The present paper develops an alternative formulation of deformable models. We decompose deformations into a reference component, which may represent an arbitrary shape, and a displacement component allowing deformation away from this reference shape. The reference component evolves according to the laws of rigid-body dynamics. Equations of nonrigid motion based on linear elasticity govern the dynamics of the displacement component. With nonrigid and rigid dynamics operating in unison, this hybrid formulation yields well-conditioned discrete equations, even for complicated refrence shapes, particularly as the rigidity of models is increased beyond the stability limits of our prior formulation. We illustrate the application of our deformable models to a physically-based computer animation project.