Dynamic Animation of Elastic Bodies

We describe an animation system that simulates the dynamics of viscoelastic bodies subject to equality and inequality constraints. The equations of motion are derived from Lagrange's equation, and constraint forces are computed by the method of Lagrange multipliers. Each elastic body is modeled as a collection of tetrahedral nite elements whose deformation is restricted to a ne transformations of their rest shapes. We use an original non-linear formula for the elastic forces, especially devised to prevent elements from collapsing to zero or negative volume. We also describe a general algorithm to detect violation of inequality constraints. For collisions, in particular, we use the optimization technique of Lin and Manocha to cut the detection time from quadratic to almost linear. Collisions are handled by temporary contact springs.