Abstract

We describe an animation system that simulates the dynamics of viscoelastic bodies subject to equality and inequality constraints. We show how Lagrange's method can be used to derive the equations of motion of such bodies from general formulas for the elastic and kinetic energy, the viscous power loss, and mechanical constraints, in terms of generalized coordinates. We also describe a convenient two-parameter non-linear model for the elastic forces, that agrees with Hooke's law for small deformations, but does not allow the material to be compressed to zero or negative volume. In particular, we derive the equations of motion for elastic bodies modeled by tetrahedral finite elements with affine deformations. Finally, we show how collisions between such bodies can be efficiently and accurately detected by combining Hermite interpolation of the non-penetration constraints with Lin and Manocha's bounding box tests.

Citations