Non-Linear Mechanics and Collisions for Subdivision Surfaces

Numerically accurate simulation of the mechanical behavior of thin flexible structures is important in application areas ranging from engineering design to animation special effects. Subdivision surfaces provide a unique opportunity to integrate geometric modeling with concurrent finite element analysis of thin flexible structures. Their mechanics are governed by the so-called thin-shell equations. We present a concise treatment of thin-shell equations including dynamic behavior, scalable material models, and the treatment of collisions (detection as well as response). The resulting energy minimization problem is non-linear and in turn able to capture effects of far more realism than linear models. We demonstrate these claims with a number of simulations which exhibit characteristic effects of real world experiments.