A unified approach for subspace simulation of deformable bodies in multiple domains

Multi-domain subspace simulation can efficiently and conveniently simulate the deformation of a large deformable body, by constraining the deformation of each domain into a different subspace. The key challenge in implementing this method is how to handle the coupling among multiple deformable domains, so that the overall effect is free of gap or locking issues. In this paper, we present a new domain decomposition framework that connects two disjoint domains through coupling elements. Under this framework, we present a unified simulation system that solves subspace deformations and rigid motions of all of the domains by a single linear solve. Since the coupling elements are part of the deformable body, their elastic properties are the same as the rest of the body and our system does not need stiffness parameter tuning. To quickly evaluate the reduced elastic forces and their Jacobian matrices caused by the coupling elements, we further develop two cubature optimization schemes using uniform and non-uniform cubature weights. Our experiment shows that the whole system can efficiently handle large and complex scenes, many of which cannot be easily simulated by previous techniques without limitations.