Physics-based multi-domain subspace deformation with component mode synthesis

Abstract

Fast and accurate simulation of 3D soft objects is important to virtual environment and reality. Simulating 3D deformation of large model in real-time is a challenging problem as it is very computation-demanding involving intensive matrix-based operation of large scale. Reduction techniques, consequently flourish where the dynamic is computed within a subspace of much smaller size with accuracy loss. This type of technique greatly boosts the simulation performance. Currently, most reduction methods use globally-computed bases. As a result, when large local deformation occurs, global bases often fail to provide necessary freedoms at the desired region. Alternatively, we construct subspaces locally based on the linear component mode synthesis (CMS) method. The components are the mutually disjoint sub-meshes (with duplicated boundary DOFs) and the local bases are called component modes which are the displacements of the components under certain mechanical equilibrium.We greatly extend the classic CMS with the following contributions. 1) We propose a new physics-based multi-domain subspace deformable model based on CMS. The subspace is locally constructed with component modes. The computation of modes follow a compact and straightforward formulation and the pre-computation is orders-faster comparing with some global subspace techniques. 2) The classic CMS does not handle large deformations with the linear modes. We extend the idea of modal warping to CMS with co-rotational elasticity to accommodate large rotational deformation. 3) A new type of mode called degenerated constraint mode is employed which constructs the subspaces of small size at components while preserving the boundary compatibility. As a result, the simulation can be performed within a small subspace and the boundary locking artifacts are also avoided. 4) We also propose another new type of mode called user constraint mode, which prevents the reduced system from being over-constrained. 5) Based on the extended CMS, we propose several simulation strategies including the hybrid simulation with the customized local mode supersets and the skeleton-driven deformable model based on the interface hierarchy.