Fully momentum-conserving reduced deformable bodies with collision, contact, articulation, and skinning

We propose a novel framework for simulating reduced deformable bodies that fully accounts for linear and angular momentum conservation even in the presence of collision, contact, articulation, and other desirable effects. This was motivated by the observation that the mere excitation of a single mode in a reduced degree of freedom model can adversely change the linear and angular momentum. Although unexpected changes in linear momentum can be avoided during basis construction, adverse changes in angular momentum appear unavoidable, and thus we propose a robust framework that includes the ability to compensate for them. Enabled by this ability to fully account for linear and angular momentum, we introduce an impulse-based formulation that allows us to precisely control the velocity of any node in spite of the fact that we only have access to a lower-dimensional set of degrees of freedom. This allows us to model collision, contact, and articulation in a robust and high visual fidelity manner, especially when compared to penalty-based forces that merely aim to coerce local velocities. In addition, we propose a new "deformable bones" framework wherein we leverage standard skinning technology for "bones," "bone" placement, blending operations, etc. even though each of our "deformable bones" is a fully simulated reduced deformable model.