Steklov-Poincaré Skinning

Abstract

We introduce a novel and efficient simulation technique for generating physics-based skinning animations of skeleton-driven characters with full support for collision handling. Although physics-based approaches may use a volumetric (e.g. tetrahedral) flesh model, operations such as rendering, collision processing and user manipulation directly involve only the surface of this mesh. Motivated by this fact we define an elastic model of the skin surface which, while directly using only the surface degrees of freedom, exhibits a mechanical response that captures the full volumetric flesh behavior. We achieve this unusual result by combining three fundamental contributions: First, we present a material model which offers a plausible approximation to corotational elasticity at significantly reduced cost, by computing local rotations via procedural skinning rather than deriving them from the mesh deformation; the result is a force model which is affine on vertex positions, with coefficients dependent on the skeletal pose (but not on the deformation). Second, we use this force model to derive a direct mapping between surface vertex positions and resulting equilibrium forces on the same boundary vertices, which is a discrete version of the Steklov-Poincaré operator of the volumetric elastic model. This mapping is conveniently shown to also be affine (with pose-dependent coefficients), but with a dense stiffness matrix which renders direct numerical solution impractical. However, as a third and final step we show how a modified Newton iteration and a skinninginspired preconditioner can solve the boundary problem with a competitive runtime cost. We assess the efficacy of our solution in simulations of high resolution human flesh models, with full external and self-collision processing.