Dynamic kelvinlets: Secondary motions based on fundamental solutions of elastodynamics

Abstract

We introduce Dynamic Kelvinlets, a new analytical technique for real-time physically based animation of virtual elastic materials. Our formulation is based on the dynamic response to time-varying force distributions applied to an infinite elastic medium. The resulting displacements provide the plausibility of volumetric elasticity, the dynamics of compressive and shear waves, and the interactivity of closed-form expressions. Our approach builds upon the work of de Goes and James [2017] by presenting an extension of the regularized Kelvinlet solutions from elastostatics to the elastodynamic regime. To finely control our elastic deformations, we also describe the construction of compound solutions that resolve pointwise and keyframe constraints. We demonstrate the versatility and efficiency of our method with a series of examples in a production grade implementation.