a) (b) (c) (d) Fig. 1. (a) We compactly model muscles as a collection of generalized rods, where volume conservation is expressed by a radius function defined on curve's vertices -vis sphere's radii. (b) The rods create a subspace on which physics is solved, and its effects later propagated to the muscle mesh via linear blend skinning; please see the animation in our supplemental video. The anatomical model is courtesy of Ziva Dynamics. (c) We show how rods and/or bundles can be skinned to a surface mesh to drive its deformation (d), resulting in an alternative to cages for real-time volumetric deformation.We extend the formulation of position-based rods to include elastic volumetric deformations. We achieve this by introducing an additional degree of freedom per vertex -isotropic scale (and its velocity). Including scale enriches the space of possible deformations, allowing the simulation of volumetric effects, such as a reduction in cross-sectional area when a rod is stretched. We rigorously derive the continuous formulation of its elastic energy potentials, and hence its associated position-based dynamics (PBD) updates to realize this model, enabling the simulation of up to 26000 DOFs at 140 Hz in our GPU implementation. We further show how rods can provide a compact alternative to tetrahedral meshes for the representation of complex muscle deformations, as well as providing a convenient representation for collision detection. This is achieved by modeling a muscle as a bundle of rods, for which we also introduce a technique to automatically convert a muscle surface mesh into a rods-bundle. Finally, we show how rods and/or bundles can be skinned to a surface mesh to drive its deformation, resulting in an alternative to cages for real-time volumetric deformation. The source code of our physics engine will be openly available 1 .
