Analytically learning an inverse rig mapping

Abstract

One of the main obstacles to applying the latest advances in motion synthesis to feature film character animation is that these methods operate directly on skeletons instead of high-level rig parameters. Loosely known as the "rig inversion problem", this hurdle has prevented the crowd department at Pixar from procedurally modifying character skeletons close to camera, knowing that these procedural edits would not be reliably transferred to the equivalent motion on the full character for polish. Prior attempts at solving this problem have tended to involve hard-coded heuristics, which are cumbersome for production to debug and maintain. To alleviate this overhead, we have adopted an approach of solving the inversion problem with an iterative least-squares algorithm. However, although there are numerous existing methods for solving this problem, the computation of the rig Jacobian is a frequent requirement, which in practice is prohibitively expensive. To accelerate this process, we propose a method wherein an approximation of the rig is derived analytically, through an offline learning process. Using this approximation, we invert full character rigs at real-time rates.