We present a fast and feature-complete differentiable physics engine, Nimble (nimblephysics.org), that supports Lagrangian dynamics and hard contact constraints for articulated rigid body simulation. Our differentiable physics engine offers a complete set of features that are typically only available in non-differentiable physics simulators commonly used by robotics applications. We solve contact constraints precisely using linear complementarity problems (LCPs). We present efficient and novel analytical gradients through the LCP formulation of inelastic contact that exploit the sparsity of the LCP solution. We support complex contact geometry, and gradients approximating continuous-time elastic collision. We also introduce a novel method to compute complementarity-aware gradients that help downstream optimization tasks avoid stalling in saddle points. We show that an implementation of this combination in a fork of an existing physics engine (DART) is capable of a 87x single-core speedup over finite-differencing in computing analytical Jacobians for a single timestep, while preserving all the expressiveness of original DART.

Film-quality characters typically display highly complex and expressive facial deformation. The underlying rigs used to animate the deformations of a character's face are often computationally expensive, requiring high-end hardware to deform the mesh at interactive rates. In this paper, we present a method using convolutional neural networks for approximating the mesh deformations of characters' faces. For the models we tested, our approximation runs up to 17 times faster than the original facial rig while still maintaining a high level of fidelity to the original rig. We also propose an extension to the approximation for handling high-frequency deformations such as fine skin wrinkles. While the implementation of the original animation rig depends on an extensive set of proprietary libraries making it difficult to install outside of an in-house development environment, our fast approximation relies on the widely available and easily deployed TensorFlow libraries. In addition to allowing high frame rate evaluation on modest hardware and in a wide range of computing environments, the large speed increase also enables interactive inverse kinematics on the animation rig. We demonstrate our approach and its applicability through interactive character posing and real-time facial performance capture.