To achieve real-time rates, we phrase the model fitting in terms of a nonlinear least-squares problem so that the energy can be optimized based on a highly efficient GPU-based Gauss-Newton optimizer. We show state-of-the-art results in scenes that exceed the complexity level demonstrated by previous work, including tight two-hand grasps, significant inter-hand occlusions, and gesture interaction. 1 CCS Concepts: • Computing methodologies → Tracking; Computer vision; Neural networks.

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Simulating (elastically) deformable models that can collide with each other and with the environment remains a challenging task. The resulting contact problems can be elegantly approached using Lagrange multipliers to represent the unknown magnitude of the response forces. Typical methods construct and solve a Linear Complementarity Problem (LCP) to obtain the response forces. This requires the inverse of the generalized mass matrix, which is generally hard to obtain for deformable-body problems. In this article, we tackle such contact problems by directly solving the Mixed Linear Complementarity Problem (MLCP) and omitting the construction of an LCP matrix. Since a convex quadratic program with linear constraints is equivalent to an MLCP, we propose to use a Conjugate Residual (CR) solver as the backbone of our collision response system. By dynamically updating the set of active constraints, the MLCP with inequality constraints can be solved efficiently. We also propose a simple yet efficient preconditioner that ensures faster convergence. Finally, our approach is faster than existing methods (at the same accuracy), and it allows accurate treatment of friction.

We present a method to render virtual touch, such that the stimulus produced by a tactile device on a user's skin matches the stimulus computed in a virtual environment simulation. To achieve this, we solve the inverse mapping from skin stimulus to device configuration thanks to a novel optimization algorithm. Within this algorithm, we use a device-skin simulation model to estimate rendered stimuli, we account for trajectory-dependent effects efficiently by decoupling the computation of the friction state from the optimization of device configuration, and we accelerate computations using a neural-network approximation of the device-skin model. Altogether, we enable real-time tactile rendering of rich interactions including smooth rolling, but also contact with edges, or frictional stick-slip motion. We validate our algorithm both qualitatively through user experiments, and quantitatively on a BioTac biomimetic finger sensor.

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