Substructuring permits parallelization of physics simulation on multi-core CPUs. We present a new substructuring approach for solving stiff multibody systems containing both bilateral and unilateral constraints. Our approach is based on the non-overlapping domain-decomposition Schur complement method, which we extend to systems involving contact formulated as mixed bounds linear complementarity problems. At each time step, we alternate between solving the subsystem and interface constraint impulses, which leads to the identification of the active constraints. By using the correct active constraints in the computation of the effective mass of subsystems within the interface solve, we directly obtain an exact solution. We demonstrate that our simulations have preferable behavior in comparison to standard iterative methods and force based subsystem coupling. We also show that our method works well with user selected semantic partitioning, as well as with a minimum degree partitioning scheme. Finally, because our method makes use of direct solvers, we are able to achieve interactive and real-time frame rates for a number of challenging scenarios involving large mass ratios, redundant constraints, and ill-conditioned systems.

Seamless global parametrization of surfaces is a key operation in geometry processing, e.g. for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular the locations of singularities (cones), and solve a non-convex optimization problem minimizing a distortion measure, with local injectivity imposed through constraints or barrier terms. In both cases, an initial valid parametrization is essential to serve as feasible starting point for obtaining an optimized solution. While convexified versions of the constraints eliminate this initialization requirement, they narrow the range of solutions, causing some problem instances that actually do have a solution to become infeasible. We demonstrate that for arbitrary given sets of topologically admissible parametric cones with prescribed curvature, a global seamless parametrization always exists (with the exception of one well-known case). Importantly, our proof is constructive and directly leads to a general algorithm for computing such parametrizations. Most distinctively, this algorithm is bootstrapped with a convex optimization problem (solving for a conformal map), in tandem with a simple linear equation system (determining a seamless modification of this map). This map can then serve as valid starting point and be optimized with respect to specific distortion measures using injectivity preserving methods.

Immersive computer graphics systems strive to generate perceptually realistic user experiences. Current-generation virtual reality (VR) displays are successful in accurately rendering many perceptually important effects, including perspective, disparity, motion parallax, and other depth cues. In this paper we introduce ocular parallax rendering, a technology that accurately renders small amounts of gaze-contingent parallax capable of improving depth perception and realism in VR. Ocular parallax describes the small amounts of depth-dependent image shifts on the retina that are created as the eye rotates. The effect occurs because the centers of rotation and projection of the eye are not the same. We study the perceptual implications of ocular parallax rendering by designing and conducting a series of user experiments. Specifically, we estimate perceptual detection and discrimination thresholds for this effect and demonstrate that it is clearly visible in most VR applications. Additionally, we show that ocular parallax rendering provides an effective ordinal depth cue and it improves the impression of realistic depth in VR.

Computer animation in conjunction with 3D printing has the potential to positively impact traditional stop-motion animation. As 3D printing every frame of a computer animation is prohibitively slow and expensive, 3D printed stop-motion can only be viable if animations can be faithfully reproduced using a compact library of 3D printed and efficiently assembled parts. We thus present the first system for processing computer animation sequences (typically faces) to produce an optimal replacement library for use in 3D printed stop-motion animation. Given an input animation sequence of topology invariant deforming meshes, our problem is to output a replacement library and per-animation-frame assignment of the library pieces, such that we maximally approximate the input animation, while minimizing the amount of 3D printing and assembly. Our evaluation is threefold: we show results on a variety of facial animations, both digitally and 3D printed, critiqued by a professional animator; we show the impact of various algorithmic parameters; and compare our results to naive solutions. Our approach can reduce the printing time and cost significantly for stop-motion animated films.

We present a framework for the simulation of rigid and deformable bodies in the presence of contact and friction. In contrast to previous methods which solve linearized models, we develop a non-smooth Newton method that solves the underlying nonlinear complementarity problems (NCPs) directly. Our method supports two-way coupling between hyperelastic deformable bodies and articulated rigid mechanisms, includes a nonlinear contact model, and requires only the solution of a symmetric linear system as a building block. We propose a new complementarity preconditioner that improves convergence, and develop an efficient GPU-based solver based on the conjugate residual (CR) method that is suitable for interactive simulations. We show how to improve robustness using a new geometric stiffness approximation and evaluate our method's performance on a number of robotics simulation scenarios, including dexterous manipulation and training using reinforcement learning.

This paper presents a new computational framework for constructing 3D self-supporting surfaces. Inspired by the self-supporting property of catenary and the fact that catenoid, the surface of revolution of the catenary curve, is a minimal surface, we discover the relation between 3D self-supporting surfaces and 4D minimal hypersurfaces (which are 3-manifolds). We prove that the hyper-generatrix of a 4D minimal hyper-surface of revolution is a 3D self-supporting surface, implying that constructing a 3D self-supporting surface is equivalent to volume minimization. We show that the energy functional is simply the surface's gravitational potential energy, which in turns can be converted into a surface reconstruction problem with mean curvature constraint. Armed with our theoretical findings, we develop an iterative algorithm to construct 3D self-supporting surfaces from triangle meshes. Our method guarantees convergence and can produce near-regular triangle meshes thanks to a local mesh refinement strategy similar to centroidal Voronoi tessellation. It also allows users to tune the geometry via specifying either the zero potential surface or its desired volume. We show that 1) given a boundary condition, if a stable minimal surface exists, so does the 3D self-supporting surface; and 2) the solution is not unique in general.

We propose a method for generating (near) video-realistic animations of real humans under user control. In contrast to conventional human character rendering, we do not require the availability of a production-quality photo-realistic 3D model of the human, but instead rely on a video sequence in conjunction with a (medium-quality) controllable 3D template model of the person. With that, our approach significantly reduces production cost compared to conventional rendering approaches based on production-quality 3D models, and can also be used to realistically edit existing videos. Technically, this is achieved by training a neural network that translates simple synthetic images of a human character into realistic imagery. For training our networks, we first track the 3D motion of the person in the video using the template model, and subsequently generate a synthetically rendered version of the video. These images are then used to train a conditional generative adversarial network that translates synthetic images of the 3D model into realistic imagery of the human. We evaluate our method for the reenactment of another person that is tracked in order to obtain the motion data, and show video results generated from artist-designed skeleton motion. Our results outperform the state-of-the-art in learning-based human image synthesis.