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.

We propose a novel technique to provide multi-user real walking experiences with physical interactions in VR applications. In our system, multiple users walk freely while navigating a large, virtual environment within a smaller, physical workspace. These users can interact with other real users or objects in the same physical locations. The success of our method relies on two key components. The first is a redirected smooth mapping that incorporates the redirected walking technique to warp the input virtual scene with small bends and low distance distortion. Users possess a wide field of view to explore the mapped virtual environment while being redirected in the real workspace. The second component is an automatic collision avoidance technique that introduces dynamic virtual avatars to keep multiple users away from the overlaps of the mapped virtual scenes. These avatars naturally appear, move, and disappear, producing as little influence as possible on users walking experiences. We evaluate our technique through formative user studies, and demonstrate the capability and practicability of our method in two multi-user applications.

Point clouds provide a flexible and scalable geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. Hence, the design of intelligent computational models that act directly on point clouds is critical, especially when efficiency considerations or noise preclude the possibility of expensive denoising and meshing procedures. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent success of convolutional neural networks for image analysis suggests the value of adapting insight from CNN to the point cloud world. We propose a new neural network module EdgeConv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv is differentiable and can be plugged into existing architectures. Compared to existing modules operating in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. Beyond proposing this module, we provide extensive evaluation and analysis revealing that EdgeConv captures and exploits fine-grained geometric properties of point clouds.

We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent component analysis, which we extend to improve performance and enable its application to integration problems. First, we introduce piecewise-polynomial coupling transforms that greatly increase the modeling power of individual coupling layers. Second, we preprocess the inputs of neural networks using one-blob encoding, which stimulates localization of computation and improves inference. Third, we derive a gradient-descent-based optimization for the KL and Chi2 divergence for the specific application of Monte Carlo integration with unnormalized stochastic estimates of the target distribution. Our approach enables fast and accurate inference and efficient sample generation independent of the dimensionality of the integration domain. We demonstrate the benefits of our approach for generating natural images and in two applications to light-transport simulation. First, we show how to learn joint path-sampling densities in primary sample space and how to importance sample multi-dimensional path prefixes thereof. Second, we use our technique to extract conditional directional densities driven by the triple product of the rendering equation, and leverage them for path guiding. In all applications, our approach yields on-par or higher performance than competing techniques at equal sample count.

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.

While three-dimensional landforms, such as arches and overhangs, occupy a relatively small proportion of most computer-generated landscapes, they are distinctive and dramatic and have an outsize visual impact. Unfortunately, the dominant heightfield representation of terrain precludes such features, and existing in-memory volumetric structures are too memory intensive to handle larger scenes. In this paper, we present a novel memory-optimized paradigm for representing and generating volumetric terrain based on implicit surfaces. We encode feature shape and terrain geology using construction trees that arrange and combine implicit primitives. The landform primitives themselves are positioned using Poisson sampling, built using open shape grammars guided by stratified erosion and invasion percolation processes, and, finally, queried during polygonization. Users can also interactively author landforms features using high-level modeling tools to create or edit the underlying construction trees, with support for iterative cycles of editing and simulation. We demonstrate that our framework is capable of importing existing large-scale heightfield terrains and amplifying them with such diverse structures as slot canyons, sea arches, stratified cliffs, fields of Hoodoos, and complex karst cave networks.

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.