Partial differential equations (PDEs) with spatially varying coefficients arise throughout science and engineering, modeling rich heterogeneous material behavior. Yet conventional PDE solvers struggle with the immense complexity found in nature, since they must first discretize the problem—leading to spatial aliasing, and global meshing/sampling that is costly and error-prone. We describe a method that approximates neither the domain geometry, the problem data, nor the solution space, providing the exact solution (in expectation) even for problems with extremely detailed geometry and intricate coefficients. Our main contribution is to extend the walk on spheres (WoS) algorithm from constant- to variable-coefficient problems, by drawing on techniques from volumetric rendering. In particular, an approach inspired by null-scattering yields unbiased Monte Carlo estimators for a large class of 2nd order elliptic PDEs, which share many attractive features with Monte Carlo rendering: no meshing, trivial parallelism, and the ability to evaluate the solution at any point without solving a global system of equations.

We describe the design and evolution of UberBake, a global illumination system developed by Activision, which supports limited lighting changes in response to certain player interactions. Instead of relying on a fully dynamic solution, we use a traditional static light baking pipeline and extend it with a small set of features that allow us to dynamically update the precomputed lighting at run-time while introducing little to no overhead. This means that our system works on the complete set of target hardware, ranging from high-end PCs to previous generation gaming consoles, allowing the use of lighting changes for gameplay purposes. In particular, we show how to efficiently precompute lighting changes due to individual lights being enabled and disabled and doors opening and closing. Finally, we provide a detailed performance evaluation of our system using a set of production levels and discuss how to extend its dynamic capabilities in the future.

Signed distance fields (SDFs) are a powerful implicit representation for modeling solids, volumes and surfaces. Their infinite resolution, controllable continuity and robust constructive solid geometry operations, coupled with smooth blending, enable powerful and intuitive sculpting tools for creating complex SDF models. SDF metric properties also admit efficient surface rendering with sphere tracing. Unfortunately, SDFs remain incompatible with many popular direct deformation techniques which re-position a surface via its explicit representation. Linear blend skinning used in character articulation, for example, directly displaces each vertex of a triangle mesh. To overcome this limitation, we propose a variant of sphere tracing for directly rendering deformed SDFs. We show that this problem reduces to integrating a non-linear ordinary differential equation. We propose an efficient numerical solution, with controllable error, which first automatically computes an initial value along each cast ray before walking conservatively along a curved ray in the undeformed space according to the signed distance. Importantly, our approach does not require knowledge, computation or even global existence of the inverse deformation, which allows us to readily apply many existing forward deformations. We demonstrate our method’s effectiveness for interactive rendering of a variety of popular deformation techniques that were, to date, limited to explicit surfaces.

AnimVR allows users to animate, integrate and share animated assets in Virtual Reality, revolutionizing traditional 3D content production. In AnimVR we leverage the possibilities of VR to enhance the CG Animation pipeline both by translating traditional animation workflows to VR as well as by exploring new ways to tell stories.