As scenes become ever more complex and real-time applications embrace ray tracing, path sampling algorithms that maximize quality at low sample counts become vital. Recent algorithms building on resampled importance sampling reuse paths spatiotemporally to render surprisingly complex light transport with a few samples per pixel (e.g. ReSTIR). But sample reuse introduces correlation, so ReSTIR-style iterative reuse loses most convergence guarantees that RIS theoretically provides. We introduce generalized resampled importance sampling (GRIS) to extend the theory, allowing RIS on correlated samples, with unknown PDFs and taken from varied domains. This solidifies the theoretical foundation, allowing us to derive variance bounds and convergence conditions in ReSTIR-based samplers. It also guides practical algorithm design and enables advanced path reuse between pixels via complex shift mappings.

Simulations of deformable objects initialized using a given initial shape result in sagging, the undesirable deformation under gravity as soon as the simulation begins. We introduce a novel solution to the sagging problem that can be applied to a variety of simulation systems and materials, presenting examples with mass-spring systems, cloth simulations, the finite element method, the material point method, and position-based dynamics. The key feature of our approach is that we avoid solving a global nonlinear optimization problem by performing the initialization in two stages.

We introduce virtual blue noise lighting, a rendering pipeline for estimating indirect illumination with a blue noise distribution of virtual lights. Our pipeline is designed for virtual lights with non-uniform emission profiles that are more expensive to store, but required for properly and efficiently handling specular transport. We generate virtual lights starting from the camera and use an adaptive sample elimination strategy to achieve a blue noise distribution. For computing the virtual light emission profiles, we present a photon splitting technique. During lighting estimation, our method allows using novel sampling techniques for reducing the estimation error.

Volume rendering under complex, dynamic lighting is challenging, especially if targeting real-time. To address this challenge, we extend a recent direct illumination sampling technique, spatiotemporal reservoir resampling, to multi-dimensional path space for volumetric media. By fully evaluating just a single path sample per pixel, our volumetric path tracer shows unprecedented convergence. To achieve this, we properly estimate the chosen sample’s probability via approximate perfect importance sampling with spatiotemporal resampling. With this reformulation, we achieve low-noise, interactive volumetric path tracing with arbitrary dynamic lighting, including volumetric emission, and maintain interactive performance even on high-resolution volumes.

Robustly handling collisions between individual particles in a large particle-based simulation has been a challenging problem. This project introduces particle merging-and-splitting, a simple scheme for robustly handling collisions between particles that prevents inter-penetrations of separate objects without introducing numerical instabilities. This scheme can be used for stable and robust collisions within a particle-based simulation and also for coupling different simulation systems using different and otherwise incompatible integrators.

Interpolation is a core operation that has widespread use in computer graphics. Though higher-order interpolation provides better quality, linear interpolation is often preferred due to its simplicity, performance, and hardware support. We present a unified refactoring of quadratic and cubic interpolations as standard linear interpolation plus linear interpolations of higher-order terms and show how they can be applied to regular grids and (triangular/tetrahedral) simplexes Our formulations can provide significant reduction in computation cost, as compared to typical higher-order interpolations and prior approaches that utilize existing hardware linear interpolation support to achieve higher-order interpolation.

This project explores new algorithms and new hardware architectures for highly realistic computer graphic image synthesis that provides high performance and consume significantly less power than current GPU growth trends. Specifically we focus on Ray Tracing as a rendering algorithm. Ray tracing has well-understood advantages in supporting realistic rendering with high quality composite global lighting effects. It is also highly amenable to parallel processing, albeit utilizing a different type of parallelism than offered by current commercial GPUs. Ray tracing can also be naturally throttled to adjust the image quality given real-time temporal or energy constraints. This is much more difficult with the z-buffer based rendering techniques used by current commercial GPUs.