Abstract Modeling the wave nature of light and the propagation and diffraction of electromagnetic fields is crucial for the accurate simulation of many phenomena, yet wave simulations are significantly more computationally complex than classical ray‐based models. In this work, we start by analyzing the classical path integral formulation of light transport and rigorously study which wave‐optical phenomena can be reproduced by it. We then introduce a bilinear path integral generalization for wave‐optical light transport that models the wave interference between paths. This formulation subsumes many existing methods that rely on shooting‐bouncing rays or UTD‐based diffractions, and serves to give insight into the challenges of such approaches and the difficulty of sampling good paths in a bilinear setting. With this foundation, we develop a weakly‐local path integral based on region‐to‐region transport using elliptical cones that allows sampling individual paths that still model wave effects accurately. As with the classic path integral form of the light transport equation, our path integral makes it possible to derive a variety of practical transport algorithms. We present a complete system for wave tracing with elliptical cones, with applications in light transport for rendering and efficient simulation of long‐wavelength radiation propagation and diffraction in complex environments.

Sampling strategies in computer graphics have long been divided between local approaches, which optimize sample distributions independently at each pixel, and global approaches, which use high-dimensional low-discrepancy sequences to ensure uniformity across all dimensions, including adjacent pixels. While global samplers are most-commonly used thanks to generally having better convergence rates, it comes at a cost of very limited user control over the distribution of samples on subspaces, making it difficult to handle common aliasing artifacts. We introduce a novel modular meta-sampler architecture that bridges local and global sampling, allowing integrator designers to employ specialized low-dimensional samplers while still achieving high-dimensional uniformity. Our approach leverages high-dimensional low-discrepancy sequences to orchestrate sample generation by a collection of local samplers operating over power-of-two hierarchical intervals. We demonstrate how existing local sampling techniques, including stratified, blue noise, and dyadic nets sampling, can be reformulated to be used with this framework, enabling hybrid sampling strategies that combine the benefits of both paradigms.

Low-discrepancy sequences have seen widespread adoption in computer graphics thanks to the superior rates of convergence that they provide. Because rendering integrals often are comprised of products of lower-dimensional integrals, recent work has focused on developing sequences that are also well-distributed in lower-dimensional projections. To this end, we introduce a novel construction of binary-based (0, 4)-sequences; that is, progressive fully multi-stratified sequences of 4D points, and extend the idea to higher power-of-two dimensions. We further show that not only it is possible to nest lower-dimensional sequences in higher-dimensional ones—for example, embedding a (0, 2)-sequence within our (0, 4)-sequence—but that we can ensemble two (0, 2)-sequences into a (0, 4)-sequence, four (0, 4)-sequences into a (0,16)-sequence, and so on. Such sequences can provide excellent rates of convergence when integrals include lower-dimensional integration problems in 2, 4, 16,... dimensions. Our construction is based on using 2×2 block matrices as symbols to construct larger matrices that potentially generate a sequence with the target (0, s )-sequence in base s property. We describe how to search for suitable alphabets and identify two distinct, cross-related alphabets of block symbols, which we call s and z , hence SZ for the resulting family of sequences. Given the alphabets, we construct candidate generator matrices and search for valid sets of matrices. We then infer a simple recurrence formula to construct full-resolution (64-bit) matrices. Because our generator matrices are binary, they allow highly-efficient implementation using bitwise operations and can be used as a drop-in replacement for Sobol matrices in existing applications. We compare SZ sequences to state-of-the-art low discrepancy sequences, and demonstrate mean relative squared error improvements up to 1.93× in common rendering applications.

Monte Carlo rendering algorithms often utilize correlations between pixels to improve efficiency and enhance image quality. For real-time applications in particular, repeated reservoir resampling offers a powerful framework to reuse samples both spatially in an image and temporally across multiple frames. While such techniques achieve equal-error up to 100× faster for real-time direct lighting [Bitterli et al. 2020 ] and global illumination [Ouyang et al. 2021 ; Lin et al. 2021 ], they are still far from optimal. For instance, spatiotemporal resampling often introduces noticeable correlation artifacts, while reservoirs holding more than one sample suffer from impoverishment in the form of duplicate samples. We demonstrate how interleaving Markov Chain Monte Carlo (MCMC) mutations with reservoir resampling helps alleviate these issues, especially in scenes with glossy materials and difficult-to-sample lighting. Moreover, our approach does not introduce any bias, and in practice, we find considerable improvement in image quality with just a single mutation per reservoir sample in each frame.

Free-space diffractions are an optical phenomenon where light appears to "bend" around the geometric edges and corners of scene objects. In this paper we present an efficient method to simulate such effects. We derive an edge-based formulation of Fraunhofer diffraction, which is well suited to the common (triangular) geometric meshes used in computer graphics. Our method dynamically constructs a free-space diffraction BSDF by considering the geometry around the intersection point of a ray of light with an object, and we present an importance sampling strategy for these BSDFs. Our method is unique in requiring only ray tracing to produce free-space diffractions, works with general meshes, requires no geometry preprocessing, and is designed to work with path tracers with a linear rendering equation. We show that we are able to reproduce accurate diffraction lobes, and, in contrast to any existing method, are able to handle complex, real-world geometry. This work serves to connect free-space diffractions to the efficient path tracing tools from computer graphics.

Ray optics is the foundation of modern path tracing and sampling algorithms for computer graphics; crucially, it allows high-performance implementations based on ray tracing. However, many applications of interest in computer graphics and computational optics demand a more precise understanding of light: as waves. For example, accurately modelling scattering effects like diffraction or interference requires a model that provides the coherence of light waves arriving at surfaces. While recent work in Physical Light Transport [Steinberg et al. 2022; Steinberg and Yan 2021] has introduced such a model, it requires tracing light paths starting from the light sources, which is often less efficient than tracing them from the sensor, and does not allow the use of many effective importance sampling techniques. We introduce a new model for wave optical light transport that is based on the fact that sensors aggregate the measurement of many light waves when capturing an image. This allows us to compactly represent the statistics of light waves in a generalized ray. Generalized rays allow sampling light paths starting from the sensor and applying sophisticated path tracing sampling techniques while still accurately modelling the wave nature of light. Our model is computationally efficient and straightforward to add to an existing path tracer; this offers the prospect of wave optics becoming the foundation of most renderers in the future. Using our model, we show that it is possible to render complex scenes under wave optics with high performance, which has not been possible with any existing method.

We present a novel algorithm for implementing Owen-scrambling, combining the generation and distribution of the scrambling bits in a single self-contained compact process. We employ a context-free grammar to build a binary tree of symbols, and equip each symbol with a scrambling code that affects all descendant nodes. We nominate the grammar of adaptive regular tiles (ART) derived from the repetition-avoiding Thue-Morse word, and we discuss its potential advantages and shortcomings. Our algorithm has many advantages, including random access to samples, fixed time complexity, GPU friendliness, and scalability to any memory budget. Further, it provides two unique features over known methods: it admits optimization, and it is in-vertible, enabling screen-space scrambling of the high-dimensional Sobol sampler.

Abstract Even with the advent of hardware‐accelerated ray tracing in modern GPUs, only a small number of rays can be traced at each pixel in real‐time applications. This presents a significant challenge for path tracing, even when augmented with state‐of‐the art denoising algorithms. While the recently‐developed ReSTIR algorithm [BWP∗20] enables high‐quality renderings of scenes with millions of light sources using just a few shadow rays at each pixel, there remains a need for effective algorithms to sample indirect illumination. We introduce an effective path sampling algorithm for indirect lighting that is suitable to highly parallel GPU architectures. Building on the screen‐space spatio‐temporal resampling principles of ReSTIR, our approach resamples multi‐bounce indirect lighting paths obtained by path tracing. Doing so allows sharing information about important paths that contribute to lighting both across time and pixels in the image. The resulting algorithm achieves a substantial error reduction compared to path tracing: at a single sample per pixel every frame, our algorithm achieves MSE improvements ranging from 9.3× to 166× in our test scenes. In conjunction with a denoiser, it leads to high‐quality path traced global illumination at real‐time frame rates on modern GPUs.

Abstract We introduce a Monte Carlo importance sampling method for integrands composed of products and show its application to rendering where direct sampling of the product is often difficult. Our method is based on warp functions that operate on the primary samples in [0,1)n, where each warp approximates sampling a single factor of the product distribution. Our key insight is that individual factors are often well‐behaved and inexpensive to fit and sample in primary sample space, which leads to a practical, efficient sampling algorithm. Our sampling approach is unbiased, easy to implement, and compatible with multiple importance sampling. We show the results of applying our warps to projected solid angle sampling of spherical triangles, to sampling bilinear patch light sources, and to sampling glossy BSDFs and area light sources, with efficiency improvements of over 1.6× on real‐world scenes.

Efficiently rendering direct lighting from millions of dynamic light sources using Monte Carlo integration remains a challenging problem, even for off-line rendering systems. We introduce a new algorithm---ReSTIR---that renders such lighting interactively, at high quality, and without needing to maintain complex data structures. We repeatedly resample a set of candidate light samples and apply further spatial and temporal resampling to leverage information from relevant nearby samples. We derive an unbiased Monte Carlo estimator for this approach, and show that it achieves equal-error 6×-60× faster than state-of-the-art methods. A biased estimator reduces noise further and is 35×-65× faster, at the cost of some energy loss. We implemented our approach on the GPU, rendering complex scenes containing up to 3.4 million dynamic, emissive triangles in under 50 ms per frame while tracing at most 8 rays per pixel.

Abstract Distributions of samples play a very important role in rendering, affecting variance, bias and aliasing in Monte‐Carlo and Quasi‐Monte Carlo evaluation of the rendering equation. In this paper, we propose an original sampler which inherits many important features of classical low‐discrepancy sequences (LDS): a high degree of uniformity of the achieved distribution of samples, computational efficiency and progressive sampling capability. At the same time, we purposely tailor our sampler in order to improve its spectral characteristics, which in turn play a crucial role in variance reduction, anti‐aliasing and improving visual appearance of rendering. Our sampler can efficiently generate sequences of multidimensional points, whose power spectra approach so‐called Blue‐Noise (BN) spectral property while preserving low discrepancy (LD) in certain 2‐D projections. In our tile‐based approach, we perform permutations on subsets of the original Sobol LDS. In a large space of all possible permutations, we select those which better approach the target BN property, using pair‐correlation statistics. We pre‐calculate such “good” permutations for each possible Sobol pattern, and store them in a lookup table efficiently accessible in runtime. We provide a complete and rigorous proof that such permutations preserve dyadic partitioning and thus the LDS properties of the point set in 2‐D projections. Our construction is computationally efficient, has a relatively low memory footprint and supports adaptive sampling. We validate our method by performing spectral/discrepancy/aliasing analysis of the achieved distributions, and provide variance analysis for several target integrands of theoretical and practical interest.

We present a system for acquiring, processing, and rendering panoramic light field still photography for display in Virtual Reality (VR). We acquire spherical light field datasets with two novel light field camera rigs designed for portable and efficient light field acquisition. We introduce a novel real-time light field reconstruction algorithm that uses a per-view geometry and a disk-based blending field. We also demonstrate how to use a light field prefiltering operation to project from a high-quality offline reconstruction model into our real-time model while suppressing artifacts. We introduce a practical approach for compressing light fields by modifying the VP9 video codec to provide high quality compression with real-time, random access decompression. We combine these components into a complete light field system offering convenient acquisition, compact file size, and high-quality rendering while generating stereo views at 90Hz on commodity VR hardware. Using our system, we built a freely available light field experience application called Welcome to Light Fields featuring a library of panoramic light field stills for consumer VR which has been downloaded over 15,000 times.

research-article Free Access Share on Guest Editor's Introduction: Special Issue on Production Rendering Author: Matt Pharr Google, Inc., Mountain View, CA Google, Inc., Mountain View, CAView Profile Authors Info & Claims ACM Transactions on GraphicsVolume 37Issue 3June 2018 Article No.: 28pp 1–4https://doi.org/10.1145/3212511Published:27 July 2018Publication History 4citation1,611DownloadsMetricsTotal Citations4Total Downloads1,611Last 12 Months89Last 6 weeks5 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteView all FormatsPDF

We describe a new mathematical framework for solving a wide variety of rendering problems based on a non-linear integral scattering equation. This framework treats the scattering functions of complex aggregate objects as first-class rendering primitives; these scattering functions accurately account for all scattering events inside them. We also describe new techniques for computing scattering functions from the composition of scattering objects. We demonstrate that solution techniques based on this new approach can be more efficient than previous techniques based on radiance transport and the equation of transfer and we apply these techniques to a number of problems in rendering scattering from complex surfaces.

Modeling and rendering of natural scenes with thousands of plants poses a number of problems. The terrain must be modeled and plants must be distributed throughout it in a realistic manner, reflecting the interactions of plants with each other and with their environment. Geometric models of individual plants, consistent with their positions within the ecosystem, must be synthesized to populate the scene. The scene, which may consist of billions of primitives, must be rendered efficiently while incorporating the subtleties of lighting in a natural environment. We have developed a system built around a pipeline of tools that address these tasks. The terrain is designed using an interactive graphical editor. Plant distribution is determined by hand (as one would do when designing a garden), by ecosystem simulation, or by a combination of both techniques. Given parametrized procedural models of individual plants, the geometric complexity of the scene is reduced by approximate instancing, in which similar plants, groups of plants, or plant organs are replaced by instances of representative objects before the scene is rendered. The paper includes examples of visually rich scenes synthesized using the system.

Simulating realistic lighting and rendering complex scenes are usually considered separate problems with incompatible solutions. Accurate lighting calculations are typically performed using ray tracing algorithms, which require that the entire scene database reside in memory to perform well. Conversely, most systems capable of rendering complex scenes use scan-conversion algorithms that access memory coherently, but are unable to incorporate sophisticated illumination. We have developed algorithms that use caching and lazy creation of texture and geometry to manage scene complexity. To improve cache performance, we increase locality of reference by dynamically reordering the rendering computation based on the contents of the cache. We have used these algorithms to compute images of scenes containing millions of primitives, while storing ten percent of the scene description in memory. Thus, a machine of a given memory capacity can render realistic scenes that are an order of magnitude more complex than was previously possible.