Abstract Spatiotemporal resampling methods such as ReSTIR decrease noise in Monte Carlo rendering of dynamic content by reusing paths across frames and pixels. Standard ReSTIR reuses spatially from a small number of randomly selected neighbors. This reuse suffers when few neighbors contain contributing samples, reducing quality toward that of the underlying path sampler. This commonly occurs during camera or object motion, as regions not present in prior frames are revealed. Increasing the number of spatial neighbors helps but also increases cost. We propose a novel spatial neighbor selection technique, stochastic pairwise MIS, which enables unbiased reuse from many neighbors in real time and focuses reuse on pixels with contributing samples. This provides a significant increase in image quality overall, especially in regions with poor input samples.

Abstract Gradient‐domain rendering accelerates realistic image synthesis by also estimating pixel color differences, which helps reconstruct high frequencies in the image domain. Converged images still require many samples per pixel even with denoising, and to this date, no real‐time gradient‐domain rendering methods have been proposed. We enable gradient‐domain methods in real‐time rendering by spatiotemporal sample reuse with a novel path space extension in gradient image rendering. We further explore this concept by implementing ReSTIR G‐PT, ReSTIR gradient‐domain path tracing, and find that relative sparsity of the gradient image allows highly selective spatial reuse and real‐time frame rates. Our method outperforms the baseline methods visually and statistically.

We present ReSTIR Path Guiding (ReSTIR-PG), a real-time method that extracts guiding distributions from resampled paths produced by ReSTIR and uses them to generate improved initial candidates for the next frame. While ReSTIR significantly reduces variance through spatiotemporal resampling, its effectiveness is ultimately limited by the quality of the initial candidates, which are often poorly distributed and introduce correlation artifacts. Our key observation is that ReSTIR’s accepted paths already approximate the target path contribution density, and that their bounce directions follow the ideal distribution for local path guiding – the product of incident radiance and the cosine-weighted BSDF. We exploit this structure to fit lightweight guiding distributions using each frame’s resampled paths by density estimation. Compared to conventional guiding based on raw path-traced samples, ReSTIR-PG closes the loop between guiding and resampling. Our method achieves lower variance, faster response time to scene change, reduced correlation artifacts, all while preserving real-time performance.

Abstract We present a practical method targeting dynamic shadow maps for many light sources in real‐time rendering. We compute full‐resolution shadow maps for a subset of lights, which we select with spatiotemporal reservoir resampling (ReSTIR). Our selection strategy automatically regenerates shadow maps for lights with the strongest contributions to pixels in the current camera view. The remaining lights are handled using imperfect shadow maps, which provide low‐resolution shadow approximation. We significantly reduce the computation and storage compared to using all full‐resolution shadow maps and substantially improve shadow quality compared to handling all lights with imperfect shadow maps.

Recent spatiotemporal resampling algorithms (ReSTIR) accelerate real-time path tracing by reusing samples between pixels and frames. However, existing methods are limited by the sampling quality of path tracing, making them inefficient for scenes with caustics and hard-to-reach lights. We develop a ReSTIR variant incorporating bidirectional path tracing that significantly improves the sampling quality in these scenes. Combining bidirectional path tracing and ReSTIR introduces multiple challenges: the generalized resampled importance sampling (GRIS) behind ReSTIR is, by default, not aware of how a path was sampled, which complicates reuse of bidirectional paths. Light tracing is also challenging since light subpaths can contribute to all pixels. To address these challenges, we apply GRIS in a sampling technique-aware extended path space, design a bidirectional hybrid shift mapping, and introduce caustics reservoirs that can accumulate caustics across frames. Our method takes around 50ms per frame across our test scenes, and achieves significantly lower error compared to prior unidirectional ReSTIR variants running in equal time.

Computing derivatives of path integrals under evolving scene geometry is a fundamental problem in physics-based differentiable rendering, which requires differentiating discontinuities in the visibility function. Warped-area reparameterization is a powerful technique to compute differential visibility, and key is construction of a velocity field that is continuous in the domain interior and agrees with defined velocities on boundaries. Robustly and efficiently constructing such fields remains challenging. We present a novel velocity field construction for differential visibility. Inspired by recent Monte Carlo solvers for partial differential equations (PDEs), we formulate the velocity field via Laplace's equation and solve it with a walk-on-spheres (WoS) algorithm. To improve efficiency, we introduce a fixed-step WoS that terminates random walks after a fixed step count, resulting in a continuous but non-harmonic velocity field still valid for warped-area reparameterization. Furthermore, to practically apply our method to complex 3D scenes, we propose an efficient cone query to find the closest silhouettes on a boundary. Our cone query finds the closest point under the geodesic distance on a unit sphere, and is analogous to the closest point query by WoS to compute Euclidean distance. As a result, our method generalizes WoS to perform random walks on spherical caps over the unit sphere. We demonstrate that this enables a more robust and efficient unbiased estimator for differential visibility.

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.

Recent advancements in spatiotemporal reservoir resampling (ReSTIR) leverage sample reuse from neighbors to efficiently evaluate the path integral. Like rasterization, ReSTIR methods implicitly assume a pinhole camera and evaluate the light arriving at a pixel through a single predetermined subpixel location at a time (e.g., the pixel center). This prevents efficient path reuse in and near pixels with high-frequency details. We introduce Area ReSTIR , extending ReSTIR reservoirs to also integrate each pixel's 4D ray space, including 2D areas on the film and lens. We design novel subpixel-tracking temporal reuse and shift mappings that maximize resampling quality in such regions. This robustifies ReSTIR against high-frequency content, letting us importance sample subpixel and lens coordinates and efficiently render antialiasing and depth of field.

Recent work on generalized resampled importance sampling (GRIS) enables importance-sampled Monte Carlo integration with random variable weights replacing the usual division by probability density. This enables very flexible spatiotemporal sample reuse, even if neighboring samples (e.g., light paths) have intractable probability densities. Unlike typical Monte Carlo integration, which samples according to some PDF, GRIS instead resamples existing samples. But resampling with GRIS assumes samples have tractable marginal contribution weights, which is problematic if reusing, for example, light subpaths from unidirectionally-sampled paths. Reusing such subpaths requires conditioning by (non-reused) segments of the path prefixes.

Recently, great progress has been made in physics-based differentiable rendering. Existing differentiable rendering techniques typically focus on static scenes, but during inverse rendering---a key application for differentiable rendering---the scene is updated dynamically by each gradient step. In this paper, we take a first step to leverage temporal data in the context of inverse direct illumination. By adopting reservoir-based spatiotemporal resampled importance resampling (ReSTIR), we introduce new Monte Carlo estimators for both interior and boundary components of differential direct illumination integrals. We also integrate ReSTIR with antithetic sampling to further improve its effectiveness. At equal frame time, our methods produce gradient estimates with up to 100× lower relative error than baseline methods. Additionally, we propose an inverse-rendering pipeline that incorporates these estimators and provides reconstructions with up to 20× lower error.

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 resampling algorithms building on Talbot et al.'s [2005] resampled importance sampling (RIS) reuse paths spatiotemporally to render surprisingly complex light transport with a few samples per pixel. These reservoir-based spatiotemporal importance resamplers (ReSTIR) and their underlying RIS theory make various assumptions, including sample independence. 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. We show a path-traced resampler (ReSTIR PT) running interactively on complex scenes, capturing many-bounce diffuse and specular lighting while shading just one path per pixel. With our new theoretical foundation, we can also modify the algorithm to guarantee convergence for offline renderers.

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. A key observation is recognizing that applying cheaper, biased techniques to approximate scattering along candidate paths (during resampling) does not add bias when shading. This allows us to combine transmittance evaluation techniques: cheap approximations where evaluations must occur many times for reuse, and unbiased methods for final, per-pixel evaluation. 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. When paired with denoising, our low-noise sampling helps preserve smaller-scale volumetric details.

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.

Recent rendering advances dramatically reduce the cost of global illumination. But even with hardware acceleration, complex light paths with multiple glossy interactions are still expensive; our new algorithm stores these paths in precomputed light probes and reprojects them at runtime to provide interactivity. Combined with traditional light maps for diffuse lighting our approach interactively renders all light paths in static scenes with opaque objects. Naively reprojecting probes with glossy lighting is memory-intensive, requires efficient access to the correctly reflected radiance, and exhibits problems at occlusion boundaries in glossy reflections. Our solution addresses all these issues. To minimize memory, we introduce an adaptive light probe parameterization that allocates increased resolution for shinier surfaces and regions of higher geometric complexity. To efficiently sample glossy paths, our novel gathering algorithm reprojects probe texels in a view-dependent manner using efficient reflection estimation and a fast rasterization-based search. Naive probe reprojection often sharpens glossy reflections at occlusion boundaries, due to changes in parallax. To avoid this, we split the convolution induced by the BRDF into two steps: we precompute probes using a lower material roughness and apply an adaptive bilateral filter at runtime to reproduce the original surface roughness. Combining these elements, our algorithm interactively renders complex scenes while fitting in the memory, bandwidth, and computation constraints of current hardware.

We further describe and analyze the idea of hashed alpha testing from Wyman and McGuire [1] , which builds on stochastic alpha testing and simplifies stochastic transparency. Typically, alpha testing provides a simple mechanism to mask out complex silhouettes using simple proxy geometry with applied alpha textures. While widely used, alpha testing has a long-standing problem: geometry can disappear entirely as alpha mapped polygons recede with distance. As foveated rendering for virtual reality spreads, this problem worsens as peripheral minification and prefiltering introduce this problem on nearby objects. We first introduce the notion of stochastic alpha testing, which replaces a fixed alpha threshold of ατ = 0.5 with a randomly chosen ατ ∈ [0..1). This entirely avoids the problem of disappearing alpha-tested geometry, but introduces temporal noise. Hashed alpha testing uses a hash function to choose ατ procedurally. With a good hash function and inputs, hashed alpha testing maintains distant geometry without introducing more temporal flicker than traditional alpha testing. We also describe how hashed alpha interacts with temporal antialiasing and applies to alpha-to-coverage and screen-door transparency. Because hashed alpha testing addresses alpha test aliasing by introducing stable sampling, it has implications in other domains where increased sample stability is desirable. We show how our hashed sampling might apply to other stochastic effects.

The papers in this special section are extended versions of four papers from the 2017 ACM Symposium on Interactive 3D Graphics and Games (I3D), the 21st conference in a series starting in 1986. I3D 2017 was held February 25th to 27th, 2017 in San Francisco, California, USA at the Intercontinental Mark Hopkins Hotel.

Renderers apply alpha testing to mask out complex silhouettes using alpha textures on simple proxy geometry. While widely used, alpha testing has a long-standing problem that is underreported in the literature, but observable in commercial games: geometry can entirely disappear as alpha mapped polygons recede with distance. As foveated rendering for virtual reality spreads this problem worsens, as peripheral minification and prefilitering also cause this problem for nearby objects.

Foveated rendering synthesizes images with progressively less detail outside the eye fixation region, potentially unlocking significant speedups for wide field-of-view displays, such as head mounted displays, where target framerate and resolution is increasing faster than the performance of traditional real-time renderers. To study and improve potential gains, we designed a foveated rendering user study to evaluate the perceptual abilities of human peripheral vision when viewing today's displays. We determined that filtering peripheral regions reduces contrast, inducing a sense of tunnel vision. When applying a postprocess contrast enhancement, subjects tolerated up to 2× larger blur radius before detecting differences from a non-foveated ground truth. After verifying these insights on both desktop and head mounted displays augmented with high-speed gaze-tracking, we designed a perceptual target image to strive for when engineering a production foveated renderer. Given our perceptual target, we designed a practical foveated rendering system that reduces number of shades by up to 70% and allows coarsened shading up to 30° closer to the fovea than Guenter et al. [2012] without introducing perceivable aliasing or blur. We filter both pre- and post-shading to address aliasing from undersampling in the periphery, introduce a novel multiresolution- and saccade-aware temporal antialising algorithm, and use contrast enhancement to help recover peripheral details that are resolvable by our eye but degraded by filtering. We validate our system by performing another user study. Frequency analysis shows our system closely matches our perceptual target. Measurements of temporal stability show we obtain quality similar to temporally filtered non-foveated renderings.

We further describe and analyze a real-time system for rendering antialiased hard shadows using irregular z-buffers (IZBs) that we first presented in Wyman et al. [1]. We focus on identifying bottlenecks, exploring these from an algorithmic complexity standpoint, and presenting techniques to improve performance. Our system remains interactive on a variety of game assets and CAD models while running at resolutions 1920 1080 and above and imposes no constraints on light, camera or geometry, allowing fully dynamic scenes without precomputation. We render sub-pixel accurate, 32 sample per pixel hard shadows at roughly twice the cost of a single sample per pixel. This allows us to smoothly animate even subpixel shadows from grass or wires without introducing spatial or temporal aliasing. Prior algorithms for irregular z-buffer shadows rely heavily on the GPU's compute pipeline. Instead we leverage the standard rasterization-based graphics pipeline, including hardware conservative raster and early-z culling. Our key observation is noting a duality between irregular z-buffer performance and shadow map quality; irregular z-buffering is most costly exactly where shadow maps exhibit the worst aliasing. This allows us to use common shadow map algorithms, which typically improve aliasing, to instead reduce our cost. Compared to state of the art ray tracers, we spawn similar numbers of triangle intersections per pixel yet completely rebuild our data structure in under 1 ms per frame.

We present a real-time system that renders antialiased hard shadows using irregular z-buffers (IZBs). For subpixel accuracy, we use 32 samples per pixel at roughly twice the cost of a single sample. Our system remains interactive on a variety of game assets and CAD models while running at 1080p and 2160p and imposes no constraints on light, camera or geometry, allowing fully dynamic scenes without precomputation. Unlike shadow maps we introduce no spatial or temporal aliasing, smoothly animating even subpixel shadows from grass or wires.

Shadow aliasing due to limited storage precision has been plaguing discrete shadowing algorithms for decades. We present a simple method to eliminate false self-shadowing through adaptive depth bias. Unlike existing methods which simply set the weight of the bias based on surface slope or utilize the second nearest surface, we evaluate the bound of bias for each fragment and compute the optimal bias within the bound. Our method introduces small overhead, preserves more shadow details than widely used constant bias and slope scale bias and works for common 2D shadow maps as well as 3D binary shadow volumes.

Rough refraction commonly occurs when light scatters on rough transparent surfaces. It presents a computational challenge, as every pixel's color depends on incoming light from numerous directions. De Rousiers et al. [2011] compute rough refraction interactively using a convolution of Gaussian normal and transmittance distribution functions (NDFs and BTDFs), but their work is limited to a constant roughness surfaces. We introduce two methods that allow for varying roughness by representing surface normals using LEAN mapping and Gaussian sum reduction (GSR).

This tutorial will cover the basics of physically-based rendering such as reflection models (BRDF), volume scattering (phase functions), optical phenomena (dispersion and polarization). It will also cover image formation via basic camera models. A brief summary of popular algorithms will be covered including radiosity, path tracing, photon tracing, and Metropolis Light Transport. The course will end with a more detailed description of adjoint photon tracing so that attendees can later implement their own physically-based renderer.

The three papers in this special section were presented at the Symposium on Interactive 3D Graphics and Games (I3D) that was held in San Francisco, CA, 18-20 February 2011.

No abstract available.

No abstract available.

Current algorithms for rendering shadows inside participating media hit a bottleneck when computing light visibility throughout the media. These algorithms rely either on sampling along viewing rays, often thrashing memory caches, or slower analytic solutions using object-space computations, such as shadow volumes.

Abstract Area lights add tremendous realism, but rendering them interactively proves challenging. Integrating visibility is costly, even with current shadowing techniques, and existing methods frequently ignore illumination variations at unoccluded points due to changing radiance over the light's surface. We extend recent image‐space work that reduces costs by gathering illumination in a multiresolution fashion, rendering varying frequencies at corresponding resolutions. To compute visibility, we eschew shadow maps and instead rely on a coarse screen‐space voxelization, which effectively provides a cheap layered depth image for binary visibility queries via ray marching. Our technique requires no precomputation and runs at interactive rates, allowing scenes with large area lights, including dynamic content such as video screens.

Global illumination provides a visual richness not achievable with the direct illumination models used by most interactive applications. To generate global effects, numerous approximations attempt to reduce global illumination costs to levels feasible in interactive contexts. One such approximation, reflective shadow maps, samples a shadow map to identify secondary light sources whose contributions are splatted into eye space. This splatting introduces significant overdraw that is usually reduced by artificially shrinking each splat's radius of influence. This paper introduces a new multiresolution approach for interactively splatting indirect illumination. Instead of reducing GPU fill rate by reducing splat size, we reduce fill rate by rendering splats into a multiresolution buffer. This takes advantage of the low-frequency nature of diffuse and glossy indirect lighting, allowing rendering of indirect contributions at low resolution where lighting changes slowly and at high-resolution near discontinuities. Because this multiresolution rendering occurs on a per-splat basis, we can significantly reduce fill rate without arbitrarily clipping splat contributions below a given threshold-those regions simply are rendered at a coarse resolution.

We introduce the general pinhole camera (GPC), defined by a center of projection (i.e., the pinhole), an image plane, and a set of sampling locations in the image plane. We demonstrate the advantages of the GPC in the contexts of remote visualization, focus-plus-context visualization, and extreme antialiasing, which benefit from the GPC sampling flexibility. For remote visualization, we describe a GPC that allows zooming-in at the client without the need for transferring additional data from the server. For focus-plus-context visualization, we describe a GPC with multiple regions of interest with sampling rate continuity to the surrounding areas. For extreme antialiasing, we describe a GPC variant that allows supersampling locally with a very high number of color samples per output pixel (e.g., 1,024{\times}), supersampling levels that are out of reach for conventional approaches that supersample the entire image. The GPC supports many types of data, including surface geometry, volumetric, and image data, as well as many rendering modes, including highly view-dependent effects such as volume rendering. Finally, GPC visualization is efficient-GPC images are rendered and resampled with the help of graphics hardware at interactive rates.

Global illumination provides a visual richness not achievable with the direct illumination models used by most interactive applications. To generate global effects, numerous approximations attempt to reduce global illumination costs to levels feasible in interactive contexts. One such approximation, reflective shadow maps, samples a shadow map to identify secondary light sources whose contributions are splatted into eye-space. This splatting introduces significant overdraw that is usually reduced by artificially shrinking each splat's radius of influence. This paper introduces a new, multi-resolution approach for interactively splatting indirect illumination. Instead of reducing GPU fill rate by reducing splat size, we reduce fill rate by rendering splats into a multi-resolution buffer. This takes advantage of the low-frequency nature of diffuse and glossy indirect lighting, allowing rendering of indirect contributions at low resolution where lighting changes slowly and at high resolution near discontinuities. Because this multi-resolution rendering occurs on a per-splat basis, we can significantly reduce fill rate without arbitrarily clipping splat contributions below a given threshold---those regions simply are rendered at a coarse resolution.

Abstract We introduce image‐space radiosity and a hierarchical variant as a method for interactively approximating diffuse indirect illumination in fully dynamic scenes. As oft observed, diffuse indirect illumination contains mainly low‐frequency details that do not require independent computations at every pixel. Prior work leverages this to reduce computation costs by clustering and caching samples in world or object space. This often involves scene preprocessing, complex data structures for caching, or wasted computations outside the view frustum. We instead propose clustering computations in image space, allowing the use of cheap hardware mipmapping and implicit quadtrees to allow coarser illumination computations. We build on a recently introduced multiresolution splatting technique combined with an image‐space lightcut algorithm to intelligently choose virtual point lights for an interactive, one‐bounce instant radiosity solution. Intelligently selecting point lights from our reflective shadow map enables temporally coherent illumination similar to results using more than 4096 regularly‐sampled VPLs.

Abstract Caustic maps provide an interactive image‐space method to render caustics, the focusing of light via reflection and refraction. Unfortunately, caustic mapping suffers problems similar to shadow mapping: aliasing from poor sampling and map projection as well as temporal incoherency from frame‐to‐frame sampling variations. To reduce these problems, researchers have suggested methods ranging from caustic blurring to building a multiresolution caustic map. Yet these all require a fixed photon sampling, precluding the use of importance‐based photon densities. This paper introduces adaptive caustic maps. Instead of densely sampling photons via a rasterization pass, we adaptively emit photons using a deferred shading pass. We describe deferred rendering for refractive surfaces, which speeds rendering of refractive geometry up to 25% and with adaptive sampling speeds caustic rendering up to 200%. These benefits are particularly noticable for complex geometry or using millions of photons. While developed for a GPU rasterizer, adaptive caustic map creation can be performed by any renderer that individually traces photons, e.g., a GPU ray tracer.

Interactive applications typically rely on local models for lighting, occasionally augmented by GPU-friendly methods for approximating global illumination. Caustic mapping approximates the specular focusing of light using a light-space image, akin to a shadow map, which is projected onto the scene during final rendering. Unfortunately, existing caustic map implementations must choose between quality and speed. Quickly generated maps use few photons and look extremely blurry, while sharper maps created from millions of photons only render at a few frames per second. This paper introduces a number of hierarchical enhancements to caustic mapping that allow real-time rendering with high quality caustic maps, even when using maps from multiple light sources. These techniques utilize the geometry processing stage of recent GPUs to avoid processing every photon and to render a pyramidal caustic map that allows photon splats of varying diameters without the increased costs inherent in rasterizing large splats.

A requirement for rendering realistic images interactively is efficiently simulating material properties. Recent techniques have improved the quality for interactively rendering dielectric materials, but have mostly neglected a phenomenon associated with refraction, namely, total internal reflection. We present an algorithm to approximate total internal reflection on commodity graphics hardware using a ray-depth map intersection technique that is interactive and requires no precomputation. Our results compare favorably with ray traced images and improve upon approaches that avoid total internal reflection.

A fundamental challenge for existing shadow map based algorithms is dealing with partially illuminated surfaces. A conventional shadow map built with a pinhole camera only determines a binary light visibility at each point, and this all-or-nothing approach to visibility does not capture penumbral regions. We present an interactive soft shadow algorithm based on a variant of the depth discontinuity occlusion camera, a non-pinhole camera with rays that reach around blockers to sample normally hidden surfaces. Our soft shadow occlusion camera (SSOC) classifies a fragment on a continuum from fully visible to fully hidden, as seen from the light. The SSOC is used directly in fragment illumination computation without building an explicit "soft shadow map." This method renders plausible soft shadows at interactive speeds under fully dynamic conditions.

Interactive applications require simplifications to lighting, geometry, and material properties that preclude many effects encountered in the physical world. Until recently only the most simplistic reflections and refractions could be performed interactively, but state-of-the-art research has lifted some restrictions on such materials. This paper builds upon this work, but examines reflection and refraction from the light's viewpoint to achieve interactive caustics from point sources. Our technique emits photons from the light and stores the results in image-space, similar to a shadow map. We then examine various techniques for gathering these photons, comparing their advantages and disadvantages for rendering caustics. These approaches run interactively on modern GPUs, work in conjunction with existing techniques for rendering specular materials, and produce images competitive with offline renderings using comparable numbers of photons.

We present a mathematical framework for enforcing energy conservation in a bidirectional reflectance distribution function (BRDF) by specifying halfway vector distributions in simple two-dimensional domains. Energy-conserving BRDFs can produce plausible rendered images with accurate reflectance behavior, especially near grazing angles. Using our framework, we create an empirical BRDF that allows easy specification of diffuse, specular, and retroreflective materials. We also present a second BRDF model that is useful for data fitting; although it does not preserve energy, it uses the same halfway vector domain as the first model. We show that this data-fitting BRDF can be used to match measured data extremely well using only a small set of parameters. We believe that this is an improvement over table-based lookups and factored versions of BRDF data.

In many applications, volumetric data sets are examined by displaying isosurfaces, surfaces where the data, or some function of the data, takes on a given value. Interactive applications typically use local lighting models to render such surfaces. This work introduces a method to precompute or lazily compute global illumination to improve interactive isosurface renderings. The precomputed illumination resides in a separate volume and includes direct light, shadows, and interreflections. Using this volume, interactive globally illuminated renderings of isosurfaces become feasible while still allowing dynamic manipulation of lighting, viewpoint and isovalue.

Many interactive applications strive for realistic renderings, but framerate constraints usually limit realism to effects that run efficiently in graphics hardware. One effect largely ignored in such applications is refraction. We introduce a simple, image-space approach to refractions that easily runs on modern graphics cards. Our method requires two passes on a GPU, and allows refraction of a distant environment through two interfaces, compared to current interactive techniques that are restricted to a single interface. Like all image-based algorithms, aliasing can occur in certain circumstances, but the plausible refractions generated with our approach should suffice for many applications.

Bright patterns of light focused via reflective or refractive objects onto matte surfaces are called "caustics". We present a method for rendering dynamic scenes with moving caustics at interactive rates. This technique requires some simplifying assumptions about caustic behavior allowing us to consider it a local spatial property which we sample in a preprocessing stage. Storing the caustic locally limits caustic rendering to a simple lookup. We examine a number of ways to represent this data, allowing us to trade between accuracy, storage, run time, and precomputation time.