Abstract Recent years have seen increasing attention and significant progress in many‐light rendering, a class of methods for efficient computation of global illumination. The many‐light formulation offers a unified mathematical framework for the problem reducing the full lighting transport simulation to the calculation of the direct illumination from many virtual light sources. These methods are unrivaled in their scalability: they are able to produce plausible images in a fraction of a second but also converge to the full solution over time. In this state‐of‐the‐art report, we give an easy‐to‐follow, introductory tutorial of the many‐light theory; provide a comprehensive, unified survey of the topic with a comparison of the main algorithms; discuss limitations regarding materials and light transport phenomena and present a vision to motivate and guide future research. We will cover both the fundamental concepts as well as improvements, extensions and applications of many‐light rendering.

Materials with visually important heterogeneous subsurface scattering, including marble, skin, leaves, and minerals are common in the real world. However, general, accurate, and efficient rendering of these materials is an open problem. In this paper, we describe a finite element (FE) solution of the heterogeneous diffusion equation (DE) that solves this problem. Our algorithm is the first to use the FE method to solve the difficult problem of heterogeneous subsurface rendering. To create our algorithm, we make two contributions. First, we correct previous work and derive an accurate and complete heterogeneous diffusion formulation with two key elements: the diffusive source boundary condition (DSBC)-an accurate model of the reduced intensity (RI) source-and its associated render query function. Second, we solve this formulation accurately and efficiently using the FE method. With these contributions, we can render subsurface scattering with a simple four step algorithm. To demonstrate that our algorithm is simultaneously general, accurate, and efficient, we test its performance on a series of difficult scenes. For a wide range of materials and geometry, it produces, in minutes, images that match path traced references, that required hours.

The radiative transfer framework that underlies all current rendering of volumes is limited to scattering media whose properties are invariant to rotation. Many systems allow for "anisotropic scattering," in the sense that scattered intensity depends on the scattering angle, but the standard equation assumes that the structure of the medium is isotropic. This limitation impedes physics-based rendering of volume models of cloth, hair, skin, and other important volumetric or translucent materials that do have anisotropic structure. This paper presents an end-to-end formulation of physics-based volume rendering of anisotropic scattering structures, allowing these materials to become full participants in global illumination simulations. We begin with a generalized radiative transfer equation, derived from scattering by oriented non-spherical particles. Within this framework, we propose a new volume scattering model analogous to the well-known family of microfacet surface reflection models; we derive an anisotropic diffusion approximation, including the weak form required for finite element solution and a way to compute the diffusion matrix from the parameters of the scattering model; and we also derive a new anisotropic dipole BSSRDF for anisotropic translucent materials. We demonstrate results from Monte Carlo, finite element, and dipole simulations. All these contributions are readily implemented in existing rendering systems for volumes and translucent materials, and they all reduce to the standard practice in the isotropic case.

Abstract This paper presents a new, scalable, single pass algorithm for computing subsurface scattering using the diffusion approximation. Instead of pre‐computing a globally conservative estimate of the surface irradiance like previous two pass methods, the algorithm simultaneously refines hierarchical and adaptive estimates of both the surface irradiance and the subsurface transport. By using an adaptive, top‐down refinement method, the algorithm directs computational effort only to simulating those eye‐surface‐light paths that make significant contributions to the final image. Because the algorithm is driven by image importance, it scales more efficiently than previous methods that have a linear dependence on translucent surface area. We demonstrate that in scenes with many translucent objects and in complex lighting environments, our new algorithm has a significant performance advantage.

We study the well documented problem of systematically navigating the potentially exponentially many roots or realizations of well-constrained, variational geometric constraint systems. We give a scalable method called the Equation and Solution Manager (ESM) that can be used both for automatic searches and visual, user-driven searches for desired realizations. The method incrementally assembles the desired solution of the entire system and avoids combinatorial explosion by offering the user a visual walk-through of the solutions to recursively constructed subsystems and by permitting the user to make gradual, adaptive solution choices.We isolate requirements on companion methods that are essential and desirable for efficient, meaningful solution space navigation. Specifically, they permit (a) incorporation of many existing approaches to solution space steering or navigation into the ESM; and (b) integration of the ESM into a standard geometric constraint solver architecture. We address the latter challenge and explain how the integration is achieved. Additionally, we sketch the ESM implementation as part of an opensource, 2D and 3D geometric constraint solver, FRONTIER.

Multidimensional lightcuts is a new scalable method for efficiently rendering rich visual effects such as motion blur, participating media, depth of field, and spatial anti-aliasing in complex scenes. It introduces a flexible, general rendering framework that unifies the handling of such effects by discretizing the integrals into large sets of gather and light points and adaptively approximating the sum of all possible gather-light pair interactions.We create an implicit hierarchy, the product graph, over the gather-light pairs to rapidly and accurately approximate the contribution from hundreds of millions of pairs per pixel while only evaluating a tiny fraction (e.g., 200--1,000). We build upon the techniques of the prior Lightcuts method for complex illumination at a point, however, by considering the complete pixel integrals, we achieve much greater efficiency and scalability.Our example results demonstrate efficient handling of volume scattering, camera focus, and motion of lights, cameras, and geometry. For example, enabling high quality motion blur with 256x temporal sampling requires only a 6.7x increase in shading cost in a scene with complex moving geometry, materials, and illumination.

Wood coated with transparent finish has a beautiful and distinctive appearance that is familiar to everyone. Woods with unusual grain patterns. such as tiger, burl, and birdseye figures, have a strikingly unusual directional reflectance that is prized for decorative applications. With new, high resolution measurements of spatially varying BRDFs. we show that this distinctive appearance is due to light scattering that does not conform to the usual notion of anisotropic surface reflection. The behavior can be explained by scattering from the matrix of wood fibers below the surface, resulting in a subsurface highlight that occurs on a cone with an out-of-plane axis. We propose a new shading model component to handle reflection from subsurface fibers, which is combined with the standard diffuse and specular components to make a complete shading model. Rendered results from fits of our model to the measurement data demonstrate that this new model captures the distinctive appearance of wood.

Lightcuts is a scalable framework for computing realistic illumination. It handles arbitrary geometry, non-diffuse materials, and illumination from a wide variety of sources including point lights, area lights, HDR environment maps, sun/sky models, and indirect illumination. At its core is a new algorithm for accurately approximating illumination from many point lights with a strongly sublinear cost. We show how a group of lights can be cheaply approximated while bounding the maximum approximation error. A binary light tree and perceptual metric are then used to adaptively partition the lights into groups to control the error vs. cost tradeoff.We also introduce reconstruction cuts that exploit spatial coherence to accelerate the generation of anti-aliased images with complex illumination. Results are demonstrated for five complex scenes and show that lightcuts can accurately approximate hundreds of thousands of point lights using only a few hundred shadow rays. Reconstruction cuts can reduce the number of shadow rays to tens.