ABSTRACT. We present an integral equation which generallzes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient new technique for a wide variety of monte carlo procedures. The resulting renderlng algorithm extends the range of optical phenomena which can be effectively simulated.

In this paper we identify sources of error in global illumination algorithms and derive bounds for each distinct category. Errors arise from three sources: inaccuracies in the boundary data, discretization, and computation. Boundary data consist of surface geometry, reflectance functions, and emission functions, all of which may be perturbed by errors in measurement or simulation, or by simplifications made for computational efficiency. Discretization error is introduced by replacing the continuous radiative transfer equation with a finite-dimensional linear system, usually by means of boundaryelements and a corresponding projection method. Finally, computational errors perturb the finite-dimensional linear system through imprecise form factors, inner products, visibility, etc., as well as by halting iterative solvers after a finite number of steps. Using the error taxonomy introduced in the paper we examine existing global illumination algorithms and suggest new avenues of research. ...

We describe the basis of the work he have currently under way to implement a new rendering algorithm called light-driven global illumination. This algorithm is a departure from conventional raytracing and radiosity renderers which addresses a number of deficiencies intrinsic to those approaches. 1 Introduction In computer graphics, we use illumination -- the study of how light interacts with matter to produce visible scenes -- to produce realistic images. Illumination encompasses both local and global phenomena. Local illumination describes the interaction of light with a single, small volume or surface element with given incident and viewing directions. We take the fundamental equation describing local illumination to be L = L e + Z \Omega R N f r (S 0 ; V)L i jN \Delta S 0 j d! 0 i + Z \Omega T N f t (S 0 ; V)L i jN \Delta S 0 j d! 0 i (1) where N is the surface normal, L is the total radiance given off (either L r , reflected, or L t , transmitted) in direct...

We present a new method for efficiently simulating the scattering of light within participating media. Using a theoretical reformulation of volumetric photon mapping, we develop a novel photon gathering technique for participating media. Traditional volumetric photon mapping samples the in-scattered radiance at numerous points along the length of a single ray by performing costly range queries within the photon map. Our technique replaces these multiple point-queries with a single beam-query, which explicitly gathers all photons along the length of an entire ray. These photons are used to estimate the accumulated in-scattered radiance arriving from a particular direction and need to be gathered only once per ray. Our method handles both fixed and adaptive kernels, is faster than regular volumetric photon mapping, and produces images with less noise.

Abstract: The problem of global illumination is virtually synonymouswith solving the rendering equation. Although a great deal of research has been directed toward Monte Carlo and finite element methods for solving the rendering equation, little is known about the continuous equation beyond the existence and uniqueness of its solution. The continuous problem may be posed in terms of linear operators acting on infinite-dimensional function spaces. Such operators are fundamentally different from their finite-dimensional counterparts, and are properly studied using the methods of functional analysis. This paper summarizes some of the basic concepts of functional analysis and shows how these concepts may be applied to a linear operator formulation of the rendering equation. In particular, operator norms are obtained from thermodynamic principles, and a number of common function spaces are shown to be closed under global illumination. Finally, several fundamental operators that arise in global illumination are shown to be nearly finite-dimensional in that they can be uniformly approximated by matrices. 1

Traditional methods for evaluating the low-albedo volume rendering integral do not include bounds on the magnitude of approximation error. In this paper, we examine three techniques for solving this integral with error bounds: trapezoid rule, Simpson's rule, and a power series method. In each case, the expression for the error bound provides a mechanism for computing the integral to any specified precision. The formulations presented are appropriate for polynomial reconstruction from point samples; however, the approach is considerably more general. The three techniques we present differ in relative efficiency for computing results to a given precision. The trapezoid rule and Simpson's rule are most efficient for low- to medium-precision solutions. The power series method converges rapidly to a machine precision solution, providing both an efficient means for high-accuracy volume rendering, and a reference standard by which other approximations may be measured. CR Categoriesand Subject...

In this article we present a novel radiance caching method for efficiently rendering participating media using Monte Carlo ray tracing. Our method handles all types of light scattering including anisotropic scattering, and it works in both homogeneous and heterogeneous media. A key contribution in the article is a technique for computing gradients of radiance evaluated in participating media. These gradients take the full path of the scattered light into account including the changing properties of the medium in the case of heterogeneous media. The gradients can be computed simultaneously with the inscattered radiance with negligible overhead. We compute gradients for single scattering from lights and surfaces and for multiple scattering, and we use a spherical harmonics representation in media with anisotropic scattering. Our second contribution is a new radiance caching scheme for participating media. This caching scheme uses the information in the radiance gradients to sparsely sample as well as interpolate radiance within the medium utilizing a novel, perceptually based error metric. Our method provides several orders of magnitude speedup compared to path tracing and produces higher quality results than volumetric photon mapping. Furthermore, it is view-driven and well suited for large scenes where methods such as photon mapping become costly.

Subsurface scattering and light transport in volumetric media are critical to achieve a realistic depiction of a material. We describe several analytical approximations and methods for volumetric light transport in media of various optical properties that are efficient and easy to compute. Most natural materials exhibit a sudden surge in brightness called the opposition effect around the zero phase angle, where incident and viewing directions coincide. We present an approximation to the opposition effect in a particulate medium using a few physically realistic mathematical approximations. These analytical approximations can be used as tools or as a starting point for modeling the appearance of complex volumetric materials such as biological materials(skin, leaves) or inorganic materials (snow, clouds, rocks, paint). We demonstrate these approximations for several natural materials that exhibit substantial volumetric light transport and show how to use them to model complex materials.

We present a framework for knitwear modeling and rendering that accounts for characteristics that are particular to knitted fabrics. We first describe a model for animation that considers knitwear features and their effects on knitwear shape and interaction. With the computed free-form knitwear configurations, we present an efficient procedure for realistic synthesis based on the observation that a single cross-section of yarn can serve as the basic primitive for modeling entire articles of knitwear. This primitive, called the lumislice, describes radiance from a yarn cross-section that accounts for fine-level interactions among yarn fibers. By representing yarn as a sequence of identical but rotated cross-sections, the lumislice can effectively propagate local microstructure over arbitrary stitch patterns and knitwear shapes. The lumislice accommodates varying levels of detail, allows for soft shadow generation, and capitalizes on hardware-assisted transparency blending. These modeling and rendering techniques together form a complete approach for generating realistic knitwear. Index terms: knitwear, image-based rendering, photorealistic rendering, animation models, parametric surfaces, transparency blending 1

We present two contributions to the area of volumetric rendering. We develop a novel, comprehensive theory of volumetric radiance estimation that leads to several new insights and includes all previously published estimates as special cases. This theory allows for estimating in-scattered radiance at a point, or accumulated radiance along a camera ray, with the standard photon particle representation used in previous work. Furthermore, we generalize these operations to include a more compact, and more expressive intermediate representation of lighting in participating media, which we call “photon beams. ” The combination of these representations and their respective query operations results in a collection of nine distinct volumetric radiance estimates. Our second contribution is a more efficient rendering method for participating media based on photon beams. Even when shooting and storing less photons and using less computation time, our method significantly reduces both bias (blur) and variance in volumetric radiance estimation. This enables us to render sharp lighting details (e.g. volume caustics) using just tens of thousands of photon beams, instead of the millions to billions of photon points required with previous methods.