This paper presents a rapid hierarchical radiosity algorithm for illuminating scenes containing lar e polygonal patches. The afgorithm constructs a hierarchic“J representation of the form factor matrix by adaptively subdividing patches into su bpatches according to a user-supplied error bound. The algorithm guarantees that all form factors are calculated to the same precision, removing many common image artifacts due to inaccurate form factors. More importantly, the al o-rithm decomposes the form factor matrix into at most O? n) blocks (where n is the number of elements). Previous radiosity algorithms represented the element-to-element transport interactions with n2 form factors. Visibility algorithms are given that work well with this approach. Standard techniques for shooting and gathering can be used with the hierarchical representation to solve for equilibrium radiosities, but we also discuss using a brightness-weighted error criteria, in conjunction with multigrldding, to even more rapidly progressively refine the image.

In a distribution ray tracer, the crucial part of the direct lighting calculation is the sampling strategy for shadow ray testing. Monte Carlo integration with importance sampling is used to carry out this calculation. Importance sampling involves the design of integrand-specific probability density functions which are used to generate sample points for the numerical quadrature. Probability density functions are presented that aid in the direct lighting calculation from luminaires of various simple shapes. A method for defining a probability density function over a set of luminaires is presented that allows the direct lighting calculation to be carried out with one sample, regardless of the number of luminaires. CR Categories and Subject Descriptors: G.1.4 [Mathematical Computing]: Quadrature and Numerical Differentiation; I.3.0 [Computer Graphics]: General; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism. Additional Key Words and Phrases: direct lighting, importanc...

Realistic image generation is presented in a theoretical formulation that builds from previous work on the rendering equation. Previous and new solution techniques for the global illumination are discussed in the context of this formulation. The basic

Several ways of improving the realism of the results of traditional ray tracing are presented. The essential physical quantities of spectral radiant power and spectral radiance and their use in lighting calculations are discussed. Global illumination terms are derived by employing illumination ray tracing for calculation of quickly changing indirect lighting components, and radiosity ray tracing for slowly changing indirect lighting components. Direct lighting is calculated during the viewing phase allowing the use of bump maps. Finally, a method is introduced that reduces the total number of shadow rays to no more than the total number of viewing rays for a given picture. Keywords: Bump Mapping, Illumination, Radiosity, Radiance, Ray Tracing, Realism, Stratified Sampling, Texture Mapping. 1 Introduction The quest for accurate lighting models in computer graphics has taken two very different approaches in the 1980s. The first approach is based on ray tracing (point sampling) techniqu...

Contents Acknowledgements 3 Foreword 9 1 Introduction 11 2 PreviousWork 14 2.1 The Radiosity equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.1 Rendering Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.2 Rendering Equation for diffuse surfaces . . . . . . . . . . . . . . . . . . . . 16 2.1.3 The Radiosity system of equations . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.4 Two forms of the Form Factor integral . . . . . . . . . . . . . . . . . . . . . 18 2.1.5 The Form Factor integral as a contour integral . . . . . . . . . . . . . . . . 18 2.1.6 Differential area to area Form Factor . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Computing the Form Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.1 Deterministic numerical solutions . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3 Monte Carlo evaluation of the Form Factor integral . . . . . . . . . . . . . . . . .

The time complexity of Monte Carlo radiosity is discussed, and a proof is given that the expected number of rays required to produce a statistical radiosity solution below a specified variance for N zones is O(N ). A satisfactory solution is defined to be one in which the variance of radiance estimates for each zone is below a predefined threshold. The proof assumes that the radiance is bounded, and the area ratio of the largest to smallest zone is bounded. 1 Introduction In a radiosity (zonal) program, the surfaces in the environment are broken into N zones, z i , and the radiance, L i , of each zone is calculated [6, 7]. In the most straightforward radiosity method, all N 2 relationships (form-factors) are explicitly calculated, so the time complexity of the program is at least O(N 2 ). One of the first schemes to lower the radiosity calculation time was to group the N zones into p patches, and transfer power from patches to zones (elements) [4]. Still, the computation time wil...

: We propose a method for solving the global illumination problem with no restrictive assumptions concerning the behaviour of light either on surface or volume objects in the scene. Surface objects are defined either by facets or parametric patches and volume objets are defined by voxel grids which define arbitrary density distributions in a discrete tridimensional space. The rendering technique is a Monte-Carlo ray-tracing based radiosity which unifies the processing of objects in a scene, whether they are surfacic or volumic. The main characteristics of our technique are the use of separated Markov chains to prevent the explosion of the number of rays and an optimal importance sampling to speed-up the convergence. Keywords : Global Illumination, Monte-Carlo Ray-Tracing, Importance Sampling, Participating Media. 1 Introduction Solving the global illumination problem is necessary to achieve photorealism in image synthesis [7, 16, 14]. To account for all complex reflection/transmission...

This paper presents a rapid hierarchical radiosity algorithm for illuminating scenes containing large polygonal patches. The algorithm constructs a hierarchical representation of the form factor matrix by adaptively subdividing patches into subpatches according to a user-supplied error bound. The algorithm guarantees that all form factors are calculated to the same precision, removing many common image artifacts due to inaccurate form factors. More importantly, the algorithm decomposes the form factor matrix into at most O(n) blocks (where n is the number of elements). Previous radiosity algorithms represented the element-to-element transport interactions with n 2 form factors. Visibility algorithms are given that work well with this approach. Standard techniques for shooting and gathering can be used with the hierarchical representation to solve for equilibrium radiosities, but we also discuss using a brightness-weighted error criteria, in conjunction with multigridding, to even mor...

This dissertation is a discussion and development of hierarchical algorithms for illumination. These algorithms operate through recursive, adaptive refinement of the environment into hierarchical meshes --- rather than computing light transport only between elements at the finest level of refinement, the algorithms allow computation of transport between higher level subpatches, as controlled by user specified error bounds. As discussed in this dissertation, employment of hierarchical methods yields significant savings in computation. The initial work in hierarchical methods was that of Hanrahan and Salzman for the computation of radiosity over unoccluded environments. In this dissertation, we discuss extension of the algorithm to occluded environments, incorporating visibility heuristics and acceleration via radiosity weighting. Given an environment consisting of k polygonal patches and n elements at the finest level of refinement, the algorithm requires at most O(n + k 2 ) transpor...

The radiosity method models the interaction of light between diffuse surfaces, thereby accurately predicting global illumination effects. Due to the high computational effort to calculate the transfer of light between surfaces and the memory requirements for the scene description, a distributed, parallelized version of the algorithm is needed for scenes consisting of thousands of surfaces. We present