A Survey of Radiosity and Ray-tracing Methods in Global Illumination

This paper surveys Radiosity and Ray-tracing methods used in global illumination. Global illumination is based on light transport mechanism in real world. The light transport mechanism can be expressed in terms of BRDF of each element, and the most common and practical way is dividing the BRDF into specular and diffuse component. Mathematically Global illumination is a problem of solving numerical equations concerning with the convergence, converging speed and if it converges to right answer. The initial value is the given light sources and their characteristics. The energy of the light source is propagated into the geometrical space. The Radiosity and Ray-tracing methods are used to calculate the energy propagation in each iteration step. The BRDF of geometrical element is important to the efficiency of each method. If the BRDF is ideal diffuse, Radiosity method will converge and converge to right answer. However, Raytracing algorithm works more efficiently in calculating specular reflection, refraction and caustic surfaces. Those Radiosity and Ray-tracing algorithms can be measured in two aspects, the accuracy and efficiency in BRDF simulation and the rendering speed. Introduction The Global illumination techniques are inspired by Radiosity method. It’s a robust method to ideal diffuse inter-reflection within a closed environment. The environment is subdivided into patches or elements, over which the intensity of light is constant. A hemicube method is exploited to calculate form factor—measurement of any other patch’s contribution. Kajia established a concrete equation for the global illumination. The early works in Radiosity method is to find out more efficient and accurate way to calculate form-factors. Instead of hemi-cube method, Wallace introduced a ray-tracing method to calculate form factor, while eliminating the aliasing and inadequate sampling problems in hemi-cube method. Meanwhile Baum et al. introduced an analytically determined form factor calculation method when the traditional hemi-cube method can not treat well. Global illumination problem can be seen through the BRDF measurement. If we consider the light transport mechanism in two patches, there would be four types of transfer mechanisms: diffuse to diffuse, diffuse to specular, specular to specular, specular to diffuse. The former radiosity methods only dealt with diffuse to diffuse reflection. A twopass solution combining Enhanced Ray-tracing and Enhanced Radiosity method is used to solve the specular and diffuse reflection in global illumination. Path tracing method suggested by kajia is a non-uniform importance sampling in infinite ray-space. And the variance reduction techniques are used to control sampling rates. Later, Sillion extended the two-pass method, which overcome the limitation of planar specular surface and included any number of specular reflections and refraction in its path. An alternative trend in radiosity is progressive refinement method. Instead of calculating final radiance at each patch, update radiosity of every patch in each step. Chen extended progressive refinement method to an interactive system, which allows incremental rendering with changing geometry and lighting condition. Recently, an interactive updating of global illumination using line-space hierarchy introduced by Drettakis. Global illumination method, in another viewpoint, is a kind of finite element method. Some traditional techniques used by Finite element method are also useful in global illumination. The error associated with each patch should be at the same level. Baum et al. Suggested an automatic meshing technique to generate accurate radiosity solution. Pat Harahan presented a rapid hierarchical radiosty algorithms for illuminating scenes with large patches. This paper will concentrate on light transport and calculation models using ray-tracing method to generate global illumination. Gregory Ward introduced an efficient ray tracing method to calculate interreflection between diffuse and specular component. It’s based on important sampling of light source and adaptive calculation of diffuse interreflection using Monte Carlo ray-tracing. It’s also used caching mechanism for reuse pre rendered radiance in the successive frames. Monte Carlo method is inefficient in most cases and Eric Veach proposed a metropolis sampling method incorporated with Monte Carlo Ray Tracing. Metropolis method generates a sequence of light path and randomly mutates a single current path, and each mutation is accepted or reject by a probability function. To render a participating media Eric Lafortune and Yves D. Willems suggested a technique integrating light shooting and gathering for participating media. Henrik Wann Jenson and Per H. Christensen introduced a photon map algorithm to simulate light transport in scenes. It’s also used bi-directional Monte Carlo ray tracing with photon maps to increase the efficiency and reduced the noise. In the following chapters, we will describe fundamental issues in global illumination and compare various techniques in ray tracing global illumination methods. We will mainly choose the hem-cube method, two-pass method, extended two pass method for the fundamental issues, and compare Kaija’s path tracing method, Radiance method, Metropolis light tracing, bi-directional light tracing and photon map method. Definition and Solutions Rendering equation suggested by Kajia set a concrete framework to solve the global illumination problem. The transport intensity light from one surface point to another is simply the sum of emitted light and the total light intensity which is scattered toward viewing point from all other surface points. To solve this equation we should take into account the reflectance model of each surface patch. So the analysis of BRDF should be accomplished. BRDF is the abbreviation of bidirectional reflectance distribution function. The main characteristics of BRDF is positive, symmetric and energy conserving. To solve the problem practically, most works have divided the surface reflectance to Diffuse and specular component. Later, people also pay attention to the light transporting among non-uniform media. [ ] ∫ ′ ′ ′ ′ ′ ′ ′ ′ + ′ ′ = ′ s x d x x I x x x x x x x g x x I ) , ( ) , , ( , ( ) , ( ) , ( ρ ε θ cos ) , , ’ ( ) , , ( w x w w w x w fr = ′ Radiosity and Ray tracing algorithms exploited in global illumination can be measured with their solution to the surface BRDF. We can classify the major solutions into a table illustrating the capability of each method dealing with BRDF and its complexity. Category BRDF and its complexity Solutions Radiosity Diffuse only Hemi-cube Radiosity Progressive Radiosty Analytical form-factor method Radiosity and ray tracing Diffuse and specular (planar surface only) and single pass Two-pass method Diffuse and specular (nonplanar surface) multi pass General Two-pass method Forward statistic ray tracing enables caustic Kajia’s Path tracing Diffuse and specular (nonplanar surface) deterministic forward ray tracing Radiance method Forward and backward combination Bi-directional path tracing Path mutation in ray tracing Metropolis light transfer method Ray tracing (for solving the diffuse component, various techniques are suggested) Bi-directional Photon tracing Photon map method However, these solutions have common interest in some points. One major thing is important sampling. To solve a problem using iteration or numerical integration, the variables with large value should be considered first. It is a kind of importance sampling. The other thing is error level adjustment. For the radiosity method, it presented as hierarchical or meshing techniques. In ray tracing, it is represented as ray path level and ray sampling rates. We will discuss these solutions in some detail.