TABLE OF CONTENTS The algorithms discussed in Sections 6.3 and 6.4 solved the radiosity system of linear equations (Equation 6.6) stochastically. By sampling according to the form factors, the numerical value for the form factors was never needed. In this section, we will discuss a number of random walk methods that are highly related to those of Section 6.4, but that solve the radiosity integral equation (Equation 6.3), or the general rendering equation (Equation 6.2), rather than the radiosity system of equations. Indeed, just like discrete random walks are used to solve linear systems, random walks in a continuous state space can be used to solve integral equations like the radiosity or rendering integral equation. They are, therefore, sometimes also called continuous random walk radiosity methods.
The random walks that are introduced in this section are nothing but simulated trajectories of photons emitted by light sources and bouncing throughout a scene, as dictated by the laws of light emission and scattering described in Chapter 2. The surface hit points of these photons are recorded in a data structure, for later use. An essential property of such particle hit points is that their density at any given location (the number of hits per unit of area) is proportional to the radiosity at that location (Section 6.5.1). This density can be estimated at any surface location where this needs to be done, by means of density estimation methods known from statistics [175]. The basic density estimation methods that...
