TABLE OF CONTENTS The global illumination problem is basically a transport problem. Energy emitted by light sources is transported by means of reflections and refractions in a three-dimensional environment. We are interested in the energy equilibrium of the illumination in the environment. Since the human eye is sensitive to radiance values, and since we want to compute photorealistic images, we are primarily interested in radiance values or average radiance values computed over certain areas and solid angles in the scene. The latter means that we should compute flux values for several areas of interest, which will be referred to as sets. The exact geometric shape of these sets can vary substantially, depending on the requested level of accuracy. As will be explained in subsequent chapters, ray tracing algorithms define sets as surface points visible through a pixel, with regard to the aperture of the eye. Radiosity algorithms often define sets as surface patches with the reflecting hemisphere as the directional component (Figure 4.1). Other algorithms might follow different approaches, but the common factor is always that for a number of finite surface elements and solid angle combinations, average radiance values need to be computed.
As explained in Chapter 2, the fundamental transport equation used to describe the global illumination problem is called the rendering equation and was first introduced into the field of computer graphics by Kajiya [85]. The rendering equation describes the...
