The goal of rendering algorithms is to create images that accurately represent the appearance of objects in scenes. For every pixel in an image, these algorithms must find the objects that are visible at that pixel and then display their appearance to the user. What does the term appearance mean? What quantity of light energy must be measured to capture appearance ? How is this energy computed? These are the questions that this chapter will address.

In this chapter, we present key concepts and definitions required to formulate the problem that global illumination algorithms must solve. In Section 2.1, we present a brief history of optics to motivate the basic assumptions that rendering algorithms make about the behavior of light (Section 2.2). In Section 2.3, we define radiometric terms and their relations to each other. Section 2.4 describes the sources of lights in scenes; in Section 2.5, we present the bidirectional distribution function, which captures the interaction of light with surfaces. Using these definitions, we present the rendering equation in Section 2.6, a mathematical formulation of the equilibrium distribution of light energy in a scene. We also formulate the notion of importance in Section 2.7. Finally, in Section 2.8, we present the measurement equation, which is the equation that global illumination algorithms must solve to compute images. In the rest of this book, we will discuss how global illumination algorithms solve the measurement equation.