## Chapter 31. Computing Solutions to the Rendering Equation: Theoretical Approaches

### 31.1. Introduction

In this chapter we discuss the theory of solving the rendering equation, concentrating on the mathematics of various approaches and on what kinds of approximations are involved in these approaches, deferring the implementation details to the next chapter. Fortunately, much of the mathematics can be understood by analogy with far simpler problems. When we render, we’re trying to compute values of *L*, the radiance field, or expressions involving combinations (typically integrals) of many values of *L*. Thus, the unknown is the whole *function L*. That’s in sharp contrast to the equations like

that we see in algebra class, where the unknown, *x*, is a ...