# 13 Light Transport I: Surface Reflection

This chapter brings together the ray-tracing algorithms, radiometric
concepts, and Monte Carlo sampling algorithms of the previous chapters to
implement two different integrators that compute scattered radiance from
surfaces in the scene. These integrators are much more effective than the
`RandomWalkIntegrator` from the first chapter; with them, some scenes
are rendered with hundreds of times lower error.

We start by deriving the light transport equation, which was first introduced in
Section 1.2.6. We can then formally
introduce the path-tracing algorithm, which applies Monte Carlo integration
to solve that equation. We will then describe the implementation of the
`SimplePathIntegrator`, which provides a
pared-down implementation of path tracing that is useful for understanding
the basic algorithm and for debugging sampling algorithms. The chapter
concludes with the `PathIntegrator`, which is a more complete path
tracing implementation.

Both of these integrators find light-carrying paths starting from the camera, accounting for scattering from shapes’ surfaces. Chapter 14 will extend path tracing to include the effects of participating media. (The online edition of this book also includes a chapter that describes bidirectional methods for constructing light-carrying paths starting both from the camera and from light sources.)