On the Importance of Sampling

Abstract

With the recent arrival of ray tracing to the real-time graphics pipeline, developers are faced with a new challenge: figuring out how to make the most of the rays that they’re able to trace. One important question to decide is for which lighting effects to trace rays—choices include shadows, reflections, ambient occlusion, and full global illumination.

Another important question is how to choose which rays to trace for the chosen effect; an introduction to that question is the topic of this chapter. In the following, we will see how most lighting calculations in rendering can be interpreted as estimating the values of integrals and how tracing rays is a natural fit to an effective numerical integration technique: Monte Carlo. Given some background in Monte Carlo integration, we then see how well-chosen rays can dramatically improve the speed of convergence, which in turn can either improve overall system performance—by getting the same quality result for fewer rays—or improve image quality—by getting lower error from the same number of rays.