# Reading Veach’s Thesis

If you’ve studied path tracing or physically-based rendering in the last twenty years, you’ve probably heard of Eric Veach. His Ph.D thesis, published in 1997, has been hugely influential in Monte Carlo rendering. Veach introduced key techniques like multiple importance sampling and bidirectional path tracing, and clarified a lot of the mathematical theory behind Monte Carlo rendering. These ideas not only inspired a great deal of later research, but are still used in production renderers today.

Recently, I decided to sit down and read this classic thesis in full. Although I’ve seen expositions of the central ideas in other places such as PBR, I’d never gone back to the original source. The thesis is available from Stanford’s site (scroll down to the very bottom for PDF links). It’s over 400 pages—a textbook in its own right—but I’ve found it very readable, with clearly presented ideas and incisive analysis. There’s a lot of formal math, too, but you don’t really need more than linear algebra, calculus, and some probability theory to understand it. I’m only about halfway through, but there’s already been some really interesting bits that I’d like to share. So hop in, and let’s read Veach’s thesis together!