In 1991, I took a leave of absence to attend Princeton University and work on a PhD in Computer Science. A respected colleague, Pat Hanrahan, had recently left Pixar and joined the faculty at Princeton. He invited me to come and do research at Princeton and get another degree while I’m at it.

That year, Pat brought in three students, Craig Kolb, Peter Schröder, and myself. We shared a big corner office on the fourth floor, with Pat just down the hall. It was quite a fun crew, Craig was the author of Rayshade, a powerful public domain ray tracer, and Peter had just spent a couple years at the MIT Media Lab. Peter is a remarkably intelligent and disciplined person, and he completed a PhD in only three years.

Graduate school is a different game from getting a bachelor’s degree in college. A Master’s degree usually finishes up the “book learning” phase, with classes, homework and exams in advanced topics. A Doctorate degree is about learning to read and write journal papers, getting to know the actual people in a field, and learning the scientific (and social) process of doing research. A student’s PhD thesis is an extended publication taking years to complete, written under the supervision of an advisor — a journal publication with training wheels.

I recommend getting a Master’s degree, and getting through the PhD candidacy. It’s a a total immersion in computer science, and while not very pleasant I have to say, it was a good learning experience. It’s a little unusual to return to graduate school at my age, as an established researcher in a field. But I wanted to round out my knowledge, since I was a specialist and had been trained in another field (physics). In some circles, a PhD is necessary for respect, regardless of whatever publications or accomplishments. Industry is more of a meritocracy though, and Craig and I ultimately both returned to that world and never had time to finish our theses.

That November of 1991, I had an idea. I walked into Pat’s office and told him that I knew how to render caustics. Caustics are when wavefronts of light fold into singularities, such as the bright cardioid curve you see inside an empty coffee cup when light shines into it. For various reasons, this was something known rendering and shading algorithms could not calculate. Two tricks were needed to do caustics, interval arithmetic optimization, and wavefront curvature. Pat’s immediate response was, “Let’s go to the Geometry Center in Minneapolis and work on this without distraction, so we can send a paper to SIGGRAPH!”

The deadline for a paper submission was only about a month away, and we had to write a completely new rendering system based on second order differential geometry, and implicit surfaces that could be evaluated in several different arithmetic systems (real numbers, intervals, and automatic-differentiation pairs). We got to Minneapolis, and they had just received 3 feet of snow, then the temperature dropped to 0° F. We froze our asses off that week, walking to and from the center, sometimes in howling winds and blowing snow.

One of the world’s foremost mathematicians, Bill Thurston, was there at the center too, so our little group had some amazing dinners and conversations. We described what we were doing with caustic reflections, “It’s unfortunately that we can only do this for mirror smooth surfaces”. Thurston replied that it could be generalized to rough surfaces, and told us how, but in mathematical terms that were completely over our heads. Pat and I still wonder what he was trying to tell us. One day there was a fire drill at the center. While we were standing outside, I asked Thurston a question about manifolds, and he picked up a stick and drew some diagrams in the side of a snowbank. I thought of Archimedes doing geometry in the sand.

A few months later, I stopped by Pat’s office. He had a sheepish expression on his face, like a boy who’d just done something mischievious. “I just won an Academy Award.”, he said. Pat was one of the primary inventors of the RenderMan system at Pixar, used in their movies and for many special effects in other films, and its development team had won a technical Oscar. The CS department was greatly surprised and pleased.