hanRahan: How do you bend a polygon?
CaTmuLL: Well, it was kind of ad hoc. And it largely worked, but as you might imagine, if you don't have a well-defined surface, then you're going to come up with cases that break. So, I figured out how to work with B-spline surfaces, but the difficulty was it would take way too long to render a picture. At the time, I thought my most ingenious idea was a new method for subdividing a surface. It was the equivalent of a finite difference equation, except that it split the curve in half with each iteration. Think of a line: with a difference equation, four adds gets you the next point in a cubic curve; every four adds gets you a new point. I came up with a method such that every four adds got you the point in the middle of the curve. It turns out that for doing subdivision surfaces, it's really fast.
hanRahan: Can it be made recursive? Ca TmuLL: It was recursive. I thought this was my neatest idea at the time, and to my knowledge, it actually was. It's an original contribution for difference equations. But as computers got faster, it just wasn't the main problem. I implemented it, and sure enough, it was fast; but it still took 45 minutes to make pictures on the PDP- 10.
hanRahan: Evans and Sutherland Corporation placed heavy emphasis on real-time graphics, but you were willing to step back a little and say, "I know there's this emphasis on making things efficient, but we should explore this frontier of non-real-time stuff, and see what's possible—not just what we can do in real time at the time."
CaTmuLL: It's true there was a division, but the breadth of the support from Dave and Ivan encompassed both approaches. At the time, I wanted to develop the technology so we could make motion pictures. I had a very clear goal.
hanRahan: Was your goal different from the rest of them?
Ca TmuLL: Yes, but that was perfectly
fine. In fact, Ivan at one point started
a film company called the Electric Pic-
ture Company. He was going to hire
Gary Demos and me, but they couldn't
get the funding, so it fell apart. Ivan
had an interest in pushing the direc-
tion of motion pictures, and he knew
that was my drive, too. I was working
on the good-looking pictures, and they
were working on interactivity.