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.