Doing the Math

By Julia Van Develder

Doing the Math

When Toy Story was released on Thanksgiving weekend in 1995, it represented the most revolutionary advance in animated filmmaking since Snow White and the Seven Dwarfs in 1937. 

The highest grossing film of 1995, Toy Story was the first fully computer-animated feature film, created using software developed at Pixar Animation Studios by a handful of brilliant computer scientists, including Eben Ostby ’77, who also has the distinction of being Vassar’s first computer science major. 

“Someone else would have done it had we not done it, I’m sure,” says Ostby, vice president for software at Pixar. But they did do it. They reinvented the discipline of animation and redefined the animated feature film as a vehicle for sophisticated storytelling. 

Ostby started working at Pixar before it was Pixar. “In 1983, when I started there, we were just this little group within Lucasfilm,” he says. “When we spun off as Pixar, we numbered 40-something people. We were tiny.” 

That was in 1986, the year Apple co-founder Steve Jobs purchased the computer graphics division of Lucasfilm and christened it “Pixar.” “In the beginning, we were setting out to make a go of doing computer graphics as a technical discipline,” Ostby says. “We were selling hardware to companies that were doing medical imaging and petroleum exploration and other things where you might want to use image processing to do complicated visualizations. But there was this little group that I was lucky enough to be part of that was tasked with doing research into animation.”

The animation group was headed by Ed Catmull, who had been vice president of the computer graphics division at Lucasfilm. Ostby says, “Ed loved this stuff and was really interested in pursuing it and thought it could pay off in some way. Honestly, I don’t think we knew in what way it would pay off, but we did a few short films.” Every year they produced a new, award-winning short—Luxo Jr., Red’s Dream, Tin Toy, Knick Knack. “These were all short films where we were kind of figuring out how to do animation. One of the things I quickly learned is that all my math, particularly linear algebra, was directly applicable to the stuff we were doing. Sines and cosines and matrices—these were all part and parcel of everyday life for people who were doing the technical side of animation. We learned how to model ever more expressive characters and how to do lighting and shading in ways that were ever more difficult until, finally, we had captured enough of the discipline that we could foresee doing an actual feature film.” 

During this time, Ostby and his colleagues William Reeves and Tom Duff were building the software that would be used to create Toy Story, Marionette 3-D Animation Systems. “The way the animation system works is not conceptually complicated,” Otsby says. “You build the geometries—the characters, say—in a modeling system, and then you bring them into our animation system, which allows you to control the motion. So, if you have a character and you’ve built it as a bunch of linked parts, our system allows you to specify the timing of when you move an elbow, say, or a wrist, or fingers. And if you take that basic concept and then go wild with it, you can actually make a film.

“Over time, we built a more sophisticated platform for doing animation. So at first, maybe you could just rotate something. Later, you started to add in the flexing of the skin and the movement of cloth. Later still, you tried to simulate the way cloth actually moves using the physics of cloth. Those are the kinds of things we’ve brought to animation over the years.” 

Ostby, Reeves, and Duff won the Scientific and Engineering Academy Award for Marionette 3-D in 1998, and the system has been used to create award-winning film after award-winning film, from Toy Story to Up, the second animated feature in history to receive a Best Picture nomination at the Oscars. Now, Ostby is heading a large team of about 100 computer scientists who are rewriting the software from scratch. “It had gotten a little long in the tooth, and it was time to rewrite it from first principles,” he explains. “When you grow software, it gets to be increasingly hard for any one person to really understand it well enough to maintain it or grow it. Growing our software is something we do all the time because every film has expressive needs that are a little bit higher. One film has five plants in it, the next film has a field of brush, the film after that has a jungle. So in each case, we need to up the level of what we’re able to do. And at some point the software becomes crusty enough that it is hard to keep extending that.” 

His favorite Pixar film? “Probably Cars. There’s something I love about each of them. Cars I like because I had a really interesting role in it, where I was in charge of all the technical crew. I also like Monsters Inc. because it was creatively a more daring film than some of the previous ones I’d worked on. And of course Toy Story. Toy Story was amazing. It was groundbreaking.” 

Eben Ostby ’77 came to Vassar expecting to major in English. “It turns out that I was never a good English student because I was a little shy, and I didn’t want to speak up in class. So I decided not to pursue that. I liked English, I liked the sciences, I liked math—I liked all of these things, and Vassar let me try things out.” 

He’d been interested in computer science since high school, and Vassar offered courses in computer science, but there was no computer science major as yet. Winifred Asprey, who would eventually succeed in establishing the department at Vassar, worked with Ostby to craft a major through the Independent Program. “I had to convince a panel of faculty members that this was worthy of granting me a bachelor’s degree,” says Ostby. “Professor Asprey and I came up with a plan for a major that was fairly theoretical and very heavily rooted in math, so it fit in with the liberal arts philosophy. As a result, I really felt that I learned a lot about what it meant to study computer science as a theoretical discipline as well as a practical one. It was great fun, and putting together the major and getting approval for it taught me a ton—taught me as much as any class.”

Even at that stage, Ostby was interested in the graphic capabilities of the computer. “It was not easy to do computer graphics at that point because the hardware just didn’t exist,” he says, “but I was doing visual projects—cartography, for example. I’ve always liked the connection between computers and the visual.”

Which is why Pixar is perfect. “This place is great for me. It is wonderful to be able to use both the rational side and the more—I shouldn’t say creative—the other side of the brain, the visual side. The whole place here is like one big left-brain, right-brain object lesson. We have right-brain people and left-brain people, and working together we are able to create a result that is much greater than the sum of the parts.”