Everybody knows Pixar employs some of the most talented storytellers in the business. But the company employs some wonderfully sharp mathematicians, too. In fact, without those mathematicians working fastidiously behind the scenes, many of your favorite Pixar stories would not have gotten told — at least not in the adorable way we've come to love.
One such math wiz in Pixar's employ is Tony DeRose, Senior Scientist and Lead of the Research Group at Pixar Animation Studios. With a Ph.D. in Computer Science from U.C. Berkeley, DeRose spent a decade teaching at the University of Washington before joining Pixar to work on the Academy Award-winning animated short Geri's Game. (You may remember it as the one where the old man from Toy Story 2 plays chess.)
As DeRose explains in the video above, his particular focus at Pixar is in geometric modeling, which is a fancy way of saying that he's paid to make shapes. And as it turns out, making shapes is one of the most foundational jobs in any Pixar film since, as DeRose notes, many of the company's characters are made up of complicated shapes. What DeRose needed to do, then, was to develop shapes that both artists and computers could deal with quickly.
Before DeRose came on the scene, animators relied on polygons to create 3D objects. But polygons proved problematic to otherwise seamless animation, as Tim Carmody notes at The Verge: "The problem with polygons is that at close detail, you can see every one of them — a fatal problem when the illusion depends on ignoring individual frames and pixels." What DeRose did, says Carmody, was find "new ways of quickly generating smooth curves with high fidelity."
So how'd he do it? Basically, he used very simple geometric formulas to split a line into midpoints, and then to keep doing that until he got the shape he wanted.
Take a look at the video above, made by Numberphile, to see what we mean.