Math at the Movies

It’s no secret that most students love when class is canceled. Usually, it means more free time to do whatever you want (e.g., sleep, study, socialize). However, when my EAS10X Seminar was rescheduled, my friends and I didn’t go hang out in the lounge with the rest of our hallmates — we went to a different lecture. This lecture was the first in the Milton Wing Lecture series put on by the Math Department.

Ewww, right? Who goes to lectures about math? Well, trust me when I say you would have gone to this lecture too. First of all, it was titled “How Mathematics Has Changed Hollywood.” If for some reason, you’re still not embracing your inner nerd, the speaker was Dr. Tony DeRose, Senior Scientist, and Lead of the Research Group at Pixar.

Now, this was a very general lecture, meant for an audience with an average understanding of math and computer science, but it was an interesting look into how Pixar uses math in creating their movies. For example, to determine how light reflects off objects, integrals are used. Differential equations are often used to plot movement, and to create the flowing motion of Merida’s hair (from Brave), Pixar created a derivative machine. Looking at these examples, it appears that only more advanced math is used, yet geometry and trigonometry also play a large part in the making of Pixar films. Even matrices have an application.

One of the coolest examples was how shapes are changed to appear smoother, so that characters aren’t obviously made up of tiny squares. Using four reference points, the average is taken between then, and the midpoint is plotted. This can be done many times, and will produce a smooth shape. Or the weighted average can be taken between points. However, if one uses arbitrary weights, the shape is not smooth, but jagged. Instead, the values from Pascal’s triangle are used. I’d only ever used Pascal’s triangle to expand a binomial, so seeing it in a new application was wicked cool.

Dr. DeRose also gave two other talks as part of the Milton Wing lecture series (on “Wavelets in Computer Graphics”), but I had class, so I was unable to attend those. However, I find it impressive the talk I could attend was funded by a man who graduated from the University of Rochester with a BA in mathematics in 1944, worked on the Manhattan Project, and then earned his master’s degree in 1947.  Pixar wasn’t even founded when he graduated, but due to the strong relationship University of Rochester maintains with its alumni, I was able to learn about how they use mathematics to make movies “ever better.”

(A special thank you to Professor Allan Greenleaf, chairman of the math department for the biographical information on Milton Wing and Tony DeRose, and for not looking at me too strangely when I asked for it.)