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Explore The Hidden Math Behind Your Favorite Pixar Movies

The TEDEd talk from Pixar Senior Research Scientist Tony Derose explores how math made 'Monsters, Inc.'

by Emerson Rosenthal
Apr 25 2014, 5:00pm

This one goes out to all the creatives who couldn't cut the math muster in Middle School. Somewhere around 8th grade, my understanding of the practical uses of the numbers and symbols I was learning started to peter out. Just as succinctly, so went my algebra scores—I couldn't figure out why I needed to map this parabola, or divine that derivative, and the result was a snowball effect of staggeringly poor performance. Like millions of others, my mind for mathematics had all but melted. 

Thankfully, there's a TED Talk that has me reconsidering my distaste for discrete mathematics within the universally-loved realm of Pixar. How do translation function connect to "Toy Story"? And how is calc necessary for turning CGI from polygonal blocks into the smooth (and now-iconic) characters we hold so dear? From the good folks at TEDEd and Pixar, allow the smooth science teacher-esque stylings of Pixar Research Senior Scientist, Tony DeRose, to rekindle your appetite for line curves. Below, Pixar: The Math Behind the Movies:

While it comes as no surprise that the award-winning animation team at Pixar are mathematicians in addition to storytellers, it put a smile on my face to know that the solutions to some of CGI's biggest setbacks were sitting right in my old textbooks. 

How does Woody from Toy Story move from Bo Peep to the toybox, for instance? A simple translation function:

And midpoints? (See diagram below)

Who thought midpoints were responsible for taking blocky polygons... 

...And morphing them into the smooth, realistic skin textures we find adorable? 

Well, I do now. Tonight I'll sleep better knowing that even I have the mental flexibility to fathom the algorithms at work in Jerry's Game. It makes me feel like this: 

Check out Pixar: The Math Behind the Movies on TEDEd, and test your knowledge with the supplementary review quiz at the end. Mathematical!

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Tony Derose