Pixar movies are always the perfect choice when you want to sit down on a Saturday night and watch a feel-good film. Whether you’re young or old, there’s something about Pixar that suit all ages, and there are some tear-jerkers too.
Surprisingly, there’s a ton of mathematics behind the production of Pixar flicks that is probably taught to kids at school today, including geometry, addition, multiplication and trigonometry.
As well as the traditional style of mathematics, Pixar believe they also create new mathematics in a lot of their films.
In a TED-ed video, Tony Derose, senior scientist at Pixar, talks about the concept of ‘new mathematics’ that is displayed a lot throughout their movies. He uses the films Finding Nemo, Monsters Inc and Toy Story 2 as examples of this.
The shapes behind the faces and parts of each character are very complicated, and in Tony’s words: “It’s not just a bunch of spheres and cylinders stuck together”.
Tony goes on to talk about ‘midpoints’ which calculate the way they move in two dimensions. The team uses geometry and equations to produce a coordinate system and uses averaging to calculate the movements.
The idea of ‘subdivision’ was first used in the short Pixar film in 1997 called ‘Geri’s Game’, and put it this way, there’s more to the main character's hands than just fingers and fingernails.
But what does it mean?
Well, in mathematics, a finite subdivision rule is a recursive way of dividing a polygon or other two-dimensional shape into smaller and smaller pieces.
In the video, you’ll see how subdivision smooths out each aspect of the character and generally makes them look a lot more realistic.
Since back in 1997, they’ve built all their characters that way, including Merida in Brave, whose dress was a subdivision, as well as her hands and face.
It doesn’t stop there though. We bet you didn’t think there was mathematics behind Woody from Toy Story? He’s not just a cowboy, he’s quite literally a walking calculator.
Tony explains that even when a character like Woody walks across from left to right, there is a ton of mathematics involved. As all artists and designers think in terms of shapes and images and computers think in numbers and equations, it’s pretty understandable.
Their concept of ‘coordinate geometry’ marry the two to create coordinates to signify how far to the left or right a character will go, and how high. To work out where each character needs to go, they need to work out addition, which is of course, another skill kids are taught in school at a very young age. For example, if they want to make an object bigger in the film, they have to figure out the mathematics behind ‘scaling.’
Intrigued? You should be. The mathematics of scaling in Pixar movies is as follows:
Xend = 2 * Xstart
This basically translates to multiplying the x from the start and the end by 2. When it comes to rotation, things get a little complicated. Kids will usually know this in 8th or 9th grade (which is age 14/15.)
To rotate a character, they follow this equation:
Xend = cos0 * Xstart + sin0 * Ystart
Long story short, if a child ever wonders if they really need to pay attention to complicated equations involving lots of X’s and lots of Y’s, the answer is yes, because they could end up working at Pixar.
Granted, mathematics isn’t for everyone, but as shown by Tony Derose, it’s everywhere, even in your favourite movies.
