## Pixar Math — Inside and Out

Co-authored by by David Borland and Tabitha Peck

In just over 90 minutes, audiences from young to old feel numerous emotions watching Pixar’s Inside Out. While such an emotional reaction fits the film, this experience isn’t new, at least for many of us. Think of a Pixar character, possibly Nemo, Woody, or now Joy, and you can probably also think of emotions you felt during that character’s tale. What goes into making such characters? An important step is creating storyboards, like the one below drawn by Inside Out Story Supervisor Josh Cooley, which pre-visualize the film. The sketches are placed side by side in sequence, so that they convey scenes and deliver a rough sense of how the story unfolds. This storyboard is one of approximately 177,096 drawn for the film.

Of course, Pixar films are computer animated so such drawings must be represented in 3D in a computer. This is done with wireframes, like the one below for the set of Headquarters, the control center inside Riley’s mind.

If you were to zoom in, you’d see there are sharp corners in the wireframe at the edges. However, if you were to look at the final rendered image below, you’d find the edges have been smoothed. This is especially important in character design like those placed in the set below. How does Pixar create smooth surfaces from its initial wireframes? Simply put: mathematics! In fact, an important step uses weighted averages. Did you ever compute your final (or potential) grade for a class where quizzes might be worth less than tests? Weighted averages played a role. Let’s see how Pixar uses such math as part of its animated storytelling movie magic!

Pixar’s short film Geri’s Game (1997) demonstrated their weighted-average based —> Read More