From the zealous facial expressions in “The Incredibles” to the detailed environments of “Ratatouille,” and even the way light moves and sparkles under the ocean in “Finding Nemo,” all Pixar films are indebted to mathematical creativity.
In a series of talks spanning the East Coast titled “Math at the Movies,” Tony DeRose, senior scientist and head researcher for Pixar Animation Studios, discussed how algebra, geometry and calculus all play a role in animation.
“You hear a lot of people today saying math is pointless,” said DeRose. “They don’t realize, though, that math is what makes the movies they love.”
Even the simple act of moving a character across the screen involves math.
Using coordinate geometry allows the animators to move a character along a grid axis, creating movement.
The process of making animated movies involves multiple steps, starting at the story department. The story and art departments start creating story panels, or scene-by-scene drawings of every shot in a movie. Monsters Inc. alone had about 25,000 panels in its first draft.
Next, the art department starts creating models to use. These geometric marionettes undergo a process called rigging, which allows the animators to control the models.
“We currently use about 300 facial controls out of 700 total. This gives us the precision to control the degree in which the right corner of your mouth moves,” said DeRose.
The final steps of lighting and shading help fill in the sets and bring more detail into every shot.
DeRose showed off several examples of how mathematics is used to create different scenarios, from light bouncing off of the environment to how the movement of cloth is simulated in every scene.
“It really puts into perspective how much more work is put into a single frame of animation over live action shots,” said David Pickett, a junior cinema and cultural studies major.
Math plays the largest part in actually building the 3-D models of characters.
While characters can include millions of pieces made up of polygons that each need their own equation, a geometric technique called subdivision surfaces makes the process easier. Under multiple iterations of a split-and-average process, animators are able to make smooth surfaces that are easy to animate. This improves the looks of the models, making them seem like one organic piece rather than something being assembled.
This technique was used for the first time in the Oscar-winning short film “Geri’s Game” in 1997 and has been used in every Pixar work since.
“The hardest film to make by far was ‘Toy Story 2,’” said DeRose. “Not only did we have story problems, but we also had to rebuild every model from scratch using our new tech.”
Once the model is made, the actual animation process can be completed. To actually control the models, animators use a spreadsheet to control every variable within a character’s movement and use subdivision to fill in the holes in the action.
The whole process of successfully building a movie takes about four years of work, with the animation process taking up only a single year.
“While it’s not something you see transitioned on the screen, every single object you see on the screen is there because of math,” said DeRose.
DeRose closed his speech by refusing to answer the question on everyone’s mind: whether or not there will be another “Toy Story.”