What kind of math do animators use

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Approximating the integral equation as a set of linear equations—one equation for every piece, with typically 1 million to 10 million pieces—we have that many equations to solve for every frame of the film, DeRose said. The geometric technique of subdivision surfaces allows artists to represent complex surfaces and complicated shapes efficiently on a computer, while maintaining an illusion of smoothness. Under many iterations of this split-and-average process, a faceted model converges to a smooth surface that can be easily animated.

To create and control volume deformations used to articulate characters, Pixar has recently turned to harmonic coordinates.

DeRose indicated that harmonic coordinates are generalized barycentric coordinates that can be extended to any dimension; they describe how interior points move within polygons in the plane or polyhedra in space. As far as I know, it's a novel use of Laplace's equation. This technique greatly simplifies the controls necessary to animate a character, DeRose added. He received a B. DeRose was a professor of computer science and engineering at the University of Washington.

An Interview with Tony DeRose. Old reliable Woody, charmingly forgetful Dory or maybe the fierce Merida from Brave? No matter who your favorite childhood hero or heroin is, all pixar characters are brought to life using the same basic tools: creativity, of course, and a whole lot of maths.

In his new and insightful TED-Ed talk, Pixar animator Tony DeRose explains how each character is brought to life using a series of basic mathematical functions. As Tony explains, one of the most-used techniques to create the smooth and detailed appearances of hands and faces uses geometry.

Starting with a four-point polygon, the animators find the mid point of each line then split and average these points to gradually create a smooth outline. Using this method, the animators can make a realistic 3D object beginning from a few straight lines. The object is then animated by simply manipulating the first four original points of the polygon.