# Number Sense Blog

By Mathnasium | Added Mar 26, 2018

You’re in 4th grade, dreaming about what you want to do when you grow up. What could possibly be cooler, you think, than bringing the characters from “A Bugs Life” and “Toy Story” to life?

That’s how David Kim, technical director for Nickelodeon Animation, started his journey into the world of animation.

“I was part of an after-school program in ‘stop-motion animation’ given by the guys who did ‘A Nightmare Before Christmas,'" he recalled. “Then in high school, I took a two-semester computer graphics class that piqued my interest. By sophomore year, I was shooting video with my own camera. ‘A Bugs Life’ and ‘Toy Story’ had come out, and that gave me faith in the medium to pursue it as a career.”

Today, David directs a team of animators who do “3D character rigging” for Nick’s movies and TV shows such as “Teenage Mutant Ninja Turtles,” “Penguins of Madagascar,” and “Monsters vs Aliens.”

To animate a character model, a character rigger uses computer graphics to create a “rig,” or “skeleton” for the character, complete with joints, controls, and "deformers," which consist of mathematical algorithms. The controls are carefully designed to manipulate the joints and deformers, using additional mathematical algorithms, to produce appealing shapes.

Green "bones" pose a hand. The animator uses the blue "handles" to make the fingers bend.     © Blender Foundation/www.sintel.org, CC BY-SA 3.0

A good character rigger, therefore, is part animator, part programmer, and part interface designer.1 And all of that takes some skill in math. You don’t have to be a math genius, but you do need to use algebra, geometry, trigonometry, and occasionally a little calculus.

“We’re just moving points in space to achieve different looks, from the corner of a smile to the bend of an elbow,” he said.

David was fortunate that his parents enrolled him in an after-school math program from 3rd through 6th grade, and that taught him math skills far beyond what was expected in school.

“Math is extremely important for what I do now,” he said. By knowing the math, we can achieve really flexible rigs,” he said. Creating rigs that are flexible and easy-to-use are his job’s primary goals.

“There was a very complex character called ‘Muckman’ on “Ninja Turtles,” he recalled. “His skin was gooey, and he had 70-100 pieces of trash and props stuck onto him that needed to look believable. Even his eyeball was its own character—it would come out of his head and talk to him! His brain was made of 100 worms. It took a lot of math to figure out where the ‘normals’ [vectors perpendicular to the character’s surface] were and to get the props onto the character.

The aptly named "Muckman" of "Ninja Turtles" fame. Courtesy Nickelodeon.

David is grateful that he can use his math ability to address difficult animation challenges on the job.

“The higher up in the company you go,” he said, “the more you need higher levels of math to answer your team’s questions.”

And when he hires character animators, he looks for candidates who have strong problem-solving ability, a skill that mathematical learning helps to hone. David helps them work on the aesthetic and technical problems they encounter. The result is great-looking, believable animated characters.

And how cool is that?

1Maestri, George. Digital Character Animation 3. New Riders, 2006.

### Favorites

Bedtime Math: http://bedtimemath.org/

National PTA: http://www.pta.org/

NCTM: http://www.nctm.org/

Numberphile: http://www.numberphile.com/

PTO Today: http://www.ptotoday.com/

STEM Connector: http://blog.stemconnector.org/

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