Researchers Build 3-D Model of Curly Hair

In animated films it is rare to find a character with curly hair, since animators lack a simple mathematical means of describing the curls. However, in a paper appearing in the Feb. 13 issue of Physical Review Letters, researchers at MIT and the Université Pierre et Marie Curie in Paris provide the first detailed model for the 3-D shape of a strand of curly hair.

"This work could have applications in the computer animation film industry, but it also could be used by engineers to predict the curve that long steel pipes, tubing, and cable develop after being coiled around a spool for transport. In the field, these materials often act like a stubborn garden hose whose intrinsic curves make it behave in unpredictable ways. In engineering terminology, these items - and hair - are all examples of a slender, flexible rod," writes the press release announcing the findings.

"Our work doesn't deal with the collisions of all the hairs on a head, which is a very important effect for animators to control a hairstyle," said Pedro Reis, an assistant professor in MIT's Department of Civil and Environmental Engineering and Department of Mechanical Engineering. "But it characterizes all the different degrees of curliness of a hair and describes mathematically how the properties of the curl change along the arc length of a hair."

With the help of lab experimentation, computer simulation and theory - "the perfect triangle of science," Reis said - the team identified the main parameters for curly hair. They then simplified them into dimensionless parameters for curvature and weight. Given curvature, length, weight and stiffness, their model will output the shape of a hair, steel pipe or Internet cable suspended under its own weight, said the statement.

Because the researchers used dimensionless numbers to describe curvature the equation will hold true at all scales. This could inform work from animation to oil well drilling. "We think of steel pipes as being nice and straight but usually at some point they're getting wrapped around something," Miller said. "And at large dimensions, they're so flexible that it's like you and I dealing with a limp spaghetti noodle."