Brilliant 10: The Computational Contortionist
Rendering complex objects realistically requires a whole new kind of geometry When Eitan Grinspun's adviser at the California Institute of Technology asked him to help develop a better way to model how cans bend when crushed, the young mathematician did not think it would be a major project. "He lured me into something that took years and years," says Grinspun, now at Columbia University. But the journey to model a crushed Coke can ended with an entirely new field of geometry. Differential geometry can describe how the curves and surfaces of a given object will bend and crease. The problem, Grinspun says, is "that differential geometry is built for smooth surfaces with infinite detail." Computers can process only a finite amount of detail. For example, to describe a circle, computers must divide that circle into a series of connecting short sides-the greater the number of sides, the smoother the circle. Describing...