Grinspun examines the basic rules of motion and turns them into computer programs that are animating Hollywood movies and creating new tools for graphic designers. The programs are also used for medical research and to study problems involving flexible strands, sheets, liquids and even icicles. They could have applications for the laying down of transoceanic communications cables, the design of nanoscale wiring for stretchable electronics, and even for faster, more compact bottling of shampoo.
“For all of these applications,” Grinspun says, “you need to understand the motion of materials and how they behave. We’re bringing to it our knowledge of computers.” He and his collaborators have pioneered the use of a new kind of mathematics—discrete differential geometry—as a new mathematical “language” in which the behavior of physical materials can be described and directly translated into fast computer codes.
Grinspun, who directs Columbia Engineering’s Computer Graphics Group, part of the Columbia Vision and Graphics Center, has been collaborating with Disney (Tangled) and the New Zealand visual effects company Weta Digital (Rise of the Planet of the Apes, The Adventures of Tintin), to see how his technology can be used to make animated objects move more realistically and to animate complex scenes. Adobe Systems Inc. included a new paintbrush tool based on his work as part of its most recent editions of Adobe Photoshop and Adobe Illustrator.
“We are interested in computing how materials move,” said Grinspun, 34, who was born in Israel to Chilean parents but grew up in Ann Arbor, Mich., and Toronto.
Take, for example, a rubber mat. Like all elastic materials, rubber resists changes to its shape. If you could measure the energy required to roll up a rubber mat, you could predict how quickly and completely that mat could unfurl. Grinspun uses geometry to take into account the “bendiness” of an object by measuring how much the material curves under different pressures.
Rubber mats, Grinspun explained, share the same properties as syrups, textiles and plastics. “With elastic materials, the more you bend them, the more they want to unbend,” he said. “If you bend a sheet of rubber, the more it’s bent, the more it will fight to return to a straight shape. But with honey, it doesn’t matter how much you’ve bent it—it matters how fast.”
Grinspun partners with physicists and mathematicians to determine the best formulas to use as a starting point for his work. From there, his research team refines and customizes the formulas they use in their programs. By using discrete differential geometry, Grinspun is able to produce simpler, faster algorithms that “get the physics right.”