Computer Science Colloquium
Correct by Construction: Simulation with Discrete Differential Geometry
Etienne Vouga, Columbia University
April 08, 2013
Warren Weaver Hall, 1302
251 Mercer Street
New York, NY 10012
Spring 2013 Colloquia Calendar
Science and industry increasingly use computation to predict the motion and behavior of materials, and such simulations are only useful if they faithfully reflect reality. A common measure of accuracy is convergence: how well the simulation approaches the behavior of the exact physics as we increase the simulation's computational budget. In practice, however, the amount of time and power we are willing to devote to any given simulation is limited, and we would like even coarse simulations to well-approximate reality.
The correctness of physical systems is often characterized by the system's geometric structure -- its conservation laws, symmetries, and invariants. Naive translation of smooth physics equations into discrete ones solvable by the computer ignores and often destroys this structure. The alternative is to first build from the ground up a theory of discrete differential geometry that mirrors the system's smooth geometry. Using this discrete geometry, we can construct simulation algorithms that are not only mathematically elegant, but also conserve the system's important structure by construction. In this talk, I show this paradigm's power to more efficiently and accurately simulate a variety of everyday objects, including hair, honey, cloth, and masonry.
Etienne Vouga is a computer science PhD candidate and Presidential Fellow at Columbia University, and received his BA degrees in mathematics and computer science from Rice University. His research interests include physical simulation, geometry processing, and discrete differential geometry, with applications to computer graphics and computational mechanics. Special effects studios Disney and Weta Digital have used his work on cloth and hair simulation in movies such as Tangled and The Hobbit. He was awarded an NVIDIA graduate fellowship in 2011, a Google graduate fellowship in computer graphics in 2012, and his work on Asynchronous Contact Mechanics was featured in the 2012 Communications of the ACM Research Highlights.