David Harmon
Columbia University
Etienne Vouga
Columbia University
Breannan Smith
Columbia University
Rasmus Tamstorf
Walt Disney Animation Studios
Eitan Grinspun
Columbia University


We develop a method for reliable simulation of elastica in complex contact scenarios. Our focus is on firmly establishing three parameter-independent guarantees: that simulations of well-posed problems (a) have no interpenetrations, (b) obey causality, momentum- and energy-conservation laws, and (c) complete in finite time. We achieve these guarantees through a novel synthesis of asynchronous variational integrators, kinetic data structures, and a discretization of the contact barrier potential by an infinite sum of nested quadratic potentials. In a series of two- and three-dimensional examples, we illustrate that this method more easily handles challenging problems involving complex contact geometries, sharp features, and sliding during extremely tight contact.


SIGGRAPH (ACM Transactions on Graphics) 2009 [PDF] [Supplemental Tech Report]

         author = {David Harmon and Etienne Vouga and Breannan Smith and Rasmus Tamstorf and Eitan Grinspun},
         title = {Asynchronous contact mechanics},
         journal = {SIGGRAPH '09 (ACM Transactions on Graphics)},
         year = {2009},
	 isbn = {978-1-60558-726-4},
	 publisher = {ACM},
	 address = {New York, NY, USA}


An overview of our method

Source Code

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