Reflections on Simultaneous Impact

Breannan Smith1 Danny M. Kaufman1 Etienne Vouga1

Rasmus Tamstorf2 Eitan Grinspun1

1Columbia University 2Walt Disney Animation Studios


Resolving simultaneous impacts is an open and significant problem in collision response modeling. Existing algorithms in this domain fail to fulfill at least one of five physical desiderata. To address this we present a simple generalized impact model motivated by both the successes and pitfalls of two popular approaches: pair-wise propagation and linear complementarity models. Our algorithm is the first to satisfy all identified desiderata, including simultaneously guaranteeing symmetry preservation, kinetic energy conservation, and allowing break-away. Furthermore, we address the associated problem of inelastic collapse, proposing a complementary generalized restitution model that eliminates this source of nontermination. We then consider the application of our models to the synchronous time-integration of large-scale assemblies of impacting rigid bodies. To enable such simulations we formulate a consistent frictional impact model that continues to satisfy the desiderata. Finally, we validate our proposed algorithm by correctly capturing the observed characteristics of physical experiments including the phenomenon of extended patterns in vertically oscillated granular materials.


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Supplemental Materials:


    author = {Breannan Smith and Danny M. Kaufman and Etienne Vouga and Rasmus Tamstorf and Eitan Grinspun},
    title = {Reflections on Simultaneous Impact},
    journal = {ACM Transactions on Graphics (Proceedings of SIGGRAPH 2012)},
    year = {2012},
    volume = {31},
    number = {4},
    pages = {106:1--106:12}