Projective Dynamics: Fusing Constraint Projections for Fast Simulation

Sofien Bouaziz
Sebastian Martin
VM Research
Tiantian Liu
University of Pennsylvania
Ladislav Kavan
University of Pennsylvania

Mark Pauly

We propose a new "projection-based" implicit Euler integrator that supports a large variety of geometric constraints in a single physical simulation framework. In this example, all the elements including building, grass, tree, and clothes (49k DoFs, 43k constraints), are simulated at 3.1ms/iteration using 10 iterations per frame (see also accompanying video).


We present a new method for implicit time integration of physical systems. Our approach builds a bridge between nodal Finite Element methods and Position Based Dynamics, leading to a simple, efficient, robust, yet accurate solver that supports many different types of constraints. We propose specially designed energy potentials that can be solved efficiently using an alternating optimization approach. Inspired by continuum mechanics, we derive a set of continuumbased potentials that can be efficiently incorporated within our solver. We demonstrate the generality and robustness of our approach in many different applications ranging from the simulation of solids, cloths, and shells, to example-based simulation. Comparisons to Newton-based and Position Based Dynamics solvers highlight the benefits of our formulation.


Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Kavan, Mark Pauly. Projective Dynamics: Fusing Constraint Projections for Fast Simulation. ACM Transaction on Graphics 33(4) [Proceedings of SIGGRAPH], 2014.  

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We thank James O'Brien, Adam Bargteil, Basil Fierz and Bernhard Thomaszewski for the insightful discussions and the reviewers for their valuable comments. We are grateful to luismigabril for providing the cartoon house model and to Daniel Grauer for modeling the teaser scene. We also thank Yuliy Schwartzburg for his narration of the accompanying video. This research is supported by the Swiss National Science Foundation grant 20PA21L 129607, by the European Research Council under the European Unions Seventh Framework Programme (FP/2007- 2013)/ERC Grant Agreement n. 257453: COSYM and by the NSF Career Award IIS-1350330.