FEPR: Fast Energy Projection for Real-Time Simulation of Deformable Objects

Dimitar Dinev
University of Utah
Tiantian Liu
University of Pennsylvania
Jing Li
University of Utah
Bernhard Thomaszewski
Universite de Montreal

Ladislav Kavan
University of Utah

Our fast energy projection method produces vivid motion for an animated rabbit.


We propose a novel projection scheme that corrects energy fluctuations in simulations of deformable objects, thereby removing unwanted numerical dissipation and numerical "explosions". The key idea of our method is to first take a step using a conventional integrator, then project the result back to the constant energy-momentum manifold.We implement this strategy using fast projection, which only adds a small amount of overhead to existing physicsbased solvers. We test our method with several implicit integration rules and demonstrate its benefits when used in conjunction with Position Based Dynamics and Projective Dynamics. When added to a dissipative integrator such as backward Euler, our method corrects the artificial damping and thus produces more vivid motion. Our projection scheme also effectively prevents instabilities that can arise due to approximate solves or large time steps. Our method is fast, stable, and easy to implement -- traits that make it well-suited for real-time physics applications such as games or training simulators.


Dimitar Dinev, Tiantian Liu, Jing Li, Bernhard Thomaszewski, Ladislav Kavan. FEPR: Fast Energy Projection for Real-Time Simulation of Deformable Objects. ACM Transactions on Graphics 37(4) [Proceedings of SIGGRAPH], 2018.  

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We thank Robert Bridson, Mathieu Desbrun, Dominik Michels, Junior Rojas, Eftychios Sifakis, Daniel Sykora, Nghia Troung and Cem Yuksel for many insightful discussions.We also thank Saman Sepehri Nejad for modelling and animating the delicious Jell-O and Nathan Marshak for proofreading. This material is based upon work supported by the National Science Foundation under Grant Numbers IIS-1617172 and IIS-1622360. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. We also gratefully acknowledge the support of Activision and hardware donation from NVIDIA Corporation.