Projective dynamics

• DOI: 10.1145/2601097.2601116
• Publication Date: 2014-07-22T15:08:20Z
• Authors: Sofien Bouaziz; Sebastian Martin; Tiantian Liu; Ladislav Kavan; Mark Pauly
• Keywords: implicit Euler method; continuum mechanics; Engineering; Computer Sciences; Graphics and Human Computer Interfaces; 0202 electrical engineering, electronic engineering, information engineering; 006; 02 engineering and technology; physics-based animation; position based dynamics

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 continuum-based 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.