Projective dynamics

Abstract

EPFL Figure 1: 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). AbstractWe 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.

Early Termination of Conjugate Gradients for Corotated Finite Elements

“…Limitations and Future Work. This short paper demonstrates that the conjugate gradient method combined with linearly implicit Euler and corotational finite elements may be competitive with existing techniques for real-time animation of soft bodies, but it leaves open many directions for future work, including a more comprehensive comparison to alternative approaches such as projective dynamics [Bouaziz et al 2014;Liu et al 2013;Wang 2015]. Our experiments are limited to volumetric soft bodies where the linear system is guaranteed to be positive definite.…”

“…Recently, researchers have developed faster techniques that make use of precomputation of matrix decompositions or clever preconditioners [Bouaziz et al 2014;Brandt et al 2018;Dinev et al 2018;Hecht et al 2012;Liu et al 2013;Narain et al 2016;Wang 2015;Wang and Yang 2016]. Some of these approaches place limits on material models or other aspects of the animation.…”

Real-Time Collision Detection for Deformable Characters with Radial Fields

“…We then perform "smart averaging" between them. This is based on the approach of Bouaziz et al [50] and Weiler et al [51]. Our cloth system operates entirely on the GPU using compute shaders.…”

Dynamic implicit muscles for character skinning

“…Projective Dynamics [83] have been considered in place of PBD. It averages all constraint projections in one global step which limits oscillations.…”