Laplacian Damping for Projective Dynamics

Abstract

Damping is an important ingredient in physics-based simulation of deformable objects. Recent work introduced new fast simulation methods such as Position Based Dynamics and Projective Dynamics. Explicit velocity damping methods currently used in conjunction with Position Based Dynamics or Projective Dynamics are simple and fast, but have some limitations. They may damp global motion or non-physically transport velocities throughout the simulated object. More advanced damping models do not have these limitations, but are slow to evaluate, defeating the benefits of fast solvers such as Projective Dynamics. We present a new type of damping model specifically designed for Projective Dynamics, which provides the quality of advanced damping models while adding only minimal computing overhead. The key idea is to define damping forces using Projective Dynamics' Laplacian matrix. In a number of simulation examples we show that this damping model works very well in practice. When used with a modified Projective Dynamics solver that uses a non-dissipative implicit midpoint integrator, our damping method provides fully user-controllable damping, allowing the user to quickly produce visually pleasing and vivid animations.