Physics-Based Animation

Pontus Pall, Oskar Nylèn, Marco Fratarcangeli

We introduce a practical iterative solver for mass-spring systems which can be trivially mapped to massively parallel architectures, in particular GPUs.We employ our solver for the interactive animation of virtual cloth and show that it is computationally fast, robust and scalable, making it suitable for real-time graphics applications. Under the assumption that the input system is represented by a quadrangular network of masses connected by springs, we first partition the particles into two independent sets. Then, during the animation, the dynamics of all the particles belonging to each set is computed in parallel. This enables a full Gauss-Seidel iteration in just two parallel steps, leading to an approximated solution of large mass-spring systems in a few milliseconds. We use our solver to accelerate the solution of the popular Projective Dynamics framework, and compare it with other common iterative solvers in the current literature.

Fast Quadrangular Mass-Spring Systems using Red-Black Ordering

Jing Li, Tiantian Liu, Ladislav Kavan

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.

Laplacian Damping for Projective Dynamics

Liyou Xu, Xiaowei He, Wei Chen, Sheng Li, and Guoping Wang

Peridynamics is a formulation of the classical elastic theory that is targeted at simulating deformable objects with discontinuities, especially fractures. Till now, there are few studies that have been focused on how to model general hyperelastic materials with peridynamics. In this paper, we target at proposing a general strain energy function of hyperelastic materials for peridynamics. To get an intuitive model that can be easily controlled, we formulate the strain energy density function as a function parameterized by the dilatation and bond stretches, which can be decomposed into multiple one-dimensional functions independently. To account for nonlinear material behaviors, we also propose a set of nonlinear basis functions to help design a nonlinear strain energy function more easily. For an anisotropic material, we additionally introduce an anisotropic kernel to control the elastic behavior for each bond independently. Experiments show that our model is flexible enough to approximately regenerate various hyperelastic materials in classical elastic theory, including St.Venant-Kirchhoff and Neo-Hookean materi

Reformulating Hyperelastic Materials with Peridynamic Modeling

George E. Brown, Matthew Overby, Zahra Forootaninia, Rahul Narain

We propose a method for accurately simulating dissipative forces in deformable bodies when using optimization-based integrators. We represent such forces using dissipation functions which may be nonlinear in both positions and velocities, enabling us to model a range of dissipative effects including Coulomb friction, Rayleigh damping, and power-law dissipation. We propose a general method for incorporating dissipative forces into optimization-based time integration schemes, which hitherto have been applied almost exclusively to systems with only conservative forces. To improve accuracy and minimize artificial damping, we provide an optimization-based version of the second-order accurate TR-BDF2 integrator. Finally, we present a method for modifying arbitrary dissipation functions to conserve linear and angular momentum, allowing us to eliminate the artificial angular momentum loss caused by Rayleigh damping.

Accurate dissipative forces in optimization integrators