Physics-Based Animation

Libin Liu, KangKang Yin, Bin Wang, Baining Guo

In this paper we present a physics-based framework for simulation and control of human-like skeleton-driven soft body characters. We couple the skeleton dynamics and the soft body dynamics to enable two-way interactions between the skeleton, the skin geometry, and the environment. We propose a novel pose-based plasticity model that extends the corotated linear elasticity model to achieve large skin deformation around joints. We further reconstruct controls from reference trajectories captured from human subjects by augmenting a sampling-based algorithm. We demonstrate the effectiveness of our framework by results not attainable with a simple combination of previous methods.

Simulation and Control of Skeleton-Driven Soft Body Characters

Tiantian Liu, Adam Bargteil, James F. O’Brien, Ladislav Kavan

We describe a scheme for time integration of mass-spring systems that makes use of a solver based on block coordinate descent. This scheme provides a fast solution for classical linear (Hookean) springs. We express the widely used implicit Euler method as an energy minimization problem and introduce spring directions as auxiliary unknown variables. The system is globally linear in the node positions, and the non-linear terms involving the directions are strictly local. Because the global linear system does not depend on run-time state, the matrix can be pre-factored, allowing for very fast iterations. Our method converges to the same final result as would be obtained by solving the standard form of implicit Euler using Newton’s method. Although the asymptotic convergence of Newton’s method is faster than ours, the initial ratio of work to error reduction with our method is much faster than Newton’s. For real-time visual applications, where speed and stability are more important than precision, we obtain visually acceptable results at a total cost per timestep that is only a fraction of that required for a single Newton iteration. When higher accuracy is required, our algorithm can be used to compute a good starting point for subsequent Newton’s iteration.

Fast Simulation of Mass-Spring Systems

Jia Pan, Xinyu Zhang, Dinesh Manocha

We present a new method for efficiently computing the global penetration depth between two rigid objects using machine learning techniques. Our approach consists of two phases: offline learning and performing run-time queries. In the learning phase, we pre-compute an approximation of the contact space of a pair of intersecting objects from a set of samples in the configuration space. We use active and incremental learning algorithms to accelerate the pre-computation and improve the accuracy. During the run-time phase, our algorithm performs a nearest-neighbor query based on translational or rotational distance metrics. The run-time query has a small overhead and computes an approximation to global penetration depth in a few milliseconds. We use our algorithm for collision response computations in Box2D and Bullet game physics engines and observe more than an order of magnitude improvement over prior PD computation techniques.

Efficient Penetration Depth Approximation using Active Learning

Alexey Stomakhin, Craig Schroeder, Lawrence Chai, Joseph Teran, Andrew Selle

Snow is a challenging natural phenomenon to visually simulate. While the graphics community has previously considered accumulation and rendering of snow, animation of snow dynamics has not been fully addressed. Additionally, existing techniques for solids and fluids have difficulty producing convincing snow results. Specifically, wet or dense snow that has both solid- and fluid-like properties is difficult to handle. Consequently, this paper presents a novel snow simulation method utilizing a usercontrollable elasto-plastic constitutive model integrated with a hybrid Eulerian/Lagrangian Material Point Method. The method is continuum based and its hybrid nature allows us to use a regular Cartesian grid to automate treatment of self-collision and fracture. It also naturally allows us to derive a grid-based semi-implicit integration scheme that has conditioning independent of the number of Lagrangian particles. We demonstrate the power of our method with a variety of snow phenomena including complex character interactions.

A Material Point Method for Snow Simulation

Tobias Pfaff, Nils Thuerey, Theodore Kim

Over the last decade, the special effects industry has embraced physics simulations as a highly useful tool for creating realistic scenes ranging from a small camp fire to the large scale destruction of whole cities. While fluid simulations are now widely used in the industry, it remains inherently difficult to control large scale simulations, and there is an constant struggle for increasing visual detail.

In this course, we will tackle these problems using turbulence methods. Turbulent detail is what makes typical fluid simulations look impressive, and the underlying physics motivate a powerful approach for control: they allow for an elegant split of large scale motion and small scale turbulent detail. This results in a two-stage work flow that is highly convenient for artists: first, a rough, and fast initial simulation is performed, which is then turned into a more detailed one by adding turbulent effects.

This course aims at giving an overview and providing practical guide to employing turbulence modeling techniques for fluid simulations in computer graphics. After reviewing the basics of fluid solvers, and the popular wavelet turbulence approach, we will present several powerful methods to capture advanced effects such as boundary layers, and turbulence with directional preferences. In addition, the difficulties of liquid simulations will be explained, and an approach for liquid turbulence that is based on wave dynamics will be presented.

Turbulent Fluids

Ke-Sen’s full list here. Without further ado:

• Physics-based Animation of Large-scale Splashing Liquids
• Fast Simulation of Mass-Spring Systems
• Inverse Dynamic Hair Modeling with Frictional Contacts
• Versatile Surface Tension and Adhesion for SPH Fluids
• Efficient Penetration Depth Approximation using Active Learning
• Simulation and Control of Skeleton-Driven Soft Body Characters
• An Efficient Construction of Reduced Deformable Objects
• Spatio-temporal Extrapolation for Fluid Animation
• Modeling and Estimation of Internal Friction in Cloth
• Interactive Localized Liquid Motion Editing

Bo Zhu, Wenlong Lu, Matthew Cong, Byungmoon Kim, Ronald Fedkiw

We present an efficient grid structure that extends a uniform grid to create a significantly larger far-field grid by dynamically extending the cells surrounding a fine uniform grid while still maintaining fine resolution about the regions of interest. The far-field grid preserves almost every computational advantage of uniform grids including cache coherency, regular subdivisions for parallelization, simple data layout, the existence of efficient numerical discretizations and algorithms for solving partial differential equations, etc. This allows fluid simulations to cover large domains that are often infeasible to enclose with sufficient resolution using a uniform grid, while still effectively capturing fine scale details in regions of interest using dynamic adaptivity.

A New Grid Structure for Domain Extension

Jan Hegemann, Chenfanfu Jiang, Craig Schroeder, Joseph M. Teran

We utilize the shape derivative of the classical Griffith’s energy in a level set method for the simulation of dynamic ductile fracture. The level set is defined in the undeformed configuration of the object, and its evolution is designed to represent a transition from undamaged to failed material. No re-meshing is needed since the resulting topological changes are handled naturally by the level set method. We provide a new mechanism for the generation of fragments of material during the progression of the level set in the Griffith’s energy minimization. Collisions between different material pieces are resolved with impulses derived from the material point method over a background Eulerian grid. This provides a stable means for colliding with embedded interfaces. Simulation of corotational elasticity is based on an implicit finite element discretization.

A Level Set Method for Ductile Fracture

Fabian Hahn, Bernhard Thomaszewski, Stelian Coros, Sebastian Martin, Robert Sumner, Markus Gross

We present an efficient method for augmenting keyframed character animations with physically-simulated secondary motion. Our method achieves a performance improvement of one to two orders of magnitude over previous work without compromising on quality. This performance is based on a linearized formulation of rig-space dynamics that uses only rig parameters as degrees of freedom, a physics-based volumetric skinning method that allows our method to predict the motion of internal vertices solely from deformations of the surface, as well as a deferred Jacobian update scheme that drastically reduces the number of required rig evaluations. We demonstrate the performance of our method by comparing it to previous work and showcase its potential on a production-quality character rig.

Efficient Simulation of Secondary Motion in Rig-Space

David Harmon, Denis Zorin

Subspace techniques greatly reduce the cost of nonlinear simulation by approximating deformations with a small custom basis. In order to represent the deformations well (in terms of a global metric), the basis functions usually have global support, and cannot capture localized deformations. While reduced-space basis functions can be localized to some extent, capturing truly local deformations would still require a very large number of precomputed basis functions, significantly degrading both precomputation and online performance. We present an efficient approach to handling local deformations that cannot be predicted, most commonly arising from contact and collisions, by augmenting the subspace basis with custom functions derived from analytic solutions to static loading problems. We also present a new cubature scheme designed to facilitate fast computation of the necessary runtime quantities while undergoing a changing basis. Our examples yield a two order of magnitude speedup over full-coordinate simulations, striking a desirable balance between runtime speeds and expressive ability.

Subspace Integration with Local Deformations