Physics-Based Animation

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

Duo Li, Shinjiro Sueda, Debanga R. Neog, Dinesh K. Pai

We present a novel approach to simulating thin hyperelastic skin. Real human skin is only a few millimeters thick. It can stretch and slide over underlying body structures such as muscles, bones, and tendons, revealing rich details of a moving character. Simulating such skin is challenging because it is in close contact with the body and shares its geometry. Despite major advances in simulating elastodynamics of cloth and soft bodies for computer graphics, such methods are difficult to use for simulating thin skin due to the need to deal with non-conforming meshes, collision detection, and contact response. We propose a novel Eulerian representation of skin that avoids all the difficulties of constraining the skin to lie on the body surface by working directly on the surface itself. Skin is modeled as a 2D hyperelastic membrane with arbitrary topology, which makes it easy to cover an entire character or object. Unlike most Eulerian simulations, we do not require a regular grid and can use triangular meshes to model body and skin geometry. The method is easy to implement, and can use low resolution meshes to animate high resolution details stored in texture-like maps. Skin movement is driven by the animation of body shape prescribed by an artist or by another simulation, and so it can be easily added as a post-processing stage to an existing animation pipeline. We provide several examples simulating human and animal skin, and skin-tight clothes.

Thin Skin Elastodynamics

Saket Patkar, Mridul Aanjaneya, Dimitriy Karpman, Ronald Fedkiw

A Hybrid Lagrangian-Eulerian Formulation for Bubble Generation and Dynamics

R. Elliot English, Linhai Qiu, Yue Yu, Ronald Fedkiw

We introduce a new method for large scale water simulation using Chimera grid embedding, which discretizes space with overlapping Cartesian grids that translate and rotate in order to decompose the domain into different regions of interest with varying spatial resolutions. Grids can track both fluid features and solid objects, allowing for dynamic spatial adaptivity without remeshing or repartitioning the domain. We solve the inviscid incompressible NavierStokes equations with an arbitrary-Lagrangian-Eulerian style semiLagrangian advection scheme and a monolithic SPD Poisson solver. We modify the particle level set method in order to adapt it to Chimera grids including particle treatment across grid boundaries with disparate cell sizes, and strategies to deal with locality in the implementation of the level set and fast marching algorithms. We use a local Voronoi mesh construction to solve for pressure and address a number of issues that arise with the treatment of the velocity near the interface. The resulting method is highly scalable on distributed parallel architectures with minimal communication costs.

Chimera Grids for Water Simulation

Theodore Kim, John Delaney

We present a new subspace integration method that is capable of efficiently adding and subtracting dynamics from an existing high-resolution fluid simulation. We show how to analyze the results of an existing high-resolution simulation, discover an efficient reduced approximation, and use it to quickly “re-simulate” novel variations of the original dynamics. Prior subspace methods have had difficulty re-simulating the original input dynamics because they lack efficient means of handling semi-Lagrangian advection methods. We show that multi-dimensional cubature schemes can be applied to this and other advection methods, such as MacCormack advection. The remaining pressure and diffusion stages can be written as a single matrix-vector multiply, so as with previous subspace methods, no matrix inversion is needed at runtime. We additionally propose a novel importance sampling-based fitting algorithm that asymptotically accelerates the precomputation stage, and show that the Iterated Orthogonal Projection method can be used to elegantly incorporate moving internal boundaries into a subspace simulation. In addition to efficiently producing variations of the original input, our method can produce novel, abstract fluid motions that we have not seen from any other solver.

Subspace Fluid Re-Simulation