Physics-Based Animation

Beibei Liu, Gemma Mason, Julian Hodgson, Yiying Tong, Mathieu Desbrun

We present a model-reduced variational Eulerian integrator for incompressible fluids, which combines the efficiency gains of dimension reduction, the qualitative robustness of coarse spatial and temporal resolutions of geometric integrators, and the simplicity of sub-grid accurate boundary conditions on regular grids to deal with arbitrarily-shaped domains. At the core of our contributions is a functional map approach to fluid simulation for which scalar- and vector-valued eigenfunctions of the Laplacian operator can be easily used as reduced bases. Using a variational integrator in time to preserve liveliness and a simple, yet accurate embedding of the fluid domain onto a Cartesian grid, our model-reduced fluid simulator can achieve realistic animations in significantly less computational time than full-scale non-dissipative methods but without the numerical viscosity from which current reduced methods suffer. We also demonstrate the versatility of our approach by showing how it easily extends to magnetohydrodynamics and turbulence modeling in 2D, 3D and curved domains.

Model Reduced Variational Fluid Simulation

Tao Yang, Jian Chang, Bo Ren, Ming Lin, Jian Jun Zhang, Shi-Min Hu

Multiple-fluid interaction is an interesting and common visual phenomenon we often observe. In this paper, we present an energybased Lagrangian method that expands the capability of existing multiple-fluid methods to handle various phenomena, such as extraction, partial dissolution, etc. Based on our user-adjusted Helmholtz free energy functions, the simulated fluid evolves from high-energy states to low-energy states, allowing flexible capture of various mixing and unmixing processes. We also extend the original Cahn-Hilliard equation to be better able to simulate complex fluid-fluid interaction and rich visual phenomena such as motionrelated mixing and position based pattern. Our approach is easily integrated with existing state-of-the-art smooth particle hydrodynamic (SPH) solvers and can be further implemented on top of the position based dynamics (PBD) method, improving the stability and incompressibility of the fluid during Lagrangian simulation under large time steps. Performance analysis shows that our method is at least 4 times faster than the state-of-the-art multiple-fluid method. Examples are provided to demonstrate the new capability and effectiveness of our approach.

Fast Multiple-Fluid Simulation Using Helmholtz Free Energy

Zhili Chen, Byungmoon Kim, Daichi Ito, Huamin Wang

We present a real-time painting system that simulates the interactions among brush, paint, and canvas at the bristle level. The key challenge is how to model and simulate sub-pixel paint details, given the limited computational resource in each time step. To achieve this goal, we propose to define paint liquid in a hybrid fashion: the liquid close to the brush is modeled by particles, and the liquid away from the brush is modeled by a density field. Based on this representation, we develop a variety of techniques to ensure the performance and robustness of our simulator under large time steps, including brush and particle simulations in non-inertial frames, a fixed-point method for accelerating Jacobi iterations, and a new Eulerian-Lagrangian approach for simulating detailed liquid effects. The resulting system can realistically simulate not only the motions of brush bristles and paint liquid, but also the liquid transfer processes among different representations. We implement the whole system on GPU by CUDA. Our experiment shows that artists can use the system to draw realistic and vivid digital paintings, by applying the painting techniques that they are familiar with but not offered by many existing systems.

Wetbrush: GPU-based 3D painting simulation at the bristle level

Huamin Wang

In this paper, we study the use of the Chebyshev semi-iterative approach in projective and position-based dynamics. Although projective dynamics is fundamentally nonlinear, its convergence behavior is similar to that of an iterative method solving a linear system. Because of that, we can estimate the “spectral radius” and use it in the Chebyshev approach to accelerate the convergence by at least one order of magnitude, when the global step is handled by the direct solver, the Jacobi solver, or even the Gauss-Seidel solver. Our experiment shows that the combination of the Chebyshev approach and the direct solver runs fastest on CPU, while the combination of the Chebyshev approach and the Jacobi solver outperforms any other combination on GPU, as it is highly compatible with parallel computing. Our experiment further shows position-based dynamics can be accelerated by the Chebyshev approach as well, although the effect is less obvious for tetrahedral meshes. The whole approach is simple, fast, effective, GPU-friendly, and has a small memory cost.

A Chebyshev Semi-iterative Approach for Accelerating Projective and Position-based Dynamics

Xiaofeng Wu, Rajaditya Mukherjee, Huamin Wang

Multi-domain subspace simulation can efficiently and conveniently simulate the deformation of a large deformable body, by constraining the deformation of each domain into a different subspace. The key challenge in implementing this method is how to handle the coupling among multiple deformable domains, so that the overall effect is free of gap or locking issues. In this paper, we present a new domain decomposition framework that connects two disjoint domains through coupling elements. Under this framework, we present a unified simulation system that solves subspace deformations and rigid motions of all of the domains by a single linear solve. Since the coupling elements are part of the deformable body, their elastic properties are the same as the rest of the body and our system does not need stiffness parameter tuning. To quickly evaluate the reduced elastic forces and their Jacobian matrices caused by the coupling elements, we further develop two cubature optimization schemes using uniform and non-uniform cubature weights. Our experiment shows that the whole system can efficiently handle large and complex scenes, many of which cannot be easily simulated by previous techniques without limitations

A Unified Approach for Subspace Simulation of Deformable Bodies in Multiple Domains

SIGGRAPH Asia 2015:

• Surface Turbulence for Particle-Based Liquid Simulations
• A unified approach for subspace simulation of deformable bodies in multiple domains
• A Chebyshev semi-iterative approach for accelerating projective and position-based dynamics
• Wetbrush: GPU-based 3D painting simulation at the bristle level
• Expediting Precomputation for Reduced Deformable Simulation
• Fast Multiple-fluid Simulation Using Helmholtz Free Energy
• Nested Cages
• Model Reduced Variational Fluid Simulation
• Data-driven Fluid Simulation using Regression Forests
• Smoothed Aggregation Multigrid for Cloth Simulation
• Subspace Dynamic Simulation Using Rotation-Strain Coordinates
• Non-Manifold Level Sets: A Multivalued Implicit Surface Representation with Applications to Self-Collision Processing

TOG papers:

• Continuum Foam: A Material Point Method for Shear-Dependent Flows

Olivier Mercier, Cynthia Beauchemin, Nils Thuerey, Theodore Kim, Derek Nowrouzezahrai

We present a method to increase the apparent resolution of particlebased liquid simulations. Our method first outputs a dense, temporally coherent, regularized point set from a coarse particle-based liquid simulation. We then apply a surface-only Lagrangian wave simulation to this high-resolution point set. We develop novel methods for seeding and simulating waves over surface points, and use them to generate high-resolution details. We avoid error-prone surface mesh processing, and robustly propagate waves without the need for explicit connectivity information. Our seeding strategy combines a robust curvature evaluation with multiple bands of seeding oscillators, injects waves with arbitrarily fine-scale structures, and properly handles obstacle boundaries. We generate detailed fluid surfaces from coarse simulations as an independent post-process that can be applied to most particle-based fluid solvers.

Surface Turbulence for Particle-Based Liquid Simulations

Yin Yang, Dingzeyu Li, Weiwei Xu, Yuan Tian, Changxi Zheng

Model reduction has popularized itself for simulating elastic deformation for graphics applications. While these techniques enjoy orders-of-magnitude speedups at runtime simulation, the efficiency of precomputing reduced subspaces remains largely overlooked. We present a complete system of precomputation pipeline as a faster alternative to the classic linear and nonlinear modal analysis. We identify three bottlenecks in the traditional model reduction precomputation, namely modal matrix construction, cubature training, and training dataset generation, and accelerate each of them. Even with complex deformable models, our method has achieved orders-of-magnitude speedups over the traditional precomputation steps, while retaining comparable runtime simulation quality.

Expediting Precomputation for Reduced Deformable Simulation

Rahul Sheth, Wenlong Lu, Yue Yu, Ronald Fedkiw

We propose a novel framework for simulating reduced deformable bodies that fully accounts for linear and angular momentum conservation even in the presence of collision, contact, articulation, and other desirable effects. This was motivated by the observation that the mere excitation of a single mode in a reduced degree of freedom model can adversely change the linear and angular momentum. Although unexpected changes in linear momentum can be avoided during basis construction, adverse changes in angular momentum appear unavoidable, and thus we propose a robust framework that includes the ability to compensate for them. Enabled by this ability to fully account for linear and angular momentum, we introduce an impulse-based formulation that allows us to precisely control the velocity of any node in spite of the fact that we only have access to a lower-dimensional set of degrees of freedom. This allows us to model collision, contact, and articulation in a robust and high visual fidelity manner, especially when compared to penalty-based forces that merely aim to coerce local velocities. In addition, we propose a new “deformable bones” framework wherein we leverage standard skinning technology for “bones,” “bone” placement, blending operations, etc. even though each of our “deformable bones” is a fully simulated reduced deformable model.

Fully Momentum-Conserving Reduced Deformable Bodies with Collision, Contact, Articulation, and Skinning

Saket Patkar, Ning Jin, Ronald Fedkiw

We present a novel sharp-crease bending element for the folding and wrinkling of surfaces and volumes. Based on a control curve specified by an artist or derived from internal stresses of a simulation, we create a piecewise linear curve at the resolution of the computational mesh. Then, the key idea is to cut the object along the curve using the virtual node algorithm creating new degrees of freedom, while subsequently reattaching the resulting pieces eliminating the translational degrees of freedom so that adjacent pieces may only rotate or bend about the cut. Motivated by an articulated rigid body framework, we utilize the concepts of pre-stabilization and post-stabilization in order to enforce these reattachment constraints. Our cuts can be made either razor sharp or relatively smooth via the use of bending springs. Notably, our sharp-crease bending elements can not only be used to create pleats in cloth or folds in paper but also to create similar buckling in volumetric objects. We illustrate this with examples of forehead wrinkles and nasolabial folds for facial animation. Moreover, our sharp-crease bending elements require minimal extra simulation time as compared to the underlying mesh, and tend to reduce simulation times by an order of magnitude when compared to the alternative of mesh refinement.

A New Sharp-Crease Bending Element for Folding and Wrinkling Surfaces and Volumes