Physics-Based Animation

Oleksiy Busaryev, Tamal Dey, Huamin Wang, Ren Zhong

Bubbles and foams are important features of liquid surface phenomena, but they are difficult to animate due to their thin films and complex interactions in the real world. In particular, small bubbles (having diameter <1cm) in a dense foam are highly affected by surface tension, so their shapes are much less deformable compared with larger bubbles. Under this small bubble assumption, we propose a more accurate and efficient particle-based algorithm to simulate bubble dynamics and interactions. The key component of this algorithm is an approximation of foam geometry, by treating bubble particles as the sites of a weighted Voronoi diagram. The connectivity information provided by the Voronoi diagram allows us to accurately model various interaction effects among bubbles. Using Voronoi cells and weights, we can also explicitly address the volume loss issue in foam simulation, which is a common problem in previous approaches. Under this framework, we present a set of bubble interaction forces to handle miscellaneous foam behaviors, including foam structure under Plateau’s laws, clusters formed by liquid surface bubbles, bubble-liquid and bubble-solid coupling, bursting and coalescing. Our experiment shows that this method can be straightforwardly incorporated into existing liquid simulators, and it can efficiently generate realistic foam animations, some of which have never been produced in graphics before.

Animating Bubble Interactions in a Liquid Foam

Doyub Kim, Seung Woo Lee, Oh-young Song, Hyeong-Seok Ko

The explosive or volcanic scenes in motion pictures involve complex turbulent flow as its temperature and density vary in space. To simulate this turbulent flow of an inhomogeneous fluid, we propose a simple and efficient framework. Instead of explicitly computing the complex motion of this fluid dynamical instability, we first approximate the average motion of the fluid. Then, the high-resolution dynamics is computed using our new extended version of the vortex particle method with baroclinity. This baroclinity term makes turbulent effects by generating new vortex particles according to temperature/density distributions. Using our method, we efficiently simulated a complex scene with varying density and temperature.

Baroclinic Turbulence with Varying Density and Temperature

Efficient and scalable simulation of solids and fluids – Jonathan Su, Stanford

Catching up on a collection I had never assembled…

• Langevin Particle: A Self-Adaptive Lagrangian Primitive for Flow Simulation Enhancement

STAR:

• Interactive Character Animation using Simulated Physics

Melina Skouras, Bernhard Thomaszewski, Bernd Bickel, Markus Gross

This paper presents an automatic process for fabrication-oriented design of custom-shaped rubber balloons. We cast computational balloon design as an inverse problem: given a target shape, we compute an optimal balloon that, when inflated, approximates the target as closely as possible. To solve this problem numerically, we propose a novel physics-driven shape optimization method, which combines physical simulation of inflatable elastic membranes with a dedicated constrained optimization algorithm. We validate our approach by fabricating balloons designed with our method and comparing their inflated shapes to the results predicted by simulation. An extensive set of manufactured sample balloons demonstrates the shape diversity that can be achieved by our method.

Computational Design of Rubber Balloons

Florence Bertails-Descoubes

Piecewise clothoids are 2D curves with continuous, piecewise linear curvature. Due to their smoothness properties, they have been extensively used in road design and robot path planning, as well as for the compact representation of hand-drawn curves. In this paper we present the Super-Clothoid model, a new mechanical model that for the first time allows for the computing of the dynamics of an elastic, inextensible piecewise clothoid. We first show that the kinematics of this model can be computed analytically depending on the Fresnel integrals, and precisely evaluated when required. Secondly, the discrete dynamics, naturally emerging from the Lagrange equations of motion, can be robustly and efficiently computed by performing and storing formal computations as far as possible, recoursing to numerical evaluation only when assembling the linear system to be solved at each time step. As a result, simulations turn out to be both interactive and stable, even for large displacements of the rod. Finally, we demonstrate the versatility of our model by handling various boundary conditions for the rod as well as complex external constraints such as frictional contact, and show that our model is perfectly adapted to inverse statics. Compared to lower-order models, the super-clothoid appears as a more natural and aesthetic primitive for bridging the gap between 2D geometric design and physics-based deformation.

Super-Clothoids

Ke-Sen’s steadily growing list of SIGGRAPH 2012 papers is here. Below is the subset of physics-based animation papers…

SIGGRAPH papers:

• Continuous Penalty Forces
• Energy-Based Self-Collision Culling for Arbitrary Mesh Deformations
• Discrete Viscous Sheets
• Animating Bubble Interactions in a Liquid Foam
• Interactive Editing of Deformable Simulations
• Underwater Rigid Body Dynamics
• Efficient Geometrically Exact Continuous Collision Detection
• Ghost SPH for Animating Water
• Lagrangian Vortex Sheets for Animating Fluids
• Reflections on Simultaneous Impact
• Tracking Surfaces with Evolving Topology
• Mass-Splitting for Jitter-Free Parallel Rigid Body Simulation
• Adaptive Image-Based Intersection Volume
• Versatile Rigid-Fluid Coupling for Incompressible SPH
• Interactive Space-Time Control of Deformable Objects
• Rig-Space Physics
• Deformable Objects Alive!

TOG Papers:

• Updated Sparse Cholesky Factors for Co-Rotational Elastodynamics
• VolCCD: Fast continuous collision culling between deforming volume meshes
• Poly-Depth: Real-Time Penetration Depth using Iterative Contact-Space Projection
• MultiFLIP for Energetic Two-Phase Fluid Simulation
• Topology-Adaptive Interface Tracking Using the Deformable Simplicial Complex
• Fluid Simulation Using Laplacian Eigenfunctions
• Fast Simulation of Skeleton-Driven Deformable Body Characters

Min Tang, Dinesh Manocha, Miguel Otaduy, Ruofeng Tong

We present a simple algorithm to compute continuous penalty forces to determine collision response between rigid and deformable models bounded by triangle meshes. Our algorithm provides a well-behaved solution in contrast to the traditional stability and robustness problems of penalty methods, induced by force discontinuities. We trace contact features along their deforming trajectories and accumulate penalty forces along the penetration time intervals between the overlapping feature pairs. Moreover, we present a closed-form expression to compute the continuous and smooth collision response. Our method has very small additional overhead compared to previous penalty methods, while significantly improves the stability and robustness. We highlight its benefits on several benchmarks.

Continuous Penalty Forces

Tyler de Witt, Christian Lessig, Eugene Fiume

We present an algorithm for the simulation of incompressible fluid phenomena that is computationally efficient and leads to visually convincing simulations with far fewer degrees of freedom than existing approaches. Rather than using an Eulerian grid or Lagrangian elements, we represent vorticity and velocity using a basis of global functions defined over the entire simulation domain. We show that choosing Laplacian eigenfunctions for this basis provides benefits, including correspondence with spatial scales of vorticity and precise energy control at each scale. We perform Galerkin projection of the Navier-Stokes equations to derive a time evolution equation in the space of basis coefficients. Our method admits closed form solutions on simple domains but can also be implemented efficiently on arbitrary meshes.

Fluid Simulation Using Laplacian Eigenfunctions

Florian Hecht, Yeon Jin Lee, Jonathan Shewchuk, James O’Brien

We present warp-canceling corotation, a nonlinear finite element formulation for elastodynamic simulation that achieves fast performance by making only partial or delayed changes to the simulation’s linearized system matrices. Coupled with an algorithm for incremental updates to a sparse Cholesky factorization, the method realizes the stability and scalability of a sparse direct method without the need for expensive refactorization at each time step. This finite element formulation combines the widely used corotational method with stiffness warping so that changes in the per-element rotations are initially approximated by inexpensive per-node rotations. When the errors of this approximation grow too large, the per-element rotations are selectively corrected by updating parts of the matrix chosen according to locally measured errors. These changes to the system matrix are propagated to its Cholesky factor by incremental updates that are much faster than refactoring the matrix from scratch. A nested dissection ordering of the system matrix gives rise to a hierarchical factorization in which changes to the system matrix cause limited, well-structured changes to the Cholesky factor. We show examples of simulations that demonstrate that the proposed formulation produces results that are visually comparable to those produced by a standard corotational formulation. Because our method requires computing only partial updates of the Cholesky factor, it is substantially faster than full refactorization and outperforms widely used iterative methods such as preconditioned conjugate gradients. Our method supports a controlled trade-off between accuracy and speed, and unlike most iterative methods its performance does not slow for stiffer materials but rather it actually improves.

Updated Sparse Cholesky Factors for Corotational Elastodynamics