Physics-Based Animation

We focus on the challenging problem of simulating thin elastic rods in contact, in the presence of friction. Most previous approaches in computer graphics rely on a linear complementarity formulation for handling contact in a stable way, and approximate Coulombs’s friction law for making the problem tractable. In contrast, following the seminal work by Alart and Curnier in contact mechanics, we simultaneously model contact and exact Coulomb friction as a zero finding problem of a nonsmooth function. A semi-implicit time-stepping scheme is then employed to discretizethe dynamics of rods constrained by frictional contact: this leads to a set of linear equations subject to an equality constraint involving a non-differentiable function. To solve this one-step problem we introduce a simple and practical nonsmooth Newton algorithm, which proves to be reasonably efficient and robust for systems that are not over-constrained. We show that our method is able to finely capture the subtle effects that occur when thin elastic rods with various geometries enter into contact, such as stick-slip instabilities in free configurations, entangling curls, resting contacts in braid-like structures, or the formation of tight knots under large constraints. Our method can be viewed as a first step towards the accurate modeling of dynamic fibrous materials.

A Nonsmooth Newton Solver for Capturing Exact Coulomb Friction in Fiber Assemblies

We present a novel approach to fluid simulation, allowing us to take into account the surface energy in a precise manner. This new approach combines a novel, topology-adaptive approach to deformable interface tracking, called the deformable simplicial complexes method (DSC) with an optimization-based, linear finite element method for solving the incompressible Euler equations. The deformable simplicial complexes track the surface of the fluid: the fluid-air interface is represented explicitly as a piecewise linear surface which is a subset of tetrahedralization of the space, such that the interface can be also represented implicitly as a set of faces separating tetrahedra marked as inside from the ones marked as outside. This representation introduces insignificant and controllable numerical diffusion, allows robust topological adaptivity and provides both a volumetric finite element mesh for solving the fluid dynamics equations as well as direct access to the interface geometry data, making inclusion of a new surface energy term feasible. Furthermore, using an unstructured mesh makes it straightforward to handle curved solid boundaries and gives us a possibility to explore several fluid-solid interaction scenarios.

Optimization-based Fluid Simulation on Unstructured Meshes

We develop a new Lagrangian primitive, named Langevin particle, to incorporate turbulent flow details in fluid simulation. A group of the particles are distributed inside the simulation domain based on a turbulence energy model with turbulence viscosity. A particle in particular moves obeying the generalized Langevin equation, a well-known stochastic differential equation that describes the particle’s motion as a random Markov process. The resultant particle trajectory shows self-adapted fluctuation in accordance to the turbulence energy, while following the global flow dynamics. We then feed back Langevin forces to the simulation based on the stochastic trajectory, which drive the flow with necessary turbulence. The new hybrid flow simulation method features nonrestricted particle evolution requiring minimal extra manipulation after initiation. The flow turbulence is easily controlled and the total computational overhead of enhancement is minimal based on typical fluid solvers.

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

Cem Yuksel, Texas A&M, 2010: Real-Time Water Waves with Wave Particles

Hybrid Multiresolution Wire

We present a fluid simulation method based on Smoothed Particle Hydrodynamics (SPH) in which incompressibility and boundary conditions are enforced using holonomic kinematic constraints on the density. This formulation enables systematic multiphysics integration in which interactions are modeled via similar constraints between the fluid pseudo-particles and impenetrable surfaces of other bodies. These conditions embody Archimede’s principle for solids and thus buoyancy results as a direct consequence. We use a variational time stepping scheme suitable for general constrained multibody systems we call SPOOK. Each step requires the solution of only one Mixed Linear Complementarity Problem (MLCP) with very few inequalities, corresponding to solid boundary conditions. We solve this MLCP with a fast iterative method. Overall stability is vastly improved in comparison to the unconstrained version of SPH, and this allows much larger time steps, and an increase in overall performance by two orders of magnitude. Proof of concept is given for computer graphics applications and interactive simulations.

Constraint Fluids

We present a hexahedral finite element method for simulating cuts in deformable bodies using the corotational formulation of strain at high computational efficiency. Key to our approach is a novel embedding of adaptive element refinements and topological changes of the simulation grid into a geometric multigrid solver. Starting with a coarse hexahedral simulation grid, this grid is adaptively refined at the surface of a cutting tool until a finest resolution level, and the cut is modeled by separating elements along the cell faces at this level. To represent the induced discontinuities on successive multigrid levels, the affected coarse grid cells are duplicated and the resulting connectivity components are distributed to either side of the cut. Drawing upon recent work on octree and multigrid schemes for the numerical solution of partial differential equations, we develop efficient algorithms for updating the systems of equations of the adaptive finite element discretization and the multigrid hierarchy. To construct a surface that accurately aligns with the cuts, we adapt the splitting cubes algorithm to the specific linked voxel representation of the simulation domain we use. The paper is completed by a convergence analysis of the finite element solver and a performance comparison to alternative numerical solution methods. These investigations show that our approach offers high computational efficiency and physical accuracy, and that it enables cutting of deformable bodies at very high resolutions.

A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects

A thesis from 2009 that I missed:

Barbara Solenthaler, University of Zurich: Incompressible Fluid Simulation and Advanced Surface Handling with SPH

I was recently asked whether there exists any internet forum dedicated to physics-based animation. The two that came to mind are Gamedev’s Math & Physics forum and Bullet’s physics simulation forums (both linked in the right column of the page), though my impression is that these naturally tend to be focused towards games, and with somewhat greater emphasis on rigid bodies and collision detection. So I wanted to pose some questions to you…

1. Are there other forum sites that focus on physical simulation for computer graphics? If so please post a link in the comments.
2. Would a dedicated physics-based animation forum be of genuine use to you? (Alternatively, do existing forums already serve this purpose, or do you not see a need for such a forum?)

Feel free to share any other thoughts you have on the subject.

We present a volumetric iso-geometric finite element analysis based on Catmull-Clark solids. This concept allows one to use the same representation for the modeling, the physical simulation, and the visualization, which optimizes the design process and narrows the gap between CAD and CAE. In our method the boundary of the solid model is a Catmull-Clark surface with optional corners and creases to support the modeling phase. The crucial point in the simulation phase is the need to perform efficient  integration for the elements. We propose a method similar to the standard subdivision surface evaluation technique, such that numerical quadrature can be used.
Experiments show that our approach converges faster than methods based on tri-linear and tri-quadratic elements. However, the topological structure of Catmull-Clark elements is as simple as the structure of linear elements. Furthermore, the Catmull-Clark elements we use are C2-continuous on the boundary and in the interior except for irregular vertices and edges.

Iso-geometric Analysis Based on Catmull-Clark Subdivision Solids