Physics-Based Animation

We present a weakly compressible form of the Smoothed Particle Hydrodynamics method (SPH) for fluid flow based on the Tait equation. In contrast to commonly employed projection approaches that strictly enforce incompressibility, time-consuming solvers for the Poisson equation are avoided by allowing for small, user-defined density fluctuations. We also discuss an improved surface tension model that is particularly appropriate for single-phase free-surface flows. The proposed model is compared to existing models and experiments illustrate the accuracy of the approach for free surface flows. Combining the proposed methods, volume-preserving low-viscosity liquids can be efficiently simulated using SPH. The approach is appropriate for medium-scale and small-scale phenomena. Effects such as splashing and breaking waves are naturally handled.

Weakly Compressible SPH for Free Surface Flows

Although mesh-based methods are efficient for simulating simple hyperelasticity, maintaining and adapting a mesh-based representation is less appealing in more complex scenarios, e.g. collision, plasticity and fracture. Thus, meshless or point-based methods have enjoyed recent popularity due to their added flexibility in dealing with these situations. Our approach begins with an initial mesh that is either conforming (as generated by one’s favorite meshing algorithm) or non-conforming (e.g. a BCC background lattice). We then propose a framework for embedding arbitrary sample points into this initial mesh allowing for the straightforward handling of collisions, plasticity and fracture without the need for complex remeshing. A straightforward consequence of this new framework is the ability to naturally handle T-junctions alleviating the requirement for a manifold initial mesh. The arbitrarily added embedded points are endowed with full simulation capability allowing them to collide, interact with each other, and interact with the parent geometry in the fashion of a particle-centric simulation system. We demonstrate how this formulation facilitates tasks such as arbitrary refinement or resampling for collision processing, the handling of multiple and possibly conflicting constraints (e.g. when cloth is nonphysically pinched between two objects), the straightforward treatment of fracture, and sub-element resolution of elasticity and plasticity.

Hybrid Simulation of Deformable Solids

We propose a flexible geometric algorithm for placing arbitrary cracks and incisions on tetrahedralized deformable objects. Although techniques based on remeshing can also accommodate arbitrary fracture patterns, this flexibility comes at the risk of creating sliver elements leading to models that are inappropriate for subsequent simulation. Furthermore, interactive applications such as virtual surgery simulation require both a relatively low resolution mesh for efficient simulation of elastic deformation and highly detailed surface geometry to facilitate accurate manipulation and cut placement. Thus, we embed a high resolution material boundary mesh into a coarser tetrahedral mesh using our cutting algorithm as a meshing tool, obtaining meshes that can be efficiently simulated while preserving surface detail. Our algorithm is similar to the virtual node algorithm in that we avoid sliver elements and their associated stringent timestep restrictions, but it is significantly more general allowing for the arbitrary cutting of existing cuts, sub-tetrahedron resolution (e.g. we cut a single tetrahedron into over a thousand pieces), progressive introduction of cuts while the object is deforming, and moreover the ability to accurately cut the high resolution embedded mesh.

Arbitrary Cutting of Deformable Tetrahedralized Objects

“Simulation of deformations and collision detection are two highly intertwined problems that are often treated separately. This is especially true in existing elegant adaptive simulation techniques, where standard collision detection algorithms cannot leverage the adaptively selected degrees of freedom.We propose a seamless integration of multi-grid algorithms and collision detection that identifies boundary conditions while inherently exploiting adaptivity. We realize this integration through multiscale bounding hierarchies, a novel unified hierarchical representation, together with an adaptive multigrid algorithm for irregular meshes and an adaptivity-aware hierarchical collision detection algorithm. Our solution produces detailed deformations with adapted computational cost, but it also enables robust interactive simulation of self-colliding deformable objects with high-resolution surfaces.”

Adaptive Deformations with Fast Tight Bounds

“This paper describes a simulation method for animating the behavior of incompressible liquids with complex free surfaces. The region occupied by the liquid is discretized with a boundary-conforming tetrahedral mesh that grades from fine resolution near the surface to coarser resolution in the interior. At each time step, semi-Lagrangian techniques are used to advect the fluid and its boundary forward, and a new conforming mesh is constructed over the fluid-occupied region. The tetrahedral meshes are built using a variation of the body centered cubic lattice structure that allows octree grading and deviation from the lattice structure at boundaries. The semi-regular mesh structure can be generated rapidly and allows efficient computation and storage while still conforming well to boundaries and providing a mesh-quality guarantee. Pressure projection is performed using an algebraic multigrid method, and a thickening scheme is used to reduce volume loss when fluid features shrink below mesh resolution. Examples demonstrate that the method can capture complex liquid motions that include fine detail on the free surfaces without suffering from excessive amounts of volume loss or artificial damping.”

Liquid Simulation on Lattice-Based Tetrahedral Meshes

“In this work we propose a new Eulerian method for handling the dynamics of a liquid and its surface attributes (for example its color). Our approach is based on a new method for interface advection that we term the Marker Level Set (MLS). The MLS method uses surface markers and a level set for tracking the surface of the liquid, yielding more efficient and accurate results than popular methods like the Particle Level Set method (PLS). Another novelty is that the surface markers allow the MLS to handle non-diffusively surface texture advection, a rare capability in the realm of Eulerian simulation of liquids. We present several simulations of the dynamical evolution of liquids
and their surface textures.”

Textured Liquids Based on the Marker Level Set

 “We present a method for animating deformable objects using a novel finite element discretization on convex polyhedra. Our finite element approach draws upon recently introduced 3D mean value coordinates to define smooth interpolants within the elements. The mathematical properties of our basis functions guarantee convergence. Our
method is a natural extension to linear interpolants on tetrahedra: for tetrahedral elements, the methods are identical. For fast and robust computations, we use an elasticity model based on Cauchy strain and stiffness warping. This more flexible discretization is particularly useful for simulations that involve topological changes, such as cutting or fracture. Since splitting convex elements along a plane produces convex elements, remeshing or subdivision schemes used in simulations based on tetrahedra are not necessary, leading to less elements after such operations. We propose various operators for cutting the polyhedral discretization. Our method can handle arbitrary cut trajectories, and there is no limit on how often elements can be split.”

A Finite Element method on Convex Polyhedra

“We present a new method for the real-time simulation of fluid surface waves and their interactions with floating objects. The method is based on the new concept of wave particles, which offers a simple, fast, and unconditionally stable approach to wave simulation. We show how graphics hardware can be used to convert wave particles to a height field surface, which is warped horizontally to account for local wave-induced flow. The method is appropriate for most fluid simulation situations that do not involve significant global flow. It is demonstrated to work well in constrained areas, including wave reflections off of boundaries, and in unconstrained areas, such as an ocean surface. Interactions with floating objects are easily integrated by including wave forces on the objects and wave generation due to object motion. Theoretical foundations and implementation details are provided, and experiments demonstrate that we achieve plausible realism. Timing studies show that the method is scalable to allow simulation of wave interaction with several hundreds of objects at real-time rates.”

Wave Particles

“Many textiles do not noticeably stretch under their own weight. Unfortunately, for better performance many cloth solvers disregard this fact. We propose a method to obtain very low strain along the warp and weft direction using Constrained Lagrangian Mechanics and a novel fast projection method. The resulting algorithm acts as a velocity filter that easily integrates into existing simulation code.”

Efficient Simulation of Inextensible Cloth

The official list of SIGGRAPH was posted today… Thought I would re-post the physics sub-list for good measure.

Official list

Unofficial SIGGRAPH 2007 papers on the web

Physics papers:

• A Finite Element Method for Animating Large Viscoplastic Flow
• Many-Worlds Browsing for Control of Multibody Dynamics
• Simulation of Bubbles in Foam With The Volume Control Method
• Adaptively Sampled Particle Fluids
• FastLSM: Fast Lattice Shape Matching for Robust Real-Time Deformation
• Volume Conserving Finite Element Simulation of Deformable Models
• Wrinkled Flames and Cellular Patterns
• Curl-Noise for Procedural Fluid Flow
• A Variational Approach to Eulerian Geometry Processing
• A Fast Variational Framework for Accurate Solid-Fluid Coupling
• Continuous Collision Detection for Articulated Models using Taylor Models and Temporal Culling
• TRACKS: Toward Directable Thin Shells
• Isosurface Stuffing: Fast Tetrahedral Meshing with Good Dihedral Angles
• Efficient Simulation of Inextensible Cloth
• Bubbling and Frothing Liquids
• Wave Particles