“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.”
Month: May 2007
Textured Liquids Based on the Marker Level Set
“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.”
A Finite Element Method on Convex Polyhedra
“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.”
Wave Particles
“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.”
Efficient Simulation of Inextensible Cloth
“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.”
*Updated* SIGGRAPH papers list
The official list of SIGGRAPH was posted today… Thought I would re-post the physics sub-list for good measure.
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
Wrinkled Flames and Cellular Patterns
“We model flames and fire using the Navier-Stokes equations combined with the level set method and jump conditions to model the reaction front. Previous works modeled the flame using a combination of propagation in the normal direction and a curvature term which leads to a level set equation that is parabolic in nature and thus overly dissipative and smooth. Asymptotic theory shows that one can obtain more interesting velocities and fully hyperbolic (as opposed to parabolic) equations for the level set evolution. In particular, researchers in the field of detonation shock dynamics (DSD)
have derived a set of equations which exhibit characteristic cellular patterns. We show how to make use of the DSD framework in the context of computer graphics simulations of flames and fire to obtain interesting features such as flame wrinkling and cellular patterns.”
FastLSM: Fast Lattice Shape Matching for Robust Real-Time Deformation
“We introduce a simple technique that enables robust approximation of volumetric, large-deformation dynamics for real-time or large-scale offline simulations. We propose Lattice Shape Matching, an extension of deformable shape matching to regular lattices with embedded geometry; lattice vertices are smoothed by convolution of rigid shape matching operators on local lattice regions, with the effective mechanical stiffness specified by the amount of smoothing via region width. Since the naive method can be very slow for stiff models — per-vertex costs scale cubically with region width — we provide a fast summation algorithm, Fast Lattice Shape Matching (FastLSM), that exploits the inherent summation redundancy of shape matching and can provide large-region matching at constant per-vertex cost. With this approach, large lattices can be simulated in linear time. We present several examples and benchmarks of an efficient CPU implementation, including many dozens of soft bodies simulated at real-time rates on a typical desktop machine.”
FastLSM: Fast Lattice Shape Matching for Robust Real-Time Deformation
TRACKS: Toward Directable Thin Shells
“We combine the often opposing forces of artistic freedom and mathematical determinism to enrich a given animation or simulation of a surface with physically based detail. We present a process called tracking, which takes as input a rough animation or simulation and enhances it with physically simulated detail. Building on the foundation of constrained Lagrangian mechanics, we propose weak-form constraints for tracking the input motion. This method allows the artist to choose where to add details such as characteristic wrinkles and folds of various thin shell materials and dynamical effects of physical forces. We demonstrate multiple applications ranging from enhancing an artist’s animated character to guiding a simulated inanimate object.”
Volume Conserving Finite Element Simulations of Deformable Models
“We propose a numerical method for modeling highly deformable nonlinear incompressible solids that conserves the volume locally near each node in a finite element mesh. Our method works with arbitrary constitutive models, is applicable to both passive and active materials (e.g. muscles), and works with simple tetrahedra without
the need for multiple quadrature points or stabilization techniques. Although simple linear tetrahedra typically suffer from locking when modeling incompressible materials, our method enforces incompressibility per node (in a one-ring), and we demonstrate that it is free from locking. We correct errors in volume without introducing oscillations by treating position and velocity in separate implicit solves. Finally, we propose a novel method for treating both object contact and self-contact as linear constraints during
the incompressible solve, alleviating issues in enforcing multiple possibly conflicting constraints.”
Volume Conserving Finite Element Simulations of Deformable Models