Physics-Based Animation

“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

“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.”

Wrinkled Flames and Cellular Patterns

“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

“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.”

TRACKS: Toward Directable Thin Shells

“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

“We present a fast continuous collision detection (CCD) algorithm for articulated models using Taylor models and temporal culling. Our algorithm is a generalization of conservative advancement (CA) from convex models [Mirtich 1996] to articulated models with non-convex links. Given the initial and final configurations of a moving articulated model, our algorithm creates a continuous motion with constant translational and rotational velocities for each link, and checks for interferences between the articulated model under continuous motion and other models in the environment and for self-collisions. If collisions occur, our algorithm reports the first time of contact (TOC) as well as collision witness features. We have implemented our CCD algorithm and applied it to several challenging scenarios including locomotion generation, articulated body dynamics and character motion planning. Our algorithm can perform CCDs including self-collisions for articulated models consisting of many links and tens of thousands of triangles in 1.22 ms on average running on a 3.6 GHz Pentium 4 PC. This is an improvement on the performance of prior algorithms of more than an order of magnitude.”

Continuous Collision Detection for Articulated Models using Taylor Models and Temporal Culling

“We present novel adaptive sampling algorithms for particle-based
fluid simulation. We introduce a sampling condition based on geometric
local feature size that allows focusing computational resources
in geometrically complex regions, while reducing the number
of particles deep inside the fluid or near thick flat surfaces. Further
performance gains are achieved by varying the sampling density
according to visual importance. In addition, we propose a novel
fluid surface definition based on approximate particle–to–surface
distances that are carried along with the particles and updated appropriately.
The resulting surface reconstruction method has several
advantages over existing methods, including stability under
particle resampling and suitability for representing smooth flat surfaces.
We demonstrate how our adaptive sampling and distancebased
surface reconstruction algorithms lead to significant improvements
in time and memory as compared to single resolution particle
simulations, without significantly affecting the fluid flow behavior.”

Adaptively Sampled Particle Fluids

“The isosurface stuffing algorithm fills an isosurface with a uniformly
sized tetrahedral mesh whose dihedral angles are bounded
between 10.7◦ and 164.8◦, or (with a change in parameters) between
8.9◦ and 158.8◦. The algorithm is whip fast, numerically robust,
and easy to implement because, like Marching Cubes, it generates
tetrahedra from a small set of precomputed stencils. A variant
of the algorithm creates a mesh with internal grading: on the boundary,
where high resolution is generally desired, the elements are fine
and uniformly sized, and in the interior they may be coarser and
vary in size. This combination of features makes isosurface stuffing
a powerful tool for dynamic fluid simulation, large-deformation
mechanics, and applications that require interactive remeshing or
use objects defined by smooth implicit surfaces. It is the first algorithm
that rigorously guarantees the suitability of tetrahedra for
finite element methods in domains whose shapes are substantially
more challenging than boxes. Our angle bounds are guaranteed by
a computer-assisted proof. If the isosurface is a smooth 2-manifold
with bounded curvature, and the tetrahedra are sufficiently small,
then the boundary of the mesh is guaranteed to be a geometrically
and topologically accurate approximation of the isosurface.”

Isosurface Stuffing: Fast Tetrahedral Meshing with Good Dihedral Angles

Again, although this is a geometry paper at heart, it has obvious applications to fluids and finite element simulation, so it’s definitely relevant. And allow me to editorialize for a moment and say, wow, that’s fast.

“We present an extension to Lagrangian finite element methods to allow for large plastic deformations of solid materials. These behaviors are seen in such everyday materials as shampoo, dough, and clay as well as in fantastic gooey and blobby creatures in special effects scenes. To account for plastic deformation, we explicitly update the linear basis functions defined over the finite elements during each simulation step. When these updates cause the basis functions to become ill-conditioned, we remesh the simulation domain to produce a new high-quality finite-element mesh, taking care to preserve the original boundary. We also introduce an enhanced plasticity model that preserves volume and includes creep and work hardening/softening. We demonstrate our approach with simulations of synthetic objects that squish, dent, and flow. To validate our methods, we compare simulation results to videos of real materials.”

A Finite Element Method for Animating Large Viscoplastic Flow