Ronald Fedkiw

Visual simulation of smoke

In this paper, we propose a new approach to numerical smoke simulation for computer graphics applications. The method proposed here exploits physics unique to smoke in order to design a numerical method that is both fast and efficient on the relatively coarse grids traditionally used in computer graphics applications (as compared to the much finer grids used in the computational fluid dynamics literature). We use the inviscid Euler equations in our model, since they are usually more appropriate for gas modeling and less computationally intensive than the viscous Navier-Stokes equations used by others. In addition, we introduce a physically consistent vorticity confinement term to model the small scale rolling features characteristic of smoke that are absent on most coarse grid simulations. Our model also correctly handles the inter-action of smoke with moving objects.

Robust treatment of collisions, contact and friction for cloth animation

We present an algorithm to efficiently and robustly process collisions, contact and friction in cloth simulation. It works with any technique for simulating the internal dynamics of the cloth, and allows true modeling of cloth thickness. We also show how our simulation data can be post-processed with a collision-aware subdivision scheme to produce smooth and interference free data for rendering.

Practical animation of liquids

We present a general method for modeling and animating liquids. The system is specifically designed for computer animation and handles viscous liquids as they move in a 3D environment and interact with graphics primitives such as parametric curves and moving polygons. We combine an appropriately modified semi-Lagrangian method with a new approach to calculating fluid flow around objects. This allows us to efficiently solve the equations of motion for a liquid while retaining enough detail to obtain realistic looking behavior. The object interaction mechanism is extended to provide control over the liquid s 3D motion. A high quality surface is obtained from the resulting velocity field using a novel adaptive technique for evolving an implicit surface.

Simulating water and smoke with an octree data structure

We present a method for simulating water and smoke on an unrestricted octree data structure exploiting mesh refinement techniques to capture the small scale visual detail. We propose a new technique for discretizing the Poisson equation on this octree grid. The resulting linear system is symmetric positive definite enabling the use of fast solution methods such as preconditioned conjugate gradients, whereas the standard approximation to the Poisson equation on an octree grid results in a non-symmetric linear system which is more computationally challenging to invert. The semi-Lagrangian characteristic tracing technique is used to advect the velocity, smoke density, and even the level set making implementation on an octree straightforward. In the case of smoke, we have multiple refinement criteria including object boundaries, optical depth, and vorticity concentration. In the case of water, we refine near the interface as determined by the zero isocontour of the level set function.

Fast surface reconstruction using the level set method

We describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from a scattered data set. The data set might consist of points, curves and/or surface patches. A weighted minimal surface-like model is constructed and its variational level set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the level set method we can handle complicated topology and deformations, as well as noisy or highly nonuniform data sets easily. The method is based on a simple rectangular grid, although adaptive and triangular grids are also possible. Some consequences, such as hole filling capability, are demonstrated, as well as the viability and convergence of our new fast tagging algorithm.

Physically based modeling and animation of fire

We present a physically based method for modeling and animating fire. Our method is suitable for both smooth (laminar) and turbulent flames, and it can be used to animate the burning of either solid or gas fuels. We use the incompressible Navier-Stokes equations to independently model both vaporized fuel and hot gaseous products. We develop a physically based model for the expansion that takes place when a vaporized fuel reacts to form hot gaseous products, and a related model for the similar expansion that takes place when a solid fuel is vaporized into a gaseous state. The hot gaseous products, smoke and soot rise under the influence of buoyancy and are rendered using a blackbody radiation model. We also model and render the blue core that results from radicals in the chemical reaction zone where fuel is converted into products. Our method allows the fire and smoke to interact with objects, and flammable objects can catch on fire.

Automatic determination of facial muscle activations from sparse motion capture marker data

We built an anatomically accurate model of facial musculature, passive tissue and underlying skeletal structure using volumetric data acquired from a living male subject. The tissues are endowed with a highly nonlinear constitutive model including controllable anisotropic muscle activations based on fiber directions. Detailed models of this sort can be difficult to animate requiring complex coordinated stimulation of the underlying musculature. We propose a solution to this problem automatically determining muscle activations that track a sparse set of surface landmarks, e.g. acquired from motion capture marker data. Since the resulting animation is obtained via a three dimensional nonlinear finite element method, we obtain visually plausible and anatomically correct deformations with spatial and temporal coherence that provides robustness against outliers in the motion capture data. Moreover, the obtained muscle activations can be used in a robust simulation framework including contact and collision of the face with external objects.

Invertible finite elements for robust simulation of large deformation

We present an algorithm for the finite element simulation of elastoplastic solids which is capable of robustly and efficiently handling arbitrarily large deformation. In fact, our model remains valid even when large parts of the mesh are inverted. The algorithm is straightforward to implement and can be used with any material constitutive model, and for both volumetric solids and thin shells such as cloth. We also provide a mechanism for controlling plastic deformation, which allows a deformable object to be guided towards a desired final shape without sacrificing realistic behavior. Finally, we present an improved method for rigid body collision handling in the context of mixed explicit/implicit time-stepping.

A vortex particle method for smoke, water and explosions

Vorticity confinement reintroduces the small scale detail lost when using efficient semi-Lagrangian schemes for simulating smoke and fire. However, it only amplifies the existing vorticity, and thus can be insufficient for highly turbulent effects such as explosions or rough water. We introduce a new hybrid technique that makes synergistic use of Lagrangian vortex particle methods and Eulerian grid based methods to overcome the weaknesses of both. Our approach uses vorticity confinement itself to couple these two methods together. We demonstrate that this approach can generate highly turbulent effects unachievable by standard grid based methods, and show applications to smoke, water and explosion simulations.

Creating and simulating skeletal muscle from the visible human data set

Simulation of the musculoskeletal system has important applications in biomechanics, biomedical engineering, surgery simulation, and computer graphics. The accuracy of the muscle, bone, and tendon geometry as well as the accuracy of muscle and tendon dynamic deformation are of paramount importance in all these applications. We present a framework for extracting and simulating high resolution musculoskeletal geometry from the segmented visible human data set. We simulate 30 contact/collision coupled muscles in the upper limb and describe a computationally tractable implementation using an embedded mesh framework. Muscle geometry is embedded in a nonmanifold, connectivity preserving simulation mesh molded out of a lower resolution BCC lattice containing identical, well-shaped elements, leading to a relaxed time step restriction for stability and, thus, reduced computational cost. The muscles are endowed with a transversely isotropic, quasiincompressible constitutive model that incorporates muscle fiber fields as well as passive and active components. The simulation takes advantage of a new robust finite element technique that handles both degenerate and inverted tetrahedra.