Particle-Based Simulation of Granular Materials

Granular materials, such as sand and grains, are ubiquitous. Simulating the 3D dynamic motion of such materials represents a challenging problem in graphics because of their unique physical properties. In this paper we present a simple and effective method for granular material simulation. By incorporating techniques from physical models, our approach describes granular phenomena more faithfully than previous methods. Granular material is represented by a large collection of non-spherical particles which may be in persistent contact. The particles represent discrete elements of the simulated material. One major advantage of using discrete elements is that the topology of particle interaction can evolve freely. As a result, highly dynamic phenomena, such as splashing and avalanches, can be conveniently generated by this meshless approach without sacrificing physical accuracy. We generalize this discrete model to rigid bodies by distributing particles over their surfaces. In this way, two-way coupling between granular materials and rigid bodies is achieved.

Videos can be found here.

Taming Liquids for Rapidly Changing Targets

Following rapidly changing target objects is a challenging problem in fluid control, especially when the natural fluid motion should be preserved. The fluid should be responsive to the changing configuration of the target and, at the same time, its motion should not be overconstrained. In this paper, we introduce an efficient and effective solution by applying two different external force fields. The first one is a feedback force field which compensates for discrepancies in both shape and velocity. Its shape component is designed to be divergence free so that it can survive the velocity projection step. The second one is the gradient field of a potential function defined by the shape and skeletion of the target object. Our experiments indicate a mixture of these two force fields can achieve desirable and pleasing effects.

Videos can be found here.

Controllable Smoke Animation with Guiding Objects

This paper addresses the problem of controlling the density and dynamics during smoke simulation so that the synthetic appearance of the smoke resembles a still or moving object. Both the smoke region and the target object are represented as implicit functions. As a part of the target implicit function, a shape transformation is generated between an initial smoke region and the target object. In order to match the smoke surface with the target surface, we impose carefully designed velocity constraints on the smoke boundary during a dynamic fluid simulation. The velocity constraints are derived from an iterative functional minimization procedure for shape matching. The dynamics of the smoke is formulated using a novel compressible fluid model which can effectively absorb the discontinuities in the velocity field caused by imposed velocity constraints while reproducing realistic smoke appearances. As a result, a smoke region can evolve into a regular object and follow the motion of the object while maintaining its smoke appearance.

A related earlier technical report:
"Object Modeling and Animation with Smoke"
Lin Shi and Yizhou Yu
Tech Report UIUCDCS-R-2002-2262, January 2002. PDF

Controllable Motion Synthesis in a Gaseous Medium

The generation of realistic motion satisfying user-defined requirements is one of the most important goals of computer animation. Our aim in this paper is the synthesis of realistic, controllable motion for lightweight natural objects in a gaseous medium.We formulate this problem as a large-scale spacetime optimization with user controls and fluid motion equations as constraints. We have devised novel and effective methods to make this large optimization tractable. Initial trajectories are generated with data-driven synthesis based on stylistic motion planning. Smoothed particle hydrodynamics (SPH) is used during optimization to produce fluid simulations at a reasonable computational cost, while interesting vortex-based fluid motion is generated by recording the presence of vortices in the initial trajectories and maintaining them through optimization. Object rotations are refined as a postprocess to enhance the visual quality of the results. We demonstrate our techniques on a number of animations involving single or multiple objects.

Inviscid and Incompressible Fluid Simulation on Triangle Meshes

Simulating fluid motion on manifold surfaces is an interesting but rarely explored area because of the difficulty of establishing plausible physical models. In this paper, we introduce a novel method for inviscid fluid simulation over meshes. It can enforce incompressibility on closed surfaces by utilizing a discrete vector field decomposition algorithm. It also includes effective implementations of semi-Lagrangian tracing and velocity interpolation schemes. Different from previous work, our method performs simulations directly on triangle meshes and thus eliminates parametrization distortions. Our implementation can produce convincing fluid motion on surfaces and has interactive performance for meshes with tens of thousands of faces.

Videos can also be found here.

Visual Smoke Simulation with Adaptive Octree Refinement

Three dimensional fluid simulation becomes expensive on high resolution grids which can easily consume a large amount of physical memory. This paper presents an octree-based algorithm for visual simulation of smoke on ordinary workstations. This method adaptively subdivides the whole simulation volume into multiple subregions using an octree. Each leaf node in the octree also holds a uniform subgrid which is the basic unit for simulation. A previous smoke simulation algorithm based on a semi-Lagrangian scheme has been adapted to this hybrid octree-based data structure. A pair of PullUp and PushDown procedures are designed to solve the Poisson equation for pressure at each octree node. A novel node subdivision and merging scheme is also developed to dynamically adjust the octree during each iteration of the simulation so that regions containing more details are more likely to be subdivided to achieve better accuracy.