A new method for the visualization of two-dimensional fluid flow is presented. The method is based on the advection and decay of dye. These processes are simulated by defining each frame of a flow animation as a blend between a warped version of the previous image and a number of background images. For the latter a sequence of filtered white noise images is used: filtered in time and space to remove high frequency components. Because all steps are done using images, the method is named Image Based Flow Visualization (IBFV). With IBFV a wide variety of visualization techniques can be emulated. Flow can be visualized as moving textures with line integral convolution and spot noise. Arrow plots, streamlines, particles, and topological images can be generated by adding extra dye to the image. Unsteady flows, defined on arbitrary meshes, can be handled. IBFV achieves a high performance by using standard features of graphics hardware. Typically fifty frames per second are generated using standard graphics cards on PCs. Finally, IBFV is easy to understand, analyse, and implement.

Figure 1: A silver block catapulting some wooden blocks into an oncoming wall of water. We present the Rigid Fluid method, a technique for animating the interplay between rigid bodies and viscous incompressible fluid with free surfaces. We use distributed Lagrange multipliers to ensure two-way coupling that generates realistic motion for both the solid objects and the fluid as they interact with one another. We call our method the rigid fluid method because the simulator treats the rigid objects as if they were made of fluid. The rigidity of such an object is maintained by identifying the region of the velocity field that is inside the object and constraining those velocities to be rigid body motion. The rigid fluid method is straightforward to implement, incurs very little computational overhead, and can be added as a bridge between current fluid simulators and rigid body solvers. Many solid objects of different densities (e.g., wood or lead) can be combined in the same animation.

We describe a method for controlling smoke simulations through user-specified keyframes. To achieve the desired behavior, a continuous quasi-Newton optimization solves for appropriate "wind" forces to be applied to the underlying velocity field throughout the simulation. The cornerstone of our approach is a method to efficiently compute exact derivatives through the steps of a fluid simulation. We formulate an objective function corresponding to how well a simulation matches the user's keyframes, and use the derivatives to solve for force parameters that minimize this function. For animations with several keyframes, we present a novel multipleshooting approach. By splitting large problems into smaller overlapping subproblems, we greatly speed up the optimization process while avoiding certain local minima.

In this paper we introduce a method to simulate fluid flows on smooth surfaces of arbitrary topology: an effect never seen before. We achieve this by combining a two-dimensional stable fluid solver with an atlas of parametrizations of a Catmull-Clark surface. The contributions of this paper are: (i) an extension of the Stable Fluids solver to arbitrary curvilinear coordinates, (ii) an elegant method to handle cross-patch boundary conditions and (iii) a set of new external forces custom tailored for surface flows. Our techniques can also be generalized to handle other types of processes on surfaces modeled by partial differential equations, such as reactiondiffusion. Some of our simulations allow a user to interactively place densities and apply forces to the surface, then watch their effects in real-time. We have also computed higher resolution animations of surface flows off-line.

We present a fast and stable system for animating materials that melt, flow, and solidify. Examples of real-world materials that exhibit these phenomena include melting candles, lava flow, the hardening of cement, icicle formation, and limestone deposition. We animate such phenomena by physical simulation of fluids -- in particular the incompressible viscous Navier-Stokes equations with free surfaces, treating solid and nearly-solid materials as very high viscosity fluids. The computational method is a modification of the Marker-and-Cell (MAC) algorithm in order to rapidly simulate fluids with variable and arbitrarily high viscosity. This allows the viscosity of the material to change in space and time according to variation in temperature, water content, or any other spatial variable, allowing different locations in the same continuous material to exhibit states ranging from the absolute rigidity or slight bending of hardened wax to the splashing and sloshing of water. We create detailed polygonal models of the fluid by splatting particles into a volumetric grid and we render these models using ray tracing with sub-surface scattering. We demonstrate the method with examples of several viscous materials including melting wax and sand drip castles.

In this paper we present a new method for efficiently controlling animated smoke. Given a sequence of target smoke states, our method generates a smoke simulation in which the smoke is driven towards each of these targets in turn, while exhibiting natural-looking interesting smoke-like behavior. This control is made possible by two new terms that we add to the standard flow equations: (i) a driving force term that causes the fluid to carry the smoke towards a particular target, and (ii) a smoke gathering term that prevents the smoke from diffusing too much. These terms are explicitly defined by the instantaneous state of the system at each simulation timestep. Thus, no expensive optimization is required, allowing complex smoke animations to be generated with very little additional cost compared to ordinary flow simulations.

Varied, realistic motion in a complex environment can bring an animated scene to life. While much of the required motion comes from the characters, an important contribution also comes from the passive motion of other objects in the scene. We use the term secondary motion to refer to passive motions that are generated in response to environmental forces or the movements of characters and other objects. For example, the movement of clothing and hair adds visual complexity to an animated scene of a jogging figure. In this paper, we describe how secondary motion can be generated by coupling physically based simulations of passive systems to active simulations of the main characters. We discuss three coupling methods for the interface between the passive and active systems: two-way, one-way, and hybrid. These three methods allow the animator to make an appropriate tradeoff between accuracy and computational speed. We use a basketball passing through a net as an illustrative example to demonstrate each of the three coupling methods. To provide guidance as to when each method is most appropriate, we present additional examples including a gymnast on a trampoline, a man on a bungee cord, a stunt kite, a gymnast landing on a exible mat, a diver entering the water, and several human gures wearing clothing. The information gained from analyzing these examples is summarized in a decision tree and a set of guidelines for coupling active and passive systems.

A key topic in computer graphics is the realistic representation of natural phenomena. Among the natural objects, one of the most interesting (and most difficult to deal with) is water. Its inherent complexity, far beyond that of most artificial objects, represents an irresistible challenge for the computer graphics world. Thus, during the last two decades we have witnessed an increasing number of papers addressing this problem from several points of view. However, the computer graphics community still lacks a survey classifying the vast literature on this topic, which is certainly unorganized and dispersed and hence, difficult to follow. This paper aims to fill this gap by offering a historical survey on the most relevant computer graphics techniques developed during the 1980s and 1990s for realistic modeling, rendering and animation of water.

this dissertation is drawn from the two publications, "Melting and Flowing" [8] and "Rigid Fluid: Animating the Interplay Between Rigid Bodies and Fluid" [7]. I am extremely grateful to my coauthors, Greg Turk, Peter Mucha and Brooks Van Horn, without whose help those articles would not exist

We present our original methodology for acceleration of fluids simulation computed by structured fluid simulators and solvers. The methodology is based on storing Pre-Calculated Fluid Simulator States (FSS) and organizing them in hierarchical tree structures allowing incremental solving, interactive replaying and modifications of simulated tasks. Thus, the parameters and boundary conditions of the simulation can be real-time modified during replaying. The simulation using our methodology is based on only partial computation with synchronous utilization of pre-calculated fluid simulator states stored on hard disk storage. We have incorporated this concept into real-time simulation and visualization system of combustion processes in pulverized coal boilers. The system is based on a simple fluid simulator and a coal particle system. We have made comparison of FSS features with classical approach of storing data sets and saving the visualization output to common movie formats. Furthermore, we have performed measurements of overall acceleration of simulation and discussed disk space demands. The disk space requirements are in orders less demanding than the ones needed for storing corresponding data sets. This allows better scalability and storing and interactive replaying simulation results of complex tasks with large grids and/or ten thousands of particles. Key words