Building animation tools for fluid-like motions is an important and challenging problem with many applications in computer graphics. The use of physics-based models for fluid flow can greatly assist in creating such tools. Physical models, unlike key frame or procedural based techniques, permit an animator to almost effortlessly create interesting, swirling fluid-like behaviors. Also, the interaction of flows with objects and virtual forces is handled elegantly. Until recently, it was believed that physical fluid models were too expensive to allow real-time interaction. This was largely due to the fact that previous models used unstable schemes to solve the physical equations governing a fluid. In this paper, for the first time, we propose an unconditionally stable model which still produces complex fluid-like flows. As well, our method is very easy to implement. The stability of our model allows us to take larger time steps and therefore achieve faster simulations. We have used our model in conjuction with advecting solid textures to create many fluid-like animations interactively in two- and three-dimensions.

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.

The ever-changing nature of liquids makes them very difficult to model and animate. This paper addresses the simulation of one aspect of liquids, i.e. droplets running down surfaces. We present a model oriented towards a visually-satisfying simulation and efficiency. The efficiency results

Abstract. A computer model of wave refraction is desirable, in the context of landscape modeling, to generate the familiar wave patterns seen near coastlines. In this article, we present a new method for the calculation of shallow water wave refraction. The method is more accurate than previously existing methods and provides realistic wave refraction effects. We resort to Fermat’s principle of the shortest path and compute the propagation of wavefronts over an arbitrary inhomogeneous medium. The propagation of wavefronts produces a phase map for each terrain. This phase map is then coupled with a geometric model of waves to generate a heightfield representation of the sea surface. 1

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 survey paper discusses the state-of-the-art in solid modeling, subdivision modeling, and physics-based modeling. Although related to each other, these research areas have yet to be integrated into a single framework. We present a historical review of each area separately, discuss research that has combined two of the above domains, and suggest directions for future work that combine concepts from all three. Solid modeling includes the study of different ways of representing and analyzing virtual solid objects. We examine several approaches to modeling solids and analyze their advantages and shortcomings. Subdivision modeling uses procedural algorithms to recursively define smooth curves, surfaces, and solids. We show the connections between subdivision modeling and spline-based modeling and demonstrate that the former is actually a generalization of the latter. Physics-based modeling augments geometric objects with physical attributes for the purposes of dynamic sculpting, physica...

We present a new method for enhancing shallow water simulations by the effect of overturning waves. While full 3D fluid simulations can capture the process of wave breaking, this is beyond the capabilities of a pure height field model. 3D simulations, however, are still too expensive for real-time applications, especially when large bodies of water need to be simulated. The extension we propose overcomes this problem and makes it possible to simulate scenes such as waves near a beach, and surf riding characters in real-time. In a first step, steep wave fronts in the height field are detected and marked by line segments. These segments then spawn sheets of fluid represented by connected particles. When the sheets impinge on the water surface, they are absorbed and result in the creation of particles representing drops and foam. To enable interesting applications, we furthermore present a two-way coupling of rigid bodies with the fluid simulation. The capabilities and efficiency of the method will be demonstrated with several scenes, which run in real-time on today’s commodity hardware. 1

Abstract. A simple method for animation of water waves is presented. The two-dimensional wave equation with damping is used to obtain a finite difference scheme for height distribution. A computational procedure employs explicit time integration. High frame rates are typically obtained for real-time animation of water waves. 1

In this paper we show how to incorporate effects of wind fields in cloth animations. We discuss two different approaches to model force fields describing air motion and show how these models can be augmented to exhibit interaction with deformable thin objects such as textiles. The first model is based on the Navier-Stokes equations, while the second method extends simple particle tracing methods by the effect of lee. In each case, we present a method for simulating the interaction of cloth movements with the wind field. Both methods have been integrated in an existing cloth simulation system, and we compare their respective advantages and disadvantages.