We present a comprehensive methodology for realistically animating liquid phenomena. Our approach unifies existing computer graphics techniques for simulating fluids and extends them by incorporating more complex behavior. It is based on the Navier-Stokes equations which couple momentum and mass conservation to completely describe fluid motion. Our starting point is an environment containing an arbitrary distribution of fluid, and submerged or semi-submerged obstacles. Velocity and pressure are defined everywhere within this environment, and updated using a set of finite difference expressions. The resulting vector and scalar fields are used to drive a height field equation representing the liquid surface. The nature of the coupling between obstacles in the environment and free variables allows for the simulation of a wide range of effects that were not possible with previous computer-graphics fluid models. Wave effects such as reflection, refraction and diffraction, as well as rotational effects such as eddies, vorticity, and splashing are a natural consequence of solving the system. In addition, the Lagrange equations of motion are used to place buoyant dynamic objects into a scene, and track the position of spray and foam during the animation process. Typical disadvantages to dynamic simulations such as poor scalability and lack of control are addressed by assuming that stationary obstacles align with grid cells during the finite difference discretization, and by appending terms to the Navier-Stokes equations to include forcing functions. Free surfaces in our system are represented as either a collection of massless particles in 2D, or a height field which is suitable for many of the water rendering algorithms presented by researchers in recent years.

Over the years, there have been two main branches of computer graphics image-synthesis research; one focused on interactivity, the other on image quality. Procedural shading is a powerful tool, commonly used for creating high-quality images and production animation. A key aspect of most procedural shading is the use of a shading language, which allows a high-level description of the color and shading of each surface. However, shading languages have been beyond the capabilities of the interactive graphics hardware community. We have created a parallel graphics multicomputer, PixelFlow, that can render images at 30 frames per second using a shading language. This is the first system to be able to support a shading language in real-time. In this paper, we describe some of the techniques that make this possible. CR Categories and Subject Descriptors: D.3.2 [Language Classifications] Specialized Application Languages; I.3.1 [Computer Graphics] Hardware Architecture; I.3.3 [Computer Graphic...

In computer graphics, rendering is the process by which an abstract description of a scene is converted to an image. When the scene is complex, or when high-quality images or high frame rates are required, the rendering process becomes computationally demanding. To provide the necessary levels of performance, parallel computing techniques must be brought to bear. Although parallelism has been exploited in computer graphics since the early days of the field, its initial use was primarily in specialized applications. The VLSI revolution of the late 1970Õs and the advent of scalable parallel computers during the late 1980Õs changed this situation. Today, parallel hardware is routinely used in graphics workstations, and numerous software-based rendering systems have been developed for general-purpose parallel architectures. This article provides a broad introduction to the subject of parallel rendering, encompassing both hardware and software systems. The focus is on the underlying concepts and the issues which arise in the design of parallel rendering algorithms and systems. We examine the different types of parallelism and how they can be applied in rendering applications. Concepts from parallel computing, such as data decomposition, task granularity, scalability, and load balancing, are considered in relation to the rendering

We present an extension to existing techniques to provide for more accurate resolution of specular to diffuse transfer within a global illumination framework. In particular this new model is adaptive with a view to capturing high frequency phenomena such as caustic curves in sharp detail and yet allowing for low frequency detail without compromising noise levels and aliasing artefacts. A 2-pass ray-tracing algorithm is used, with an adaptive light-pass followed by a standard eye-pass. During the light-pass, rays are traced from the light sources (essentially sampling the wavefront radiating from the sources), each carrying a fraction of the total power per wavelength of the source. The interactions of these rays with diffuse surfaces are recorded in `illumination-maps', as first proposed by Arvo [Arvo86]. The key to reconstructing the intensity gradients due to this light-pass lies in the construction of the illumination maps. We record the power carried by the ray as a `splat' of ener...

There are five fundamental concerns in the synthesis of realistic imagery of fractal landscapes: 1) convincing geometric models of terrain; 2) efficient algorithms for rendering those potentially-large terrain models; 3) atmospheric effects, or aerial perspective, to provide a sense of scale; 4) surface textures as models of natural phenomena such as clouds, water, rock strata, and so forth, to enhance visual detail in the image beyond what can be modelled geometrically; and 5) a global context in which to situate the scenes. Results in these five areas are presented, and some aspects of the development of computer graphics as a new process and medium for the fine arts are discussed. Heterogeneous terrain models are introduced, and preliminary experiments in simulating fluvial erosion are presented to provide fractal drainage network features. For imaging detailed terrain models we describe grid tracing, a time- and memory-efficient algorithm for ray tracing height fields. To obtain aerial perspective we develop geometric models of aerosol density distributions with efficient integration schemes for determining scattering and extinction, and an efficient Rayleigh scattering approximation. We also describe physically-based models of the rainbow and mirage. Proceduralism is an underlying theme of this work; this is the practice of abstracting models of complex form and behaviors into relatively terse algorithms, which are evaluated in a lazy fashion. Procedural textures are developed as models of natural phenomena such as mountains and clouds, culminating a procedural model of an Earth-like planet which in the future may be explored interactively in a virtual reality setting.

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

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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.

displacement and shading. (b) Low frequencies used for displacement and all frequencies used for shading. (c) Damping of high frequencies closer to the camera due to shallow water and presence of vegetation. We present a multi-band Fourier domain approach to synthesizing and rendering deep-water ocean waves entirely on the graphics processor. Our technique begins by using graphics hardware to generate and animate a Fourier domain spectrum of ocean water. We subsequently use the graphics hardware to apply an IFFT to transform the spectrum into a realistic height map of ocean water in the spatial domain. As a result, this technique can be used to efficiently synthesize and render height maps and normal maps which are spatially periodic. GPU-synthesized low frequency height maps are used to displace geometry while broad spectrum GPU-synthesized waveforms are used to generate a normal map for shading. The model also allows for compositing of other waveforms such as wakes or eddies caused by objects interacting with the water. The primary contributions of this work are the use of the GPU to perform all synthesis and rendering steps as well as the multi-band approach which enables efficient simulation of the natural filtering of high frequencies at different points on the water surface due to depth variation or the presence of plant matter. 1