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 NavierStokes 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 interaction of smoke with moving objects. Keywords: Smoke, computational fluid dynamics, Navier-Stokes equations, Euler equations, Semi-Lagrangian methods, stable fluids, vorticity confinement, participating media 1

This tutorial survey paper reviews several different models for light interaction with volume densities of absorbing, glowing, reflecting, and/or scattering material. They are, in order of increasing realism, absorption only, emission only, emission and absorption combined, single scattering of external illumination without shadows, single scattering with shadows, and multiple scattering. For each model I give the physical assumptions, describe the applications for which it is appropriate, derive the differential or integral equations for light transport, present calculations methods for solving them, and show output images for a data set representing a cloud. Special attention is given to calculation methods for the multiple scattering model.

This paper presents new algorithms to trace objects represented by densities within a volume grid, e.g. clouds, fog, flames, dust, particle systems. We develop the light scattering equations, discuss previous methods of solu-tion, and present a new approximate solution to the full three-dimensional radiative scattering problem suitable for use in computer graphics. Additionally we review dynamical models for clouds used to make an animated movie.

This paper introduces a simple model for subsurface light transport in translucent materials. The model enables efficient simulation of effects that BRDF models cannot capture, such as color bleeding within materials and diffusion of light across shadow boundaries. The technique is efficient even for anisotropic, highly scattering media that are expensive to simulate using existing methods. The model combines an exact solution for single scattering with a dipole point source diffusion approximation for multiple scattering. We also have designed a new, rapid image-based measurement technique for determining the optical properties of translucent materials. We validate the model by comparing predicted and measured values and show how the technique can be used to recover the optical properties of a variety of materials, including milk, marble, and skin. Finally, we describe sampling techniques that allow the model to be used within a conventional ray tracer.

The reflection of light from most materials consists of two major terms: the specular and the diffuse. Specular reflection may be modeled from first principles by considering a rough surface consisting of perfect reflectors, or micro-facets. Diffuse reflection is generally considered to result from multiple scattering either from a rough surface or from within a layer near the surface. Accounting for diffuse reflection by Lambert's Cosine Law, as is universally done in computer graphics, is not a physical theory based on first principles. This paper presents

We derive and analyze transport equations for the energy density ofwaves of any kind in a random medium. The equations take account of nonuniformities of the background medium, scattering by random inhomogeneities, polarization e ects, coupling of di erent types of waves, etc. We also show that di usive behavior occurs on long time and distance scales and we determine the di usion coe cients. The results are specialized to acoustic, electromagnetic, and elastic waves. The analysis is based on the governing equations of motion and uses the Wigner distribution.

Lambert's model for diffuse reflection is extensively used in computational vision. It is used explicitly by methods such as shape from shading and photometric stereo, and implicitly by methods such as binocular stereo and motion detection. For several realworld objects, the Lambertian model can prove to be a very inaccurate approximation to the diffuse component. While the brightness of a Lambertian surface is independent of viewing direction, the brightness of a rough diffuse surface increases as the viewer approaches the source direction. A comprehensive model is developed that predicts reflectance from rough diffuse surfaces. The model accounts for complex geometric and radiometric phenomena such as masking, shadowing, and interreflections between points on the surface. Experiments have been conducted on real samples, such as, plaster, clay, sand, and cloth. All these surfaces demonstrate significant deviation from Lambertian behavior. The reflectance measurements obtained are in s...

This paper introduces an efficient two-pass rendering technique for translucent materials. We decouple the computation of irradiance at the surface from the evaluation of scattering inside the material. This is done by splitting the evaluation into two passes, where the first pass consists of computing the irradiance at selected points on the surface. The second pass uses a rapid hierarchical integration technique to evaluate a diffusion approximation based on the irradiance samples. This approach is substantially faster than previous methods for rendering translucent materials, and it has the advantage that it integrates seamlessly with both scanline rendering and global illumination methods. We show several images and animations from our implementation that demonstrate that the approach is both fast and robust, making it suitable for rendering translucent materials in production.

We present fast methods for separating the direct and global illumination components of a scene measured by a camera and illuminated by a light source. In theory, the separation can be done with just two images taken with a high frequency binary illumination pattern and its complement. In practice, a larger number of images are used to overcome the optical and resolution limitations of the camera and the source. The approach does not require the material properties of objects and media in the scene to be known. However, we require that the illumination frequency is high enough to adequately sample the global components received by scene points. We present separation results for scenes that include complex interreflections, subsurface scattering and volumetric scattering. Several variants of the separation approach are also described. When a sinusoidal illumination pattern is used with different phase shifts, the separation can be done using just three images. When the computed images are of lower resolution than the source and the camera, smoothness constraints are used to perform the separation using a single image. Finally, in the case of a static scene that is lit by a simple point source, such as the sun, a moving occluder and a video camera can be used to do the separation. We also show several simple examples of how novel images of a scene can be computed from the separation results.

Lambert's model for body reflection is widely used in computer graphics. It is used extensively by rendering techniques such as radiosity and ray tracing. For several realworld objects, however, Lambert's model can prove to be a very inaccurate approximation to the body reflectance. While the brightness of a Lambertian surface is independent of viewing direction, that of a rough surface increases as the viewing direction approaches the light source direction. In this paper, a comprehensive model is developed that predicts body reflectance from rough surfaces. The surface is modeled as a collection of Lambertian facets. It is shown that such a surface is inherently non-Lambertian due to the foreshortening of the surface facets. Further, the model accounts for complex geometric and radiometric phenomena such as masking, shadowing, and interreflections between facets. Several experiments have been conducted on samples of rough diffuse surfaces, such as, plaster, sand, clay, and cloth. All...