Abstract The visual appearance of volumes of water particles, such as clouds, waterfalls, and fog, depends both on microscopic interactions between light rays and individual droplets of water, and also on macroscopic interactions between multiple droplets and paths of light rays. This paper presents a model that builds upon a typical single-scattering volume renderer to correctly account for these effects. To accurately simulate the visual appearance of a surface or a volume of particles in a computer-generated image, the properties of the material or particle must be specified using a Bidirectional Reflectance Distribution Function (BRDF), which describes how light reflects off of a material, and the Bidirectional Transmittance Distribution Function (BTDF), which describes how light refracts into a material. This paper describes an optimized BRDF and BTDF for volumes of water droplets, which takes their geometry into account in order to produce well-known effects, such as rainbows and halos. It also describes how a multiple-scattering path tracing volume integrator can be used to more accurately simulate macroscopic light transport through a volume of water, creating a more “cloudlike” appearance than a single-scat-tered volume integrator. This paper focuses on replicating the visual appearance of volumes of water particles, and although it makes use of physical models, the techniques presented are not intended to be physically accurate.
Analysis of Desired Visual Effects On a macroscopic level, light that a viewer sees when he/she looks at a volume of water particles is light that travels from a light source, interacts with water particles, and then hits the viewer’s eye. There is angular and wavelength dependence between the amount of light that enters and exits a water droplet. Vibrant bands of color appear in certain viewing situations, depending on the angles between the viewer, the light source, and the volume of particles. Viewers see rainbows when the sun is behind them. The light from the sun enters droplets at certain angles and then bounces back at the viewer in the distinctive pattern of a colored bow. Because of the large angle at which this occurs, typically only half of the rainbow can be seen. However, the band appears in a conic shape in front of the viewer; theoretically, the whole circle of the rainbow could be seen. Viewers see glories and halos when water particles are between the viewer and the light; the effect seen is a concentration of rays transmitted through the drops towards the viewer. It should be noted that these effects only appear when the sun is the light source, because it acts as an ideal directional light. Typical omnidirectional lights, such as tungsten bulbs, would not exhibit these effects because rainbows, halos, and others would get “blurred out” as the light from multiple directions enters a volume of particles and creates multiple “copies” of the pattern on top of itself, thus obscuring the pattern. Methods of simulating these macroscopic effects with a microscopic model will now be described.
Glories describes the physical interactions between light and water droplets [ 1]. As a light ray enters a water drop, it bounces around in the drop multiple times, each time reflecting part of the light back into the drop and refracting part of it out of the drop, based on elementary physical models of wave transport. The refracted light obeys Snell’s law (Formula 1), and the reflected light obeys the reflection law (Formula 2). The combination of reflected and refracted light depends on Fresnel’s reflection law (Formula 3). An example of a single ray traced through the sphere is shown in Figure 1. The black line on the left is the ray that enters the sphere. It is bent when it is inside the sphere, and it is bent again as it leaves the sphere as an exiting ray, the red line. The blue lines are multiple reflections of this ray inside the sphere; the rays resulting from these internal reflections do not have sufficient energy to be visible, so they are not shown.
Formula 1: Snell’s law: n is the index of refraction and theta is the ray angle relative to the normal [ 8].
Formula 2: Vector reflection law: I is the incident ray, N is the normal, and R is the refracted ray [ 2].
Microscopic Water Droplet Light Transport Water droplet light transport on a microscopic level can be approximated by tracing rays through a spherical object with a BRDF and BTDF similar to water. Robert Greenler’s book Rainbows, Halos, and
Formula 3: Fresnel’s equations: R is the strength of the reflected light and theta is the angle of incident and transmitted rays relative to the normal [ 7].
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