Three-dimensional graphic physically based simulator of rainbows together with the background scene.

This paper presents a single scattering 3D graphics simulator of rainbows that includes the thickness of the rain shaft and the background scenery. The simulator is devised so that we can find a good configuration of the sun, the viewers, and the volume of water drops in a complicated geometric setting. The background-scene geometry and light-reflecting properties are modelled using 3D graphics tools. The simulator allows both the light reflected from the background surface and the light scattered by water drops to contribute to the final image by taking the depth to the background surface into account. The simulator generates an image of the rainbow by using the radiative transfer equation (RTE). We use ray optics to compute the average scattering cross section and the average phase function of particles that are the main parameters of the RTE. Depending on the density distribution of the water drops, the rainbow is perceived to be translucent, and the background scene is visible through the rainbow. We simulate other effects of the variation of the water-dropdensity and the location of the viewer, e.g., the visibility of the secondary rainbow, the brightness of the sky around the rainbow, the close-up view of the rainbow, and the full-circle rainbow. We explain these effects partly by computing the luminance contrasts of the primary and secondary bows against their local backgrounds.