This is a study of the shadows you would get at night on a ringworld. Night is provided by shadow squares that orbit the sun inside the main ring, periodically blocking the sun and bringing night. At night, illumination is only provided by scattered light from the lit segments of the ring. With the light coming from many directions at once, the nature of nighttime illumination and shadows is not immediately apparent, although like so many problems, seems obvious once you know the answer.
Here, the sphere is mainly illuminated from the sides. Little light is recieved from above since the shadow squares block light from that direction, and the lit ring segments are farther away. No light is recieved from directly below. All light is from the plane of the ring, the "poles" of the sphere aligned with the ring axis recieve no light and are thus dark. The shadows are greatly elongated. Suprizingly, the lit ring segments are so extended that they do not cast apparent individual shadows, rather all the shadows look to the eye to merge together into one long blur.
The light scattered from the lit ring segments was simulated by placing square spotlights on each ring segement, flattened so that they illuminated the entire ring except for the ring segemnt they were placed on. The extended nature of the light source was simulated by using eleven evenly spaced lights for each ring segment.
There are two renderings of the lighting and shadows, the top one with the spotlights set to linear falloff, the bottom one with the spotlights set to squared falloff. Squared falloff more accurately reflects the physics of light as it diverges from a source, so the bottom image is probably a more accurate depiction of what the shadows would look like, with the sides much more strongly illuminated than the top and the shadows very indistinct.
All images copyright Luke Campbell 2001. For information on use of these images, click here