This slide set will explain the radiosity method for computer image generation and how the basic algorithm has been extended.
Every surface in an environment is illuminated by a combination of direct light and reflected light. The direct light is light energy which comes directly from a light source or light sources, attenuated only by some participating media (smoke, fog, dust). The reflected light is light energy which, after being emitted from a light source or light sources, is reflected off of one or more surfaces of the environment.
When light energy is reflected from a surface it is attenuated by the reflectivity of the surface, as some of the light energy may be absorbed by the surface, and some may pass through the surface. The reflectivity of a surface is often defined as its color.
Three images are displayed on this slide, illustrating several facets of computer image generation.
The image in the upper right corner was rendered with a scanline rendering algorithm, where the ambient component of light is approximated with a constant value. This results in even shading, even in areas where shadows or less illumination would be expected. No shadows are calculated.
The image in the middle and the image in the lower left corner were both rendered with a ray tracing global illumination algorithm. The image in the middle exhibits some of the characteristics of a typical ray tracing algorithm: mirror-like reflections and no ambient light component. Notice the hard-edged shadows cast by the light source. The image in the lower left corner retains the mirror-like reflection typical of a ray tracing algorithm, and adds an accurate ambient component of light, by allowing the rereflection of light energy through the environment, as well as soft shadows.
If a surface is defined to be a "diffuse reflector" of light energy, any light energy which strikes the surface will be reflected in all directions, dependent only on the angle between the surface's normal and the incoming light vector. This relationship is known as Lambert's law.
Light which is reflected from a surface is attenuated by the reflectivity of the surface, which is closely associated with the color of the surface. The reflected light energy often is colored, to some small extent, by the color of the surface from which it was reflected.
This reflection of light energy in an environment produces a phenomenon known as "color bleeding," where a brightly colored surface's color will "bleed" onto adjacent surfaces. The image in this slide illustrates this phenomenon, as both the red and blue walls "bleed" their color onto the white walls, ceiling and floor.
The "radiosity" method of computer image generation has its basis in the field of thermal heat transfer. Heat transfer theory describes radiation as the transfer of energy from a surface when that surface has been thermally excited. This encompasses both surfaces which are basic emitters of energy, as with light sources, and surfaces which receive energy from other surfaces and thus have energy to transfer.
This "thermal radiation" theory can be used to describe the transfer of many kinds of energy between surfaces, including light energy.
As in thermal heat transfer, the basic radiosity method for computer image generation makes the assumption that surfaces are diffuse emitters and reflectors of energy, emitting and reflecting energy uniformly over their entire area. It also assumes that an equilibrium solution can be reached; that all of the energy in an environment is accounted for, through absorption and reflection.
It should be noted the the basic radiosity method is viewpoint independent: the solution will be the same regardless of the viewpoint of the image.
The "radiosity equation" describes the amount of energy which can be emitted from a surface, as the sum of the energy inherent in the surface (a light source, for example) and the energy which strikes the surface, being emitted from some other surface.
The energy which leaves a surface (surface "j") and strikes another surface (surface "i") is attenuated by two factors: