Rendering Equation - Limitations

Limitations

Although the equation is very general, it does not capture every aspect of light reflection. Some missing aspects include the following:

• Transmission, which occurs when light is transmitted through the surface, like for example when it hits a glass object or a water surface,
• Subsurface scattering, where the spatial locations for incoming and departing light are different. Surfaces rendered without accounting for subsurface scattering may appear unnaturally opaque — however, it is not necessary to account for this if transmission is included in the equation, since that will effectively include also light scattered under the surface,
• Polarization, where different light polarizations will sometimes have different reflection distributions, for example when light bounces at a water surface,
• Phosphorescence, which occurs when light or other electromagnetic radiation is absorbed at one moment in time and emitted at a later moment in time, usually with a longer wavelength (unless the absorbed electromagnetic radiation is very intense),
• Interference, where the wave properties of light are exhibited,
• Fluorescence, where the absorbed and emitted light have different wavelengths,
• Non-linear effects, where very intense light can increase the energy level of an electron with more energy than that of a single photon (this can occur if the electron is hit by two photons at the same time), and emission of light with higher frequency than the frequency of the light that hit the surface suddenly becomes possible, and
• Relativistic Doppler effect, were light that bounces on an object that moves with a very high speed will get its wavelength changed; if the light bounces at an object that is moving towards it, the impact will compress the photons, so the wavelength will become shorter and the light will be blueshifted and the photons will be packed more closely so the photon flux will be increased; if it bounces at an object that is moving from it it will be redshifted and the photons will be packed more sparsely so the photon flux will be decreased.

For scenes that are either not composed of simple surfaces in a vacuum or for which the travel time for light is an important factor, researchers have generalized the rendering equation to produce a volume rendering equation suitable for volume rendering and a transient rendering equation for use with data from a time-of-flight camera.