Rendering Equation - Equation Form

Equation Form

The rendering equation may be written in the form

where

• is a particular wavelength of light
• is time
• is the location in space
• is the direction of the outgoing light
• is the negative direction of the incoming light
• is the total spectral radiance of wavelength directed outward along direction at time, from a particular position
• is emitted spectral radiance
• is the unit hemisphere containing all possible values for
• is an integral over
• is the bidirectional reflectance distribution function, the proportion of light reflected from to at position, time, and at wavelength
• is spectral radiance of wavelength coming inward toward from direction at time
• is the weakening factor of inward irradiance due to incident angle, as the light flux is smeared across a surface whose area is larger than the projected area perpendicular to the ray

Two noteworthy features are: its linearity—it is composed only of multiplications and additions, and its spatial homogeneity—it is the same in all positions and orientations. These mean a wide range of factorings and rearrangements of the equation are possible.

Note this equation's spectral and time dependence — may be sampled at or integrated over sections of the visible spectrum to obtain, for example, a trichromatic color sample. A pixel value for a single frame in an animation may be obtained by fixing motion blur can be produced by averaging over some given time interval (by integrating over the time interval and dividing by the length of the interval).