Mathematical Topics from 3D Graphics - 3D Math Primer for Graphics and Game Development - page 416

A rectangular spot light forms a pyramid rather than a cone. Rectan-
gular spot lights are especially interesting because they are used to project
an image. For example, imagine walking in front of a movie screen while a
movie is being shown. This projected image goes by many names, includ-
ing projected light map, gobo, and even cookie. 17 The term gobo originated
from the world of theater, where it refers to a mask or filter placed over a
spot light used to create a colored light or special effect, and it's the term
we use in this topic. Gobos are very useful for faking shadows and other
lighting effects. If conical spot lights are not directly supported, they can
be implemented with an appropriately designed circular gobo.
A directional light represents light emanating from a point in space
su ciently far away that all the rays of light involved in lighting the scene
(or at least the object we are currently considering) can be considered as
parallel. The sun and moon are the most obvious examples of directional
lights, and certainly we wouldn't try to specify the actual position of the
sun in world space in order to properly light the scene. Thus directional
lights usually do not have a position, at least as far as lighting calculations
are concerned, and they usually do not attenuate. For editing purposes,
however, it's often useful to create a “box” of directional light that can be
moved around and placed strategically, and we might include additional
attenuation factors to cause the light to drop off at the edge of the box.
Directional lights are sometimes called parallel lights. We might also use
a gobo on a directional light, in which case the projection of the image is
orthographic rather than perspective, as it is with rectangular spot lights.
As we've said, in the rendering equation and in the real world, lights
are emissive surfaces with finite surface areas. Abstract light types do not
have any surface area, and thus require special handling during integration.
Typically in a Monte Carlo integrator, a sample is specifically chosen to be
in the direction of the light source, and the multiplication by d ω in is ignored.

Imagine if, rather than the light coming from a single point, it comes instead
from a disk of some nonzero surface area that is facing the point being
illuminated. Now imagine that we shrink the area of the disk down to
zero, all the while increasing the radiosity (energy flow per unit area) from
the disk such that radiant flux (total energy flow) remains constant. An
abstract light can be considered the result of this limiting process in a
manner very similar to a Dirac delta (see Section 12.4.3). The radiosity is
infinite, but the flux is finite.
While the light types discussed so far are the classic ones supported
by fixed-function real-time pipelines, we certainly are free to define light
volumes in any way we find useful. The volumetric lights discussed in

17 “Gobo” is short for “go between,” and “cookie” is short for “cucoloris.” The subtle
technical difference between these terms from the world of theater is not relevant for
computer-generated imagery.