Mathematical Topics from 3D Graphics - 3D Math Primer for Graphics and Game Development - page 398

about a single incident direction for the light. To summarize, the original
goal of the standard model was to determine the light reflected back in the
direction of the camera, only considering direct reflections, incident from a
finite number of directions, one direction for each light source.
Now for the model. The basic idea is to classify light coming into the
eye into four distinct categories, each of which has a unique method for
calculating its contribution. The four categories are
• The emissive contribution, denoted c emis , is the same as the rendering

equation. It tells the amount of radiance emitted directly from the
surface in the given direction. Note that without global illumination
techniques, these surfaces do not actually light up anything (except
themselves).

• The specular contribution, denoted c spec , accounts for light incident

directly from a light source that is scattered preferentially in the di-
rection of a perfect “mirror bounce.”

• The diffuse contribution, denoted c diff , accounts for light incident

directly from a light source that is scattered in every direction evenly.

• The ambient contribution, denoted c amb , is a fudge factor to account
for all indirect light.
The letter c is intended to be short for “contribution.” Note the bold
typeface, indicating that these contributions are not scalar quantities rep-
resenting the amount of light of a particular wavelength, but rather they are
vectors representing colors in some basis with a discrete number of compo-
nents (“channels”). As stated before, due to the tri-stimulus human vision
system, the number of channels is almost always chosen to be three. A less
fundamental choice is which three basis functions to use, but in real-time
graphics, by far the most common choice is to make one channel for red, one
channel for blue, and one channel for green. These details are surprisingly
irrelevant from a high-level discussion (they will not appear anywhere in
the equations), but, of course, they are important practical considerations.
The emissive term is the same as in the rendering equation, so there's not
much more detail to say about it. In practice, the emissive contribution is
simply a constant color at any given surface point x . The specular, diffuse,
and ambient terms are more involved, so we discuss each in more detail in
the next three sections.

10.6.2 The Specular Component
The specular component of the standard lighting model accounts for the
light that is reflected (mostly) in a “perfect mirror bounce” off the sur-
face. The specular component is what gives surfaces a “shiny” appearance.