Mathematical Topics from 3D Graphics - 3D Math Primer for Graphics and Game Development - page 397

general framework of shaders and generic constants and interpolants. The
great diversity and flexibility available is usually used to determine the best
way to feed the parameters into the model (for example, by doing multiple
lights at once, or doing all the lighting at the end with deferred shad-
ing), rather than using different models. But even ignoring programmable
shaders, at the time of this writing, the most popular video game console is
the Nintendo Wii, 13 which has hardwired support for this standard model.
The venerable standard lighting model is the subject of this section.
Since its development precedes the framework of the BRDF and the ren-
dering equation by at least a decade, we first present this model in the
simplified context that surrounded its creation. This notation and perspec-
tive are still predominant in the literature today, which is why we think we
should present the idea in its own terms. Along the way, we show how one
component of the model (the diffuse component) is modeled as a BRDF.
The standard model is important in the present, but you must understand
the rendering equation if you want to be prepared for the future.
10.6.1 The Standard Lighting Equation: Overview
Bui Tuong Phong [54] introduced the basic concepts behind the standard
lighting model in 1975. Back then, the focus was on a fast way to model
direct reflection. While certainly researchers understood the importance of
indirect light, it was a luxury that could not yet be afforded. Thus while
the rendering equation (which, as we noted previously, came into focus
a decade or so after the proposal of the standard model) is an equation
for the radiance outgoing from a point in any particular direction, the
only outgoing direction that mattered in those days were the directions
that pointed to the eye. Similarly, while the rendering equation considers
incident light from the entire hemisphere surrounding the surface normal,
if we ignore indirect light, then we need not cast about in all incident
directions. We need to consider only those directions that aim at a light
source. We examine some different ways that light sources are modeled in
real-time graphics in more detail in Section 10.7, but for now an important
point is that the light sources are not emissive surfaces in the scene, as
they are in the rendering equation and in the real world. Instead, lights are
special entities without any corresponding geometry, and are simulated as
if the light were emitting from a single point. Thus, rather than including
a solid angle of directions corresponding to the projection of the emissive
surface of each light source onto the hemisphere surrounding x , we only care
13 This is a very important lesson. Realistic graphics might be important to hardcore
gamers, but for a more general audience they are not nearly as important as we once
believed. The recent surge in popularity of facebook games further underscores this
point.