430 10. The Rendering Engine
A BRDF calculates the ratio of the outgoing (refl ected) radiance along a given
viewing direction V to the incoming irradiance along the incident ray L.
A BRDF can be visualized as a hemispherical plot, where the radial dis-
tance from the origin represents the intensity of the light that would be seen if
the refl ection point were viewed from that direction. The diff use Phong refl ec-
tion term is kD(N · L). This term only accounts for the incoming illumination
ray L, not the viewing angle V. Hence the value of this term is the same for all
viewing angles. If we were to plot this term as a function of the viewing angle
in three dimensions, it would look like a hemisphere centered on the point at
which we are calculating the Phong refl ection. This is shown in two dimen-
sions in Figure 10.24.
The specular term of the Phong model is kS(R · V)α. This term is dependent
on both the illumination direction L and the viewing direction V. It produces
a specular “hot spot” when the viewing angle aligns closely with the refl ection
R of the illumination direction L about the surface normal. However, its con-
tribution falls off very quickly as the viewing angle diverges from the refl ected
illumination direction. This is shown in two dimensions in Figure 10.25.10.1.3.3. Modeling Light Sources
In addition to modeling the light’s interactions with surfaces, we need to de-
scribe the sources of light in the scene. As with all things in real-time rendering,
we approximate real-world light sources using various simplifi ed models.Figure 10.24. The diffuse term of the Phong refl ection model is dependent upon N • L, but is
independent of the viewing angle V.Figure 10.25. The specular term of the Phong refl ection model is at its maximum when the
viewing angle V coincides with the refl ected light direction R and drops off quickly as V di-
verges from R.