Graphics Reference
In-Depth Information
z
L
i
(
θ
i
,
φ
i
)
L
r
(
θ
r
,
φ
r
)
θ
i
θ
r
→
d
ω
i
y
φ
r
x
φ
i
Figure 8.1
Coordinates for BRDFs.
needed. Such a function is called a
BRDF model
. As described in Chapter 1,
a BRDF model must satisfy the conditions of bidirectionality and energy conser-
vation. Bidirectionality requires that the value remains the same if the incident
and reflected directions are interchanged. Energy conservation assures that no
more light can be reflected out than comes in. The latter condition is surprisingly
difficult to satisfy, and many models used in practice are not always energy con-
serving. There is also an implicit requirement that a BRDF be fairly simple (or at
least easy to evaluate) because of the huge number of times the function is likely
to be evaluated in rendering computations. Early BRDF models were designed
with efficient rendering in mind, even though they were only used for direct light-
ing at the time. The ambient term was originally invented to approximate global
illumination over the entire environment.
If a BRDF varies across a surface, it becomes a function of six variables as
noted above. Although a few BRDF models do incorporate position dependence,
for the most part they depend only on the two directions. Position-dependent
reflection is typically handled with a surface texture map or something similar.
Early BRDFs split the reflection into diffuse and specular parts. The diffuse part
is independent of the outgoing direction, while the specular part measures the
“spread” of light around the direction of mirror reflection. Recently, BRDF mod-
els have been proposed by representing the four-dimensional BRDF as a product
of two-dimensional functions (akin to the separation of variables applied in the
surface light field mapping of Chapter 5). In the paper “Interactive Rendering with
Arbitrary BRDFs Using Separable Approximations,” Jan Kautz and Michael D.
McCool show how the 2D functions can be stored in texture maps and then com-
bined at rendering time using operations available in graphics hardware [Kautz
and McCool 99]. Jason Lawrence, Szymon Rusinkiewicz, and Ravi Ramamoor-
thi proposed a different kind of factorization in the paper “Efficient BRDF Im-
