Graphics Reference
In-Depth Information
dent, which means it has to be computed separately for different color channels.
As noted in Chapter 1, materials that exhibit specular reflection can be broadly
classified into either conductors (metals) or dielectrics. Generally, Fresnel reflec-
tion captures the intrinsic color of metals but not that of dielectrics.
The next thing to consider is self-occlusion. In terms of microfacets, self-
occlusion can be more precisely defined: self-shadowing occurs when light that
would be incident on one facet is blocked by another facet; self-masking occurs
when light reflected off a facet is blocked by another facet (
Figure 8.5
)
. The
Torrance-Sparrowmodel handles self-occlusion with a
geometric attenuation fac-
tor
denoted by
G
. This factor accounts for light not reaching the microfacet due to
self-shadowing, and light not reflected from the facet due to self-masking. Blinn
proposed the formula
min
1
·
h
·
h
·
l
2
(
n
)(
n
·
v
)
2
(
n
)(
n
)
G
=
,
,
(8.4)
·
h
·
h
(
v
)
(
v
)
for the geometric attenuation term in the paper “Models of Light Reflection for
Computer Synthesized Pictures,” which introduced microfacet models into com-
puter graphics [Blinn 77]. The second term in Equation (8.4) is the effect of
self-shadowing; the third is that of self-masking.
The full Torrance-Sparrow BRDF model is constructed from the product
of the three effects described so far: the fraction
D
(
θ
h
)
of microfacets aligned
to the half-vector, the Fresnel reflectance
F
(
θ
i
)
, and the geometric attenuation
factor
G
:
DGF
f
r
=
π
cos
θ
i
cos
θ
r
θ
r
are measured from the microfacet normal.
While studying physically based surface reflection as a graduate student at
Cornell University, Rob Cook came across the paper describing the Torrance-
Sparrowmodel and found that Ken Torrance was actually working in the Mechan-
ical Engineering department at Cornell at the time. Cook met with Torrance, and
eventually developed an improved version of the Torrance-Sparrow model de-
signed for realistic rendering. The primary modification was to replace the Gaus-
sian microfacet distribution with a distribution based on the
Beckman function
,
where
θ
i
and
2
e
−
[(
tanβ
)
/
m
]
D
=
β
,
4
m
2
cos
4
is the angle between the normal of a microfacet and the surface normal,
and
m
is a parameter for the roughness of the surface. The model, which is now
where
β
