Graphics Reference
In-Depth Information
Figure 1.19.
Disk area light fit to GGX distribution.
In the case of specular (equation (1.12)), we need to integrate
Specular
Lookup
(
pp
sc
,g
)=
A
L
i
(
p,ω
i
)
D
(
h,g
)
F
(
ω
o
,h
)
G
(
ω
i
,ω
o
,h
)
4(
cosθ
o
)
dω
i
,
(1.25)
where
p
is the point being shaded and
p
sc
is the most important point of the
specular integral with
g
defined as surface roughness. Unfortunately, such a rep-
resentation would require a 4D lookup table. We would like to free ourselves from
knowledge of point
p
. According to reasoning from Section 1.3.4, we know that
the integral will effectively depend on the projected cone of importance sampling
radius. We also know how to create functions to calculate the specular importance
cone apex angle from the surface roughness for given BRDFs (equations (1.17)
and (1.18)). The projected importance cone radius depends on distance
r
to the
light and the cone opening angle
α
(see Figure 1.20). Therefore, we can calculate
the integral from equation (1.25) for point
p
sc
and the new roughness
g
,where
g
=
f
BRDF
(
g,r
)
.
(1.26)
To make this assumption viable, we have to restrict only to radially symmetrical
PDFs:
Specular
Lookup
(
p
sc
,g
)=
A
L
i
(
p,ω
i
)
D
(
h,g
)
F
(
ω
o
,h
)
G
(
ω
i
,ω
o
,h
)
4(
cosθ
o
)
dω
i
,
(1.27)
