Graphics Reference
In-Depth Information
We also need to set additional requirements to make this BRDF physically
based:
0
,
f
r
(
p,ω
o
,ω
i
)=
f
r
(
p,ω
i
,ω
o
)
,
f
r
(
p,ω
o
,ω
i
)
≥
(1.6)
f
r
(
p,ω
o
,ω
i
)cos
θ
i
dω
i
≤
1
.
ω
o
H
2
For our
k
d
we can use the standard Lambertian diffuse model [Lambert 60]. When
expressed as a part of
f
r
(
p,ω
o
,ω
i
), it takes a very simple form:
k
d
=
C
d
,
(1.7)
where
C
d
defines the surface diffusion color.
We choose the generalized Cook-Torrance BRDF [Cook and Torrance 81] for
a base of our microfacet specular model:
k
s
(
p,ω
o
,ω
i
)=
D
(
h
)
F
(
ω
o
,h
)
G
(
ω
i
,ω
o
,h
)
4(
cosθ
i
)(
cosθ
o
)
,
(1.8)
where
D
(
h
) is the distribution of micro-facets around surface normal
n
,
F
(
ω
o
,h
)
is the Fresnel reflectance function, and
G
(
ω
i
,ω
o
,h
) is the geometric function. As
previously defined,
θ
i
is the angle between
n
and
ω
i
,and
θ
o
is the angle between
n
and
ω
o
. Generally,
h
is called the
half vector
, defined as
ω
o
+
ω
i
h
=
.
(1.9)
ω
o
+
ω
i
We are interested in finding radiance in the direction of the viewer, per light,
described as follows:
L
o
(
p,ω
o
)=
A
(
n
)
f
r
(
p,ω
o
,ω
i
)
L
i
(
p,ω
i
)cos
θ
i
dω
i
(
n
)
.
For now, we can assume, as in equation (1.2), that
L
i
(
p,ω
i
) is constant over
light:
L
o
(
p,ω
o
)=
L
n
A
(
n
)
f
r
(
p,ω
o
,ω
i
)cos
θ
i
dω
i
(
n
)
.
(1.10)
Now substitute parts of equation (1.10) with equations (1.5), (1.7), and (1.8):
L
o
(
p,ω
o
)=
L
n
A
(
n
)
C
d
+
D
(
h
)
F
(
ω
o
,h
)
G
(
ω
i
,ω
o
,h
)
4(
cosθ
i
)(
cosθ
o
)
cosθ
i
dω
i
(
n
)
.
