Graphics Reference
In-Depth Information
g'
r
n
dA
g
r
α
p
Figure 1.20.
Relationship between cone angle, projected cone, and roughness.
where
h
is orthogonal to view direction
ω
o
. This effectively forces us to use Phong
as our
D
function.
With these assumptions we can calculate equation (1.27) as a 3D lookup
table indexed by
p
sc
.xy
coordinates in the light space and
g
calculated using
equation (1.26) derived for the used BRDF.
Finally, the full specular integral approximation is
L
n
D
(
h,
)
F
(
ω
o
,h
)
G
(
ω
i
,
−−→
pp
sc
,h
)
4(
cosθ
o
)
A
S
Specular
Lookup
(
p
sc
,g
)
.
(1.28)
It is worth noting that, based on choice, functions
DFG
might depend on
g
or other surface parameters. Every additional parameter, apart from already
included
g
, would add one more dimension to our lookup table or would have to
be factored out. This is entirely based on the final choices for the specular model.
Specular
(
p,ω
o
,g
)
∼
1.3.6 Solving Area Light BRDF
We presented a framework for ecient derivation of area-based lighting models
based on currently known and well-researched BRDFs. The final lighting model
should follow all procedures from Section 1.3, with the choice of particular
DFG
functions and appropriate derivation of additional parameters based directly on
them. Then, diffuse and specular lighting per point can be approximated for
various light types (equations (1.16) and (1.20)), including colored, non-uniform
lights (equations (1.24) and (1.28)). See Figures 1.21, 1.22, and 1.23.
