Graphics Reference
In-Depth Information
Figure 1.18.
Disk area light fit to Phong distribution.
where
p
d
is a point on the light plane with normal
n
l
and
r
is the distance away
from the light.
To simplify, we assume that occlusion does not influence the result. Then the
integral can be pre-computed in a 3D lookup table indexed by
p
d
.xy
coordinates
in the light space and by distance
r
between points
p
and
p
d
. The distance can
be normalized against the maximum distance at which computing the integral
still makes a visual difference. Such a distance maximum can be calculated by
solving the light shape's solid angle (equation (1.3)) for
r
, irrespective of
cosθ
o
,
where
σ
sets the boundary importance of the solid angle weight:
r
max
>
dA
σ
.
For distances larger than
r
max
, the solid angle would be too small and, as a result,
the integral would not further change visually.
Every Z layer of the lookup table would contain the diffuse integral for point
p
d
, set on coordinates
p
d
.xy
in the light space, max(
r/r
max
,
1) away from the
light plane. Finally, the full diffuse integral approximation is
dAcosθ
o
r
2
Diffuse
(
p,ω
o
)
∼
IC
d
cos
θ
−−→
Diffuse
Lookup
(
p
d
,r
)
.
(1.24)
pp
d
