Graphics Reference
In-Depth Information
This generalizes to arbitrary emitter shapes; in general, a one-sided planar
Lambertian emitter of power
Φ
and area
A
emits light of radiance
Φ
π
L
=
A
.
(26.59)
Irradiance
is the density (with respect to area, time, and wavelength) of the light
energy arriving at a surface from all directions. (It's often described as the mea-
sure of the light hitting a surface “independent of direction,” but if the light energy
varies
with direction, then the meaning of that phrase isn't entirely clear.) Irradi-
ance is a useful notion when the surface is known to respond to incoming light in
a way that's direction-independent, where “respond to” might mean “absorb” or
“reflect.” In cases where the response is direction-dependent, irradiance is gener-
ally irrelevant: Knowing only the total light energy hitting a surface will tell you
nothing certain about the reflected energy.
Irradiance is usually defined only for a point
P
on a surface in the scene (or
on a surface of some sensor like that of a virtual camera), and typically for a point
where only
reflective
scattering takes place, that is, where there's no transmission
through the surface, so we need only consider light arriving from one side of the
surface. Equation 26.42 says that the energy arriving at a region
R
from directions
opposite those in a solid angle
Ω
is
energy
=
t
1
t
0
λ
1
L
(
t
,
P
,
−
v
λ
)
|
v
·
|
λ
,
n
d
v
dP d
dt
.
(26.60)
λ
0
P
∈
R
v
∈
Ω
The solid angle that interests us is
S
+
(
P
)=
{
v
:
v
·
n
(
P
)
≥
}
,thesetofall
outgoing directions at
P
. So the irradiance at a point
P
where the surface normal is
n
is the innermost integral, using
S
+
(
P
)
as
Ω
. Within that integral, the dot product
is always positive, so we can drop the absolute value signs,
0
)=
E
(
t
,
P
,
λ
L
(
t
,
P
,
−
v
i
,
λ
)
v
i
·
n
d
v
i
,
(26.61)
v
i
∈
S
+
(
P
)
where we've substituted
(see Figure 26.29).
This definition introduces some notational conventions we'll follow for the
next several chapters. First,
P
typically denotes a point on some surface in the
v
i
for
v
n
P
Figure 26.29: Notation for irradiance definition.
