Graphics Reference
In-Depth Information
The variable
L
ri
is known as the
reduced intensity
, as it represents the inten-
sity of the outside light source after it is reduced by absorption and out-scattering
within the medium. It is, however, a radiance value and is called the “direct radi-
ance” in this work because it comes directly from the light source and is therefore
analogous to the direct lighting in surface reflection. However, this term is not
standard, and it must be remembered that this “direct radiance” has been attenu-
ated by the medium.
All the scattered light in the medium ultimately comes from multiple scatter-
ing of the direct radiance. The radiance due to single scattering is governed by
the phase function:
s
(
ω
,
ω
)
d
ω
.
(
,
ω
)=
σ
(
,
ω
)
Q
x
p
L
ri
x
Ω
4π
This single-scattering function
Q
can be regarded as source of radiance in-
side the medium; in fact, it is no different than a directional emission function. In
other words, single-scattered light can be treated as volumetric emission, and can
therefore be used in place of the emission term in the LTE:
(
x
,
ω
)
(
ω
·
∇
)
(
,
ω
)=
−
σ
(
,
ω
)+
S
d
(
,
ω
)+
(
,
ω
)
.
L
x
t
L
x
x
Q
x
(4.2)
The term
Q
is sometimes called the
source term
, as it amounts to a source of
radiance inside the medium (also it comes from the light source). Moving the sin-
gle scattering into the source term
Q
,
ω
)
in Equation (4.2) depends only on multiple scattering. The advantage to this
comes from the notion of diffusion: multiply scattered light tends to lose its direc-
tional dependence. This suggests that a simple approximation to diffuse scattering
S
d
(
,
ω
)
(
x
means the scattering term
S
d
(
x
,
ω
)
x
might be sufficient.
Some extra definitions are required to make this precise. The quantities
,
ω
)
d
ω
,
φ
(
x
)=
L
(
x
Ω
4π
E
(
x
)=
L
(
x
,
ω
)
ω
d
ω
Ω
4π
are known as the
fluence
and the
vector irradiance
, respectively. The vector ir-
radiance is a generalization of surface irradiance:
E
(
x
)
·
n
gives the irradiance
through a hypothetical surface perpendicular to
n
at
x
. Analogous quantities can
