Graphics Reference
In-Depth Information
point
x
:
,
ω
)=
σ
a
(
,
ω
)
emission
,
ω
)
,
ω
)
absorption
dL
(
x
x
)
L
e
(
x
+
in-scattering
−
S
(
x
σ
t
(
x
)
L
out-scattering
.
(
x
(3.4)
+
Equation (3.4) is one version of the
light transport equation
(LTE). The emission
term is usually omitted because the emission of light in the medium is seldom
significant. The most common form of the LTE is thus
,
ω
)=
−
σ
t
(
,
ω
)+
,
ω
)
.
dL
(
x
x
)
L
(
x
S
(
x
The LTE is an integro-differential equation: a derivative of the radiance appears
on the left side, and the scattering term
S
,
ω
)
(
x
contains an integral of the radiance.
3.3.3 Characteristics of Participating Media
Like surface reflection, scattering can be quite complicated. One way of quanti-
fying the degree of scattering is to compare the amount of scattering to the total
attenuation in the medium. Accordingly, the ratio of the scattering coefficient to
the extinction coefficient,
=
σ
s
W
σ
t
,
is the
scattering albedo
of the medium. A larger scattering albedo indicates a
greater degree of scattering.
As described above, the computation of in-scattered light is a significant com-
plication in solving the LTE. When the effect of in-scattering is considered neg-
ligible, the LTE is much simpler; in fact, it can be solved in closed form if the
extinction coefficient
σ
t
is constant:
e
−
σ
t
Δ
x
L
(
+
Δ
,
ω
)=
(
,
ω
)
.
L
x
x
x
(3.5)
Equation (3.5) thus expresses the attenuation of radiance as it travels a distance
of
through a homogeneous participating medium in
which the in-scattering is negligible.
The influence of in-scattering cannot be excluded if the degree of scattering is
very large. The in-scattering term is computed by integrating the incoming light
Δ
x
along a ray in direction
ω
θ
Figure 3.10
The phase function depends on the angle of deflection θ .
