Graphics Reference
In-Depth Information
d
L
ω
→
(
x
,
)
L
L+
d
L
σ
s
(
x
)
ds
Figure 3.9
In-scattering at a differential segment. (Courtesy of Pat Hanrahan.)
energy takes the form of heat. As the temperature of the body increases it emits
radiation according to a known spectral emission. In other words, the hot soot
particles absorb light even as they emit it, and the emission depends on the tem-
perature, which depends on the rate of absorption; i.e., the emission is related
to the absorption. The differential change in radiance at a point is actually the
emission function
L
e
(
x
,
ω
)
times the absorption coefficient:
dL
(
x
,
ω
)=
σ
a
(
x
)
L
e
(
x
,
ω
)
ds
.
Absorbed light is assumed to be lost in the medium (in reality it is just con-
verted to a different form of energy). In contrast, scattered light is merely di-
verted to a different direction. This results in an increase in radiance in this other
direction, a phenomenon known as
in-scattering
at the point in that direction (
Fig-
,
ω
)
at any point can be increased by in-scattered light
from any other direction. Computing the in-scattered contribution is similar to
computing surface reflection: incoming light has to be integrated over all direc-
tions. The in-scattered integral encompasses the entire sphere about the point
rather than just the hemisphere above the surface.
Light scattering in a medium is governed by a
phase function p
(
x
,
ω
,
ω
)
(
x
,
,
ω
,
ω
)
which is something like a BRDF:
p
represents the fraction of light inci-
dent from direction ω
that is scattered at
x
into direction ω
(
x
. The phase function
is normalized so that its value integrated over the sphere becomes 1 (recall that
a BRDF is not normalized). The increase in radiance from in-scattering is com-
puted by integrating the incoming radiance against the phase function over the
sphere, then scaling the result by the scattering coefficient:
,
ω
,
ω
)
,
ω
)
d
ω
ds
,
ω
)=
σ
s
(
S
(
x
x
)
p
(
x
L
(
x
(3.3)
Ω
4π
(
Ω
4π
denotes the full sphere). A larger value of the phase function thus implies
greater in-scattering.
The effects of emission, absorption, out-scattering, and in-scattering combine
to produce the total differential change in the strength of light in direction
ω
at
