Graphics Reference
In-Depth Information
(a)
(b)
Figure 3.6
Surface reflection compared to scattering by a participating medium.
faces (
Figure 3.6(a)
)
, rendering of environments that contain participating media
has to account for how light is affected by the media
(
Figure 3.6(b)
)
.
The effect of light passing through a medium (unless otherwise stated,
“medium” implies “participating medium” hereafter) falls in the domain of
trans-
port theory
, which is the study of how particles such as electrons, mesons, and
photons are affected as they travel through other materials. Transport theory was
actively studied in statistical physics in the 1950s. The
light transport equation
(LTE) describes the physical effect on light as it propagates through a medium.
Light transport includes not only the loss of light energy by absorption and scat-
tering, but also the gain in energy from
emission
within the medium. The LTE
governs the gain and loss of this energy by relating the differential change in radi-
ance to the physical properties of the medium. The behavior of light in a medium
is generally computed by solving the volume rendering equation. In computer
graphics, the integral of the LTE along the the line segment from a viewpoint to a
light source is called the
volume rendering equation
.
3.3.2 The Light Transport Equation (LTE)
The light transport equation is formulated in terms of the differential change in
radiance
dL
,
ω
)
(
x
at a point
x
in space along a differential section
ds
of the ray
in a direction ω
,
ω
)
/
(
Figure 3.7
)
. More precisely,
dL
(
x
ds
denotes the derivative
s
ω
,
ω
)
of the radiance function
L
with respect to
s
. There are two basic causes
of light attenuation along a ray: particles in the medium absorb some of the light,
and collisions with particles deflect the light in other directions. The
absorption
is defined as the amount of light lost as it travels a differential distance
ds
.Itis
assumed that the differential absorption is proportional to the radiance:
(
x
+
,
ω
)=
−
σ
a
(
,
ω
)
dL
(
x
x
)
L
(
x
ds
;
i.e., the differential light loss from absorption is a fraction of the strength of light
(
Figure 3.7
)
. The proportionality constant
σ
a
(
x
)
is the
absorption coefficient
or
