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function against the cosine of the scattering angle
θ
results in a single number
, ω , ω )
d ω .
g
=
p
(
x
cos
θ
Ω
Some authors call g the scattering anisotropy , but the term is not universal. The
cos
term encodes the direction: forward scattering is associated with directions
where cos
θ
θ
is near 1 (
θ
is near 0), while backward scattering occurs when cos
θ
is near
1. Consequently, a positive value of g indicates predominately forward
scattering and a negative value indicates backward scattering. Furthermore, larger
|
implies more bias in the scattering direction, so g also provides a measure of
anisotropy.
The usefulness of g in characterizing scattering anisotropy has led to the de-
velopment of phase function models that use g (or something similar) as a param-
eter. This makes tuning the model more intuitive. An example is the Henyey-
Greenstein function
g
|
g 2
1
4
1
p
( θ )=
2 ,
π
g 2
3
/
(
1
+
2 g cos
θ )
which is often used for modeling light scattering in natural objects such as smoke,
clouds, flame, and human skin.
3.3.4 Participating Media and CG Rendering
The introduction of the light transport equation into computer graphics in the early
1980s marked the beginning of the connection between rendering and transport
theory. As described previously, transport theory was well established in physics
and engineering by then. Much of the development of transport theory actually
came out of the Manhattan Project during World War II; in fact, it is said to have
been key to the development of the atomic bomb. The Radiative Transfer textbook
originally published in 1950 by Subrahmanyan Chandrasekhar, is considered the
“bible” of the field [Chandrasekhar 50]. Early CG efforts in solving the LTE
came out of this work. However, the primary goal of general transport theory is
to achieve accurate numerical results, for which it is necessary to solve a lot of
differential equations at a high computational cost. The original purpose of the
LTE for rendering was to simulate light transmission in the medium in order to
render phenomena such as smoke, fog, and coulds with greater realism. The CG
field therefore needed efficient algorithms to simulate the overall behavior of light
in participating media.
In 1982, Jim Blinn presented the first rendering paper that approaches the so-
lution of the LTE , although the paper considers only a restricted version of the
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