Graphics Reference
In-Depth Information
p
(
θ
)
g
= 0
g
= 0.5
a
b
θ
g
= 0.8
c
Figure 3.11
Polar plots of several phase function. The plot marked (a) is that of an isotropic phase
function; (b) and (c) show examples of forward (anisotropic) scattering with increasing
anisotropy.
,
ω
,
ω
)
fully characterizes the scattering in the medium, much like the BRDF character-
izes surface reflection. However, practical phase functions are much simpler than
BRDFs: it is known that the phase functions for most media depends only on the
angle between the incident and scattering directions (the angle
against the phase function as in Equation (3.3). The phase function
p
(
x
θ
in
Figure 3.10
)
,
which is known as the
angle of deflection
.
The dependence of phase functions on the single angle
makes them suit-
able for plotting in polar coordinates. The graph is usually circular or is roughly
cle. Scattering by a constant phase function is called
isotropic scattering
.A
nonconstant phase function implies
anisotropic scattering
, which has a direc-
tional element. The graph of an anisotropic phase function usually looks like
an ellipse with its long axis on the horizontal axis where
θ
θ
=
0or
θ
=
π
.Ifthe
ellipse is elongated toward the
0, then scattering is predominately in the form
of a small deflection of the angle of incoming light. This is known as
forward
scattering
. If the elongation is in the opposite direction, most light is scattered
back toward the direction from which it came. This is
backward scattering
.
In practice, anisotropic scattering can usually be categorized as either forward
or backward. For the purposes of rendering participating medium, it is helpful to
know which. The notion of forward and backward scattering can be formalized
in terms of an average scattering direction. More precisely, integrating the phase
θ
=
1
An important counterexample is the Rayleigh scattering function, which has a two-lobed shape
with equal forward and backward scattering. This shape is a result of the nature of the scattering, in
which the particles are assumed to be much smaller than the wavelength of light. Rayleigh scattering
is the cause of the blue color of the sky and its reddening at sunset. It is also the primary cause of blue
eye color.
