Graphics Reference
In-Depth Information
We've discussed models for scattering from surfaces, which is a fairly good
approximation for metals, for instance, but is increasingly inadequate as the mate-
rials we encounter become less surfacelike. In this section, we'll briefly discuss
volumetric materials, which are sometimes called participating media, and sub-
surface scattering, which helps determine the appearance of materials like human
skin.
We'll now give a very brief description of how light interacts with participating
media like colored water, or fog.
When you sit in a dark room on a sunny day, with sunlight streaming through
a window, shafts of sunlight typically fill the room. These appear because the
sunlight hits tiny particles in the air of the room (usually dust), and is scattered
by these particles to the eye. Even though the particles are scarce and small, the
intensity of the sunlight is such that the net reflected light may be substantial com-
pared to that reflected by the dark walls of the room. The result is that we “see
the beam of light.” The same kind of “volumetric scattering” explains the appear-
ance of the rings of Saturn, and the dark regions at the bottom of cumulus clouds.
Because we usually consider the air in a room as a medium through which light
passes untouched, until it's scattered by a surface, our ordinary model no longer
applies. Now the medium (air with dust particles)
participates
in the scattering
process, and so the term
participating media
is often used in connection with
such situations.
The exact modeling of participating media requires the precise measurement
of several physical properties [Rus08]; even with these necessary constants, the
associated computations are quite complex. In broad strokes, however, for sparsely
distributed scatterers uniformly distributed in a medium (e.g., dust in the air of a
room), the light passing through the medium is exponentially attenuated, that is,
its radiance, after passing through a distance
d
in the medium, is multiplied by
exp(
−σ
d
)
for some small constant
σ>
0. This attenuation is explained by think-
ing of the probability of a bit of light making it through the whole medium with-
out encountering a particle. Suppose that the probability of making it through one
millimeter of the medium is 0.95. Then the probability of light making it through
the first millimeter will be 0.95, while the probability of making it through
two
millimeters will be 0.95
2
, etc., leading to an exponential decay. For a nonuniform
participating medium, the decay rate
A
becomes a function of location, and the
amount of light exiting the medium ends up being the amount entering, multiplied
by a constant that's an integral of a function of
σ
along a ray.
What we've just described is
absorption,
and it can be used to describe the
interaction of light with materials like soot which absorb light and convert it to
heat, but hardly emit or reflect it. Figure 27.18 schematically shows absorption
at the orange particle just to the right of center. Absorption generally depends on
wavelength, so this analysis really only applies to light of a single wavelength.
σ
R
Three other phenomena arise for general participating media. The first of these
is
emission,
shown by the red particle in the bottom left of the figure: Just as in
the analysis of light's interaction with surfaces, we can encounter media that glow
(think of the liquid in glow sticks, or the heated soot in flame). The second is
Figure 27.18: The ray R starts
at A in direction
and passes
through a participating medium.
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