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7.5. BRDF Theory 239
stones, crystals, and clear liquids such as water, oil, and wine. Such sub-
stances can partially absorb light traveling though them, but do not change
its direction.
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Transmitted light continues on a straight line through such
objects until it undergoes internal reflection and transmission out of the ob-
ject. Techniques for rendering such substances are discussed in Sections 5.7,
9.4, 9.5, and 10.16.
Most insulators (including common substances such as wood, stone,
snow, earth, skin, and opaque plastic—any opaque non-metal) are
heterogeneous—they contain numerous discontinuities, such as air bubbles,
foreign particles, density variations, and structural changes. These will
cause light to scatter inside the substance. As the light travels through
the substance, it may be partially or completely absorbed. Eventually, any
light not absorbed is re-emitted from the surface. To model the reflectance
with a BRDF, it is necessary to assume that the light is re-emitted from
the same point at which it entered. We will call this case local subsurface
scattering. Methods for rendering in cases where this assumption cannot
be made (global subsurface scattering) are discussed in Section 9.7.
The scattering albedo ρ of a heterogeneous insulator is the ratio between
the energy of the light that escapes a surface compared to the energy of the
light entering into the interior of the material. The value of ρ is between
0 (all light is absorbed) and 1 (no light is absorbed) and can depend on
wavelength, so ρ is modeled as an RGB vector for rendering. One way
of thinking about scattering albedo is as the result of a “race” between
absorption and scattering—will the light be absorbed before it has had a
chance to be scattered back out of the object? This is why foam on a
liquid is much brighter than the liquid itself. The process of frothing does
not change the absorptiveness of the liquid, but the addition of numerous
air-liquid interfaces greatly increases the amount of scattering. This causes
most of the incoming light to be scattered before it has been absorbed,
resulting in a high scattering albedo and bright appearance. Fresh snow
is another example of high scattering albedo; there is a lot of scattering
in the interfaces between snow granules and air, but very little absorption,
leading to a scattering albedo of 0.8 or more across the visible spectrum.
White paint is slightly less—about 0.7. Many common substances, such as
concrete, stone, and soil, average between 0.15 and 0.4. Coal is an example
of very low scattering albedo, close to 0.0.
Since insulators transmit most incoming light rather than reflecting it
at the surface, the scattering albedo ρ is usually more visually important
than the Fresnel reflectance R
F
(θ
i
). Since it results from a completely
different physical process than the specular color (absorption in the inte-
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Although we have seen that light may change its direction when entering or exiting
these substances, it does not change within the substance itself.