Graphics Reference
In-Depth Information
i
o
P
Q
A
Figure 26.33: Subsurface scattering. To describe the scattering of light that arrives in direc-
tion
i
at a point P of a surface that's not a pure reflector, but rather allows multiple
subsurface bounces before the light is emitted, requires a description of the emitted light at
every nearby point Q in every outgoing direction
−
v
v
o
.
This tells us, for example, that we need not place the light source and sensor at
every possible pair of positions when we measure the BRDF with a gonioreflec-
tometer; we can skip half of the positions.
But the Helmholtz reciprocity law also tells us that not just any function can
be the BRDF of a material. In fact, there are further restrictions. For instance,
if a certain amount of power arrives at a surface and is reflected, the amount of
power leaving the surface must be no more than the amount that arrived, because
of energy conservation. This places restrictions on various integrals of the BRDF.
Helmholtz reciprocity holds for a great many materials; indeed, there have
been several purported proofs of it. Those proofs are thrown into doubt by the
existence of materials that have been measured and shown to not satisfy the “law.”
Veach [Vea97] discusses the hypotheses necessary for reciprocity to hold.
A thin sheet of colored vinyl may both reflect light and transmit it; in such a case,
one can build a gonioreflectometer to measure the transmitted light instead of the
reflected light; the portion of the function
f
r
that we'd defined as zero for purely
reflective surfaces becomes nonzero in this case, and the “reflectance” portion
of the function is set to zero. The resultant function is called the
bidirectional
transmittance distribution function,
or
BTDF.
The sum of these two is called the
bidirectional scattering distribution func-
tion,
or
BSDF,
which we'll denote
f
s
.
When a ray of light meets a surface at a point
P
, we've been assuming that it
is reflected (or transmitted) and again leaves from the point
P
. In many interest-
ing materials, including human skin, hair, many forms of wood, and tree leaves,
light actually enters the material, reflects multiple times under the surface, and is
reemitted from some point near
P
(see Figure 26.33). This scattering is character-
ized by a
bidirectional surface scattering reflectance distribution function,
or
BSSRDF,
which has, as arguments, the point
P
, the direction of the arriving light
v
i
, the point
Q
from which the light exits, and the direction
v
o
in which it exits.
Fortunately, for many surfaces the simpler BSDF suffices. Rendering materials
using the BSSRDF, however, can produce some spectacular results [JMLH01]
(see Figure 26.34).
