Graphics Reference
In-Depth Information
Figure 26.34: Subsurface scattering lets light pass through the marble and skin in these
images. (Courtesy of Stephen Marschner, ©2001 ACM, Inc. Reprinted by permission.)
Imagine trying to measure the BRDF for a perfect mirror using a gonioreflectome-
ter. The sensor computes the incoming radiance by measuring the arriving power
and dividing by the sensor area, which implicitly makes the assumption that the
radiance along all rays from the sample to the sensor is approximately constant.
But if the source is so tiny that its reflected rays all lie well within the sensor area,
this assumption is invalid: For much of the sensor, no light is arriving at all. So a
gonioreflectometer for measuring the BRDF of a mirror must have a sensor whose
size is adjustable so that the whole sensor area is saturated with light. Of course,
because mirror reflection is so “concentrated” (the rays of light don't spread out
at all after reflection), it makes sense to try to measure the BRDF with a very
tiny light source, perhaps a source with an adjustable iris. As we shut down the
iris on the source, we'll have to make the sensor area smaller to compensate. The
one thing we know is that the radiance of a ray from the source to the sample is
the same as the radiance from the sample to the sensor, because the material is a
perfect mirror. Now consider our definition for the BRDF:
L
(
t
,
P
,
v
o
,
λ
)
f
r
(
P
,
v
i
,
v
o
,
λ
)=
)
m
(Ω)
.
(26.82)
L
(
t
,
P
,
−
v
i
,
λ
)cos(
φ
Suppose we first perform the measurement with a source at
=
0 whose solid
angle, measured from the sample, is 0.01 sr. The two radiances in the formula are
the same, so they cancel, and the BRDF measurement is 100 sr
−
1
.
Now suppose that we close down the iris on the light source so that it subtends
a solid angle of 0.005 sr. We'll have to shrink the sensor as well to get a valid radi-
ance measurement, but when we do so we'll again find that the received radiance
is the same as the emitted radiance. The BRDF measurement will be 200 sr
−
1
.
As we continue closing the iris, the measurements will increase without bound.
The conclusion is that for a perfect mirror, the BRDF is infinite. To be more pre-
cise: If the reflection of
φ
v
i
is
v
o
, and the surface being measured is a mirror, then
f
r
(
P
,
)
is infinite.
It doesn't actually make sense to say that a function takes on the value “infin-
ity,” but there is a mathematical theory of a different class of objects, called dis-
tributions, which
can
take on infinite values. The name “bidirectional reflectance
distribution
function” reflects this. One difficulty with this notion of infinite val-
ues arises when we consider an
imperfect
mirror, one that reflects only half the
v
i
,
v
o
,
λ
