Graphics Reference
In-Depth Information
simplify things by assuming that the material is homogeneous and anisotropic so
that
f
ss
depends only on the distance from
P
to
Q
rather than on their absolute posi-
tions in the material; this substantially reduces the memory required to represent
the scattering. But for many materials (like the palm of your hand), the geometric
structure of the subsurface material is neither isotropic nor homogeneous. Things
like veins, arteries, capillaries, muscle, cartilage, and fat all affect the scattering of
light differently.
How does the use of subsurface models influence the rendering equation?
Recall that the basic model had the form
+
v
i
L
(
P
,
v
o
)=
...
L
(
P
,
v
i
)
f
s
(
P
,
v
i
,
v
o
)
...
,
(27.44)
that is, the emitted radiance was basically the value of an integral over all incoming
directions at
P
. But with subsurface scattering, light arriving at some other point
Q
might eventually be emitted at
P
, and the form becomes
+
L
(
P
,
v
o
)=
...
L
(
P
,
v
i
)
f
ss
(
P
,
Q
,
v
i
,
v
o
)
...
.
(27.45)
v
i
Q
Computing subsurface scattering adds another integral. In practice, for most
materials the new integral (over all points
Q
of the material) can be replaced by
one over a bounded area (like a disk) around
P
: Light entering at your finger-
tip is unlikely to exit at your nose in any substantial amount. If the material is
homogeneous and anisotropic, and the arriving radiance is nearly constant over
the surface, the scattered radiance can be precomputed and stored in a lookup
table, and the new computation is not much worse than that for the simpler ren-
dering equation.
What are the practical effects of modeling subsurface scattering? First, it's
possible for light to diffuse across shadow boundaries so that a “hard shadow”
on skin, for instance, ends up slightly softened. Second, it allows color bleeding
within objects: A cup of tea with milk has its color affected, near the edge of the
tea's surface, by the color of the cup itself.
How does one model the subsurface scattering? In much the same way as we
model surface scattering: either with acquired data, or by phenomenological or
physical models. One can acquire data by modifying a gonioreflectometer to allow
the sensor to be adjusted so that it measures light received from some location
Q
that's not the center,
P
, of the sample stage—either by translating the entire sensor
assembly in the plane of the sample stage, or by making a small, two-axis rota-
tion of the sensor about its center. One could equally well translate or rotate the
illumination source, of course, and/or rotate or translate the sample stage. Alterna-
tively, one can illuminate the sample stage and then replace the usual sensor with
a camera. This allows the measurement of light from many material points and
directions at once. This approach is described by Jensen et al. [JMLH01] in some
detail.
As for physical modeling of the subsurface scattering, it involves physics and
mathematics well beyond the scope of this topic. Jensen et al. describe some fea-
sible approximations, and give a general overview and pointers to the physics
literature.
