Graphics Reference
In-Depth Information
absorption and scattering. However, these parameters are unintuitive and proved
quite difficult for artists to use. So the authors replaced these physical parameters
with two that are more convenient: there is one parameter for diffuse color and
another for the translucency of the object. The diffuse color is actually a kind of
average diffuse albedo, defined by the integral
∞
1
3
A
√
3
(
1
−
α
)
e
−
√
3
(
1
−
α
)
,
=
α
2
e
−
ρ
d
=
2
π
R
d
(
r
)
rdr
+
(4.14)
0
where
R
d
is the multiple scattering reflectance defined in Equation (4.13). This
diffuse albedo
ρ
d
is essentially the integral of the multiple scattering reflectance
over the entire surface, assuming the object is uniformly illuminated by light of
constant radiance coming from all directions. Given
ρ
d
, Equation (4.14) can be
α
=
σ
a
/
σ
s
. The translucency parameter is the mean free path
l
d
of
light in the medium. As mentioned previously,
l
d
=
solved for
1
/
σ
tr
. The values of
σ
a
and
σ
s
can be determined from
α
and
σ
tr
:
σ
tr
σ
t
=
σ
s
=
σ
σ
t
,
σ
a
=
σ
t
−
σ
s
.
3
−
α
)
,
(
1
The parameters
ρ
d
and
l
d
were later used to control the variation in subsurface
scattering across a surface using a form of a texture map known as an
albedo
map
. This technique is now widely utilized in movie production.
4.3.5 The Multipole Model
The dipole model assumes the scattering medium is homogeneous and extends
infinitely deep below the surface. This assumption is sufficient for some objects,
but it breaks down for many real objects because they are not homogeneous or
they are simply too thin. Some natural objects, such as plant leaves and human
skin, can be regarded as having several thin (somewhat) homogeneous layers (
Fig-
of using positive and negative virtual point sources does. Craig Donner and Hen-
rik Wann Jensen developed a
multipole
method that extends the dipole model to
subsurface scattering of multilayered objects [Donner and Jensen 05].
The core of the dipole BSSRDF model is the function
R
d
(
of Equation (4.13),
which gives the ratio of light exiting the surface after multiple scattering to the in-
cident light. There is only one interface, the surface of the scattering medium,
and the virtual sources are arranged to satisfy the boundary condition that the net
inward flux at the surface is zero. In a thin slab or multilayered structure however,
there is an interface between each layer, and the transmittance of light through the
layers has to be taken into account. Furthermore, appropriate boundary conditions
at all the interfaces have to be satisfied simultaneously.
r
)
