Graphics Reference
In-Depth Information
Renderingwith themultipole model.
In order to apply the multipole model
in practice, the reflectance and transmittance parameters and the thickness are
needed for each layer. Layer thicknesses can generally be measured easily enough
for a real object, but the other parameters present more of a challenge. The pro-
cess of determining the reflectance and transmittance parameters for the dipole
model described in Section 4.3.3 is relatively simple: the object is photographed
and parameters are fit to match the reflectance curve. While the same approach
could conceivably be used for a multilayered object, fitting of the parameters
becomes a much more difficult inverse problem. It is complicated by the fact that
the photograph provides only the convolution of the reflectance of the multiple
layers, and in general it is not possible to deconvolve them. Faithfully measuring
a real object requires examining each layer separately. Even so, measurements
for the dipole model may not be immediately applicable to the multipole model
because the dipole model tries to match the general appearance of subsurface
scattering.
Another problem with the multipole model is that it assumes the layers are
homogeneous. This is not true of many real objects, including plant leaves and
human skin. The most visually significant variation occurs across the surface
rather than beneath it—freckles and moles on skin, and patterns seen on plant
leaves are examples. Existing measurements typically represent the average of
the parameters over the surface. In the case of a single layer, the parameters at
each position can be determined from the diffuse reflectance of the object based on
the diffuse albedo of Equation (4.14). But this is more difficult for multilayer ma-
terials. Furthermore, the positional dependence of reflectance and transmittance
acts as a kind of filter, and therefore must be included in the convolutions above.
Donner and Jensen employ a simpler approach that uses an ordinary albedo map
at the top surface. The same approach was used in the fast translucency paper,
and is analogous to a texture map used in surface rendering wherein the reflected
light is multiplied by the position dependent texture map value. The albedo map
is convolved with the final diffuse reflectance and transmittance functions as il-
lustrated in Figure 4.22. While this is not physically accurate, it has the effect of
blurring the albedo map in a visually plausible manner.
The multipole model is derived under the assumption that all the interfaces
(surfaces) are perfectly smooth. But real objects have rough surfaces. Donner
and Jensen use the the microfacet-based BRDF model developed by Torrance and
Sparrow (see Chapter 8) to model surface roughness. This changes the boundary
conditions of Equations (4.15) and (4.16): the diffuse Fresnel reflectance
F
dr
has
to be replaced by an average diffuse reflectance
ρ
d
, which is computed by numeri-
cally integrating the BRDF function. Surface BRDF rendering without subsurface
scattering normally assumes that light not reflected is absorbed by the surface and
