Graphics Reference
In-Depth Information
(a) (b) (c)
Figure 4.19
Rendering of a parchment using (a) the dipole model, (b) the multipole model and (c) a
Monte Carlo simulation. (From [Donner and Jensen 05] c
2005 ACM, Inc. Included here
by permission.)
light comes from light transmitted through the parchment, which is a fairly thin
material compared to the mean free path. Not surprisingly, the dipole model fails
to capture the essential lighting in the image. In contrast, the differences in the
images rendered using the multipole model and the Monte Carlo simulation are
hardly noticeable.
Handling multiple layers.
The multipole model is derived for an infinite slab.
Parchment is one example of a real object for which a thin slab is a good model.
As described earlier in the section, some natural materials are better modeled by
several thin layers. The multipole model does not immediately apply in this case.
Simply stacking several thin layers and applying a multipole model to each does
not work, because the light reaching the second layer is diffused by the first. The
dipole and models are derived for a thin beam of light hitting the surface at a
specific point. Applying them to diffuse incident light requires integrating the
multipole model over the surface, as if there is a separate differential multipole at
each surface point. The reflectance and transmittance profiles for combined layers
are therefore quite complicated. Donner and Jensen employ Fourier transforms,
a technique commonly used in signal and image processing, efficiently construct
multilayer reflectance and transmittance profiles.
The transmittance of a slab can be interpreted as a kind of filter for the in-
coming flux. The transmittance of light through two slabs amounts to applying
the filter of the second slab to the result of the incident flux filtered by the first
slab. The net effect of two filters is determined by the
convolution
of the fil-
ters, which is a function whose value at a point
x
is the result of integrating one
filter shifted by
x
against the other without a shift. For example, the net transmit-
