Graphics Reference
In-Depth Information
Fourier transforms used in combining layers come essentially for free. d'Eon and
his collaborators discovered that a single Gaussian function could not reproduce
the realism of the multipole or even the dipole model. So the next step was to
try summing multiple Gaussians of varying width. They found that a sum of as
few as six Gaussians could adequately approximate the diffusion profiles of the
multipole model. Their model also uses a more precise convolution expression
for combining layers that depends on the direction of light propagation:
T
12
=
T
1
∗
T
2
+
T
1
∗
R
2
∗
R
1
∗
T
2
+
T
1
∗
R
2
∗
R
1
∗
R
2
∗
R
1
∗
T
2
+
···
(4.22)
where the “
” superscripts indicate direction. The model is amenable to
implementation in graphics hardware. The authors' implementation was able to
render a human head model at rates as high as 60 frames per second.
In 2008 Craig Donner, Tim Weyrich, Eugene d'Eon, Ravi Ramamoorthi and
Szymon Rusinkiewicz published an enhanced multilayer model for subsurface
scattering in human skin [Donner et al. 08]. The model includes a number of
things the multipole model does not. For example, each layer has its own set
of spatially varying reflectance parameters, and it also accounts for absorption at
the interface between layers. The parameters are chosen from physical measure-
ments computed from a series of photographs. The photographs are taken by a
calibrated camera through a variety of filters, including a cross-polarization fil-
ter to eliminate unwanted glossy reflection. The measurements are then fit to the
model. A notable advantage of the model is that it allows for greater flexibility in
controlling skin parameters, e.g., the amount of melanin.
The representation of the effects of subsurface scattering by combining a sin-
gle scattering model with a diffuse multiple scattering model became popular
after the publication of the dipole-based BSSRDF model. However, it is based
on the assumption that multiple scattering is diffuse. The diffusion approxima-
tion is after all only an approximation, and it only applies to materials exhibiting
a high degree of scattering. The researchers who developed the diffusion-based
models understood that subsurface scattering can also be important in materials
in which the diffuse assumption breaks down. Donner et al. proposed a more
generic BSSRDF model for homogeneous materials in the paper “An Empirical
BSSRDF model” [Donner et al. 09] that neither splits scattering into single and
multiple components nor relies on the diffusion approximation. The model em-
ploys a fairly simple analytic function of six parameters, although there may be
many sets of such parameters for a single material. The parameters are deter-
mined by running a large scale particle simulation in the scattering medium. The
exitant light distribution for the material is then examined for the distinct features
corresponding to each parameter, e.g., anisotropy, peak direction, lobe shape and
+
”and“
−
