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The BRDF fit to the measurement of the hair cluster is a summation of a single
scattering component f dir and multiple scattering component f indir :
=
+
.
f fit
f dir
f indir
The components correspond to direct and indirect illumination, respectively, as
the subscripts indicate. Basically, f dir comes from the Marschner model, and f indir
comes from the local multiple scattering function in the “dual scattering” model
described in Section 8.5.2. However, the goal of better reproduction of measured
data required an extra diffuse term to be added to both models. These diffuse
terms approximate some more complicated scattering effects not included in the
original models, such as “TRRT” and off-specular scattering. The single scatter-
ing (direct) component of the reflectance is a modified version of the Marschner
model,
) · s R ·
M TRT +
r d
π
N TRT ·
f dir =(
1
d
f R +
f TT +
d
·
2 ,
(8.16)
where d is the magnitude of the diffuse component. The multiple scattering com-
ponent f indir comes from the local backscattering model.
Besides the elimination of the azimuthal dependence, Equation (8.16) em-
ploys two other modifications. One is the extra scaling parameter s R of the R
(simple reflection) term. This controls the relative importance of the R compo-
nent compared to the TRT and TT components. This scaling parameter can be
thought of as a way of accounting for azimuthally dependent properties, which
are not directly measured. In the Marschner model (Equation (8.15)), the R term
is the product of a longitudinal factor M R and an azimuthal factor N R ( θ , φ i , φ r )
.
The variation in N R is primarily a result of noncircular cross sections of the hair
fibers. The value of the scaling parameter s R represents an average value of N R .
The azimuthal dependence is more significant in the TRT component. For this,
the authors explicitly average the azimuthal factor N TRT over the azimuthal direc-
tions:
π / 2
s
π
N TRT =
N TRT ( φ i , θ i , φ r , θ r )
d
φ i
π / 2
for use in Equation (8.16). The extra parameter s is used in the fitting process.
The BRDF parameter fitting involves a collection of parameters, including the
diffuse magnitude d , the R scaling parameter s R ,andthe N TRT scaling parameter
s . The fitting process minimizes the error of the fit over all the parameters. Be-
cause the reflectance model is nonlinear, a search algorithm is employed to find
the minimum error. Unfortunately, nonlinear optimization of this form is not easy.
Most methods employ a searching approach, but a common problem is that the
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