Game Development Reference
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compress this data. This step should maintain the characteristics of the BTF as much
as possible and offer a quick decompression.
A large number of compression methods consider a BTF as a collection of discrete
textures or an “apparent BRDF varying spatially'' (ABRDF Wong et al., 1997). Note
that in this approach, the ABRDF are not physically plausible as non reciprocal, since
they consider the scattering of other parts of the surface.
The most natural compression is to approach the BTF in each pixel by a BRDF
BTF ( x , ρ r , ρ i )
f r , x ( ω i
ω r )
The BRDFmodels f r ( ω i
ω r ) must be, however, quick enough in assessment to provide
a rendering with acceptable calculation time. Thus, McAllister et al. (2002) suggest a
method which is based on the approximation of Lafortune's model of BRDF (Lafortune
et al., 1997), based on a sum of lobes.
f r ( ω i
ω r )
ρ d +
ρ s , j
s j ( ω i , ω r )
The parameters of each lobe j and albedo ρ d are obtained by a non-linear optimisa-
tion of the set of measurements. However, this model cannot be used to represent the
ABRDF that can have self-shadowing and self-occultation effects specific to light phe-
nomena related to the mesogeometry of the surface. To solve this problem, Daubert
et al. (2001) suggests adding a term T x ( ω r ) to this model; this term represents the
self-occultation of the material. The BTF is then estimated as follows:
ρ d , x +
BTF ( x , ω r , ω i )
T x ( ω r )
s x , j ( ω r , ω i )
The storage cost of this approach is however much higher than the McAllister method
and its use in real-time rendering is limited.
Another approach where it is possible to take into account these light effects is
based on the concept of residual function. After approximation of the BRDF using the
Lafortune model as per the McAllister method, we get a set of measurements ( BTF )
which can be referred to for calculating the error of approximation. This remainder can
be considered as whatever remains to be approximated and can thus represent the result
of a residual function. The objective of this approach is obtaining this function in order
to take into account the different effects of the material materialised in the bidirectional
reflectance function. The BTF is then approximated by using the following equation:
BTF ( x , ω r , ω i )
f r , x ( ω r , ω i )
δ ( x , ω r , ω i )
ρ d + j ρ s , j ( ω r ·
ω i ) n j : BRDF of Lafortune
f r , x ( ω r , ω i )
C j
δ ( x , ω r , ω i )
BTF ( x , ω r , ω i )
f r , x ( ω r , ω i ): Remainder of the previous approximation
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