Game Development Reference

In-Depth Information

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

model.

BTF
(
x
,
ρ
r
,
ρ
i
)

≈

f
r
,
x
(
ω
i

→

ω
r
)

(15.2)

→

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
)

(15.3)

j

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
)

(15.4)

j

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
)

(15.5)

where:

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

Search Nedrilad ::

Custom Search