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Figure 7.23. Copper vases rendered with isotropic microfacet distributions. The first two
images use a single roughness value of
=
0.1
(left) and
=
0.25
(center). The right-
m
m
1
2
most image combines these using the weights
w
=
0.4
and
w
=
0.6
.
1
2
7.9.5 The Geometrical Attenuation Factor
Some of the light incident on a single microfacet may be blocked by adjacent
microfacets before it reaches the surface or after it has been reflected. This block-
ing results in a slight darkening of the specular reflection and is accounted for by
the geometrical attenuation factor. Blocked light is essentially scattered in ran-
dom directions and ultimately contributes to the surface's diffuse reflection.
We can derive an estimate of how much light is blocked due to surface
roughness by assuming that microfacets always form V-shaped grooves. Figure
7.24(a) illustrates a situation in which light reflected by a microfacet is partially
blocked by an adjacent microfacet. In this case, light is blocked after being re-
flected. Reversing the direction in which the light travels exhibits the case in
which light is blocked before reaching the microfacet, as shown in Figure
7.24(b).
The application of a little trigonometry leads us to a formula giving the frac-
tion of light reflected by a microfacet that still reaches the viewer after being par-
tially blocked by an adjacent microfacet. As shown in Figure 7.25, we would like
to determine the portion x of the width w of a microfacet that is visible to the
viewer. We first observe that
1
sin
,
(7.75)
w
=
α
and that by the law of sines (see Appendix B, Section B.6),
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