Game Development Reference

In-Depth Information

L

V

H

H

V

L

(a)

(b)

Figure 7.24.
(a) Light reflected by the left microfacet is partially blocked by the right

microfacet. (b) Light is blocked by the right microfacet before reaching the left micro-

facet.

2sin

γ

x

=

.

(7.76)

(

)

sin

β π

+

2

We can express each of the sine functions in Equations (7.75) and (7.76) as co-

sine functions that have been shifted by

π
radians by writing

(

)

sin

α

=

cos

π α

2

−

=

NH

VH

NV

⋅

(

)

(

sin

βπ

+

2

=

cos

β

=

⋅

)

(7.77)

sin

γ

=

cos

π γ

2

−

=

⋅

.

Using the dot products corresponding to each of the cosine functions lets us ex-

press the fraction of light
G
reaching the viewer as

(

)(

)

2

NH NV

VH

⋅

⋅

x

G

==

.

(7.78)

1

w

⋅

When light is blocked before reaching a microfacet, we can calculate the

fraction
G
that still reaches the viewer by simply exchanging the vectors
V
and

L
in Figure 7.25 to obtain

(

)(

)

2

NH NL

LH

⋅

⋅

x

G

==

.

(7.79)

2

w

⋅

The three possible cases pertaining to light reflected by a microfacet are that

the light is completely unobstructed (the fraction of light reaching the viewer is

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