Game Development Reference

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Figure 7.20.
Surface roughness is characterized by how much the slopes of the micro-

facets vary.

microfacets
. Each microfacet is treated as a perfect reflector that obeys the reflec-

tive laws of electromagnetic theory. The roughness of a surface is characterized

by the slopes of the microfacets. As shown in Figure 7.20, a rough surface is

composed of microfacets having greatly varying slopes, whereas the microfacets

for a relatively smooth surface have only small slopes.

Cook and Torrance use the following formula for the specular component

of the BRDF given in Equation (7.53).

(

)

(

)

VL

,

G

VL

,

D

(

)

(

)

VL

,

=

VL

,

(7.54)

s

(

)(

)

π

NV NL

⋅

⋅

is the Fresnel factor, which describes the amount and color of light reflected as

a function of the angle of incidence;
D
is the microfacet distribution function,

which returns the fraction of microfacets oriented in a given direction; and
G
is

the geometrical attenuation factor, which accounts for self-shadowing of the mi-

crofacets. Since the microfacets are perfect reflectors, only those microfacets

whose normal vectors point in the direction of the halfway vector
H
contribute to

the specular reflection.

The
π
appearing in the denominator of Equation (7.54) is a normalization

factor that accounts for the fact that the incident flux density
Φ
I
at a surface for a

constant emitted radiance
C
is given by

ππ

2

(

)

Φ

=

C

NL

⋅

dω

=

cos

φ φdφdθ C

sin

=

.

(7.55)

I

E

E

Ω

00

7.9.3 The Fresnel Factor

The interaction of an electromagnetic wave and a surface results in a reflected

wave and a transmitted wave. The energy contained in the reflected wave is equal

to the energy contained in the incident wave minus the energy contained in the

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