Game Development Reference

In-Depth Information

We can modify the microfacet distribution function to account for aniso-

tropic surface roughness by changing Equation (7.71) to

(

)

2

(

)

2

(

)

2

1

TP

⋅

1

−

TP

⋅

NH

⋅

−

1

(

)

D

VL

,

=

exp

+

, (7.72)

m

(

)

4

2

2

(

)

2

4

mm

NH

⋅

m

m

NH

⋅

xy

x

y

where
m
is a two-dimensional roughness vector,
T
is the tangent to the surface

aligned to the direction in which the roughness is
m
, and
P
is the normalized

projection of the halfway vector
H
onto the tangent plane:

(

)

HNHN

−⋅

P

=

HNHN
.

(7.73)

(

)

−⋅

Figure 7.22 shows a disk rendered with both isotropic and anisotropic surface

roughness values. Some surfaces exhibit roughness at multiple scales. This can

be accounted for by calculating a weighted average of microfacet distribution

functions

n

m

(

)

D

VL

,

=

wD

(

VL
,

,

)

(7.74)

i

i

i

=

1

where multiple roughness values
m
are used and the weights
w
sum to unity.

Figure 7.23 shows two objects rendered with different values of
m
and another

object rendered using a weighted sum of those same values.

Figure 7.22.
A disk rendered using the anisotropic distribution function given by Equa-

tion (7.72). For each image

. From left to right the values of
m
are 0.1 (iso-

tropic), 0.12, 0.15, and 0.2. The tangent vectors are aligned to concentric rings around the

center of the disk—they are perpendicular to the radial direction at every point on the

surface.

=

0.1

m

y

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