Reconstruction of Reflectance - The Magic of Computer Graphics - page 215

Figure 8.6 A surface can be approximated with very small facets called microfacets .

A microfacet model of a surface regards the microgeometry as a collection
of mirror polygons ( Figure 8.6 ) . Because the facets are perfect mirrors, the only
facets that reflect light (directly) from a particular incoming direction l to an-
other outgoing direction

v are those having normals that match the direction of
the half-vector of the given directions l and

v ( Figure 8.7 ) . The microfacets are
not explicitly modeled; rather, the microgeometry is described in terms of the
distribution of the microfacet surface normals. If the microfacets were explicitly
modeled, there would be a finite number of microfacet directions and the proba-
bility of there being a microfacet exactly aligned to a particular half-vector would
therefore be zero. The distribution is assumed to be continuous.
The BRDF value for a pair of directions l and v depends on the percentage of

facets whose normals correspond to the half-vector. This is given by the distri-
bution of microfacet surface normal directions. The distribution is governed by a
function D ( h

, which provides the fraction of all microfacets that align with the
vector h . The Torrance-Sparrow model assumes a Gaussian distribution based on
the angle

)

between the vector h and the surface normal ( Figure 8.7 ) , α

be − c 2

2
h

θ

D ( θ h )= .

Figure 8.8 shows a plot of a Gaussian distribution. The maximum value is at
θ h =

0. A geometric interpretation is that microfacets are most likely to be nearly
parallel to the macroscopic surface normal.
Because each microfacet is assumed to be a perfect mirror, Fresnel reflection
applies. If L i is radiance coming from the direction that makes an angle θ i with

→

→ →

l

n

h

→

v

α

θ i

θ r

Microfacet

Figure 8.7 Reflection from a microfacet depends on the angle its surface normal makes with the

macroscopic surface normal.