Graphics Reference
In-Depth Information
Using
h
, the geometric attenuation is
v
o
)=min
1, 2
(
n
.
·
h
)(
n
·
v
)
,2
(
n
·
h
)(
n
·
v
i
)
G
(
v
i
,
(27.38)
(
v
·
h
)
(
v
·
h
)
The slope distribution function
D
describes the fraction of facets that are ori-
ented in each direction; letting
=cos
−
1
(
n
α
·
v
i
)
, we can write
D
as a function of
α
, thus implicitly assuming that it's symmetric around the surface normal, that is,
that the microfacet distribution is isotropic. Cook and Torrance use the
Beckmann
distribution function
1
m
2
cos
4
e
−
[
tan
m
]
2
D
(
α
)=
,
(27.39)
α
which has the single parameter
m
.
Inline Exercise 27.9:
Convince yourself that if
m
is very small, then most
facets are nearly perpendicular to the normal vector
n
, while if
m
is large, the
surface is very rough with sharply angled facets.
They also note that a surface may be rough at several different scales; thus,
the function
D
could be a weighted sum of multiple terms like the one in Equa-
tion 27.39.
Finally, they model the spectral distribution of the reflected light. For diffuse
reflectance, they use measured reflectance spectra, which are typically measured
with illumination at normal incidence; they note (as in our discussion of Fresnel
reflectance above) that the diffuse reflectance spectra for most materials do not
vary substantially for incidence angles up to 70
◦
off normal, and even then vary
relatively little. They therefore use the normal-incidence reflectance spectrum as
the diffuse reflectance spectrum at all angles.
Inline Exercise 27.10:
There are man-made materials that are designed to have
reflectance spectra that vary with viewing angle; one example is a diffraction
grating. Try to think of a diffuse material with this property. Hint: textiles.
For the specular term, they model the angle dependence of the reflectance
spectrum as coming entirely from the Fresnel term, as above. The results repre-
sented a huge step forward in computer graphics: Because the color of the spec-
ular highlights could now be different from that of either the underlying surface's
diffuse color
or
the color of the incident light, it became possible to plausibly
simulate a much wider variety of materials (see Figure 27.15).
Closely related to the microfacet models for specular reflection is the Oren-Nayar
model [ON94] for reflection from rough surfaces such as unglazed clay pots, ten-
nis balls, or the moon's surface. Oren and Nayar observed that these diffuse reflec-
tors did not actually follow Lambert's law very well at all; in particular, the areas
near the silhouette tended to be much lighter than Lambertian reflectance would
predict. This is particularly obvious with the moon, whose brightness appears
almost uniform across the surface (except for surface-texture features). They sug-
gest that this brightness near the silhouettes can be explained by noting that the
