Graphics Reference
In-Depth Information
n
= 8
n
= 80
n = 8
n = 80
1
1
n
= 600
n
= 20
n = 500
n = 20
−
1
−
0. 5
−
1
−
0. 5
0. 5
1
0. 5
1
(a)
(b)
General cosine lobes. (a) The cosine lobe cos
n
Figure 8.3
α becomes more narrow as the exponent
n
increases. (From [Lafortune et al. 97] c
1997 ACM, Inc. Included here by permission.)
larger
n
thus produces a narrower lobe and a more specular surface, so the specular
exponent
n
models how shiny the surface appears.
4
Figure 8.3(b) shows the effect
of adding the diffuse term.
Variants and improvements of the Phong model.
As BRDF, the Phong
model has some problems. One is that the lobes are symmetric about the specular
direction. This is reasonable near normal incidence, but the symmetric shape of
the lobe is unrealistic for more oblique incoming light. A particular interesting
area for BRDF models occurs as the angle of incidence approaches 90
◦
, i.e., when
the incident and reflected directions get close to the plane tangent to the surface.
This is called
grazing reflection
. Most real surfaces become more reflective at
grazing angles; in fact, some surfaces essentially become mirrors when viewed
from an angle nearly parallel to the surface (see
Figure 8.4
)
. The Phong model
fails to capture this behavior. Furthermore, the original Phong model fails to con-
serve energy; the Phong lobe needs to be increasingly scaled down toward grazing
in order to satisfy the energy conservation requirement. The scale of the lobes is
another issue with the Phong model. As the lobes get narrower, less light ends up
being reflected. Really the lobes need to get longer as they are narrowed. This was
Figure 8.4
Specularity often increases near grazing angles of reflection. (From [Lafortune et al. 97]
c
1997 ACM, Inc. Included here by permission.)
4
The story is that after Phong got his model working, he and his colleagues at the University of
Utah went around the building pointing out the exponent of all the objects they could find.
