Graphics Reference
In-Depth Information
Figure 9.4.
More realistic specular
drop off.
r
s
=
1
0
,
,
if
otherwise
VR
=
=
.
This is not realistic. There is a specular contribution also when
V
is close to
R
. See
Figure 9.4(a). Phong ([BuiT75]) used the angle f between
R
and
V
to control the
decrease in the intensity of reflected light as one moves away from the mirror direc-
tion. Specifically, he used a power m of cos f=
R
•
V
to adjust the sharpness of the
highlights and defined r
s
by
(
)
(
)
=
m
()
=
m
(
)
rr
s
=
f
max cos
f
,
0
max
RV
∑
,
0
(9.3)
s
()
=
() ()
+
()
(
()
+
)
Phong's specular reflectance model
:I
l
I
l
k
l
I
l
k
l
r kr
(9.4)
a
a
p
d
d
s s
Although some topics say that the constant exponent m measures the “shininess”
of a surface, with a large m corresponding to glossy surfaces and a small one to dull
surfaces, a better visual description would be that it changes the apparent size of the
light by making the highlight smaller or larger, respectively. Typical values of m range
from 50 to 60. Note that the specular reflection coefficient k
s
is
not
a function of wave-
length. This is so that highlights appear to have the color of the source.
In practice, one makes some simplifications to Phong's model. First of all, one
approximates the ambient term by a constant. Another simplification is made if the
light source and viewer are at infinity. In this case, one replaces the angle f by the
angle a between the normal
N
and
H
. The justification for this is that
H
specifies
the direction that the surface normal should be for
V
to be the mirror direction. When
that happens, then f=2a. Therefore, we can compensate for the difference in the dot
products by changing the power m. The nice consequence of this is that since
L
and
V
are constant,
H
is also constant, and so we save ourselves some computations. This
leads to the following ([Blin77]):
A simplified Phong specular reflectance model
:
(
)
m
()
=
()
()
∑
(
)
+
(
)
I
l
ambient constant
+
I
l
k
l
NL
k
NH
∑
(9.5)
p
d
s
Phong's model was derived empirically. It produced results that were better than
those using previous methods. To get better results yet, one needs to go back to theory.
Experimentally one has a pretty good match to Phong's model except that the peak
