Graphics Reference
In-Depth Information
(a) Make a conjecture about why these are not combined into a single RGB triple,
since they are, after all, multiplied together in the model.
(b) The diffuse and specular colors in the Cook-Torrance model are specified by
RGB triples (or more generally, by spectral distributions). Why do you suppose
the specular exponent does
not
get expressed as an RGB triple?
(c) Suppose that the entire model was divided up by wavelength so that the spec-
ular exponent
could
vary from color to color. Suppose the red exponent was 3,
while the blue and green exponents were 5, and that both the diffuse and specular
colors were pure white. What would be the appearance of the specular highlight
from a white point light?
Exercise 27.5:
Plot
F
R
, the Fresnel reflectance, as a function of
θ
i
, for an
interface where
r
=
n
1
/
n
2
is 1, 1.5, 2, and 3. To do so you'll need to compute
θ
t
using Snell's law.
Exercise 27.6:
Compare the Schlick approximation of the reflectance with
the Fresnel expression for the reflectance for aluminum and magnesium oxide at
500 nm. Magnesium oxide is nonmetallic, so the Schlick approximation should
not necessarily be expected to work. Use 1.0 as the index of refraction of air, 1.44
for aluminum, and 1.74 for magnesium oxide.
Exercise 27.7:
The Fresnel term used in graphics assumes that the arriving
light is unpolarized; on the other hand, the different reflection constants for paral-
lel and perpendicular polarization mean that the light
leaving
the surface
is
actu-
ally polarized. Yet we generally assume, when it reaches the next surface, that it's
unpolarized. Try to imagine a physical situation in which this inconsistency would
manifest itself in a visible artifact.
