Graphics Reference
In-Depth Information
Figure 9.5.
Facets shadowing others.
F:
This term corresponds to the fraction of light actually reflected rather than
absorbed, which, using the Fresnel reflection law, is a function of the angle
of incidence and index of refraction n.
2
2
(
)
È
[
(
) -
]
˘
gc
-
cg c
+
1
F
=
1
+
(9.7)
Í
˙
2
2
(
)
[
(
) +
]
gc
+
Î
cg c
-
1
˚
where c = ( V H ) and g = n 2
+ c 2
- 1.
Other Ds have been used which are simpler in order to offset the computation for
G and F. See [Blin77] for more details.
In the discussion of reflectance models above we assumed a single-point light
source. For multiple light sources one adds the diffuse and specular contribution of
each but uses only one ambient term.
Finally, one fact that has not been touched on so far is how the distance between
an object and a light source affects its intensity. If one does not take distance into
account, then two equally sized spheres, one of which is much further away from the
light than the other, would be visually indistinguishable in a picture, which is not what
one would experience in real life. Laws of physics imply that light intensity is inversely
proportional to the square of the distance from the source. It turns out, however, that
if one models this effect, a lot of the time the pictures do not come out right and so
this factor is often ignored. Sometimes a factor inversely proportional to the distance
(rather than its square) is used. There are times when one wants to assume that the
light is “infinitely” far away (the rays are all parallel) and, in that case, clearly dis-
tance has to be ignored otherwise one would have zero intensity. The sun shining on
a scene is an example of this. If one wants to add a distance factor f, then one should
use an intensity equation of the form
(
) ,
IIk fIkr kr
=
+
+
(9.8)
aa
p dd
ss
where f could be 1/D 2 , D being the distance.
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