Graphics Reference
In-Depth Information
r
n
p
Figure 1.12.
Visualization of reflection ray spread due to surface roughness.
Due to the nature of specular reflection, most samples that have meaningful
weights would focus around
r
. Their weights toward a final solution would be
directly correlated to the angular distance of the ray being integrated to
r
.They
would also relate directly to material parameter
g
. Therefore, we can define
a specular cone of importance sampling, centered around
r
, encompassing all
important ray samples (see Figure 1.12).
By the term
important
, we mean every ray that has absolute weight greater
than a threshold
σ
(assuming that a ray shot in the direction of
r
would have a
weight of 1.0). We can easily see that, with a constant
σ
, the cone apex angle
α
depends only on the surface glossiness factor
g
(see Figure 1.13). Therefore, we
are interested in finding a function that calculates the specular cone angle from
the surface glossiness, with a given specular model and constant
σ
.
As an example, we can apply this reasoning to find such a function for the
Phong specular model:
n
)
g
.
k
Phong
=(
r
·
(1.17)
We prepare data containing the specular cone angles
α
,atwhich
k
Phong
>σ
.
Then, for a given dataset, we find an approximation function. From possible
candidates we pick a function with the lowest computational cost. In our case
the function of choice is
α
(
g
)=2
2
g
+2
.
(1.18)
It coincides with the Beckmann distribution definition of roughness
m
[Beckmann
and Spizzichino 63], where
m
is given as the root mean square of the specular
cone slope.
