Graphics Reference
In-Depth Information
Figure 1.11.
Comparison between Monte Carlo raytraced reference and proposed ana-
lytical solution: proposed model (left) and Monte Carlo sampled reference (right).
We can also express the differential solid angle as a function of distance and
differential area using equation (1.3). Therefore, our final approximated diffuse
integral is
dAcosθ
o
r
2
Diffuse
(
p,ω
o
)
∼
L
n
C
d
cos
θ
−−→
,
(1.16)
pp
d
where
θ
o
is the angle between the surface normal
n
and the light plane orientation
normal
n
l
and
dA
is given by the light shape.
1.3.4 Approximating Specular Integral
Introduction.
We followed the idea of leveraging importance sampling to estimate
the specular integral. First we analyzed the behavior of typical specular light-
ing models relying on probability distribution functions (PDFs). This led us to
the definition of a specular cone of importance sampling, used to find the most
important point for the specular integral and the actual integration area.
Specular in importance sampling.
If we were to render specular reflection using
Monte Carlo methods, we would cast a ray in every direction around the point
being shaded and evaluate specular BRDF for given functions
DFG
from equa-
tion (1.12). Also, every PDF used to model
D
depends on some kind of surface-
roughness parameter, denoted
g
. This parameter describes how focused lighting
remains after reflecting off the surface.
In the case of specular reflection, we can define a vector created by reflecting
in the viewer's direction
ω
o
against the surface normal
n
. Such a vector is called
the reflection vector
r
.
