Graphics Reference
In-Depth Information
n
dA
p˝
=
p
r
p
p
p
Figure 1.7.
Geometric construction of point
p
r
when the light plane is pointing away
from the surface.
As previously discussed, we were searching for the most important sample of
the integral on a segment between points
p
r
and
p
c
representing component-wise
local maximums (see Figure 1.8).
With those conditions set, we used a computational software package to nu-
merically find a point on line
p
c
p
r
that approximates the most important point
as much as possible. We worked on a data set of several hundred area lights ran-
domly generated as disk or rectangle light shapes. For every light shape we found
a point on the plane that best resembles the full integral. Then, we computed the
end points of our line between
p
c
and
p
r
(as if it would be calculated at runtime).
Then, we numerically checked the points along the line, computing the lighting
equation and comparing against a reference, using the least squares method to
find point
p
d
, which would most accurately represent the integral.
p'
p
c
n
dA
p
r
p
p
p
Figure 1.8.
Geometric construction of line
p
c
p
r
.
