Graphics Reference
In-Depth Information
p'
p
c
n
dA
p
Figure 1.5.
Geometric construction of point
p
c
.
We can easily find
cosθ
o
maximum on
A
geometrically by casting a ray from
point
p
in the direction of the normal
n
of the surface, creating point
p
,inter-
secting with the light plane and finding the closest location on the shape to
p
,
called
p
c
(see Figure 1.5). It is worth noting that in the case when the light
plane is pointing away from the surface normal (i.e.,
n
n
>
0), vector
pp
should
be skewed in the direction of the light plane in order to obtain intersection (see
Figure 1.5).
A maximum of
·
1
r
2
can be found by projecting point
p
on the light plane,
creating point
p
p
, finding the closest point on positive hemisphere to
p
p
, called
p
, and finally finding a closest point on the light shape to
p
r
(see Figures 1.6
and 1.7).
p˝
p
r
n
dA
p
Figure 1.6.
Geometric construction of point
p
r
when the light plane is pointing toward
the surface.
