Graphics Reference
In-Depth Information
9 Projections
9.1 Introduction
Normally, one does not require vectors to derive the basic perspective transform— simple ratios
are sufficient, but if the projection plane is rotated or oblique to the view direction, vector analysis
comes to the rescue. So let's investigate how vectors can resolve some aspects of projections.
9.2 Perspective transform
Figure 9.1 assumes that an observer is located at the origin O and directed along the z-axis.
Consequently, any point P x
P
y
P
z
P
in R
3
can be projected onto a projection plane revealing
a point Q in R
2
. The projection plane is orthogonal to the view direction, and the screen axes
are parallel with the camera axes.
P
m
p
Y
λ
Q
q
n
Z
ε
D
d
j
l
k
O
i
X
Figure 9.1.
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