Graphics Reference
In-Depth Information
9.2.3 Arbitrary orientation of the projection plane
The above technique of using a rotation matrix to relate the
lmn
-axes with the
ijk
-axes provides
the solution to this problem. This time the projection plane is subjected to yaw, pitch, and roll
rotations, as shown in Fig. 9.4.
P
m
p
Y
Q
λ
n
ε
q
Z
D
d
l
j
k
O
i
X
Figure 9.4.
The transform relating coordinates in
ijk
with
lmn
is given by
⎡
⎤
⎡
⎤
⎡
⎤
l
m
n
t
11
t
12
t
13
t
21
t
22
t
23
t
31
t
32
t
33
i
j
k
⎣
⎦
=
⎣
⎦
·
⎣
⎦
(9.8)
We begin by declaring the following conditions:
=
−
OD
=
−
OQ
=
−
OP
d
=
d
k q
p
Q is the point on the projection plane intersected by
p
, and once more, our task is to
find the scalars and .
From Fig. 9.4, we see that
+
−
DQ
q
=
d
but
−
DQ
=
l
+
m
Therefore,
q
=
d
+
l
+
m
or
l
+
m
=
q
−
d
(9.9)
