Graphics Reference
In-Depth Information
9.2.2 Vertically oblique projection plane
Now let's consider the case where the projection plane is rotated about the horizontal
l
-axis,
as shown in Fig. 9.3.
P
m
p
Y
λ
Q
θ
q
Z
ε
θ
D
d
n
j
l
k
O
i
X
Figure 9.3.
We begin by declaring the following conditions:
j
·
m
=
cos
l
=
i m
·
i
=
cos
=
−
OD
=
−
OQ
=
−
OP
d
=
d
k q
p
n
·
d
=
d cos
The relationship between the rotated axial system
lmn
and
ijk
can be represented as
⎡
⎤
⎡
⎤
⎡
⎤
l
m
n
10 0
0
i
j
k
⎣
⎦
=
⎣
⎦
·
⎣
⎦
cos sin
(9.5)
0
−
sin cos
and represents the transform relating coordinates in
ijk
to
lmn
. Q is the point on the
projection plane intersected by
p
, and once more, our task is to find the scalars and .
From Fig. 9.3, we have
+
−
DQ
=
q
d
but
−
DQ
=
l
+
m
and
q
=
d
+
l
+
m
=
i
+
m
