Graphics Reference
In-Depth Information
t
y
=1
t
z
=1
The transform is
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
·
⎡
⎣
⎤
⎦
x
y
z
1
−
100 0
01 0
x
y
z
1
−
1
=
00
−
1
1
00 0
1
which is identical to the equation used for direction cosines. Another example
is shown in Figure 7.23, where the following conditions exist:
roll
=90
◦
pitch
= 180
◦
yaw
=0
◦
t
x
=0
.
5
t
y
=0
.
5
t
z
=11
The transform is
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
·
⎡
⎣
⎤
⎦
x
y
z
1
0
−
10
.
5
x
y
z
1
−
100
.
5
00
=
1 1
0001
−
0
.
5
,
10) for (
x
,y
,z
). Sim-
ilarly, substituting (0, 0, 1) for (
x
,
y
,
z
) produces (0.5, 0.5, 10) for (
x
,y
,z
),
which can be visually verified from Figure 7.23.
Substituting (1, 1, 1) for (
x
,
y
,
z
) produces (
−
0
.
5
,
−
Y
(1, 1, 1)
Z
′
Y
′
(0.5, 0.5, 11)
X
Z
X
′
Fig. 7.23.
The secondary axial system is subjected to a
roll
of 90
◦
,a
pitch
of 180
◦
,
and a translation of (0.5, 0.5, 11).