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).
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