Graphics Reference
In-Depth Information
2.5.1.4.
Show that the motion
1
2
1
2
1
2
x
¢ =
x
+
y
+
z
-
2
1
2
1
2
y
¢ =-
x
+
z
1
2
1
2
1
2
z
¢ =
x
-
y
+
z
-
2
is a screw motion, where
Definition.
A motion in
R
3
of the form RT, where R is a rotation that is not the iden-
tity map and T is a translation with translation vector parallel to the line that R is
rotating about, is called a
screw motion
.
2.5.1.5.
Find the equations for the rotation whose roll-pitch-yaw representation is (p/2,p/3,p).
2.5.1.6.
Find the equations for the rotation whose X-Y-Z Euler angle representation is
(p/2,p/3,p).
Section 2.5.2
2.5.2.1.
Solve Exercise 2.5.1.2 using frames.
2.5.2.2.
Solve Exercise 2.5.1.3 using frames.
2.5.2.3.
Use frames to find the equations of the motion that sends the points
A
(1,0,0),
B
(0,1,0),
C
(0,0,1), and
D
(1,2,1) to
2
13
2
13
1
13
1
13
3
13
3
13
Ê
Ë
ˆ
¯
Ê
Ë
ˆ
¯
¢
Ê
Ë
ˆ
¯
¢
Ê
Ë
ˆ
¯
¢
-
¢ -
A
01
,,
,
B
, ,
2
,
C
,,
1
,
and
D
, , ,
30
respectively.
