Graphics Reference
In-Depth Information
Fig. 8.9
Using a rotor
R
to
rotate
XY
to
X
Y
8.5.2 Rotated Frame of Reference
We have already shown that in order to compute the coordinates of a point
P
in
a rotated frame of reference
X
Y
, we rotate the point by an angle in the opposite
direction as shown in Fig.
8.9
to
P
. Thus if the new frame of reference is rotated
β
,
and
p
is
P
's position vector, then
p
points to the new point
P
and is computed as
follows:
p
=
R
β
p
where
R
β
=
cos
β
+
sin
β
e
12
.
Let's test this with the same example used above by rotating the frame of reference
45° and computing the coordinates of the point
(
1
,
1
)
p
=
e
1
+
e
2
R
†
45
°
=
cos 45°
+
sin 45°
e
12
√
2
2
+
√
2
2
=
e
12
√
2
2
+
√
2
2
e
12
(
e
1
+
p
=
e
2
)
√
2
2
√
2
2
√
2
2
√
2
2
=
e
1
+
e
2
−
e
2
+
e
1
√
2
e
1
and
P
=
(
√
2
,
0
)
, which is correct.
=
