Biomedical Engineering Reference
In-Depth Information
y
x
y
45°
Target point Q
A
x
Q
B
A
p
2
x
A
5
Target point Q
FIGURE 2.5
Calculating the coordinates of the target point Q after rotation and translation from one
configuration to another.
T
. The person also rotates an angle of 45
(line of sight by 45
CCW). It is required to calculate the vector describing the
final target point with respect to the
A
-coordinate system.
The rotation matrix representing this rotation can be written as the dot product
of the
B
-coordinate system with the
A
-coordinate system.
A
A
-coordinate system as
p
5
½
52
"
#
A
B
A
B
x
:
x
x
:
y
A
R
B
5
A
B
A
B
y
:
x
y
:
y
(2.3)
0
:
707
0
:
707
2
A
R
B
5
0
:
707
0
:
707
The vector describing the coordinates of the target point
Q
after
rotation and translation, and as seen by the original coordinate system
A
,is
calculated as
1
1
0
5
5
2
0
:
707
0
:
707
5
:
707
2
A
A
A
R
B
B
A
x
Q
p
1
x
Q
5
R
B
5
(2.4)
0
:
707
0
:
707
2
:
707
It is now evident that the rotation matrix plays an important role in various ways.
a.
The rotation matrix can be used to describe the orientation of a set of vectors
in one coordinate system to another.
b.
The rotation matrix can be used to calculate the coordinates of a point after a
rotation and translation of coordinate systems.
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