Graphics Reference
In-Depth Information
The above rotations are also known as
yaw
,
pitch
and
roll
. Great care
should be taken with these terms when referring to other topics and technical
papers. Sometimes a left-handed system of axes is used rather than a right-
handed set, and the vertical axis may be the
y
-axis or the
z
-axis.
Consequently, the matrices representing the rotations can vary greatly. In
this text all Cartesian coordinate systems are right-handed, and the vertical
axis is always the
y
-axis.
The roll, pitch and yaw angles can be defined as follows:
•
roll
is the angle of rotation about the
z
-axis
•
pitch
is the angle of rotation about the
x
-axis
yaw
is the angle of rotation about the
y
-axis.
Figure 7.9 illustrates these rotations and the sign convention. The homo-
geneous matrices representing these rotations are as follows:
•
•
rotate
roll
about the
z
-axis:
⎡
⎣
⎤
⎦
cos(
roll
)
−
sin(
roll
)00
sin(
roll
)
cos(
roll
)00
(7.61)
0
0
1
0
0
0
0
1
•
rotate
pitch
about the
x
-axis:
⎡
⎣
⎤
⎦
1
0
0
0
0
pitch
)
−
sin(
pitch
)0
(7.62)
0
sin(
pitch
)
cos(
pitch
)0
0
0
0
1
•
rotate
yaw
about the
y
-axis:
⎡
⎤
cos(
yaw
)
0
sin(
yaw
)0
⎣
⎦
0
1
0
0
(7.63)
−
sin(
yaw
)0
yaw
)0
0
0
0
1
Y
pitch
roll
Z
X
yaw
Fig. 7.9.
The convention for
roll
,
pitch
and
yaw
angles.
