Graphics Reference
In-Depth Information
Fig. 9.7
An example of gimbal lock
9.5 Yaw, Pitch and Roll
The above Euler rotations are also known as
yaw
,
pitch
and
roll
, and great care
should be taken with these angles when referring to other topics and technical pa-
pers. 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, and might even point down-
wards. 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 terms yaw, pitch and roll are often used in aviation and to describe the mo-
tion of ships. For example, if a ship or aeroplane is heading in a particular direction,
the axis aligned with the heading is the roll axis, as shown in Fig.
9.8
(a). A perpen-
dicular axis in the horizontal plane containing the heading axis is the pitch axis, as
shown in Fig.
9.8
(b). The axis perpendicular to both these axes is the yaw axis, as
shown in Fig.
9.8
(c).
Clearly, there are many ways of aligning a set of Cartesian axes with the yaw,
pitch and roll axes, and consequently, it is impossible to define an absolute set of
yaw, pitch and roll transforms. However, if we choose the following alignment:
•
the
roll
axis is the
z
-axis
•
the
pitch
axis is the
x
-axis
•
the
yaw
axis is the
y
-axis
we have the situation as shown in Fig.
9.9
, and the transforms representing these
rotations are as follows:
