Game Development Reference

In-Depth Information

Fig 2.22
A simple gyroscope.

(a) Gimbals and rotation points;

(b) attaching the gyroscope to

a plane; (c) a clockwise yaw

of the plane forces the first

gimbal to move with it, as it is

attached and has no freedom

of movement in that direction,

while the second gimbal is

free to move in response in the

opposite direction; (d) a 90°

yaw will cause the first and

second gimbals to align, thereby

entering a state of locked; and (e)

after the first and second gimbals

become locked, a pitch will retain

the integrity of the third gimbal.

(f ) However, a roll can cause

erratic behavior from gimbal 3.

y

1st gimbal

rotates around
x
axis

2nd gimbal

rotates around
y
axis

und
y
axis

y

3rd gimbal

rotates around
y
axis

orientation

plate

(b)

Gyroscope attached to plane

x

z

(a)

1st gimbal rotates

with plane

1st and 2nd gimbal

are aligned:

(locked)

2nd gimbal rotates

anticlockwise

plane yaws 90 degrees

clockwise

plane yaws clockwise

(c)

(d)

plane pitches

plane rolls

gyroscope

locked

gyroscope

reorientates

(e)

(f)

Quaternions to the Rescue

Quaternions are mathematical constructs that allow for rotations around the

three axes to be calculated all at once in contrast to Euler angles, which are

calculated one after the other. A quaternion has
x
,
y
, and
z
components, as

well as a rotation value.

In games using Euler angles, rotations can cause erratic orientations of

objects. This is illustrated in
Figure 2.23
where the rotations of two planes are

compared. Each plane is rotated continually around the
x
,
y
, and
z
axes by