Game Development Reference
In-Depth Information
not to rely on terminology when using Euler angles. Always make
sure you get a precise working definition, or you're likely to get very
confused.
•
In most situations, Euler angles are more intuitive for humans to work
with compared to other methods of representing orientation.
•
When memory is at a premium, Euler angles use the minimum amount
of data possible for storing an orientation in 3D, and Euler angles are
more easily compressed than quaternions.
•
There is no such thing as an invalid set of Euler angles. Any three
numbers have a meaningful interpretation.
•
Euler angles suffer from aliasing problems due to the cyclic nature
of rotation angles and because the rotations are not completely inde-
pendent of one another.
•
Using canonical Euler angles can simplify many basic queries on Eu-
ler angles. An Euler angle triple is in the canonical set if heading
and bank are in the range (−180
o
,+180
o
] and pitch is in the range
[−90
o
,+90
o
]. What's more, if pitch is ±90
o
, then bank is zero.
Gimbal lock occurs when pitch is ±90
o
. In this case, one degree
of freedom is lost because heading and bank both rotate about the
vertical axis.
•
•
Contrary to popular myth, any orientation in 3D can be represented
by using Euler angles, and we can agree on a unique representation
for that orientation within the canonical set.
•
The wrapPi function is a very handy tool that simplifies situations in
which we have to deal with the cyclic nature of angles. Such situations
arise frequently in practice, especially in the context of Euler angles,
but at other times as well.
•
Simple forms of aliasing are irritating, but there are workarounds.
Gimbal lock is a more fundamental problem with no easy solution.
Gimbal lock is a problem because the parameter space of orientation
has a discontinuity. This means small changes in orientation can
result in large changes in the individual angles. Interpolation between
orientations using Euler angles can freak out or take a wobbly path.
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