Game Development Reference
In-Depth Information
object can be stored in one of several ways including Euler angles,
angle axis or quaternions.
If the orientation is stored as Euler angles, then three scalar values are
used to hold the rotation of the object in the x -, y - and z -axes. We use
heading ( h ) to define the rotation in the y -axis, pitch ( p ) for the rotation
about the x -axis and bank ( b ) for the rotation about the z -axis. As we know
from Chapter 1, Euler angles describe a unique orientation only if we
know the order in which the rotations are applied. Euler angle rotation
suffers from the distinct disadvantage that gimbal lock occurs when a
rotation through 90° maps one axis onto another. If the order in which
rotations are applied is HPB , heading, pitch then bank problems can arise
with a rotation of 90° in the pitch. The effect of this rotation is to map the
z -axis onto the y -axis; consequently, heading rotations about y seem to be
the same as bank rotations about z . This problem is very frustrating for
animators. For much of the last 5 years I have been running a company
where we use Lightwave for TV animation. Lightwave up to version 5.6
used Euler angles to store and interpolate the orientation. Sometimes
animators can get very annoyed with their monitors when it seems
impossible to bend a character into the orientation that they want. At this
point they become very aware of the problems of gimbal lock. Thankfully,
this annoying problem can be avoided with version 6+ of Newtek's
otherwise excellent software.
If the orientation is stored as angle axis, then four scalar values are
used. Three define a vector that describes the axis about which a rotation
takes place. The fourth value defines the angle of rotation about this axis.
This method has the advantage that it does not suffer from gimbal lock.
The final alternative is to use quarternions. This rather exotic mathemat-
ical device is the method of choice for interpolating orientation in many
computer games because it is computationally more efficient and gives
pleasing results.
As well as the ability to store the position, scale and orientation, we
need to store the time during the animation that we wish this to occur. We
could store the position, scale and orientation all together for a particular
time interval. But if we want total control over the way the character
animates, it is better that each channel of position, scale and orientation
is stored separately with its own time parameter. Using totally separate
channels ensures that interpolating a channel does not suffer from the
artefacts of another channel. Suppose that the x position moves smoothly
over the interval of 2 seconds. During this interval, the object rotates in a
complex fashion using keys at one third of a second intervals. If all
channels are stored for a key value, then the x position is stored at one
third of a second intervals. It will be more difficult to ensure a smooth
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