Graphics Reference
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y
y
x
x
z
z
Original definition
(0, 90, 0) orientation
FIGURE 2.17
Fixed-angle representation of (0, 90, 0).
y
y
y
x
x
x
z
(
z
z
(0, 90,
/
e
) orientation
/
e
, 90, 0) orientation
(0, 90
/
e
, 0) orientation
FIGURE 2.18
Effect of slightly altering values of fixed-angle representation (0, 90, 0).
parameter, which rotates the original data points around the
x
-axis, will also have the effect of rotating
the transformed object slightly about the
z
-axis (
Figure 2.18
)
. This results because the 90-degree
y
-axis
rotation has essentially made the first axis of rotation align with the third axis of rotation. The effect is
called
gimbal lock
. From the orientation (0, 90, 0), the object can no longer be rotated about the global
x
-axis by a small change in its orientation representation. Actually, the representation that will perform
an incremental rotation about the
x
-axis from the (0, 90, 0) orientation is (90, 90
þe
, 90), which is not
very intuitive.
The cause of this problem can often make interpolation between key positions problematic. Con-
sider the key orientations (0, 90, 0) and (90, 45, 90), as shown in
Figure 2.19
. The second orientation is a
y
y
x
x
z
z
(0, 90, 0) orientation
(90, 45, 90) orientation; the object lies in the
y-z
plane
FIGURE 2.19
Example orientations to interpolate.
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