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Figure 11
(a) The quaternion point (a, b), in contrast, corresponds via the double-angle formula to coordinate frames that rotate twice as rapidly as (a, b) progresses around the unit circle that is a simplified version of quaternion space. (b) The set of 2D frames associated with the entire circle of quaternion points (a, b); each diametrically opposite point corresponds to an identical frame. For later use in displaying full quaternions, we show how color coding can be used to encode the sign of one of the coordinates on the circle.

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