Figure 4.

Geometric context involved in choosing a quaternion distance that will result in the correct average rotation matrix when the quaternion measures are optimized. Because the quaternion vectors represented by t and −t give the same rotation matrix, one must choose or the minima, that is or , of the alternative distance measures to get the correct items in the arc-length or chord measure summations. (a) and (b) represent the cases when the first or second choice should be made, respectively.