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Some body parts, such as the head and the hand, change their orientation during motion. Orientation can be conveniently and elegantly represented using quaternions. The method has several advantages over Euler angles in that the problem of gimbal lock is avoided and that the orientation is represented by a single mathematical object rather than a collection of angles that can be redefined in various arbitrary ways. The use of quaternions has been popular in animation applications for some time, especially for interpolating motions. We will introduce some new applications involving statistical methods for quaternions that will allow us to present meaningful averages of repeated motions involving orientations and make regression predictions of orientation. For example, we can model how the glancing behavior of the head changes according to the target of the reach and other factors.

Motion prediction models may give the average reach for an individual of specified characteristics. The actual reach will vary from this reach in a manner that may depend on both systematic and random factors. We describe a modeling approach that incorporates the variability within the reaches of a given subject and that between subjects. This information is useful to designers in investigating phenomena that may not occur during the average reach but may occur during variants such as collision with an obstacle or injury due to over-exertion.