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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.

A complete scheme for motion prediction based on motion capture data is presented. The scheme rests on three main components: a special posture representation, a diverse motion capture database and prediction method. Most prior motion prediction schemes have been based on posture representations based on well-known local or global angles. Difficulties have arisen when trying to satisfy constraints, such as placing a hand on a target or scaling the posture for a subject of different stature. Inverse kinematic methods based on such angles require optimization that become increasingly complex and computationally intensive for longer linkages. A different representation called stretch pivot coordinates is presented that avoids these difficulties. The representation allows for easy rescaling for stature and other linkage length variations and satisfaction of endpoint constraints, all without optimization allowing for rapid real time use.