Kinematics of the eye.

Abstract

A mathematical discussion is presented of eye positions and eye movements in terms of quaternion theory. An eye movement may be regarded as a rotation of the eye about an axis through the center of rotation. The parameters of the axis of rotation and the extent of the rotation are associated to form a higher complex number, and this leads to the definition of an eye position in terms of the rotation by which it is reached from the prinary position. Equations are derived for the parameters of the single rotation equivalent to two successive finite rotations, for Listing’s law, for torsional movements, for the angle between the primary horizontal meridian of the eye and the plane of regard, and for the angle between the primary vertical meridian of the eye and the true vertical plane through the fixation line.