Abstract
The anatomical configuration of the eye ball in the orbit is similar to that of a ball-and-socket joint, and the arrangement of extra-ocular muscles gives the globe three rotational degrees of freedom (DOF). If one describes a three-dimensional (3D) eye position using three consecutive rotations about the horizontal, vertical, and torsional eye-fixed axes, the value of torsion, so-called false torsion, depends on the order of rotation. This is a result of the non-commutativity of rotatory movements. The problem of false torsion can be avoided by representing a 3D eye position by a single axis rotation from a chosen reference position to the current eye position, e. g. rotation vectors (Haustein, 1989).
According to Listing's law, all axes about which the eye rotates from the reference position to other positions lie in a plane, so-called Listing's plane, provided the head is erect and stationary (Helmholtz, 1867). If the reference position coincides with the primary position, Listing's plane is perpendicular to the direction of gaze in primary position. Listing's law is a remarkable example, of how a motor system reduces DOF (from 3 to 2) to simplify multidimensional motor control.
Characteristic changes in the orientation of Listing's plane have been reported under several conditions: Static tilts in the frontal plane of the head induce ocular counterrolling, i.e. parallel shifts of Listing's plane along the torsional axis. Static tilts in the sagittal plane counter-rotate Listing's plane about the vertical axis. Convergence leads to a temporal rotation of Listing's plane about the horizontal axis. During sleep, Listing's plane is not preserved, which implies neural implementation of Listing's law.
