MATHEMATICS OF 3-DIMENSIONAL EYE ROTATIONS

The recording of three-dimensional eye position has become the accepte d standard in oculomotor research. In this paper we review the mathema tics underlying the representation of three-dimensional eye movements. Rotation matrices, rotation vectors and quaternions are presented, an d their relations described. The connection between search coils and r otation matrices is explained, as well as the connection between eye p osition and eye velocity. While examples of applications of the formul as to vestibulo-ocular research are given, the methods and mathematica l analyses are also useful for studying other motor systems.