Properties of 3D rotations and their relation to eye movement control

Rotations of the eye are generated by the torques that the eye muscles apply to the eye. The relationship between eye orientation and the direction of the torques generated by the extraocular muscles is therefore central to any understanding of the control of three-dimensional eye movements of any type. We review the geometrical properties that dictate the relationship between muscle pulling direction and 3D eye orientation. We then show how this relation can be used to test the validity of oculomotor control hypotheses. We test the common modeling assumption that the extraocular muscle pairs can be treated as single bidirectional muscles. Finally, we investigate the consequences of assuming fixed muscle pulley locations when modeling the control of eye movements.