Geometric Kinematics of Human Eyes

In previous studies by the author on binocular vision with the asymmetric eye (AE), which models a healthy human eye with misaligned optical components, the results were primarily presented in the Rodrigues' vector (RV) framework and supported by simulations and 3D visualizations in GeoGebra's dynamic geometry environment. In this paper, the novel geometric kinematics of the human eye, that is, the eye with misaligned optics, and simplified assumptions about the eye rotations (the eye's translational movements are disregarded), are developed within the framework of rigid-body rotations. The originality of the analysis lies in a precise geometric decomposition of a full rotation of the eye's posture into a torsion-free rotation (the geodesic part) and a torsional rotation (the non-geodesic extension of the geodesic part). This decomposition is extended to the corresponding decomposition of the angular velocity. A novel derivation of the eye's angular velocity from the RV formulation of the eye kinematics is proposed.