Turski, J.

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, i.e., the eye with misaligned optics, and simplified assumptions about eye rotations (the eye's translational movements are disregarded) are developed within the framework of rigid body rotations. Despite the eye's misaligned optical components (all eyes' axes differ), the geometric formulation, which can only be approximated, yields excellent accuracy as demonstrated by simulations. The originality of the analysis lies in a precise geometric decomposition of the eye's posture changes into torsion-free (geodesic) and torsional (non-geodesic) rotations. 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.