Modeling the 3D kinematics of the eye in the geometric algebra framework

Abstract

In this paper the authors apply the Clifford or geometric algebra for the modeling of the mathematics of 3D kinematics of the eye. Using a geometric approach we discuss the Listing's law that is fundamental for understanding of the 3D operations of the oculomotor system. We prove algebraically a fact observed by medical experimentation that the rotation vectors from a reference position lie on a straight Listing's plane. The authors formulate the motion of the Listing's plane by means of the geometric algebra of the motors. The difference between our approach and current approaches that use matrices or quaternions is that our model yields linear equation systems. Using this kind of formulation the authors analyze also the shifting and the curvatures of the displacement plane under physiological and pathological conditions. Our geometric approach due to its elegance and transparency offers to the researchers a powerful tool for the study of binocular systems involving characteristics of the Listing's plane.