Invariant body kinematics: I. Saccadic and compensatory eye movements

A new invariant formulation of 3D eye-head kinematics improves on the computational advantages of quaternions. This includes a new formulation of Listing’s Law parameterized by gaze direction leading to an additive rather than a multiplicative saccadic error correction with a gaze vector difference control variable. A completely general formulation of compensatory kinematics characterizes arbitrary rotational and translational motions, vergence computation, and smooth pursuit. The result is an invariant, quantitative formulation of the computational tasks that must be performed by the oculomotor system for accurate 3D gaze control. Some implications for neural network modeling are discussed.