The geometry of binocular projection is analyzed in relation to the primate visual system. An oculomotor parameterization that includes the classical vergence and version angles is defined. It is shown that the epipolar geometry of the system is constrained by binocular coordination of the eyes. A local model of the scene is adopted in which depth is measured relative to a plane containing the fixation point. These constructions lead to an explicit parameterization of the binocular disparity field involving the gaze angles as well as the scene structure. The representation of visual direction and depth is discussed with reference to the relevant psychophysical and neurophysiological literature.