We have recently reported that objects seen at near distances require adjustments of the relative torsion of the eyes to avoid blurred binocular images or double vision and ultimately to allow binocular fusion. The reason underlying these rotational adjustments is that converging eye movements undo the eyes' torsional alignment, generating disparate binocular images of objects outside the horizontal plane of regard. We show mathematically that it is the distance between the two eyes, their relative orientation in the frontal plane and the distances from each eye to the binocularly intended visual target, that determine the binocular alignment of the lines of sight. As an example, we analyze the binocular disparity field that is generated when a viewer examines objects on a planar surface whose viewing distances differ in each gaze direction. The underlying geometric computations are simple, and require no explicit knowledge of 3D eye movement kinematics.