Although moving human observers actively fixate their eyes on points in the world, computer vision approaches to the estimation of structure-from-motion or egomotion typically do not make use of this constraint. In this paper, we investigate the computational advantage of fixation. The main contribution of this work is to precisely specify the form of the optical flow field for a fixating observer moving in a rigid world. We show that the use of a hemispherical (retinal) imaging surface combined with the active process of fixation generates an optical flow field of a particularly simple form. A further contribution is the finding that the sign of retinal flow at the retinal periphery can be used to predict collisions.