Visualizing 3D vector fields is challenging because of occlusion problems and the difficulty of providing depth cues that adequately support the perception of direction of flow lines in 3D space. One of the depth cues that has proven most valuable for the perception of other kinds of 3D data, notably 3D networks and 3D point clouds, is structure‐from‐motion (also called the Kinetic Depth Effect); another powerful depth cue is stereoscopic viewing. We carried out an experiment of the perception of direction for short streamlines passing through a cutting plane. The conditions included viewing with and without structure‐from‐motion and with and without stereoscopic depth. Conditions also include comparing streamtubes to lines. The results show that for this particular task, stereo provided an effective depth cue, but structure‐from‐motion did not. Ringed streamtubes and streamcones provided good 3D direction information, even without stereoscopic viewing. We conclude with guidelines for viewing slices through vector fields.