We are trying to understand how the visual system groups and segments multiple motions into surfaces. A common theory is that our visual system segments surfaces based on a 2D velocity smoothness constraint. To test this theory we have designed stimuli that are exactly matched with respect to their 2D velocity smoothness, but have different 3D interpretations. Shown below are the flow fields corresponding to our stimuli, the leftmost is consistent with a plane rotating rigidly about its vertical axis, denoted as [Vx,Vy]. The center and rightmost flow fields are constructed from the first as [Vx,-Vy], and [-Vy,Vx]. Note that these flow fields are equally smooth, however they give rise to different 3D interpretations.