Displays consisted of orthographic and perspective projections of three collinear dots rotating rigidly around a fixed centre in a plane slanted 45 degrees in depth. Observers were asked to decide whether the middle of the three dots was exactly centred in 3-D space between the other two dots. The visible rotation segments were 120 degrees, 160 degrees, or 200 degrees and the displacements were 2%, 4%, or 6%. Our untrained observers performed more poorly overall than well-practised observers tested earlier by Lappin and Fuqua (1983 Science 221 480-482). Results of additional manipulations suggested that 2-D image properties played a more important role than acknowledged by Lappin and Fuqua. First, displacement size and the position of the rotation centre produced nonlinear effects. Second, the direction of displacement affected performance. Third, projection type and display type (static snapshots versus elliptic traces) were involved in complex interactions. Clearly, performance was affected by 2-D image properties that should be irrelevant to the calculation of 3-D projective invariants.