Parallel projections of dots on the surface of a transparent sphere rotating about a vertical axis provide strong impressions of depth and spherical shape. The hypothesis was tested that these impressions are the result of three perceptual heuristics: (a) The sinusoidal projected velocity function of each dot in the horizontal dimension tends to be perceived as a rotary motion in depth; (b) the projected velocity gradient in the vertical dimension is perceived as curvature in depth; and (c) the simultaneously visible fields of dots moving in opposite directions are perceived as surfaces separated in depth. When each factor was varied independently, all three significantly affected judgments of spherical shape and depth. Similar results were obtained with cylinders. The first factor was more important for shape judgments; the second was generally more important for depth judgments. These results, together with those of earlier studies in which these factors led to similar effects for different stimuli and transformations, suggest that these are general principles applicable to the perception of structure from both rigid and nonrigid motion.