In four experiments, observers were required to discriminate interval or ordinal differences in slant, tilt, or curvedness between designated probe points on randomly shaped curved surfaces defined by shading, texture, and binocular disparity. The results reveal that discrimination thresholds for judgments of slant or tilt typically range between 4 degrees and 10 degrees; that judgments of one component are unaffected by simultaneous variations in the other; and that the individual thresholds for either the slant or tilt components of orientation are approximately equal to those obtained for judgments of the total orientation difference between two probed regions. Performance was much worse, however, for judgments of curvedness, and these judgments were significantly impaired when there were simultaneous variations in the shape index parameter of curvature.