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A new theorem is discussed that relates the apparent curvature of the occluding contour of a visual shape to the intrinsic curvature of the surface and the radial curvature. This theorem allows the formulation of general laws for the apparent curvature, independent of viewing distance and regardless of the fact that the rim (the boundary between the visible and invisible parts of the object) is a general, thus twisted, space curve. Consequently convexities, concavities, or inflextions of contours in the retinal image allow the observer to draw inferences about local surface geometry with certainty. These results appear to be counterintuitive, witness to the treatment of the problem by recent authors. It is demonstrated how well-known examples, used to show how concavities and convexities of the contour have no obvious relation to solid shape, are actually good illustrations of the fact that convexities are due to local ovoid …