The Shape of Smooth Objects and the Way Contours End

Abstract

It is shown, by elementary mathematical reasoning, that visual contours can only be concave at their endpoints. This simple natural fact is contrasted with general mannerisms of draftsmen: in the great majority of cases contours are drawn to have convex ends. It is argued that this results from our general concept of solid shapes: a general shape is conceived of as a conglomerate of convex (‘ovoid’) elementary shapes, these shapes act as ‘figure’ and the way they are glued together is treated as the—relatively unimportant—‘ground’. The hypothesis is supported through citations from academic-art literature. An attempt is made to give a geometrical specification of just what draftsmen draw if they disregard the contour.