Previous demonstrations show that adults use the information provided by surface contours (e.g. reflectance edges) to perceive object shape and layout (Stevens, 1981; Todd and Reichel, 1990; Knill, 1992). Figure 1 shows a dramatic example of this. In order for surface contours to provide information about surface shape, surface markings (from which surface contours project) must be constrained relative to the shapes of the surfaces on which they lie. Two such constraints have been proposed in the computational literature; that parallel surface markings are lines of curvature on cylindrical surfaces (Stevens, 1981), and that surface markings tend toward being geodesic (follow paths of minimal length between points on a surface) (Knill, 1992). The latter of these can be viewed as a generalization of the former, as lines of curvature on cylindrical surfaces are special examples of geodesics.