The perception of a three-dimensional (3-D) surface shape can be inferred from a 2-D image of two intersecting curves. Three experiments are reported in which we examined a possible method for determining the surface shape as a function of the geometry at the point of intersection. The method involves a two-step process in which the tangents to the two curves determine a skewed Cartesian coordinate system. The angle of the quadrant containing two arcs, the double arc quadrant (DAQ), is then examined. Experiment 1 showed that the surface is perceived as hyperbolic when the DAQ is acute and as locally convex when the DAQ is obtuse. Experiments 2 and 3 showed that even when the DAQ is 90°, the underlying 3-D shape may be unambiguously judged as either hyperbolic or locally convex. It is suggested that the viewer may use an extrapolation process in order to differentiate between these potentially ambiguous stimulus configurations.