Line-drawing interpretation: straight lines and conic sections

Line drawings of man-made scenes often exhibit instances of straight lines and conic sections, i.e. ellipses, parabolas, and hyperbolas. Constraints imposed on the scene by such instances are investigated, under the assumption of general viewpoint, i.e. the mapping of the viewed surface onto the line drawing is stable under perturbation of the viewpoint within some open set. Both orthographic and perspective projection are considered. The viewed surfaces are assumed to be piecewise C³. It is shown that straight lines and conic sections in line drawings are projections of scene edges which are also straight lines and conic sections, respectively. It is also shown that scene events which project onto straight lines or conic sections cannot be combinations of view-point-independent and viewpoint-dependent edges. Further, continuous-surface-normal depth discontinuities which project onto straight lines can be locally described by developable surfaces, and those which project onto conic sections can be locally described by nondevelopable quadric surfaces. Each of these quadric surfaces is determined up to four degrees-of-freedom by its projection