Shadow geometry and occluding contours of generalized cylinders (artificial intelligence)

Given a line drawing from an image with shadows regions identified, the shapes of the shadows can be used to generate constraints on the orientations of the surfaces involved. This thesis describes the theory which governs those constraints and shows how it can be applied to polyhedra and certain types of generalized cylinders. One of the topics explored is the use of shadows to determine 3D surface orientation. A "Basic Shadow Problem" is posed, in which a polygon casts its shadow on a flat surface. There are six parameters to determine: the orientation (2 parameters) for each surface and the direction of the illumination (2 parameters). If some set of 3 of these are given in advance, the remaining 3 can be determined geometrically. The solution method consists of identifying "illumination surfaces" consisting of illumination sectors, assigning Huffman-Clowes line labels to their edges, and applying the resulting constraints in the gradient space. The analysis is extended to shadows cast by and upon polyhedra and curved surfaces, and the consequences of varying the number and position of light sources are discussed. Another topic addressed is the analysis of images of solids of revolution. When the angle between the line of sight and the solid's axis is known, the contours in the image can be analyzed to precisely determine the shape description. This angle can be determined from the image when shadows are present by applying the results obtained for curved surfaces in general. The thesis also includes a collection of properties of the gradient space, a representation scheme for 3D orientation, and a taxonomy and analysis of properties of generalized cylinders, a volumetric representation for solid shapes.