Silhouette-Slice Theorems.

This thesis presents a new theory analyzing the relations in orthographic projections. The theory is based on three new representations of 3 D surfaces in terms of scalar, vector and tensor functions on the Guassian sphere, and the matching representations of 2 D curves by functions on the Guassian circle. The key advantage of these representations is that a slice through the spherical representation of 3 D object is closely related to the circular representation fo the silhouette of the object in a plane parallel to the slice. This relation is formalized in three Silhouette-Slice theorems, which underline the duality between silhouettes in object space and slices in the representation space. These theorems apply to opaque objects and have a conceptual similarity with the Projection-Slice theorem, which applies to absorbing objects. Silhouette construction with the theorems is demonstrated by examples silhouettes of complex curved surfaces. Applications to the reconstruction of object shapes from silhouettes measurements and to the recognition of objects based on their silhouettes are suggested.