Silhouette-Slice Theorems

摘要

A new theory describes the relations between the shapes of 3-D convex objects and the shapes of their silhouettes in orthographic projections. The theory is based on three representations of 3-D surfaces in terms of scalar, vector and tensor functions on the Gaussian sphere, and on the matching representation of 2-D curves by functions on the Gaussian circle. A slice through the spherical representation of a 3-D object is closely related to the circular representation of the silhouette of the object in a plane parallel to the slice. The new theory provides interesting insight into problems of computer graphics and computer vision.