Contour generation and shape restoration of the straight homogeneous generalized cylinder

Abstract

The author explores the properties of some simple artificial objects which can be modeled as straight homogeneous generalized cylinders (SHGCs). He considers the analysis of tangency contours of SHGCs by presenting the condition which must be satisfied by the points on the contour generator of any SHGC. The contour generator is planar in an end view or side view of any right SHGC and in any oblique view of any linear right SHGC. In an oblique view of a nonlinear right SHGC, the contour generator is nonplanar. It is possible to describe the visible contour in an image of solid SHGCs as they depend on the radius function and viewing angle. These relationships can be inverted to determine the radius function from the image contours when the viewing angle is known in advance. The viewing angle can be determined if the object has a visible flat end surface. The shape restoration of the SHGCs can be obtained if the models of the viewed objects and the viewing angles can be predefined. >