Sheet Modeling and Thickening Operations Based on Non-manifold Boundary Representations

This paper describes sheet modeling and thickening operations based on a non-manifold topological representation for efficient solid modeling of thin-walled plastic or sheet metal parts. Since the existing methods have adopted boundary representations for solid models, it is difficult to represent the exact adjacency relations between topological entities in a sheet model, and to describe a mixture of wireframe and sheet objects that appear in the intermediate steps of sheet modeling operations. Accordingly, it is difficult to devise and implement the algorithms for sheet modeling and thickening operations. To solve these problems, we introduce a non-manifold boundary representation as a topological framework and propose a sheet thickening algorithm by presenting variations to a general non-manifold offset algorithm that is based on the mathematical definition of offsets. In addition, to facilitate sheet modeling operations, not only a set of generalized Euler operators for non-manifold models are provided, but also sheet modeling capabilities, including adding, bending, and punching functions with two-dimensional curve editors.