Offsetting Operations on Non-manifold Boundary Representation Models with Simple Geometry

摘要

This paper describes non-manifold offsetting operations that add or remove a uniform thickness from a given non-manifold object with simple geometry. Each offsetting operation for wireframes, sheets and solids is applicable to different engineering areas with a great potential usefulness. However, the representation schemes of conventional geometric modeling systems have not described all of the wireframes, sheets and solids together; each offsetting capability has been developed and applied separately in each system. In recent years, non-manifold geometric modelers have been developed and more widely spread. Since they can manipulate different levels of models with a unified data structure, these three types of offsetting operations can be integrated into one. Moreover, non-manifold offsetting operations can be used to give flesh to abstract models that are generated as a mixture or wireframes and sheets in conceptual design. Therefore, in this paper, the mathematical definitions and properties of the non-manifold offsetting operations are described first and then an offset algorithm using the non-manifold Euler and Boolean operations is suggested. In this algorithm, offset models for all or a subset of the vertices, edges and faces of a given non-manifold model are generated first. Then, they are united into one body using the non-manifold Boolean operations. Finally, all topological entities that are within offset distance are detected and removed in turn. In addition to the general offset algorithm, this paper discusses its variations for wireframes and sheets to provide the more practical offset solids for pipelines, plastic parts and sheet metal parts.