Exact offset procedures for simple solids
This paper outlines exact offset procedures for three basic classes of solid primitives: (1) solids of revolution with simple profile curves; (2) solids of linear extrusion with simple profile curves; and (3) convex planar polyhedra. Concepts from differential geometry are used to illustrate the complexity of offsets to general curves and surfaces, and to identify conditions under which offset geometries degenerate. Qualitative descriptions for offset surfaces to simple solids are then presented, in terms of their elementary constituent patches, and the geometrical and topological relationship of these patches to the progenitor primitives. Precise mathematical representations for the required surface elements, as parametric rational polynomial forms, are given. The uses and limitations of offset solids in a solid modeling environment are briefly assessed, and the difficulties of offsets for complex solids are enumerated.
scientific article; zbMATH DE number 3934380