Built-up Edge Elimination in Mirror Cutting of Hardened SteelA Theoretical Examination of Switching Functions for Solid Modeling Data Structures

Abstract

The role of geometrical modeling is of increasing importance in the field of CAD/CAM. In the present paper a new concept is presented for geometric modeling of the data structure using volumetric representation via switching functions in a Gray coded space (3-D Karnaugh map). The data structure consists of a single generic cuboid primitive which may vary in size and aspect ratios. This provides for more generalized and flexible object representation than uniform spatial occupancy enumeration. The combination of a single primitive, Gray coded space, and representation via switching functions yields a very efficient data structure oriented toward set operations which can be carried out via a simple assembler program or a parallel logic processor. As objects are represented by a nonhierarchial list of fixed format terms, uniform algorithms can be used to perform given tasks regardless of object shape, dimensions, or complexity.