A Theoretical Examination of Switching Functions for Solid Modeling Data Structures

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.