Sculptered surface technology as a unified approach to geometric definition

A comprehensive approach to representing and machining complex surface shapes in an APT programming system is described. The APT (Automatically Programmed Tools) user language was extended to permit the definition of a hierarchy of curves and surfaces. Much of the logic has been implemented using matrix canonical forms which are closed under the full family of projective transformations - permitting family of parts storage and retrieval and part compensation. The area of numerical control machining was addressed, but the solutions for tool positioning were only partially successful due to the complexity of the algorithmic problem. Some of the mathematical methods adopted are outlined, and their implementation with an APT part programming example is illustrated.