The Sweep-Envelope Differential Equation Algorithm and Its Application to NC Machining Verification

A new method, called the sweep-envelope differential equation, for characterizing swept volume boundaries is introduced. This method is used as the theoretical foundation of an algorithm for computing swept volumes using the trajectories of the sweep-envelope differential equation which start at the initial grazing points of the moving object. The major advantages of this algorithm are: (1) the grazing point set need essentially only be computed at the initial position of the object—the remaining grazing points are generated by the flow of the sweep-envelope equation—so the computation complexity is drastically reduced; and (2) it provides automatic connectivity for computed boundary points that facilitates integration with standard algorithms andcad software for visual realization and Boolean operations. Examples are presented that illustrate successful integration of a prototype program (based on the algorithm) with commercial NC verification software