Discrete simulation of NC machining

We describe a method for simulating and verifying the correctness of Numerical Control (NC) programs. NC programs contain the sequence of cutting tool movements which machine raw stock into a finished object. Our method is based on a discrete approximation of the object by a set of points. A vector is passed through each of the points and machining is simulated by finding the intersections of tool movements with these vectors. We present a point-selection method and an analysis that shows that the error introduced by the approximation can be made as small as desired. The run time is inversely proportional to the allowable error and the size of the cutting tool, and directly proportional to the distance that the cutting tool moves.