Abstract: A computing unit (12) produces control signals which, when applied to the control inputs of a conventional numerically controlled lathe (10), cause the lathe cutting tool (60) to be positioned such that contours varying in three dimensions may be realized in a spindle (18) mounted, rotating workpiece (20). The control signals include x and z position signals, defining the position of the cutting tool with respect to the radial (24) and axial (22) axes, respectively, of the workpiece (20), and i and k lead control signals which define the distance traveled by the cutting tool, per revolution of the workpiece, in the radial (24) and axial (22) workpiece axes, respectively.A filtering process (134, 136, 140) operates to delete each control signal having i and k values which are within the x and z tolerance values, respectively, of the immediately preceding control signal, to thereby reduce both the volume of stored data and machining time.