Abstract: A numerical control device is arranged to calculate offset curves and generate signals for the movement of tools along the offset curves. The offset curves are derived from contour data, preferably in the form of cubic splines, describing the shape of a workpiece to be machined and from an offset value. By using Hermite's formula for approximation of the offset curves by splines, the number of spline segments is minimized while limiting the deviation between the splines and the offset curve to a preset tolerance value. Even when using moderate computing power, the calculation of the splines will in most circumstances be fast enough to be performed on-line without slowing down the throughput of the machining apparatus.