Abstract: CD playback apparatus for reproducing information from unfinalized CD-R disks which have no index information stored in a table of contents (TOC) area which scans a disk coarsely to detect the end of the recorded area approximately and scans the disk finely in the area of the detected approximate end, to detect the end of the recorded area with greater accuracy. The apparatus has an optical pick-up unit which jumps across a disk with predetermined intervals, to detect partial index information for the disk during the coarse scanning, analyses the partial index information, performs the fine scanning, jumps to an area in which missing index information is judged to exist as a result of the analysis, and reads out data in the jumped-to area to detect the missing index information.

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.

Abstract: Machining apparatus wherein the cutting tool is controlled to follow a path defined by successive splines, the geometry of a spline being described as a function of a parameter other than arc length along the spline and which is related to time. At a present position along a spline, the change in such parameter corresponding to a change in arc length is explicitly determined by approximation and used to determine an incremented position on the spline. A desired constant tool speed can thereby be maintained. By using only the first or the first two terms of a Taylor series approximation, a change in the parameter can be explicitly approximated as a linear or quadratic predictor. Alternatively, polynomial or rational approximations may be employed.