In the machining of complex-shaped parts such as aircraft parts, there is a strong demand for high-precision machined surfaces with high productivity. Recently, barrel tools with extremely small curvature of cutting edges have been used. Barrel tools enable smooth surface finishing and high productivity even with a large pick feed. Currently, there are various shapes of barrel tools such as barrel-shape, taper-shape, oval-shape, and lens-shape. For all of these complex tool shape, it is desirable to be able to calculate the cutter location data from the cutting point with a single generalized formula. In this study, we propose the data format for all types of barrel tool, and introduce a tool path generation method based on the proposed data format.