A method and apparatus are provided to machine a curved surface such as an inner or outer peripheral surface of a pipe. The pipe is held stationary during machining and a rotatable spindle of a machine head moves along multiple orthogonal axes to align the rotational axis of the spindle with the longitudinal pipe axis. Preferably, the pipe axis is located by using a touch probe to engage the curved surface at multiple spots and the calculating the location of the pipe axis. The cutting tool, which is preferably a cutting tool insert, is rotated by the spindle to machine the curved surface.