Process planning for the manufacture of free surfaces is mainly concerned with determination of machining configuration. In this paper, we investigate the machining configuration problem stated as: For a given surface model, find (1) The minimum number of control axes, (2) The minimum range of the rotational axes, and (3) The workpart setup orientation. In deriving the solution algorithm, we ensured implementability by casting the problem into an algebraic domain. Using a digitized visibility map, called thebinary spherical map, the machining configuration problem can be solved in a unified fashion without falling into numerical complexity. The solution algorithms are implemented and validated via computer simulations, indicating they can be implemented on the CAD/CAM system as a process planner.