In the common machining process of free-form surfaces, CAM software generates approximated tool paths because of the input tool path format of the industrial CNC. Then, marks on finished surfaces may appear due to non smooth feedrate planning during interpolation. The Direct Trajectory Interpolation on the Surface (DTIS) method allows managing the tool path geometry and the kinematical parameters to achieve higher productivity and a better surface quality. Machining experiments carried out with an Open CNC on a 5-axis high speed milling machine show the benefits of the proposed method compare to the classical strategies available with an industrial CNC.