Free-form surfaces are used for many industrial applications from aeronautical parts, to molds or biomedical implants. In the common machining process, computer-aided manufacturing (CAM) software generates approximated tool paths because of the limitation induced by the input tool path format of the industrial CNC. Then, during the tool path interpolation, marks on finished surfaces can appear induced by non smooth feedrate planning. Managing the geometry of the tool path, as well as the kinematical parameters of the machine tool, are two key factors for quality and productivity improvements. The aim of this paper is to present a unified method to compute the trajectory directly on the surface to be machined avoiding CAM approximations and producing a smoother trajectory. This paper proposes an interpolation of the trajectory based on the free-form surface mathematical model while considering the kinematical limitations of a high-speed milling machine (velocity, acceleration, and jerk). The amelioration of the data exchange between computer-aided design (CAD)/CAM and CNC opens new ways to optimize the manufacturing process. The direct trajectory interpolation on the surface (DTIS) method allows to obtain both a 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 compared to the classical strategies available with an industrial CNC.