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In modern mechanical engineering, the number of parts with spatially complex surfaces is growing, the shape of which is determined analytically according to certain criteria. They are most widely used in the energy, aviation, tool industries (turbine blades, unicycles). With the current practice of processing such parts on CNC machines, when developing control programs, the analytically calculated shape of the surfaces is replaced by an approximate graphical model, which is used to calculate tool trajectories. This practice is due to the historically existing in the 1970-90s the capabilities of electronics and electrically driven devices. Despite the fundamentally new modern possibilities of computer control and electric drive devices, CNC machines retained the traditional initial principle of surface shaping using approximation and interpolation methods. At the same time, already at the stage of technological preparation of control programs, certain assumptions and losses in accuracy are assumed. The solution of this problem is relevant in connection with the current trend of increasing requirements for the accuracy of critical parts with spatially complex surfaces. The article proposes the principle of alternative control of shaping feeds when milling parts with spatially complex surfaces using the form of specifying the surface in an analytical form. The application of this principle excludes intermediate stages associated with the transformation of the analytical form of the task into a graphic one, the choice of coordinates of reference points and the interpolation of elementary sections. It is proposed, based on the proposed functional relationship between the geometric shape of a spatially complex surface and the established ratio of the components of the contour feed, based on the use of modern capabilities of computing devices and an electric drive, to provide a fundamentally new approach to shaping. The use of the proposed approach ensures complete automation of the preparation of control programs. [ABSTRACT FROM AUTHOR]