==========================================================Available online: 31 December 2020This article has been retracted by International Journal on Advanced Science, Engineering and Information Technology Editorial team, following clear correspondence and confirmation with authors.The paper is retracted from 29 November 2021.==========================================================The development of the CNC machine and its advantages led to the constantly developing fields for this system, which are CAD (Computer-Aided Design) and CAM (Computer-Aided Manufacturing). However, surface issues were rarely mentioned in these studies, but mainly on tool path calculations or cutting modes. Reasonable selection of cutting tools, optimal tooling strategy for surfaces, and cutting mode parameters impact productivity and form quality of details containing complex surfaces. This study evaluates free surface based on Gaussian curvature and mean curvature, thereby providing a suitable instrument selection for the evaluated free surface areas. In this paper, the authors analyze and select tools and tool paths when machining freedom faces on 3-axis CNC machines to satisfy surface shaping accuracy requirements and reduce machining time related to the traditional freedom-face machining method. Before doing experimental research, the authors designed experimental samples on CATIA V5R20, simulating the machining process to verify the theoretical calculation. Empirical models for machining on 3-axis CNC milling machines were built and measured the parameters on 3-coordinate measuring machines to evaluate the effect of tool selection and tool paths in the machining of freedom surface areas. Experimental results show that the tool path when machining freedom surfaces dramatically affects the quality of freedom surface shaping. Moreover, the experimental results also show that when processing saddle-face samples, the one direction tooling path should be selected.