3-axis computer numerical control machining centers are used in machining due to their simple operation. When machining curved surfaces, the 3-axis CNC machining centers use interpolation lines segment to fit the curved surfaces. The quality of the machined surface is affected by the length of the interpolation line segment. Sharp corners are formed at the junction of straight segments. The appearance of sharp corners will lead to increased stress concentration. To study the relationship between surface quality and interpolation straight line in surface processing, this paper establishes the mathematical model of surface topography in 3-axis ball-end milling curved surfaces based on the acceleration and deceleration control. Based on the surface topography model, the surfaces stress concentration factor analysis is carried out in machining curved surfaces with variable curvatures with different lengths of interpolation lines. The results show that when the length of interpolation lines and the radius of curvature are kept constant, the stress concentration factor decreases with the increase of the central angle. When the length of the interpolation lines and the central angle are kept constant, the stress concentration factor decreases with the increase of the radius of curvature. When the radius of curvature and the central angle are kept constant, the stress concentration factor increases as the length of the interpolation lines increases. A method of selecting the length of interpolation lines based on the surface’s stress concentration is proposed. Through the optimization of the tool path, the quality of the machined surfaces can be improved.