Abstract : This paper proposes a unified interpolation algorithm for the direct machining of three types of curves: ellipse, parabola, and hyperbola, based on the characteristics of typical quadratic curves. Keywords : quadratic curve; interpolation; deviation discrimination function 0 Introduction Typical quadratic curves are commonly used part contour lines. However, general CNC machine tool system control programs do not fully have the function of directly machining the three types of typical quadratic curves (ellipse, hyperbola, and parabola). Even if some CNC systems have the function of directly machining these curves, due to the strong "specificity" of the algorithm, each type of curve must be stored in the program memory, and a general interpolation program cannot be used to interpolate these three types of curves. This paper proposes an interpolation algorithm that can directly machine the three types of curves based on the commonalities of quadratic curves. To solve the problem of unifying the interpolation algorithm for the three types of typical quadratic curves, the following points must be addressed: (1) unification of the curve equation expression; (2) automatic determination of which quadrant the curve point on the coordinate axis belongs to; (3) unification of the recursive formula of the deviation discrimination function; (4) automatic quadrant crossing and endpoint judgment. 1. Standardization of Curve Equations For typical conic sections (ellipses, hyperbolas, and parabolas), a single standardized equation can be used to represent them. That is: [b][align=center]For details, please click: Standardized Interpolation for Typical Conic Sections[/align][/b]