Abstract: The parameter tracking method is a curve-oriented interpolation method. Firstly, the principle of the parameter tracking method is analyzed and the calculation formula of the step size in the interpolation method is derived, and the calculation process of the interpolation method is explained in detail. Secondly, the ellipse, parabola and hyperbola were used as the object to analyze the process and characteristics of the interpolation method. An example is used to illustrate the range and interpolation results of the parametric differential equations when the parametric curve method is used. Thirdly, it is shown that the interpolation method can complete the interpolation of any arbitrary conic curve in the plane and is verified with a parabolic example. Finally, for the tool compensation function of the conic curve, the algorithm of the compensation vector and the calculation process of the tool center trajectory are given, and an ellipse interpolation example is used to verify it.