<p>In recent years, smoothing techniques have emerged as one of the most significant research topics in the field of CAD/CAM. Accordingly, a tool path smoothing approach based on spline trajectories has been developed for pocket milling applications in high-speed machining (HSM). This study proposes an optimization framework for parametric curves employed in the smoothing of CAM milling strategies. The “Morph Spiral” strategy was selected as the case study and modeled using Bspline and NURBS interpolations. The influence of interpolation order and discretization parameters on machine tool dynamics and machining accuracy was systematically investigated. The obtained results indicate that the integration of parametric curves within CAM strategies considerably enhances the efficiency of HSM operations. The optimal configuration was identified as an interpolation order of 2 with a discretization parameter of <i>n</i> = 1000. Under these conditions, the proposed smoothing approach reduced the milling cycle time by approximately 60% for both Bspline and NURBS interpolations, while maintaining acceptable chordal deviations. Increasing the interpolation order from 2 to 5 resulted in a 9.7% increase in chord error for Bspline curves, whereas its effect on NURBS interpolation was negligible. Conversely, increasing the discretization parameter from <i>n</i> = 1000 to <i>n</i> = 3000 led to a reduction in chord error of 64.49% for Bspline and 77.39% for NURBS. These findings confirm the effectiveness of the proposed methodology in optimizing the trade-off between machining accuracy and productivity in freeform high-speed milling applications.</p> Graphical abstract <p></p>