This invention provides a novel tool path planning method for five-axis flank milling by imposing the constraints of curve interpolation on the tool path. The tool motion is described in the form of spline curves during its optimization-driven calculation process, instead of discrete cutter locations in CNC linear interpolation. The coefficients of the curve equations are generated by minimizing accumulated geometrical errors on the machined surface using optimization algorithms. The continuity imposed by the spline motion reduces uneven modifications of cutter locations during the optimization process. The resultant tool path yields superior.