For acquiring the mean line of workpiece profile,a new kind of digital smoothing filter based on cubic generalized spline function was proposed.The generalized B spline functions were derived from the linear differential equation,and the digital smoothing filter consisting of a IIR filter and indirect generalized B spline transformation was deduced by combination with generalized B spline functions and variational principles.Then,the recursive algorithm of the filter was presented concretely,and the filter's universal property was testified.Finally,this filter process was applied to a workpiece to acquire mean line.The experimental results indicate that the filter has a better cut-off property than that of Gauss filter,and total calculation only requires 0.002 s for 11 200 data points by PC.The filter has advantages in adjustable smoothing property and zero phase transmission,which can overcome the drawbacks of low curvature and serious oscillations of traditional cubic spline interpolation.The recursive algorithm is efficient and simple.