A Natural Spline that Approximates A Smoothing Spline

A smoothing spline is generally used as a filter that smoothes measurement data for estimating its global shape. The smoothing spline is one of the natural splines, and it is the smoothest function. However, since the coefficient matrix of the smoothing spline is not easy to deal with due to the large number of knots, it is expected to use B-spline curve of which coefficient matrix is easy to deal with. Here it is essential to modify B-spline curve as natural spline. Therefore, in order to solve this basic problem, this paper proposes a method for approximating the smoothing spline by the natural spline, where the smoothing spline has N knots and the natural spline has smaller N' (< N ) knots. Successively we propose a method for expressing this natural spline with B-spline curves and another method for estimating an approximated SN ratio in the frequency domain. Some experimental demonstrate the effectiveness of the proposed methods for CAD.