Smoothing curvature and torsion with spring splines

A method is presented for generating piecewise parametric cubic spline functions with derivatives free of spurious oscillations. The tradeoff between smoothness and goodness of fit is controlled by adjusting the stiffness ratio of the spline and springs. Beam on elastic foundation theory is used to derive a set of transfer functions that relate the amplitude of the noise in the data to the amplitude of the noise in the curvature and torsion. Guidance is provided for specifying the stiffness ratio and the end conditions of the spring spline.