Chordal cubic spline interpolation is fourth-order accurate

It is well known that complete cubic spline interpolation of functions with four continuous derivatives is fourth-order accurate. In this paper we show that this kind of interpolation, when used to construct parametric spline curves through sequences of points in any space dimension, is again fourth-order accurate if the parameter intervals are chosen by chord length. We also show how such chordal spline interpolants can be used to approximate the arc-length derivatives of a curve and its length.