Chordal cubic spline interpolation is fourth-order accurate

^** Email: michaelf{at}ifi.uio.no It is well known that complete cubic spline interpolation offunctions with four continuous derivatives is fourth-order accurate.In this paper we show that this kind of interpolation, whenused to construct parametric spline curves through sequencesof points in any space dimension, is again fourth-order accurateif the parameter intervals are chosen by chord length. We alsoshow how such chordal spline interpolants can be used to approximatethe arc-length derivatives of a curve and its length.