Second Order Spiral Splines

Abstract

Second order spiral splines are $C^2$ unit-speed planar curves that can be used to interpolate a list $Y$ of $n+1$ points in $\R ^2$ at times specified in some list $T$, where $n\geq 2$. Asymptotic methods are used to develop a fast algorithm, based on a pair of tridiagonal linear systems and standard software. The algorithm constructs a second order spiral spline interpolant for data that is convex and sufficiently finely sampled.