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 $ngeq 2$. 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.
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