Second Order Spiral Splines
Provides a computationally efficient interpolation method for planar curves, but is limited to convex data and fine sampling, making it incremental for geometric design applications.
The paper develops a fast algorithm for constructing $C^2$ unit-speed planar curves (second order spiral splines) to interpolate convex, finely sampled point data, using asymptotic methods and tridiagonal linear systems.
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.