Second Order Spiral Splines

TL;DR

This paper introduces a fast algorithm for constructing second order spiral splines, which are smooth, unit-speed curves that interpolate a set of points in the plane, using asymptotic methods and linear systems.

Contribution

The paper develops a novel, efficient algorithm for second order spiral spline interpolation based on asymptotic analysis and linear systems, suitable for convex, finely sampled data.

Findings

Algorithm efficiently constructs second order spiral splines.

Uses asymptotic methods and linear systems for interpolation.

Applicable to convex, well-sampled data sets.

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.