Approximation by planar elastic curves

TL;DR

This paper presents an algorithm that approximates a plane curve segment with an elastic curve using an analytic representation, geometric initial guess, and gradient optimization.

Contribution

It introduces a novel method combining analytic, geometric, and optimization techniques for elastic curve approximation.

Findings

Effective approximation of plane curves by elastic curves demonstrated.

The method provides good initial guesses for optimization.

Gradient-driven optimization refines the elastic curve approximation.

Abstract

We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient-driven optimization is then used to find the approximating elastic curve.