On approximation of planar curves by circular arcs with length preservation

TL;DR

This paper analyzes and extends a method for approximating planar curves with circular arcs while preserving length, introduces inequalities for convex spiral arcs, and proposes a computer modeling scheme to explore properties of planar curves.

Contribution

It extends the applicability of an existing approximation method, derives new inequalities for convex spiral arcs, and introduces a computer modeling scheme for analyzing planar curves.

Findings

Extended the approximation method for planar curves.

Derived inequalities for convex spiral arcs with Hermite data.

Developed a computer modeling scheme for curve properties.

Abstract

The method for approximation of planar curve by circular arcs with length preservation, proposed by I.Kh. Sabitov and A.V. Slovesnov, is analyzed. We extend the applicability of the method, and consider some corollaries, not related to the approximation problem. Inequalities for the length of a convex spiral arc with prescribed two-point $G^1$ or $G^2$ Hermite data are derived. We propose a scheme of computer modelling to explore properties of planar curves. As an example, closeness of ovals is tested, leading to some conjectures about closeness conditions.