  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.
