Approximation of plane curves by circular arcs

A method is proposed for approximating plane curves by circular arcs with length preservation. It is proved that, under certain rather mild constraints, any $C^3$-smooth curve (open or closed, possibly, with self-intersections) can be approximated by a $C^1$-smooth curve consisting of smoothly joined circular arcs. The approximation passes through interpolation nodes where it is tangent to the original curve, with the arc lengths between the nodes being preserved. The error of the approximation is estimated, and numerical examples are presented.