Curve subdivision with arc-length control

In this paper we present a new nonstationary, interpolatory, curve subdivision scheme. We show that the scheme converges and the subdivision curve is continuous. Moreover, starting with the chord length parametrization of the initial polygon, we obtain a subdivision curve parametrized by a multiple of the arc-length. The proposed method focuses on convexity preservation, limiting the oscillations of the subdivision curve and avoiding artifacts. A bound for the Hausdorff distance between the limit curve and the initial polygon is also obtained.