A Convexity Preserving Subdivision Scheme for Curve Interpolation

A geometric driven subdivision scheme for curve interpolation is proposed.For the initial control polygon,the newly generating points are determined by the old control points as well as their tangent vectors,and the tangent vector at a point is determined by its adjacent points.In each subdivision step,the tangent vectors are adjusted adaptively and the limit curve is G¹ continuous and convexity preserving.It can reproduce circular arc segment if all the initial points are sampled from a circular arc.Numerical examples show that curves generated by this subdivision scheme are fair curves.