Two-order Hermite vector-interpolating subdivision schemes

A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and continuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of C2 continuity are proved. Geometric features of subdivision curves, such as line segments, cusps and inflection points, are obtained by appending some conditions to initial vectorial Hermite sequence. An algorithm is presented for generating geometric features. For an initial sequence of two-order Hermite elements from unit circle, the numerical error of the 4th subdivided level is O(10-4).