Analysis of uniform binary subdivision schemes for curve design

The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form {Mathematical expression} The convergence of the control polygons to a C° curve is analysed in terms of the convergence to zero of a derived scheme for the differences f_i+1^k-f_i^k. The analysis of the smoothness of the limit curve is reduced to the convergence analysis of "differentiated" schemes which correspond to divided differences of f_i^k:i∈ Z with respect to the diadic parametrization t_i^k=i/2^k. The inverse process of "integration" provides schemes with limit curves having additional orders of smoothness.