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 [GRAPHICS] The convergence of the control polygons to a C0 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 member-of Z} with respect to the diadic parametrization t(i)k = i/2k. The inverse process of "integration" provides schemes with limit curves having additional orders of smoothness.