A Binary Five-point Relaxation Subdivision Scheme ⋆

Based on the classical four-point interpolating subdivision scheme, a new binary five-point relaxation subdivision scheme is presented. The generating polynomial method is used to investigate the uniform convergence and C k continuity of this subdivision scheme. The subdivision scheme generates a family of C n (n = 1; 2; 3; 4; 5) limiting curves for certain range of tension parameter w. Especially, when w take some specific values, the limiting curves will turn out to be fractals. Some examples of the subdivision curves are given to demonstrate the efficiency of the scheme.