Abstract: A binary five-point approximating subdivision scheme is described. The
generating polynomial method is used to investigate the uniform convergence and Ck -continuity
of this subdivision scheme. The subdivision scheme generates a family of Cn (n=1, 2,3,4,5)
limiting curves for certain range of tension parameter μ and a C7 limiting curves forμ=9/256.
Some examples of the subdivision curve design are given to demonstrate the efficiency of the
scheme.

Key words: binary approximating subdivision, generating polynomial, Ck-continuity;
limiting curves