Ternary Even Symmetric 2n-Point Subdivision

In this paper, we design a ternary even symmetric 2n-point approximating subdivision scheme which generates smooth curves of high order. We illustrate the technique with a new 4-point ternary approximating subdivision scheme which is C
⁴
and a new 6-point ternary approximating subdivision scheme which can achieve C
⁷
-continuity. The smoothness of the new schemes is proved using Laurent polynomials.