A Non-stationary Combined Ternary 5-point Subdivision Scheme with C⁴ Continuity

In this paper, a family of non-stationary combined ternary 5-point subdivision schemes with multiple variable parameters is proposed. The construction of the scheme is based on the generalized ternary subdivision scheme of order 4, which is built upon refinement of a family of generalized B-splines, using the variable displacements. For such a non-stationary scheme, we study its smoothness and get that it can generate C² interpolating limit curves and C⁴ approximating limit curves. Besides, we investigate the exponential polynomial generation/reproduction property and approximation order. It can generate/reproduce certain exponential polynomials with suitable choices of the variable parameters, and reach approximation order 5.