Constructing 2n-1-Point Ternary Interpolatory Subdivision Schemes by Using Variation of Constants

Based on Lagrange polynomials and variation of constants, we devise a novel 2n-1-point interpolatory ternary subdivision scheme that reproduces polynomials of degree 2n-2. We illustrate the technique with a 3-point ternary interpolatory subdivision scheme which can rebuild Hassan and Dodgson´s interpolating 3-point ternary subdivision scheme and a new 5-point ternary interpolatory subdivision scheme which can achieve C²-continuity. The smoothness of the new schemes is proved using Laurent polynomial method.