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Based on the linear spaces spanned respectively by the functions {1, x, x2, x3, x4, x5}, {1,x, x2, x3, esx, e−sx} and {1, x, x2, x3, eisx, e−isx}, a non-stationary two order Hermite interpolatory subdivision scheme with one parameter is constructed for the given function values and the first and second order derivatives at two sequential points. Also, the convergence, C2 continuity and geometric properties...
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 C4 and a new 6-point ternary approximating subdivision scheme which can achieve C7-continuity. The smoothness of the new schemes is proved using Laurent polynomials.
Based on the p-ary subdivision rules for B-splines, we show how to design more general subdivision schemes that preserve the B-spline smoothness exactly or almost. We illustrate the technique with new 4-point C5 binary, 4-point C3 ternary and C4 ternary subdivision schemes.
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...
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