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The n-ary subdivision
schemes contrast favorably with their binary analogues because they are capable
to produce limit functions with the same (or higher) smoothness but smaller
support. We present an algorithm to generate the 4-point n-ary non-stationary scheme for trigonometric, hyperbolic and
polynomial case with the parameter for describing curves. The performance,
analysis and comparison of the 4-point ternary scheme are also presented.
A general formula for 4-point α-Ary approximating subdivision scheme for curve designing is introduced
for any arity α≥2. The new scheme is extension of B-spline of degree 6.
Laurent polynomial method is used to investigate the continuity of the scheme.
The variety of effects can be achieved in correspondence for different values
of parameter. The applications of the proposed scheme are illustrated in
comparison with the established subdivision schemes.