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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.