Abstract

Subdivision schemes are acknowledged as an important tool in computer aided geometric design. The new binary non-stationary three-point approximating subdivision schemes have been proposed that generate wide variations of $C^1$ and $C^2$ continuous curves using shape control parameter $ξ^0$. The proposed schemes are the counterpart of stationary schemes introduced by Hormann and Sabin (2008) and Siddiqi and Ahmad (2007). Curve variations using the shape control parameter $ξ^0$ have been demonstrated by the several examples.

Keywords:

Approximating, binary, non-stationary, smooth curves, subdivision,

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Competing interests

The authors have no competing interests.

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