### Shape Preservation of the Stationary 4-Point Quaternary Subdivision Schemes

Khurram Pervez

#### Abstract

In this paper, the shape preserving properties of the stationary 4-point quaternary approximating and interpolating subdivision schemes of Ko [9] are fully investigated. We will analyzed what conditions should be introduced on the initial control points so that the limit curve achieved by the subdivision schemes presented in [9] are both monotonicity and convexity preserving. Conclusively the whole discussion is followed by examples.

#### Keywords

Quaternary; Approximating; Interpolating; Monotonicity; Convexity

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#### References

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DOI: http://dx.doi.org/10.26713%2Fcma.v9i3.719

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