From the perspective of geometry

based on the geometric interpretation of the four-point binary interpolating subdivision scheme

this paper analyzes the geometric meaning of the four-point ternary interpolating subdivision scheme

and modify the scheme to combine approximating subdivision; then a blending ternary subdivision scheme with parameters is obtained. Many existing interpolating subdivision schemes and approximating subdivision schemes can be seen as special cases of this scheme. We also use generating polynomial method to analyze the

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continuity of limit curve produced by the blending subdivision. A new

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continuous five-point ternary curve subdivision scheme is obtained. Numerical examples show that the proposed blending subdivision scheme can be used to contr

ol the shape of limit curves by selecting appropriate parameters.