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A Controllable Ternary Interpolatory Subdivision Scheme  

Zheng, Hongchan (Department of Applied Mathematics, Northwestern Polytechnical University)
Ye, Zhenglin (Department of Applied Mathematics, Northwestern Polytechnical University)
Chen, Zuoping (Department of Applied Mathematics, Northwestern Polytechnical University)
Zhao, Hongxing (Yulin College Shaanxi)
Publication Information
International Journal of CAD/CAM / v.5, no.1, 2005 , pp. 29-38 More about this Journal
Abstract
A non-uniform 3-point ternary interpolatory subdivision scheme with variable subdivision weights is introduced. Its support is computed. The $C^0$ and $C^1$ convergence analysis are presented. To elevate its controllability, a modified edition is proposed. For every initial control point on the initial control polygon a shape weight is introduced. These weights can be used to control the shape of the corresponding subdivision curve easily and purposefully. The role of the initial shape weight is analyzed theoretically. The application of the presented schemes in designing smooth interpolatory curves and surfaces is discussed. In contrast to most conventional interpolatory subdivision scheme, the presented subdivision schemes have better locality. They can be used to generate $C^0$ or $C^1$ interpolatory subdivision curves or surfaces and control their shapes wholly or locally.
Keywords
Ternary subdivision; Interpolation; $C^k$-continuity; Shape controllability; Surface modeling;
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Times Cited By KSCI : 1  (Citation Analysis)
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