Abstract
A Family of 2n-Point Ternary Non-Stationary Interpolating Subdivision Scheme
Highlights
Subdivision schemes are the most important, significant and emerging modeling tools in computer aided geometric design, computer applications, medical image processing and scientific visualization
Zheng et al [3] devise a novel (2n-1)-point interpolatory ternary subdivision scheme that reproduces polynomial of degree 2n-2
We proposed 2n-point nonstationary ternary interpolating schemes in Section 3, providing the user with a tension parameter that, when increased within its range of definition, can generate continuous limit curves
Summary
Subdivision schemes are the most important, significant and emerging modeling tools in computer aided geometric design, computer applications, medical image processing and scientific visualization. Bari and Mustafa [11] proposed a family of 4-point n-ary interpolating scheme They worked on odd-point non-stationary interpolating subdivision scheme [12]. We proposed 2n-point nonstationary ternary interpolating schemes, providing the user with a tension parameter that, when increased within its range of definition, can generate continuous limit curves. It provides the convergence of proposed interpolating schemes; such schemes repair the draw backs of its stationary analogue [1,2,12] which does not give the possibility to appreciate significant modification, such that the limit curve of stationary subdivision scheme is determined completely by its initial control mesh. Other conics such that ellipse, parabola and hyperbola are formed by taking the initial data points from their parametric equation and in the result after applying proposed schemes, the limit curve will be ellipse, parabola and hyperbola respectively
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