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A New Paradigm to Design a Class of Combined Ternary Subdivision Schemes

Author

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  • Humaira Mustanira Tariq
  • Rabia Hameed
  • Ghulam Mustafa
  • Jia-Bao Liu

Abstract

Subdivision schemes play a vital role in curve modeling. The curves produced by the class of 2n+2-point ternary scheme (Deslauriers and Dubuc (1989)) interpolate the given data while the curves produced by a class of 2n+2-point ternary B-spline schemes approximate the given data. In this research, we merge these two classes to introduce a consolidated and unified class of combined subdivision schemes with two shape control parameters in order to grow versatility for overseeing valuable necessities. However, the proposed class of subdivision schemes gives optimal smoothness in the final shapes, yet we can increase its smoothness by using a proposed general formula in form of its Laurent polynomial. The theoretical analysis of the class of subdivision schemes is done by using various mathematical tools and using their coding in the Maple environment. The graphical analysis of the class of schemes is done in the Maple environment by writing the codes based on the recursive mathematical expressions of the class of subdivision schemes.

Suggested Citation

  • Humaira Mustanira Tariq & Rabia Hameed & Ghulam Mustafa & Jia-Bao Liu, 2021. "A New Paradigm to Design a Class of Combined Ternary Subdivision Schemes," Journal of Mathematics, Hindawi, vol. 2021, pages 1-19, February.
    • Handle: RePEc:hin:jjmath:6679201
    DOI: 10.1155/2021/6679201
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