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Construction and Application of Nine-Tic B-Spline Tensor Product SS

Author

Listed:
  • Abdul Ghaffar

    (Department of Mathematical Sciences, Balochistan University of Information Technology, Engineering and Management Sciences (BUITEMS), Quetta 87300, Pakistan
    These authors contributed equally to this work.)

  • Mudassar Iqbal

    (Department of Mathematical Sciences, Balochistan University of Information Technology, Engineering and Management Sciences (BUITEMS), Quetta 87300, Pakistan
    These authors contributed equally to this work.)

  • Mehwish Bari

    (Department of Mathematics, NCBA&E, Bahawalpur 63100, Pakistan
    These authors contributed equally to this work.)

  • Sardar Muhammad Hussain

    (Department of Mathematical Sciences, Balochistan University of Information Technology, Engineering and Management Sciences (BUITEMS), Quetta 87300, Pakistan
    These authors contributed equally to this work.)

  • Raheela Manzoor

    (Department of Mathematics, SBK Women University, Quetta 87300, Pakistan
    These authors contributed equally to this work.)

  • Kottakkaran Sooppy Nisar

    (Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
    These authors contributed equally to this work.)

  • Dumitru Baleanu

    (Department of Mathematics, Cankaya University, Ankara 06530, Turkey
    Institute of Space Sciences, Magurele-Bucharest 76900, Romania
    These authors contributed equally to this work.)

Abstract

In this paper, we propose and analyze a tensor product of nine-tic B-spline subdivision scheme (SS) to reduce the execution time needed to compute the subdivision process of quad meshes. We discuss some essential features of the proposed SS such as continuity, polynomial generation, joint spectral radius, holder regularity and limit stencil. Some results of the SS using surface modeling with the help of computer programming are shown.

Suggested Citation

  • Abdul Ghaffar & Mudassar Iqbal & Mehwish Bari & Sardar Muhammad Hussain & Raheela Manzoor & Kottakkaran Sooppy Nisar & Dumitru Baleanu, 2019. "Construction and Application of Nine-Tic B-Spline Tensor Product SS," Mathematics, MDPI, vol. 7(8), pages 1-33, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:675-:d:252723
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    References listed on IDEAS

    as
    1. Cheng, Li & Zhou, Xinlong, 2017. "Necessary conditions for the convergence of subdivision schemes with finite masks," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 34-41.
    2. Rabia Hameed & Ghulam Mustafa, 2016. "Construction and Analysis of Binary Subdivision Schemes for Curves and Surfaces Originated from Chaikin Points," International Journal of Analysis, Hindawi, vol. 2016, pages 1-15, December.
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