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Open AccessArticle

A New Class of 2q-Point Nonstationary Subdivision Schemes and Their Applications

1
Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan
2
Department of Mathematics, NCBA&E, Bahawalpur 63100, Pakistan
3
Department of Mathematics, University of Education Lahore, Campus DG Khan, Dera Ghazi Khan 54770, Pakistan
4
Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
5
Department of Mathematics, Cankaya University, Ankara 06530, Turkey
6
Institute of Space Sciences, Magurele-Bucharest 76900, Romania
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(7), 639; https://doi.org/10.3390/math7070639
Received: 1 May 2019 / Revised: 1 July 2019 / Accepted: 15 July 2019 / Published: 18 July 2019
(This article belongs to the Special Issue Discrete and Computational Geometry)
The main objective of this study is to introduce a new class of 2 q -point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstationary counterparts of the proposed ANSSs. View Full-Text
Keywords: stationary; nonstationary; subdivision scheme; continuity; curvature and torsion stationary; nonstationary; subdivision scheme; continuity; curvature and torsion
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MDPI and ACS Style

Ghaffar, A.; Bari, M.; Ullah, Z.; Iqbal, M.; Nisar, K.S.; Baleanu, D. A New Class of 2q-Point Nonstationary Subdivision Schemes and Their Applications. Mathematics 2019, 7, 639.

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