A New Class of 2<i>q</i>-Point Nonstationary Subdivision Schemes and Their Applications

A New Class of 2<i>q</i>-Point Nonstationary Subdivision Schemes and Their Applications

The main objective of this study is to introduce a new class of <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mi>q</mi> </mrow> </semantics> </math> </inline-formula>-point approximating nonst...

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Bibliographic Details
Main Authors: Abdul Ghaffar, Mehwish Bari, Zafar Ullah, Mudassar Iqbal, Kottakkaran Sooppy Nisar, Dumitru Baleanu
Format: Article
Language:English
Published: MDPI AG 2019-07-01
Series:Mathematics
Subjects:
stationary
nonstationary
subdivision scheme
continuity
curvature and torsion
Online Access:https://www.mdpi.com/2227-7390/7/7/639
Description
Summary:The main objective of this study is to introduce a new class of <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mi>q</mi> </mrow> </semantics> </math> </inline-formula>-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.
ISSN:2227-7390

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