scholarly journals Analysis of the Gibbs phenomenon in stationary subdivision schemes

2018 ◽  
Vol 76 ◽  
pp. 157-163 ◽  
Author(s):  
Sergio Amat ◽  
Juan Ruiz ◽  
J. Carlos Trillo ◽  
Dionisio F. Yáñez
Keyword(s):  
Gibbs Phenomenon ◽  
Subdivision Schemes ◽  
Stationary Subdivision

A family of 4-point odd-ary non-stationary subdivision schemes

SeMA Journal ◽  
2015 ◽  
Vol 67 (1) ◽  
pp. 77-91
Author(s):  
Ghulam Mustafa ◽  
Pakeeza Ashraf
Keyword(s):  
Subdivision Schemes ◽  
Stationary Subdivision

Ternary approximating non-stationary subdivision schemes for curve design

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
Shahid Siddiqi ◽  
Muhammad Younis
Keyword(s):  
Trigonometric Polynomials ◽  
Asymptotic Equivalence ◽  
Conic Sections ◽  
Subdivision Schemes ◽  
Linear Spaces ◽  
Curve Design ◽  
Trigonometric Splines ◽  
Stationary Subdivision

AbstractIn this paper, an algorithm has been introduced to produce ternary 2m-point (for any integer m ≥ 1) approximating non-stationary subdivision schemes which can generate the linear spaces spanned by {1; cos(α.); sin(α.)}. The theory of asymptotic equivalence is being used to analyze the convergence and smoothness of the schemes. The proposed algorithm can be consider as the non-stationary counter part of the 2-point and 4-point existing ternary stationary approximating schemes, for different values of m. Moreover, the proposed algorithm has the ability to reproduce or regenerate the conic sections, trigonometric polynomials and trigonometric splines.

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

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 639 ◽  
Author(s):  
Abdul Ghaffar ◽  
Mehwish Bari ◽  
Zafar Ullah ◽  
Mudassar Iqbal ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Curve Surface ◽  
Asymptotic Equivalence ◽  
Shape Parameters ◽  
Limit Curve ◽  
Subdivision Schemes ◽  
Local Shape ◽  
New Class ◽  
Stationary Subdivision

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.

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