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.

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 2m-point binary non-stationary subdivision schemes

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Abdul Ghaffar ◽  
Zafar Ullah ◽  
Mehwish Bari ◽  
Kottakkaran Sooppy Nisar ◽  
Maysaa M. Al-Qurashi ◽  
...  
Keyword(s):  
Subdivision Schemes ◽  
New Class ◽  
Stationary Subdivision

scholarly journals Univariate approximating schemes and their non-tensor product generalization

2018 ◽  
Vol 16 (1) ◽  
pp. 1501-1518 ◽  
Author(s):  
Ghulam Mustafa ◽  
Robina Bashir
Keyword(s):  
Initial Data ◽  
Tensor Product ◽  
Limit Curve ◽  
Subdivision Schemes ◽  
Tension Parameter ◽  
The Family

AbstractThis article deals with univariate binary approximating subdivision schemes and their generalization to non-tensor product bivariate subdivision schemes. The two algorithms are presented with one tension and two integer parameters which generate families of univariate and bivariate schemes. The tension parameter controls the shape of the limit curve and surface while integer parameters identify the members of the family. It is demonstrated that the proposed schemes preserve monotonicity of initial data. Moreover, continuity, polynomial reproduction and generation of the schemes are also discussed. Comparison with existing schemes is also given.

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

scholarly journals Construction of Local Shape Adjustable Surfaces Using Quintic Trigonometric Bézier Curve

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1205
Author(s):  
Muhammad Ammad ◽  
Md Yushalify Misro
Keyword(s):  
Basis Functions ◽  
Bézier Curve ◽  
Shape Parameters ◽  
Bernstein Basis ◽  
Suggested Approach ◽  
Local Shape ◽  
General Surface ◽  
Different Types ◽  
Swept Surface ◽  
Shape Adjustment

Based on quintic trigonometric Bézier like basis functions, the biquintic Bézier surfaces are modeled with four shape parameters that not only possess the key properties of the traditional Bézier surface but also have exceptional shape adjustment. In order to construct Bézier like curves with shape parameters, we present a class of quintic trigonometric Bézier like basis functions, which is an extension of a traditional Bernstein basis. Then, according to these basis functions, we construct three different types of shape adjustable surfaces such as general surface, swept surface and swung surface. In addition to the application of the proposed method, we also discuss the shape adjustment of surfaces showing with curvature nephogram (with and without fixing the boundaries). However, the modeling examples shows that the suggested approach is efficient and easy to implement.

Sign in / Sign up

Export Citation Format

Share Document