scholarly journals Fractal Generation by 7-Point Binary Approximating Subdivision Scheme

2018 ◽  
pp. 105-111
Author(s):  
Mehwish Bari ◽  
◽  
Ghulam Mustafa ◽  
Abid Hussain
Keyword(s):  
Subdivision Scheme ◽  
Approximating Subdivision Scheme

A ternary 4-point approximating subdivision scheme

2007 ◽  
Vol 190 (2) ◽  
pp. 1563-1573 ◽  
Author(s):  
Kwan Pyo Ko ◽  
Byung-Gook Lee ◽  
Gang Joon Yoon
Keyword(s):  
Subdivision Scheme ◽  
Approximating Subdivision Scheme

A unified three point approximating subdivision scheme

2011 ◽  
Vol 27 (1) ◽  
pp. 10-20 ◽  
Author(s):  
Ghulam Mustafa ◽  
Faheem Khan ◽  
Muhammad Sadia Hashmi ◽  
Muhammad Zeshan Afzal
Keyword(s):  
Subdivision Scheme ◽  
Approximating Subdivision Scheme

scholarly journals Subdivision Collocation Method for One-Dimensional Bratu’s Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ghulam Mustafa ◽  
Syeda Tehmina Ejaz ◽  
Sabila Kouser ◽  
Shafqat Ali ◽  
Muhammad Aslam
Keyword(s):  
Boundary Value Problem ◽  
Collocation Method ◽  
Boundary Value ◽  
Accurate Solution ◽  
Subdivision Scheme ◽  
Algebraic Equations ◽  
Physical Sciences ◽  
One Dimensional ◽  
Bratu’S Problem ◽  
Approximating Subdivision Scheme

The purpose of this article is to employ the subdivision collocation method to resolve Bratu’s boundary value problem by using approximating subdivision scheme. The main purpose of this researcher is to explore the application of subdivision schemes in the field of physical sciences. Our approach converts the problem into a set of algebraic equations. Numerical approximations of the solution of the problem and absolute errors are compared with existing methods. The comparison shows that the proposed method gives a more accurate solution than the existing methods.

scholarly journals A New 4-PointC3Quaternary Approximating Subdivision Scheme

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Ghulam Mustafa ◽  
Faheem Khan
Keyword(s):  
Shape Parameter ◽  
Approximation Order ◽  
Subdivision Scheme ◽  
Subdivision Schemes ◽  
Approximating Subdivision Scheme

A new 4-pointC3quaternary approximating subdivision scheme with one shape parameter is proposed and analyzed. Its smoothness and approximation order are higher but support is smaller in comparison with the existing binary and ternary 4-point subdivision schemes.

scholarly journals Generalized 5-Point Approximating Subdivision Scheme of Varying Arity

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 474 ◽  
Author(s):  
Sardar Muhammad Hussain ◽  
Aziz Ur Rehman ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar ◽  
Abdul Ghaffar ◽  
...  
Keyword(s):  
Error Bound ◽  
Shape Parameter ◽  
Geometric Design ◽  
Hölder Regularity ◽  
Subdivision Scheme ◽  
Subdivision Schemes ◽  
Computer Aided Geometric Design ◽  
Approximating Subdivision Scheme ◽  
Computer Aided ◽  
Holder Regularity

The Subdivision Schemes (SSs) have been the heart of Computer Aided Geometric Design (CAGD) almost from its origin, and various analyses of SSs have been conducted. SSs are commonly used in CAGD and several methods have been invented to design curves/surfaces produced by SSs to applied geometry. In this article, we consider an algorithm that generates the 5-point approximating subdivision scheme with varying arity. By applying the algorithm, we further discuss several properties: continuity, Hölder regularity, limit stencils, error bound, and shape of limit curves. The efficiency of the scheme is also depicted with assuming different values of shape parameter along with its application.

scholarly journals A C6 approximating subdivision scheme

2008 ◽  
Vol 21 (7) ◽  
pp. 722-728 ◽  
Author(s):  
Shahid S. Siddiqi ◽  
Nadeem Ahmad
Keyword(s):  
Subdivision Scheme ◽  
Approximating Subdivision Scheme

scholarly journals A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Rabia Hameed ◽  
Ghulam Mustafa ◽  
Amina Liaqat ◽  
Dumitru Baleanu ◽  
Faheem Khan ◽  
...  
Keyword(s):  
Tensor Product ◽  
Numerical Experiments ◽  
Subdivision Scheme ◽  
Shape Parameters ◽  
New Approach ◽  
Quadrilateral Meshes ◽  
Displacement Vectors ◽  
Approximating Subdivision Scheme ◽  
Interpolatory Subdivision

In this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to three displacement vectors containing two shape parameters. We first study the characteristics of the new subdivision scheme analytically and then present numerical experiments to justify these analytical characteristics geometrically. We also extend the new derived scheme into its bivariate/tensor product version. This bivariate scheme is applicable on quadrilateral meshes to produce smooth limiting surfaces up to C 3 continuity.

Sign in / Sign up

Export Citation Format

Share Document