scholarly journals Hyperbolic forms of ternary non-stationary subdivision schemes originated from hyperbolic B-splines

2016 ◽  
Vol 301 ◽  
pp. 16-27 ◽  
Author(s):  
Shahid S. Siddiqi ◽  
Wardat us Salam ◽  
Kashif Rehan
Keyword(s):  
Subdivision Schemes ◽  
B Splines ◽  
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.

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