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A symmetric $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}C^{3}$ non-stationary subdivision scheme

Part of: Approximations and expansions Numerical approximation and computational geometry

Published online by Cambridge University Press:  01 June 2014

S. S. Siddiqi  and
M. Younis
S. S. Siddiqi
Affiliation:
Department of Mathematics, University of the Punjab, Lahore, Pakistan email shahidsiddiqiprof@yahoo.co.uk
M. Younis
Affiliation:
Department of Mathematics, University of the Punjab, Lahore, Pakistan email shahidsiddiqiprof@yahoo.co.uk

Abstract

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This paper proposes a new family of symmetric $4$-point ternary non-stationary subdivision schemes  that can generate the limit curves of $C^3$ continuity. The continuity of this scheme is higher than the existing 4-point ternary approximating schemes. The proposed scheme has been developed using trigonometric B-spline basis functions and analyzed using the theory of asymptotic equivalence. It has the ability to reproduce or regenerate the conic sections, trigonometric polynomials and trigonometric splines as well. Some graphical and numerical examples are being considered, by choosing an appropriate tension parameter $0<\alpha <\pi /3 $, to show the usefulness of the proposed scheme. Moreover, the Hölder regularity and the reproduction property are also being calculated.

MSC classification

Secondary: 41A15: Spline approximation 65D07: Splines 65D17: Computer aided design (modeling of curves and surfaces) 68U07: Computer-aided design
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Issue 1 , 2014 , pp. 259 - 272
Copyright
© The Author(s) 2014 

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