Non-stationary subdivision schemes originated from uniform trigonometric B-spline
Numerical Analysis
2013-02-06 v1
Abstract
The paper proposes, an algorithm to produce novel m-point (for any integer m>=2) binary non-stationary subdivision scheme. It has been developed using uniform trigonometric B-spline basis functions and smoothness is being analyzed using the theory of asymptotically equivalence. The results show that the most of well-known binary approximating schemes can be considered as the non-stationary counterpart of the proposed algorithm. Furthermore, the schemes developed by the proposed algorithm has the ability to reproduce or regenerate the conic sections, trigonometric polynomials and trigonometric splines as well. Some examples are considered, by choosing an appropriate tension parameter 0<alpha<pi/3, to show the usefulness.
Keywords
Cite
@article{arxiv.1302.0937,
title = {Non-stationary subdivision schemes originated from uniform trigonometric B-spline},
author = {Shahid S. Siddiqi and Muhammad Younis},
journal= {arXiv preprint arXiv:1302.0937},
year = {2013}
}