A new paradigm for increasing the continuity of subdivision schemes

Ghulam Mustafa
Department of Mathematics, The Islamia University of Bahawalpur, Pakistan.
Muhammad Asghar
Department of Mathematics, The Islamia University of Bahawalpur, Pakistan.
Madiha Naveed
Department of Mathematics, NCBA & E Sub-Campus Bahawalpur , Pakistan.

\(^{1}\)Corresponding Author: ghulam.mustafa@iub.edu.pk

Copyright © 2018 Ghulam Mustafa, Muhammad Asghar, Madiha Naveed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2018.

Abstract

Subdivision schemes having high continuity are always required for designing of smooth curves and surfaces. In this paper, we present a paradigm to generate a family of binary approximating subdivision schemes with high continuity based on probability distribution. The analysis and convexity preservation of some members of the family are also presented. Subdivision schemes give skewed behavior on convex data due to probability parameter.

Keywords:

Binary, approximating subdivision schemes, binomial probability distribution, convexity preservation.