# A Family of High Continuity Subdivision Schemes Based on Probability Distribution

• Muhammad Asghar Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan.
• Muhammad Javed Iqbal Department of Mathematics, National College of Business Administration & Economics, Sub campus , Bahawalpur, Pakistan
• Ghulam Mustafa Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

### Abstract

Subdivision schemes are famous for the generation of smooth curves and surfaces in CAGD (Computer Aided Geometric Design). The continuity is an important property of subdivision schemes. Subdivision schemes having high continuity are always required for geometric modeling. Probability distribution is the branch of statistics which is used to find the probability of an event. We use probability distribution in the field of subdivision schemes. In this paper, a simplest way is introduced to increase the continuity of subdivision schemes. A family of binary approximating subdivision schemes with probability parameter p is constructed by using binomial probability generating function. We have derived some family members and analyzed the important properties such as continuity, Holder regularity, degree of generation, degree of reproduction and limit stencils. It is observed that, when the probability parameter p = 1/2, the family of subdivision schemes have maximum continuity, generation degree and Holder regularity. Comparison shows that our proposed family has high continuity as compare to the existing subdivision schemes. The proposed family also preserves the shape preserving property such as convexity preservation. Subdivision schemes give negatively skewed, normal and positively skewed behavior on convex data due to the probability parameter. Visual performances of the family are also presented.

Published
Apr 1, 2019
How to Cite
ASGHAR, Muhammad; IQBAL, Muhammad Javed; MUSTAFA, Ghulam. A Family of High Continuity Subdivision Schemes Based on Probability Distribution. Mehran University Research Journal of Engineering and Technology, [S.l.], v. 38, n. 2, p. 389-398, apr. 2019. ISSN 2413-7219. Available at: <http://publications.muet.edu.pk/index.php/muetrj/article/view/959>. Date accessed: 17 oct. 2019.
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This is an open Access Article published by Mehran University of Engineering and Technolgy, Jamshoro under CCBY 4.0 International License