A Family of Binary Approximating Subdivision Schemes based on Binomial Distribution

A simplest way is introduced to generate a generalized algorithm of univariate and bivariate subdivision schemes. This generalized algorithm is based on the symbol of uniform B-splines subdivision schemes and probability generating function of Binomial distribution. We present a family of binary app...

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Main Authors: Muhammad Asghar, Ghulam Mustafa
Format: Article
Language:English
Published: Mehran University of Engineering and Technology 2019-10-01
Series:Mehran University Research Journal of Engineering and Technology
Online Access:https://publications.muet.edu.pk/index.php/muetrj/article/view/1264
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spelling doaj-59dad5e62ae34defbdb570bd0a51932f2020-11-25T01:29:12ZengMehran University of Engineering and TechnologyMehran University Research Journal of Engineering and Technology0254-78212413-72192019-10-01384108711001264A Family of Binary Approximating Subdivision Schemes based on Binomial DistributionMuhammad Asghar0Ghulam Mustafa1Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan.A simplest way is introduced to generate a generalized algorithm of univariate and bivariate subdivision schemes. This generalized algorithm is based on the symbol of uniform B-splines subdivision schemes and probability generating function of Binomial distribution. We present a family of binary approximating subdivision schemes which has maximum continuity and less support size. Our proposed family members P4, P5, P6, and P7, have C7, C9, C11 and C13 continuities respectively. In fact, we use Binomial probability distribution to increase the continuity of uniform B-splines subdivision schemes up to more than double. We present the complete analysis of one family member of proposed schemes and give a visual performance to check smoothness graphically. In our analysis, we present continuity, Holder regularity, degree of generation, degree of reproduction and limit stencils analysis of proposed family of subdivision schemes. We also present a survey of high continuity subdivision schemes. Comparison shows that our proposed family of subdivision schemes gives high continuity of subdivision schemes comparative to existing subdivision schemes. We have found that as complexity increases the continuity also increases. In the last, we give the general formula for tensor product surface subdivision schemes and also present the visual performance of proposed tensor product surface subdivision schemes.https://publications.muet.edu.pk/index.php/muetrj/article/view/1264
collection DOAJ
language English
format Article
sources DOAJ
author Muhammad Asghar
Ghulam Mustafa
spellingShingle Muhammad Asghar
Ghulam Mustafa
A Family of Binary Approximating Subdivision Schemes based on Binomial Distribution
Mehran University Research Journal of Engineering and Technology
author_facet Muhammad Asghar
Ghulam Mustafa
author_sort Muhammad Asghar
title A Family of Binary Approximating Subdivision Schemes based on Binomial Distribution
title_short A Family of Binary Approximating Subdivision Schemes based on Binomial Distribution
title_full A Family of Binary Approximating Subdivision Schemes based on Binomial Distribution
title_fullStr A Family of Binary Approximating Subdivision Schemes based on Binomial Distribution
title_full_unstemmed A Family of Binary Approximating Subdivision Schemes based on Binomial Distribution
title_sort family of binary approximating subdivision schemes based on binomial distribution
publisher Mehran University of Engineering and Technology
series Mehran University Research Journal of Engineering and Technology
issn 0254-7821
2413-7219
publishDate 2019-10-01
description A simplest way is introduced to generate a generalized algorithm of univariate and bivariate subdivision schemes. This generalized algorithm is based on the symbol of uniform B-splines subdivision schemes and probability generating function of Binomial distribution. We present a family of binary approximating subdivision schemes which has maximum continuity and less support size. Our proposed family members P4, P5, P6, and P7, have C7, C9, C11 and C13 continuities respectively. In fact, we use Binomial probability distribution to increase the continuity of uniform B-splines subdivision schemes up to more than double. We present the complete analysis of one family member of proposed schemes and give a visual performance to check smoothness graphically. In our analysis, we present continuity, Holder regularity, degree of generation, degree of reproduction and limit stencils analysis of proposed family of subdivision schemes. We also present a survey of high continuity subdivision schemes. Comparison shows that our proposed family of subdivision schemes gives high continuity of subdivision schemes comparative to existing subdivision schemes. We have found that as complexity increases the continuity also increases. In the last, we give the general formula for tensor product surface subdivision schemes and also present the visual performance of proposed tensor product surface subdivision schemes.
url https://publications.muet.edu.pk/index.php/muetrj/article/view/1264
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