A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme

A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme

In this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to thr...

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Main Authors: Rabia Hameed, Ghulam Mustafa, Amina Liaqat, Dumitru Baleanu, Faheem Khan, Maysaa M. Al-Qurashi, Yu-Ming Chu
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2020/6096545
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spelling doaj-ba3ae332857247249dded0eaadc1b2c52020-11-25T01:40:32ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/60965456096545A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision SchemeRabia Hameed0Ghulam Mustafa1Amina Liaqat2Dumitru Baleanu3Faheem Khan4Maysaa M. Al-Qurashi5Yu-Ming Chu6Department of Mathematics, The Government Sadiq College Women University Bahawalpur, Bahawalpur, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, PakistanDepartment of Mathematics, The Government Sadiq College Women University Bahawalpur, Bahawalpur, PakistanDepartment of Mathematics, Cankaya University, Ankara 06530, TurkeyDepartment of Mathematics, Faculty of Sciences, King Saud University, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, University of Sargodha, Sargodha, PakistanDepartment of Mathematics, Huzhou University, Huzhou 313000, ChinaIn this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to three displacement vectors containing two shape parameters. We first study the characteristics of the new subdivision scheme analytically and then present numerical experiments to justify these analytical characteristics geometrically. We also extend the new derived scheme into its bivariate/tensor product version. This bivariate scheme is applicable on quadrilateral meshes to produce smooth limiting surfaces up to C3 continuity.http://dx.doi.org/10.1155/2020/6096545
collection DOAJ
language English
format Article
sources DOAJ
author Rabia Hameed
Ghulam Mustafa
Amina Liaqat
Dumitru Baleanu
Faheem Khan
Maysaa M. Al-Qurashi
Yu-Ming Chu
spellingShingle Rabia Hameed
Ghulam Mustafa
Amina Liaqat
Dumitru Baleanu
Faheem Khan
Maysaa M. Al-Qurashi
Yu-Ming Chu
A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme
Mathematical Problems in Engineering
author_facet Rabia Hameed
Ghulam Mustafa
Amina Liaqat
Dumitru Baleanu
Faheem Khan
Maysaa M. Al-Qurashi
Yu-Ming Chu
author_sort Rabia Hameed
title A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme
title_short A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme
title_full A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme
title_fullStr A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme
title_full_unstemmed A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme
title_sort new approach to increase the flexibility of curves and regular surfaces produced by 4-point ternary subdivision scheme
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2020-01-01
description In this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to three displacement vectors containing two shape parameters. We first study the characteristics of the new subdivision scheme analytically and then present numerical experiments to justify these analytical characteristics geometrically. We also extend the new derived scheme into its bivariate/tensor product version. This bivariate scheme is applicable on quadrilateral meshes to produce smooth limiting surfaces up to C3 continuity.
url http://dx.doi.org/10.1155/2020/6096545
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