A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes

Subdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after <i>k</i>-...

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Main Authors: Aamir Shahzad, Faheem Khan, Abdul Ghaffar, Ghulam Mustafa, Kottakkaran Sooppy Nisar, Dumitru Baleanu
Format: Article
Language:English
Published: MDPI AG 2020-01-01
Series:Symmetry
Subjects:
Online Access:https://www.mdpi.com/2073-8994/12/1/66
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spelling doaj-74b04e915c984cbf9f1c649785a61ac72020-11-25T02:20:25ZengMDPI AGSymmetry2073-89942020-01-011216610.3390/sym12010066sym12010066A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision SchemesAamir Shahzad0Faheem Khan1Abdul Ghaffar2Ghulam Mustafa3Kottakkaran Sooppy Nisar4Dumitru Baleanu5Department of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematical Sciences, BUITEMS, Quetta 87300, PakistanDepartment of Mathematics, The Islamia University of bahawalpur, Punjab 63100, PakistanDepartment of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi ArabiaDepartment of Mathematics, Cankaya University, Ankara 06530, TurkeySubdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after <i>k</i>-fold subdivisions. In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modification of the results given by Mustafa et al in 2006. This algorithm is very useful for implementation of the parametrization.https://www.mdpi.com/2073-8994/12/1/66numerical analysisalgorithmsubdivision schemeserror boundssubdivision depth
collection DOAJ
language English
format Article
sources DOAJ
author Aamir Shahzad
Faheem Khan
Abdul Ghaffar
Ghulam Mustafa
Kottakkaran Sooppy Nisar
Dumitru Baleanu
spellingShingle Aamir Shahzad
Faheem Khan
Abdul Ghaffar
Ghulam Mustafa
Kottakkaran Sooppy Nisar
Dumitru Baleanu
A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes
Symmetry
numerical analysis
algorithm
subdivision schemes
error bounds
subdivision depth
author_facet Aamir Shahzad
Faheem Khan
Abdul Ghaffar
Ghulam Mustafa
Kottakkaran Sooppy Nisar
Dumitru Baleanu
author_sort Aamir Shahzad
title A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes
title_short A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes
title_full A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes
title_fullStr A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes
title_full_unstemmed A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes
title_sort novel numerical algorithm to estimate the subdivision depth of binary subdivision schemes
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2020-01-01
description Subdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after <i>k</i>-fold subdivisions. In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modification of the results given by Mustafa et al in 2006. This algorithm is very useful for implementation of the parametrization.
topic numerical analysis
algorithm
subdivision schemes
error bounds
subdivision depth
url https://www.mdpi.com/2073-8994/12/1/66
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