Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme

The frequent use of subdivision schemes (SSs) for curve sketching can be seen in various papers published during recent years. These SSs provides efficient method for producing curves and surfaces. Further, these SSs can be divide in various categories but we focused only one of the type of SS calle...

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Main Authors: Iqbal, M., Abdul Karim, S.A., Shafie, A., Sarfraz, M.
Format: Article
Published: Springer Science and Business Media Deutschland GmbH 2022
Online Access:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85115389602&doi=10.1007%2f978-3-030-79606-8_1&partnerID=40&md5=400b4154ada44514c6169f0da3e9b943
http://eprints.utp.edu.my/28866/
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spelling my.utp.eprints.288662022-03-17T02:21:19Z Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme Iqbal, M. Abdul Karim, S.A. Shafie, A. Sarfraz, M. The frequent use of subdivision schemes (SSs) for curve sketching can be seen in various papers published during recent years. These SSs provides efficient method for producing curves and surfaces. Further, these SSs can be divide in various categories but we focused only one of the type of SS called interpolating SS. Here, we have discussed some properties of the �ternary 6-point interpolating subdivision scheme� introduced by Faheem and Mustafa 1 in 2008. The aim of this paper is to discuss about a geometric property called �Convexity� with the tension parameter μ and its effect on curve sketching. The scheme is analyzed and its convexity preserving property is proved using mathematical induction. Strictly convex initial data is used for the evaluation of the condition on the tension parameter μ. This condition shows that our scheme is more efficient than other schemes in terms of lower value of tension parameter μ. The significance of the condition is displayed through numerical applications. © 2022, Institute of Technology PETRONAS Sdn Bhd. Springer Science and Business Media Deutschland GmbH 2022 Article NonPeerReviewed https://www.scopus.com/inward/record.uri?eid=2-s2.0-85115389602&doi=10.1007%2f978-3-030-79606-8_1&partnerID=40&md5=400b4154ada44514c6169f0da3e9b943 Iqbal, M. and Abdul Karim, S.A. and Shafie, A. and Sarfraz, M. (2022) Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme. Studies in Systems, Decision and Control, 383 . pp. 1-23. http://eprints.utp.edu.my/28866/
institution Universiti Teknologi Petronas
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collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Petronas
content_source UTP Institutional Repository
url_provider http://eprints.utp.edu.my/
description The frequent use of subdivision schemes (SSs) for curve sketching can be seen in various papers published during recent years. These SSs provides efficient method for producing curves and surfaces. Further, these SSs can be divide in various categories but we focused only one of the type of SS called interpolating SS. Here, we have discussed some properties of the �ternary 6-point interpolating subdivision scheme� introduced by Faheem and Mustafa 1 in 2008. The aim of this paper is to discuss about a geometric property called �Convexity� with the tension parameter μ and its effect on curve sketching. The scheme is analyzed and its convexity preserving property is proved using mathematical induction. Strictly convex initial data is used for the evaluation of the condition on the tension parameter μ. This condition shows that our scheme is more efficient than other schemes in terms of lower value of tension parameter μ. The significance of the condition is displayed through numerical applications. © 2022, Institute of Technology PETRONAS Sdn Bhd.
format Article
author Iqbal, M.
Abdul Karim, S.A.
Shafie, A.
Sarfraz, M.
spellingShingle Iqbal, M.
Abdul Karim, S.A.
Shafie, A.
Sarfraz, M.
Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme
author_facet Iqbal, M.
Abdul Karim, S.A.
Shafie, A.
Sarfraz, M.
author_sort Iqbal, M.
title Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme
title_short Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme
title_full Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme
title_fullStr Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme
title_full_unstemmed Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme
title_sort convexity preservation of the ternary 6-point interpolating subdivision scheme
publisher Springer Science and Business Media Deutschland GmbH
publishDate 2022
url https://www.scopus.com/inward/record.uri?eid=2-s2.0-85115389602&doi=10.1007%2f978-3-030-79606-8_1&partnerID=40&md5=400b4154ada44514c6169f0da3e9b943
http://eprints.utp.edu.my/28866/
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