Geometric modeling of some engineering GBT-Bézier surfaces with shape parameters and their applications

Abstract This study is based on some C 1 $C^{1}$ , C 2 $C^{2}$ , and C 3 $C^{3}$ continuous computer-based surfaces that are modeled by using generalized blended trigonometric Bézier (shortly, GBT-Bézier) curves with shape parameters. Initially, generalized blended trigonometric Bernstein-like (shor...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Sidra Maqsood, Muhammad Abbas, Kenjiro T. Miura, Abdul Majeed, Samia BiBi, Tahir Nazir
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Generalized blended trigonometric Bernstein-like basis Shape parameters GBT-Bézier curves Parametric continuity GBT-Bézier surfaces Computer-based engineering surfaces Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/558bc660883b476aa0dbf881ca632314
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:558bc660883b476aa0dbf881ca632314
record_format	dspace
spelling	oai:doaj.org-article:558bc660883b476aa0dbf881ca6323142021-11-14T12:10:25ZGeometric modeling of some engineering GBT-Bézier surfaces with shape parameters and their applications10.1186/s13662-021-03643-y1687-1847https://doaj.org/article/558bc660883b476aa0dbf881ca6323142021-11-01T00:00:00Zhttps://doi.org/10.1186/s13662-021-03643-yhttps://doaj.org/toc/1687-1847Abstract This study is based on some C 1 $C^{1}$ , C 2 $C^{2}$ , and C 3 $C^{3}$ continuous computer-based surfaces that are modeled by using generalized blended trigonometric Bézier (shortly, GBT-Bézier) curves with shape parameters. Initially, generalized blended trigonometric Bernstein-like (shortly, GBTB) basis functions with two shape parameters are derived in explicit expression which satisfied the basic geometric features of the traditional Bernstein basis functions. Moreover, the GBT-Bézier curves and tensor product GBT-Bézier surfaces with two shape parameters are also presented. All geometric features of the proposed GBT-Bézier curves and surfaces are similar to the traditional Bézier curves and surfaces, but the shape-adjustment is the additional feature that the traditional Bézier curves and surfaces do not hold. Finally, a class of some complex computer-based engineering surfaces via GBT-Bézier curves with shape parameters is presented. In addition, two adjacent GBT-Bézier surfaces segments are connected by higher C 2 $C^{2}$ and C 3 $C^{3}$ continuity constraints than the existing only C 1 $C^{1}$ shape adjustable Bézier surfaces. Some practical examples are provided to show the efficiency of the proposed scheme and to prove it as another powerful way for the construction and modeling of various complex composite computer-based engineering surfaces using higher-order continuities.Sidra MaqsoodMuhammad AbbasKenjiro T. MiuraAbdul MajeedSamia BiBiTahir NazirSpringerOpenarticleGeneralized blended trigonometric Bernstein-like basisShape parametersGBT-Bézier curvesParametric continuityGBT-Bézier surfacesComputer-based engineering surfacesMathematicsQA1-939ENAdvances in Difference Equations, Vol 2021, Iss 1, Pp 1-36 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Generalized blended trigonometric Bernstein-like basis Shape parameters GBT-Bézier curves Parametric continuity GBT-Bézier surfaces Computer-based engineering surfaces Mathematics QA1-939
spellingShingle	Generalized blended trigonometric Bernstein-like basis Shape parameters GBT-Bézier curves Parametric continuity GBT-Bézier surfaces Computer-based engineering surfaces Mathematics QA1-939 Sidra Maqsood Muhammad Abbas Kenjiro T. Miura Abdul Majeed Samia BiBi Tahir Nazir Geometric modeling of some engineering GBT-Bézier surfaces with shape parameters and their applications
description	Abstract This study is based on some C 1 $C^{1}$ , C 2 $C^{2}$ , and C 3 $C^{3}$ continuous computer-based surfaces that are modeled by using generalized blended trigonometric Bézier (shortly, GBT-Bézier) curves with shape parameters. Initially, generalized blended trigonometric Bernstein-like (shortly, GBTB) basis functions with two shape parameters are derived in explicit expression which satisfied the basic geometric features of the traditional Bernstein basis functions. Moreover, the GBT-Bézier curves and tensor product GBT-Bézier surfaces with two shape parameters are also presented. All geometric features of the proposed GBT-Bézier curves and surfaces are similar to the traditional Bézier curves and surfaces, but the shape-adjustment is the additional feature that the traditional Bézier curves and surfaces do not hold. Finally, a class of some complex computer-based engineering surfaces via GBT-Bézier curves with shape parameters is presented. In addition, two adjacent GBT-Bézier surfaces segments are connected by higher C 2 $C^{2}$ and C 3 $C^{3}$ continuity constraints than the existing only C 1 $C^{1}$ shape adjustable Bézier surfaces. Some practical examples are provided to show the efficiency of the proposed scheme and to prove it as another powerful way for the construction and modeling of various complex composite computer-based engineering surfaces using higher-order continuities.
format	article
author	Sidra Maqsood Muhammad Abbas Kenjiro T. Miura Abdul Majeed Samia BiBi Tahir Nazir
author_facet	Sidra Maqsood Muhammad Abbas Kenjiro T. Miura Abdul Majeed Samia BiBi Tahir Nazir
author_sort	Sidra Maqsood
title	Geometric modeling of some engineering GBT-Bézier surfaces with shape parameters and their applications
title_short	Geometric modeling of some engineering GBT-Bézier surfaces with shape parameters and their applications
title_full	Geometric modeling of some engineering GBT-Bézier surfaces with shape parameters and their applications
title_fullStr	Geometric modeling of some engineering GBT-Bézier surfaces with shape parameters and their applications
title_full_unstemmed	Geometric modeling of some engineering GBT-Bézier surfaces with shape parameters and their applications
title_sort	geometric modeling of some engineering gbt-bézier surfaces with shape parameters and their applications
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/558bc660883b476aa0dbf881ca632314
work_keys_str_mv	AT sidramaqsood geometricmodelingofsomeengineeringgbtbeziersurfaceswithshapeparametersandtheirapplications AT muhammadabbas geometricmodelingofsomeengineeringgbtbeziersurfaceswithshapeparametersandtheirapplications AT kenjirotmiura geometricmodelingofsomeengineeringgbtbeziersurfaceswithshapeparametersandtheirapplications AT abdulmajeed geometricmodelingofsomeengineeringgbtbeziersurfaceswithshapeparametersandtheirapplications AT samiabibi geometricmodelingofsomeengineeringgbtbeziersurfaceswithshapeparametersandtheirapplications AT tahirnazir geometricmodelingofsomeengineeringgbtbeziersurfaceswithshapeparametersandtheirapplications
_version_	1718429402463731712

Geometric modeling of some engineering GBT-Bézier surfaces with shape parameters and their applications

Ejemplares similares