Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters

In order to solve the problem of geometric design and architectural design of complex engineering surface, we introduce the parametric and geometric continuity constraints of generalized C-Bézier curves and surfaces with shape parameters. Firstly, based on C-Bézier basis with parameters, we study th...

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Autores principales:	Wei Meng, Caiyun Li, Qianqian Liu
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	C-Bézier basis geometric continuity parametric continuity shape parameters Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/3a5620744fd84394be2e8df1058bbb22
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id	oai:doaj.org-article:3a5620744fd84394be2e8df1058bbb22
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spelling	oai:doaj.org-article:3a5620744fd84394be2e8df1058bbb222021-11-11T18:13:47ZGeometric Modeling of C-Bézier Curve and Surface with Shape Parameters10.3390/math92126512227-7390https://doaj.org/article/3a5620744fd84394be2e8df1058bbb222021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2651https://doaj.org/toc/2227-7390In order to solve the problem of geometric design and architectural design of complex engineering surface, we introduce the parametric and geometric continuity constraints of generalized C-Bézier curves and surfaces with shape parameters. Firstly, based on C-Bézier basis with parameters, we study the constraints of the control points of the curves needed to be satisfied when connecting them. Moreover, we study the continuity conditions between two adjacent C-Bézier surfaces with parameters. By the continuity conditions and different shape parameters, the curve and surface can be changed easily and be more flexible without altering its control points. Therefore, by adjusting the values of shape parameters, the curve and surface still preserve its characteristics and geometrical configuration. Some graphical examples ensure that the proposed method greatly improves the ability to design complex curves and surfaces and easy to implement.Wei MengCaiyun LiQianqian LiuMDPI AGarticleC-Bézier basisgeometric continuityparametric continuityshape parametersMathematicsQA1-939ENMathematics, Vol 9, Iss 2651, p 2651 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	C-Bézier basis geometric continuity parametric continuity shape parameters Mathematics QA1-939
spellingShingle	C-Bézier basis geometric continuity parametric continuity shape parameters Mathematics QA1-939 Wei Meng Caiyun Li Qianqian Liu Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters
description	In order to solve the problem of geometric design and architectural design of complex engineering surface, we introduce the parametric and geometric continuity constraints of generalized C-Bézier curves and surfaces with shape parameters. Firstly, based on C-Bézier basis with parameters, we study the constraints of the control points of the curves needed to be satisfied when connecting them. Moreover, we study the continuity conditions between two adjacent C-Bézier surfaces with parameters. By the continuity conditions and different shape parameters, the curve and surface can be changed easily and be more flexible without altering its control points. Therefore, by adjusting the values of shape parameters, the curve and surface still preserve its characteristics and geometrical configuration. Some graphical examples ensure that the proposed method greatly improves the ability to design complex curves and surfaces and easy to implement.
format	article
author	Wei Meng Caiyun Li Qianqian Liu
author_facet	Wei Meng Caiyun Li Qianqian Liu
author_sort	Wei Meng
title	Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters
title_short	Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters
title_full	Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters
title_fullStr	Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters
title_full_unstemmed	Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters
title_sort	geometric modeling of c-bézier curve and surface with shape parameters
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/3a5620744fd84394be2e8df1058bbb22
work_keys_str_mv	AT weimeng geometricmodelingofcbeziercurveandsurfacewithshapeparameters AT caiyunli geometricmodelingofcbeziercurveandsurfacewithshapeparameters AT qianqianliu geometricmodelingofcbeziercurveandsurfacewithshapeparameters
_version_	1718431877494210560

Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters

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