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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2651 |
| _version_ | 1827678083762618368 |
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| author | Wei Meng Caiyun Li Qianqian Liu |
| author_facet | Wei Meng Caiyun Li Qianqian Liu |
| author_sort | Wei Meng |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:56:39Z |
| format | Article |
| id | doaj.art-3a5620744fd84394be2e8df1058bbb22 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:56:39Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3a5620744fd84394be2e8df1058bbb222023-11-22T21:16:50ZengMDPI AGMathematics2227-73902021-10-01921265110.3390/math9212651Geometric Modeling of C-Bézier Curve and Surface with Shape ParametersWei Meng0Caiyun Li1Qianqian Liu2School of Mathematical Sciences, Dalian University of Technology, Panjin 124221, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Panjin 124221, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Panjin 124221, ChinaIn 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.https://www.mdpi.com/2227-7390/9/21/2651C-Bézier basisgeometric continuityparametric continuityshape parameters |
| spellingShingle | Wei Meng Caiyun Li Qianqian Liu Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters Mathematics C-Bézier basis geometric continuity parametric continuity shape parameters |
| title | 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_short | Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters |
| title_sort | geometric modeling of c bezier curve and surface with shape parameters |
| topic | C-Bézier basis geometric continuity parametric continuity shape parameters |
| url | https://www.mdpi.com/2227-7390/9/21/2651 |
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