A Novel Approach of Hybrid Trigonometric Bézier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation Surfaces
The modeling of Bézier curves and surfaces with their shape parameters is the most popular area of research in computer aided geometric design/computer aided manufacturing (CAGD/CAM) due to their geometric characteristics. In this paper, we propose an important idea to tackle the problem...
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| Format: | Article |
| Language: | English |
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IEEE
2019-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8901109/ |
| _version_ | 1818416111460286464 |
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| author | Samia BiBi Muhammad Abbas Md Yushalify Misro Gang Hu |
| author_facet | Samia BiBi Muhammad Abbas Md Yushalify Misro Gang Hu |
| author_sort | Samia BiBi |
| collection | DOAJ |
| description | The modeling of Bézier curves and surfaces with their shape parameters is the most popular area of research in computer aided geometric design/computer aided manufacturing (CAGD/CAM) due to their geometric characteristics. In this paper, we propose an important idea to tackle the problem in construction of some engineering symmetric revolutionary curves and symmetric rotation surfaces by using the generalized hybrid trigonometric Bézier (or GHT-Bézier, for short) curve. The shape of the curves and surfaces can be modified by the alteration of shape parameters. The free-form complex curves using GHT-Bézier curves with constraints of parametric continuity are constructed. Finally, by using the GHT-Bézier curves with their continuity conditions and symmetric formulas, we construct different types of symmetric figures, symmetric revolutionary curves and symmetric rotation surfaces in R<sup>2</sup> and R<sup>3</sup> to show the efficiency of modeling. These symmetric examples show that the proposed method is time saving, effective and efficient in construction of complex engineering symmetric curves and surfaces. |
| first_indexed | 2024-12-14T11:45:42Z |
| format | Article |
| id | doaj.art-9c0c90f5cb87427ba33f8a145e5f4166 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-14T11:45:42Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-9c0c90f5cb87427ba33f8a145e5f41662022-12-21T23:02:35ZengIEEEIEEE Access2169-35362019-01-01716577916579210.1109/ACCESS.2019.29534968901109A Novel Approach of Hybrid Trigonometric Bézier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation SurfacesSamia BiBi0Muhammad Abbas1https://orcid.org/0000-0002-0491-1528Md Yushalify Misro2Gang Hu3Department of Mathematics, University of Sargodha, Sargodha, PakistanDepartment of Mathematics, University of Sargodha, Sargodha, PakistanSchool of Mathematical Sciences, Universiti Sains Malaysia, Penang, MalaysiaDepartment of Applied Mathematics, Xi’an University of Technology, Xi’an, ChinaThe modeling of Bézier curves and surfaces with their shape parameters is the most popular area of research in computer aided geometric design/computer aided manufacturing (CAGD/CAM) due to their geometric characteristics. In this paper, we propose an important idea to tackle the problem in construction of some engineering symmetric revolutionary curves and symmetric rotation surfaces by using the generalized hybrid trigonometric Bézier (or GHT-Bézier, for short) curve. The shape of the curves and surfaces can be modified by the alteration of shape parameters. The free-form complex curves using GHT-Bézier curves with constraints of parametric continuity are constructed. Finally, by using the GHT-Bézier curves with their continuity conditions and symmetric formulas, we construct different types of symmetric figures, symmetric revolutionary curves and symmetric rotation surfaces in R<sup>2</sup> and R<sup>3</sup> to show the efficiency of modeling. These symmetric examples show that the proposed method is time saving, effective and efficient in construction of complex engineering symmetric curves and surfaces.https://ieeexplore.ieee.org/document/8901109/GHT-Bernstein basis functionsGHT-Bézier curvesparametric continuityshape parameterssymmetric revolutionary curvessymmetric rotation surfaces |
| spellingShingle | Samia BiBi Muhammad Abbas Md Yushalify Misro Gang Hu A Novel Approach of Hybrid Trigonometric Bézier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation Surfaces IEEE Access GHT-Bernstein basis functions GHT-Bézier curves parametric continuity shape parameters symmetric revolutionary curves symmetric rotation surfaces |
| title | A Novel Approach of Hybrid Trigonometric Bézier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation Surfaces |
| title_full | A Novel Approach of Hybrid Trigonometric Bézier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation Surfaces |
| title_fullStr | A Novel Approach of Hybrid Trigonometric Bézier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation Surfaces |
| title_full_unstemmed | A Novel Approach of Hybrid Trigonometric Bézier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation Surfaces |
| title_short | A Novel Approach of Hybrid Trigonometric Bézier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation Surfaces |
| title_sort | novel approach of hybrid trigonometric b x00e9 zier curve to the modeling of symmetric revolutionary curves and symmetric rotation surfaces |
| topic | GHT-Bernstein basis functions GHT-Bézier curves parametric continuity shape parameters symmetric revolutionary curves symmetric rotation surfaces |
| url | https://ieeexplore.ieee.org/document/8901109/ |
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