Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parameters
Abstract A Bézier model with shape parameters is one of the momentous research topics in geometric modeling and computer-aided geometric design. In this study, a new recursive formula in explicit expression is constructed that produces the generalized blended trigonometric Bernstein (or GBT-Bernstei...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-03001-4 |
| _version_ | 1828893586976931840 |
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| author | Sidra Maqsood Muhammad Abbas Kenjiro T. Miura Abdul Majeed Azhar Iqbal |
| author_facet | Sidra Maqsood Muhammad Abbas Kenjiro T. Miura Abdul Majeed Azhar Iqbal |
| author_sort | Sidra Maqsood |
| collection | DOAJ |
| description | Abstract A Bézier model with shape parameters is one of the momentous research topics in geometric modeling and computer-aided geometric design. In this study, a new recursive formula in explicit expression is constructed that produces the generalized blended trigonometric Bernstein (or GBT-Bernstein, for short) polynomial functions of degree m. Using these basis functions, generalized blended trigonometric Bézier (or GBT-Bézier, for short) curves with two shape parameters are also constructed, and their geometric features and applications to curve modeling are discussed. The newly created curves share all geometric properties of Bézier curves except the shape modification property, which is superior to the classical Bézier. The C 3 $C^{3}$ and G 2 $G^{2}$ continuity conditions of two pieces of GBT-Bézier curves are also part of this study. Moreover, in contrast with Bézier curves, our generalization gives more shape adjustability in curve designing. Several examples are presented to show that the proposed method has high applied values in geometric modeling. |
| first_indexed | 2024-12-13T13:55:56Z |
| format | Article |
| id | doaj.art-690c6ccd82eb417081b5444cef251c9d |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-13T13:55:56Z |
| publishDate | 2020-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-690c6ccd82eb417081b5444cef251c9d2022-12-21T23:42:54ZengSpringerOpenAdvances in Difference Equations1687-18472020-10-012020111810.1186/s13662-020-03001-4Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parametersSidra Maqsood0Muhammad Abbas1Kenjiro T. Miura2Abdul Majeed3Azhar Iqbal4Department of Mathematics, University of SargodhaDepartment of Mathematics, University of SargodhaDepartment of Mechanical Engineering, Shizuoka UniversityDepartment of Mathematics, University of EducationDepartment of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd UniversityAbstract A Bézier model with shape parameters is one of the momentous research topics in geometric modeling and computer-aided geometric design. In this study, a new recursive formula in explicit expression is constructed that produces the generalized blended trigonometric Bernstein (or GBT-Bernstein, for short) polynomial functions of degree m. Using these basis functions, generalized blended trigonometric Bézier (or GBT-Bézier, for short) curves with two shape parameters are also constructed, and their geometric features and applications to curve modeling are discussed. The newly created curves share all geometric properties of Bézier curves except the shape modification property, which is superior to the classical Bézier. The C 3 $C^{3}$ and G 2 $G^{2}$ continuity conditions of two pieces of GBT-Bézier curves are also part of this study. Moreover, in contrast with Bézier curves, our generalization gives more shape adjustability in curve designing. Several examples are presented to show that the proposed method has high applied values in geometric modeling.http://link.springer.com/article/10.1186/s13662-020-03001-4GBT-Bernstein-like polynomial functionsGBT-Bézier curveProperties of GBT-Bézier curvesContinuities of GBT-Bézier curvesShape parameters |
| spellingShingle | Sidra Maqsood Muhammad Abbas Kenjiro T. Miura Abdul Majeed Azhar Iqbal Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parameters Advances in Difference Equations GBT-Bernstein-like polynomial functions GBT-Bézier curve Properties of GBT-Bézier curves Continuities of GBT-Bézier curves Shape parameters |
| title | Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parameters |
| title_full | Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parameters |
| title_fullStr | Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parameters |
| title_full_unstemmed | Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parameters |
| title_short | Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parameters |
| title_sort | geometric modeling and applications of generalized blended trigonometric bezier curves with shape parameters |
| topic | GBT-Bernstein-like polynomial functions GBT-Bézier curve Properties of GBT-Bézier curves Continuities of GBT-Bézier curves Shape parameters |
| url | http://link.springer.com/article/10.1186/s13662-020-03001-4 |
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