New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral Segment
This work presents the new cubic trigonometric Bézier-type functions with shape parameter. Basis functions and the curve satisfy all properties of classical Bézier curve-like partition of unity, symmetric property, linear independent, geometric invariance, and convex hull property and have been prov...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6330649 |
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| _version_ | 1832545914606059520 |
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| author | Abdul Majeed Muhammad Abbas Amna Abdul Sittar Mohsin Kamran Saba Tahseen Homan Emadifar |
| author_facet | Abdul Majeed Muhammad Abbas Amna Abdul Sittar Mohsin Kamran Saba Tahseen Homan Emadifar |
| author_sort | Abdul Majeed |
| collection | DOAJ |
| description | This work presents the new cubic trigonometric Bézier-type functions with shape parameter. Basis functions and the curve satisfy all properties of classical Bézier curve-like partition of unity, symmetric property, linear independent, geometric invariance, and convex hull property and have been proved. The C3 and G3 continuity conditions between two curve segments have also been achieved. To check the applicability of proposed functions, different types of open and closed curves have been constructed. The effect of shape parameter and control points has been observed. It is observed that, by decreasing the value of shape parameter, the curve moves toward the control polygon and vice versa. The CT-Bézier curve is closer to the cubic Bézier curve for a fixed value of shape parameter. The proposed CT-Bézier curve can be used to represent ellipse. Using proposed basis functions, we have constructed the spiral segment which is very useful to construct fair curves and desirable to design trajectories of mobile robots, highway, and railway routes’ designing. |
| format | Article |
| id | doaj-art-430b065a09f249238bd0e496c4a5660f |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-430b065a09f249238bd0e496c4a5660f2025-02-03T07:24:25ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/63306496330649New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral SegmentAbdul Majeed0Muhammad Abbas1Amna Abdul Sittar2Mohsin Kamran3Saba Tahseen4Homan Emadifar5Department of Mathematics, Division of Science and Technology, University of Education, Lahore, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, Division of Science and Technology, University of Education, Lahore, PakistanDepartment of Mathematics, Division of Science and Technology, University of Education, Lahore, PakistanDepartment of Mathematics, Division of Science and Technology, University of Education, Lahore, PakistanDepartment of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, IranThis work presents the new cubic trigonometric Bézier-type functions with shape parameter. Basis functions and the curve satisfy all properties of classical Bézier curve-like partition of unity, symmetric property, linear independent, geometric invariance, and convex hull property and have been proved. The C3 and G3 continuity conditions between two curve segments have also been achieved. To check the applicability of proposed functions, different types of open and closed curves have been constructed. The effect of shape parameter and control points has been observed. It is observed that, by decreasing the value of shape parameter, the curve moves toward the control polygon and vice versa. The CT-Bézier curve is closer to the cubic Bézier curve for a fixed value of shape parameter. The proposed CT-Bézier curve can be used to represent ellipse. Using proposed basis functions, we have constructed the spiral segment which is very useful to construct fair curves and desirable to design trajectories of mobile robots, highway, and railway routes’ designing.http://dx.doi.org/10.1155/2021/6330649 |
| spellingShingle | Abdul Majeed Muhammad Abbas Amna Abdul Sittar Mohsin Kamran Saba Tahseen Homan Emadifar New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral Segment Journal of Mathematics |
| title | New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral Segment |
| title_full | New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral Segment |
| title_fullStr | New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral Segment |
| title_full_unstemmed | New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral Segment |
| title_short | New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral Segment |
| title_sort | new cubic trigonometric bezier like functions with shape parameter curvature and its spiral segment |
| url | http://dx.doi.org/10.1155/2021/6330649 |
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