The Development of Log Aesthetic Patch and Its Projection onto the Plane
In this work, we introduce a new type of surface called the Log Aesthetic Patch (LAP). This surface is an extension of the Coons surface patch, in which the four boundary curves are either planar or spatial Log Aesthetic Curves (LACs). To identify its versatility, we approximated the hyperbolic para...
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| Format: | Article |
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/1/160 |
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| author | Yee Meng Teh R. U. Gobithaasan Kenjiro T. Miura Diya’ J. Albayari Wen Eng Ong |
| author_facet | Yee Meng Teh R. U. Gobithaasan Kenjiro T. Miura Diya’ J. Albayari Wen Eng Ong |
| author_sort | Yee Meng Teh |
| collection | DOAJ |
| description | In this work, we introduce a new type of surface called the Log Aesthetic Patch (LAP). This surface is an extension of the Coons surface patch, in which the four boundary curves are either planar or spatial Log Aesthetic Curves (LACs). To identify its versatility, we approximated the hyperbolic paraboloid to LAP using the information of lines of curvature (LoC). The outer part of the LoCs, which play a role as the boundary of the hyperbolic paraboloid, is replaced with LACs before constructing the LAP. Since LoCs are essential in shipbuilding for hot and cold bending processes, we investigated the LAP in terms of the LoC’s curvature, derivative of curvature, torsion, and Logarithmic Curvature Graph (LCG). The numerical results indicate that the LoCs for both surfaces possess monotonic curvatures. An advantage of LAP approximation over its original hyperbolic paraboloid is that the LoCs of LAP can be approximated to LACs, and hence the first derivative of curvatures for LoCs are monotonic, whereas they are non-monotonic for the hyperbolic paraboloid. This confirms that the LAP produced is indeed of high quality. Lastly, we project the LAP onto a plane using geodesic curvature to create strips that can be pasted together, mimicking hot and cold bending processes in the shipbuilding industry. |
| first_indexed | 2024-03-10T03:32:11Z |
| format | Article |
| id | doaj.art-bc8a2b7636d94730a3e8403d94b37e81 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:32:11Z |
| publishDate | 2022-01-01 |
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| series | Mathematics |
| spelling | doaj.art-bc8a2b7636d94730a3e8403d94b37e812023-11-23T11:55:03ZengMDPI AGMathematics2227-73902022-01-0110116010.3390/math10010160The Development of Log Aesthetic Patch and Its Projection onto the PlaneYee Meng Teh0R. U. Gobithaasan1Kenjiro T. Miura2Diya’ J. Albayari3Wen Eng Ong4School of Mathematical Sciences, Universiti Sains Malaysia, Minden 11800, MalaysiaSpecial Interest Group on Modelling & Data Analytics, Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, Kuala Nerus 21030, MalaysiaGraduate School of Science & Technology, Shizuoka University, Hamamatsu 432-8561, Shizuoka, JapanMathematics Department, Ibn Rushd National Academy-International Section IB, Amman 17126, JordanSchool of Mathematical Sciences, Universiti Sains Malaysia, Minden 11800, MalaysiaIn this work, we introduce a new type of surface called the Log Aesthetic Patch (LAP). This surface is an extension of the Coons surface patch, in which the four boundary curves are either planar or spatial Log Aesthetic Curves (LACs). To identify its versatility, we approximated the hyperbolic paraboloid to LAP using the information of lines of curvature (LoC). The outer part of the LoCs, which play a role as the boundary of the hyperbolic paraboloid, is replaced with LACs before constructing the LAP. Since LoCs are essential in shipbuilding for hot and cold bending processes, we investigated the LAP in terms of the LoC’s curvature, derivative of curvature, torsion, and Logarithmic Curvature Graph (LCG). The numerical results indicate that the LoCs for both surfaces possess monotonic curvatures. An advantage of LAP approximation over its original hyperbolic paraboloid is that the LoCs of LAP can be approximated to LACs, and hence the first derivative of curvatures for LoCs are monotonic, whereas they are non-monotonic for the hyperbolic paraboloid. This confirms that the LAP produced is indeed of high quality. Lastly, we project the LAP onto a plane using geodesic curvature to create strips that can be pasted together, mimicking hot and cold bending processes in the shipbuilding industry.https://www.mdpi.com/2227-7390/10/1/160log aesthetic curveslog aesthetic space curvessurface designCoons patchlines of curvature |
| spellingShingle | Yee Meng Teh R. U. Gobithaasan Kenjiro T. Miura Diya’ J. Albayari Wen Eng Ong The Development of Log Aesthetic Patch and Its Projection onto the Plane Mathematics log aesthetic curves log aesthetic space curves surface design Coons patch lines of curvature |
| title | The Development of Log Aesthetic Patch and Its Projection onto the Plane |
| title_full | The Development of Log Aesthetic Patch and Its Projection onto the Plane |
| title_fullStr | The Development of Log Aesthetic Patch and Its Projection onto the Plane |
| title_full_unstemmed | The Development of Log Aesthetic Patch and Its Projection onto the Plane |
| title_short | The Development of Log Aesthetic Patch and Its Projection onto the Plane |
| title_sort | development of log aesthetic patch and its projection onto the plane |
| topic | log aesthetic curves log aesthetic space curves surface design Coons patch lines of curvature |
| url | https://www.mdpi.com/2227-7390/10/1/160 |
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