Explicit Continuity Conditions for G<sup>1</sup> Connection of S-<i>λ</i> Curves and Surfaces
The S-<i>λ</i> model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is due to its good geometric properties such as symmetry, shape adjustable property. With the aim to solve the problem that complex S-<...
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MDPI AG
2020-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/8/1359 |
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| author | Gang Hu Huinan Li Muhammad Abbas Kenjiro T. Miura Guoling Wei |
| author_facet | Gang Hu Huinan Li Muhammad Abbas Kenjiro T. Miura Guoling Wei |
| author_sort | Gang Hu |
| collection | DOAJ |
| description | The S-<i>λ</i> model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is due to its good geometric properties such as symmetry, shape adjustable property. With the aim to solve the problem that complex S-<i>λ</i> curves and surfaces cannot be constructed by a single curve and surface, the explicit continuity conditions for G<sup>1</sup> connection of S-<i>λ</i> curves and surfaces are investigated in this paper. On the basis of linear independence and terminal properties of S-<i>λ</i> basis functions, the conditions of G<sup>1</sup> geometric continuity between two adjacent S-<i>λ</i> curves and surfaces are proposed, respectively. Modeling examples imply that the continuity conditions proposed in this paper are easy and effective, which indicate that the S-<i>λ</i> curves and surfaces can be used as a powerful supplement of complex curves and surfaces design in computer aided design/computer aided manufacturing (CAD/CAM) system. |
| first_indexed | 2024-03-10T17:29:37Z |
| format | Article |
| id | doaj.art-53fc40a52fe346fbad00f39fe19b3695 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T17:29:37Z |
| publishDate | 2020-08-01 |
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| spelling | doaj.art-53fc40a52fe346fbad00f39fe19b36952023-11-20T10:04:11ZengMDPI AGMathematics2227-73902020-08-0188135910.3390/math8081359Explicit Continuity Conditions for G<sup>1</sup> Connection of S-<i>λ</i> Curves and SurfacesGang Hu0Huinan Li1Muhammad Abbas2Kenjiro T. Miura3Guoling Wei4Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, ChinaDepartment of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, ChinaDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8011, JapanDepartment of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, ChinaThe S-<i>λ</i> model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is due to its good geometric properties such as symmetry, shape adjustable property. With the aim to solve the problem that complex S-<i>λ</i> curves and surfaces cannot be constructed by a single curve and surface, the explicit continuity conditions for G<sup>1</sup> connection of S-<i>λ</i> curves and surfaces are investigated in this paper. On the basis of linear independence and terminal properties of S-<i>λ</i> basis functions, the conditions of G<sup>1</sup> geometric continuity between two adjacent S-<i>λ</i> curves and surfaces are proposed, respectively. Modeling examples imply that the continuity conditions proposed in this paper are easy and effective, which indicate that the S-<i>λ</i> curves and surfaces can be used as a powerful supplement of complex curves and surfaces design in computer aided design/computer aided manufacturing (CAD/CAM) system.https://www.mdpi.com/2227-7390/8/8/1359S-<i>λ</i> basis functionsS-<i>λ</i> curves and surfacesgeometric continuity conditionscomplex curve and surface design |
| spellingShingle | Gang Hu Huinan Li Muhammad Abbas Kenjiro T. Miura Guoling Wei Explicit Continuity Conditions for G<sup>1</sup> Connection of S-<i>λ</i> Curves and Surfaces Mathematics S-<i>λ</i> basis functions S-<i>λ</i> curves and surfaces geometric continuity conditions complex curve and surface design |
| title | Explicit Continuity Conditions for G<sup>1</sup> Connection of S-<i>λ</i> Curves and Surfaces |
| title_full | Explicit Continuity Conditions for G<sup>1</sup> Connection of S-<i>λ</i> Curves and Surfaces |
| title_fullStr | Explicit Continuity Conditions for G<sup>1</sup> Connection of S-<i>λ</i> Curves and Surfaces |
| title_full_unstemmed | Explicit Continuity Conditions for G<sup>1</sup> Connection of S-<i>λ</i> Curves and Surfaces |
| title_short | Explicit Continuity Conditions for G<sup>1</sup> Connection of S-<i>λ</i> Curves and Surfaces |
| title_sort | explicit continuity conditions for g sup 1 sup connection of s i λ i curves and surfaces |
| topic | S-<i>λ</i> basis functions S-<i>λ</i> curves and surfaces geometric continuity conditions complex curve and surface design |
| url | https://www.mdpi.com/2227-7390/8/8/1359 |
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