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Construction of Generalized Hybrid Trigonometric Bézier Surfaces with Shape Parameters and Their Applications

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Abstract

To tackle the problem of modeling and shape designing of complex engineering surfaces, the continuity constraints between generalized hybrid trigonometric Bézier (GHT-Bézier for short) surfaces with three different shape parameters are proposed in this study. Initially, we describe the basic properties of GHT-Bézier surface and influence of shape parameters. Some special triangular surfaces and biangular surfaces by varying the different values of shape control parameters are described. \(G^{2}\) continuity conditions in various directions between two adjacent GHT-Bézier surfaces with graphical representation are studied. Finally, the construction of some free-form complex engineering surfaces such as cylindrical surface, swung surface, ruled surface, and swept surface by using GHT-Bézier surfaces is also studied. Some graphical examples ensure that the proposed method greatly improves the ability to design complex surfaces and is easy to implement.

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Acknowledgements

This research was supported by Ministry of Higher Education Malaysia through Fundamental Research Grant Scheme (FRGS/1/2020/STG06/USM/03/1) and School of Mathematical Sciences, Universiti Sains Malaysia. The authors are very grateful to the anonymous referees for their valuable suggestion.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia

    Samia Bibi & Md Yushalify Misro

  2. Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan

    Muhammad Abbas & Tahir Nazir

  3. Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan

    Abdul Majeed

Authors
  1. Samia Bibi
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  2. Muhammad Abbas
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  3. Md Yushalify Misro
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  4. Abdul Majeed
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  5. Tahir Nazir
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Correspondence to Muhammad Abbas, Md Yushalify Misro or Abdul Majeed.

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Bibi, S., Abbas, M., Misro, M.Y. et al. Construction of Generalized Hybrid Trigonometric Bézier Surfaces with Shape Parameters and Their Applications. J Math Imaging Vis 63, 1118–1142 (2021). https://doi.org/10.1007/s10851-021-01046-y

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  • DOI: https://doi.org/10.1007/s10851-021-01046-y

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