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Leaf Surface Reconstruction Using a Hybrid Interpolation Finite Element Method

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Abstract

The goals of the research presented in this paper are first, construction a leaf surface from large real 3D scanned data points using a new hybrid interpolation finite element method so-called a hybrid Clough–Tocher cubic polynomial interpolation method (CT-CPI). Secondly, a comparison between the hybrid CT-CPI method and hybrid CT-Taylor series method (CT-TS) for the leaf surface reconstruction is presented. Realistic leaf surfaces models are essential for many applications in the sciences of plant, such as modelling spray and spreading droplet movement on the surface, photosynthesis and a canopy light environment or it can be implemented for visual purposes only. For these goals, a precise mathematical depiction of the boundary and surface is mandatory. Although an operative method is to apply either CT-TS or CT-CPI algorithm to recreate the surface of the leaf from 3D scanned data, difficulties occur when dealing with Anthurium leaves, which tend to have many branches. To solve this issue, we implemented interpolating in combined with the CT method. Our algorithm uses finite element methods to represent the surface as a mesh of triangles. Numerical results confirm that the CT-CPI techniques produces more realistic virtual representations of Anthurium leaves than using CT-TS method.

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Data Availability Statement

The data sets used during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The author would like to thank the reviewers for the valuable comments.

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  1. Department of Mathematics, Faculty of Science, Al-Balqa’ Applied University, P.O. Box 19117, Al Salt, Amman, Jordan

    Moa’ath N. Oqielat

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  1. Moa’ath N. Oqielat
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Correspondence to Moa’ath N. Oqielat.

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Oqielat, M.N. Leaf Surface Reconstruction Using a Hybrid Interpolation Finite Element Method. Int. J. Appl. Comput. Math 7, 232 (2021). https://doi.org/10.1007/s40819-021-01192-2

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  • DOI: https://doi.org/10.1007/s40819-021-01192-2

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