Modelling leaf surface reconstruction using Bernstein polynomials method
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Modelling leaf surface reconstruction using Bernstein polynomials method Moa’ath N. Oqielat1 Received: 30 June 2020 / Revised: 30 June 2020 / Accepted: 17 August 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract In this research paper, we adapt for the first time Bernstein polynomials for reconstructing a continuous differentiable surfaces of a real leaf from 3D scanned data points. As such model is essential for modelling the plant architecture, fluid movement, and biological structure such as photosynthesis. To evaluate the accuracy of the proposed method, we apply it on a real scattered data points collected from a genuine Frangipani and Anthurium leaf surface using a laser scanner. We found that the Bernstein polynomials develop precise model of the leaf surface. Keywords Interpolation · Surface fitting · Leaf surface model · Bernstein polynomials · 65Zxx Mathematics Subject Classification 65Zxx
1 Introduction The application of surface fitting techniques to model the leaf surface is the main goal of the research given in this article, for instant, the application of water droplet or pesticide spreading on the leaf surface and modelling virtual plant; for more details, see (Dorr et al. 2014; Lisa et al. 2016; Oqielat et al. 2011; El-Ajou et al. 2019). Recently, many researchers have been interest in modelling leaves surfaces such as Kempthorne et al. (2015a) applied the discrete smoothing D 2 -splines to model the cotton and wheat leaf. Oqielat et al. (2017) and Oqielat and Ogilat (2018) introduced a model for two types of leaves, see Fig. 1, using either Gaussian or Hardy’s multiquadrics RBF interpolant and then the author extended his model to include linear or cubic term to the RBF (Oqielat 2018). Additionally, Oqielat et al. (2009,2007) and Oqielat (2019, 2020) proposed a new hybrid clough-Tocher (CT) and radial basis function (RBF) method for modelling leaves surfaces. Furthermore, Oqielat (2018) compared many surface fitting techniques to reconstruct the surfaces of leaves and conclude
Communicated by Eduardo Souza de Cursi.
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Moa’ath N. Oqielat [email protected] Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan 0123456789().: V,-vol
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M. N. Oqielat
Fig. 1 Photos of the a Frangipani and b Anthurium leaf
that the hybrid RBF-CT method produces more accurate leaf model. More models introduced by Turner et al. 2010; Belward et al. 2008; Oqielat et al. 2017; Kempthorne et al. 2015b; Loch et al. 2003. In this paper, we implement the interpolating Bernstein polynomials to reconstruct the leaf surface from 3D scattered points. This paper composed of four sections. In Sect. 2, an outline of the Bernstein polynomials is introduced. In Sect. 3, the Bernstein polynomials interpolant method is employed to construct a surface model for the Frangipani and Anthurium leaf as well as the choice of the orthogonal distance regression plane as a reference plane for the data of the leaf is explained. Further
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