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Original articles

Scattered data approximation using radial basis function with a cubic polynomial reproduction for modelling leaf surface

Pages 331-337 | Received 13 Mar 2018, Accepted 13 Apr 2018, Published online: 10 May 2018

References

  • Dorr G, Kempthorne D, Mayo L, et al. Towards a model of spray–canopy interactions: interception, shatter, bounce and retention of droplets on horizontal leaves. Ecol Model. 2014;290:94–101. doi: 10.1016/j.ecolmodel.2013.11.002
  • Lisa C, McCue S, Moroney T, et al. Simulating droplet motion on virtual leaf surfaces. R Soc Open Sci. 2016;2: 1–17.
  • Oqielat M, Turner I, Belward J, et al. Modelling water droplet movements on a leaf surface. Math Comput Simulat. 2011;81:1553–1571. doi: 10.1016/j.matcom.2010.09.003
  • Loch B. Surface fitting for the modelling of plant leaves [Ph.D. thesis]. Brisbane: University of Queensland; 2004.
  • Oqielat M, Turner I, Belward J. A hybrid Clough-Tocher method for surface fitting with application to leaf data. Appl Math Model. 2009;33:2582–2595. doi: 10.1016/j.apm.2008.07.023
  • Oqielat MN, Belward JA, Turner IW, et al. A hybrid Clough–Tocher radial basis function method for modelling leaf surfaces. In: Oxley L, Kulasiri D, editors. MODSIM 2007: International Congress on Modelling and Simulation, December 2007. Model Simu Soc Aust New; 2007. p. 400–406.
  • Oqielat M. Surface fitting methods for modelling leaf surface from scanned data. J King Saud Univ – Sci. Forthcoming.
  • Oqielat M, Ogilat O, Al-Oushoush N, et al. Radial basis function method for modelling leaf surface from real leaf data. Aust J Basic Appl Sci. 2017;11(13):103–111.
  • Oqiela M, Ogilat O. Application of Gaussion radial basis function with cubic polynomial for modelling leaf surface. J Math Anal. 2018;9(2):78–87.
  • Oqielat M. Comparison of surface fitting methods for modelling leaf surfaces. Ital J Pure Appl Math. Forthcoming.
  • Kempthorne D, Turner I, Belward J, et al. Surface reconstruction of wheat leaf morphology from three-dimensional scanned data. Funct Plant Biol. 2015;42:444–451. doi: 10.1071/FP14058
  • Kempthorne D, Turner I, Belward J. A comparison of techniques for the reconstruction of leaf surfaces from scanned data. SIAM J Sci Comput. 2014;36(6):B969–B988. doi: 10.1137/130938761
  • Hardy R. Theory and applications of the multiquadric-biharmonic method 20 years of discovery 1968–1988. Comput Math Appl. 1990;19:163–208. doi: 10.1016/0898-1221(90)90272-L
  • Hon Y, Sarler B, Yun D. Local radial basis function collocation method for solving thermo-driven fluid-flow problems with free surface. Eng Anal Bound Elem. 2015;57:2–8. doi: 10.1016/j.enganabound.2014.11.006
  • Buhmann M. Radial basis functions: theory and implementations. New York: Cambridge University Press; 2003.
  • Rippa S. An algorithm for selecting a good value for the parameter c in radial basis function interpolation. Adv Comput Math. 1999;11:193–210. doi: 10.1023/A:1018975909870
  • Scheuerer M. An alternative procedure for selecting a good value for the parameter c in RBF-interpolation. Adv Comput Math. 2011;34(1):105–126. doi: 10.1007/s10444-010-9146-3
  • Gregory E, Fasshauer G, Zhang J. On choosing optimal shape parameters for RBF approximation. Numer Algorithms. 2007;45(1–4):345–368. doi: 10.1007/s11075-007-9072-8
  • Majdisova Z, Skala V. Radial basis function approximations: comparison and applications. Appl Math Model. 2017;51:728–743. doi: 10.1016/j.apm.2017.07.033
  • Skala V. RBF interpolation with CSRBF of large data sets. Int Conference Comp Sci. 2017;12–14.
  • Turner I, Belward J, Oqielat M. Error bounds for least square gradient estimates. SIAM J Sci Comput. 2008;32(4):2146–2166. doi: 10.1137/080744906
  • Franke R. Scattered data interpolation: tests of some methods. Math Comput. 1982;38:181–200.
  • Hanan J, Loch B, McAleer T. Processing laser scanner plant data to extract structural information. Brisbane: Advanced Computational Modelling Centre, University of Queensland; 2007.
  • Sheikholeslami M, Shehzad S. Simulation of water based nanofluid convective flow inside a porous enclosure via non-equilibrium model. Int J Heat Mass Transfer. 2018;120:200–1212.
  • Sheikholeslami M, Seyednezhad M. Simulation of nanofluid flow and natural convection in a porous media under the influence of electric field using CVFE. Int J Heat Mass Transfer. 2018;120:772–781. doi: 10.1016/j.ijheatmasstransfer.2017.12.087
  • Sheikholeslami M, Rokni H. CVFEM for effect of Lorentz forces on nanofluid flow in a porous complex shaped enclosure by means of non-equilibrium model. J Mol Liq. 2018;254:446–462. doi: 10.1016/j.molliq.2018.01.130
  • Sheikholeslami M. Numerical investigation for CuO-H2O nanofluid flow in a porous channel with magnetic field using mesoscopic method. J Mol Liq. 2018;249:739–746. doi: 10.1016/j.molliq.2017.11.069
  • Sheikholeslami M. CuO-water nanofluid flow due to magnetic field inside a porous media considering Brownian motion. J Mol Liq. 2018;249:921–929. doi: 10.1016/j.molliq.2017.11.118
  • Sheikholeslami M. Numerical investigation of nanofluid free convection under the influence of electric field in a porous enclosure. J Mol Liq. 2018;249:1212–1221. doi: 10.1016/j.molliq.2017.11.141