A hybrid Clough–Tocher method for surface fitting with application to leaf data

The leaves play an important role in the development of a plant and are an integral component of any plant model. Mathematical models of leaves are therefore essential for their accurate representation and may be used only for visualization purposes, or for the purposes of studying biological processes such as photosynthesis [H. Sinoquet, S. Thanisawanyangkura, H. Mabrouk, P. Kasemsap, Characterization of the light environment in canopies using 3D digitising and image processing, Annals of Botany 82 (1998) 203–212], or a canopy light environment [M. Espana, F. Baret, F. Aries, B. Andrieu, M. Chelle, Radiative transfer sensitivity to the accuracy of canopy structure description: the case of a maize canopy, Agronomie 19 (1999) 241–254; W.K. Anderson, A grid generation and flow solution method for the Euler equations on unstructured grids, Journal of Computational Physics 110 (1994) 23–38]. This paper presents a brief survey of surface fitting strategies and then a new hybrid technique for modelling a leaf surface is proposed, which is based on combining the Clough–Tocher and radial basis function methods. We demonstrate the accuracy of this hybrid approach by applying it to two scattered data sets. The first set is taken from Franke [R. Franke, Scattered data interpolation: tests of some methods, Mathematics of Computation 38(157) (1982)], while the second set is sampled from an Anthurium leaf using a laser scanner [B. Loch, Surface Fitting for the Modelling of Plant Leaves, Ph.D. Thesis, University of Queensland, 2004. ]. It is found that the new hybrid surface fitting methodology produces an accurate and realistic leaf surface representation.