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

Modelling water droplet movement on a leaf surface

“…In previous work by the authors [28,29] we have introduced a new surface fitting interpolation method that combines the Clough-Tocher method with radial basis functions for this purpose. A set of representative data points sampled from a Frangipani leaf using a laser scanner was used to reconstruct the surface of the leaf.…”

“…This method is based on a large number of three-dimensional data points captured from an actual leaf surface using a laser scanner. To apply the hybrid method to the leaf data sets, preprocessing steps are required, which include the determination of a reference plane for the data and the subsequent triangulation for the leaf surface mesh [28,29]. In this paper, the hybrid method is used to construct the surface of a Frangipani leaf for the purpose of simulating water droplet movement on that surface.…”

“…Loch [22] uses two such approaches based on the finite element method to model the leaf surface. In earlier work [28,29] we introduced a new surface fitting method based on hybrid strategies that combine the Clough-Tocher method [20,4] with radial basis functions [13,33] for this purpose. This method is based on a large number of three-dimensional data points captured from an actual leaf surface using a laser scanner.…”

“…To this end, we present a simple mathematical model for this process, report on experimental results generated with a particular type of leaf (Frangipani leaf), and compare the results from each of the two studies. A crucial aspect of our approach is to construct the surface of the leaf using a recently developed surface fitting method [28,29] based on a combination of the Clough-Tocher method with radial basis functions.…”

“…Two forces are assumed to affect the droplet movement on the leaf surface namely an internal force, which consists of a friction and resistance component between the surface and the droplet, and an external force due to gravity. The surface is divided into a mesh of triangles [28,29] and the motion of the droplet is computed over each triangle. The inclusion of a thin-film concept enables the motion of the droplet to be stopped at a point where the height of the thin-film along the polygonal path is less than some specified tolerance.…”