Application of interpolation finite element methods to a real 3D leaf data

Abstract

In this paper we proposed a new surface fitting method based on combining the Clough-Tocher method (CT) and multiquadric radial basis function enhanced with a cubic polynomial (MRBFC) method to accurately reconstruct a real leaf surface from 3D scattered data. The accuracy of the CT-MRBFC method is validated by implementing it to a real 3D leaf data.The accuracy of the method depends highly on the RBF shape parameter and the triangular mesh structure. Consequently we employed three different methods numerically to estimate the RBF parameter as variable or constant including the square root method, the cubic root method and the fminbnd method which is a MATLAB command based on minimizing a single-variable function locally on a fixed interval. Moreover, the quality of the triangles in the mesh is measured to ensure that each triangle is close to equilateral triangle to achieve a better accuracy of the proposed CT-MRBFC method. It is concluded that the proposed CT-RBFC method generates an accurate representation of the leaf surface.