Approximation of Radial Basis Function with Linear Polynomial: Comparison and Application
In this research paper we proposed an interpolation approach to model a continuous differntiable surfaces of a real leaf from 3D scanned data points. As such model is essential for modellig the plant architecture, fluid movement and biological structure such as photosynthesis. The interpolation approach is based on adding a linearpolynomial P_1 (x) to the multiquadric Radial basis function (LMRBF) to improve the accuracy and constancy of the interpolation method.Moreover, a comparison between the LMRBF and the Cubic multiquadric Radial basis function (CMRBF) methodintroduced by the author  is presented.
To evaluate the accuracy of the LMRBF method we apply itinto two sets of scattered data points. The first set is taken from Franke  while the second set is taken from Loch which is sampled from a real Frangipani and Anthurium leaf using a laser scanner. We found that the proposed method constructs accurate model of the leaf surface.Furthermore, the LMRBF produced slightly more accuarte leaf model than the CMRBF.
Keywords - Interpolation, virtual leaf, Radial basis function, AMS classification numbers.