Application of the Hybrid Piecewise Quadratic Triangular Elements (PQTE) method and Taylor Series (TS) method to a Data Set

Abstract

In this article, we proposed a new surface fitting method so-called hybrid PQTE-TS method for fitting surfaces that combines the piecewise quadratic triangular elements (PQTE) method and Tayler series (TS) method to achieve a smooth surface. Then, we investigated the possibility of applying the hybrid PQTE-TS methodology to a data sets taken from Franke [1], to reconstruct a six different surfaces. The accuracy of the proposed methods is evaluated by numerical experimentation and we concluded that the hybrid PQTE-TS method is an effective method for constructing an accurate surfaces and can be employed in the future to reconstruct a real surfaces from a real data such as leaf surface. Such models of leaf simplify an understanding of plant growth and allow the modelling of the plants interaction with their environment. Moreover, Accurate leaves representation is a significant research area because it is a part of plant model development as well as it has many applications, for example, the leaf model can be employed to investigate the droplet path on the leaf surface which is essential for realizing how a droplet of nutrient, pesticide or water will be imbibed within the leaf surface. Therefore, the hybrid PQTE-TS methodology can be applied for this purpose.