Application of Mathematical 3D Surface Using Bi-cubic B-Spline Models

Abstract

This paper describes a modified mathematical method that used for controlling and generating three dimensional surfaces based on different axes (X, Y, and Z) and free axis. The main aim of the proposed method is to allow the designer to change the shape of the surface to the desired one without changing the original data points which is presented in the earlier version of this paper under title "3D Surface Reconstruction of Mathematical Modelling Used for Controlling the Generation of Different Bi-cubic B-Spline in Matrix Form without Changing the Control Points". The proposed method has been done by changing the t and s, parameters value that are assigned secretly by the designer. Therefore, in case off the control points have been discovered by others, the same design will not be created because the secrete parameters values are known only by the designer. Besides, the proposed method can be used by various applications such as banknote design, shape design, decorations, and governmental documents. Finally, the proposed method shows high level of accuracy in generating 3D surfaces without changing the control points