3D Surface Reconstruction of Mathematical modelling Used for Controlling the Generation of Different Bi-cubic BSpline in Matrix Form without Changing the Control Points

Abstract

This paper introduces a 3D surface reconstruction of mathematical modelling by using blossoming, dependent on a parameter in the coefficient of the control points, the bi-cubic B-spline surface in matrix form scheme can be utilized to obtain a better quality of reconstructed surface, by using different values of parameter of coefficients used for controlling generating 3D complex surface, which is not easy to recreate. The de-Boor method is used to upgrade the matrix form of 2D to bicubic 3D- b-spline surface depends on parameter value. The model can be seen more efficient of surface in comparison with that needed in conventional methods. The effectiveness of the proposed algorithm is illustrated through several comparative examples of 3D matrices surface. The change in surface is made without any change in the control points. Applications of the modeling in both the curve and surface can be used in many fields, such as banknote design, shape design, decorations, governmental document, and other documents, all of which are of high impotence. And it is used to find the appropriate solutions that prevent or reduce the forgery and counterfeiting of the important and vital documents