Application of Bezier Surface in Matrix Form for Measuring and Controlling the Time of 3D Design

Abstract

Traditional three dimension (3D) bicubic Bezier surface requires to fix Bezier surface parameters to accurately generate the 3D surface from the two-dimension (2D) curve. In this paper, a modified mathematical technique presents to measure and control of the time of 3D bicubic Bezier surface using De-Casteljau and Blossoming algorithms in matrix form. The approach modifies the Blossoming algorithm to construct a cubic Bezier curve in matrix form. The De-Casteljau method harnessed to upgrade the matrix form of 2D to bicubic 3D-Bezier surface depending on t and v values in matrix form that provides numerous solutions for designers to control of 3D design time. It is an efficient technique that can be used in two-dimensional curves and is well suited to many computer graphics and geometric fields. The approach tested based on changing the coefficient of parametric surfaces of Bezier surface. Results of the suggested method indicate that the proposed approach accurately measures and controls the design time to find the optimal time of 3D surfaces. The proposed method produces a better and optimal time of surface generation design leading to more dominant over a design which provides flexibility to the designers to smooth a design from the time points of surface generation.