Precise Approach for Modified 2 Stage Algorithm to Find Control Points of Cubic Bezier Curve

This paper presents a new approach for the modified algorithm to efficiently extract the control points of the cubic Bezier curve. It uses the modified two-stage approximation learning algorithm with a new approach. In this regard, in the 1st stage, we modify the determination procedure of 1st and 4th control points and also modify the procedure to compute the height. This paper employs the height where we presume approximate locations of the second and third control points and in second stage, we alter the step size in effect it shifts the presumed control points towards the accurate control points. This paper discusses the control point determination of Bezier curves having initial and final curve points at different y position. This paper also discusses a new approach for arranging the random curve points of a convex curve in the order of the tracing path of the curve. Experimental results demonstrate that the proposed method minimizes the RMS error level and determines the control points of any cubic Bezier curve with any orientation than the previous one. The proposed method outperforms the existing methods.