An efficient algorithm for finding the control point of 3<sup>rd</sup> order Bezier curve

Abstract

This paper represents a modified algorithm to recover the control points of 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> order Bezier curves more efficiently. It uses the two stage approximation learning algorithm with some modifications. In this regards, at 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> stage we modify the height (H) where we assume approximate 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> and 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> control points and at 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> stage we modify the step size (δ) which moves the assumed control points towards the accurate control points. Experimental results demonstrate that our proposed method minimize the error level and reduce computation time for recovering the control points than the previous one. Our computer simulation proves the effectiveness of our proposed method.