On Approximation Sine Wave with the 5(Th) and 7(Th) Order Bezier Paths in Plane

Abstract

There are many studies to approximate to sine curve or sine wave. In this study, it has been examined the way how the sine wave can be written as any order Bezier curve. First, it has been written the 5(th) and the 7(th) degree Maclaurin series expansion of the parametric form of sine curve. Also, they are 5(th) and the 7(th) order Bezier paths, based on the control points with matrix form in E-2. Hence it has been given the control points of the 5(th) and the 7(th) order Bezier curve based on the coefficients of the 5(th) and the 7(th) degree Maclaurin series expansion of the sine curves in three steps. Further it has been given the coefficients based on the control points of the 5(th) and the 7(th) order Bezier curve too.