On Approximation of Helix by 3(rd), 5(th) and 7(th) Order Bezier Curves in E-3

Abstract

Approximation of helices has been studied by using in many ways. In this study, it has been examined how a circular helix can be written as Bezier curve and written the 3(th) degree, 5(th) degree, and the 7(th) degree Maclaurin series expansions of helices for the polynomial forms. Hence, they can be written cubic, 5(th) order, and 7(th) order Bezier curves, based on the control points with matrix form we have already given in E-3. Further we have given the control points of the Bezier curve based on the coefficients of the Maclaurin series expansion of the circular helix.