On approximation of helix by 3rd, 5th and 7th order Bezier curves in E3

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 3th degree, 5th degree, and the 7th degree Maclaurin series expansions of helices for the polynomial forms. Hence, they can be written cubic, 5th order, and 7th order Bezier curves, based on the control points with matrix form we have already given in E3. Further we have given the control points of the Bezier curve based on the coefficients of the Maclaurin series expansion of the circular helix.