turkmath.org

Helical curves are constructed by the property that their unit tangents make a constant angle with a chosen constant direction. There are relations between polynomial planar curves, helices and Pythagorean-hodograph or shortly PH-curves. The aim of this paper is to obtain a method which generates PH-curves and PH-helical curves from a planar curve in Euclidean Space $\mathbb{E}^{n+1}$. Furthermore, some examples are given in $\mathbb{ E}^{4}$ and $\mathbb{E}^{5}$ to explain the method neatly.