A New Method For Construction Of Ph-Helical Curves In E-3

Abstract

Helices curves are characterized by the property that their unit tangents maintain a constant inclination with respect to a fixed line, the axis of the helix. If a polynomial space curve is helical, it must be a Pythagorean-hodograph PH-curve. In this paper, a method for constructing PH-helices in 3-dimensional Euclidean space E-3 is proposed, based on a method given by IZUMIYA and TAKEUCHI [(9)] for helices and Bertrand curves in 3-dimensional Euclidean space. We show that the method is true for the polynomial space curves to be PH-helix if the planar curve is a polynomial curve. We also obtain all planar polynomial curve in E-3. We give a new method to construct PH-helices from planar polynomial curves.