A NEW METHOD FOR CONSTRUCTION OF PH-HELICAL CURVES IN E-3


CAMCI Ç. , İLARSLAN K.

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, vol.72, no.3, pp.301-308, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.7546/crabs.2019.03.03
  • Title of Journal : COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
  • Page Numbers: pp.301-308

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.