A NEW METHOD FOR CONSTRUCTION OF PH-HELICAL CURVES IN E-3
COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, cilt.72, sa.3, ss.301-308, 2019 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 72 Sayı: 3
- Basım Tarihi: 2019
- Doi Numarası: 10.7546/crabs.2019.03.03
- Dergi Adı: COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.301-308
- Çanakkale Onsekiz Mart Üniversitesi Adresli: Evet
Özet
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.