A New Method to Obtain PH-Helical Curves in E^(n+1)

Objective & Hypothesis:Helical curves are constructed by the property that their unit tangents make a constant angle with a chosen constant direction.

📊

Key Findings & Data:The aim of this paper is to obtain a method which generate PH-curves and PH-helical curves from a planar curve in Euclidean Space E^(n+1).

💡

Conclusion & Impact:Furthermore, some examples are given in E^4 and E^5 to explain the method neatly.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:PH-curve · helical curve · PH-helical curve

Abstract

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 generate PH-curves and PH-helical curves from a planar curve in Euclidean Space E^(n+1). Furthermore, some examples are given in E^4 and E^5 to explain the method neatly.

Keywords

PH-curve helical curve PH-helical curve planar curve polynomial curve

🔖

Cite This Article

MOLLAOĞULLARI, A., GÜMÜŞ, M., İLARSLAN, K., CAMCI, Ç. (2021). A New Method to Obtain PH-Helical Curves in E^(n+1). Journal of New Theory, Sayı: 37, 45–57. https://ajindex.com/articles/681463

📄 Full Text PDF Viewer

Open in New Tab ↗

↗New Tab

📄

PDF görüntüleyici hazırlanıyor...

References (18)

M. A. Lancret, Mémoire sur la théorie des courbes à double courbure, Mémoires présentés ‘a l’Institut des Sciences, Letters et arts par divers savants, Tome 1(1802) 416–454.
W. Kuhnel, Differential Geometry: Curves-Surfaces-Manifolds, Braunchweig, Friedr. Vieweg & Sohn, 1999.
R. T. Farouki, T. Sakkalis, Pythagorean Hodographs, IBM Journal of Research and Development 34(5) (1999) 736–752.
R. T. Farouki, T. Sakkalis, Pythagorean-Hodograph Space Curves, Advances in Computational Mathematics 2(1) (1994) 41–66.
R. T. Farouki, C. Y. Han., C. Manni, A. Sestini, Characterization and Construction of Helical Polynomial Space Curves, Journal of Computational and Applied Mathematics 162(2) (2004) 365–392.
R. T. Farouki, Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, Springer, Berlin, Heidelberg, 2008.
R. T. Farouki, C. Giannelli, A. Sestini, Helical Polynomial Curves and Double Pythagorean Hodographs I Quaternion and Hopf map representations, Journal of Symbolic Computation 44(2) (2009) 161–179.
R. T. Farouki, C. Giannelli, A. Sestini, Helical Polynomial Curves and Double Pythagorean Hodographs II. Enumeration of Low-Degree Durves, Journal of Symbolic Computation 44(4) (2009) 307–332.
R. T. Farouki, M. Al-Kandari, T. Sakkalis, Structural Invariance of Spatial Pythagorean Hodographs, Computer Aided Geometric Design 19(6) (2002) 395–407.
R. T. Farouki, Z. Šír, Rational Pythagorean-Hodograph Space Curves, Computer Aided Geometric Design 28(2) (2011) 78–88.
H. Pottman, Curve Design with Rational Pythagorean-Hodograph Curves, Advances in Computational Mathematics 3 (1995) 147–170.
S. Izumiya, N. Takeuchi, Generic Properties of Helices and Bertrand Curves, Journal of Geometry 74 (2002) 97–109.
Ç. Camcı K. İlarslan, A New Method for Construction of PH-Helical Curves in E^3, Comptes Rendus De L Academıe Bulgare Des Scıences, 72(3) (2019) 301–308.
H. Gluck, Higher Curvatures of Curves in Euclidean Space, The American Mathematical Monthly 37 (1966) 699–704.
M. C. Romero-Fuster, E. Sanabria-Codesal, Generalized Helices Twistings and Flattenings of Curves in n-Space, Matematica Contemporanea 17 (1999) 267–280.
E. Ödamar, H. H. Hacısalihoğlu, A Characterization of Inclined Curves in Euclidean n-Space, Communications Faculty of Sciences University of Ankara Series A1-Mathematics and Statistics 24 (1975) 15–23.
Ç. Camcı K. İlarslan, L. Kula, H. H. Hacısalihoğlu, Harmonic Curvature and General Helices, Chaos Solitons Fractals 40 (2009) 2590–2596.
K. K. Kubota, Pythag