Classification of Ruled Surfaces Family with Common Characteristic Curve in Euclidean 3-space
Classification of Ruled Surfaces Family with Common Characteristic Curve in Euclidean 3-space
Classification of ruled surfaces that satisfying certain geometric conditions has been studied
by many researchers in the past years. The purpose of this paper is to study and classify the family of ruled
surfaces whose common directrix satisfies the requirements of characteristic curves in three-dimensional
Euclidean space. The family of ruled surfaces is parameterized by its directrix curve and director vector
that is expressed by a linear combination of Frenet frame with angular functions as coefficients. According
to the type of characteristic directrix curve, the family of ruled surfaces is classified into three types, and
one type when the family is developable.
Keywords:
Ruled surfaces family, Characterstic curve Classification,
___
- [1] Bayram, E., G¨ uler, F., Kasap, E. Parametric representation of a surface pencil with a common asymptotic curve. Computer-Aided Design. 44(2012), 637-643.
- [2] Carmo, M.D. Differential Geometry of Curves and Surfaces. Prentice-Hall. New Jersey (1976).
- [3] Faux, I.D., Pratt, M.J. Computational geometry for design and manufacture. Ellis Horwood. England (1979).
- [4] Fosdick, R., Fried, E. editors. The mechanics of ribbons and M¨obius bands. Springer Netherlands (2016).
- [5] Helmut, P., Andreas, A., Michael, H., Axel, K. Architectural geometry. Bentley Institute Press (2007).
- [6] Honda, A., Naokawa, K., Saji, K., Umehara, M., and Yamada, K. Curved foldings with common creases and crease patterns. Advances in Applied Mathematics. 121, 2020, 102083.
- [7] Li, C. Y., Wang, R. H., Zhu, C. G. Parametric representation of a surface pencil with a common line of curvature, Comput. Aided Des. 43(9), 2011, 1110-1117. [8] Li, C.Y., Wang, R. H., Zhu, C. G. An approach for designing a developable surface through a given line of curvature. Computer- Aided Design. 45(3), 2013, 621-627. [9] O¨ nder, M. On rectifying ruled surfaces. Kuwait Journal of Science. 47(4), 2020, 1-11.
- [10] Pressley, A.N. Elementary differential geometry. Springer Science & Business Media (2010).
- [11] Selig, J.M. Geometric fundamentals of robotics. Springer Science & Business Media (2004).
- [12] Shtogrin, M.I. Bending of a piecewise developable surface. Proceedings of the Steklov Institute of Mathematics. 275, 2011, 133-154.
- [13] Wang, G.J., Tang, K., Tai, C.L. Parametric representation of a surface pencil with a common spatial geodesic. Computer-Aided Design. 36(5), 2004, 447-459.
- [14] Zhao, H. Y, Wang, G. J. A new method for designing a developable surface utilizing the surface pencil through a given curve. Progress in Nature Science. 18(1), 2008, 105-110.
- ISSN: 2587-0971
- Başlangıç: 2016
- Yayıncı: Ahmet Ocak AKDEMİR
Sayıdaki Diğer Makaleler
Muideen OGUNNİRAN, Abdulraouv ALABİ, Qasim AMOBİ, Sabastine EMMANUEL
An examination on N − D* partner curves with common principal normal and Darboux vector in E^3.
Süleyman ŞENYURT, Şeyda KILIÇOGLU
Conformal generic Riemannian maps from almost Hermitian manifolds
Inequalities for strongly convex functions via Atangana-Baleanu Integral Operators
Şeydanur KIZIL, Merve AVCI ARDIÇ
Classification of Ruled Surfaces Family with Common Characteristic Curve in Euclidean 3-space
An Application of Least Squares Method in Nonlinear Models–Solid Waste Sample