Abstract
Bu çalışmada, verilen bir eğriden geçen ve bu eğri boyunca Gauss eğriliği sabit olan yüzeyler elde edildi. Verilen eğrinin Frenet vektör alanları kullanılarak bu eğriden geçen yüzeyler parametrik olarak ifade edildi. Ayrıca, verilen eğriden geçen ve Gauss eğriliği sabit regle yüzeyler için yeterli şartlar verildi. Bazı örnekler verilerek elde edilen yöntem görsel hale getirildi.
Keywords
References
- Bayram, E., Güler, F. and Kasap, E., 2012. Parametric representation of a surface pencil with a common asymptotic curve. Computer Aided Design, 44, 637-643.
- Ergün, E., Bayram, E. and Kasap, E., 2014. Surface pencil with a common line of curvature in Minkowski 3-space. Acta Mathematica Sinica (English Series), 30, 12, 2103-2118.
- Güler, F., Bayram, E. and Kasap, E., 2018. Offset surface pencil with a common asymptotic curve. International Journal of Geometric Methods in Modern Physics, 15, 11, 1850195.
- Li, C.Y., Wang, R.H. and Zhu, C.G., 2011. Parametric representation of a surface pencil with a common line of curvature. Computer Aided Design, 43, 9, 1110-1117.
- O’Neill, B., 1966. Elementary Differential Geometry. Academic Press, New York.
- Wang, G.J., Tang, K. and Tai, C.L., 2004. Parametric representation of a surface pencil with a common spatial geodesic. Computer Aided Design, 36, 5, 447-59.
Abstract
In this study, we find surfaces with constant Gaussian curvature along a given curve. The parametric representation of the surfaces possessing the given curve expressed using the Frenet vector fields of the curve. Also, we give conditions for ruled surfaces passing through the given curve and having constant Gaussian curvature. We present some illustrative examples validating the presented method.
Keywords
References
- Bayram, E., Güler, F. and Kasap, E., 2012. Parametric representation of a surface pencil with a common asymptotic curve. Computer Aided Design, 44, 637-643.
- Ergün, E., Bayram, E. and Kasap, E., 2014. Surface pencil with a common line of curvature in Minkowski 3-space. Acta Mathematica Sinica (English Series), 30, 12, 2103-2118.
- Güler, F., Bayram, E. and Kasap, E., 2018. Offset surface pencil with a common asymptotic curve. International Journal of Geometric Methods in Modern Physics, 15, 11, 1850195.
- Li, C.Y., Wang, R.H. and Zhu, C.G., 2011. Parametric representation of a surface pencil with a common line of curvature. Computer Aided Design, 43, 9, 1110-1117.
- O’Neill, B., 1966. Elementary Differential Geometry. Academic Press, New York.
- Wang, G.J., Tang, K. and Tai, C.L., 2004. Parametric representation of a surface pencil with a common spatial geodesic. Computer Aided Design, 36, 5, 447-59.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | November 30, 2020 |
| Submission Date | January 22, 2020 |
| Published in Issue | Year 2020 Volume: 20 Issue: 5 |
