A New Approach for Designing Ruled Surface Using the Curvature Theory

Year 2019, , 2200 - 2206, 01.12.2019

Fatma Güler

https://doi.org/10.21597/jist.566855

Cited By: 2

Abstract

In this paper, we obtain new approach ruled surface generated by a curve on the surface of sphere called the spherical indicatrix. We expressed ruled surface which the striction curve of the surface will be taken as the base curve using the generator trihedron. We have given theorems for to be the asymptotic and geodesic curve on the surface of the striction curve using the curvature theory of the ruled surfaces. Also, we have calculated the Gaussian and the mean curvature of the ruled surface. We illustrate ruled surface generated by a curve on the surface of sphere called the spherical indicatrix.

Keywords

Ruled surface, Asymptotic curve, Geodesic curve, Generator trihedron

Eğrilik Teorisi Kullanarak Regle Yüzey Tasarlamada Yeni Bir Yaklaşım

Abstract

Bu çalışmada küresel gösterge eğrisi tarafından üretilen regle yüzeyler için yeni bir yaklaşım elde edildi. Üreteç çatısı yardımıyla striksiyon eğrisi dayanak eğrisi olarak alınan regle yüzey araştırıldı. Regle yüzeylerin eğrilik teorisi kullanılarak striksiyon eğrisinin yüzey üzerinde geodezik eğri ve asimptotik eğri olması için teoremler verildi. Ayrıca, regle yüzeyin Gauss ve ortalama eğrilikleri ile temel formları hesaplandı. Küresel gösterge eğrisi tarafından üretilen regle yüzeye örnek verildi.

Keywords

Regle Yüzey, Asimptotik Eğri, Geodezik Eğri, Üreteç Çatı

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