Regle Yüzeylere Farklı Yaklaşımlar

Özet: Bu çalışmada, yüzeyler dual vektörler ve doğru transformasyonları kullanılarak tanımlanmaktadır. Sonrasında parametrik yüzey transformasyonları için yeni bir yaklaşım verilmektedir. Üç boyutlu geometric öğeler için temeli dual birim vektörlere dayanan temsili dual eğri ve dual yüzey modeli ileri sürülmektedir. Burada bazı bilinen yeni yaklaşımlar kullanılmaktadır. Ayrıca, Bishop ve Frenet geometrik tanımları sunulmaktadır. Sonuç olarak, Blaschke ve Darboux yaklaşımları arasındaki analitik mukayese ve ilişki, metodumuzun doğruluğu gösterilerek belirtilmektedir.

Anahtar Kelimeler:

Regle yüzey, dual vektörler, Bishop çatı

Different Approaches To Ruled Surfaces

Abstract: In this study, surfaces are defined by using dual vectors and line transformations. A new approach is given for the transformation of parametrically surfaces. Dual curve and dual surface representational model for 3-dimensional geometric entities based on dual unit vectors are proposed. Some well-known new approaches like Blaschke approach of ruled surfaces are used. Moreover, geometric explanations of Bishop and Frenet are presented. Finally, an analytical comparison and the relation between Blaschke and Darboux approaches are represented showing the merits of our method.

Keywords:

Ruled surface, dual vectors, Bishop frame,

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Yusuf Yaylı e-mail: yayli@science.ankara.edu.tr