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Journals / Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi / 2012 / Cilt: 7 - Sayı: 1

Different Approaches To Ruled Surfaces

Regle Yüzeylere Farklı Yaklaşımlar

Yusuf Yaylı
Semra Saraçoğlu
Pages
56–68
Publication Date
2012-06-04
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, an analytical comparison and the relation between Blaschke and Darboux approaches are represented showing the merits of our method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Abstract: In this study, surfaces are defined by using dual vectors and line transformations.
📊
Key Findings & Data:Dual curve and dual surface representational model for 3-dimensional geometric entities based on dual unit vectors are proposed.
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Conclusion & Impact:Finally, an analytical comparison and the relation between Blaschke and Darboux approaches are represented showing the merits of our method.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Regle yüzey · dual vektörler · Bishop çatı

Abstract

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.

Özet

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.

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Cite This Article

Yaylı, Y., Saraçoğlu, S. (2012). Different Approaches To Ruled Surfaces. Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, Cilt: 7 - Sayı: 1, 56–68. https://ajindex.com/articles/261133

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References (9)

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