Reconstruction of a Ruled Surface in 3-dimensional Euclidean Space

Year 2024, Volume: 17 Issue: 1, 259 - 267, 28.03.2024

Mustafa Dede , Cumali Ekici , Mahmut Koçak

https://doi.org/10.18185/erzifbed.1362369

Abstract

In this paper, we first provide a summary of certain results related to the differential geometry of ruled surfaces. Next, we introduce the signature curve for ruled surfaces in Euclidean three-space. Additionally, we present a straightforward algorithm for the reconstruction of a ruled surface, which is both efficient and entirely local, requiring only the initial motion direction and starting point. Finally, we illustrate the efficiency and accuracy of the algorithm through several examples.
Bu makalede, öncelikle regle yüzeylerin diferesiyel geometrisi ile ilgili bazı sonuçların bir özetini sunuyoruz. Daha sonra, Öklid üç uzayında regle yüzeyler için işaret eğrisini tanıtıyoruz. Ek olarak, bir regle yüzeyin yeniden yapılandırılması için hem verimli hem de tamamen yerel olan, yalnızca ilk hareket yönü ve başlangıç noktası gerektiren basit bir algoritma sunuyoruz. Son olarak, algoritmanın verimliliğini ve doğruluğunu birkaç örnekle gösteriyoruz.

Keywords

Ruled surface, Signature curve, Curvature, Reconstruction

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