Smarandache Curves According to Flc-frame in Euclidean 3-space

Şenyurt, Süleyman; Ayvacı, Kebire Hilal; Canlı, Davut

doi:10.54974/fcmathsci.1142404

Cited by 4 publications

(3 citation statements)

References 9 publications

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“…al, 2020;Şenyurt et. al, 2022;Şenyurt et al 2023a;Şenyurt et al 2023b;Turgut & Yılmaz, 2008). Sabban frame and geodesic curvature of spherical indicatrix curves were defined by Koenderink (1990).…”

Section: Introductionmentioning

confidence: 99%

Some Applications on Spherical Indicatrices of the Helix Curve

Şenyurt,

Gür Mazlum

2024

Ordu Üniversitesi Bilim Ve Teknoloji Dergisi

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Section: Introductionmentioning

confidence: 99%

Some Applications on Spherical Indicatrices of the Helix Curve

Şenyurt,

Gür Mazlum

2024

Ordu Üniversitesi Bilim Ve Teknoloji Dergisi

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“…In this study, we investigated the Smarandache curves using the modified orthogonal frame to give a new perspective to curves. The Smarandache curves are characterized using different frames in Euclidean and non-Euclidean spaces [1][2][3][4][5][6][7][8][9]. The Smarandache curves obtained from spacelike Salkowski and anti-Salkowski curves are given by Eren and Şenyurt in Minkowski space [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

On Characterization of Smarandache Curves Constructed by Modified Orthogonal Frame

Eren,

Ersoy

2024

Mathematical Sciences and Applications E-Notes

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In this study, we investigate Smarandache curves constructed by a space curve with a modified orthogonal frame. Firstly, the relations between the Frenet frame and the modified orthogonal frame are summarized. Later, the Smarandache curves based on the modified orthogonal frame are obtained. Finally, the tangent, normal, binormal vectors and the curvatures of the Smarandache curves are determined. A special curve known as the Gerono lemniscate curve whose curvature is not differentiable, the principal normal and binormal vectors are discontinuous at zero point is considered as an example, and the Smarandache curves of this curve are obtained by the aid of its modified orthogonal frame, and their graphics are given.

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“…(2015b), Dede (2018) studied “directional tubular surface” with the help of a quasi-frame, then obtained different results, and additionally, Ekici and Dede (2017) analyzed these results in the Minkowski 3-space [3–5]. Also, Ekici et al . (2018, 2019) have obtained the characterizations of the quasi-frame on the special curves by analyzing the Smarandache curves, known in the Euclid and Minkowski spaces, with the help of the quasi-frame.…”

Section: Introductionmentioning

confidence: 99%

The quasi-frame of the rational and polynomial Bezier curve by algorithm method in Euclidean space

Samanci

2023

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PurposeFrames play an important role in determining the geometric properties of the curves such as curvature and torsion. In particular, the determination of the point types of the curve, convexity or concavity is also possible with the frames. The Serret-Frenet frames are generally used in curve theory. However, the Serret-Frenet frame does not work when the second derivative is zero. In order to eliminate this problem, the quasi-frame was obtained. In this study, the quasi frames of the polynomial and rational Bezier curves are calculated by an algorithmic method. Thus, it will be possible to construct the frame even at singular points due to the second derivative of the curve. In this respect, the contribution of this study to computer-aided geometric design studies is quite high.Design/methodology/approachIn this study, the quasi frame which is an alternative for all intermediate points of the rational Bezier curves was generated by the algorithm method, and some variants of this frame were analyzed. Even at the points where the second derivative of such rational Bezier curves is zero, there is a curve frame.FindingsSeveral examples presented at the end of the paper regarding the quasi-frame of the rational Bezier curve, polynomial Bezier curve, linear, quadratic and cubic Bezier curves emphasize the efficacy and preciseness.Originality/valueThe quasi-frame of a rational Bezier curve is first computed. Owing to the quasi frame, it will have been found a solution for the nonsense rotation of the curve around the tangent.

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Smarandache Curves According to Flc-frame in Euclidean 3-space

Cited by 4 publications

References 9 publications

Some Applications on Spherical Indicatrices of the Helix Curve

Some Applications on Spherical Indicatrices of the Helix Curve

On Characterization of Smarandache Curves Constructed by Modified Orthogonal Frame

The quasi-frame of the rational and polynomial Bezier curve by algorithm method in Euclidean space

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