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Characterization of Speherical Helices in Euclidean 3-Space

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014
In this paper, we calculate Frenet frames of the tangent indicatrix (t), principal normal indicatrix (n) and binormal indicatrix (b) of the curve α in ℝ3 which are spherical curves.
Ekmekci Nejat, Okuyucu O. Zeki, Yayli Yusuf +2 more
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Quaternion-Based Representation of Rotation Minimizing Motions in Euclidean 3-space

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
This paper presents a quaternion-based framework for constructing rotation-minimizing motions in Euclidean 3-space, formulated via quaternion operator. By introducing a novel quaternion operator, we derive angular velocity representations directly from ...
Aksar Murat, Yaylı Yusuf
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Sweeping Surfaces of Polynomial Curves in Euclidean 3-space

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
In this study, we investigate the surfaces created by the movement of the profile curves through the regular polynomial spine curves. To overcome the restrictions of establishing a frame of the polynomial curves at the points where the second and higher ...
Zhu Yuting, Li Yanlin, Eren Kemal, Ersoy Soley +3 more
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Total torsion of three-dimensional lines of curvature. [PDF]