Geodesic
Creating Ruled Surfaces Using the Base Curve of the Frenet Trihedron
Journal for geometry and graphics, Tome 28 (2024) no. 1, pp. 73-85 Cet article a éte moissonné depuis la source Heldermann Verlag

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A ruled surface is formed by moving a straight line (as a generator) along a base curve. If the straight line's direction remains constant in a fixed coordinate system, the resulting surface will be cylindrical. In the general case, the direction of the generator can be described by a unit vector in the projections on the coordinate axis and will vary depending on the point on the base curve. This surface can be defined by a grid of both rectangular and oblique coordinate lines. Additionally, a ruled surface can be either developable or non-developable. In the general case, the surface is associated with an oblique grid of coordinate lines and is non-developable. In order to obtain specific cases, it is necessary to impose restrictions on the direction of the unit vector of the straight line.
Classification : 53A05
Mots-clés : Frenet formulas, curvature, torsion, vector surface equation, first quadratic form 
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     author = {S. Pylypaka and A. Nesvidomin and T. Volina and A. Trokhaniak and I. Taras },
     title = {Creating {Ruled} {Surfaces} {Using} the {Base} {Curve} of the {Frenet} {Trihedron}},
     journal = {Journal for geometry and graphics},
     pages = {73--85},
     year = {2024},
     volume = {28},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2024_28_1_JGG_2024_28_1_a5/}
}
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S. Pylypaka; A. Nesvidomin; T. Volina; A. Trokhaniak; I. Taras . Creating Ruled Surfaces Using the Base Curve of the Frenet Trihedron. Journal for geometry and graphics, Tome 28 (2024) no. 1, pp. 73-85. http://geodesic.mathdoc.fr/item/JGG_2024_28_1_JGG_2024_28_1_a5/