Geodesic
Isoptic Ruled Surfaces of Developable Surfaces
Journal for geometry and graphics, Tome 25 (2021) no. 1, pp. 1-17 Cet article a éte moissonné depuis la source Heldermann Verlag

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The planar notion of isoptics cannot be carried over directly into three-dimensional spaces. Therefore, the isoptic surface of a developable ruled surface will be defined as the set of intersection lines of pairs of tangent planes that enclose a fixed angle. The existence of a one-parameter family of tangent planes of a developable ruled surface guarantees that such a set of lines is a ruled surface, while in the case of any other surface this construction would result in a complex of lines. The isoptics of quadratic cylinders and cones shall be given. Further, the isoptic ruled surfaces of developable ruled surfaces invariant under one-parameter subgroups of the Euclidean and the equiform group of motions shall be described. Moreover, the orthoptic ruled surfaces of developables with a polynomially parametrized curve of regression shall be computed. It turns out that the orthoptic ruled surfaces allow for a projective generation.
Classification : 14J26, 53A25, 51N20
Mots-clés : Isoptic ruled surface, ruled surface, developable ruled surface, helical surface, spiral surface, cylinder, cone, isoptic curve 
@article{JGG_2021_25_1_JGG_2021_25_1_a0,
     author = {B. Odehnal },
     title = {Isoptic {Ruled} {Surfaces} of {Developable} {Surfaces}},
     journal = {Journal for geometry and graphics},
     pages = {1--17},
     year = {2021},
     volume = {25},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a0/}
}
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B. Odehnal . Isoptic Ruled Surfaces of Developable Surfaces. Journal for geometry and graphics, Tome 25 (2021) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a0/