
Journal for Geometry and Graphics 25 (2021), No. 1, 001017 Copyright Heldermann Verlag 2021 Isoptic Ruled Surfaces of Developable Surfaces Boris Odehnal University of Applied Arts, Vienna, Austria boris.odehnal@uniak.ac.at The planar notion of isoptics cannot be carried over directly into threedimensional 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 oneparameter 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 oneparameter 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. Keywords: Isoptic ruled surface, ruled surface, developable ruled surface, helical surface, spiral surface, cylinder, cone, isoptic curve MSC: 14J26; 53A25, 51N20. [ Fulltextpdf (4331 KB)] 