Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Next Article

Journal for Geometry and Graphics 25 (2021), No. 1, 001--017
Copyright Heldermann Verlag 2021

Isoptic Ruled Surfaces of Developable Surfaces

Boris Odehnal
University of Applied Arts, Vienna, Austria

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.

Keywords: Isoptic ruled surface, ruled surface, developable ruled surface, helical surface, spiral surface, cylinder, cone, isoptic curve

MSC: 14J26; 53A25, 51N20.

[ Fulltext-pdf  (4331  KB)]