Turkish Journal of Mathematics
Author ORCID Identifier
PASCUAL LUCAS: 0000-0002-4354-9736
JOSÉ-ANTONIO ORTEGA-YAGÜES: 0000-0001-9521-1051
Abstract
In this paper, we study 3D-generalized clothoids, defined as curves for which there exists another distinct curve, with proportional arclength parameter, such that the Darboux lines of both curves at corresponding points are the same. We prove that these curves are those for which the ratio of torsion and curvature τ/κ is a linear rational function of the arclength. We also show that any 3D-generalized clothoid can be constructed from a rectifying curve, which is of constant curvature in the case of a 3D-clothoid.
DOI
10.55730/1300-0098.3648
Keywords
3D-clothoid, 3D-generalized clothoid, spherical clothoid, cylindrical helix, rectifying curve, conical helix
First Page
240
Last Page
251
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
LUCAS, P, & ORTEGA-YAGÜES, J (2026). A geometric property characterizing the 3D-generalized clothoids. Turkish Journal of Mathematics 50 (2): 240-251. https://doi.org/10.55730/1300-0098.3648
