PreprintCC BY 4.0arXiv
Explicit Cartesian Coordinates for Three-Dimensional Clothoids
Abstract
We combine the spherical-clothoid reconstruction theorem of Lucas and Ortega-Yagues with an explicit spinorial parametrization of the spherical clothoid and a Kampe de Feriet evaluation of Kummer-product integrals. This gives explicit Cartesian coordinates, in arclength, for every nonhelical three-dimensional clothoid. Kummer asymptotics then yield explicit asymptotic lines, including their gamma-digamma offsets and the angle between their axes.
Related
- Wavenumber-explicit stability of three-dimensional Cartesian UPMLs with piecewise-constant profiles for Helmholtz and Maxwell equations
- An explicit lower bound for the growth exponent of three-dimensional loop-erased random walk
- ADER-ZIST - a mixed explicit ADER-DG and zonally implicit space-time DG approach for Cartesian cut cell meshes
- Complex coordinates forced by finite orthogonality hypergraphs in dimension three
- The phase coordinates transformation in Moyal noncommutative framework 2-dimensional harmonic oscillator and Painlevé second equation
BibTeX
@misc{ionut2026explicit,
title = {{Explicit Cartesian Coordinates for Three-Dimensional Clothoids}},
author = {Alexandru Ionut},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28636},
eprint = {2608.28636},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28636},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Explicit Cartesian Coordinates for Three-Dimensional Clothoids
AU - Alexandru Ionut
PY - 2026
DA - 2026/08/09
PB - arXiv
DO - 10.48550/arxiv.2608.28636
UR - https://arxiv.org/abs/2608.28636
AB - We combine the spherical-clothoid reconstruction theorem of Lucas and Ortega-Yagues with an explicit spinorial parametrization of the spherical clothoid and a Kampe de Feriet evaluation of Kummer-product integrals. This gives explicit Cartesian coordinates, in arclength, for every nonhelical three-dimensional clothoid. Kummer asymptotics then yield explicit asymptotic lines, including their gamma-digamma offsets and the angle between their axes.
ER -