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arXiv · 2608.28636

Explicit Cartesian Coordinates for Three-Dimensional Clothoids

Alexandru Ionut
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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.

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Alexandru Ionut. 2026-08-09. Explicit Cartesian Coordinates for Three-Dimensional Clothoids. https://arxiv.org/abs/2608.28636

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