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A Note on the Point-Clothoid Distance Algorithm — arXiv:2609.10179

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.10179
License (as archived): CC0-1.0
Archived: 2026-10-16T10:13:21.758Z
SHA-256 of the archived text: 5a1b75f56550de671172106f63c23f235f65ddf73d0dd2cc9ceb05861d08427f
Stable URL of this page: https://metraipolis.com/documento/dc_9b491fa970ff

How to cite

A Note on the Point-Clothoid Distance Algorithm — arXiv:2609.10179 — arXiv (en), https://arxiv.org/abs/2609.10179 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_9b491fa970ff (Metraipolis archive dc_9b491fa970ff, sha256 5a1b75f56550de671172106f63c23f235f65ddf73d0dd2cc9ceb05861d08427f)

BibTeX

@misc{dc9b491fa970ff,
  title = {A Note on the Point-Clothoid Distance Algorithm — arXiv:2609.10179},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.10179},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_9b491fa970ff; sha256 5a1b75f56550de671172106f63c23f235f65ddf73d0dd2cc9ceb05861d08427f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.10179. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Computing the closest point on a clothoid is a recurring task in geometric design, road and railway alignment, and path planning. The efficient algorithm of Frego and Bertolazzi addresses this problem, but its candidate-selection analysis assumes at most one local minimum per search interval. We exhibit admissible configurations with two local minima, raising the question of whether the existing strategy accounts for every possible minimum. Using the geometry of the clothoid evolute, we prove that, for any query point and any proper no-inflection planar clothoid segment with tangent-angle variation at most $2\pi$, the squared-distance function has at most three stationary points; if all three are local extrema, their order is min-max-min. This establishes the completeness of the original candidate-selection logic beyond the one-minimum premise. It also shows that no interior search is needed when neither endpoint derivative test is active, allowing unnecessary midpoint searches to be omitted while retaining numerical fallback. Numerical experiments demonstrate reductions in iteration count and evaluation time.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-10 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA) ; Computational Geometry (cs.CG).
Pagina del lavoro: https://arxiv.org/abs/2609.10179 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T08:46:35.707Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-10?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).