{
  "abstract": "We study polygonal general helices in Euclidean three-space using the turning and signed torsion angles of the discrete Frenet frame. For helices whose axis is not orthogonal to the edge tangents, we prove that the global constant-angle condition is equivalent to the existence of a conserved Frenet-frame vector. On the generic branch, elimination of the auxiliary coefficient yields an intrinsic finite-step compatibility relation involving three consecutive turning angles and two consecutive torsion angles. Complementary phase and linear-subspace formulations cover the antipodal-binormal case. These characterizations reconstruct the helical axis and the helix angle and yield a sharp bound for each turning angle. We also give a spherical formulation through the tangent indicatrix: its vertices lie on a plane section of the unit sphere, which is a small circle in the non-orthogonal case, whereas the orthogonal case is exactly planar. A nonconstant Frenet-data example illustrates the criterion. Finally, for uniform chordal sampling of a smooth curve, the discrete Lancret-type quotient and the reconstructed helical direction converge with second-order accuracy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00673",
  "author_total": 3,
  "authors": [
    {
      "name": "Dae Won Yoon"
    },
    {
      "name": "Chul Woo Lee"
    },
    {
      "name": "Jae won Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e87704p1tm048.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00673",
  "fulltext_url": null,
  "id": "e87704p1tm048",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00673",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7206208545",
  "pdf_url": "https://arxiv.org/pdf/2609.00673",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e87704p1tm048.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00673",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00673"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Intrinsic Finite-Step Characterizations of Discrete General Helices",
  "title_text": "Intrinsic Finite-Step Characterizations of Discrete General Helices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/e87704p1tm048",
  "venue": "arXiv",
  "versions": []
}