{
  "abstract": "We study conditions under which the metric projection onto a strictly convex body can be approximated by the projections onto polygonal approximations (in the Hausdorff-Pompeiu sense) of the strictly convex body itself. We provide a necessary condition by proving that the union of all the vertices of the polygonal approximations must be dense in the boundary of that set. To showcase our result, given a superellipse (Lamé curve) of order p>1, we prove that a sequence of polygons obtained by radially projecting the torsion subgroup of the unit circle onto the superellipse, converges to the superellipse, in the Hausdorff-Pompeiu metric. Moreover, this leads to a globally convergent new algorithm useful in approximating the metric projection onto a superelliptic disk (the convex hull of a superellipse).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.24599",
  "author_total": 2,
  "authors": [
    {
      "name": "Valerian-Alin Fodor"
    },
    {
      "name": "Virgilius-Aurelian Minuta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0gv5ztdgdafw3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.24599",
  "fulltext_url": null,
  "id": "0gv5ztdgdafw3",
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  "landing_url": "https://arxiv.org/abs/2605.24599",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
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      "arxiv",
      "math.OC"
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      "openalex",
      "1703|Optimization and Variational Analysis"
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  "openalex": "W7162420388",
  "pdf_url": "https://arxiv.org/pdf/2605.24599",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0gv5ztdgdafw3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2605.24599",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.24599"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "An algorithm for approximating the metric projection onto a superelliptic disk",
  "title_text": "An algorithm for approximating the metric projection onto a superelliptic disk",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/0gv5ztdgdafw3",
  "venue": "arXiv",
  "versions": []
}