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The longest-edge bisection algorithm may produce degenerating tetrahedra — arXiv:2608.23139

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.23139
License (as archived): CC0-1.0
Archived: 2026-10-18T08:27:52.317Z
SHA-256 of the archived text: 591bddba7c3891248a3bb688d8eedc414505dab399c00cc6e70e59d38919f3c9
Stable URL of this page: https://metraipolis.com/documento/dc_809cc91c41a4

How to cite

The longest-edge bisection algorithm may produce degenerating tetrahedra — arXiv:2608.23139 — arXiv (en), https://arxiv.org/abs/2608.23139 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_809cc91c41a4 (Metraipolis archive dc_809cc91c41a4, sha256 591bddba7c3891248a3bb688d8eedc414505dab399c00cc6e70e59d38919f3c9)

BibTeX

@misc{dc809cc91c41a4,
  title = {The longest-edge bisection algorithm may produce degenerating tetrahedra — arXiv:2608.23139},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.23139},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_809cc91c41a4; sha256 591bddba7c3891248a3bb688d8eedc414505dab399c00cc6e70e59d38919f3c9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.23139. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

An explicit sequence of tetrahedra generated by the longest-edge bisection algorithm is shown to degenerate. The example violates shape regularity and both the minimum- and maximum-angle conditions, demonstrating that arbitrary tie-breaking among longest edges does not guarantee nondegeneration.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-25 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.23139 — 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 2026-10-18T08:27:23.856Z dalla pagina https://arxiv.org/catchup/math.NA/2026-08-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).