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arXiv · 2608.23139

The longest-edge bisection algorithm may produce degenerating tetrahedra

Sergey Korotov
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Abstract

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.

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Sergey Korotov. 2026-08-24. The longest-edge bisection algorithm may produce degenerating tetrahedra. https://arxiv.org/abs/2608.23139

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