FA-88404 / Mesh topology invariants / Member archive

Pinched boundary vertex silently merges or splits loops · case 04

A bowtie vertex yields a loop answer instead of "ambiguous".

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input: consistently oriented polygon faces. A half-edge (a,b) is boundary when (b,a) is not a half-edge. If any vertex starts two boundary half-edges return "ambiguous". Otherwise walk loops along the half-edge direction, each starting at its smallest vertex, and return them sorted by descending length then first vertex.

Why this case matters

Mesh processing pipelines (remeshing, export, simulation, printing) trust these topological counts and adjacency answers; a wrong invariant silently accepts broken meshes or rejects valid ones.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
bowtie	`[[0, 3, 4], [1, 2]]`	`"ambiguous"`	Failed

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