FA-88808 / Mesh topology invariants / Member archive

Triangle boundary vertices are held to the interior valence · case 03

Open triangle meshes fail the index identity.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input [faces, kind] with kind "tri" or "quad". Valence = number of edge neighbours; boundary vertices touch an edge used once. Regular valence is 6/4 (tri interior/boundary) or 4/3 (quad). Index sum = sum of (regular - valence). Return [index sum, chi=V-E+F, index sum == k*chi] with k=6 for tri and 4 for quad.

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
open cylinder	`[16, 0, false]`	`[0, 0, true]`	Failed

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