FA-88463 / Mesh topology invariants / Member archive

Valence counts every vertex of each incident face · case 03

Quad vertices gain the diagonal corner as a neighbour.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input: polygon faces. Neighbours of a vertex are the other endpoints of its edges (consecutive face corners, skipping coincident pairs). Boundary vertices are endpoints of edges used by exactly one face. Irregular vertices have valence != 6 (interior) or != 4 (boundary). Return [{vertex: valence}, irregular count, sorted boundary vertices].

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
quad torus	`[{"0": 8, "1": 8, "2": 8, "3": 8, "4": 8, "5": 8, "6": 8, "7": 8, "8": 8}, 9, []]`	`[{"0": 4, "1": 4, "2": 4, "3": 4, "4": 4, "5": 4, "6": 4, "7": 4, "8": 4}, 9, []]`	Failed

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