FA-88465 / Mesh topology invariants / Member archive

Valence counts every vertex of each incident face · case 05

Quad vertices gain the diagonal corner as a neighbour.

Member previewVariant 5 · 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 grid	`[{"0": 3, "1": 5, "2": 3, "3": 5, "4": 8, "5": 5, "6": 3, "7": 5, "8": 3}, 9, [0, 1, 2, 3, 5, 6, 7, 8]]`	`[{"0": 2, "1": 3, "2": 2, "3": 3, "4": 4, "5": 3, "6": 2, "7": 3, "8": 2}, 9, [0, 1, 2, 3, 5, 6, 7, 8]]`	Failed

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This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

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