FA-88470 / Mesh topology invariants / Member archive

Valence counts a vertex as its own neighbour · case 05

Faces with a repeated corner raise the valence and create a fake boundary edge.

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
degenerate corner	`[{"0": 3, "1": 3, "2": 3, "3": 2}, 4, [0, 1, 2, 3]]`	`[{"0": 3, "1": 2, "2": 3, "3": 2}, 4, [0, 1, 2, 3]]`	Failed

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

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