FA-88427 / Mesh topology invariants / Member archive

Vertex is called interior when any link vertex closes the fan · case 02

Boundary vertices with more than one incident triangle are reported interior.

Member previewVariant 2 · 3 implementations · 7 checks per implementation

Case contract

Input: triangle faces. For each referenced vertex v, its link is the set of opposite edges of incident triangles. v is "nonmanifold" if a link vertex has degree above 2 or the link graph is disconnected, "interior" if every link vertex has degree 2, else "boundary". Return {vertex string: class}.

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
fan	`{"0": "interior", "1": "boundary", "2": "interior", "3": "interior", "4": "boundary"}`	`{"0": "boundary", "1": "boundary", "2": "boundary", "3": "boundary", "4": "boundary"}`	Failed

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