FA-88418 / Mesh topology invariants / Member archive

Vertex link tolerates a link vertex of degree three · case 03

Vertices on a three-sheet fin are classified as manifold.

Member previewVariant 3 · 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
book	`{"0": "boundary", "1": "boundary", "2": "boundary", "3": "boundary", "4": "boundary"}`	`{"0": "nonmanifold", "1": "nonmanifold", "2": "boundary", "3": "boundary", "4": "boundary"}`	Failed

MEMBER ARCHIVE

The complete case is available to members.

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

Member access is invitation-based. Sign in with your invited account to inspect the sources.