FA-88665 / Mesh topology invariants / Member archive

One-ring is walked clockwise · case 05

Neighbour rings come out in reverse angular order.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [faces, v] with consistently oriented polygons. Each face containing v maps its next corner p to its previous corner q (counter-clockwise order around v). A repeated p is "nonmanifold"; no incident face is "isolated". If exactly one p has no predecessor the ring is a boundary fan starting there; more than one is "nonmanifold"; otherwise start at the smallest neighbour. Walk successors; a walk that does not visit every neighbour is "nonmanifold". Return [ring, "boundary"|"interior"].

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
disk centre	`[[1, 5, 4, 3, 2], "interior"]`	`[[1, 2, 3, 4, 5], "interior"]`	Failed

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