FA-88669 / Mesh topology invariants / Member archive

Boundary one-ring starts in the middle of the fan · case 04

Boundary vertices whose smallest neighbour is not the fan start are reported non-manifold.

Member previewVariant 4 · 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
fan middle rim	`"nonmanifold"`	`[[4, 0, 2], "boundary"]`	Failed

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