FA-88558 / Mesh topology invariants / Member archive

Orientation propagation runs through three-face fins · case 03

Non-manifold books get an orientability answer instead of "non-manifold".

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input: polygon faces. If any undirected edge has more than two incident faces return "non-manifold". Otherwise propagate orientation by breadth-first search from the lowest unvisited face of each component (that seed keeps its orientation). A neighbour across an edge used in the same direction must have the opposite flip state. Any conflict returns [false, []], else [true, sorted indices of faces to flip].

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	`[false, []]`	`"non-manifold"`	Failed

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