FA-88445 / Mesh topology invariants / Member archive

Half-edge prev pointer is stored reversed · case 05

prev returns the twin direction of the real previous half-edge.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [faces, queries]. Build half-edges (f[i], f[i+1 mod n]) with face index, next and prev half-edges. A repeated directed half-edge returns ["duplicate-halfedge", [a,b]]. For each query (a,b) return null if it is not a half-edge, else [face, next, prev, twin] with twin [b,a] when that directed half-edge exists, else null.

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
quad then triangle	`[[0, [1, 2], [0, 3], null], [1, [4, 3], [2, 3], null], [1, [2, 4], [3, 4], [2, 3]], [0, [3, 0], [2, 1], [3, 2]]]`	`[[0, [1, 2], [3, 0], null], [1, [4, 3], [3, 2], null], [1, [2, 4], [4, 3], [2, 3]], [0, [3, 0], [1, 2], [3, 2]]]`	Failed

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

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