FA-88740 / Mesh topology invariants / Member archive

Faces shared by three tetrahedra are silently dropped · case 05

A non-manifold tet mesh produces a surface with a missing fin.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input: tetrahedra [a,b,c,d] (positively oriented). A tet with repeated vertices returns ["degenerate", i]. Outward faces are (b,c,d),(a,d,c),(a,b,d),(a,c,b). Faces are matched by their vertex set; a set used once is boundary (kept with its first orientation, rotated to start at its smallest vertex); used more than twice returns ["non-manifold", sorted vertices]. Output boundary faces in increasing sorted-vertex-set order.

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
fin face	`[[0, 1, 3], [0, 4, 1], [0, 1, 5], [0, 3, 2], [0, 2, 4], [0, 5, 2], [1, 2, 3], [1, 4, 2], [1, 2, 5]]`	`["non-manifold", [0, 1, 2]]`	Failed

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

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