FA-88694 / Mesh topology invariants / Member archive

Kill-edge-make-ring removes a loop instead of adding one · case 04

Creating an inner ring breaks the Euler-Poincare relation.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input: list of Euler operator names applied to counts [V,E,F,L,S,G] starting at zero. Deltas: mvfs(+V,+F,+L,+S), mev(+V,+E), mef(+E,+F,+L), kemr(-E,+L), mekr(+E,-L), kfmrh(-F,+G) and their inverses kvfs, kev, kef, mfkrh. After each op: an unknown name returns ["unknown", i]; a negative count or fewer loops than faces returns ["invalid", i]; a violated Euler-Poincare relation V-E+F-(L-F)=2(S-G) returns ["broken-invariant", i]. Return the final counts.

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
ring then remake edge	`["invalid", 5]`	`[4, 4, 2, 2, 1, 0]`	Failed

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