FA-88344 / Mesh topology invariants / Member archive

Euler count stores each shared edge once per direction · case 04

Closed meshes report twice as many edges and a strongly negative Euler characteristic.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input: list of polygon faces (vertex index lists). V counts referenced vertices, E distinct undirected edges (closing edge included), F faces, chi=V-E+F, C connected components (via edges), B boundary loops = components of the graph of edges used by exactly one face. Return [V,E,F,chi,C,B,genus] with genus=(2C-chi-B)/2 or null when that numerator is odd (non-orientable signal).

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 torus	`[9, 36, 9, -18, 1, 1, null]`	`[9, 18, 9, 0, 1, 0, 1]`	Failed

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