FA-88362 / Mesh topology invariants / Member archive

Genus formula assumes a single connected component · case 02

Two disjoint spheres are reported with genus -1.

Member previewVariant 2 · 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
tetra plus disk	`[10, 16, 9, 3, 2, 1, -1]`	`[10, 16, 9, 3, 2, 1, 0]`	Failed

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