FA-88507 / Mesh topology invariants / Member archive

Loop subdivision edge count adds F instead of 3F · case 02

Predicted edge counts are low and the Euler characteristic drifts after subdivision.

Member previewVariant 2 · 3 implementations · 7 checks per implementation

Case contract

Input [V,E,arities,B,scheme,levels]: counts of a mesh with face sizes "arities" and B boundary edges. Loop (triangles only, else "non-triangle"): V+=E, E=2E+3F, F=4F. Catmull-Clark: V=V+E+F, E=2E+sum(arities), faces become sum(arities) quads. Boundary edges double per level. Return [V,E,F,B,V-E+F] after the given levels.

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 loop 2	`[26, 48, 64, 0, 42]`	`[34, 96, 64, 0, 2]`	Failed

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