FA-88534 / Mesh topology invariants / Member archive

Loop subdivision accepts polygon faces · case 04

Quads are counted as if they were triangles.

Member previewVariant 4 · 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
quad under loop	`[8, 11, 4, 8, 1]`	`"non-triangle"`	Failed

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