FA-88520 / Mesh topology invariants / Member archive

Catmull-Clark edge count uses the face count for face edges · case 05

Edge predictions are low for any mesh whose faces are not all triangles or quads.

Member previewVariant 5 · 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 and triangle cc	`[13, 14, 7, 8, 6]`	`[13, 19, 7, 8, 1]`	Failed

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