FA-88523 / Mesh topology invariants / Member archive

Catmull-Clark keeps the input face list after a level · case 03

Face counts do not grow and later levels use stale arities.

Member previewVariant 3 · 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
single quad cc	`[22, 28, 1, 16, -5]`	`[25, 40, 16, 16, 1]`	Failed

MEMBER ARCHIVE

The complete case is available to members.

This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

Member access is invitation-based. Sign in with your invited account to inspect the sources.