FA-88779 / Mesh topology invariants / Member archive

Split triangles reverse winding · case 04

The two children of each split face point the opposite way.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input [faces, a, b] for a triangle mesh (any non-triangle returns "non-triangle"). Insert vertex m = max index + 1 on edge {a,b}: each triangle (u,w,c) with {u,w}={a,b} along its boundary becomes [u,m,c] then [m,w,c] at its original position. No such triangle returns "no-edge". Return [m, faces, number of split triangles].

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
shared diagonal	`[4, [[4, 1, 0], [2, 4, 0], [4, 2, 3], [1, 4, 3]], 2]`	`[4, [[1, 4, 0], [4, 2, 0], [2, 4, 3], [4, 1, 3]], 2]`	Failed

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