FA-88648 / Mesh topology invariants / Member archive

Edge flip accepts two triangles with the same apex · case 03

A folded pair is flipped into triangles that repeat a vertex.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input [faces, a, b] for oriented triangles. The flip needs a triangle holding half-edge a->b (apex c) and one holding b->a (apex d), else "boundary"; exactly two faces may contain both a and b, else "non-manifold"; c==d is "degenerate"; an existing undirected edge c-d is "edge-exists". Otherwise replace the first triangle in place by [c,a,d] and the second by [d,b,c] and return the face list.

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
folded pair	`[[2, 0, 2], [2, 1, 2]]`	`"degenerate"`	Failed

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