FA-88498 / Mesh topology invariants / Member archive

Tetrahedron edge collapse is allowed · case 03

Collapsing any edge of a tetrahedron is accepted and produces a degenerate surface.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input [faces, a, b] for a triangle mesh. Collapsing edge (a,b) is checked in order: missing edge -> [false,"no-edge"]; common neighbours of a and b must equal the opposite vertices of the triangles on the edge -> else [false,"link"]; if a and b are both boundary vertices the edge itself must be a boundary edge -> else [false,"boundary"]; a closed mesh with 4 or fewer vertices -> [false,"minimal"]; otherwise [true,"ok"].

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
tetrahedron edge	`[true, "ok"]`	`[false, "minimal"]`	Failed

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