FA-88614 / Mesh topology invariants / Member archive

Fan triangulation reverses triangle winding · case 04

Every generated triangle faces the opposite way from its polygon.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input: polygon faces. A face with fewer than 3 corners returns ["bad-face", face]. Triangulate each face as a fan [f0, fi, fi+1] for i=1..n-2 (orientation preserved, anchor first). Return [triangles, diagonals added (sum n-3), growth in distinct undirected edge count].

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 grid	`[[[0, 4, 1], [0, 3, 4], [1, 5, 2], [1, 4, 5]], 2, 2]`	`[[[0, 1, 4], [0, 4, 3], [1, 2, 5], [1, 5, 4]], 2, 2]`	Failed

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