FA-88620 / Mesh topology invariants / Member archive

Fan triangulation drops the last triangle of each polygon · case 05

Quads become single triangles and polygons leave a hole.

Member previewVariant 5 · 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
triangles only	`[[], 0, -5]`	`[[[0, 1, 2], [2, 1, 3]], 0, 0]`	Failed

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