FA-70744 / GIS polygon topology / Member archive

Bounded face count of an arc-node topology: loop arcs · case 04

Ring-shaped islands closed by a single loop arc lose their face.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

Input [nodes, arcs] for a planar, fully noded arc-node graph. arcs are [arc_id, from, to]; the same arc_id may be listed more than once (once per adjacent polygon) and counts once, while distinct ids between the same nodes are distinct parallel arcs. A loop arc (from == to) is an arc. Nodes listed in nodes but used by no arc are isolated nodes. Return [V, E, C, F] with V nodes, E distinct arcs, C connected components and F = E - V + C bounded faces.

Why this case matters

Topology builders check face counts against Euler characteristic to detect missing or doubled arcs after edits.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression #7	`[1, 0, 1, 0]`	`[1, 1, 1, 1]`	Failed

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