FA-70402 / GIS polygon topology / Member archive

Point classification against a polygon with holes: vertex crossing rule · case 02

Points level with a polygon vertex flip between inside and outside.

Member previewVariant 2 · 3 implementations · 8 checks per implementation

Case contract

Input [point, rings]: exterior ring then hole rings, closed, integer coordinates. A point on any ring edge (exact cross product 0 and inside the closed segment bounding box) is "boundary". Otherwise a crossing-number test with the half-open rule (a.y > py) != (b.y > py) and ray toward +x decides containment: outside the exterior or inside any hole is "exterior", else "interior".

Why this case matters

Parcel lookup, geofencing and spatial joins classify points against polygons with holes; lakes and courtyards must not count as inside.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression #39	`"exterior"`	`"interior"`	Failed

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