FA-70655 / GIS polygon topology / Member archive

Area-weighted centroid of a multipolygon with holes: edge moment terms · case 05

Centroid x coordinates drift along the edge direction.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

Input: a multipolygon as a list of polygons, each a list of closed rings (exterior first). Ring orientation is arbitrary: every ring contributes its absolute area and matching first moments, exteriors positively and holes negatively. Moments use the shoelace terms (xi + xi+1)*cross/6. If the total area is 0 return None, else the centroid [cx, cy] rounded to 6 decimals.

Why this case matters

Label placement, zonal summaries and map joins use polygon centroids; courtyards and multi-part parcels must pull the centroid correctly.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
control #0	`[6.666667, 5.0]`	`[5.0, 5.0]`	Failed

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