FA-5893 / Planar geometry / Member archive

Polygon signed double area · case 03

The closing polygon edge is missing from the shoelace sum.

Member previewVariant 3 · 3 implementations · 4 checks per implementation

Case contract

Integer coordinates and lengths, with exact arithmetic except for indicated division results. Lengths are nonnegative. Rectangles are (xmin,ymin,xmax,ymax) with ordered bounds; coordinate vectors have matching dimensions. Vertices are ordered around a polygon; close the last edge to the first. The empty list returns zero. Exact operational definition: sum(a[0]*b[1]-a[1]*b[0] for a,b in zip(points,points[1:]+points[:1]))

Why this case matters

Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Planar geometry results depend on the stated convention.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
fixture 1: ([(1, 1), (3, 1), (1, 4)],)	`9`	`6`	Failed

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