FA-5903 / Planar geometry / Member archive

Picks theorem interior points · case 03

Boundary points are subtracted with full instead of half weight.

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. double_area is twice the unsigned area and boundary is the lattice boundary-point count of a simple nondegenerate lattice polygon. Exact operational definition: (double_area-boundary+2)//2

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: (8, 8)	`-3`	`1`	Failed

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