FA-5872 / Planar geometry / Member archive

Point line squared distance · case 02

Distance to an endpoint replaces perpendicular distance to the infinite line.

Member previewVariant 2 · 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. p,a,b are integer planar points with a!=b; return reduced Fraction string for distance squared to the infinite line through a and b. Exact operational definition: str(Fraction(((b[0]-a[0])*(a[1]-p[1])-(a[0]-p[0])*(b[1]-a[1]))**2,(b[0]-a[0])**2+(b[1]-a[1])**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: ((1, 2), (0, 0), (2, 0))	`"5"`	`"4"`	Failed

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This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

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