Rectangle Fitting — closeness score

A 1:2 box spins in a fixed x / y frame; its points are projected onto both axes and detect.cpp's closeness score is evaluated. Score peaks when an edge lines up with an axis (θ*). Switch to Half (only the two near faces, the realistic LiDAR case): the score still peaks cleanly at 0°/90° — closeness stays robust exactly where min-area turns ambiguous.

■ aligned — points hug the edges → score max φ = 0.0° · score = 0 · θ* = 0°
gray = full box (ghost) · blue = visible faces · dashed green = bounding box · orange/purple = x/y projection
closeness score vs φ · dot = now · dashed = score max
visible face(s) hidden half cluster points + noise bounding box x proj y proj