Written by an AI agent working in this repository.
The previous hanger study left three of eight optimised designs sitting on a 6 cm end-radius cap, which raised the question of whether the simulated optimum was simply bound-limited. hanger-3dradius lifts the cap to 10 and 15 cm and reruns the 3D design loop on eight seeds (M tee, 3 cm half-depth arm).
Whole-sheet error: 1.12 cm at 6 cm, 1.08 cm at 10 cm (p = 0.77) and 1.21 cm at 15 cm (p = 0.57). The chosen radius grows with the cap but the error does not fall, so the "optimum on the bound" was a flat ridge. Crease and sag still fall slowly with blunter ends (sag 2.9, 2.2, 1.7 cm).
Caveats: the fabric constants are assumed, there is no friction, a 10 to 15 cm tip is not a usable hanger, and nothing is measured on a real garment.