Q: lengths [0.788896063149, 0.520324652474, 1.05970907263, 0.498849449922, 1.007747884058, 0.291463381859, 0.660047704558] 
   turns [-1.917573753423, 0.399668806274, 2.737397626102, -0.163758055996, 1.76285346819, 1.986779351882, 1.049457433073] 
   perimeter 4.827038
Figure 1(b): w_j = [(0.0, 0.0), (0.7889, 0.0), (1.2682, 0.2025), (0.2085, 0.2073), (-0.2833, 0.2908), (-0.2593, -0.7166), (0.0044, -0.5926), (0.0582, 0.0653)]
Figure 1(a): azimuthal positions r(cos phi, sin phi) of the vertices:
   v0: (0.128, 0.028)
   v1: (0.569, 0.683)
   v2: (0.582, 1.228)
   v3: (0.125, 0.272)
   v4: (-0.157, -0.139)
   v5: (0.799, -0.476)
   v6: (0.761, -0.159)
scan with 4000 midpoints per edge: bad vertex cuts [0]; bad fraction 0.0457
   e0: bad sample runs [(0.00013, 0.06688), (0.19937, 0.25488)]
   e6: bad sample runs [(0.71962, 0.80763), (0.90087, 0.99987)]
refined end points of the bad intervals (bisection, 60 steps):
   e0: (0.000000, 0.066994); crossing pairs at the middle: [(0, 6)]
   e0: (0.199227, 0.254987); crossing pairs at the middle: [(0, 7)]
   e6: (0.719468, 0.807874); crossing pairs at the middle: [(0, 7)]
   e6: (0.900760, 1.000000); crossing pairs at the middle: [(1, 7)]
bad length 0.220695 = 4.572% of the perimeter 4.827038
